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MAP

Afcoukir. Errpt ...
Acnr-i, Guinea ...
Ananmboo, Guinea
Aogra FiMjueiia, Wm
Apoltonla Cup?, Gull
Axuxn, Aby^inia . .-*£
Babelmandeb Peak, ]
lisrbira Point, W«t

Iteiiiurtt, Weat Afric
Baiabouk. WeM Aft!
Bengasi, Tripoli....
Blanco Cap*, Taniu
Hi jcerta, Tunia, ■ •«•*
HI unco Cape, Moroce
Bojador Cape, Weit ^
to. Tripoli B ■ .

, Algeria

j. Cape, Tunis .

Bravftt B**t Africa
Cabci, Tunia ......

Can tin Cnpe, Murocc
Ceuta, Morocco >■•■
Corricutes Cap* , Eaa
CoaiKp Effypt ......

Cyreoe, Tripoli ....

Dauitelta. Egypt ..
Delgado Cape, Eaat
Dendera, Egypt ....

Peru a. 1 tipoli > ■ • ■
El Ariab Fort, Egyp
Falcon Cap.\ Algeril
Ferro Cape, Algeria
¥*x, Morocco .*•*.■
JoruiOfljlCape, Weat
J no Cape, W«t Afi
Guard afui, Eas-t Afri
Hum in a met, Tun is. ,
Jerba L Tripoli ....

John (St.) Cape, W
K u 1 1 i ■ , Tripoli. * . , >|
Latnoo, Eaat Africa
l*go* B., West Afri
LaguLlaa Cape, Soutl
L«btda, Tripoli , . .
Loango K., Wefit Ai
Lopea Cape, Wtat A
Irfoaia (6t,) Fort, W
HaiTtowah* Aby»lfll
Matafou Cape, Alg«t
Uellila, Morocco* ■ .
Meiurad* Cape, We.
3SU'r uriil,i Cape, 'J u \
Mirik Cape, Wert A
Mogadore l t| Horoot
3f ouajlcer, Tunia *
Morgan Cape, South
ft at a L Cape, South j
Negro Cape, Went I
Nod Cape. Morocco
Vunez K Weat Air
Olipliint 1£.,N. W«
Oran Caitlc, Algeria
fftlmi^ Cape, West
Paul'* (6lJ Cape, TA
1'uic ..-n ufc . Weat A I
Qui.Un.ane, Eaat Af '
Itcdf Cape, South A
BaWttt* Egypt -•*
Koxo Cape, West A
Bailee, Morocco
Santa Cru*, Moroco
Seven Cape§, Weat
Socotra L, Eaat Afi
Book ran, Tripoli
Nubia

Spnrtet Cup*, More*
Suez, Egypt . .
Syene. Egypt .....
Tangier. Morocco .
Teluaup Morocco •
Three Folnta Cape*
Thebee {niltitj, Egy
Toiibrouk, liipoli
Verde Cape, Wee t
Yoitaa Oape, W«t
Wyd»,W*»tA ^

. i vm "Jm nffgwwwppp^

MAP' OF SOOTH: AMERICA.

tfMD«orn»cet.

Latitude*.

Cape Horn. .............

Mi>. i: ■ R-atnin i Handa ..

St. lljefonso IsUndft , ...

York Minster, Terra del I

FttttO.Mt.^ ....... j

Cape Noir or Negro , . , .
Cape Victory ..........

Cape Sen, Lucca

Cijw St. Jago * ........ .

Cape Three Points ......

Guaytinceo IsUiid* ■■»•»*

Cape Tret Monte* » *

Gimyiecits Island* ,....<
Fuiu't Quel an, Chiloe 1. *<
Mocha Island .».«#•.*..

Santa Maria Isbud

Aranco *****

Talcahumo ,

Valparaiso. .,..,.,.....,

Canaveral Iiland .......

Port Gu&aco .....■..*..*>

Copiapo ,,*,,,...,.,*.*

Cobijn*..*

Aiica .................

PottYLay ......

Pi<co ...... ....*.. ...

Callao

Paca# mayo Point, ......

Lobes de Afuera .......

Lo boa de Tier ra

Cape Blanco .........*.

Point Salinas
Guayaguil ,.........*..

Cape St. Loreoso «

Cape St. Francisco .....
Buenaventura Buy

Cape Corric d tea

PortFetiaa ..........*

lala del Key .... ......

Cape Success, Le 1

Hatred Strait J

SUten Ii^and.. .... .....

Cape St + Sebastian .....

Cape Virginia, Strait of '

Mage-Ian • ••<

Gracio** Diob Point . . *

Sta. Cms Hnrbour

Cape Blanco . . , .

Port Cordova ...... .1.

Rio Nrgro, entrance ...
Cape Ci<rrientea .......

Cape St. Antonio *«

Montevideo ■■

Port St. Pedro, Rio Grandi
St. Ftancif-eo ..*...*..•

Portof Sintoi v

Si. Sebastian's Island. . . .

TictdTia Island,. . ...... .

Cape Negro ..........*-

Cpipe Frio

Frado *■

Porto Seguro.

Todoa Santos B * y »....

S P Francisco Ri*er

Cape St. Augustine . «« * -

OLinda.

Cape St. Roque

Maranham Island. . ......

Alcantara ...,.......*.<

Para or Bel irn ......... 1

Amazon, entrance • *.**

Cape North . -■

Ojapok II. Fort St. Lour
Surinam R. Bram*a Poin
Cape Nassau.........**

Orinoco R. Point Barirna

Cape Three Pointa

Barcelona ........--..»

La Guayra. ....,....»»-

Porto Cabello

St. Juan's Point

Cape St, Roman .......

Babia Honda, entrance .
Cape La V tU »«*• »- *•<
Santa Marta .....,,..«*

Magdalena River

Santiago di Tolu

66° 53' 6.

56 27

55 61

65 25

54 32

52 23

51 26

50 54

49 46

47 32

46 59

44 as

4a 4t

3S 20

37
37

1
l.j

36 +3

33 2

29 2

28 27

27 20

22 30

IS 29

17 1

13 44

Longitude*.

La
7

6 30

39 N.

3 50

a 34

7 32

a 13

55 2 S.

54 42

53 27

52 18

51 43

50 IS

47 Hi

45 45

40 59

33
36 20

34 54
32
2G 7
24 1
23 56
23 48

22 57

23 1
17 21
10 27
12 49
10 29

8 21

67° ltf W.

ea 37
69 11

73 16

74 5ft

75 31
75 32
75 46

7. J
75
74

74 20

74 5

73 41

73 29

73 8

71 40

71 39

71 14

7L
70
70
72

i«;

70 13

79 28

80 41

80 js

79 40

80 43
79 52
75 6V1
77 10

77 52

78 40

65 13

63 41

67 59

63 IS

69 7

68 32
65 40
67 27
03 4
57 40
50 43
50 10
52 3
48 4<J
40 30
45 30
45 If
42 45
42 3
39 12
39 3

33 37
36 23

34 £7

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51 N.

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TURKEY IN EUROPE.
BOUNDARIES.
North : Austria and Russia.
South : Greece, and the Archipelago.
East : The Black Sea, and the Sea of Marmora.
West : Gulf of Venice and th» Ionian Sep.
DIVI8IONS.

(PROVINCES N. OF THE DANUBE.)
Province*. Chief Town*.

Moldavia, J assy.

Wallach'a, Bukharest.

(Provinces 8. op the Danubk.)
Bulgaria, Sophia.

Servia, Belgrade.

Bosnia, Boana-serai.

Croatia, Bania-louka.

Herzgovinia, Mostar.

(Southern Provinces.)
Rournelia, Constantinople.

Albania, Scutari.

Thesaaly, Yenisbehr.

Epirus, Janioa.

ISLANDS.

Names. Chief Tmrns.

Candia (Crete). Candia.

Thaso (Thasos), Volearo.

Semendrek (Samothrace*), Nubi.

Staliroene or Lemno (L»mnoa). L»mno.

SEAS, GULFS, STRAITS, &c.

Gulf of Ven ce ( Adriatic), W. of Turkey.

Archipelago (jEg»an), 8. of Turkey.

S«»a of Marmor* (Propontis), S.E. of Turkey.

Black Sea (EuxineJ, E. of Turkey.

Ionian Sea, S of the Adriatic.

G'llf of S%loniki, Archipelago.

Gulf of Caasandria, Archipelago.

Gulf of Monte Santo, Archipelago.

Strait of the Dardanelles, Hellespont.

Strait of Constantinople, Bo»phorua.

Besika Biy, S. W. of the Dardanelles.

GREECE.

Norto : Turkey in Europe.
South: The Mediterranean.
East : The Ionian Sea.
West: The Archipelago.

DIVISIONS.
Natural Divisions. Chief Towns.

IMI**, or Northern Greece, Athens.
The Morea, or 1 Nanoli di Romanii

Peninsular Greece, ] (Nauplia).

Insular Greece, Syra.

The Ionian Rspublic, Corfu.

ISLANDS.

Karnes.

Chiff lowns.

Corfu (Corcyra),

Corn.

Zante fZacynthus),

Zinte.

Theaki (Ithwca),

Bathi.

Santa Maura (Leucadia),

Sta. Maura.

Cephalonia (Cephallenia),

S*mos.

Cerigo (Cythera),

Modar*.

Koluri (Salamis),

Salamis.

Engia (Egina),
Hydra (Hydrea),

Egina.

Hydra.

Spezzia,

Spezsia.

Skyro (Scyros),

Rkvro.

Scopelo (Scopelos),
Io^ara (Ipsera),

Scopplo.

Ipaar*.

Negropnnt (Euhoea),

Ksrripo.

Audro ( Andros),

Andro.

Zea (Ceos),

Zea.

Thermia (Sythenus),
S?ra (Syros),

Thermia.

Svra.

Tino (Tenoa),

Borgo.

Miconi (Myconos),

Miconi.

Siphanto (Siphnos),

Kastron.

Paro (Paros),

Paro.

Naxta (Nazos),

Nazia.

Amorgo (Arnorgos),
Mi to (Melos),

Amorgo.

Milo.

Argeatiera (Cimolus),

Agentiera.

Nio (Ios).
ttikino (Sicinua),

Nio.

Sikino.

bamorinl (Thera),

Fjrgof.

THE

^uplar fhratnr.

VOLUME THE FOURTH.

The Poets say, " Philosophy " is " proud,"

As witness Campbell on the " Rainbow " cloud ;

Said in a haughty sense, it is not true,

For in this Volume, see what's done fur you.

Said in a sense becoming conscious pride,

In us, your Educator, and your guide.

Who thus have ran* ack'd Nature's wondrous stores,

To bring her treasures to your tcry doors,—

We own the guilt ; if guilt it can be call'd,
To gWe Irue liberty to minds enthrall'd ;
To teach men how to earn themselves a name,
And win the prize, the lasting meed of fame.
Pleasures that spring from learning and from truth,
Are, in these pages, set before our youth ;
The honours which they yield, arc greater far
Than all that circle round the name of Czar.

LONDON:

JOHN CAS8ELL, LA BELLE SAUVAOE YARD, LUPOATE HILL.

MDCCCL1V,

z6o* *£. /

TO OUR READERS.

In bringing our Fourth Volume to a close, we heartily thank all our Subscribers for their steady and unwearied
support. The letters of encouragement and of commendation which wo have received during the past six months,
have been more numerous and more gratifying than ever. We have endeavoured to Bhow our sense of these favours,
by labouring more earnestly to impart solid and usefiil instruction in various important branches of learning ; we
have, in fact, considered that wo were entrusted by our readers with the responsible task of their education, and we
\ave aimed at fulfilling our duties to their satisfaction. We have given a concise and popular summary of the leading
facts in several branches of Natural. Philosophy, as may be seen by consulting the Index ; but many highly useful and
interesting departments are soon to follow in their order ; these are Caloric and Optics, or the doctrines of Heat and
Light, including some of their most interesting applications, as the Steam Engine, the Telescope and Microscope,
Daguerreotype and Photography ; Magnetism and Electricity, including the nature of the Telegraph, the Electrotype,
and other useful applications ; and, as soon as possible, Astronomy, which is much in demand.

Chemistry has also been treated in a highly popular manner, and has converted a great number of our Subscribers
into practical Students of that art. The elegant languages of ancient Greece and of modern Rome have also occupied
our pages, and have been expounded with great care by the authors of the Lessons on these branches of Literature ;
nor have we forgot our Students in French, as a " Course of Readings " in that popular language is still appearing at
convenient intervals. The Mathematics, including Algebra and Geometry, with Instrumental Arithmetic aud Mathe-
matical Illustrations, have also been progressing under our own care, and these branches will be still more vigorously
pursued in our next Volume, where some of them, if possible, will be brought to a conclusion. Bookkeeping has
already occupied a portion of our labours, and we shall conclude this branch in a few early Numbers, with the subject
of Foreign Trade. The Lessons in Reading and Elocution will be rendered still more useful and attractive in our
next Volume ; but we cannot promise any new language till we have finished one or more of those now in hand ; the
German, however, is very near a conclusion. We are preparing for Lessons in Mechanical Drawing, and in various
other branches which have been unavoidably v postponed, on account of the great demand for those which we have
given, and which we are now carrying on. In closing these remarks, we can only say that we shall continue to place
before our Readers, as wo have always striven to do, those subjects which are the most in demand, and which are
calculated to do " the greatest possible good to the greatest possible number."

CONTENTS,

PAQi

116
249
270

327
342
381

LESSONS IN ALGEBRA.
VIII. Reduction and Addition of Fractions

IX. Subtraction and Multiplication of Fractions . .
X. Division of Fractions ; Simple Equations ....

XI. Reduction of Equations by Multiplication, and

by Division ; Numerical Substitution

XII. Problems in Simple Equations

XIII. Involution of Powers; Binomial Theorem....

BIOGRAPHY.

XIII. Zirah Colburn, the Calculating Boy 374

LESSONS IN BOOKKEEPING.
VII. Home Trade ; Memoranda of Transactions. . 108, 126
VIII. Subsidiary Books ; Cash Book ; Bill Book ; Bills

Receivable Book ; Bills Payable Book 144

IX. Day Book, from January till June 151

X. Cotton Book; Purchases; Sales: Profits .... 176
XI. The Journal, from January till June ; with the

General Balance 107

XII. XIII. The Ledger; Posting; Balancing; Index to
Ledger A; Ledger A, from January till June;
Trial Balance 214,227

ir.

III.

iy.
v.

VI.
VII.

VIII.

IX.

XI.
XII.
XIII.

XIV.

XV.

XVI.

XVII.

XVIII.

XIX.

XX.

XXI.

XXII.

XXIII.

XXIV.

XXV.

LXVII.

LXVIII.

LXIX.

LXX.

LXXI.

LXXII.

LXXVIII.

LXXIX.

LXXX.

LXXXI.

LXXXIl.

LESSONS IN CHEMISTRY.
Materials required ; Remarks on Iron and Zinc
Zinc ; Manganese ; Facts for the Student, etc. .
Chemical Testa for Metals; their Application

On Hydrogen ; Cavendish's Eudiometer

Application of the Pneumatic Trough

Experiments on) Hydrogen and Sulphuretted

Hydrogen Gases; Resumption of the Metals
White Arsenic; Experiments with the Arsenical

Solution

Experiments on Arsenic; Further Tests for

Arsenic

Reinsch's Process of detecting Arsenic

Solution of Antimony

Hydrochloric Acid ; Sulphuret of Antimony. . . .
Experiments on Tin ; the Proto-ehloride of Tin;

Bichloride of Mercury ; Chloride of Gold. . . .

Protoxide of Tin ; Experiments

Persalts of Tin ; Formation of Sulphurets ....

Oxygen ; its Generation

Properties of Oxygen Gas

The Results of Combustion in Oxygen

Experiments on Silver; Lunar Caustic ; etc. ..
Method of obtaining Silver from a Metallic

Solution

Chloride of Silver ; Mercury, Calomel, etc

Chloride of Mercury ; Calomel ; Corrosive Sub-
limate; Poison; Tests and Antidote

The Bichloride of Mercury ; Detection of Poison
Economy of Heat, chiefly in reference to Gas
Principle of the Blast Furnace ; The Argand

Gaa-Burner ; Distillation ; Still and Worm ;

Flasks and Retorts ,

LESSONS IN ENGLISH.

Agreement of the Subject and Verb

Adverbs; Syntax of the Predicate

Syntax of Predicate ; the Verb ; Object

Syntax ; Prepositions t-

Syntax ; Conjunctions ; Interjections

Compound Sentences

11.

III.

IV.

LESSONS IN FRENCH.
The Infinitive ; Government of Verbs ; etc ....
Government of Verbs ; the Past Participle ....

Remarks on the Foregoing Rules, etc

Adverbs of Negation ; the Preposition

The Conjunction, its regimen; Collocation of
Words r

FRENCH READINGS.

Sections I. II., with Exercises, etc

Sections III., IV., and V., with Exercises, etc.

Section VI., wi'h Exercise

8ection VII. Le Chate-ui De One*; M. De

Lajolais, Section 1

M. De Lajolais, Section II

3
37
69
77
92

113

123

141
155
173
191

201
218
236
247
261
280
292

304
320

336
355
366

380

14-
-33
.48,
64
79

287
ul6

341

373

LESSONS IN GEOGRAPHY.
Map of France, with the Railways, and Divisions
into Provinces and Departments; Map of
Turkey in Europe, with Greece and the Ionian
Islands; and Division into Provinces and
Islands ; Map of the Austrian Empire, with
Divisions into Provinces and Population;
Map of Russia in Europe, with Divisions into
Provinoes and Territories—to be prefixed to the
volume. i

LESSONS IN GEOLOGY. '

XLII. Icebergs 28

XLIII. Botanic Agents; Plants and Trees 29

XLIV. Animalculite Contributions to the Formation

of Rocks 72

XLV. Agency of Coral Insects in producing Rocks . . 96
XLVI. Results of the Agency of Man, by Agriculture,

etc 139

XLVII. Classification of the Rocks in the Earth's Crust 165
XLV1II. Relative Position of Rocks in their vertical order 231
XLIX. Rocks of Recent Formation; Rocks in course
of Formation ; Rocks formed since the Crea-
tion of Man and Animals 262

L. The Tertiaries ; their Lithological Character. ... 313
LESSONS IN GEOMETRY.

XXIII. Lectures on Euclid, Book I. Props. XVI.,

XVII., XVIII.; with 8cholis, Corollaries, and
Exercises 49

XXIV. Book I. Props. XIX., XX.; with Scholia, Corol-

laries, and Exercises 194

XXV. Props. XXI., XXII., XXIII; with Scholia,

and Exercises 254

XXVI. Props. XXIV., XXV., XXVI.; with Scholia

Corollaries, and Exercises 268

XXVII., XXVIII., XXIX; Props. XXVII., XXVIII;
with Scholia and Exercises; Discussion on
the Theory of Parallel Straight Lines ; Thirty
different methods for removing the difficulty
ff the Twelfth Axiom of Euclid's First
liDok 295,311,321

LESSONS IN GERMAN.
LXVIII., LXIX. Irregular Verbs; Verbs of the New

Conjugation 18, 32

LXX. Paradigm of a Verb of the New Form; the

Mixed Conjugation; Verbs of the same .... 75
LXXI., LXXII., LXXII1., LXXIV., LXXV., Paradigms

of Irregular Verbs; Passive Verbs 86,94, 1 12,131,154
LXXVI. Paradigm of a Passive Verb ; Reflexive Verbs 172
LXX VII. Paradigm of a Reflexive Verb ; Impersonal

Verbs; Compound Verbs 187

LXXVII(. Compound Prefixes Separable; Paradigm of a

Compound Verb Separable 205

LXXIX. Observations on the Paradigm of a Compound

Verb ; Inseparable Prefixes, 219

LXXX. Prefixes, Separable and Inseparable; the Ad-
verbs ; the Prepositions • 238

LXXXI. Table of the Prepositions ; the Conjunctions ;

The Interjections , 246

LXXXIl. Syntax; the Articles; the Noun, etc 309

LXXXIII. Rules and Observations relating to Nouns, etc. 325
LXX XIV. TheJ Pronouns; |the Adjectives; the Verbs 339
LXXXV. Use of the Tenses ; Rules and Observations. ... 358
LXXX VI. The Tenses; Participles; Adverbs; Preposi-
' tions; Conjunctions; Interjections 371

LESSONS IN GREEK.
VIII., IX., X., XI. The Third Declension; Paradigms 10,39,65, 71
XII., XIII. The Second Declension contracted; the Three

Declensions reviewed ; Exercises, etc 97, 1 15

XIV., XV. Comparison of Adjectives; General View 121, 170

I XVI. Adverbs ; Comparison of Adverbs 185

XVII., XVIII. The Pronouns; Personal; Reflective;
Reciprocal; Possessive; Demonstrative; Rela-
tive ; Indefinite and Interrogative, etc. . . .209, 222
XIX. The Numerals; with Declension of the Firtt 23)
XX. Numeral Adverbs; Remarks; General View.. 211
XXL, XXII. The Verb; Voices, Tenses, Moods; the
Participle; Numbers; Conjugations; Prefixes,
Suffixes, Stems ; the VerD to be 282, 307

CONTENTS.

PAGK

XXIII. Conjugation; Augment; Characteristic Let-
ters; Flexional Terminations 337

XXIV., XXV. Conjugation of a Pure Verb in w; Para-
digm of the Ac tire Personal Voice; Termi-
nations of the Active Voice; Paradigm of
the Middle Voice 352, 365

INSTRUMENTAL ARITHMETIC.

II. The Plane Scale : its construction and use .... 13
III. The Plane Scale and Protractor; Principles of

Trigonometry 89

IV. Scales of Various Equal Parts to an Inch 375

KEY TO THE LATIN EXERCISES.

Lessons XLVI. to L 57

Lessons L. to LI 74

Lessons LIl. to LIU 119

Lessons Llll. to LVII 135

Lessons LVII. to LXI 163

KEY TO THE LESSONS IN GREEK.
Lessons II. to VII 161

LESSON8 IN ITALIAN.

I. Introduction ; Pronunciation 8

II. Pronunciation of Vowels and Consonants ; First

Pronouncing Table 19

I I I. First Pronouncing Table continued ; Semivowels 41

IV. Pronunciation continued; Second Pronouncing

Table 52

V. Of Diphthongs ; Third Pronouncing Table .... 65
VI. Fourth Pronouncing Table 83

VII., VIII. Fifth Pronouncing Table 103, 110

IX. Sixth Pronouncing Table, Accents, etc 133

X. On the use of the Apostrophe 147

XL, XII. The Articles; Declension of Nouns 159,178

XIII., XIV., XV. Use of the Preposition or case-sign

ZX; etc 192,211,232

XVI. Use of the Particle a ; Vocabulary 253

XVII., XVIII. Use ofthe Preposition Da; etc 265,281

XIX. Use of the Preposition In ; etc 298

XX. Useof the Preposition Con; etc 306

XXI. Use of the Preposition Per, and Exercises 356

LESSONS ON MUSIC.

XX. Introduction to the Old Notation ; Relative

Length of Notes ; Absolute Length of Notes

and Speed of Movement ; Pauses of the V nice ;

Time Signatures ; Absolute Pitch and Clefs ;

Keys and their Signatures 181

XXI. Of accidendal Flats and Sharps, and Rules
for recognising on the Staff the Notes of Tran-
sition, the Distinguishing Notes of Minor
Keys, and Chromatic Notes ; other Symb >ls

of frequent occurrence 225

XXII. Minor Tunes ; Exercises ; Remarks on the Com-
mon Scale ; Conclusion 273

LESSONS IN NATURAL PHILOSOPHY.

I. Object of the Science ; Definitions 1

II. General Properties of Material Bodies ; Prelimi-
nary Notions on Force and Motion 21

III. On the Composition and Resolution of Forces. • 35

IV. On Gravity and Molecular Attraction; on Den-

city, Weight, Centre of Gravity, Eauilibrium 45
V. Laws of Falling Bodies, Intensity of Gravity,
Inclined Plane, At wood's Machine, Morin's

Apparatus, etc 61

VI. Laws of Gravity ; the Pendulum 81

VII. Molecular Forces; Particular Properties of

Solids ; Tenacity of Metals, etc 100

VIII. Hydrostatics; Properties of Liquids; Piesome-
ters; the Principle of Pascal; Pressure in
Liquids from Gravity; Hydrostatic Paradox 105
IX. On the Equilibrium of Liquids, in single and
communicating vessels; the Hydraulic Press ;
Levels and Levelling; Fountains and Arte-
sian Wells 121

X. Bodies immersed in Liquids ; Principle of
Archimedes ; Hydrostatic Balance ; Meta-
centre ; Specific Gravity ; the Areometer .... 137
XI. Specific Gravity ; Tables of the Specific Weights

of Solids and Liquids ; use of these Tables . . 157
XII. Areometers ; Nicholson's and Bauml's Areome-
ters ; Gay-Lussac's Densimeter 168

XIII. Hydrodynamics; Efflux of Liquids; Liquid
Vein; Vena Contracta; Theorem of Torri-
celli ; Discharge, theoretical and effective, etc. 188

PAGE

XIV., XV. Capillary Attraction i iU Effects; Laws of
the Ascent and Depression of Liquids in Capil-
lary Tubes, between Plates of Glass, in 8iphons;
of Liquids in Contact with Solids, etc. . . 203, 213

XVI. Endosmose, Absorption, and Imbibition; Ab-
sorption in Plants and Animals 234

XVII. Pneumatics ; Gases and the Atmosphere ; Msg-
deburgh Hemispheres; Measure of Atmo-
spheric Pressure; Torricellian Experiment;

Pascal's Experiment 241

XVIII. The Atmosphere ; its Pressure ; the Barometer,
Cistern, Portable, and Siphon ; Variations in
the Height of the Barometer ; its Relation to
the Weather ; the Wheel and Aneroid Baro-
meters ; Measurement of Heights, etc 2>)7

XIX. The Elastic Force of Gasea; Experiments of

Boyle ; Mariotte's Law ; Manometers 27G

XX. Mixture of Gases and Liquids; Aerostation;

Balloons ; the Parachute, etc 2S9

XXI. Pneumatic and Hydraulic Machines; the Air-
pump ; its Uses ; the Fountain in a Vacuum ;

the Atmospheric Railway 301

XXII. TheCondenscr; Condensing Syringe; Condensed
Air Fountain; Air-gun; Hero's Fountain;
Intermittent Fountain ; Siphons 317

XXIII. Pumps; the Suction-Pump, Forcing-Pump,

Lift -and -Force Pump; Valves; Bramah's
Press; Mariotte's Bottle 333

XXIV. Acoustics: Production, Propagation, and Reflec-

tion of Sound ; Intensity of Sound • Sararfs
Apparatus for Increasing Sound; Effect of
Tubes ; Velocity of Sound ; Laws of Reflected

Sound 349

XXV. Echoes and Ringing Sounds ; the Speaking and
Hearing Trumpets ; Vibrations of Cords ; the
Monocnord; Nodes and Nodal Line-"; Savart's
Toothed Wheel; the Siren; the Blowing

Machine. » 361

XXVI. Physical Theory of Music; Quality of Musical
Sound ; Unison ; Gamut ; Diatonic Scale ;
Intervals, Sharps and Flats ; Harmony, Dis-
cord; Pulsation; Tuning Fork; Vibrations
of Rods, Plates, and Membranes 377

LESSONS IN READING AND ELOCUTION.

I. Punctuation; Characters employed .' 251

II. The Period ; the Note of Interrogation ; the

Note of Exclamation ; Rules and Examples. . 285

III. The Comma; Rules and Examples 3.0

IV. The Semicolon; the Colon; the Parenthesis,

Crotchets, and Brackets ; Rules, etc 370

SKELETON MAPS.
IV. Description of the Skeleton Map of Africa, with
Table of Latitudes and Longitudes ; Table of
the Length of Degrees in Different Latitudes 7
V. Description of the Skeleton Map of South Ame-
rica, with Table of Latitudes and Longitudes 295

SKETCHES FOR YOUNG THINKERS.

IV. Milton : Intellectual Excellence, etc 16

V. Alfred the Great ; Sir Isaac Newton ; Wesley ;

Dr. Erans ; JSimonides 51

VI. Moral Excellence; Cyrus; Confucius ; Socrates ;

Ignatius ; Polycarp 81

VII. Louis IX ; Salmasius ; Caesar Borgia ; Pascal 143
VIII. Lord Bacon ; Locke ; Boyle ; Lyttleton ; West ;

Addison 175

MATHEMATICAL ILLUSTRATIONS.

I. Asymptotes to Curves ; the Conchoid ; the Conic

Sections, etc , 110

MISCELLANEA.
On Preparing Shells, 87. Poery: •« Look Aloft," 132. French
Sentences, 176. University of London, Nos. IV., V., and VI., 2 7,
220, 288, 345. Poetry : " Curiosity," 293. Mr. Cassell'a Publica-
tions, 347.

CORRESPONDENCE.

On Bathing when Heated, 27. Arithmetic, 59. Sloane's Ba-
lance, Solutions, 60. The Gift of Oratory, 120. University of
London : Lectures to Schoolmasters, 224. Industry and Charity,
240. The Blowpipe, 288. Tonic Sol-Fa Association, 300. Mutual
Instruction Classes, 331. University of London : Classical Sub-
jects Calendar, 347.

C|p poplar € hnkt

ON PHYSICS, OR NATURAL PHILOSOPHY.-No I.
OBJECT OF THE SCIENCE.

Tax object of physics, or natural philosophy, is the study of all
phenomena which material substances present, except those
which relate to changes of internal composition; the latter
come under the domain of chemistry. For example, selecting
the metal iron as a subject of contemplation, we may study its
specific gravity, its degree of hardness, its property of weld-
ing, of being drawn out into wire, and rolled or beaten into
plates ; all these phenomena depend upon the physical proper*
ties of the metal, and the study of such phenomena comes under
the domain of physics, or natural philosophy, sometimes called
mechanical philosophy. But iron is endowed with another
set of qualities. It is capable of being dissolved in certain
acids, and rendered invisible as iron, although its presence may
be recognised by various tests. All this department of study
belongs to chemistry.

We have stated that matter (or material bodies) admits of
being studied under two aspects : but what is matter? It is
necessary to arrive at some understanding as to this question
before proceeding farther. Perhaps the best definition of mat-
ter is comprehended in the expression, whatever falls or is
capable of falling under the immediate cognisance of the

At this time, there are sixty-three known elementary or
simple bodies ; that is to say, bodies out of which chemical
analysis has not succeeded in extracting more than one species
cf matter. Nevertheless the number sixty-three is by no
means to be regarded as the permanent representative of simple
bodies. Possibly their number may hereafter be increased or
diminished, according as new simple bodies may be discovered,
or those with which chemists are at present acquainted may
be proved to be made up of simple constituents.

Bodies, Atoms, Molecules. — Every definite or limited amount
of matter is termed a body or mass, and the properties of such
bodies or masses show that the matter of which they are com-
posed is not continuous, but is made up of elements, as it were,
infinitely small ; so small that they are incapable of physical
or mechanical division, and not in actual contact, but in near
proximity ; the distances between them being maintained by
reciprocal repulsions, known under the name of molecular
forces. These minute elements of bodies are termed atoms,
and groups of atoms are termed molecules, — of which latter, a
body or mass is only an aggregated collection.

Mass.— The term mass of a body is applied to the amount of
matter which it contains. The absolute mass of a body cannot
be determined, but its relative mass, considered with regard
to the mass of some other body taken as unity, can be readily
arrived at.

Physical Conditions or States in which Bodies exist.— These states
are three, each being well characterised and readily distin-
guishable from the others. 1. The solid state. This condition
u manifested at ordinary temperatures by wood, stone, and
metals. It is characterised by an entire adherence of mole-
cules amongst themselves ; so that they only admit of separa-
tion by the exercise of a certain degree of force, varying for
different solids, and for the same under different circumstances.
It is a direct consequence of this molecular adherence, that
solid bodies retain their original forms. 2. The liquid state.
Of which we are furnished with examples in water, alcohol,
and oils. The distinctive character of liquids is an adherence
of so f«eble a degree between their molecules, that the latter
slide upon and pass each other with extreme facility, in conse-
quence of which it results that liquid bodies do not affect any
external form of their own, but invariably assume that of the
containing vessel. 3. The gaseous state. Of this we have examples

VOL. IV.

in the air, and a great number of other bodies, to which the
general appellation gas or aeriform fluid is applied. In gases
the mobility of the molecules is still greater than in liquids ; but
the special characteristic of gases is their unceasing tendency
to expand into a greater volume ; a characteristic expressed by
the term expansibility, and which will hereafter be demonstrated
experimentally. The general term fluid is applied both to
liquids and to gases. The greater number of simple bodies,
and many compound ones, are capable of presenting themselves
successively under the three forms of solid, liquid, and gaseous,
according to ine variations of temperature to which they are
exposed. Of this successive change, water affords a well-known
example. Hereafter, when we farther advance into the regions
of natural philosophy, it will be found that the three states of
solid, liquid and gaseous, depend chiefly on variations of
molecular attraction and repulsion.

On Physical Phenomena. — Every change which the state of a
body may undergo without involving: alteration of composition
Is a physical phenomenon. The falling of a body, the sound
produced by such falling, the freezing of water, all are physical
phenomena.

Laws and Physical Theories. — The term physical law is applied
to designate the constant relation which exists between any
particular phenomenon and its cause. For example, in demon-
strating the fact that a given volume of gas becomes one-half,
one-third, one-fourth, &c, its original size, according as it is
exposed to a degree of pressure, twice, three times, &c, we illus-
trate the well-known physical law which is expressed by say-
ing that the volumes of gases are in an inverse ratio to the
pressures under which they exist. A physical theory is the col-
lection of laws relating to the same class of phenomena. Thus
we speak of the theory of light, the theory of electricity.
Nevertheless this expression also applies, though in a mora
restricted sense, to the explication of certain particular pheno-
mena. In this latter sense, we speak of the theory of d*sw, the
theory of mirage, &c.

Physical Agents.— As causes of the phenomena which bodies
present, philosophers admit the existence of physical agents ox
natural forces, by the operation of which all matter is governed.
These agents are universal attraction, caloric or heat, light,
magnetism and electricity. Mere physical agents only manifest
themselves to us by their effects, their ultimate nature being
completely unknown. In the present state of science, the
question still remains undetermined, whether the physical
agents are to be regarded as properties inherent in matter, or
whether they are in themselves subtle material bodies, impal-
pable, pervading all nature, and the effects of which are the
result of movements impressed upon their mass. The latter
hypothesis is that most generally admitted ; but being admit-
ted, next follows the important question, — "Are these kinds of
matter distinct amongst themselves, or are we to refer them to
one and the same source?" This latter opinion appears to gain
ascendency in proportion as the boundaries of natural philoso-
phy become expanded. Under the assumption that the phy-
sical agents are subtle forms of matter, devoid of all appreci-
able weight when tested by balances of the highest sensibility,
they have been termed imponderable fluids ; hence arises the
distinction between ponderable matter, or matter properly
so called, and imponderable matter, or imponderable physical
agents.

ON THE GENERAL PROPERTIES OF BODIES.

Different Kinds of Properties. — By the term properties of bodies
or of matter is understood, the different methods by which they

THE POPULAR EDUCATOR.

come within the sphere of our cognisance. These properties
are distinguished into general and special. The former are
those whioh belong to all bodies, of whatever kind and in what-
ever state they may De examined. The properties necessary to
be considered at this time, are impenetrability, extension, divisi-
bility, porosity, compressibility, elasticity, mobility and inertia.
Special properties are such as are observed in certain bodies,
or under certain physical conditions. Of this kind are solidity,
fluidity, tenacity, ductility, malleability, hardnets, transparency,
colour, &c. For the present we shall only be concerned with
the general properties of matter already mentioned ; but it is
proper to remark that impenetrability and extension, are not
so much to be regarded in the light of general properties of
matter as the essential attributes of matter itself, and which
serve to define it. Furthermore we mar here remark, that
the terms divisibility, porosity, compressibility, and elasticity
only apply to bodies regarded as made up of aggregated mole-
cules ; they are inapplicable to atoms.

Impenetrability. — This is the property by virtue of which no
two material elements can simultaneously occupy the same
point in space. This property, strictly speaking, only applies
to atoms. In a great number of cases bodies appear to be
susceptible of penetration. For example, there exist certain
alloys, of which the volume is less than the joint volume of the
metals entering into their composition. Again, on mixing
water with oil of vitriol or with alcohol, the mixture contracts
in volume. Such phenomena do not represent actual penetra-
tion. The appearance is solely referable to the fact, that the
materials of which the acting bodies are composed are not in
actual contact. Certain intervals exist between them, and
these intervals are susceptible of being occupied by other
ma iters, as will be demonstrated further on, when we come to
treat of porosity.

Extension, — This is the property which every material body
possesses of occupying a limited and definite portion of
■pace. A multiplicity of instruments has been constructed,
laving for their object the measuring of space. Amongst
-these the vernier and the micrometric screw are very
important; we will therefore proceed to their consideration.
The Vernier is so called from the name of its inventor, a
Frenoh mathematician, who died in 1637. This instrument
enters into the construction of numerous kinds of apparatus
used in the study of the physical sciences, such, for example, as
barometers, cathetometers, goniometers, &c. It is composed of
two engraved rules, the larger of which a b (fig. 1), is fixed and
divided into equal parts. The smaller rule is moveable, and to
this in strict language the term vernier is alone applicable.
To graduate the vernier, the process is as follows. First of
all it is cut to such a length as corresponds with nine divisions
of the large or fixed rule. It is then divided into ten equal
parts, from which arrangement it follows that every division
of the rule a 4 is smaller than a division of the rule ▲ b by
one- tenth.

Fig.l.

^= I -

1 I I I

T~r

The vernier being thus constructed as already described, let
us explain the manner of its application. S appose it was desired
to measure the length of an object m n. "WV place it as repre-
sented in the figure upon the great rule, the long axis of which
eorrt sponds with that of the body to be measured, and we
find that its length equals four units plus a certain frac-
tion. To value the amount of this fraction is the object of
the vernier. This is accomplished by sliding the vernier
along the length of the fixed rule, until the end of the vernier
corresponds with the end M n of the object to be measured.
This adjustment being made, we next seek for the point of
coincidence between the divisions of the two rules. In the

diagram this correspondence occurs at the eighth -division or
the vernier, counting from the point n. This coincidence
' shows that the fraction to be measured is equal to eight-tenths.
In other words, the divisions on the vernier being smaller than
than those on the fixed rule by one-tenth, it follows that if we
begin to count at the point of coincidence, and proceed in the
direction from right to left, each successive degree on the ver-
nier falls in arrear of the corresponding degree on the fixed
rule by one-tenth. Hence it follows, that in the case under
consideration from the extremity * of the vernier, to the fourth
division on the fixed rule, the intervening space is eight- tenths,
and we arrive at the final conclusion that the length of the
object m n to be measured, is equal to four of the divisions of a b
plus eight- tenths. Consequently if the divisions on the great or
fixed rule are hundredths of inches the length of m n will be
obtained almost exactly correct to one- thousandth of an inch.
Were it desired to be still more accurate, to obtain the length
correct to the two or three thousandth part of an inch, it would
then be necessary to divide ab into hundredths of an inch, to cut
off the vernier rule until its length should be equal to nineteen
or twenty-nine divisions of the great rule, as the case might be,
and finally to divide the vernier into twenty or thirty equal parts.
But when such minute divisions as these have to be observed,
and the exact line of coincidence between the degrees of the ver-
nier and the fixed rule accurately read off, the aid of a lens is
absolutely necessary. The Vernier is not invariably a linear
measure, as we have already desoribed it ; very frequently gra-
duated circular arcs are supplied with verniers, which are
then usually engraved in such a manner that fractions of a
degree are read off in minutes and seconds. It may be proper
here to remark that the vernier is also occasionally termed a
nonius, and still more frequently in mathematical books of a
past era, the nonius vernier* It derives this name from Nunez,
a Portuguese mathematician, who is considered by some to
have been its inventor. This, however, is not the case. The
instrument of Nunez, although designed for accomplishing a
similar purpose with the vernier, differed from it in some im-
portant respects, and was far less efficient.

The Micrometric Scrap and Dividing Machines. The term micro-
metric is applied to that variety of screw employed for measur-
ing with precision the extension of length and breadth. It
follows, from the very nature of a screw, that when it is well
and accurately made, its pitch, or the interval existing between
any two successive threads, must be everywhere throughout its
length the same. From this it follows, that if a screw be rota-
ted in a fixed nut, the former will advance a certain equal dis-
tance for each revolution, the rate of advance being propor-
tionate to the degree of obliquity of the screw-thread. It fol-
lows, moreover, that for every fraction of a turn, say T&ffth, i'
only advances the liath of the length of an interval between
any two threads. Consequently if this interval be equal to a
hundreth of an inch, and if at the handle extremity of the screw
there is attached a wheel or circle graduated into 400 divisions,
and turning with the screw, then on turning the graduated
wheel through only one division, the screw itself will be caused
to advance to the extent of one 400th of an inch.

Dividing machines, as they are termed, depend on the applica-
tion of this principle. Fig. 2 represents a dividing machine, in-
tended for the division of straight lines. It is composed of a
long screw, the thread of which ought to be perfectly regular,
working through a fixed metallic plate, and its handle part
attached to a fixed metallic circle a. Adjacent to this
graduated wheel is attached a fixed index b, — by means of
which every fraction of a turn made by the wheel, and conse-
quently the screw itself, may be easily discriminated. The nut
b, through which the screw plays, is attached to an iron rule
o d, which moves with the nut by a motion parallel to the axis
of the screw. It is upon this rule which is fixed the object
m n intended to be divided. Lastly, the table is supplied with
two brass grooves perpendicular to d c, and upon whioh moves
the slide-rest x, armed with the steel graver o.

The machine being arranged according to the description
just given, two different cases may present themselves. Either
the rule m n has to be divided into equal parts of a determinate
length — for example, four hundredths of an inch— or it may
have to be graduated into a given number of equal parts. Under
the first conditions, the course of the screw, or its length from
thread to thread, being equal to one hundredth of an inch* the

LESSONS ON CHEMISTRY.

operator turns the circle ▲ through one -fourth of an entire revo-
lution, engraves a mark on the rule, then turns the wheel through
another fourth of a revolution, engraves another mark, and so
proceeds until the operation is completed. Under the second
-conditions, let us suppose the division of the rule mn into
eighty equal parts to be the problem for solution. The
operator now commences by causing the screw to turn in
the direction from right to left, as relates to our diagram,
until the extremity m exactly coincides with the point of the
graver ; then reversing the direction of rotation, and causing
the wheel to move from left to right, in relation to the diagram
until the other extremity n of the rule corresponds with the
point of the graver. The operator counts the number of turns,

substance in an apartment the air of which 14 frequently
renewed.

Another example of the extreme divisibility of matter, ev%n
when organised, is furnished by the globules of the blood.
Blood is made up of red globules, floating in a liquid termed
wrwrn. In man, these globules are spheroidal, and their dia-
meter only amounts to about the *0003tb part of an inch.
Nevertheless, the particle of blood capable of being taken up
on the point of a needle contains nearly 1,000,000 of sucn
globules. But, what is more wonderful still, certain animals
exist so amazingly small, that they can only be seen by the aid
of a mieroscope of high power. They move about as large
animals do; they are nourished; they possess organs; how

Fig. 2.

and the value of the fraction of a turn, if such exist, gone
through by the graduated wheel in causing the rule od to
advance from one extremity of the object mn to the other.
Then, dividing the total number ef revolutions by 80, the
quotient indicates the space along which the screw x must
advance for each -^jth of mn. It only now remains to engrave
a mark on mn at the cessation of each partial revolution of
the wheel.

Divisibility. — This is the property which all bodies possess
of being susceptible of division into distinct parts. Numerous
examples might be cited illustrative of the extreme divisibility
of matter. Thus one grain of musk is sufficient to evolve
during many years the peculiar odorous particles of that

immeasurably small must those particles be of which mtik
animals are composed !

The divisibility of any kind of matter having been pushed
so far that its particles are altogether imperceptible, even by
the aid of the most powerful microscope, experiments can
no longer determine whether such matter be finitely or
infinitely divisible. Nevertheless, the stability of chemical
properties belonging to each kind of matter, the invariability
of relation subsisting between the weights of combining ele-
ments, and other important considerations, point to a
belief in a finite limit to material divisibility. Circumstances
of this kind have led philosophers to assume that bodies are
constituted of material elements not susceptible of division,
and to which, therefore, the term atoms is applied.

LESSONS ON CHEMISTRY.— No. II.

Taking up the subject at the point where we left off in our
last lesson, the reader will remember that he must perform
certain operations on certain corks. He must then adapt these
corks so treated, one to a four-ounce phial, another to a
Florence flask, in such a manner that two instruments may be
formed as represented in the diagram annexed.

flf.U

The four-ounce bottel with its tobacco-pipe attachment, will
not be required just now, but we shall speedily want it, there-
fore let the arrangement be made at once. Now the treatment
of the cork involves two separate processes, boring and exter-
nal fitting, and the order in which these operations are per-
formed is not immaterial. The boring operation must come
first. There are two methods of boring a cork; either by
thrusting a pointed red-hot wire through it, and afterwards
accurately enlarging the orifice by means of a rat's-tail file, or
by the use of a special instrument termed a cork- borer. The

latter is by far the more convenient plan of the two. I have
not assumed the student to possess a cork-borer, but I will
describe the instrument, so that it may be made or procured at
once if convenient. It merely consists of a piece of brass tube,
such as is employed for the ferrules of fishers rods, of equal sise
with the hole to be bored, and sharpened by filing to a rough
saw-edge at one end. If a transverse hole be bored through
the brass tube towards the other end, all the better ; the con-
Fig.*

trivance permitting the insertion of an iron wire as represented
by *, thus attaching to the instrument a sort of gimlet handle,
and conferring that kind of additional power which mechanics
term for the sake of brevity "purchase, ' — with such an instru-
ment as this, cork-boring is a very simple affair. A cork-bore,

THE POPULAR EDUCATOR.

being taken of the proper diameter, its edge is sharpened by a
few rubs of the file, and pressed against the cork under con-
tinuous rotatory motion, when it soon penetrates through the
central core, escaping through the tube itself. As there is
tome little chance, however, that the side of the cork where the
hole emerges may assume a ragged aspect, it is better to com-
mence the operation at one end of the cork, then without
penetrating quite through withdraw the borer, and recom-
mence at the other end, thus causing the operation to termi-
nate in the middle. If the aperture be clean and smooth it
may be considered finished ; if it be rugged and uneven, how*
ever, it will require trimming with the rat's-tail file. The
aperture being made* we now come to the insertion of the
tobacco-pipe shank, a matter of much simplicity ; one would
think that no special instructions were necessary. It is not
so :— the operation requires to be set about in a systematic
way ; and although in this case, the operator might succeed
after many attempts, and tobacco-pipes being cheap enough,
these numerous attempts might be made without the objection
of great expense ; yet considering the necessity for performing
similar operations under modified circumstances to which the
objection of expense and many others would strongly apply ,
it is better to cultivate the right habit at once. Remember,
then, tobacco-pipes and glass tubes . are not like metal rods.
We cannot fit them tightly, by violently twisting, turning, and
pushing, nevertheless we must fit them air-tight. Our object
is accomplished by eating them in, to use a popular but an
expressive word. Their accuracy of adjustment is secured by
paying attention to various little circumstances of detail. If,
then, the end of the tobacco-pipe shank be ragged, as it most
likely will be, rub off those ragged inequalities oy mtans of a
file. Had we been concerned with a thin glass tube instead
of a tobacco-pipe, the better plan of treatment would have
consisted in melting the extreme end of the same by holding
it for a few instants in the flame of a spirit-lamp or a jet of

rjf.8.

it remains to attach the length of India-rubber tubing to the
tobacco-pipe shank, and a few inches of glass tubing to that ot
India-rubber, so that eventually an apparatus may result of the
following shape, where a represents the point of attachment
between the India-rubber tube, and tobacco-pipe shank ; and

Our present operations having reference to clay, not glass,
we have not this resource ; but on the other hand a tobacco-
pipe shank is stronger than a glass tube, in consideration of
which I have chosen it, otherwise a piece of glass tube would
have answered the purpose equally well.

Having finished the attachment of the tobacco-pipe shank,
we now come to the attachment of the cork itself, which is
effected by accurate filing, a slightly conical form being im-
parted to the cork, in order that it may tightly fit with the
minimum of pressure. This precaution is especially requisite
when a thin necked flask has to be corked. In this case a
very slight amount of pressure will infallibly break the neck
of the flask.

The cork I will now assume to have been accurately adapted,
Dy filing, to its orifice ; but it is hard and rigid. Corks may be
softened by immersion in boiling water, a treatment which
will answer all present ends; but esses frequently present
themselyes when a cork, forming part of a chemical apparatus,
must be absolutely dry, under which circumstances it must be
softened by immersion in hot sand, or more extemporaneously,
but less rapidly, by holding it for a few seconds in the flame
of a spirit-lamp.

Having completed the arrangements to the extent described,

•'the point of attachment between the latter, and the associated
glass tube.* Perhaps it is scarcely necessary to indicate that
round or oval glass flasks will not stand upright without some
kind of support ; they may require to be supported whilst ex-
posed to heat or after removal from heat. In the former case
rings or triangles are usually employed, attached to a vertical
stand, and capable of elevation or depression (fig. 5). Instru-
ments of this kind can be procured ready made, but every
experimenter possessed of moderate ingenuity can prepare them
or their substitutes for himself. A carpet-rod, around one
extremity of which has been cast a block of lead, answers per-
fectly, and the rings may be made of stout iron wire, as
represented in fig. 6.

An examination of the mechanical conditions to which the
wire ring is subjected will prove that it requires no screw or
other contrivance for fixing, when moderate weights have to
be supported.

Matters are now ready for the commencement of our opera-
tions. The subject of this lesson is sine, but it is iron which
must first claim our attention. We require to effect a combi-
nation of this metal with sulphur, in order that something may
be made wherewith certain properties of the zinc may be
tested. The combination of sulphur with iron is called sul-
phurs* of iron, occasionally the sulphufc of iron, and let the
reader well remember that

A8ULPH*fe

or
A 8uLPHuret

}

is not

{

A SuLPHtte

or a
A 8uLPHate.

the termination ids or uret express the same compound, but the
terminations tie and ate express two different compounds ; dif-
ferent not only as materially between themselves, but as

• The a to the right in the cut tb?uld be a\

LESSONS IN CHEMISTRY.

between themselves collectively and a sulphuret or sulphide.
What is the difference? No matter. That point will come under
consideration by-and-by ; we are not now treating of sulphur
compounds, but of the metal sine. If the collateral facts just
mentioned choose to attach themselves to the learner's memory,
well and good ; if not, let them pass, they will be made to
attach themselves in the sequel. Sometimes, however, when
one gives a collateral fact on the understanding that it may stick

rif.«.

in the brain or take flight just as best suits its own good plea-
sure, it sticks there all the firmer. I always give collateral
fact* an option of this kind. To effect the union of sulphur
with iron, in other woids, to make sulphuret of iron, it is
merely necessary to bring a white-hot bar of iron in contact
with a roll of sulphur; then the iron drops into melted
globules which seem like iron itself, but which in reality are a
compound of iron and sulphur, and weigh heavier than the iron
by the weight of the sulphur wherewith they have combined.
The greater number of metals can be made to combine with
sulphur, by a similar treatment to that now described, and,
indeed, perhaps the act or combination just effected may have
presented itself to the reader's attention under the aspect of na-
tural msgic. To melt a nail in a walnut-shell, is a proposition
often constituting the subject of a wager. The learner now sees
how that wager might be won. A nail being heated to white-
ness, is dropped into a walnut-shell containing sulphur, when
the fusion of the nail immediately takes place.

Let the sulphuret of iron thus resulting be transferred to a
bottle labelled Sulphuret of Iron, and put away, — we shall
require it presently. We will now return to the sine solution,
which has been so long neglected that the student may fear
the original subject of the lesson has been forgotten. Not so.
Every point expatiated on, everything done, has had reference
to the metal sine.

I have already said that the metallic zinc employed remains
in the solution ; the next point, then, is to ascertain the con-
ditions it has assumed, and this information may be obtained
by driving off the liquid in which it is dissolved. This is
accomplished by the application of heat, which, causing the
liquid to become steam or vapour, tho latter is driven ott, and
all bodies contained in the liquid, not capable of assuming
this vsporous condition, necessarily remain.

The application of heat in many processes of evaporation
and distillation requires many precautions. For the most part
risked fires arc ineligible ; frequently a sand-bath is the best
means of applying heat, and it ia the source of heat we shall
employ now, fig. 7; but occasionally the heat capable of
being imparted by *and would be injuriously high, hence

a proper substitute must be found to tuko its place, and
the terms water-bath, oil-bath, &c.

Flf.7.

A sand-bath consists of an iron dish (a saucepan answers
very well) containing sand, and hung or rested over any
convenient source of heat. A few pieces of lighted charcoal
supply a very convenient source of heat ; and by putting the
lighted charcoal into a perforated earthenware flower-pot,
strengthened by banding with copper or iron wire, we gain
all the advantages of a furnace ; a temporary grating may
readily be made of strong wire, and the pots, pans, and other
vessels to be heated may be supported on triangles of hoop
iron, fig. 8* '

Flff.S.

The preceding diagram re pr es e nts a furnace of this Hind,
which may be worked on a table, the latter being protected
from heat by the intervention of a Welch tile or flatstone. Pro-
bably the furnace will crack, owing to tho intense heat
within. It is, however, none the worse for this accident —
the binding wires prevent all separation between the various
pieces of which the furnace is composed ; and, in short, the
furnace is no less useful than before.

Supposing the solution of zinc in oil of vitriol and water to
be placed in a saucer or porcelain dish, specially made for the
purpose, under the name of evaporating dish ; supposing the
solution and its dish to be embedded in the sand-bath, and
the latter placed on its hoop-iron tripod over a fire/lieat will
rapidly penetrate the sand, and evaporation will ensue. If
the solution were to be evaporated v$ry slowly, the saucer or
pan would eventually contain white crystals. If, however,
the evaporation be more rapidly pushed, then crystals do not
appear, but a white confused mass. I suppose the latter to
be the case. As soon as evaporation is complete, and the
residue has become thoroughly dry, remove the saucer from
the sand-bath, allow it to cool, and when cold dissolve the
evaporated material in distilled water. The liquid now returns
to the state in which it originally was before evaporation, with
this difference, any excess of oil of vitriol over and above the
quantity necessary to dissolve the zinc, has been driven away

THE POPULAR EDUCATOR.

by era]

oration Poor the solution now into a wine-glass, and
I as follows :—
Into the Florence flask put about half an ounce of the
sulphuret of iron, broken small (about the size of peas) ; add
a mixture of six parts by measure of water, and one part by
measure of oil of vitriol ; quickly replace the cork of the
Florence flask, and dip the end of the .glass tube into the follows
vessel containing the zinc solution. From the contents of the
Florence flask a very offensive, but at the same time a very
useful gas will pass t — it is called sulphuretted hydrogen, or
hydro-sulphuric acid. The general disposition of the appa-
ratus is represented in the accompanying wood-cut, fig. 9.

Fiz. 9.

of the zinc has been effected, is a very offensive gas. It is,
however, soluble in water, which solution is less offensive
than the gas itself, and sufficient for many purposes. Before,
therefore, disposing of our apparatus, let us make a solution.

Begin by taking out the terminal glass tube from the India
rubber, supply a clean glass tube in its place, and proceed as

FW. U.

Observe now the result. The zinc solution immediately
deposits a white powder, and no other metal, except tine, would,
under the conditions of our experiment, have deposited a white
powder. Thus arises a most important addition to our know-
ledge concerning zinc. To obtain this white powder, which
is called sulphuret of zinc, being a compound of sulphur and
zinc, — to obtain this white compound, I say, is the object to
which all our care and attention have been directed— all our
cork-boring, and furnace-making energies, brought into play.

Perhaps some Chemical beginner may think the result
hardly justifies the trouble with which it has been achieved.
Not so ; the result U all important, as will soon be perceived. I
One instance of itt Importance, slightly anticipating another
part of our subject* t Will now give.

Zinc is readily thrown down out of lis solution in oil of
vitriol and water, by transmitting through it a current of
sulphuretted hydrogen gas, as we have seen. Most other
metals art also capable 01 being thrown down by this gas, but
iron si OM of a few exceptions. Hence, supposing iron and
zinc hid both been dissolred in oil of vitriol and water, and
the proposition had been to separate the iron from the zinc,
this might readily have been effected by pouring through the
mixed solution a stream of sulphuretted hydrogen gas, which
would have thrown down the zinc, but left the iron.

We have not quite left the zinc yet. We shall return to it
hereafter | meantime, let the wine-glass be libelled "«•*■
phew* ofJOnd," covered with a pane of glass to protect II from
dust, and set aside, ig. 10.

Pour into the four-ounce phial cold distilled water, until
the vessel is about two-thirds full, than cause the gas to pass
through it in bubbles— the operator agitating the bottle fre-
quently, fig. 1 1 . Continue the operation until the water refuses
to dissolve any further portion of gas, which may be known by
removing the bottle from the table on which it stands ; grasp it
firmly", pressing the thumb against its mouth ; agitate briskly.
If the water bt not yet satisfied, it will endeavour to suck in
the thumb, fig* II. Give it, therefore, more gas, and when
fully charged, label it thus— " Hydre-eulphmric Aeid Solution,"
and set it aside, fig. 13.

The student will have noticed that the sulphuretted hydro-
gen* or hydro-sulphuric acid gas, by which the throwing down

LESSONS IN ENGLISH.— No. LXV1I.
By John R. Bbard, D.D.
AGREEMENT OF THE SUBJECT AND VERB.
Whilz the subject of a proposition may agree with a qualifying
adjective and a limiting or defining article, it specially agrees with
the verb. The agreement is of two kinds, one of form, another of
•substance ; one fiexional, another logical.

We may express these facts differently, by saying that if the
•verb Is In the plural number, its subject must be in the plural num-
ber ; and if the subject is in the plural number, in the plural
number must the verb be. In other words, both subject and verb
take the same condition ; and this is what I mean by stating that
the subject and the verb must agree. Avoid, therefore, the error
common with uneducated people, of joining together subjects and
verbs of different numbers. This error most commonly consists in
omitting the s where it should be placed, namely, in the third per-
son singular, and putting the s where it should not be placed,
namely, in the third person plural. I subjoin the present tense
in its

SKELETON MAPS.

BAD ENGLISH,

1. Il0TC»

2. thou lores

3. he love

Pfnttdt

we lores
you lores
they loves

we love
you love
they love

OP ENOIISH.

1. I love

2. thou lovest

3. he loves

In the third person singular ami plural, nouns may take the
place of pronouns ; thus, we say,

Pronouns: he drinks they drink they drink

Kouns: the man drinks the men drink the women drink

The subject and the verb then must he in the tame person.
Now the only person that ends in t is the third person » conse-
quently, an t put to the verb in any other person is an
ungrammatioal addition.

In general, then, the rule is this :—

The subject and the verb must be in the tame number and person ;
or, to state the same fact differently, the subjects arid their verb must
eyre* in number and person.

Nouns of multitude^, e., nouns signifying many, take their verbs
in the plural.

When, however, the idea of one predominates, that is, when you
regard the object spoken of at a whole, and not as consisting of
parts, then a collective noun requires its verb to be in the singular
number; as,

The Parliament was dissolved; but

The People were admitted to the Queen's presence ;

for the word people gives the idea of many persons.

Nouns are of the third person. But some grammarians have
ascribed all the three persons to nouns. In only one form of con-
struction, however, namely, the form that bears the name, of
apposition, can nouns have a first, a second, as well as a third
person ; e. g.,

Nouns in the first person: It is /, your old friend.
„ second „ Thou, the man of my heart.

,, third „ He, the king of the Jews.

Let me distinctly state that two or more nouns, or a noun and
a pronoun, are said to be in apposition, when, being in the same
number, person , and case, they refer to the same person or thing,
and when the second is put in order to explain or add something
in meaning to the first.

The essence of apposition is in the fact that a word or words are
apposed (ad, to, ami pono, J put), with a view to explain, enlarge,
or quality a foregoing noan or pronoun.

Observe that in every case of apposition there are two parts, the
apposed part, and the park to which the apposition is made. Thus,
in the sentence, *' Richard, the king, lost his crown," the king is
the apposed part, and Richard is the part to which the apposition
is made.

Yon will now readily see that the added part will partake of the
person as well aa the number of the part to which the addition is
made. Call the latter the principal part ; call the former the sub*
ordinate. Then the rule may stand thus : —

In app ositio n, the subordinate part agrees with the principal
pari.

And this agreement will in general be not only in person and
number, but also in gender and in case ; so that if the principal
part U of the feminine gender, in the feminine gender will the sub-
ordinate part be ; and whether the principal part stand to the verb
of the proposition in the relation of subject or object, in the same
relation will the subordinate part stand.

In the sentences, •• J* is I\ it is the Lord ; the Lord sitteth king
for ever/ 9 and others in which the second noun or pronoun aids to
make op the intended idea, the second must of course have the
same grammatical relations as the first which it aids. Thus, king
has the same grammatical relations as the Lord. In other words,
the rule may be stated thus :—

The verb to be, and other verbs which in themselves do not
express a complete idea, take the same -ease after as before them.

Consequently, to say " It U me," in answer to the question
" who is that ? " is ungrammatical.

Remark, however, that it, used generally, is an exception bo far
as gender and number are concerned, for it is idiomatic to say

It is she, it is he, (t<s they, it is we.
Apposition may be regarded as a case of a compound sentence,
and so might hare been reserved until we treat of that part of our
subject. Thus, in the instance

11 But he, our gracious master, kind as Just."— .BardwwJd.
m ay be written out in full in this way : —

He who is our gracious master and who is kind and just

Co&RBCT THE FOLLOWING INACOUBAOIBS.

The master and mistress is going to town. I loves to tee boyt
at play. The consequence of your follies are that yon will be
miserable. To die and to be no more is not the same thing. Ton
gives the children too many sweetmeats. Let thou and 1 serve

man as me contemptible for mj garb,"-»

e Almighty.
" Do not think such a
Addison.

« His wealth and him bid adieu to each other."— Priestie*.
" The Jesuits had more interest at court than him.— dbofle*.
" We sorrow not as them that have no hope. "— JTotart*.
M A stone is heavy and the sand weighty ; but a fool's wrath is
heavier than them both."— (Prov. xxvtt. I.)

M Better leave undone, than by our deeds acquire
Too high a fame, when him we serve *s away."— Shakspeare.
" Now therefore come, let us make a covenant, I and thou."— (Gen.
xxxf. 44 )

M Yet I supposed It necessary to send to yon Bpaphroditns, my
brother, and companion in labour, and fellow-soldier, but your mes-
senger, and he that ministered to my want*.— (Phlllpp. U. is.)
Amid the tumult of the routed train,
The sons of false Antimaehos were slain ;
He, who for bribes his faithless counsels sold,
And voted Helen's stay for Paris' gold."— Pope's JUad.
* The first, the court baron, is the freeholder*' or freemen's court."—
Cote.

" The angels adoring of Adam is also mentioned in the Talmud."—
Sale,

" It was necessary to have both the physician and the surgeon's
advice. M — Gboner.

" And love's and friendship's finely-pointed dart
Falls blunted from each indurated heart."— Goldsmith.

SKELETON MAPS.— No. IV.
AFRICA.
Ouk Map of France, with the Railways, not being ready for this
number, we have inserted, for the use of our Geographical Stu-
dents, a Skeleton Map of Africa, which they would do well tc
endeavour to fill up, as we trust they have done the former
Skeleton Maps, from the lists of the Latitudes and Longitudes
of places given on the margin or in the text.* Under the
vacant space in the left hand corner at the bottom of this Map,
intended for the name Africa, is a scale of British miles, of
which each division' stands for 100 miles distance on the Map.
The middle parallel of Latitude, marked at both ends, is the
Equator; from this parallel, the Latitudes which are marked
10, 20, 30, &c. on the sides, and proceed upwards to the top of
the map, are North Latitudes ; and those which are marked 10,
20, 30, &c. on the sides, and proceed downwards to the bottom
of the map, are South Latitudes. The dotted parallels of Lati-
tude are the tropics ; the one in Lat. 23° 28' N. being the tropic
of Cancer, and the other in Lat. 23° 28' S. being the tropic of
Capricorn ; between these two parallels, the sun shines vertically
at noon on every place of the torrid tone, two -days in the year.
In laying down the Latitudes on this map, there will bo
little or no difficulty, inasmuch as the parallels of latitude have
been made parallel straight lines ; only let it be observed that
every black or white space on the sides of this Map must ba
reckoned two degrees of Latitude, that is, 120 Geographical
miles, or about 140 British miles. In laying down the Longi-
tudes, however, there will be considerable difficulty, owing to
the curvature of the meridian lines. This will be obviated by
graduating with a pencil the Equator, or the parallel of Lati-
tude marked at both ends, exaotly like the degrees of Lati-
tude st the sides of the map ; for on the Equator the distance
between one degree of Longitude and another is exactly equal
to the distance between one degree of Latitude and another

* The list of the Latitudes and Longitudes of the Capitals or
Chief Cities in Africa will be found at page 62, vol. iii., of the
" Popular Educator."

THE POPULAR EDUCATOR.

on any meridian. Supposing, then, that the Latitude and
Longitude of a place are given, and you wiah to find iu place
on the map in order to lay it down ; supposing, also, that the
Equator has been so graduated as we nave said, and that
fhe degrees of Longitude are marked at every 10 degrees,
exactly like the degrees at the top and bottom of the map ;
then place a piece of whalebone, or other equally flexible sub-
stance, on the given degree of Longitude at the top, at the
Equator or middle, and at the bottom, and it will assume
very nearly the proper curve form of the meridian ; while in
this position, make a mark close alongside the piece of whale-
bone at the given degree of Latitude, and this mark will repre-
sent the exact position of the place on the map whose Lati-
tude and Longitude are given. Remember, nowever, that
every black or white space at the top and bottom of this map
must be reckoned two degree* of Longitude, or 120 miles of Longi-
tude ; these degrees or mile* of Longitude vary in sise according
to their position on the map,— a fact which must be sufficiently
obvious to the attentive reader, seeing that the meridian lines
taper towards the poles both northward and southward, and that
all meridian lines do actually meet at the poles on the globe itself.
The following table will show the exact sise of the
degrees of Longitude in Geographical miles of Latitude
according to their distance from the Equator ; if the size of
ihese degrees be wanted in British miles, you have only
to add to the number of Geographical miles given, one-sixth
part of itself for a first approximation to the truth ; to obtain
the next approximation, a very close one, deduct one-tenth of,
the preceding eixth-part from the first approximation, and you
will have the number of British miles required. Suppose, for
example, that you wished to know the length of a degree of
Longitude in Lat. 40° north or south of the Equator. Look in
the table, in the column marked Deg. La*, for 40, and in the
adjoining column to the right marked Geog. miles, you will find
45*96 ; this shows that the length of a degree of Longitude in
Lat. 40°, is only about 46 Geographical miles, or exactly 45
such miles and 96 hundredth parts of a mile. In order to find
the number of British miles, take one-sixth part of 45*96, which
is 7*66, and add this part to itself; this gives 53*62 for a first
approximation to the truth; next take one- tenth part of 7*66,
which is '766 or *77 nearly, and deduct this part from 53*62,
the first approximation ; this gives 52*85 for the next approxi-
mation. Tnus, we find that a degree of Longitude in Lat. 40*
is only 52*85 British miles.

Table showing the Length of a Degree of Longitude on

any FaraUel

of Latitude, between the Equator and the FoUe :—

Dee. Lat

Gee*. Milet.

Dec. Lat.

Geo j. Milet

Deg. Ltt.

Geog. Mile*.

60 00

5143

2817

59 99

50-88

27 24

59 96

5032

26-30

59 92

49 74

25 36

59 85

4915

24-40

59 77

48 54

23 45

59 67

4792

22-48

69 55

47 28

2150

5942

46 63

20-52

59 26

45 96

1953

10 69 09

4528

1854

68 89

44 59

17-54

58 69

43 88

16-54

58 40

4316

15-53

68 22

42 34

1452

5795

4168

13 50

57 67

40-92

12-48

57 38

4015

11-45

67 06

39 36

1042

5373

50 1 38-57

9*38

56 38

37 76

835

5601

36 94

7-31

65 63

30- 11

6-27

55 23

35-27

5-22

54-81

3441

418

5438

33-63

314

53 93

32 68

209

63-46

31-79

105

52 97

30 90

000

52-48

30 00

5196

29 09

The trigonometrical rule for the construction of this table,
is to multiply 60 Geographical miles, the length of a degree of
Longitude on the Eouator, bv the cosine of the given Latitude,
the product will be the length of a degree of Longitude in the
given Latitude.

LESSONS IN ITALIAN GRAMMAR.— No. I.

By CHARLES TAUSENAU, M.D.,

Of the University of Pavia, and Profeeaor of the German and Italian
Lang uagef at the Kenalngton Proprietary Grammar School

INTRODUCTION.
I propose to teach the grammar, structure, and vocabulary of
the Italian language by a method not commonly adopted by
the learned. A considerable experience in tuition has con-
vinced me that a strict adherence to scientific forms, though
all-important in the cultivation of a language, does not tend to
the advantage of the learner. Writers of practical grammar err,
for the most part, in studying system too much. They teach
grammar as they would the pure mathematics, as if an abstract
science of itself, and not as a practical guide through the
idiomatic intricacies of living languages. Such instructions
may be very scientific in form, but they do not follow nature.
There is no due separation of that which is the foundation, or
us it were the skeleton of a language, from those things which
axe the ornaments, the delicacies, the accidents and exceptions
of speech. A language should be taught as anatomy is
taught. We must first thoroughly study the bones, if we
would successfully trace the intricate ramifications of nerves
and arteries. The learner of a foreign tongue cannot for him-
self judge of what is material or immaterial to his sure and
jrapid progress. It will be my endeavour to instruct by a col-
loquial and natural, rather than a grammatical and purely
scientific method.

The Italian language has for a long time been regarded in
this country as a fashionable branch of education. Knowledge
of it has been reckoned an indispensable accomplishment of
cultivated society, but rather, as it would seem to me, as a
serviceable attendant at Italian picture galleries and operas,
than as a guide to the philosophy of a Dante, the invention of
an Ariosto, or the sagacity of a Machiavelli. The present is
perhsps the first considerable attempt that has been made to
popularise this noble and melodious tongue.

The Italian is the first born of the old language of Rome,
and owns a strength and beauty worthy of its noble origin.
In cultivation, it is the oldest of European tongues. When
Dante wrote, English, French, and German were comparatively
rude dialects. To Italy, the world owes the preservation and re-
generation of learning and the Arts ; and its fine soil, the fertile
mother of great spirits of old, has produced to the latest times
men who have enriched every intellectual pursuit alike by their
genius and learning. The language in which they expressed
that infinite variety of thought and sentiment, contains a
literature, the rich mine of which is in foreign countries only
known to solitary and toilsome explorers. The time may no*
be distant when the increased intercommunication of nations,
and the progress of popular education, will lay these rich
treasures open to the many.

For its own intrinsic merits, however, as a language, Italian
deserves to be studied by every one who would enjoy the
pleasures of style, inexhaustible in variety : the energy of Dante,
the graphic power of Boccaccio, the lyrical grace of Petrarca,
the refinement of Ariosto, the ornament of Tasso, the satire
of Berni and Aretino, the historical dignity of Ouicciardini and
Botta, the point and perspicuity of Macchiavelli, the hilarity of
Casti, the music of Metaatasio, and the Roman manlincbs of
Alfieri. And ihey who would cultivate language lor iu excel
lence must seek that of Italy for the ideal beauty of expression.

My method will be a natural, a simple, and, I trust, an easy
one. I shall discard, as much as possible, all the conventional
terms of grammar. I shall not travel by the old beaten path-
[ way through the psrts of speech. My grammatical progress
will imitate the action of the mind in the formation ox a sen-
tence, with a due regard to peculiarities of idiom. As a child
first learns the name of a thirig, 1 begin with the noun, as soon
as I have clearly explained the principles of pronunciation ; and
as the child demonstrates its progress in thinking, by connect-
ing an action or suffering with the object named, I shall

LESSONS IN ITALIAN.

proceed at once to the verbs. The verb is the life of a language,
and he who knows the verbs thoroughly has mastered the
chief difficulty of his task. The remaining kinds of words will
be taught and discussed in the same natural order.

These lessons will contain, if I may so speak, two grammars.
Presuming that I may find two classes of readers, — one anxious
for knowledge by the most easy and rapid manner, the other
with more preparation, inclination, and leisure for study, — I
have so shaped my labour as to combine in a form sufficiently
marked though not separated, an elementary grammar which
shall give the before-mentioned indispensable foundation and
skeleton ; and a grammatical treatise which shall, with philo-
sophical reasons, satisfactorily explain the ornaments, the
delicacies, the accidents, and exceptions of the language.

As I have said, I shall not divide my grammar into parts of
speech, but into paragraphs. In the paragraphs I shall dis-
tinctly mark the line of separation between the elementary
grammar and the grammatical treatise by the title of "addi-
tional remarks." The student who only desires to learn the
language sufficiently to enable him to read, speak, and write
with tolerable accuracy, need only attend to the numbertd
paragraph ; but he who would learn the language thoroughly,
must follow me closely and carefully in all I may find occasion
to say in the additional remarks.

Each paragraph will oe complete in iteelf— a decided step in
knowledge of the language. Every principle of the language
will be clearly illustrated by examples, including vocabularies
and exercises.

I have now only to ask the earnest and patient attention of
my pupil readers.

I shall teach the pronunciation of the Italian language in
more detail than is generally pursued in English tuition. The
profit to be derived from the study of any living language is
much less if we are unable to pronounce it correctly. We can
make little practical use of our theoretical acquirements, if in
communication with those to whom this language is the
mother tongue, we can neither make ourselves understood when
we speak, nor understand when we are spoken to. And besides,
no man, though he may gather the sense, can relish or even
comprehend the beauties or delicacies of great poets, and prose
writers too, in any language, and more especially in that
of Italy, without an accurate knowledge of the sounds. In
reading such poets as Ariosto or Tasso, the pleasure does not
consist altogether in appreciating the thoughts or even shades
of thoughts, but in the faculty to enjoy that divine harmony
to which they have attuned the language. One may relish the
beauty of the rose, but if he is deprived of the sense of smell,
he can admire only a lifeless beauty. Such students of the
Italian poets, to use a more homely figure, may read their poetry
with the satisfaction with which one might admire a Turkey
carpet, who has seen the reverse side only. There is no insu-
perable or even very considerable difficulty in mastering
Italian pronunciation ; but a thoughtful attention to some
leading principles, and a student-like diligence, are conditions
essential to success. My thoughtful and industrious pupils
will very soon find that a prolixity in this the very outset of
my labours which might seem trifling, is really most impor-
tant—one of the fundamental parts of the language.

I am aware that I am writing for the most part for adult
readers ; but let them for a little space forget the dignity of
manhood ; for every learner of a language, be He as old as Cato
was when he learnt Greek, should be regarded as a child
learning to express his thoughts. Indeed the more he is
taught a foreign tongue as the child his mother's speech, the
better for him.

A living language can never be accurately and completely
expressed by signs. They who profess the contrary only
mislead the uninformed. But a tolerable approach to accuracy
in fixing pronunciation may be made by letter- signs represent*
ing analogous sounds familiar to the ear in one's own lan-
guage. If one has made himself so familiar with the imitated
sounds, as to have acquired a considerable vocal command of
the leading ones, he may very soon accurately and perma-
nently acquire them, by a few brief communications with an
educated native.

Perhaps the most useful beginning I can make, is to point

out the leading errors which Englishmen commit in pronounc- .
ing Italian. The reason of this is, that men are apt to transfer-
involuntarily the peculiarities of their own language to that
whiph they are studying. The first effort therefore in learning to

Eronounce Italian, should be to forget your native peculiarities.
a the mastery of the pronunciation of the continental lan-
guages, and particularly of Italian, the Englishman's great diffi-
culty is in the vowels.

The Englishman, perhaps from childhood, has heard no vowel
sounds but those of his own island — his four sounds of 0, his
four sounds of 0, his three sounds of «, his two sounds of e, and
his two sounds of t, — sounds little swayed by rule, and changing
continually. He begins Italian, but carrying to the study the
complex vocal habit of his language, it must be some time
before he can comprehend and practise the simplicity and per-
manence of the sound of one Italian a, one Italian t, one Italian u,
two Italian *'s, and two Italian o's. He therefore pronounces no
vowel purely, and wherever he may move in Italy, his insular
nativity will be instantly recognised by ihe facchino of any
village inn, from his inveterate habit of giving to the Italian a,
that most comical of sounds to a Tuscan ear, of a in hat and fat.

Another radical error committed by Englishmen in pro-
nouncing Italian, atises from two opposite principles which
may be said to be the fundamental rules of the accentuation of
the languages. In English, every word has it* leading, marked,
or strongly accented syllable— generally speaking the rooi of
the word ; and it follows that while this syllable i« distinctly
marked by the voice, the subordinate unaccented fade a* ay
in the utterance into an airy nothingness that can hardly be
described. It is quite different with Italian. It has its
accented syllables just as English, but the accent on the one
does not destroy the vocal enunciation of the others. On the
contrary, full and substantial justice must be done to every
syllable, each being clearly sounded, full and roundly with
the vowels, and in a resonant or vibrating tone with the con-
sonants. The contrast may be observed in the pronunciation
of any of the many words of a kindred sound in both languages
derived from the same classic stock. Take the following :

JSnglith,
Difficulty.
Voluntarily.
Detestably.
Generously.
Indifferently.
Repetition.

Italian.
Dif-fi-col-td.
Vo-lon - ta-rta-nun- ti.
Da- te-sta-bil- men- te.
Ge-ne-ro-sa- men-te.
ln-dif fe-rm-te- men-te.
Re.pe-ti-zi-o-ns,

This peculiarity of the English language, it may be remarked,
is the great obstacle which every English poet has en-
countered in the effort to naturalise the classic measures of
antiquity. Contrasted with the open limpid vocalisation of
Italy, the pronunciation of the English is to an Italian so
obscure or indistinct, as very frequently not to be even under-
stood. It might be presumed that in a word so sonorous as
deteetabilmente or volontariamente it would be impossible to miss
the true sounds, yet an Englishman will, generally speaking so
slur over what he would from the analogy of his own language
conceive to be the subordinate parte of the word, as to be often
quite unintelligible to an Italian.

A third and radical difference between the two languages, as
regards the principles of pronunciation, proceeds from what
may be termed the vocal mechanUm or the physical principles
of enunciation. Shortly stated, the physical difference is this,
in England, they speak from the mouth ; in Italy, from the
chest. The Englishman whispers his words through the palate,
tongue, teeth, or lips ; the Italian throws them out with the
vigour of his lungs. When therefore the Englishman attempts
the pronunciation of Italian after his accustomed mode, he con-
fines the open sounds of Italy to the limited mechanism of lis
hissing or lisping articulation above the throat, and turns
Italian melody into harmonious discord, now a croak, now a
hiss.

These are the radical differences and difficulties which my
readers must strive to overcome. This is only to be accom-
plished by a constant recollection of these points of difference
in connection with the rules I am about to state and illustrate,
and by reading aloud, and with a clear and distinct voice uttered
from the chest, every Italian word which I may have occasion
to give in the course of the grammar

THE POPULAR EDUCATOR.

Je pretends vous traMer oomme
moll propre Hit. Baciite.

St )e Rhin de so* Hots ira grostkr

la Loire,
▲▼ant que tes favours 1011604 do

ma memoire. Boilbau.

/ intend to treat you at my om
ton.

And the Rhine will go and eweli
the Loire with ite waves, before the
remembrance of thy
my memory.

\ 131.— Verbs requiring the Proposition d bbtorb ax
Infinitive.

The (*') placed after the verb shows it to be reflective.

Etre, etre a lire, \ to be reading,

a ecrire, *e. j writing, *je.
Entendre (s*), to be expert in
Evertuer (s'), to strive
Exeeller, to excel
Exciter, to excite
Extorter, to exhort
Exposer (s* ), to expoee one's ee\f
Fatiguer (se), to weary one's self
Habituer (•'), to become used to
Hasarder (se), to venture
Hester, to hesitate
Instruire, to instruct
Iut4re«scr. to interest
Inviter, to invite
Hettre, to set to put
Hettre (se), to commence
Montrer, to show, to teach
Ob-tiner (*'), to persist in
Offrir(s), toofer
Pen eher, to incline
Peneer, to think, to intend
Peree' vdrer. to per sev er e
PrntUtcr, to persist
P»aire(se) to delight in
Prendre plaisir, to take pleasure
Preparer (se), to prepare
Porter, 1 to induce, to
Provoqaer, } to urge
Pousser, to urge
Require, to constrain
Beduire (ee). to tend, to end
Benoneer, to renounce
Blpugner, to be repugnant
Be'signer (se). to be reconciled
Roster, to tarry too long
Blussir, to succeed
Risquer, to risk
Servir, to serve
Songer, to think, to intend
8 a Aire, (not unip.), to svfice.
Tarder, to tarry
Tendre, to tend
Tenir, to intend, to aim
Travsiller, to labour
Viser, to aim
Voaer, to devote

r (•'), to stoop
Abontir, to end m
Aoeorder (s*), to agree
Aooouturaer, to accustom
Aoharner (s') t to strive
Admettre, to admit, to permit *
Afienir (s*J, to become inured
Aider, to help in
Aimer, to like

Appliqner (■'), to endeavour, to
Apprendre, to learn {apply

Appreter (»•*). to prepare
Aspirer, t < aspire
A»signer, to summon
Aa»ujeuir {» ), to subject ones se}/
Attacher (s' ) . to apply
Attendre (s*). U expect
Attendre, to put off
Augmenter (»'). to increase
Autoriser, to authorise
Avilir (a*), to debate one's self
Avoir, to have

Avoir peine, to have difficulty in
Bsianoer. to hesitate
Dorner (se), to confine one's self
Chercher. to endeavour
Coraplaire, to delight in
Conooorir, to co-operate
Oondamner (se), to condemn one's

eel/
Oondeteendre, to condescend
Oonseotir. to consent
Oonsister, to consist
Couspirer, to conspire
Consumer, to destroy
Conirlbner, to contribute
Convier, to invite
Couter, to cost
Determiner, to induce
Determiner (se), to resolve
Disposer (se), to prepare one's self
Divertir (se), to amuse one's self
Employer, to employ, to devote
Eoooorager, to encourage
Engager, to induce
Enhardlr, to encourage
Bastigner, to teach

L'homme n'aime point a 1*0000-
per de son neant,et de sa bassease.
Massiixob.
Avex.voos jamais \penti a offrir a
Dion t.utes oes sonflraneesr

Thb Samb.

Man does not like to contemplate
his nothingness and his vilenets.

Have you ever thought of offering
all these sufferings to Godt

ANSWERS TO CORRESPONDENTS.

B abbixt 8ttli : The German U very correctly translated into English ;
not so the English into German, as might be expected. All substantives
should begin with a capital letter, and the final s should not be need any-
where else than at the end of a word. The inverted arrangement, according
to which the verb is placed at the end of a sentence, only takes place in rela-
tive and other subordinate clauses. * •

W. Mabbaison : We cannot, as we have before said, undertake to correct
exercises. Those sent by our correspondent contain a good many errors.
In translating from German to English, he appears more anxious to make
t of sense than to get at the exact meaning; of the oririnal. Thus

to get at the exact meaning of the original. Thin
mis was die Nachtigall einst sudor Lerche smote I

hs renders : IFoe tenet

by M Wherefore as the nightingale said to'the lark.** The proper transla-
tion is: " What else than what the nightingale once said to the lark r**
Again, maehte er s em en Gruss staler alien Qottem der Juno musrst, does
not mean " he made his salutation to all the gods of Juno first." which is
scarcely sense at all, but «* he made his obeisance to Juno first of all the
gods (and goddesses)." It is not English to say—" those which my brother
in his hands has had." This is carrying literal translation too far. Our
correspondent seems to havs forgotten that in writing German two dis- 1
tSBst characters are used for the Jotter s. Be puts the >btof one at the

[ beginning and in the middle of the words. Weleher Segensehirm haben 8te
cannot be right. It should be Welch**, aoousative masculine to agree with
J tegense hirm. We have not time or room to point out more mistakes.

D. D. Causality : For something of the Art of Photography, see the
" Magasine of Art.** For proving your Apothecaries weights, apply to her
Majesty's inspector of Weights and Measures in your own district— A-
Lima (D d ) : We know of no cure for lisping but a strong effort of the
will to speak without lisping.— B. La mbi a (Glasgow): OasseU's French
Dictionary will be completed in two divisions— 1, French-English, which
is now published, price 4s. in stiff covers, or 5*. in cloth. The English-
French Division will be completed in December. The entire work will be
published, bound, at 8s. 6d.— 8. Gbaham (Liverpool): We have had lessons
on Floriculture and Horticulture in view ; and we shall by no means lose
sight of them.— J. M. (Aberdeen): We have seen some American (U.S.)
publications on Book-keeping, and they are so extremely similar to our own.
that it is very evident that brother Jonathan is indebted to us for this as
well as many other lessons relating to the business of human 111b. There
is one difference which must be carefully looked into, vis., that of Enteral
Money Instead of Storting Money, When we come to Exchanges in oar
Arithmetic, this will be considered; and ws shall soon give aa inklingof it
under the head of Reduction. As to the conversion of the money of difieren
nations, see Belly's " Universal Cambist," or Macculloch's " Commercial
Dictionary."— Jambs Wabdlb (Dean Mills): Bight.

Apollo (Cheltenham) should apply to B. Cocks and Co., New Burlington-
street, about Musical Instruments, fee.— T. CHora (Hartland): HH sug
?»lionft are good, and will be considered.— J. Houlubn, Jr. (Bdlnr.): The
erpetual Almanac extends only from 1736 to 18301— Ipooisitivb (Llver-
Cm>1) must omit the word of in the sentences to which he refers. As to
K»ks which are deemed authorities for excellence of style, we say Addison's
Kpers in the " Spectator," and his writings generally ; Dean Swift's N Qui-
ver's Travels." and his writings generally; and Dr. 8amuel Johnson's
papers in the *' Rambler." and his writings generally. Macaulay, our most
recent historian, is admired for his style, but it Is too flippant for us ; those
of Sir James Macintosh, Dugald 8tewart, and Professor Playfair, are vastly
superior.— O. Akchbold (8t. Peter's): Bight.— H. 8.: We can't tell.— A
Lbabnbb (Swaffham): The plants referred to, grow from seeds that pre-
ceded them. Griffith's " Chemistry of the 8easons" is good and useful. There
is a larger edition than the 4s. one which is greatly improved.

Qcintin Pbinolb (Glasgow): His solutions of the teak and pine question
are correct.— G. 8. (Cupar): 8ee p. 223 vol. HI, P. E.— J. L. (Duke-st.):
Binding 2d. vol. Is. 6d.— G. J. B Ativans had better write to Professor De
Lolme.— Samukl Esouibb (Logierait) will find an explanation of his diffi-
culties in a note to the Article Duodecimals of the 1st vol. of Hutton'e
Mathematics, at pp. 63 and 64 of the 18th ediUon.— Zsxo (Glasgow): We
strongly advise him to persevere at self- education in the midst of all
his difficulties and discouragements, as he will be ultimately rewarded •
The errors to which he refers are now corrected, ovv becomes ov/ft
when combined with fiovkn tor the sake of euphony.— G. Eltow (Beat-
ton): The writing out of the French Exercises is generally considered
all that is necessary ; and the committing of the rules to memory in
the best way you can; but we may be allowed to remark that the
writing out of a rule once is equivalent to reading it carefully, at least,
sis or seven times.— W. Taylob: The best and the cheapest are seldom
combined ; we know of no case where this is certain, but the Bible.
As to globes, try Smith in the Strand.— «. O. (Camberwell) : Right.— T.
Huntxx should add the study of English to that of Chemistry.— J. Bossbll
(Kingseavil) : Received.

Ebbata.
Vol. III., p. 216, cot 1, Ant. to Ex. 14, for 96 read 84.

„ „ „ 8,Ans.toEx.38,for4rl-preadl-H S *

„ 877, „ 1, line 49, insert Xacpss, I rejoice.

„ „ w „ „ 65,for/3Xaicfnrsread/3XaiC€vcr«.

„ „ „ 2, „ 37, for ovv read ovv.

LITERARY NOTICES.

FRENCH.

Now ready, price 4s. in stiff Wrapper, or 5s. strongly bound in cloth,
the First Part complete, consisting of toe French and English, of Cassbll's
Fbbboh Dictionaby: the entire work in two Parte— 1. French and bog-
llsh : 8. English and French. The French Department carefully Edited by
Professor De Lolme, and the English Department by Prolessor Wallace and
H. Bridgeman, Esq., will be completed in Twenty-six Threepenny Numbers,
and will form one handsome Volume of eight hundred and thirty- two pages.
Price 8s. 6d. bound in cloth, or the Two Divisions may be had separate.

Cassbll's Lbssons im Fbbmoh (from the " Popular Educator"), in a neat
volume, price 2s. in stiff covers, or 2s. 6d. neatly bound in cloth.

A Ebt to Cassbll's Lbssons ik Fbbboh, containing Translations of all
the Exercises, with numerous references to the Grammatical Boles, price
Is. paper covers, or Is. 6d. cloth.

GERMAN.

Cassbll's Gbbmaw Diotiowabt is now Issuing In Weekly Numbers, at
Sd. each ; Monthly Parts, Is. each.

Oassbll's Lbssons xh Qbbmam (from the •• Popular Educator •), price
Is. in stiff covers, or 9a. Sd. doth.

MISCELLANEOUS EDUCATIONAL WOBK8.

.Cassbll's Euclid <— Thb Elbmbnts or Gbombtbt. Containing the
first Six, and the Eleventh and Twelfth Books of Euclid. Edited by Professor
Wallace, A.M., price Is. in stiff covers, or la. Sd. neat cloth.

Cassbll's Elbmbhts or Abithkbtio (uniform with OasseU's Euouo)
Is now ready, price is. In stiff covers, or Is. fd. neat cloth.

INSTRUMENTAL ARITHMETIC.

INSTRUMENTAL ARITHMETIC— No. II.

THE PLANE SCALE ; ITS CONSTRUCTION AND USE.

In oar first lesson on Instrumental Arithmetic, we explained
the nature and use of an apparatus called the Neperian Abacus.
In this lesson* we propose to explain the construction and use
of the Plane Scale. This scale is usually found in a case or
box of Mathematical Instruments, and is one of the most
useful inventions we know for the purpose of the practical
Mathematician, the Artist, the Mechanical Draughtsman, and
the Designer and Drawer of Plans, whether relating to Archi-
tecture, Machinery, or Civil Engineering. In our illustrations,
fig. 1 and 2, we have given an example of a Plane Scale of the
most useful construction, for there are several varieties in this
respect, which we shall have occasion to explain. This example
is *foe iimUe of an ivory Plane Scale which has been in our own
possession for more than thirty years, snd a more useful instru-
ment in the solution of practical problems in Mathematics is
not easy to be found. This instrument, although only six
inches long, contains the same Lines as those which are put

mark it; you can then take 5*5 inches from the scale and
mark it in a straight line with the former ; then the whole
length will be that of the line of 11*5 inches required. Under
the line or rule thus described, there is another consisting of
six inches divided into 5 equal parts, and having these parte
in like manner subdivided into tenth parts. These parts are
marked at every large division, thus : 10, 20, 30, &c«, which
means 10 hundredths, 20 hundredths, 30 hundredths, &c„ of a
foot, or I tenth, 2 tenths, 3 tenths, &c, of a foot. This, then^
is a decimal scale of a foot, containing tenths and hundredths
of a foot without regard to inches ; and from it you may lay
down or measure lengths of lines very accurately to hundredths
of a foot, as far as it goes, and it may be extended to the laying
down or the measurement of a line longer than the scale itself
by doing it by parts as shown above. Thus, if you wished to
lay down a line of 2 37 feet, that is, 2 feet 3 tenths of a foot
and 7 hundredths of a foot ; you would draw an indefinite
straight line, and repeat the length of the scale four times in
succession on that line, this would give the length of the 2
feet, then stretch the legs of your compasses so that the dis-
tance between the two points of the legs may extend from the

Fir. l.

upon one side of the Gunter s Scale, called the Common Gunter
by sailors who use this instrument, and who solve their problems
in Navigation by its means. The Common Gunter is 24 inches
long, and contains on the other side of it, Lines representing
the ^Logarithms of the numbers which are represented by the
lines on the one side just alluded to. In explaining the
nature and use of the Plane Scale, therefore, we are explaining
the nature and use of one side of Gunter' s Scale, so useful in
the etod* end practice of Navigation.

In fig. 1, from a to n there is a common six inch rule, with
the inches marked on it from 1 to 6 each inch being sub-
divided into tenths of an inch ; this, then, is a decimal inch-

extremity a to the 7th vertical division beyond that marked 90,
and this will give the length of the '37 of a foot ; next place
this length on the straight line above mentioned, in continua-
tion of the 2 feet already laid down, and you will have a line of the
whole length of 2*37 feet as required. By comparing the two
scales extending from a to b, just explained, at the points where
their divisions coincide, you will see that 5 hundredths of a
foot is 6 tenths of an inch ; 10 hundredths or 1 tenth of a foot
is 1 inch and 2 tenths of an inch ; 15 hundredths of a foot is 1
inch and 8 tenths of an inch ; 20 hundredths or 2 tenths of a
foot is 2 inches and 4 tenths of an inch ; 30 hundredths or
3 tenths of a foot is 3 inches snd 6 tenths of an inch ; 35

Fig. ».

Scale, and yon may measure or lay down the lengths of lines by
its means very accurately to tenths of an inch, as far as it

Thus, if you stretch the legs of a pair of compasses,
so that the distance between the two points of the legs msy
extend from the extremity a to the fourth vertical division
beyond that marked 3, you have in this distance the measure
or the length of 3*4 inches or 3 A inches. If you wish to
measure or lay dosm a longer line, you can do it from the same
scale by parts ; thus, to measure or lay down a line of 11*5
inches, you can ftrsyske e inches complete from the scale and

hundredths of a foot is 4 inches and 2 tenths of an inch ; 40
hundredths or 4 tenths of a foot is 4 inches and 8 tenths of an
inch ; 45 hundredths of a foot is 5 inches and 4 tenths of an
inch ; and ao on, according to the length of the scale.

We come now to the most useful and accurate Scale drawn
on this Instrument, fig. 1, we mean the Diagonal Scale of Equal
Parts. The larger Divisions of this scale are sometimes an
inch, as on the Common Gunter, which is 2 feet long ; and
sometimes half an inch as on the Plane Scale, which is only
half a toot long. In fig. 1 the larger divisions from o to d are

«,- .Lit: t

v.i (.

#"l Jt

X..

s «vU: -r— ~g »*• **■ — ** ~"3r - -. x at -am ^cas.

-34*- - *r~ 4- IS *i-*-> 'JteJl&k t>4. XX -Bff wmt.

i£ 1*1

it 2» -*:vu± y,u

T?r*rw ^;-afc -. .^x-x»"sv». Trm. — tr« ^ eit. :

- - ? a.— *•**

fc-T z r« —•■*>»» .5.1 M Mf

* m

^ak -4^r» db. -mm/act .^

.^ivs* A i* Ma

' **•»► JL

LESSONS IN ENGLISH.

In most sentences having an adverbial phrase, there may also be
an adverb ; e. g.,

The sick man drank in hit chamber copiously.

Instead of an adverb and an adverbial phrase, you may hare two
adverbs, or even more ; e. g.,

The sick man drunk water eagerly and copiously.

Position m of tlu Adverb.

The ordinary place for the adverb is immediately before or after
the verb. Euphony, as well as idiom, has an influence in determin-
ing the position of the adverb. Sometimes an adverb is placed
before the verb in order to allow ihe verb and its object to stand
together ; e. g.,

The sick man copiously drank water.

The position of the adverb hat much to do with the sense. There
is a great difference between these two statements : —
Only ihe man went out.
The man only tocnt out.
The first states that the man went out and no one else ; the second
states that the man did nothing but go out.
Agreement of Adverbs,

Adverbs, though so called because they are put to verbs, qualify
adjectives as well as verbs ; e. g.,

" Any passion that habitually discomposes our temper, or unfits
us for properly discharging the duties of life, has mo$t certainly
gained a very dangerous ascendancy." — Blair

Adjectives may also be said to qualify participles, but as the par-
ticiple is only a part of the verb, a separate statement of the fact
ia hardly necessary.

There are elliptical forms which seem to make some adverbs in-
dependent of any verb. But the independence is only apparent.
In reality every adverb on examination will be found to qualify an
affirmation.

The words yes and no are exceptions. When I ask a child
"Do you love mer*' and the child answers " Yes," the adverb
yes is only an abbreviated form of the sentence / do love you.

No and not are often misused. No is the answer to a question
when no other answer is given; not is prefixed to the verb em-
ployed in giving the answer ; e. g ,

Are you ill ? No,
Are you ill ? I am not ill.
Hence in all sentences not should be used; consequently
" whether or no " is wrong ; it should be whether or not.

When not is prefixed to the verb, and so affects or negatives the
whole affirmation, if a negative is required with a succeeding mem-
ber, or should be used ; hut if the not (or neither) negatives only
one word or one phrase, then with the succeeding or corresponding
word or phrase employ nor ; e. g.,

For two months I could not think or speak.
He allowed me not to speak nor to write.
He gave me neither money nor clothes.

Observe that neither is properly used of two only, meaning not
either , that is not one of two. Hence it takes in the second clause
nor.

Double negatives in English make a positive, when they are
applied to the same affirmation ; e. g.,

He is not unlearned ; that i», he is learned.

The positive thus made is not a mere positive ; thus,

He is not unlearned means that he is somewhat learned.

A negative may, however, be repeated so as to give force to the
negation ; e. g.,

" There is none righteous, no, not ©we."— (Rom. iii. 10.)

It is essential that the two negatives should be in the same pro-
position, if they are to cancel each other. In the last case the pro-
positions are different, the first being equivalent to " there is none
righteous, there is not one righteous."

When it is meant that a proposition should be negative, care
must be taken lest you make it affirmative, as in the phrase "nor
I neither " (for which read either) in this sentence : —

•• He will never consent, not he, no never, nor I neither."—
Bolingbroke.

Care most be taken to weigh the force of the negative. There is,
or instance, a great difference between net every one T and none (not

one) ; every one includes all, not every one excludes only a part ; th«
opposite of every one is no one or none ; e. g.,

" Not every one that saith unto me Lord. Lord, shall enter into
the kingdom."— (Matt. viii. 21.)

"None of those men who were invited shall taste of my
supper."— (Luke xiv. 24.)

No one, when employed thus in separation, may be considered an
indefinite pronoun (not one) of the singular number, and of course
requiring the verb to be in the singular. When combined, as in
ndne, the pronoun implies plurality, and has its verb in the plural ;
e.g.,

'•How many are come ?" " None are come." " What, not one ?"
*' No, not or e is come."

The word amen may seem to be independent. But it is a
Hebrew term, signifying so let it be, and forms a part of the preceding
sentence or paragraph, and indeed is in itself a sentence expressive
of a wish or a prayer.

There are cases in which the adverb' seems to qualify a pre*
position; e. g.,

" This mode of pronunciation runs considerably beyond ordinary
discourse . ' ' — Blair .

But the verb consists of the two words runs beyond, beyond being
an uncombined or free affix, here appended to the verb run, so that the
adverb really qualifies the affirmation, which is that this mode of pro-
nunciation rune beyond, &c.

When we say " not all that glitters is gold," the negative is
applied to all, and applied with such effect as to give the idea that
something that glitters is gold.

No has sometimes the force of an adjective ; e. g.,

" There is no flying hence nor tarrying here"—Shak8peart.

In their directions for the use of ever and never ineeuch phrases
as " never so rich, 1 ' grammarians have varied and blundered. The
only way to determine whether you should use ever or never is to
consider whether the proposition is affirmative or negative; if the
former employ ever, if the latter employ never. Dr. Blair has been
blamed for saying " seldom or never can we expect," and yet is he
completely correct. The proposition is that we can expect a cer-
tain thing in few instances, nay, perhaps in no instance, that is not
at all, or never.

Exception has been taken to sentences constructed like the follow-
ing, and ever his been substituted tor never: —

"Which will not hearken to the voice of charmers, charming
never so wisely."

Never is right ; the proposition in the second member is " thou^i
he (the charmer) charm so wisely as none ever before charmed ;"
the proposition is therefore negative, and requires never.

Some adverbs perform the office of adjectives. When adverbs
perform the office of adjectives, they may be accounted adjectives ;
e. g.,

" To the above remarks."— Campbell.
" In his then situation."— Johnson.

In parsing sentences of this kind it would be the better way to
describe above, then, &c, as adverbs employed adjectively.

Take care not to mistake an adjective for an adverb. In the
phrase,

" The arrows of calumny fall harmless at the feet of virtue,"
an ignorant purism has proposed harmlessly as a correction.
Harmless is right, for the word qualifies not fail but arrows, and
the statement is that they are '* harmless," that they do no injury to
virtue.

Participle.

Of the predicate in the sentence,

The man drinks a beverage made of wine and water,

the word made, the word of, and the word arid remain to be
studied.

These words might have stood in the subject. Their position in
either the subject or the predicate is of no importance. The only
thing of importance is to show that a simple sentence may embrace
all the parts of speech ; for thus you learn that, when you have
mastered the syntax of a simple sentence, you have mastered the
essential doctrines of English grammar.

The past participle made offers an instance of agreement and
government united m one word ; for made agrees with beverage, and

THE POPULAR EDUCATOR.

r with bc fcr agc it governed by drinks. In general it may I
bestated that participles admit of concord and dependence. j

Participles perform other office* besides that which is strictly
their own.*

The present participle is used as a noon sometimes without,
sosnetimrs with a pronoun, also sometimes with and sometimes
without an object ; e. g. f

" Describing a past exeat as present has a fine effect in lan-
guage."— Karnes.

"My being here, it if. that holds thee hence."— Skattpeare.
The present participle may hare the force of an infinitive ; e. g.,

"Avoid being ostentatious and affected.'* — BZair.
The present participle has the force of an infinitive also when com-
bined with the past participle ; e. g.,

" Habits are soon assum'd ; bat when we strive
To strip them off, 'tis being Jtof'd alive/"

The present participle unites with a verb to complete its signifi-
cation; e.g.,
" 7b be left pausing on a word of no meaning ii disagreeable/*—

Participles fa general have the goternment of the verbs f
they come ; c o nseq ue n tly the qaestioa whether or not a l
should be appended to a participle depends cm the mage of the
verb ; often 5/ is inserted where it is not needed, especially by the
untaught in ejmrersafioe ; e. g..

Incorrect. «• They left beating a/ PanL"— <Acts xxi. tt.)

Some verbs take a present participle after them ssstead of am
infinitive ; e. g. v
Verbs of deamtvsj. " They have done spmstsngr—Bawrie.

Verbs of amiitimg, "Hcoaits giving am aecomat of thsm."—

7oo£e.

Verbs of preventing. •• Ozx sex are prevented from eaysyss* m
thete turbulent scenes.** — West.

*»Hemig':it have avoided trsmtiny of the origin

the parties

Verbs otmroismnp.
of ideas/* — Toott.

After verbs expressive of the operations of the seasi
pie or the infinitive may be need, hat with a slight
the meaning ; the participle describing the act as at the
actoaJr proceeding ; e. g.,

The present participle is used m the way of explanation :—

M Bat ever to do ill oar sole delight,

As bemg the contrary to his high will/'— Jtf Mm.

The present participle refers to the subject of the sentence :—
"Professing themselves to be wise, them became fools,**—
(Rom. i. 22.)
The stesentpartkapkniay agree wiA the object e. g.»

"Theystaned Stephen, calling npon God and saying/'— (Acts
vii.69.)

It mast be regarded as an inaccuracy when a present participle
beginning a sentence is not followed by a subject; eg..

" By admitting such violations of established grammatical '
distinctions, confusion would be aroided/ — Murray, j

Better "yon (or they) would avoid confusion,'' for then the ■
ptrt^p*- admitting has a subject, namely yon, and the sentence is
regularly formed. !

Usage, bowerer, has sanctioned the use of the present partici]
fat an independent manner, or absolutely, that is, as dSsj
construction, and expressive of a cause or reason :—

*• I then quit the society ; to withdraw and leave them to them-
selves ap pea li ng to me a duty."

A present participle may at the same time hare the force and
construction of a participle and a noun :—

"Mr. Dryden makes a very handsome observation on Ovid's
writing a letter from Dido to .-Eneas." — Spectator.

The construction in this last example deserves study ; the pre-
position on governs writing as a noun ; meriting as a aoun governs
Orisfs, and writing as a participle governs letter.

When a present participle performs the twofold function of a
noun and a participle, being alike governed and governing, it is
said to have a gerundkl force, that is the force and construction of
the Latm gerund, or of the participle ending in due.

With the present participle used gerundislly a past participle
may he united ; e. g.,

M 8ome of these irregularities arise from oar hoeing r e ceived tie
words through a French medium/* — Allen.

The present participle used as a noun may have a preposition or an
adverb in combination with it ; e. g.,
Their hope shall be as the glvtng-up of the ghost." — (Job xi. 20.)

The two constructions of the participle with a participial force,
and as a noun, must not be placed together in the same sentence, as
in this,

" Poverty turns our thoughts too much upon the supplying of our
wants ; and riches, upon enjoying our superfluities."— Addison.

Cornet. "No mistake can arise from using either form."

1 saw the bird Jig .
I saw the bird /pan*.

I have spoken of a participle as being used ah ea tatel i
pendeatly. A word is said to be used absolutely or "
when it stands disconnected in constraetioa from w
I and anmetims from what follows as wdL instead of

mar contain two words or

Take at

are they r— (Zeeh. i.4.)

" Or / only ami Bmrnabms , have not we power ?°— (1 Cor. ix.fi.)
Xaybut, O man, who art thou that repfiest against Oodr—
(Rom. ix. 20.)

" O rare we!-— Csmnmr.

" Miserable they !"— luamtsn.

The construction in fall involves two subjects ; a. g.,

7V sun rising, the ditrenssf teeth away

• Ou ss u s su

what I have said on tbe ptrUtisjU as lernuag the subject of 1

The sun rmng. tie aartuem aeeta away.
William being dead, Fkteria succeeded.

A ouestion has been raised as to what is the
English. With the view we have taken of cases, the
little meaning or importance. For the sake of a
may call the construction in qi
and when pronouns are employed in that u mat initios! yon will
generally find them in the nominative. Yet Milton says " me
miserable I"

tea

The construction is elliptical, and whether the noun (or pronoun)
employed should be subject or object depends on the way in which
the ellipsis is supplied.

SKETCHES FOR YOUNG THINKERS.
{Continued from page 269, rW. Ill:)

Two or three observations will suffice our second instance.
We refer to John Hilton. Much as this illustrious individual
accomplished as an author and a politician, his name will
always be most prominently associated with " Paradise Lost."
He was not a wealthy student. His path was an ascent, un-
even, steep, and rugged. The poet's soul was not daunted
with difficulty, and although he feelingly laments that wisdom
was " at one entrance quite shut out," yet his soul was bathed
in light, and that light streamed from him, as the rays from
the meridian sun. He finished his poem. It was ready for
the press, and although he had drunk deeply at

" Siloa's brook that low'd
Fast by the oracle of God,"

and " soared above the Aonian mount," yet " the bard of im-
mortal subjects, and immortal fame** offered the copyright of
" Paradise Lost" for five pounds! The book orer which a
world has poured its plaudits snd which has secured itai

SKETCHES foR YOUNG THINKERS.

a lofty niche in tho temple of fame, offered for this paltry sum !
The one of three conclusions must be come to. Either the
author had no adequate conception of the value of his book,
or literature was less prized then than now, or his circum-
stances rendered it imperatively necessary that the money
should be obtained. Suffice it to know that the last was the case.
Such men as Milton do not appear often. A Milton in a cen-
tury is more probable than a Milton in less. The Creator does
at intervals suspend, as it were, those lamps from the sky, and
men gaze in wonder at their brightness. Far be it from us to
declare, that all young men or amateur poets may become
Miltona, or that all young mathematicians may become New-
tons. Variety would thus become lost in one lofty, though
monotonous uniformity. One sun in the tky is sufficient.
We love to see the moon and stars, no less because there is a
sun. Let all those stars blaze with equal intensity as the sun,
and men would be dazzled to blindness, or scorched to death.
Let the orb of day maintain its sphere, the moon shed her soft
effulgence, and the stars sparkle in the lofty dome, and there
will be beauty, sublimity, and usefulness ; but if the arrange-
ment be disturbed, there will be disorder and confusion. We
like the stars in the firmament, and the flowers on the earth,
and the music in the air ; we admire the order, and adore its
author ; to must it ever be in the mental creation. There will
be sun, moon, and stars there. Let them all shine. Light is
useful wherever it may arise. Every man should be a centre
of light, illuminating every circle, and dispelling the shades of
ignorance, error, and vice.

It will be observed that it has formed no part of the writer's
design to furnish the biography of the individuals to whom
reference has been made. Mere illustration was required,
and this is all which will be found. It were easy to fill a
volume with extracts from the lives of the eminent already pub-
lished, but the design in the present case, was to work in the
examples simply as illustrations of the sentiments which are
here advanced. This will account for the brevity of the
notices, and the abruptness and rapidity of some of the transi-
tions. We have by no means exhausted the ail-but bound-
leas stores of instances illustrative of the theme. Time would
fail us to tell of Cellini, Matsys, Ibbetson, Kent, Towne,
Kirby, Ichiavoni, and Caslon, among the artists ; of Descartes,
Jonson, Buchanan and Cervantes, among soldiers ; of Dam-
pier, Davis, Drury, Falconer, Giordani, Fransham, Oswald,
Columbus, Cook, Vancouver, and Collingwood, among sailors ;
of Homer, Milton, Salinas, Stanly, Scapinelli and Huber,
among blind men ; and of Lithgow, Niebuhr, Ledyard and
Belzoni, among travellers. Biography will unfold this, and to
the 'written memoirs of these distinguished men the reader
must be referred. This Essay is intended rather to whet than
to satiate the appetite. It is a finger-post pointing along the
road leading to intellectual excellence; or, changing the figure,
it is a guide pointing to the footprints of previous travellers,
and saying as it points, " this is the way, walk ye in it."
The temple is at the further end of this road, no tax will be
required, but labour and patience. These will clear and
smooth the way. Longfellow in his admirable " Psalm of
Life," has well sung, — "Learn to labour ami to wait." This
counsel is the secret of success. Some men have learned to
'* labour'" but have not learned to " wait." Their impatience
has been so overmastering, as to render them disquieted and
miserable. They have cast in the seed and watered it, but the
harvest tarries and they murmur. Desert does not always
meet with immediate success ; the " gem of purest ray serene"
often lies Ions in the " deep unfathomed caves of ocean," and
the •• flower often "blushes unseen," for a lengthened period,
or perhaps it may " waste its sweetness on the desert air."
Desert moreover is not always to be measured by success.
Many succeed who are undeserving, but such success is not
always to be envied. The clown may assume the manners of
a philosopher, but he is a clown after all. The jackdaw may
be arrayed in the feathers of the peacock, but well will it be
far him if a righteous indignation does not strip off the assumed
covering, and expose the delinquent in his native insignifi-
cance.

There are some general principles deducible from this train
of illustration. A brief review of these may be of service, as
ten ding to impress the facts more strongly, and bring the sub-
ject to a more practical and successful conclusion.

I. Intellectual excellence brings with it a peculiar
pleasure. It is self rewarding, and makes a man more and
more self-dependent. TRe unlettered and uncultivated mind
must go out of itself, and feed on excitement. Solitude to such
an one is misery. Study is an unmeaning term. In early days
the mind was allowed to develop without discipline; the shrub
having been neglected, the tree refuses to be trained; The
man of cultured intellect is not dependent on contingencies
for his happiness, lie has a fountain within him, supplying
what is necesfkry in the hour of need. He who knows the
pleasure of retiring within himself, and depending on his own
resources, would not readily forego the enjoyment. Here a
distinction must be made between absence of mind, and the
pleasure of which we are now speaking. We have not much
faith in "absence of mind." In a large proportion of instances,
we have reason to believe it a studied eccentricity. We know
that some profound thinkers have been so deeply engrossed in
thought, as to be oblivious of what was proceeding in their
presence, but we protest against those instances being quoted
as apologies for all the rude, boorish, and offensive stupidity in
the world. We can sympathise with Newton when buried in
mathematics, with Dwight when absorbed in theology, or
Johnson when pondering on his ethics, without being com-
pelled to subscribe to all the ridiculous tales which are told
regarding the mental absence of many distinguished men. If
men are to be absent-minded, let it be real ; bona fide, not
assumed and fictitious.

To the intellectual man, all nature is a teacher. He finds
enjoyment in everything. He discovers

" Tongues in trees, books in the running brooks,
Sermons in stones, and good in everything."

The whole world to him is an immense library. It is a living
source of enjoyment. If his spirit be what it ought, the world
will be full of types and symbols concerning the spiritual and
unseen. Every star that twinkles will teach him lessons ;
every flower will be suggestive of thought. The planet will
remind him of " the bright and morning star ;" the flower
will bring to his remembrance " the rose of Sharon." This
may be called fanaticism, or sen timen talis rn, or rhapsody. To
call names, however, is not to disprove ; if it were so, we should
have every principle in the world overturned at once.

We envy not the man who can walk through the world, and
see no cause for thankfulness ; who regards all things as the
result of accident, and as at the mercy of a blind and capricious
chance. This must necessarily cast a gloom over the world.
The thought insults our common sense, and fills our spirits
with revulsion. If there be no God, the world in itself is the
most mysterious, confounding, and insoluble of problems.
The intellectual man enjoys the world; it is filled with objects
of attraction and instructive interest to him. We have no
sympathy with the rant that is always bickering against the
world. Neither have we esteem for the man who can look
upon it without thankfulness, and as devoid of design. Apart,
however, from the physical world, the intellectual man has
sources of enjoyment. He converses with the illustrious dead.
He luxuriates amid the sumptuous provisions of literature.
Though the authors have returned to their kindred dust, their
works remain behind. Their spirits are in their writings ;
they thus speak from the grave, and shed light from the sepul-
chre. Time and space are annihilated by the power of mind.
We go at once thousands of years back, and listen to Moses, as
in strains of sublime simplicity he relates the history of the
world's creation. Wc sit by Homer as he writes his imperish-
able lines, and we look with prophets into the events of un-
born time. While the body remains in one place, the mind
traverses the world, and drinks knowledge from fountains •*
which were opened centuries before its own existence. We
have here a velocity which defies the lightning. For the sake
of happiness, then, we urge the acquisition of knowleJge. We
cannot see that " ignorance is bliss." If this were the rule,
then the brute creation would enjoy more bliss than man* The
mind would be the greatest obstacle to the attainment of hap-
piness. We would have to attend to the necessities of our phy-
sical nature, cultivate sensual desires, despise knowledge, burn
every book, close every reading-room, proscribe the press, and

THE POPULAR EDUCATOR

SlftjC

desert the pen, as the best possible means of ushering in the
millenium of bestiality, stupidity, and vice ! A little learning
is not " a dangerous thing ; it is a ray, and brings light into
the mind, and if the student does not remain content with a
single beam, he will diligently seek for more light, and his
mind "will shine more and more unto the " perfect day.'* One
acquisition prepares the way for another ; knowledge is conta-
gious and self-multiplying, and if well selected will invariably
prove a blessing, wherever it is cultivated and psjzed. Know-
ledge is not merely a pleasure, it is a poircr ; so Lord Bacon
has weightily observed. Perhaps it would not be exaggerative
to assert, that it is the greatest power which man can exercise.
By this he is enabled to invent and wield such instruments as
a barbarous mind could not possibly have devised. Nature is
made tributary to man's purposes. Science assists him in
understanding the elements, and harnessing them for the
accomplishment of his designs. Science teaches man how to
husband physical strength, and to make the most of its power.
The barbarian, by dint of brute force, may remove a given

weight, but the civilised and enlightened European, with his
lever, pully, or screw, attains the object with the most perfect
ease. How so ? Because mind has devised the means. Those
instruments are so many embodied thoughts. They were in the
mind first, and the skilful hand wrought out the idea into
mechanical form unci its intended adaptations. What is
machinery in all its multiformities, but a development of
thought, a convincing proof that •» knowledge is power."
.Every steam engine that rushes along the rail, or darts the
boat through the wave, seems to exclaim in its rapidity,
41 knowledge is power." To the pleasures of intellectual pur-
suit there is no end. Especially does this appear to the
believer in the soul's immortality, lie believes that when
the soul is freed from its physical companion, it will continue
to think, and multiply in knowledge. The grossness of nature
will be thrown off, and the soul left at liberty to explore the
amplitudes of the immeasurable universe !

(To be continued.)

LESSONS IN GERMAN.— No. LXVIIL
Irregular Verbs, continued from p. 381.

iNrnrmvB.

Jftenmn, to name,

$ftifen, to whistle,
SWcgen, x) to cherish,
$rtifen, to praise,

Ouetten, y) to gush,
0tAc$en *), to avenge,

ffiatyen, to advise,
fteifecn, to rub,
fltriptn, to tear,
0?eiten a), to ride,

Kenncn b), to run,

fttc$en, to smell,
Mingen, to wrestle,
Sttnnen, to run (of fluids)

fltufen e), to call,

Gafjen d), to salt,

Ctaufnt, to drink, to tipple,

Ctaugrn •), to rack,

ttyoff tn/), to create,

PRESENT INDICATIVE.

IMP. INDIC.

id) nenne, k.

id) tfetfe, K.
id) *flege, k.
id) preife, it.

I id) nanntc
id) pried

id) quelle, ru qutftfl, er qui fit | id) quell

id) rActye, jo. ic$rAc$te(rocf»)

•ttyeikene), to separate,
Ctycincn, to appear,
GtyUtn, to scold,

©cjmn, to shear,
Gcyiefcen, to shove,
6c?ief en, to shoot,
Cejinfcra, to flay,
e^tofen, to sleep,
Ctyfafttn A) to beat,
ttyleicfen, to sneak,

id) rat$e, feu xMhft, er raty
id) retfre, ic.
id) reipe, k.
id) reite, >c.

id) renne, k.

id) riee$e, >c
id) tinge, k.
id) rinne, ?c.

id) tnfe, ic.

id) fatyr, k

id) fanfe, feu fAufft, er fdtift

id) fauge, k.

t# Walfr, >f •

icfr fcfcfifce, k.
id) ferine, k.
id) ftyelte, feu fyiftft,

id) fc^cre, ic.
id) f<$te&c, ic.
id) jtytepe, k.
id) fatnfee, k.
id) ftylafe, feu faTAfjt,
id) ftylage, feu jtylAgft,
id) fe$fei<$e, ic.

ft ftyift

er f$(Aft
ftfalAgt

ic$ riet$
i$ ricB
tyrifl
tcf> ritt

ic$ ranntc or

rennte
id? ted)
tyring
i$ rann

ic$rief

i<V fatyc

ty fojf

ic$ fe$uf

id} f$ieb
14) fc$ien
tc$fc$att(f<$oft

id) fc$or
ic$ f^oS
i<$ frtofj
ic$ ftyunfe

ty WK«f
tdj> ftyfag
i* fd>tic$

i$ nenncte

id) tfjfe

id) fcriefe

i<$ quelle
i$ rdc$te,

MO
id) ritifft
t<$ rie&e
id) rijTe
ic$ ritte

id) rennete

ic$ rfc$e
t* range
id) rAnne
(renne)
ic^' viefc

ic^ fafjete

id) feffe

i^fogt

ic^ f^irte
id) fd)itnt
id) fd^atte
(fc^oltc)
i<$ fc^&re
\d) td)bU
id) faeffe
id) fcfiunte
t^ fc^tiefe
id) fcr/tuge
i(tj fc^Iic^

IMPERAT.I PARTICIP.

nenne gen»mnt

pfeifc(pfeif)

prrifc

quelle
xbd)t

reibc

reifie
reite

reune

i-ie»e, xitd)

ringe

rinne

rufc

f«Tje

faufe

faugc

f4wffc

fc^eibe
fc^eine
\d)i\i

fc$ere, fester
f*ier>e

\d)it$t
fc^inte
Waft
itytage
f^leic^e

stiffen,
gepflogen.
gepriefen.

gequcllen.
$tx&d)t (gcro-

4»cn).
gerattyen.
gericben.
geriffen.
geritten.

gerannt or
gerennt.
gero$en.
gerungen.
gerennen

geriifen.

gefaljen.

gefoffen

gefpgea.

gefoffen.

REMARKS.

x) When it signifies, to w*tt
upon, or to be accustomed, it
is regular.

y) OurUcn, to swell, is regular.

z) .The irregular form is no
longer used. Where it oc-
curs in former writers it most
not be confounded with the
same forms from rtec^cn.

a)$ereiten, to ride to, like all
the compounds of reUen, it
irregular; butbereuen,tomake
ready, from fareit, ready, is
regular, like all derivatives.

b) ftennte and gerennt not often
used.

gefc^irten.
geftyienen.
gefttoltex.

geftyoren.

gefc^c^en.

gefc^ofTen.

gef(^unbeit.

geftylafen.

gef^Iagen.

gefc^lic^en.

c) Regular in some writers,
but improperly so.

d) Irregular only in the par-
ticiple, and in that when
used adjectively ; as, gef<s(*
jenc &ifrf?c; er $ot fit gefatjt.

e) @dugfl and faugt are . not
supported by good usage, but
fAugen, to suckle, is regular.

/) In the signification of to
procure, to get, it is regu-
lar, as also anftyajfen, to pur-
chase, to buy ; ctbfd^tffen, to
part with, to dismiss. .
) The active verb ftydtea, to
part, to disjoin, to divide, Is
regular.

h) 9tat$f$tagen and UtttiMta*
gen, to consult, are regular. -

LESSONS IN ITALIAN.

Irregular VerU continued.

INFINITIVE.

PRESENT INDICATIVE.

IMP. INDIC.

IMP. SUBJ.

IMPERAT

PART I CI P.

REMARKS.

Gtyteifm i) to sharpen,

icf fc^tetfr, K.

icf ftftiff

icf fcf liffe

fcf Icife or

gefeftiffen.

t) Regular in all other signi-

to whet,
Gcfteifen, to silt.

fcfteif

fications, as, to demolish, or

fcf fcf Teif e, jc

«f f<f tip

icf fcf Itff*

fcfteipe

gefeftiffen.

to drag.

Ctytiefeir, to flip,

icf fcf liefe, k.

ty f<f toff

icf fcf toffc

fcftiefe

gefeftoffen.

•Jcfliefen, to shut,

ief fcf Kef e, ic.

Mf fcf Uf

icf fcf toffe

fcftiePe

gefcflcffcn.

Gcf lingen, to fling,

icf fcf Unge, je.

icf fcf (ang

icf fcf (dnge

fcftinge

gefeftungen.

6<f meifen, to fling.

icf fcf meif e, ic.

icf fcf miji

icf fcf miffe

fefmeipe

gefefmiffen.

©cf ratlin *), to melt

icf fcfmelje, tu fcfmeljefl
(fcfmttjeft), er f^metjt
(fcfmtfjt)

icf fcfniof)

icf fief me($e

ftf mitj or
fcfmetj

gefefmotjen.

k) As an active verb it is re-
gular.

©<f nauBen, to tnort,

tcf fcf nieBe or fcf ncmBc

icf fcf not

icf fcf noBe
icf fcf nitt e *

fcfnauBe

gefcfnobVn.

Gfef neifeen, to eat,

icf fcf nei*e, k.

icf fcf nitt

fefneibe

gefefnitten.

GfcfrauBen /), ta screw,

icf fcf rauBe, k.

icf fcfrauBte

icf fcfrauBete

jcftauBe

gefcfrauBt

1) Commonly regular, fcfrauBte,

(fcfroB)

(fffroBe)

(gefcfroBen)

gefcfrauBt.

©cfrtiBen, to write

icf fcf ricBe, k.

icf fcf rieB

icf fcf rieBe

fcfreiBe

gefcfricBen.

ekfieien, to cry,

icf fcfreie, jc.

icf fcf rie

icf fcf riee

fcBreie

gefefrieen.

6<f rcitcit, to stride,

icf fcf reite, k.

icf fcf ritt

icf fcf ritte

fcfrctte

gefefritten.

ftyroten, tobruise,tognaw

icf fcf rote, k.

icf fcfrotete

fcf rote

gefefroten.

Regular now except in the
participle, and this is fre-
quently gefcf rotet.

m) ©fftoierft >c. in the present

tkf*4renm), to suppurate,

icf fcftodre, k.

icf fcf toor

icf fcftocre

fcftoAre

gefeftooren.

Ctyseigen, to be silent,

icf fcf toeige, k.

icf fcf toieg

icf fcf totege

fcftoeige

gefeftoiegen.

is provincial.

etyscuai »), to swell,

icf fcftoelle, Bu fcftoittft, er
fcfwittt

icf fcf tooli

icf fcf tootle

fcftoitt or
fcftoetle

gefcftootlen.

n)» Regular, when active.

&cf tsitnntett, to swim.

icf fcftmmme, ic.

icf fcf toamm

icf fcf toAmme

fcftoimme

gefeftoom*

Ctytoiaben, to vanish,

icf fcf totnbe, ic.

icf fcf ttanb

icf fcftoftnbc

fcftoinbe

gefeftounben.

Gcf toingeu ©), to swing,

icf fcf toinge, k.

icf fcf fixing or
fcftoung

icf fcftoftnge

fcftoinge

gefeftoungen.

0) Gcftoung is less in usage

than tytoang.

feftoften, to swear,

icf fcftoore, k.

icf fcf toot or
fcftour

icf fcf toore or
fcftoure

fcftoore

gefeftooren.

Cefen, to see,

icf fef e, bu fief ft, ft fief t

tcffaf

ieffafe

rtefc

gefefen.

©ein, to be,

icf Bin, k.

icf mar, k.

icf toctre

f«

getoefen.

fenbcs, to send,

icf fenBe, ic.

1cf fanbte and
fenbete

icf fenbete

fenbe

gefanbt and
gefenbet.

CKcbeajO, to boil,

tcf fiefee, K.

icf fctt

icf fotte

ftebe

gefotten.

p) When actire it is mostly

eiogrn, to sing,

icf finge, ic.

icf fang

icf fdnge

flnge •

gefungen.

regular.

Crtafea, to sink,

icf finfe, ic.

icf fan!

icf frtnfe

finfe

gefunfen.

Cttnscn, to think, to muse,

icf flnne, ie.

iff fann

icf fAnne
(f&nne)
icB faf e

fiunc

gefonnen.

«i*cit, to sit,

icf flfce, IC.

ty faf

gefeffen.

CfeOen, to be obliged,

tcf foil, bu follft, er fofl

icf fodte

icf fottte

—

gefoHt.

©patten 9), to split,

iff fpafte, ic

icf fpatfete

icf fpaltete

fpatte

gefpatten.

q) Irregular only in the par-

Cpeien, to spit,

icf fpeie, ic

icf frie

icf fpiee

fpeie

gefpieen.

ticiple, and this is some-

tspimten, to spin,

icf fpinne, k.

icf fpann

icf fpAnne
(fronne)
icffpitffe

fpinne

gefponnen.

times gefyattet when the vert-
is active.

estetfen, to split,

uf fpTeif e, k.

icffplie*,f>(ip

fpteipe

gefptiffen.

tfeccgen, to speak,

t<f fprecfe, bu fpricf ft, et fpricf t

icf fpracf

icf fprAcf e

fpticf gefprocfen.

LESSONS IN ITALIAN GRAMMAR.— No. II.

BY CHABLE8 TATJSXNAV, M.D.,

Of tht Uaivsrtity of PstIs, ProftMor of the Italian and Gorman Lanfusfti
at tas Kontingtoa Proprietary Orammar School.

I now proceed to explain Italian pronunciation in a method
of recent adoption by some ingenious teachers of Italy, by
which all the combinations of the vowels and consonants, and
consequently all the ingredients and component parts of the
language, will pass under the eye of the reader. Let him learn
from the very beginning of his labours to pronounce each sylla-
ble of the following words and tables, and he will soon acquire
a correct method of pronunciation. No word or combination
of words can offer any difficulty to him, because he will have
mastered the component parts of all words in these tables.

The Italian language has five vowels, representing seven
sounds;

I. a invariably sounded like the English interjection ah.
II. 1 invariably sounded like et in eee.
HI. u invariably sounded like 00 in too.

IV. ^1. e invariably sounded like ay in say, but with a slight
opening of the mouth only, and with an elevated
and clear tone. It is called^pn that account, the
close sound of the vowel.
2. e invariably sounded something like e in let, set, and
the first e in every, but with a wide opening of the
mouth, and with a deep sound. It is called, on that
account, the open sound of the vowel.

V. 1. invariably sounded with a medium sound between
and 00 , which has no equivalent in the English
language, but which may be easily caught by the
ear from hearing an educated Roman or Tuscan
apeak. Perhaps an approximation is the in bone,
hole, and note, out with a slight opening of the mouth
only, and with an elevated and clear tone. It is
called, on that account, the close sound of the rowel

1*0

THE POPULAR EDUCATOR.

2. o invariably sounded something like o in Lord and
orange, but with a wide opening of the mouth, ai
with a deep sound. It is called, on that account ,
the open sound of the vowel.
The first sound of # and the first of o occur in the majority I
syllables, and may be called the ruling sounds of those two
vowels. No distinguishing sign is used in Italian to mark tit-
two # v s or two o's. Englishmen must have some mark to
indicate when e and o are to be sounded with their second Of
open sounds. I shall, in these cases, place on e and © thfi
sign *, as for example i, 6.

' The pronunciation of what, for the sake of distinction, I shs
denominate the circumflexed sounds of e and o is not uniform
throughout Italy ; but as the pronunciation of Rome and
Florence is the standard, all depaxtures from it mav I
reckoned provincialisms, which ought to be carefully avoided*

The Italian consonants, seventeen in number, are divided
into mutes and semi-vowels. Mutes are those that require a
vowel after them to render them pronounceable. Semi-vowel
are those which require a vowel before them to make them
pronounceable.

. Let me first enumerate the mutes, and show by tables their
combinations with vowels in Italian words. There are ten I

mutes:

1. b named in the alphabet bee.

II. e named in the alphabet chce, and sounded like eh in
church before the vowels e and •'. Before all other
vowels it is sounded like k in English.

III. r/ named in the alphabet dee.

IV. g named in the alphabet jce, and sounded like g in

' ginger before the vowels e and i only. Before all
other vowels it is sounded like g in gang \ go ', and gull

V. j named in the alphabet i(ee) lungo or jota, (i consonant*,)
and sounded like y in yes only at the commence
ment of a word or syllable and before a vowel.
At the termination of a word it is no longer a>
consonant, but must be sounded like a lengthened
ee.
• VI. p named in the alphabetic

VII. q named in the alphabet koo. It is an auxiliary letter

only used before u with the sound of k.

VIII. t named in the alphabet tee,

IX. v named in the alphabet vee {u consonants).

X. i named in the alphabet tsaita, sounded like it in
Switzerland, or like dz in adze. These sounds vary
in different parts of Italy. After /, u, and r, it ii
generally pronounced like tz in Switzerland. The;
same sharp sound occurs in words derived from
Latin, and ending in zia, zio, ziouc, &c.

I shall maik each word in the following spelling tables, and
indeed each word given as an example or illustration, with an
accent, which, being merely arbitrary, used for the occasion to
facilitate the progress of the English learner and not used in
Italian printing, I denominate the accent of (one. In every i
Italian word composed Of more than one syllable, there is
always one syllable on which, when we pronounce it, the voice I
ought to pause with a marked elevation of tone. This prolog

| inexpedient to hnr down now, as they would not at this stage
of our progress be thoroughly understood, but which I shall
take occasion to point out in convenient places as I proceed,
. One remark more with respect to the vowels $ and 6.
I have called the first sound of $ as ay in say, and the
first sound of o (the medium sound between o and oo t which
cannot be adequately marked by an English equivalent) the
ruling sounds of those vowels. The reason is this ; they are
heard in all syllables without distinction, whether they have
the accent of tone or not, while the second sound of $ (pronoun-
ced with a wider opening of the mouth and a deeper sound, and
something like e in let and ever) and the second sound of #
(also pronounced with a wider opening of the mouth and
deeper sound, and something like o in orange and lord) can only
be heard in accented syllables, of which there can be in each
word only one. The former sounds, therefore, are much more
frequent than the latter ; because unaccented syllables are more
numerous than those accented.

With regard to the e in unaccented syllables having an
English equivalent in ai or ay % I shall have no difficulty in
marking the pronunciation ; but with regard to o in unaccented
syllables, as there is no equivalent, I should be obliged to use
the acute accent, and thus confuse the reader, who would
perhaps be unable to determine which was the accent of tons
In a word and which the accent mat king the peculiar sound of
>. I beg it therefore to be understood once for all, that where
I shall have occasion to use an o in unaccented syllables
Without any sign above it, the vowel must invariably have
he first eound of o as above explained. I follow the authority
Hot only of the educated classes of Florence and Rome, but
also that of Celso Cittadini and the best theoretical writers on
Italian pronunciation.

FIRST PRONOUNCING TABLE.

. Showing the combination of vowels with mute consonants
in natural order.

Pronounced.
bah-do

Italian,
%ado
Bevo ,

Bice
Boce (for voce)

iuco
F.bano

ibete

tbile

bai-vo

bee-tchai*

bo-tchaif

boo-ko

e-bah-noj

ah-bc-tai

ah-bee-lai

Qbolo (Latin, obolus) 6-bo-lo}
[fatso ah-boo-zo ||

Babbo, (Tuscan) bahb-boll

English.
I take care
I drink

Beatrice, a woman's
Voice, word [name
Hole
Ebony
Fir-tree
Able
Farthing
Abuse
Papa

* The reader must not forget mv previous observation that o
before e and t is sounded like ch in the English word cMutxh.

f The acute accent over o marks not only the accent of tone,
but also the first sound of o as stated before.

X Once for all, I must refer my readers to the opening explana-

on, where I stated that there is no English equivalent to the
second, open or circumflexed sound of the e, as in the first syllable of
&ano. For that reason, I have not attempted to imitate it by an

nglish sound; and have thciefore simply marked it by the cir-
iimflex sign. In aliases of the e circumflexed, the reader must

studiously avoid the English sound of e, wi^ch could only create

the greatest confusion. He may always bear in mind what I hate

- o - , . «*,»»-., , stated, that an approximation to the circumflexed e is to be found

Stion and elevation of the voice on the syllable is similar to \- m tne c of the English words let and ever; only uttered with a
e transition of the Voice from one tone to another in music, wider opening of the mouth and deeper sound ! The circumflexed

in order to dt scend tOjthe level of the original tone from which
.the voice was raised. The accent of tone exists more or
less in every language, but it is more or less sensibly marked
in one language than another, and it is strongly so in Italian ;
and on the marked use of this accent in a great measure
depends the harmony of the language. I shall mark this accent
by the acute sign (') from right to left. It is true that this
acute sign is sometimes printed in Italian word?, but in a very
few instances only, which I shall have occasion to point out here-
after. The grave accent (*), from left to right) is used much more
frequently (the rules for its use will be given hereafter), and for
this reason I prefer using, in order to avoid confusion, the acute
accent as the arbitrary mark or sign of the accent of tone.
Twovthirda of the Italian words have «n accent of tone regu-
lated by principles clear and invariable ; which it would be

■ is invariably the accent of tone.

§ The reader must bear in mind, that this is the second or less
I equent sound of o, something like the English o in the words

ange and lord, but with a wider opening of the mouth and deeper

und. I give it the circumflex mark, because it is the lees ooss-
n.on sound. Wherever it occurs in my lessons, it will invariably

note, as in the case of the circumflexed e, the accent of tone as

•11 as the peculiar sound of the o.

II I shall have occasion to speak of the two sounds of s when I
I plain the sounds of the semi- vowels.

% I give these as exercises for the special purpose of teaching
my readers to pronounce double consonants. It is a fundamental
rule of Italian pronunciation that double consonants must be

tered and vibrated distinctly. This is essentially necessary, not

ly as it augments the beauty and marks the orthography of

>rds, but as it frequently distinguishes words of totally difitrent

lessons in Natural Philosophy.

Itmlim.

Pronounced.

iftW# (for hoove)
Qibhi [for gooh)

betb-bai"

jib'-beeff

Gobbo

g6b-bo
doob-bee

Dubbi

Cado

kah-do

Coco

tchai-tchai

Oito

tehee- to

Coda

ko-dah

Cute

koo-tai

Ducato

doo-kfch-to

Rieevo

ree-tchai-vo

Incuh

in-tchee-do

Aneona

an-k6-na}i
lah-koo-nan

lacuna

Bacco

bak-ko

Beeeo

bex-ko

Pioea

plk-kah
bok-kah

Bocca

Hueoo

s6ok-ko

Dado

dah-do

DoVO

dai-vo

hit*

dee-to

Dopo

dd-po

Dueo

d6o-tchai

Bdace

ai-dah.tchai

Adele

ah-d6-lai

Adiro

ah-dee-ro

Adoro

ah-d6-ro

Aduno

ah-d6o-no

Adda

ahd-dah

Bdda

cd-dah

Jddio

Id-dee-o

Adduce

ahd-doo-ko

Gaza

Gah-dzah

Goto

j£-to

Oiia

jee-tah

Godo

g6-do

Gu/o

g6o-fo
lai-gah-mai

Zegami

Angela

ahn-jai-lo

Angina

ahn-jee-nah

Vigors

vee-g6-rai

Arguto

ahr-g6o-to
pahd-jee§$

laggi

(To be continued.)

English.

He drank

Hunchbacks

A hunchback

Doubts

Lfall

Chickpease

Quickly

Tail

Skin

Dukedom, duoat

I receive

I cut

Aneona

Fool, swamp

Bacchua

Beak

Spear

Mouth

Juice m

Die for gaming

I ought, I must

Finger

After, afterwards

General

Gluttonous

Adeline, a woman's
name

I provoke to anger

I adore

I unite, I assemble
others

The river Adda

The Edda of Scan-
dinavian literature

God

I lead to

Gaza in Palestine

Jess (in falconry)

A walk, trip

I rejoice

A horned owl

A tie, ligament

Angel

Inflammation of the
throat

Vigour

Ingenious, witty

Puges (attendants)

meaning, but differing only in spelling by the single consonant
instead of the double one ; as, for example, caro, dear, and carro,
a ear; as I shall have occasion later more fully to illustrate.
"Where a, or any other vowel precedes a double consonant, a
particulsr stress must be laid on that vowel, snd its sound
must be shortened. I have not attempted to indicate that
shortening of the eound of the rowel by any new sign, because a
frequent change of sign only creates confusion, and the true pro-
nunciation is obvious from the ntct$$itgqf giving a vibrating clearness
to the double consonants.
> 4+ The English r, whenever it is sounded as in the word gtt t
corresponds to the shortened sound of the first sound of e (of).

■H The reader must not forget my previous observation that g
before sand i is sounded as in the English word ginger.

Xt It is obvious that not only before double consonants not in the
same ayllable, but even before one consonant in the same syllable,
• of any other vowel must be shortened in the Italian, as perhaps
m any other language. It is therefore unnecessary to use any
sign.

If The pronunciation of go depends on the vowel that follows
the latter g. If that vowel is e or <, the gg'$ are pronounced some-
what.as if the first g had merely the sound of a: and the second
#, which goes to the next syllable, like the English j in jag, only
the voice must not pause too long on the d of the syllable where the
first g occurs ; the stress must be laid on it, and the voice must
glide as quickly as possible to the pronunciation of the second
§, whkh must be very soft. In this way there will be effected a
more equal distribution of the sound J between the two syllables.
witch will or cause the correct sound of the gg*

ON PHYSICS *OR NATURAL PHILOSOPHY—

No. II.
GENERAL PROPERTIES OF MATERIAL BODIES.

(Continued from p. 3.)

ibrotify.— This is the property of matter in consequence of
which interstices exist between the particles of bodies ; these
interstices are termed pores.

Pores are of two kinds ; there are physical pores, or inter-
stices, so small, that the attractive and repulsive forces with
which matter is endowed continue to exert their actioA ; and
there are sensible pores, such as may be recognised by inspec-
tion. The latter are merely holes, across which the molecular
forcea are incompetent to exert their action. It is to the exisV
ence of physical pores that are due the phenomena of expan-
sion and contraction arising from variations of temperature.
It is in sensible pores that the organic phenomena 6t exhala*
tion and absorption take place— phenomena characteristic of
vitality, whether animal or vegetable.

Sensible pores are very apparent in sponges, in wood, and
in a great number of stones ; whereas physical pores are never
recognisable, and their existence can only be proved by argu-
ment. They are inferred to exist chiefly by considerations of
the diminution of volume which bodies experience when
exposed to the influence of cold, or to the force of mechanical
pressure.

In order to demonstrate experimentally the condition of
porosity, the following experiment may be performed. Take
a long glass tube, terminated at its upper extremity by a
copper cup ▲ (fig 3), and at its lower extremity by a foot piece of

Fig. 3.

the same metal, capable of being screwed upon the exhausting
plate of an air-pump. Tiie lower orifice of the copper cup ▲ is
closed bv a thick piece of buff leather. Let aome quicksilver bo
now poured into the copper cup until the buff leather is entirely
covered ; then create a vacuum by means of the air-pump.
Immediately this is done, atmospheric presaure being removed
from below (he leather, and still being exerted above it,
: c mercury rushes through the pores of the leather and falls

V:-

THE POPULAR EDUCATOR.

daw* the tabs in a shower of minute drops. In a similar way
water may be caned to pass through the pores of wood, if a
daw of the latter, cut perpendicularly to the direction of its
n1sfa\ be wih a titiifct tea piece of leather.

If a little chalk be thrown into water, there presently escapes
s> number of minute bubbles of air, which evidently occupied
the pans gristing within the substance of the chalk, and from
which the air is driven by reason of the water which enters.
In short, if the piece of chalk be weighed before and after
immersion, and the weights compared, a considerable increase
will be found to hare resulted as the consequence of putting
it into water. In this manner, we may determine the total
volume of the existing pores by estimating the space which
corresponds to a bulk of water equal in weight to that
experienced by the chalk by immersion. As regards the
pmosity of metals, this quality has been demonstrated by an
experiment performed by the Florentine academicians in the
year 1861. The experiment was as follows :—

A hollow sphere of gold haying been filled with water, pres-
sure was applied by forcing in a screw. Subjected to this
treatment, the contained water was found to ooze through the
golden sides of the sphere, and to appear externally in small
dew-like drops. Subsequently to this experiment of the
Florentine academicians, a modification of it has been fre-
quently repeated, various metals having been substituted for
gold. In every instance a similar porosity was demonstrated
to exist.

TkeApp*rtnt*U Real Volume of Bodies— A slight reflection on
what has been laid down concerning porosity, will lead to the
inference that distinction requires to be made between the
apparent volume which bodies occupy and the real volume.
The apparent volume of a body is equivalent to that portion
of space which it fills ; its real volume is that portion of space
which it would have occupied if all porosity in its substance
could have been annihilated ; in other words, the real volume
is the apparent volume diminished by the volume of the pores.
Ihe real volume of a substance is invariable, but its apparent
volume diminishes or augments with the volume of the
pores.

Applicmtion* of the Preceding Iket*. — The quality of porosity
has been taken advantage of in the construction of niters
with paper, felt, stone, and charcoal, substances frequently
employed in domestic economy. The pores of these bodies
are sufficiently large to admit th% passsge of liquids, but
at the same tune sufficiently small to refuse passage to the
extraneous substances which the liquids may have held in
suspension. Another frequent and useful application of the

Eity of a body, is that of splitting large masses of stone
e expansion of a wooden block. The process is as follows,
nels or clefts are first made around the base of the mass
to be separated, and into these clefts dry wooden wedges are
driven. When a sufficient number has been introduced in
this m a nner , they are moistened with water, which, penetrating
between their pores, the wood swells and exerts enormous
force, by means of which gigantic blocks are separated from
the parent rock. A variation of the same force may be
recognised in the augmentation of size, and the diminution of
length, which cords undergo when they are moistened. Some-
times the force thus called into operation is taken advantage
of for the raising of heavy burdens.

QmpreuMlity. — It is in consequence of .this property that
Dodiea are capable of being forced by pressure into smaller
•paces than those which they ordinarily JUL This property is
at once the consequence of porosity, and the proof of its exist-
ence. Indeed, the most porous bodies are those which are
also the most compressible. The extent to which different
bodies may be compressed varies exceedingly. The most
compressible of all are the gases, many if which are suscep-
tible of* reduction, when sufficient pressure is applied, to a
volume TO, 20, or even 100 times smaller than that occupied
under their original conditions. Nevertheless, in the generality
of aeriform bodies, a limit exists beyond which the gaseous
state ceases, and a liquid body results.

The compressibility of solids is much less than the compres-
sibility of gases, and varies for different bodies of the solid
class. Woven fabrics, paper, cork, wood, and all porous
tis sues ^ are susceptible amongst solids of the greatest amount
Of oppression* Metals ere also compressible, a fsct suffici-

ently demonstrated by the process of earning, which c
in making an i mpress ion on a flat metallic disc by the I
pressure of a die. In connexion with the uimaicssibfliiy of
solids, it should here be remarked that a certain point exists
at which no further amount of compression is possible. At
this point it frequently occurs that a metal still subjected to
continuous pressure crumbles to powder. As regards liquids,
their amount of compressibility is so exceedingly slight, that
during a long period the property was altogether denied.
Experiment has, nevertheless, demonstrated, the existence ot
such compressibility in liquids, and we shall hereafter treat of
of it fully under the head of hydrostatics.

2Sa*ri«ry.— Elasticity is the piop ei t t by the exercise of
which bodies are enabled to resume their primitive volume,
or primitive form, when the force which altered this form or
volume ceases to act. Elasticity may be developed in bodies
by pressure, by traction, by flexion, or by torsion. At pre-
sent we are mtrely concerned in regarding the elasticity of
pressure ; the other species of elasticicy taking place only in
solids, will be placed amongst the specific properties of material
bodies. Gases arc eminently elastic; that ia to say , if theysre
compressed, and the compressing force be removed, they at once
reassume their original bulk. A similar observation applies to
some liquids which may have beensubjeeted to compression ; but
the property of elasticity in solid bodies is not complete; If
the compressing force has been extreme, or very long applied,
solids rarely assume their original condition on the removal of
the compressing force. Nevertheless, the quality of elasticity is
very apparent in caoutchouc, ivory, glass, and marble. In fatty
bodies the quality is scarcely recognisable; and a similar
remark applies to masses of day, and to the metal lead. In solids
there is a limit to elasticity, beyond the boundaries of which
either rupture takes place, or the exact original con d ition of
the bodies does not reappear. In the case of sprains, for
example, the limits of the elasticity of the ligaments affected
have been exceeded. Gases and liquids are affected by no
such limit, and therefore always return to their primitive
volume,

Elastititr is the result of a condensation of mo lec ule s,
therefore of a change of form, which as regards solid bodies
may be demonstrated by the experiment which follows. Upon
a plane of marble, which has been smeared with a little oil, drop
a ball of ivory, of glass, or of marble; the ball rebounds to an
elevation something less than that of the space through which
it fell, after having left on the marble surface, at the point of
contact, a circular impression, the diameter of which increases
in proportion to the height from which the ball fell. It
follows from a consideration of the preceding experiment, that
the ball at the moment when it struck the table must have
become flat over a certain space of its surface, and that the
rebound of the ball ia due to the springing back of •the com*
pressed molecules constituting the flattened surface into their
original position.

Motility— Motion— Rtjo*. — Mobility is the property by which
material bodies psss from one point, to another. The term
Motion is applied to that state of a body which ia involved in
the act of changing place. The term rstf signifies the opposite
of motion, and also a permanence in the same place.
Rest and motion may be understood each in the two senses
of absolute and relative. Absolute rest would consist in the
complete privation of motion ; but we know of no such state.
If we take the most extended view of the universe, still this
condition of absolute repose is nowhere discoverable. The
absolute motion of a body would consist in its displacement
as regards another body in the state of absolute rest.

The condition of relative rest ia that assumed by a body
in relation to surrounding objects, although in reality it par*
takes with them of a common motion. For example, an object
which remains in the same place in a boat whilst sailing, may
be said to be in a condition of reat so. far aa eoncerna the
boat, but it is really in a condition of motion as regards die
river-sides. Sucb an object, then, furnishes us with an
pie of the state of relative reat.

^ The relative motion of a body is only its apparent
tion, that ia to say, the kind of motion which is
by comparison with certain other bodies assumed to be fixed*
although they are really in motion. Of this*kjad it the ana*
tion of a boat ia relation to the banks of a liy^ to ts» Jatsw

LESSONS IN GEOLOGY

participates with the boat in the double motion of rotation
and translation in space, to which our globe is continually
subjected. In nature it appears, then, that we only recog-
nise conditions of relative motion or relative rest.

Inertia. — Inertia is a purely negative quality of matter, and
constitutes the well-known inability of matter to pass of itself
from the state of rest to that of motion, or to moaify the kind
of motion with which it may have been impressed.

If occasionally objects fall when left to themselves, this
result is dependent upon the exercise of an attractive force,
which draws them towards the centre of the earth, and not
upon their own self-agency. If the velocity of a billiard ball
on the table gradually diminishes, this result is attributable
partly to the resistance of the atmospheric air, and partly to
friction against the cover. It would be incorrect, then, to
assume that the billiard bail holds within itself a tendency to
rest rather than to continuance in motion, us certain philo-
sophers of antiquity were in the habit of propounding, when
they compared the natural tendency of matter to a lazy indi-
vidual. In all cases where there is no resistance, continued
motion proceeds without alteration, as we find exemplified in
the course of the planets in their orbits around the sun.

Application of the Preceding? Deductions. — A great number of
phenomena are explicable by the doctrine of the inertia of
matter. Por example, when one is desirous of leaping across a
ditch, he takes a preliminary run, in order that at the instant
when the spring is made the impetus generated by running
may be superadded to that resulting from the spring itself.

A person who alights from a carriage in motion participates
in the motion of the carriage, and if the individual thus alight-
ing does not take care to give his body an impression contrary
in direction to that imparted by the carriage, he falls on touch-
ing the ground in the direction of the carriage. It is the
quality of inertia which renders so terrible the accidents from
concussion on railways. In fact, if the locomotive itself
should be brought suddenly to a pause, all the train would
continue its progress by reason of the force already acquired,
and the carriages would be boken by striking against each
other.

Hammers, pestles, pile-drivers, &(\, are all so many appli-
cations and illustrations of the principles of inertia; so in
like manner are the fly-wheels of steam-engines, and the
regulators of the motions of machinery.

Preliminary Notions Concerning Fohcb andHotion.

Forces.— By the term Force, is understood any cause
capable of producing motion, or modifying motion when
once produced . Thus, the m uscular action of animals, weight,
magnetic attraction and repulsion, and the tension of vapours,
are all forces. In general the term powers is applied to
designate those forces which tend to produce a certain effect ;
and the term resistance, to those forces opposed to the pro-
duction of such effects. The former in consequence of their
tondenpy to accelerate motion at each instant are called accele-
rating forces, whilst the general expression of retarding forces
is applied to the latter ;yet the same force may be considered as
a continually accelerating force at one titnc, and a continually
retarding force at another time : for example, when a stone is
allowed to fall from a state of rest, at some elevation above
the ground, the action of gravity with which the earth, and
indeed all matter, is endowed begins to affect the stone, and
continuing to do so during the whole period of its fall, it
reaches the ground with accelerated force ; but if a stone be
projected perpendicularly upwards from a place on the ground,
its motion upwards will be continually retarded by the action
of gravity during the whole period of its ascent, until it come
to a momentary state of rest, and its progress upwards will be
stopped. Gravity, when it acts in the manner described in
the latter of these cases, is called a continually retarding force.

Instantaneous and Continued Forces,— -Forces axe capable of act-
ing upon bodies in one of two ways. First, during a very
short period, as, for instance, that consequent on the shock or
explosion of gunpowder ; and second, those which continue to
act during the whole duration of the motion, as gravity, and
the traction of animals. The former are termed instantaneous,
and the latter continued forces.

Equilibrium. — When many forces are simultaneously operat-
ing upon one and the same body, it may so happen that the

forces mutually neutralise each other's effects, and that eon*
sequently the original state of the body is not affected. The
term equilibrium is used to designate this state of condition
in a body. Care must be taken not to confound the two
states of equilibrium and rest. In the former state a body is
submitted to the action of several mutually destructive forces;
in the second a body is not acted on by any force. Neverthe-
less, it is a question whether there be anybody actually at
rest in the material universe. To this question we would
answer in the negative.

Characters, Unit, and Representation of Forces, — Every force
is characterised — first, by -its point of application, that is to
say, the point at which it immediately exerts its power;
second, by its direction, that is to say, the straight line which
it tends to describe at its point of application ; third, by
its intensity, or, in other words, its relation to some other
force considered as unity.

The force chosen as unity in any particular question is
altogether arbitrary; but whatever may be the amount of
traction or pressure developed by a force, inasmuch as a cer-
tain weight may be made or considered to produce the same
effect, it is customary to refer forces to some unit of weight,
and in this country the pound weight, or some multiple of it,
is generally the unit. Thus a force is said to be equal to 20
pounds, it the pressure of 20 pounds can be substituted
for the action of the force. From a study of the characters by
which a force is determined, the force itself is completely
known when its point of application, its direction,- audita
intensity are given. In order to represent the different
elements of a force, we draw an indefinite straight line
through its point of application, and in the direction along
which it is exerted. Then upon this line some arbitrary unit
of length is marked, commencing from the point of applica-
tion, and extending in the direction of the force. This unit
of length is then repeated as often as the given force contains
the unit of force. As the consequence of this arrangement,
we have a straight line which completely determines the
force. In order to distinguish forces from each other, they
may be represented by letters, such as p, q, b, placed upon
the line indicating their several directions. In order to faci-
litate the understanding of many physical phenomena, it will
be necessary to refer to certain principles which are demon-
strated in mathematical treatises on natural philosophy.
These principles will be cited in the next and subsequent
articles.

LESSONS IN GEOLOGY.— No. XLII.
By Thomas W. Jbxxtn, D.D., F.R.O.S., F.G.S., Ac.
CHAPTER III.

ON THE INFLUENCE OP ATM03PF1ERIC AGENTS ON THE
EAETH'3 CBUST.

SECTION VIII. -ON ICEBERGS.

§ U. ON THB TRANSPORTING POWER OF DRIFTING ICEBKROS.

In the lessons which were given you on the formation and
agency of glaciers, you have learnt that all the rocky frag-
ments, which glaciers brought down from the lofty ridges of
the Alps, were deposited in a terminal moraine, and that, at
some earlier epoch, they had left behind them on the sides and
ledges of the mountain, at a much higher elevation than they
reach in our day, enormous blocks of stone called boulders.
For illustrations of this process, consult the diagrams in the
lessons on Glaciers.

Boulders, like those on the flanks of hills in the Alps, are
found in very extensive districts all over the north of Europe
and America. Some of the blocks are waterworn, others aro
rugged and angular. They consist of fragments derived from
locks of all kinds arid of all ages, primitive, volcanic, and fos-
siliferous. Many of them are of enormous dimensions, varying
from three feet to several yards in diameter.

In some cases, such a boulder deposit consists of blocks that
have been severed and torn from the rock that lies imme-
diately beneath them. In such circumstances, the boulders ate
of the colour and lithological character of the underlying strata,

THE POPULAR EDUCATOR.

red in a district of red sandstone, grey in one of shales, black
fa one of coal, sad white in one of chalk. Boulders of this
description are easily accounted for. But all over Russia,
Fotand, Germany, Holland, England, Ireland, Canada, and
North America, broad plains and the sides of mountain* have
boulders strewed over them, for which there is no parent
reek within scores snd eren hundreds of miles.

Boulders and stony fragments of this description abound in
England. They sre frequently met with, in fields, half buried
in fiie soil, snd are often turned up by excavations in road-
^Utig and railway cutting. Whenever you see a boulder, it
suggests to you two questions : first, where has it come from ?
and secondly, what brought it to the place it now occupies?
Geologists have examined these two questions with much
attention and skill, but they could find no satisfactory answers,
before they adopted the hypothesis of the transporting power
of drifting icebergs and packed ice.

To interest you in the solution of these two questions, it is
necessary to mention some of the most remarkable facts con-
nected with this boulder deposit, or, as it has been celled, the
NosTHSJur Dsnrr.

1. There can be no doubt that all the boulders hare come
from the north ; for their course, both in Europe and America,
is found to be either due north and south, or varying a few
• to north-west and soulh-enst. The immense plains of
i and Poland are covered with thousands of blocks of

^, I, all of which agree in raineralogical character with the

mountains of Lapland snd Finland. In Denmark, Holstein,

now 100 feet above the level of the sea, in the Gulf of
Bothnia. On the summit of this ridge lie scattered numerous
large boulders of gneiss, in size from nine to sixteen feet in
diameter. The sand on which the boulders rest is full of shells
which now inhabit the Baltic sea. Hence, the boulders were
brought thither after the Baltic was formed, and were trans-

. ported across the waters of that sea.

J In Scotland, the Grampian Hills are from 3,000 to 4,000 feet
hkh. To the south of these mountains lies the deep snd wide
valley of Strathmorc. To the south of Strathmore are the
Sidlsw Hills, composed of sandstone snd shales. On the flanks
of these hills, at an elevation of 1 ,500 feet above the sea, are found
large blocks of mica schist, some of them three, some of them
fifteen feet, in diameter. Blocks of precisely the same charac-
ter are strewed in the intervening valley of Strathmore, all of
which have come from the Grampians, fifteen miles from the
Sidlaws. To the South of the Sidlaws are the Pentland Hills,
about 1,100 feet above the sea. On one side of these hills
there is a huge block of mica schist, from eight to ten tons in
weight, which must have come from the Grampians fifty miles
off, and which must have been borne over the Sidlaws about
thirty miles distant.

3. The fragments which form these boulders have been
removed to an immense distance from their parent rocks, or
what geologists call rocks in situ. In the southern parts of
Russia and Germany many of these boulders sre found at the
distance of 800 miles, and some even 1,000 miles, from the
nearest rocks from which they could have been dislodged.

Fig. 95. — Boulders scattered over a Plain.

and Pomeranis, the sandy flats have, scattered over their whole
extent, fragments of syenite, gneiss, and trap, exactly of the
same description ss the rocks of Sweden and Norway.

Boulders, containing specimens of almost all known rocks,
have been transported to the eastern counties of England. In
Cambridgeshire, Huntingdonshire, Bedfordshire, Herts, Mid-
dlesex, Essex, Suffolk and Norfolk have been found fragments
from Silurian rocks, carboniferous series, lias, oolite, chalk,
trap, granite, and other crystalline rocks. Some of these boul-
ders could have come only from Norway and Sweden, for Sir
Chablss Lyell traced them from those two countries to
Denmark across the Elbe, through Westphalia, to the borders
of Holland. "We need not," he says, *' be surprised to find
them reappear on our eastern coast, between the Tweed and
the Thames, — regions not half so remote from Norway as are
many Russian erratics from the source whence they came."

On the western coast, and in the midland counties of Eng-
land, similsr facts sre met with. On the coasts, in the plains,
and on the sides of the hills, of Lancashire and Cheshire, and
through Shropshire, Staffordshire, and Worcestershire, im-
mense deposits of pebbles and a vast number of boulders are
found scattered, which must have been transported thither
from Cumberland and Dumfriesshire in Scotland.

2. Boulders have been transported across seas and lakes and
plains, and over the ridges of high hills and mountains. Near
uptals, in Sweden, there is a ridge of sand and gravel that is

Boulders from Scandinavia are found on the declivities of the
Alps. Instances of similar extent of transportation abound
among the boulders scattered over the northern districts of
the United States of America.

4. The most remarkable and the most puzzling circumstance
in this formation* is the fact, that some of these boulders have
evidently been transported from a lower to a higher level.
Near Kirby Lonsdale, there are many large blocks of
grauwacke scattered over the mountain limestone at an eleva-
tion of from 50 to 100 feet above the parent rock, and even
almost to the top of the Fell, 500 feet above their original posi-
tion. In that district there is another case in which boulders
have been transported from the Yale of Eden, where the parent
rock is 500 feet above the sea, to and over the pass of Stain*
moor, at the height of 1,400 feet, so that these boulders lie now
900 feet above the level of the rock in situ. Similar facts are
found on Ben Erin on the western side of Glen Boy, on
Arthur's Seat near Edinburgh, in the Isle of Man, and in North
America.

One of the most singular facts connected with the elevated
position of boulders occurs in North Wales. As the traveller
journeys westward on the Holyhead Road, he comes to Llyn
Ogwen, and on his left rises a precipitous mountain called
Moel Tryfaen, which attains the height of 1,392 feet above the
level of the sea. On the summit of this rock sre found chalk
flints associated with boulders of various kinds. There if

LESSONS IN GEOLOGY.

iff

good reason to believe that the chalk flints were transported
from Ireland, and therefore from a considerably lower level.
Facts of this description form one class of the difficulties which
press upon the theory of icebergs as the agents of transporta-
tion ; for no floating ice could possibly transport boulders from
a lower to a higher level. Mr. Darwin ascribes these results
to the joint action of floating icebergs and of packed coast ice.
He shows that on Moel Tryfaen the well-rounded pebbles of
chalk flints and other boulders were, in all probability, trans-
ported by coast ice, though it is at the same time evident, from
the extraordinary manner in which the laminae of the slate
rocks have there* been shattered, that icebergs have also been
driven against them when under water ; so that both actions
seem to have concurred in that neighbourhood.

You have now been informed of the remarkable positions of
distance and elevation in which boulders are discovered. Our
next business is to try to answer the question,— how they
same there? The most skilful geologists found it almost impos-
sible to account for the position of boulders, before they adopted
the glacial, or rather the iceberg theory, called also the glacio-
aqueous.

At first all inquirers were misled by the assumption that
the boulders had been transported and deposited by the deluge
of Noah, on which account they gave to this formation the
name of Diluvium. Others, and some of them very distin-
guished geologists, like Mr. Hopkins of Cambridge, ascribed
their removal to a series of diluvial waves that swept over the
land.

Though the iceberg theory has its difficulties, and does not
fully meet all the phenomena of the case, yet it seems to come

denly. This is proved from the general absence of organic
remains in the clays and sands, which are found to cover the
formation of the drift boulders, and from the complete preser-
vation of the flesh and the hair of the elephants which were
discovered in the frosen mud of Siberia.

4. This great and sudden reduotion of the temperature
would fill the glens of the Polar mountains with immense

? glaciers, which, as explained in our last lesson, would stretch
ar into the waters of the Northern Sea. Even at the present
day, many of the glaciers that descend the ravines of Spistber-
gen project several hundred feet from the coast into the sea.
Indeed, at this epoch, called the glacial period, it is probable
that northern mountains of comparatively moderate height
would have their valleys filled with glaciers, and that vast
sheets of ice would stretch eastward, and westward, and south-
ward, as far as the phenomena of boulders have been observed*

5. In other circumstances the icebergs detached from these
glaciers that protruded into the Polar seas, would take up and
convey to a distance huge masses of rock, which water alone,
however impetuous, could never have moved, and would
transport them hundreds of miles without wearing off the angu-
larity oftheir edges.

6. As the lower surface of the icebergs would either be
abraded by the action of the sea, or melted by the increased
temperature in the south, the masses of days, sands, gravels,
and boulders, which they had brought down as glaciers, or
imbedded as coast-ice, would drop down and >e scattered at
random over the bottom of the sea,

7. The bottom of this sea might be extensive plains, or high
ridges of hills. When you consider that seven parte out of

Fig. 96.— Packing of the Sea in Polar Regions,

nearest to the vera causa, or the real agency that produced the
result.

1. It is certain that all the boulders come from the north.
All the rocks, of which boulders are specimens, are in situ
towards the north. All the shells which are frequently found
in the clays associated with the boulders indicate a northern
climate. There seems also an intimate connexion between a
very cold or extreme northern climate, and the various geolo-
gical appearances which have been called glacial.

2. In the neighbourhood of the Baltic, the course of the
erratic blocks, and the grooving and the smoothing of rocks,
have been traced from the level of the sea shore to elevations
of above 3,000 feet. Nothing of this kind has been found
either on the shores or on the sides of the rocks above the
Mediterranean, nor in the equatorial parts of Asia, Africa, and
America,

3. It can be proved that at an earlier age in the history of
our globe, at the close of the tertiary period, the northern
hemisphere was considerably colder than it is at present,, and

. that this diminution y\ the temperature took place very end-

eight of a high iceberg are under water, it is obvious that such
a deep body of ice, in moving southward, would strike against
the crests or the flanks of these submarine ridges, andihere de-
posit its clays and boulders. These submarine hills became, at
another geological period, elevated, by volcanic actirn, to an
elevation much higher than the sea, and bearing on their
ridges or sides the boulders that had been imbedded in their
surface of clay or sand.

8. The application of the iceberg theory to the elucidation of
boulder phenomena is in full harmony with all that science
has taught us about glaciers. What we know of terminal
moraines corresponds with the accumulations of clay and gravel
which are called the Drift, and which are found associated
with the blocks or boulders. It also accounts for the smooth-
ing and grooving of rocks, for the parallelisms in the markings
or striae on the surface of rocks, and for the high and precipi-
tous ledges on which the boulders have been lodged.

Boulder phenomena, however, present three difficulties
which the iceberg hypothesis does not seem to obviate. .First,
boulders are frequently found water-worn and rounded M,¥*e

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paru caT the sea bvt^x, a-d depoezt ia dava a&d Uocks; b«t
tbe snaalSer ai.4 l^l^r ieel-^ss, laden wii fiaer grtTel a^i
asaaHer bcmli^Tf, v-old pan ot-t to a sieh

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lerel, it as sot §w»**d ^:at tl-js tai«* ;lai- =£ttoaUt,~!k:; c<

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r? >t

sWsaM ^ <h« dkVt^ and m'tArsu pe*ytt
< JLTJJiS^ btoefca th—<iiyat

jeeted oat of it, w-.ali
the anderlajixig r xi*.

Ita«»fcrer , t) aV.'^aW*

a? ^»«« *^f

J -F.-rwr i
h£u.«^r * fc it m .

i.ngc u w ei *' . zj kec-m

h-isv , Ltantrt. Jy u^natr
hara^>s7. 2. at r*^W

& <sr**r war's sj^"

i"*xsnx at -. st ,*sT_t- sma's ea>
Frsaac. =* ai ■Mqr
^irirr a * . a? aak cm

**cidnt «r . v; jnie aar'j sc^
Hwrir «e\art
Ui^r j*e' . U t

I2^«^ir *':-:* fcr uh

Xj^vrcr .*", i> Msut awe ear's acef

Ix^crtr. ai £ca/«nr

Jxrwr. i> nwr

Ufiw. S> i
3i:->er ^st\a?'

Xeri:«r. t? «5orrr«
X>7ur «\ la any* at
Xtfwir ;iea. ^ a* law/
X. jlijcer. ft* wfkst
XI. r. a» i*/
l k zrixta<r. t.« en.-«je
i*arl;r ft.- ijvtti
l x a«r .«; . lo •£> «2hns!
Terra* t:re. *j jy.-ime
l\r»aaJ«r, :c jwr m aidr
r ;wr i«e> % &> J*\- avwh ia
riaiaire.tojwy

HESBONS IN FRENCH.

Prendre garde, to take care, heed
Prendre win, to take oar$
Presorire, to prescribe
Fresser, to urge
Fresser (se), to hasten
Pr Isomer, to presume
Frier, to desire
Promettre, to promise
Proposer, to propose
Proposer (se), to intend
Protester, to protest
Vnnis, to punish
Rebate? (as), to be weary
Beeomnuuider, to recommend
Refuser, to refuse
Regretter, to regret
Bcjottir (se), to rejoice
Remereler, to thank
Repentir (§e), to repent

H vsut mieux hasarder de sower
an coupable que de condamner un
innocent. Voltaire.

Le monde se twite <fe /afer des
henreux. Massillow.

Reprendre, to censure
Rlprimander, to reprimand
Reprocher (m), to reproach one's
Rlsoudre, to resolve [set/ •

Ressouvenir (se), to remember
Rire, to laugh
Rougir, to blush
Soandalieer (se) t to take offence
Seoir (unlp.), to become, suit
Soramcr, to summon
Soupoonner, to stuped
Souvenir (se), to remember
Safflr»(unip ), to suffice
Sugge'rer, to suggest
Supplier, to beseech
Tenter, to attempt
Trembler, to tremble
Vanter (se), to boast

It is better to run the risk of
sparing a guilty person, thanto con-
demn an mnoctnt one.

The world boasts that U can render
men happy.

(4.) The participle past, haying avoir for an auxiliary,
agrees with its direct regimen, when that regimen precedes the
participle : —

La lettre que toos avez ecrite.

Pedro, qn'as tu fait de no* mon-
tures ?— Seigneur, j« let mi attachces
a la grille. Lb Sage.

Lea meiUeores harangues sont
celles que le coour a dicte'es.

Mabmontel.

Jelcssi cherche's dans ton* lea
coins, et je ne Its ai paa t routes.

•" — .. DE QENL18.

lhe letter which you ham written.

Pedro, what hast thou done with
our horses t My lord, I have fast-
ened them to the grate.

The best addresses are those whkh
the heart has dictated. i

1 hace sought them in every corner,
but have not found them.

(5.) But, if the direct regimen is placed after the participle,
this participle remains invariable :— •

} 133.— Rulb.

(1.) Two or more verbs may govern the same object, pro
videa they require the same regimen 2—

Nona aimons, nooa tnstruisons, I We love, we instruct, and we
etnom louonsnosenjants. \ praise our children.

This sentence is correct, because aimer, instruire, and loner,
being active verbs, govern one) and the same case, the direct
regimen.

(2.) But when the verbs require different regimens, they
cannot govern one and the same noun ; and therefore another
form must be given to the sentence. We could not say in
French, — Un grande nombre de vaisseaux entrent et sortent de
ce port tout lea mois, — A great number 0/ vessels enter and go out
of this port every month, because the verb entrer reaches its regi-
men by means of theprenosition dans, and sortier by means of
the preposition de. We should say :— •

Un grand nombre de vaisseaax I A large number of vessels enter
entrent dans ce port et en sortent this port and leave it every month.
tons lea mois. |

See i 02, (1.) (2.), also note, and § HO.

} 134.— The Participle Past.

(1.) We have seen [§ 66, (3.)] that the participle past, not
accompanied by an auxiliary, assumes the gender and number
of the noun which it qualifies : —

Ties iahnkies soordes et cachets I Quid and concealed enmity is
sont plus a ersindre que lea balnea I more to be feared than open and de»
ouvertes et declarccs. NoeX. ] dared hatred.

(2.) The participle past accompanied by the auxiliary itre,
agrees in gender and number with the subject of the verb,
whether the subject be placed before or after it. [See 6
136, (!.}]

Le fer est emoussi ; lea buchers
scat eteints. Voltaire.

La vertu obscure est souvent
meprisee. Massillow.

Lea Greca itsdent persuades, que
I'lme eat immortelle.

BabtbIlemy.

Quant A rit l'urne oil etaient
renftrmees lea cendrea d'Hippias, U
versa on torrent de larmes.

FtaeLON.

The sword is blunted', the pUes
are extinguished.
Humble virtue is often despised.

The Greeks were persuaded, that
the soul is immortal.

lVhcn he perceived the urn in
which were enclosed Vie ashes of
Uippias, he shed a torrent of tears.

(3.) The participle pasl, having avoir as its auxiliary, never
agrees with the nominative : —

You laught Put down thntshe
laughed.

My friends; hate spoken; their
hearts are mtsved.
My comim have read\

Voua riex? Ecrivez qu'elle a ri.

Racine.
Ilea amis ontparU; lenraocaura
oatattendris. Voltaire.
Mm oovswtf ont Us.

Bsschebblle.

«Tai recu votre lettre,

C'eat la verite* elle-mOme qui lui
a didf oes belles paroles.

Bossvet.

Lea dieux ont attache presque
autant de malheurs a la liber t6,
qua la servitude.

MOKTESQUIEU.

I have received your letter.
It is truth itsepwhtohmtaUte*
to,him those fine words. f

The gods have attached almas t of
many misfortunes to tiberty, of *>
servitude.

CORRESPONDENCE.

[We insert the following remarks " On Bathing when heated,*
because we think them well worthy the attention of those of our
readers who are fond of this exercise. Of course, we do not com-
mit ourselves entirely to the accuracy of every point, because we
have not had sufficient personal experience ; but we coa aider that
there is much truth in what our correspondent says.]

ON BATHING WHEN HEATED.

Sir,— At the end of the article on Physical Education which has
reference to bathing in your No. for August 27th, you place certain
rulea to be attended to by the bather before going into the water.
I am well aware that it has been long a popular aa well as profes*
aional axiom that sudden vicissitudes of temperature are dangesous,
that a previous hot state of body augments the hurtful effecta of cold
however applied ; but the proposition thus broadly stated is not
universally true. The inhabitants of Russia are in the habit, while
reekiog from vapour hatha, of immediately rolling in the snow, or
plunging into cold water without suffering from the change. Cap-
tain Scoresby, while in the Arctic Regions, often passed from his
room where the temperature was from 56" to 60° to the mast head,
where it was only 10°, without receiving any injury or inconve-
nience ; and other instances may be brought forward. Thus it is
plain that the proposition which assigns danger to extreme vicissi-
tudes of temperature requires some limitation ; the effect of a sud-
den descent from one point to another in the scale of temperature,
varies according to the state of the body at the time. Man, to-
gether with the warm-blooded animals, you are aware, by the faculty
of evolving heat, maintain the same degree of inward temperature
under very different degrees of outward temperature. Now if tbis
power of evolving heat be entire, active and persistent, no peril
need attend even violent alterations of external temperature.
Unusual heat of the body at the time when the cold is applied, so
far from implying danger, is really the condition of safety, provided
that heat is steady and permanent ; but if a peraon be exhausted
and weakened bv exercise, rapidly parting with his heat, if he
remains at rest after and during the application of cold, then it is
highly perilous, and likely to produce mischief. Thus cold is
dangerous not when the body is hot, but when the body is cooling
after having been heated. Thus those whose business it is to
advise, may caution the public against the common mistake which
has had its origin in the unqualified credit given to the maxim,
that sudden vicissitudes of external temperature and exposure to
cold while the body is hot are dangerous, whereas they are only
dangerous under certain circumstances. Thus wet feet or a wet
skin need cause no apprehension, so that active exercise is con-
tinued ; but when that exercise enda, then it ia that a change of
clothea and a further avoidance of the application of cold ia impor-
tant. You may aafely tell the bather, that after walking on a hot
day to the rivei'a side, he had better not wait to cool himself a little
before he plunges into the stream. The point to be remembered
is that the heat which is pretern&turally accumulated bv exercise is
held with little tenacity, is dissipated by profuse perspiration, and
is speedily lost when to this perspiration is added a state of rest

THB POPULAR EDUCATOR.

•Her fatigue, and it ii then that cold U mott apt to be prejudicial |
We hate an easy criterion as to the propriety of cold bathing, ii |
the feelings of the person afterwards, — if the bath is followed by
a glow of warmth, &c, it will do good, but if the bather feels cold and j
chilly, fee., it should be discontinued as being useless snd haaardous
In the former case cold bathing becomes a tonic, stimulating and i
iaTigoyating both to mind and body. The time for bathing requires
to be modified according to the health of the bather; if the powerr
are too languid to admit of the necessary reaction, much benefit ia
derived from mid-day bathing.

Apologising for thus writing,— but the interest which I take in
your taluable paper, and also on the subject of bathing, which
I consider a necessary of life, will I trust be a sufficient excuse—
I am, fcc., MiDicus.

ANSWERS TO CORRESPONDENTS.

K, PlVBTAO: oi Is pronounced nearly like ths English letter iiajlne,
though a little broader, like the Enf lish word 0$ e. Ii Is a compound of the
booms a* and ee blended together. a» is pronounced like ths English a in
taster, « like the letter i in wine, < like og in soy. vt like erf in seise, and
w» nearly like ths word you, but with more stress upon ths #c sound.
There Is a French expression, U y ovoti, (Or there was.

♦iXot: Tour plan of study is excellent, and appears from your letter
to answer well. Thanks for ths hint you throw out. It shall not be lost
sight of.

James Boincsox (Burnopfleld): We bars alreadr stated, in answer to
ether correspondents, that the capital Greek upsilon, though like ths English
T in /em, has no resemblance to it in sound. In writing Greek, it is only
necessary to imitate the printed characters as nearly as possible, giving
them a slope for the sake of convenience.

MareVn*; The Greek upsilon, when a capital letter, takes pretty
nearly the /cms, but not the pronunciation, of the English T. * has the
1 whether with a straight or a ourly tail.

Blanbus: sVtvx" msans good fortune, prosperity i and ought to havs
been given In the vocabulary. iXewf is a misprint for Use/ We are
obliged to discontinue the atymological vocabularies for want of room. Any
food Greek lexicon will supply nearly the sams information.

A Cbipplb will find the pronunciation of the German word sxaa, and the
ethers he mentions, fully explained in the interlinear pronunciation of the
lesson and the preceding directions, lie has only to notice ths figure placed
ever ths a. and look in ths directions to see what sound it Indicates. He
will also find it stated that an apostrophe after a vowel has the effect of
lengthening it. The accent at the eud of a syllable merely denotes that ths
stress is to bs laid upon that syllable.

A Powsa-LooM Wbaveb's parcel Is forwarded to ths Royal Society.—
A QovsaNSSit (Camden-town): The P. E. i» published hi New York.— W.
Liwis (Manchester): Chemistry in fnll vigour in vol. lv.— Musio is post-
poned for the present.— T. H . (Cork) : The best way to learn to express your
ideas is to join a Debating 8oeiet>.— Fabbb Liqmaxius (Turriff) : Mr. Cas-
sell's Classic*! Library, together with Dr. Beard's Latin Dictionary, will con-
tain the books beet adapted fur making progress in the Latin tongue.— 80c 1 us :
In learning Bookkeeping there is no need to go to the expense of separate
books ; separate portions of one book may be carefully and neatly adapted to
the purpose, by the student himself.— J. 8. Chapman (Manchester): The
Lessons in Latin in the P. E. are the best ws know.— J. T. Booms (Green-
wich) is wrong as to the pact of the letters inserted In tfke P. E., but right
as to the iMPaassiON ; a change will be made for the better.— A Waavsa
(Clackmannan) : Ones in the plural form, referring to a plural noun in a pre-
ceding sentence, is an adjective pronoun ; see p. 811, vol. 111. P. E.— Opticus
(London): Ths subject of Optics is announced for next volume.

Mas. Slipslop (Perthshire) must put on her spectacles, and shs will then
find Nahob in a line with Abba 11 am, p. 3, vol. 1. P. E., Genesis xi. 86. It
is not a mistake with Luke, for Moses has been misrepresented ; see the
ficptuagint.— 8. J. B. (London): All right; tho maps will be continued.—
J. E. D. (Edinburgh)-: It will be done.— W. Robists: Ths memory is
luiproved by exercising It. 8ay Chobham like Chatham, not like Kobham.—
Mask Mathstbs (Farn worth) and Q. E. D. : 8ee vol. ii. P. E„ p. 315,
sol. 8. line 34, for the Classical Subjects; the rest are never announced, the
student being required to prepare hiintelf to answer any questions that may
be proposed on the other subjets; see page 137, vol. if. P. E.— T. Jsnkins
(Cardiff; : Bee Literary Notice*.— Hookxekpino Student will have his dif-
ficulties solved in ths course of the lessons.— Gioaos thb Younger
(Pimlieo): Buy the large edition of Webster.— A. Z. 1 Foyer de dtsordres,
means a focus or centre of disorders.— A. 8corr (Liverpool): Thanks for
his note on the comet.

Caaaica (Ayr): Ws cannot tell ourselves.— W. Hymess (Barnard
Castle): The Boy'* Own Book, Tetg. London.— B. V. Gibson (Glasgow) :
If going into tbe water doe* you harm, the best precaution is to give it up. —
W. F. Stone hence (Whitehaven) should get the *' Annales de Chimin."—
ABMAOHANtJs: Very well; go on and prosper.— 8. T. M. (Brighton):
Frenth.— D. T. L. (Carmarthen) : You are right.

e (Belherbet) : 1. Ws think not. 8. We can't tell. 3. Yes. 4. Bead |
Saxonlg written books, such at *' Gulliver's Travels," " Pilgrim's Progress,*'
and BowUnd Hill's •• Village Dialogues."— Anulais (Preston): Yes.—
Heaoband (Darlington): English,— c^Xot (London): Write to Henry
Moore, Esq., Secretary of tbs Uuive-sity ol Loudon.— Eoolibb Fbancais:
tee our Literary Notices.— J. Woe ley (Beading) recommends to French
students the French New Testament, published by the Bible 8ocieur at «d n
ia roaa gilt, good type ; and a French Weekly Newspaper, called Chronique
4* Jsrssw, published at lgd. The Key to the French Lessons is publisned
sjf«ra**ly j see oar Literary Notices*— T. C. (Barking) : Yoar suggestions

are good.— Viouno (Bridport): Received, and andcr consideration.— J.
Co ebt (Woodford) : Yes, if in good condition, by paying ths difference*

A Pupil Teaouee's lines are very good, and do credit to his head aai
heart; but we cannot insert them in the P. E.— E. J. (Shelton) and A
Dboohboa Bubscbibbb will, by writing to Mr. Dunn, 8ecretaty of the
Training-School of the British and Foreign School Society, at Borough-
road, London, obtain at once all the information he requires.— H. Donkley
(Plumstead): The Lisard Point, Cornwall, is the «*•#< southerly point ol
England.— Z eta : Yes ; r is not pronounced at tbe eud of French, except
under certain conditions ; see the lessons again. Bills of Exchange will be
more fully explained.— W. J. : See Lessons in Geography, pp. SO, 61, 144,
and 168, vol. iii.— E. H. Cooke (Kidderminster) : Under consideration.—
T. G. B. (Uehester) : We fear that we cannot advise him; he should write
to ths Secretary of the Apothecaries' Company for Information.— A. M.
Gabonee (Peasenhall): The French Lee «oui, reprinted from the P. E„
parts I. and II., will completely answer your purpose.— Thomas Choi*
(Hart land): We fear that his suggestion, though good, is not practicable.—
Charles w. 'Islington): Bead the paper* on the University of London ia
vol. iii.— Puiloantb (Bowling): If hs has a special call, let him go on j tf
not, we would advise him to pause.

8bvebal who wisii to BE Aetists: Ws are desirous '* supply the
wants of all our subscribers ; but they will see from our advertissifceats ana
notices that their wishes cannot consistently with these be immediately
gratified ; the subject, however, will not be overlooked.

An Obphan (London) : Apply to the London Orphan Asylum, Clapton.-*
B. J. L. (Littlsport) should take C. W. 11. 's advice, and write to ths 8eere-
Ury of the Committee of the Council on Education. Downlng-street, London!—
YoEKSHiBE Plough Boy can get No. 43, which is ths one omitted, to buy la
8heme!d{ but he should return his copy of Part X. to the bookseller who
supplied him with it as incomplete, and gst a complete one instead of it.—
N. B. (Port sear. Not directly, but by the introduction of two or three
Lemmas.— Weitibo Clebk (Tralee) : Under consldsreUoo.— R. B. N. Boss

(Camberwell) : Bight ; yes.— Philo : Many thanks ; you axe perfectly right
in everything; the mistakes have arisen from careless printing 1 lor
instance, ths multiplier 188 should be 1*6, and th» multiplier 198 should be

86 ; try these numbers, and you will dnd that u.« answers correspond.— AH
Undbbqbaduatb op thb uniybbsity op London : Ttunks for his note.—
C. C. (Halifax): D'AubuUson, Traits Ilydraulique, 9s.— A HatcaLAXEB
(Manchester): Nicholson's work.*: Principles of Architecture; Archi-
tectural Dictionary; Student's lattmctor in tho Five Orders; Practical
Builder, &*.

Vita l'Italia : Hutton's Coarse of Mathematics improved by Dalies. or
Christie's Course for the Cadets at Woolwich.— W. A. (ftheiifsaaj ssmaM
study Writing, Arithmetic, snd Bookkeeping, in order to at hlmsslf far ft
clerkship.— A Subsgeibbb ( Bradford) and his friends had bolter not meet
00 Sunday morning lor ths studies they propose ; any other morning will sh>
better. God and his word, religion and a future state, are surely vroBTH am
day's consideration out of the seven.— A La bod ebb in tub ViHaTABfj
should not trouble himself with what might have happened had not things,
been as they are. 81n has come into the world, and God has appointed aa
easy way of escape from It; this is enough. Greek and Latin may 1 " ~
each other, but study*Latin first.— E. Blubto* (Stourbridge): W0 I
that we cannot give the required information.

LITERARY NOTICES.

FRENCH.

Now ready, price 4s. in stiff Wrapper, or as. strongly bow
ths First Part complete, consisting of ths French and English, of Cassell*S

Fbsnch Diction aet: the entire work will be completed in ____. ___
Threepenny Numbers, and will form one handsome Volume of eight hundred
and thirty-two pages. Pries 8s. 6d. bound in cloth, or the Two Divisions
may be had separate.

A Complete Manual op thb Fbbnoh Lanouaob, by Fislkssm De
Loime, just published, price 8s. neatly bound. This forms one e4 the
most simple, practical, and complete Guldeo to a thorough knowledge of the
French Language which has hitherto been published. Tho plan upon which
it is conducted is admiralty calculated to accomplish r

In the first place, the Grammatical Principles of the I^auroage areeleeriy
laid down, and, secondly, these Principles are copiously illustrated by suitable
Eaercises of English to be turned into French.

Cassell's Lessons in Fbbnoh, in a neat volume, price 9s. in stiff covers,
pr 2s. €d. neatly bound in cloth.

A Key to Cassell's Lessons inFbxnch, containing TroeMOtons of all
the Exercises, with numerous reterences to the GrammaUcai Judos, price
Is. paper covers, or Is. 6d. cloth.

GERMAN.

Cassell's Gbbman Diotiobabt is now Issuing In Numbers, at Id. eaefet
Monthly Parte, la, each.

Cassell's Lesson* in Gbbman, pries 9s. in stiff covers, or Is. 6d
cloth.

LATIN.
Cassell's Lessons in Latin, price is. in stiff covers, or 8s. Id. cloth,
Cassbll's Key to thb Latin Exbboiebs, now ready, price Is.
GREEK.

The Third Volume of Cassbll s Classical Libbaby will contain tad 1
acts of tbe AposUes in the original Greek, according to the teat or Augustus
Hahn; with grammatical, historical, and expository Notee; followed by a
Lexicon, explaining the meaning of every word— the whole carefully
revised and corrected. This work is well adapted for the use of 8 she sis,
Colleges, and Theological Seminaries, and will supply our Greek
with excellent Bsaternds for practise ia translation.

LESSONS IN GEOLOGY.

LESSONS IN GEOLOGY.— No. XLIII.
BtThos. W. Jbnxyn, D.D., F.R.G.S., F.G.S., &c.

CHAPTER IV.

ON THE INFLUENCE OF ORGANIC AGENTS UPON THE
EARTH'S CRUST.

SECTION I.

ON BOTANIC AGENTS.

In the course of our lessons, the first three chapters have taught
you the operations of fire, of water, and of the atmosphere, upon
the earth's crust. This fourth chapter, which is also the last, is
intended to illustrate the effects of vitality, in the forms of vege-
tation and animal life, in the changes which have been produced
on the surface of the earth.

The business of this lesson is with the agency of plsnts, and
with the effects which their growth and decay produce on the
earth's cruet. In this inquiry, we are not to limit our observa-
tion to the surface of the dry land, but to extend our survey to the

your attention. Ask yourself, what comes, then, of all the vege-
table masses, and of all the animal matter, that rot in forests
and woodlands, every year, over the extent of the globe ? The
answer of science is, that a portion of this vegetable and animal
mass is volatilized into the air, and that the rest is carried away by
running water, in which it either sinks into the earth, or flows
towards the sea. By this process, the same ingredients enter
again and again into the composition of a variety and a succes-
sion of organic beings in vegetable and animal life.

It is well known that thousands of carcasses of terrestrial
animals, and immense forests of drift timber, are every cen-
tury floated into the sea, where both are imbedded in subaqueous
deposits. Nevertheless, the vegetable mould on the earth's sur-
face is kept in equilibrium. The principal elements tha
ohemists have found in plants are the three gases, hydrogen, car-
bon, and oxygen. Vegetables and animals derive them from
water and from the atmosphere. But whence do water and
the atmosphere derive them, in order to supply plants with them ?
They derive them from the putrefaction of vegetable substances
and animal matter, from the decay of rocks as the result ef
weathering and abrasion, and also from the agency of mineral

J'io. 97. — Ideal L.i):t!ccopc of the Earth at the Tcriod of the Coil Formation.

larger portions of the globe which are under water, and which
are extensively covered by aquatic plants.

T. PLANTS AND TRBB8.

The quantity of plants, shrubs, bushes, and timber that grows
on most lands, and especially in tropical forests, in the course of
one century, must be enormous. Were these masses of vegeta-
tion deposited in a sea, they would pile up into a hill of consider-
able aise ; but though timber grows and decays for thousands of
Tears, yet no such wood mountains are found to pile on the sites of
forests, even within the tropics. It might have been expected
that the masses of solid matter which are every day derived from
the decay of terrestrial plants and animals would contribute to
augment the amount of soil on the earth's surface. It must,
therefore, awaken your surprise, when you learn that the vege-
table moujd which clothes the globe does not grow in thickness,

Thk statement ought to awaken not only your surprise, but

TOL.l£

springs, which bring constant supplies from the interior of the
earth.

In our chapter on Aqueous Agency, we considered the tendency
of running water to scoop out gullies in the soil, and to carry the
detritus towards the sea. This operation of streams and rivulets
is counteracted by the power of vegetation. Vegetation counter-
acts the operations of running water in two ways. 1. It is in
some degree antagonistic to the transporting power of rivers, and
may be considered as reconstructive. The agency of vegetable
life, by absorbing various gases from the atmosphere, causes a
large mass of solid matter to accumulate on the surface of the
land. Such a mass must, alone, constitute a great counterpoise
to all the earthy detritus transported by the aqueous agents of
decay. 2. The influence of vegetation is conservative, and tend-
ing to retard the waste of land. You constantly witness in a
field, where a rivulet flows from a well, that the green sward
through which the water runs prevents the soil fiom being

L*. L.T

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tt4*t 2A««t w*r% aaraai^ ^id cr inu :: ± c s«*. * • :ia:\.CA*:. " m

LESSONS IN GEOLOGY.

These immense fields of marine plants must, like land vegeta-
tion, suffer decay — and their decayed remains, as they subside and
sink to the sea bottom, must, in the course of centuries, produce
considerable beds of vegetable matter. In Holland, a submarine
peat was dug up that was formed by the decay of sea- weeds.

You have now been introduced to the agenoy which vegetation
exerts in the formation and in the conservation of the soil that
forms the green surface of the 'earth. The principles and the facts
which have been thus briefly intimated, you must now apply not
only to the superficial covering of the globe, but also to the struc-
ture of the crust of the earth, as formed at different geological
periods. As you walk or ride over plains or mountains, an
entire vegetable world may be lying in ruins under your feet.

Geology has demonstrated that, at different periods or epochs in
our world's history, vegetation has played a distinguished part,
both in rank, luxuriance, and in extensive distribution. Differ-
ent geologists have their respective systems for dividing the epochs
of ancient vegetation. M. Adolphb Brongniart divides them
into four. The first begins with the earliest traces of vegetable
life, and terminates with the coal formation. The second con-
eludes with the •triasaic The third comprises the oolite and
ohalk. The fourth ends with the tertiary period. Count Stern -

present themselves as arborescent plants with branched trunks,
sixty or seventy feet high. The third kind of vegetation is that of
horse-tails, or the Equisetaoee, distinguished in the engraving by
having jointed and furrowed trunks and branches. With us, the
largest plants of this kind attain but a very few feet in height, but
in the coal measures they are found with arborescent or tree-like
trunks, ten feet high and five or six inches in diameter. These
three families of plants form about three-fourths of the vegetal
tion of the coal period. The remainder consists of cone-bearing
trees, and of vast quantities of a kind, apparently, like the cactus.
Of the entire number of species discovered in the carboniferous
rocks, two- thirds belong to a vegetation like the Fern.

In these coal forests, there were no plants bearing flowers, no
trees bearing fleshy, juicy fruits, no kind of grass, and no birds*
It used to be thought that it was a forest without a single living;
thing to move in it ; but lately the skeleton of a reptile has bees
discovered in rooks much older than the coal series.

One remarkable characteristic of the vegetation of the coal
period is the uniformity or monotony of its plants. In our age)
we find that different countries, in different climates, produest
different plants; but, in the carboniferous era, the same plants grew
in Germany, Belgium, France, England, North America, and

^ --r ?****»■

Fig. 98.— Ideal landscape qfth$ Tsrtiary Period.

BKRO, by uniting the second and third of there epochs, reducc3
tkft periods of ancient vegetation to thru*. His divisions are —
1. the vegetation of islands ; 2. that of sea coasts; and 3. that of
continents.

The earliest vegetation of the globe, and that which terminated
in the carboniferous period, was simple but very magnificent. An
ideal landscape of the earth during the carboniferous age is repre-
sented in fig. 97. Look at the forest represented in this
engraving. The plants and trees are different from all
vegetable products that you now see. There is nothing hke
it* m the temperate sones, nor within the tropics. The
Vegetation consists of ferns — but ferns not herbaceous as
m our odld climate, but ferns which grow in the form of
trees of considerable height, with palm-like, unbranched
trunks. The next kind of vegetation is that. of club mosses, or
the Lycopodiacero. With us, these club mosses are dwarf plants,
small in sise and few in number, but in the coal formations they

Australia. This fact promts a umaikablo uniformity of climat
at that period. Whtn Noith America was discovered, there were
found in it only two wild plants that agreed with the vegetation
of Europe. But of 53 kinds of plants found in the North Ame-
rican coal beds, 35 are common in the European coal fields.

However luxuriant this vegetation of the carboniferous era was,
all the species of its plants, and almost all their genera, passed
away before the second period of vegetation set in. A few ferns
entered into the second era, but all the palms and calamites dis-
appeared. The first flora, therefore, which was universally drf-
fused over all the dry land of the ancient globe, was especially
distinguished from the second, which is regarded as the flora of
the triassio, the oolite, and the wealden, group of plants. This
second family passed imperceptibly into the third, which comprises
'the plants of the tertiary formations. In the trias the characters
of vegetation are altered by the complete disappearance of the
cactus tribe, by a diminution of the proportion of ferns, and by

THE POPULAR EDUCATOR.

the appearance of a few new species. Of this triassic vegetation very
little is known, and what is known is generally classed with that
of the tertiary. A few coniferous plants grew in the eras of the
lias and the oolites, but they were not of the species that existed
at t^it coal period.

Immediately after the chalk period, a decided change took place
rn the features of the regeUtion. The fern tribe stall continued
to diminish, but the oone-bearing wood increased in quantity.
With the palms and other tropical trees, there grew willows,
elms, poplars, cheanuts, and other similar trees, which increased
in number and variety, till the flora of the more recent tertiary
period had little to distinguish it from the vegetation of the present
day. The contrast between it and the carboniferous flora, and the
similarity between it and the present vegetation, are presented in fig.
98. In this landscape the woodlaud does not appear so strange and
foreign to you as the coal forest did. This is very little different
from the forest suenrs of the present day. Among the trees we
find the palm tree lifting up its feathered top, and a beautiful
brushwood grows in all directions. The landscape is now varied ;
Its outline is more uneven ; and its aspect is more sunny. The
forest is enlivened with quadrupeds that live on plants. Among
these woods grew that remarkable pine tree, called Pinus succi-
nifer, which produced the fossil resin called amber. This amber

is of immense interest to the geologist, as it often encloses speoi*
mens of insects, spiders, flies, small crustaceans, leaves of tr ee s,
&c, which are monuments of the flora and the fauna of that
period. Upwards of 800 species of insects have been pr e a civ e d
in fossil amber. Amber is chiefly obtained from the brown coals
of northern Germany, or the submarine beds of lignite found in
Russia, and along the coast of the Baltic These forests of amber
nines grew in the south-eastern part of what is now the bed of the
Baltic. As the amber found in the lignite and brown coal eon*
tains several fragments of vegetable matter, it has been asoer*
tained that this tertiary forest contained four other species of
pines, and several kinds of cypress, yew, juniper, oak, poplar, and
beech.

The brief hints tbat have been riven to you in this lesson upon
submarine vegetation, and upon the formation of peat and drift
wood, will prepare you for understanding the fucoid fossils which
are found in ancient rocks, and for the vegetable remains found
in the coal series. Tou hsve only to imagine layers of peat and
deposits of drift wood to become bituminised, and the different
seams of sand and mud between them to become consolidated by
pressure from above and heat from below, to be able to aoootmt
for their carbonisation, and for the structure of a genuine oosl
formation.

LESSONS IN GERMAN.— No. LXIX.
Irregular Verba , continued from p. 19.

INFINITIVE.

PRESENT INDICATIVE. .

eprkffli r), to sprout,
€pringen, to spring,
etre)rn, to sting, to prick
Ctrrfrn t), to stick, to be
fastened.
Z\t\tvi, to stand,

Cfteffai, to steal,

etcigen, to ascend,
Ctrrtat, to die,

6tic*cn Otto fly, (as dust)
Srinfrn, to stink,
Ctofrn, to push,
Ctrruyt n, to stroke,
$trcttrn, to contend,
3$un, to do,
Sragen, to bear,
Jrfffnt, to hit,
2rri6rn, fb drive,
Srcteit, to tread,
grirfrn, to drop, to trickle,
Srinfrn, to drink,
Srugrn, to deceive,
Starfogrn, to conceal,

Scrtietcn, to forbid,
Qrrfcleifccn, to remain,
XkxUtidpn, to grow pale,
SDrrtrrbrn «), to perish,

Srrtrirfrn, to offend,
©rrgrffra, to forget,

SB«r$rlrn, to conceal,

Xkxtitttn, to loose,
Srrttftycn, to extinguish,

ffifrftyauVu w), to die away
in sound,
Srrftyolntcn, to disappear,

©fttoirrm, to perplex,

fttrjeirta, to pardon,

IMP. IXDIC

id) fprifflr, k. id) fpreji

id) fpringr, k. i* fprang

id) ftetyt, tu ftt$ft, rr fiid)t id) ftacf^

id) ftaft, k. idsfttdttorftti

id) fttfe, k. id) ftant, flunt

id) f*r$tr, tu fttr tTft, rr fHeift id) fhH (ftcM)

id) fteige, k. id) ftitq

id) flrrbe, tit ftirtft, rr flirtt id) flarb

id) (Hrbr, k. id) M

id) fttnfr, k. id) ftanf

id) Mt, tu ftejUjl, ft flefit id) ftitt

id) ffrrUfre, k. id) ftrid>

id) frrrttr, w. id) firitt

id) iyUf, tu tfufl, ft tyut i* t$at

id) rragr, tu trAgft, ft trAgt id) trug

id) irrffe, tu triffjl, cr trifft id) traf

id) rrrtbr, k. id) ttitb

id) ttttt, tu txittfr, rr tritt icx> rrat

id) trirft, w. ty'troff

id) trinfe, k. id) tranf

id) rriige, tu trfigft, rr rrfigt id) trcg

id) ttettargr, tu mWrgfl, errcr id) mbarg

Hrgt

id) vcrMrtf, K. id) verfot

id) mbfribf, k. id) wbltfb

id) vexbltidjt, K. id) vtrblio)

id) mtrrbr, tu ttrtirbft, cr id) rotate

rcrtitfct

d vrrtritf t H tcrtwfc

id) sergeflr, tu srrgifffft, rr trr. id) vrrgafi

flipt

id) *cr$c$te, k. id) vttfflltt

id) vtrltcrr, jc. id) wrier
ic^ vcrlof^r, tu wrlof^ffl or i^ vrrtofc^

wrltfc^cft, rr vrr(uf(^t or rcr*

life)t
id) wrf^ine, k.

id) vcrfcfitotntr, k.

id) WTttirrf, ?c.

id)*crfd)ett.
id) vrrfc^ttKint
id) venotrrtr

IMT. SUBJ. IMPERAT. P ARTICIP.

id) frreffe
id) fptAnge
id) ftdc^e
id) fiedte or

ftAfe
id) ftante
(fiantr)
id) fttyt

id) fhege
id> OArbc

' (fturfc)
id) ft'obt
id) fiAnfe
id) ftif^c
id) fliid)t
id) fhHttc
id) tfcvlte
id) trugc
id) trdfe
\d) tritbt
id) trAte
t<^ truffr
id) trAnfe
id) trisje
tcf? mbArgr

id) vrrtotc
id) vexbiitbt
id) wrblictx
id) vertArbr
(vrrturse)
id) vcrtreffr
id) vcrgAjir

id) ttrU (ctr

id) WTlcre
id) vrrtpft^r

id) vtrftycfte
i^vrrfc^toAnte
\d) xxrteirrtr

id)iott#t1) tywrjtyr mjrifc »«|i«^at

fpriffr
fpringr

frecfe

ftefe

flie^C

flrigr
ftirfr

ftifbe
ftinfc

flo^r

fhrridie

ftrettr

t^uc

tragr

triff

twi6r

tritt

triff, triefc

trinfc

trflgr

vrrbirg

vrrttrtr

wrbtfibr

•eerMeio>c

wrtirb

REMARKS.

grfproffen.
gefprungen.
gefto^rn.
grflrdt.

grftantcn.

grflc^fcn.

gefHcgen.
gefiorbfn.

geftcben.
gcftutifrn.
grfbffn
ge|hi*cn.
gefhrittm.
^ft ban.
gftragm.
grtroffen.
gctricbat.
gctretm.
grtroffm.
getrunfrn
getrogrn
j vnrbergrn.

r) This must not be con*
founded (in the imperfect)
with the regular verb fproffca.

t) This verb is commonly rev
gular; when active it it
always so.

t) So 3<rfH<bfn, to be scattered
as dust.

wrtotrn.
wrbltebrn.
vetblidftn.
wrtorfren.

vrrtrirfr wrtrofffu.
vrrgifi vcrgrffru.

vrr^Ir

wrrlirrr
vcrlof^f or
wrlifc^

vcrfdKtRe

vcrfc^nHnte

vcrtsirrc

«rr^cU or

wr$o$len
wrlorrn.
vrrlrfArn.

verfc^cden.

verfc^muu'

trn.
t)fttt)irrt or

«) Sfrtfrbcn, to destroy (ac-
tive) is regular.

v) Ototrruft k. nearly obao
iete.

v) But little used, except ia
the imperfect and participle*

LESSONS IN ENGLISH.

irregular Verbs continued.

INFINITIVE.

.PRESENT INDICATIVE

IMP. INDIC.

ic$ tDu$6

IMP. SUBJ.

I IMPERAT.

PARTICIP.

RBMARK8.

SBoiyfen, to grow,

vd) nxictfe, tu toActff ft, cr t»a<$fl

t(y tVUCyfC

tDad;fc

%tvoad)ftn

ffidgcn, or SBiegcn *) to

ty teAgc or nriegc, tu mdgft or

i<$ n>og

tc$ toege '

todge or

getoogen.

x) SBAgctt is active, and hat

weigh,

toirgfi, rr toAgt or wicgt

totcge

wage in the imperf. subj. ;

micgen is neater, and has

totcge. SBicgen, to rock, is

regular.
y) 2BAf<$eft"and toAftyt are also
, used.
z) Regular except with the

SBafcytn y), to wash, #

id) toafcyt, sc.

i($ toufty

UytSfifCyC

feafcyt

getoaftyen.

tteScn *), to weave,

ty tsete, '*•

ty too©

to) toobc

toe&e

genwkn.

poets, or when used figura-

tively.

»c«$c» a), to yield,

i$ toetye, ic.

My tOtC^

\df toicyC

toein)e

getoi$cn

a) aBcicytn, to soften, to moli-
fy, is regular.

Octfm, to show.

ic$ fcetfe, k.

i($ ta>irt

i<$ toiefe

toeife

getotefm.

gBrnbe* 6) to turn,

id) tsenfcc, k.

i($ tec nbftc or
frantte

id) ivenbete

wente

getoenfcet or
gcnxuitt.

b) Regular when active.

SBertai, to sue for,

ic$ toerbc, bu totrfrjt, re nritW

tc£ toatB

id) totirbe

»irb

gctoarfat.

HBertcti, to become,

t$ weftr, fcu hrirfl, cr nrirb

i<$ toarb or
tourbe, bu
tturbeft er
toart or
tourte, tttr
tocrben, jc.

id? tourbc

toerte •

getverben ; &.
as an aux-
iliary)*)^'
ben.

SBerfcn, to throw,

id) tecrfc, tu toirffl, cr totrffc

id) Jcarf

id; todrfc
(tourfe)

toirf

genwrfen.

SBintcn, to wind,

id) tointe, }c.

i$ nwnb

i$ wAnte

tmtibc

gctounten.

SBiffen, to know,

i$ totis, bn toetsr, ct tociji

id) nmste

id; toufctc

n>iffe

gmujjt.

ffloOen, to will,

id) nrifl # bu toilljt, ct xoiil

ty tootttc

id; toeHte

—

getocHt

Seidell, to accuse of,

id) jetye, k.

i$gic$

i«y Jtc$r

$«£«

ge;ie$en.

Sicken c), to draw,

id) jie$e, k.

w$J°8

tyjSfl*

Stebe

gejogen.

c) 3cud)rt u. antiquated, and

Bieingrn, to force,

i$ jtoinge, jc.

i<$ jtoang

id) jtoftnge

jtoinge

genoungett.

only in poetical usage.

S 79. Verbs of the New Conjugation.

(Commonly called "Regular Verbs: 9 )

(1) In verbs of the New, or simpler form, the Imperfect Tense
and the Perfect Participle are npt produced, as in the Old con-
jugation, by a change of the radical vowels ; but by means of
the suffix ct or t, which serves as a tense characteristics thus,
taking the radical part (lob) of (oben, to praise, and affixing

thereto rt or t, we get Iobrt or frit; to which add the personal
endings and we have let tit (tcb+ct-f e) or lofoe, I praised j lofretcft
or lofaefr, thou didst praise, &c.

(2) The verbs of the New form differ again from those of the
Old, in the former having in the Perfect Participle the termi-
nation et or t, instead of en: as, gefobet or gefobt, praised. See the
table of terminations 5 75.

LESSONS IN ENGLIS H.— No. LXIX.

By John It. Beard, D.D.

SYNTAX OF THE PREDICATE ; THE VERB,-THE
OBJECT.

I must now conduct you to the predicate of a simple proposition.
In order to effect my purpose, I must modify our model sentence
a little, as thus:

Stdtfect. Predicate.

The sick man drinks a beverage made of wine and water.

The sentence thus altered brings under our notice two additional
tfaits of speech, namely, the preposition (of) and the conjunction
\and). It also directs our attention specifically to government,
namely, in the relation borne by the verb drinks to the noun btve-
rage % and in the relation borne by the preposition o/to the noun
wine and the noun water.

If, now, we look at our predicate, we find that it may be divided
nto two parts, namely, the verb and the object ; as,

Subject. Predicate.

The man

Vert.
dii.iks

Object.
a beverage made of wine and water.

Viewed in relation to its several components, the predicate contains
the verb drink* ; ibe article * ; the nouns beverage, tcvie, water ;

the past participle made ; the preposition of; finally, the conjunc-
tion and. The articles have been already handled. The nouns,
the verb, and the preposition range themselves under the general
head of government ; the past participle offers an instsnee of agree-
ment ; the conjunction acts merely in the. way of combination.

Government— The Object after a Verb.

Every transitive verb has an object, expressed or understood, and
the same verb may sometimes be used transitively or intransitively.
If no specific object is given, the verb may be considered intransi-
tive ; e. g.,

LUtansitive: Man drinks ; the horse trots'; •

Transitive : Man drinks water ; the horse trots tenmUes an hour ;

A verb which is strictly intransitive may be made transitive by a
prepositional or adverbial suffix. To fly is intransitive, and to fy"
over is transitive ; e. g.,

The eagle flew-over the eurnmit of the* mountain.

Consider drink as intransitive, and append of, then you have

The siek man drmke o/pure water.

Drinks of is here a compound verb, and might be best written with
the hyphen, thus, drinki-of. In this form, as being transitive, it
has for its object pure water. But to drink, and to drink of, have
not precisely the same import. We drink a glass of water, and
we drink of a river. In tact, of has a partitive force, that is, It
denotes a portion of; e. g.,

. ... .l.;i.L ilu «%Ui. I»— ^ ' ? Ill: .

I. 'i tip i- i. .*u«. •> .i.'.v:i.'.. :i.r

. Zr. . ' »*.*'.

- :-: ruarm. 'ami-—

•.it... 1 1.. • s

!l.*». J. U-.h

--■ - zimt ii ti B17. :aey
«- • Tit-*- niiietra izt
r^.- - -»»ii—M nts: tsar
— - t!ii^; Hi:** rura
:-.■" -ar n Tusr ni&inm

, %Mvl'-.» I.N. I'

z™s. m

in* -n *
J ^ lur

•. •.-. « .6

•:• • fu Lot u»

:;\i «j* «:

^ . * •*..*

--wmctssg

«v-v. . «t*

.■S «. •.-.

LESSONS ON NATURAL PHILOSOPHY.

The position of the object is after the verb. And the observance
•of this law is in English so imperative that by disregarding it yon
create ambiguity, if you do not change the object into the subject
and the subject into the object; e. g. f

Subject. Object.

The father ' struck the son.

Subject. Object.

The son struck the father.

As an instance of ambiguity from the inversion of the object,

take this instance : —

" This power has praise that virtue soarae can warm,
Till fame supplies the universal charm."— Johnson.
Which is the subject, and which the object ? Bo you mean that
power has praise, or that praise has power t

When, however, the perspicuity of the sentence is not abated,
the object may, for the sake of emphasis, be placed before the
verb ; e. g.,

" Silver and gold have I none."— (Acts iii. 6.)
Especially with pronouns ; e. g.,
*' Me he restored to mine offlee and Wn he hanged."— (Gen. xli. 18.)
You may find sentences in which one object stands before and
another after the verb ; e. g.,

11 Ye have the poor always with you, but me ye have not always."—
(Matt. xxvi. 11.)

Intransitive verbs have no object. The untaught are apt to con-
found the transitive with intransitive verbs, using the one for the
other. This error may be exemplified in the verbs
Transitive : lay raise

^Intransitive : lit rise

Thus, they say,

He laid a-bed all day.
The hen has lain an egg.
The price of butchers* meat has risen.
The lark rises itself in the sky.
The principal parts of the verbs are

Transitive: lay laid laid

raise raised raised
Intransitive: lie lay lain

rise rose risen

Accordingly, the statements that stand above ought to be,
He lay a-bed all day.
The hen has laid an egg.
The price of butchers* meat has been raised.
The lark raises Use V in the sky.

tween the directions, a p and a q, of those forces ; the reason
of this is plain, namely, that the point cannot move in both
directions at once ; and as no rea-
Vlg ' 5 ' * son can be assigned why it should

move in the one direction more
than in the other, it must move
in some intermediate direction,
and this direction is exactly that
of the resultant of the two forces
p and q.

All problems which relate to
the composition and resolution
of forces depend upon the fol-
lowing theorems, for the demon-
stration of which we must refer our mathematical students
to the Elementary Treatises on Statics, which are to be
found both in French and English. In particular, we would
mention the elegant demonstrations of M. Poisson, in his
Traite" de Micanique, imitations of which have been published
in English Treatises on Mechanics, by Whewell, Pratt, Barn-
shaw, and many others.

Composition and Decomposition ofParalM Form. — Theorem 1.—
When two parallel forces are applied at the same point, their
resultant is equal to their sum, when they act in the same direc-
tion, and to their difference when they act in contrary directions,
For example, if two men drag a load in parallel directions,
with forces respectively denoted by 20 and 15, their combine^
force, that is, their resultant, will be denoted by 35 if they drajj
in the same direction, and by 5 if they pull in opposite direc-i
tions. In like manner, when a number of horses are attached
to the same vehicle, and all pull in the same direction, it will
be urged along the road as if it were drawn by a single force,
equal to the sum of all the forces of the different animals
employed.

Theorem 2.— When two parallel forces, which act in the same
direction, are applied at the extremities of a rigid straight line
(a rod), their resultant is equal to their sum, acts in the same
direction, and its point of application divides the straight line
into two parts, which are inversely proportional to the numbers
which express the intensity of the forces. Thus, in fig. 6, if

Fig. 6.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. III.

ON THE COMPOSITION AND RESOLUTION OF FORCES-

Composants and Resultants.— When several forces, such as s,
p, and Q t are applied to the same material point, a, fig. 4, and
produce ar\ equilibrium at that
K «K- 4 - point, it is evident that the action

of any one of these forces, for
example s, resists the combined
action of all the rest ; for were the
force s to act in the direction a u,
contrary to its own direction, a s,
it would produce the same effect
as the two forces p and q, acting
in the directions a p and a q. Every
force which produces the same
effect as a combination of any
number of forces is called the
resultant of such forces, and these
considered in relation to their result-
ant, are called component forces, or
composants.

When a body is put in motion by the action of several
forces, it can be demonstrated that the motion always takes
place in the direction of the resultant of all the forces. Thus,
nSa material point, as at a, fig. 5, be acted on by two forces, p
ana 1 q, it will move in some intermediate direction, R a, be-

a|b denote the rigid straight line, a and b its extremities, p anoT
q the parallel forces, a p and b q their directions, and o the
point of application of their resultant b ; then c k, parallel to
a p or b a, will be its direction, and p : q : : b c : o a, that is, if
the force p be two, three, $c, times the force q in magnitude,
then the part b o will be tuo, three, $c, times the part AC in
magnitude. Whence it follows, that when the forces p and Q
are equal, the point of. application of their resultant divides the
straight line a b into two equal parts. Conversely to this pro*
position, any single force R applied at the point o in a given
rigid straight line, a b, may be resolved in£o two parallel forces
p and Q, whose sum is equal to r, if their points of application,
a and b, be in the same straight line with the point o, and if
they be so divided, that they are to one another in the inverse
ratio of their distances from o ; that is, if b o : a o : : p : a.

To find the resultant of any number of parallel forces act-
ing in the same direction, we have only to find by the preced-
ing theorem the resultant of two of these forces, then the
resultant of this resultant force and another of the given forces,
and so on, until all the given forces have been compounded.
The last resultant thus obtained will be a force equal to the
sum of the given forces, and having the same direction ; and
its point of application will be determined.

Composition and Resolution of Forces acting on a Single Point-*
If two forces, as r and q, fig. 7, act on a single material point

THE POPULAR EDUCATOR.

at a, and a p snd a ft be the direction* of th we forces, we can
determine their resultant by the following theorem. Before
we enunciate thin theorem, let ua take on the *tr;*i.;ht lines a p
and a Q, parta a b and a c having toseach o-.her the same ratio

as the intensities of the forces

ON MOTION.

Fir. 7.

let u* then cr. nip lets the paral-
lelogram a :: d •:, by drawing
n i> parallel to a c, ar.d c c
paralltl t.j a i. and lit us
rinw the di-^-.nai a d. This
f.^ure is the ^aralleiagram. cf
ecrem which

ar.d :

it 9 the r-.-L.i:i*:a between
rr.p«:s^r.;s P a^d u and

fon.es, ar.il
M T r.
th.: <:

tV.t-ir r-sulMnt a, is called TU
TAer.rvm >./ 'i-i p-srjlu&gritn
•f Frcei; \-j„ ii any two
f.n:«s airing ■.:-. a material
P' i.-st be r^pr-scn*. :d m mag-
nitude and direct: in by the tw, aJj^ent si-i--s >.£ a paral-
lelogram, their r*su!t-»nt will^be rep res- n ted ir. ruaj;r.i:ude and
direction, by the diagonal of that parallelogram which is
drawn from the point where these two aides meet. Th-is. in
the parallelogram a n c d, if a b and a c represent in magnitude
and direction any two forces p and a, acting on a material
point at a, then will the diagonal a d, drawn from the
point a, represent in magnitude and direction the resultant a
of these two forces ; in other words, the direction cf the result-
ant a of the forces p and o, will be the straight line a a, and
the resultant a will contain the unit of force as many times
as the diagonal a d contains the linear unit of measurement.
which was applied to the determination of the lengths of a a
and a c, in order to make them represent the forces p and q.

Con Tersely, a * ingle force applied to a material point may
be decomposed into two other forces applied to the same
point, and having their directions in given straight lines,
that is, straight lines which shall make given angles with
the direction of the resultant and with each ether. For
if we construct on the given straight lines a parallelogram, '
whose diagonal represents in magnitude and direction the .
given force, then its sides will represent in magnitude and .
direction the required composants. The solution of problems
relating to forces acting on a single point will be seen by the
mathematical student to resolve itself into the application of .
trigonometry to the determination of the sides and angles of .
the parallelogram of forces. Thus, if p and a represent any
two forces in numbers, and a denote the angle between their
directior.il, then their resultant n will be represented in nuxn- :
bers by the following formula: —

11=^; p 5 +ci 2 + 2pqwa J

Whftn a n-imhcr of forces are applied to the same point in
various direction*, their resultar.t will be found by applying
the preceding theorem first to two of these forces, and then to ]
the resultant thu* obtained and a third of these forces, and so !
on successively till the last force has been taken into the ■,
account. The la it resultant thus obtained will be the result-
ant of all the forces combined.

The effects of the composition and the resolution of forces are '
frequently presented to our notice. For example, when a boat
row*d by o*r* crosses) a river, it does not make way in the real ■
direction in which the oars propel it ; neither does it advance '
in the direction of tfce current; but it is urged along in the ;
direction which exactly corresponds to the resultant of the ;wo !
forces which act upon it, viz., the force which puts the oars in
motion and the force of the current in the river. In like man-
ner, when several men are employed to ring a great bell each
by a short rope attached to the main rope, the resultant of their
united force* */:t* along the main rope as the line of its direc-
tion, and their individual forces form the composants, their
lanea of direction being that of the short ropes at which the
ringers pull* in order to produce the desired effect. When
any number of forces arc in equilibrium about a point, any one
of f hem may be said to be the resultant of all the rest, but its
direction, of course, is contrary to that of the balancing force ;
and the resultant of any number of forces in equilibrium, is
mthwy.

Ififarey-t Kimia ./' Jfo/Yun. — M irim is said to be i

curvunuar a* •_■«.■ r;mg i» tiie pnL»i described by the moveable body

is as-'raiah.: '.:::•» jr i cirve ; md either of these motions maybe

iHt/orm or ?'f/- ■/ ;; - !~>i/,,~;i ttii'wn is the most simple kind of

motion, a=d is t-.I: it whi.K the moveable body describes

* qua! spaces in i-ri-u t:nv.*s. Er»ry momentary force produces

a motion which is ri-:ui:ze.ir wi izi:jra, when the moveable

body is net subjected tj the action of any other force, and

moets no resistance to i.s progress. Under the momentary

action of a force. the suv>abie. when left to isvlf, will continue

to preserve, in c:n,*»-:"ienc* of :a inertia, the direction and the

velocity which were communicated tj it by the momentary

. action of he force. Under tie continued action cf forces, a

' moveable may 1-/5. e vje be m:ide to preserve uniform motion;

■ is in the cjse w ::*_-»? :h- rv?L»tanctr* opposed to the

continually de>:r.y -l:e Lici^m-nts of v*ioi:ity which
, forces ttnd to ■:• ^.municat.: to the moveable. We see an
example ».t this in t;:* n:-t: n of a tram on a railway, where
the motion is ?r- •: . :-_Mi tv the rcntinurd action of a certain
force, but that i;ou-:n .s nevertheless *::il uniform ; this result
: arises from the 1 .** f forc-j due tj the continued resistance of
the air. the fri::ion of the nils, xc. a resistance which in-
creases as t'.v: T'/.-xity increases, and which soon establishes
such an equilibrium between the moving and resisting forces,
as produces the unnorm motion required.

Vf'v y, («■/ Lav r ' U*'f,im JcVnm. — In uniform motion,
the space described i:i a unit of time is called reiocity.

Thisunir. although entirely arbitrary, is generally a oteonH
■/" ti„i,\ From the definition of uniform motion, it is plain
that in this sr«.v.-i«s of motion &e velocity is cotutmt, that is*
always the same : », for example, in 'w, units of the time, the
space described is '*W>>, in r /</■■'.- units tripk t in femr units
'fi.idr-uSg, xc , that of the spaee described in one unit. This
law is usually expressed by raying that in uniform motiem list
inters awn)'-! -rr •.rQvortittH'tl to lk< *im*9 % or in Other WOrdSi
^c apic-Ji -.ksiribtti • •crta** it"-'."* fV times.

This law may be represented bra very simple formula ; let
r denote the velocity, i the time^ and * the space described.
Now since k denotes the *pace described in a unit of time, the
space described in 2, 3, 4, &c, units of time will be 2r, 3r, 4r 9
dec. : and generally, in the time ', it will be * r ; hence, we

have the formula i=.t c. From this formula we have r — *

/;
hence we say, that in uniform motion, the velocity is the ratio
of the space described to the time employed in describing it.

V-TrutHe Motion is that in which a moveable body describee
unequal spaces in equal times. This species of motion may be
varied in an infinite number of ways, but we shall at present
only consider that in which it uniformly varies.

Motion UnifonH'y ViniabU is that in which the spaces
described in equal times constantly increase or decrease by the
same quantity. In the first case, the motion is said to be
Utiiformly accelerated; such is the motion of a falling body,
when the resistance of the air is removed. In the second case
the motion is said to be mmi/'wWs- re! nied ; such is the motion,
of a stone thrown vertically upwards from the ground.

Motion uniformly varied" arises from a constant font, that ia,
a force continually acting with the sime intensity; and it is
considered either as a power or a resistance, according as the
motion is accelerated or retarded.

Velocity, amlLwcsof Uniformly Acceitrate-i Motion. — In motion
uniformly accelerated, the opaces described in equal times not
being equal, the velocity is no longer the space described in a
unit of the time, as it is in uniform motion. In the former
species of motion, we understand by the velocity mt s^t'iws
instant, the space which, commencing from that instant, would
be uniformly described by the moveable in every second, if
the action of the accelerating force were instantly to cease.
that is, if the motion were to become uniform. For example,
if a moveable were to acquire a Telocity of 60 Tarda per second,
after the lapse of ten seconds, during 'which it had proceeded
with uniformly accelerated motion, and if the uniformly
accelerating force were suddenly to cease its action after these
10 seconds, the moveable would, in consequence of-its inertia,
continue its motion uniformly at the rate of 60 yards per
second.

LES80N3 IN CHEMISTRY.

On this principle, every uniformly accelerated motion, what-
ever may be its increments of velocity, is reduced to the two
following laws :—

1st. The velocities increase proportionally to the times;
that is, after a time, double, triple, quadruple, &c, any given
time, the velocity acquired is double, triple, quadruple, &c,
greater than that after the given time. The action of the
continued force, indeed, which produces any accelerated mo-
tion, may be oompared to a series of equal impulses which
succeed one another at equal but infinitely small intervals of
time. Now, as each of these impulses produces in each inter-
val a constant velocity, which is continually added to that
which the moveable already possessed in the preceding interval,
it follows that the velocity goes on constantly increasing by
equal quantities in equal tunes.

2nd. The spaces described are proportional to the squares of
the times employed in describing them ; that is, if we denote
the space described in 1 second by 1, the spaces described in
2, 3, 4, 5, &c, seconds will be denoted by 4, 9, 16, 26, &c,
which are the squares of the former.

These laws are mathematically demonstrated in the scientific
treatises on Dynamics, or the laws of motion ; when we come
to treat of gravity, we shall exhibit their experimental
demonstration.

Momentum, Measure of Force. — The momentum of a body is
the product of the number expressing its mass by that expres-
ing its velocity. Thus, if a body moves with a velocity of 10
feet per second, and its mass is represented by 20, then its
momentum is said to be 200. When a force communicates a
certain velocity to a given mass, the momentum can be taken
as the measure of this force. Thus, if a body moves with a
velocity of 20 feet per second, and its mass is represented by
10, then its momentum is, as before, said to be 200 ; whence,
in this case, the moveable has the same force as .in the pre-
ceding case. The momentum of a body is frequently called
its quantity of motion. *

In mechanics, therefore, these principles are established,
that, in equal masses, the forces are proportional to the
velocities ; and that, in equal velocities, the forces are pro-
portional to the masses ; in other words, that a force double
another imparts to the same mass a double velocity ; or, to
double the same mass, an equal velocity. Now, let there be
two forces' F and/ acting upon the two masses M and m, and
communicating to them the velocities Fand * respectively. If
we suppose a third force P such that it communicates to the
mass M the velocity *, we shall then have, according to the
preceding principles, the following proportions : —

(1.) F.Pu V:v, and

(2.) P : / : : Mim: whence,

we have ~ = —,
F v

and -r =

Now, multiplying these two equations term by term, and
cancelling the common factor P, we have

F MV ,

~ = ; whence

/ mo

(3.) .F : / : : *v : mv ; that is, any two forces are to each other as
their momenta or the quantities of motion which they commu-
nicate to any two moveables. Thus we see that if we take for
the unit of force the momentum which the unit of velocity
would communicate to the unit of mass, forces may be
measured by their quantity of motion. This species of mea-
surement is equally applicable to instantaneous and to con-
tinued forces ; but in the case of continued forces, we only
consider the velocity which the force communicates in a
second.

Forces being proportional to their momenta or quantities of
motion, it follows that for the same force the product mv is
constant; that is, if the mass become twice, thrice, &c,
greater, the velocity will become, twice, thrice, &c, smaller.
This conclusion is drawn from proportion (3) above demon-
strated; for bv making f=/, we have nv.= *nt>; whence, it
follows (CasseU's Arithmetic, p. 101) that M:m::vi V; that
is, the velocities communicated by the same forces to two
different masses, are to one another in the inverse ratio of

LESSONS IN CHEMISTRY.— No. in.

Resuming the consideration of the metal sine, the learner will
remember that he has dissolved a portion of this metal in suU
phuric acid and water ; that he has evaporated this solution
to dryness, and redissolved the dried mass. He will have now
obtained a colourless solution of sulphate of zinc ; that is to
say, a solution of oxide of sine in sulphuric acid. However, I
only at the present time desire the learner to remember the
single fact, that the zinc is bv some means held in solution by
the liquid employed, i.e. sulphuric acid and water. The exact
state of its combination we need not discuss just now, this
point will come under discussion hereafter. The zinc is there,
and we require to obtain it, or at least satisfactory evidence of
its existence; that is our proposition. How is this to be
accomplished? A person conversant with Chemistry would
almost arrive at the conclusion that zinc was present by the
peculiar taste pf the liquid. And indeed the sense of taste is
• ▼ery valuable test : a far more precise indication, however, is
afforded by hydro-sulphuric acid, or its watery solution, as we
shall see. If the learner pour a little of the sulphate of sine
into a test tube ; that is to say, a little glass tube of the follow-

vi* 14 m f sha P e » or ft win © glawt *»<* *dd to this

««• i». sulphate of zinc a portion of the hydro-sul-

phuric acid solution already procured, a white
powder will fall, this white powder being a
combination of sulphur and zinc, and therefore
called sulphur** or sulphkfc of zinc.

Let the reader impress upon his memory
the fact that sulphuret or sulphide of zinc
is white, and that it is the only metal which
yields a white compound with the same agent,
applied in the same manner.

If a sufficient amount of hydro-sulphuric
acid solution be poured into the sulphate of
zinc, all the metal will be thrown down in this
condition of sulphur** or sulphkfc, and accord*
ingly this process is sometimes followed in
the course of analysis. The student, however,
will not fail to perceive that, supposing the
solution of sulphate of zinc to be very strong, a
very large portion of hydro-sulphuric acid solution must be
added, a treatment which would, under many circumstances,
produce an inconvenient bulk of liquid. This being the case,
it follows that when hydro-sulphuric acid is merely used as a
test or indicator, it is commonly employed in the state ox
aqueous solution ; when, however, it is employed as a separator,
then the more convenient plan is to cause it to permeate the
metalliferous fluid as a gas ; this remark brings me to the
consideration of the mechanical arrangement necessary to the
use of this gas.

Fif. 1&.

If a mixture of oil of vitriol and water (about 1 to 6 by measure)
be poured upon sulphuret of iron sulphuretted hydrogen, or
sulphuric acid gas, will be liberated, as we have seen ; but as
thus liberated it usually carries before it little particles of liquid,
i.e. sulphuric acid and water, consequently it is not well adapted
to be employed as a delicate precipitating agent. To spe*k more

Srecisely, the gas requires to be passed through water in smal.
ubbles, or washed, by means of an apparatus similar to that
represented in fig. 16 ;. a and b are two wide-mouthed eight or
ten-ounce bottles, to each of which is adapted a cork, and each of
which corks is perforated with two holes, as represented. Pre*
yiously to securely fixing the cork of the vessel ▲, some fragments
of sulphuret of iron are thrown in ; the bottle is then corked

THE POPULAR BDU6ATOR.

water is now poured into the Tassel B, and the latter is also
corked. It will be evident now, from the merest consideration
of the various parts of this apparatus, that if a mixture of sul-
phuric acid and water be poured into a, all the sulphuretted hy-
drogen liberated will be obliged to traverse the water b before
it can Anally escape ; in other words, it will be washed, A portion
of the gas is absorbed by the water, but this matters not ; the
maximum of absorption is soon arrived at, and the gas comes
over uninterruptedly so long as it is developed . Only one matter
remains to be spoken of in connexion with the apparatus just
described, it relates to the portion marked r. This consists
of a small tube of india-rubber vulcanised by preference, and
which is interposed between the two glass tubes. By this
arrangement not only does a flexible joint result, but the bent
glass tube admits of being removed and another placed in its
stead ; for, as a general rule, the same tube should not be used
for testing consecutively two fluids of different compositions.
In most large towns, vulcanised rubber tubes of any length
may be readily procured, and the operator, having become
possessed of them, may cut them into lengths according to his
necessities ; but supposing them not procurable, the reader
should be able to manufacture a substitute out of india-rubber
sheet. The best material for this purpose is the rubber manu-
factured into sheets, but even the native bottle rubber will
answer perfectly well.

Supposing the artificial sheet rubber to be procured, it may
be formed into tubes simply by warming it before the fire,
winding it round a glass rod or tube, pressing the sides closely
together, and cutting them off by a sharp pair of scissors.
Thus treated the two cut edges will adhere, and a tube will
result. Fig. lfl.

rif. 16.

form of a circle. Then bending the disc on itself, form a semi-
circle. Then binding the semi-circle on itself form a quadrant*
Lastly draw the quadrant into this form, fig. 17, and the filter If
complete. Large niters rea uire to be supported on funnels •
small filters may and indeed are better used without funnels*
they may be rested on the edge of the glass itself; but a far
better method consists in using a filter support made of porce-
lain, and of the shape annexed. Fig. 18.

rig. 18.

If, however, the artificial sheet rubber cannot be procured
and the bottle rubber has to be substituted, the latter mate-
rial reouires to be boiled in water for a considerable time, in
order that the necessary amount of adhesiveness may be im-
parted to it Generally speaking, india-rubber tubes, thus
manufactured, are strong enough for all uses to whioh they are
applied ; it additional strength be desired, it can be imparted
bV first constructing one tube, then overlaying it with another,
the seam of which does not correspond with the first, but is on
the opposite side of the tube.

The two bottles forming the compound apparatus just des-
cribed, are usually attached for convenience to a slab of wood,
as represented in fig. 15. The apparatus is procurable com-
plete at the philosophical instrument shops, but I strongly
recommend the young chemist to manufacture this and similar
apparatus himself.

Return we now to the metal zinc. By passing a stream oi
hydro-sulphuric acid through it sufficiently long, the whole of
the zinc will be thrown down. The operator may know when
this point has been arrived at, by filtering a little of the solu-
tion from time to time, and testing the nitrate or fluid which
passes through the filter. This remark leads us to another
digression — the operation of filtering, so necessary to the pro-
secution of chemical investigations. The usual material
employed by chemists, as a filtering agent, is paper. Filtering
paper is of various kinds. The coarser sort is made chiefly of
wool, and is of a brown colour ; the finer sort resembles in
its general aspect wkiU blotting paper, which indeed may be used

Fig. 17.

By means of this little apparatus a filter ms$ be rested oa
the edge of its correspondmgglasfl, or removed at pleasure,
with the greatest facility. Whatever is the size of the filter
employed, it should be wetted with distilled water before the
liquid to be filtered is poured upon it. A special apparatus is
employed for wetting niters and washing precipitates collected
upon them. The apparatus is of the following kind.

A thin flask slightly flattened at its base, in such a manner
that it can stand without support, is furnished with a perfo-
rated cork and two tubes, as represented in the diagram, a
mere casual examination of which will suffice to show that, if
air be blown in through the tube a, water will emerge in a jet
from the tube b, fig. 19. This jet may be so nicely regulated,
that even the most delicate filter paper can be wetted without
any fear of rupture.

Fif . 19.

at filter paper, if the true material cannot be obtained. The
to Bake a filter is this : first cut out the paper into the

By means of a little filter, as just described, it may easily be
determined when the point corresponding with the total preci-
pitation of zinc has been arrived at, and this operation may be
considered as the type of thousands which constantly occur in
the course of chemical analysis. ' ;

Here we may, with advantage, take leave of sine for a timet
and begin the consideration of another metal ; not that we
have nothing more to say concerning zinc, but that our future
remarks will most profitably come before the reader by way
of comparison. We will take up another metal, and that
metal shall be manganese, a very abstruse metal in many
respects. The abstruse points, however, connected with it J
shall omit, merely directing the student's attention to two
points — a means of obtaining it in solution, and a means oi
precipitating or throwing it down from this solution.

We succeeded in dissolving sine by means of diluted s*k
phurioacid. We cannot readily dissolve manganese, or, more
properly, commercial black oxide of manganese in this manner
Concentrated sulphuric acid, and oil of vitriol, dissqlves a.
portion of. it readily ; but I shall have recourse to an indirect
process of solution, as follows : — Rub together in a mortar two;
parts by weight of manganese, and one part by weight of sal-
ammonia. Put the mixture into a crucible of silver or pl^tSm^
if the reader possess one of these instruments ; if not, into a white
gallipot, and heat to dull redness over a powerful flame of gas
or spirit, or a charcoal fire in preference ; but a common fire
will do : allow the mixture to cool, add distilled water, anf)
filter. The filtered solution contains manganese held in sola*
tion by chlorine. How the chlorine got there, or w*vf ||

LESSONS IN GBKML

combined with the metal, are not points for diaeustion at I
present. One object was to get a solution of manganese, and
we have got it : let us now study the properties of this solu- I
tion. Our proposition is to precipitate or throw down the
dissolved manganese. How can this be effected r The student
succeeded in throwing down sine by means of hydrosulphuric
acid, either in the form of aqueous solution or gas. Will these
agents throw down manganese ) On trying the experiment,
the reader will find that the manganese cannot be precipitated
by this means. The solution will either remain absolutely
clear, or will only become slightly turbid) the manganese
remaining dissolved. But if instead of hydrosulphuric acid
gas, or solution of this gas in water, a solution of the same in
ammonia (hartshorn) be employed ; or, what amounts to the
same thing, if a little hartshorn be added to the manganese
solution simultaneously with the hydrosulphuric scid, then all
the manganese will be thrown down or precipitated. If the
manganese solution be pure, the precipitate will be white, or
rather flesh-coloured (we will call it white by courtesy) ; if the
solution contain iron or some other metal — a very probable
contingency— then the white or cream-colour will be pro-
portionately disturbed.

What I desire especially to impress upon the student's con-
sideration is this. Zinc is precipitated from ita solution whiU
by hydrosulphuric acid alone, whereas manganese is precipi-
tated white (by courtesy) only when the hydrosulphuric acid
is combined with ammonia or hydrosulphate of ammonia. Hence
we at once deduce a valuable power in analysis. Supposing
sine and ammonia to exist together in one solution, they mat
readily be separated by applying the principles already deduced
Passing a current of hydrosulphuric acid gas through the com-
pound solution, without the presence of ammonia, all the sine
will be thrown down; repeating the operation with tht
presence of ammonia, or still better, hydrosulphate of ammonia
already prepared, the manganese will fall. Both these preci
pitateawUl be sulphurets; one of zinc, the other of manganese
The reader will now observe that although we just now
dismissed the metal sine, this was only for a time. Its con
sideratlon is now reopened in connexion and by contrast witl
manganese : chemical philosophy, in point of fact, is a structure 1
made up* of this comparative knowledge of different bodies.

In addition to the fact that sine is precipitated by hydro-
sulphuric acid alone, and manganese by hydrosulphuric acid 1
in combination with ammonia, let the reader remember thai
a white precipitate by either of these agents is altogether
exceptional. The usual colour of precipitates by hydrosuU
phuric acid and hydrosulphate of ammonia is black. Two
metals are alone precipitated white : these are zino and man
ganese. The student will now recognise a means by which i
sine and manganese, if existing together in one solution, admit
of being separated ; he will perhaps remark, however, that w»
do not separate the metals— obtaining sine bodily, and manganese)
bodily— but obtsin either a metal or a sulphuret. He will
perhaps desire, like most beginners, to obtsin this bodily
presence of the metals. To this extent I cannot gratify him in
the present lesson. Suffice it to say, that the process of re-
moving sulphuric acid maybe accomplished— w accomplished
in the reduction of metals from their ores— but would be
difficult to accomplish in our present case ; it i| never ac-
complished in the course of analysis. Chemists arrive at
some of their most correct results by collateral reasoning and
calculation : thus, knowing that the white sulphuret of man-
made up of parts sulphur, and puts

that the white sulphuret of sine is made up of —
parts sine, and ■ ■ parte sulphur— of course it is eaaj
to calculate the amount of metal and of sulphur present, witl
out actually separating the sulphur and obtaining the met

It is a very common error for chemical beginners to imagu
that a certain result will siways follow the addition of d cer-
tain substance to a solution of the same body. Thus, for
example, a beginner might imagine that sine, in whatev>
state of solution, will always be thrown down by hydro-
sulphuric acid, and that manganese, in whatever solution, will
siways be thrown down by hydrosulphate of ammonis. This
is not so. The conditions necessary to ensure these, or any
Other chemical results, lie in a comparatively narrow spact
they can only be learned by practice,, and the appreciation

f rmed of them constitutes the main point of difference between
an expert and an inexpert chemical analyst.
For the present we will have done with manganese and
nc, my especial object being to fix on the reader's memory »
e nature of the changes effected on solutions of these metals
by hydrosulphuric acid, and hydrosulphate of ammonia,
he reader must not infer that the re-agents mentioned are
the only ones for zinc and manganese ; there exist several of
. jual delicacy, but the faot especially to be remembered is
this : — Hydrosulphurio acid, and hydrosulphate of ammonia, are
sts for all fhose substances which a beginner would consider to be
m etals .

" Which a beginner would consider metals," — What is the
meaning of this expression r Why, the meaning is this : Lime,
clay, and other earths, the beginner would not suspect to be
metallic compounds ; — they are nevertheless J they are each
q oxide, or rust of a corresponding metal ; and the metals
which form earths arc said to be terrigenous or earth-making
metals. Again, the reader does not usually associate the
Idea of a metal with the alkalis, potash, and soda : neverthe-
less, these also are oxides or rusts of corresponding metala
Which are said to be kaligenous or alkali-making metals.
Well, then, let the student remember the following facts : —

1. Neither the earthquaking nor the alkali-making metals are
precipitated from their solution by either hydrosulphuric acid
or hydrosulphate of ammonia.

2. All the metals remaining, constituting by far the greater
number, and termed by chemists calcigenous metala, are
precipitated by hydrosulphuric acid or hydrosulphate of
ammonia.

(3.) Solutions of all calcigenous metals save uranium, iron,
manganese, cobalt, and nickel, are precipitated by either
hydrosulphuric acid or 'hydrosulphate of ammonia.

4. The colour of the precipitate is black.

5. But solutions of sine and manganese yield a precipitate
which is white. ' *' r

0. And solutions of arsenic, cadmium, antimony, and per*
salt of tin, yield a precipitate which is yellow.

The preceding are amongst the most important of funda-
mental chemical facts; the reader should master them,
thoroughly, not resting content with being able to think them
out, but the facta should become part and parcel of the brain
itself, so that the student, if roused from his slumbers at night,
and asked any questions involved by the six generalisations
which have been given, should be instantaneously able to
supply the required answers.

LESSONS IN GREEX f -No. IX.

By Jour R. Baann, D.D.

THE THIRP DECLENSION {continued).

There is yet another class, of which the stem ends in v or
vr. As examples take t) f&ic, f>tv-oc, the nose; b M^
fcXftv-oc, a dolphin', 6 ytyac, yiyavr-oc, a giant ; 6 oSovft
ocovr-oc, a tooth (Lat. dens. Eng. dentist.)

S, N, pic JcAftc j yiyae otovg

G. plv-oc diKiplv-og i yiy avr-oc otiovr-Of

D, piv-i dtXifilv-i j yiyavr-f etiovr-i

A, plv a StXifiv-a 1 yiyavr-a o$ovr~a

V* plv foA^if {iv) I yiyav oSovc,

P. K. jilv-fc £«Xfei>-ec \ yiyavr-tc edovr-tf

O, jilv-wv &e\<piV'utv I yiyavr-«v otovr-btv

D. (ft-oi SiXji'Vi \ yiy&'Ot oiov-ot

A. piv-ac. dtX(plv ac. yiyavr-ac o&ovr-ac
V. !

D. N.A.V. piiv-t 8t\fiiv-t j ytyavr-i oSovr-t

G.D. piv-oiv SiXtplvotv I yiyavr-oiv otiovr-otv i

To this class belong the adjectives in 1, ac, aiva, av, as
pcXac, fuXaiva, ficXav, black, g. peXavoc, piXaivrjc, piXavoQ,
and raAac, raXatva, rdXaV, unhappy ; 2, irac, traoa, irov. all,
every, g. iravroQ, iraotic, sravroc, and its compound airac,
avaoa, anaV 3, Uutv, Uovoa, Uov, willing; g. Uovro^
UovonUt Uovroc, and okvv, ateovoa, oueov, unwilling (a privative
makes Uwv into <rr«v) 4, the adjectives in ttf, totra, tv, v. £,

THE POPULAB EDUCATOR.

Xafuie, xapueaa, xapuv f lotdy which here in the dative
plural of tne masculine and neuter ^.-nder f«i instead of ueu
as it U in \tif9uc, left behind, fat the participles in iif, f i*o, tv 9
form the case regularly in siet.

s. y.

P. JV.

V. 2V.jf.K.

G.D.

8. y.

P. N.

V. .

D. jv.^.f.

G.D.

Xaputc

Xapuvroc

Xapuvrt

Xapuvra

X apuv

Xapuvrtc

Xapuvrmv

Xapun

Xapuvrte
Xapuvrt

X<tpUVTQiV
XltfBtVTOQ

XufBtvrt

XttfOtvra

kttftku;

XufOimr

XitfBirrvv

XeifOun

Xu£0fvrac

XtifOlVTtC

XttfOtvrt
XtifOtvrotv

\apu99a

Xapa<r<nK

Xapuavy

XapU99av

Xapu99a

Xapavvai

XapU9amv

XapU99aiq

Xapuevaf

Xapaevai

Xapuava

Xapuacaty

XtifBtura

\n£0iioav

\«ia&t<ra

XufQttgat

XufB&wv

XujOuffatg

Xt*Jf9ttoaQ

XttfOuvai

XiifOuaa

XtifBmratv

Xapuv

Xapuvroc

Xapum

Xapuv

Xapuvra

XapuvTwv

Xapuv*.

Xapuvra

\apavrt

\apavn*v

Xii+Bir

Xii+Qivroc

Xno9tvn

XufBtv

XiifOtv

Xitf&tvra

XufBlvrmv

Xttf&um

XiipQtvra

Xu+Bivra

XtiipBtvrt

Xiiffavrotv

at the end of the word and before „

disappears in the middle between rowel*. Noons in tug name,
in the accusadre lingular a. as d in the seccsaxire plural «cj
take in the genitive •ingular what is called :he Attic form m
*#Ct instead cf »c; and in the dartre s;ng*iUr as well as in the
! nominative plural* admit contraction ; which, however, as
j commonly not found in the accusatiTe plural. If a Towel
| precedes erf, the whole singular and plural is contracted, as at
i x<**Y- Nouns in ait »°d ore take the contraction only in the
I sccusatiTe pluraL The words about to be «*— «*t^ arc •
i 3a*i\ivc, m kinf ; o x°**Y» « sssssnrir of liquid (about a gallon) ;
o, if 3of f , a bmil or rs*\ «* ox ^Xatin *•*, bow) ; and *} <
mm o>.H 1

>W«C

1 D.
' A.

» r.

P..V.
G.
Z>.
-d.

D.-V^.r.

CD.

3aft\iv£

SaTiXi a

Aifi\i?

SariXilc

,$an\it-9t
iaTLVi -a f

JaviAc-oiy

Xoerc

Xotl

\oia a
\ocr

\Oflf

\otivt
\o % ta,as

Xoc-ocr

VoCABCXAaT.

£o-<*
4e-i

.3orr
Jof

7r»C

IP"**
ipor

Tfdwt
(7P«-«C)

7P«-«
nw-sir

VoCABULAnT.

Evs-opoc, ov (with gen.} ( easily
passed, abounding.

K*riXo£ t a. «y v loquacious.

+i\av9p*Toc, man-loring, phi-
lanthropic.

Auuv*, I make smooth, polish,
masticate.

Oafpatvofuu 'g ), I smell some-

Acrtf , ivot, 4» * beam, ray.
EXffoct avrot, &, an elephant,

irory.
Bpv/ia, arog, to, food.
M«x». »tc. if. flfc^it, battle.
Xwpa af, if, country, district.
Ai/3wy, ifc, if, Lybia, Africa.
'HXcoc ov, o, the sun.
A tfroct he himself, (Lot. ipse) ; thing.

6 avroc, the same, {1st. lion, once (an enclitic).

idem).

Exxbcisbs.— Gnixsi-EvoLisH.
Ov wafiv avBpvroic avroc rare nmv. Tvtf otuvm ra
fipt^fiara Xiatrofuv. Oi ctXf*y%£ ftXavffpmroi tiaiv. Evnv*
avipoi ayaQov xavra mama arcpci«*c erociv. FloXXat AtJiijf
X«^mic ipwopoi U9\v tXi+avroc. Tlavriz mmrtXov avQpvvov
txOaipowtv. T«f yiyam s*arf ay suixa s*poc rorc ©corf. Taic
rstr sjAiov asrieY x ai P < Y ur ' '*"*»' < f7 Mf 'trip oc+paivi99ai* m

ExoLisB-Gmns:.

We bare irory. Ifory is produced (717^0/104) in districts of
Africa. The rays of the sun delight the shepherds. The bro-
thers and the sisters are delighted by the rays of the sun.
The sister is lorely. We admire fine irory. Many elephants
are in Africa. The business of the teeth is to masticate the food.
It is the duty of every man to worship the dirinity To the
gods there ones was (in idiomatic English, the gods once
a) a war against (s-poc) the giants.

Ax*-VX«i-Ct **£t tft the hero

Act ilie*.
O0r**irf, K*f, «j. Urate*.
Tort re, <«»c, o, a parent.
"Iiiv*»r. tmc. 6. a jTitsr.
No/icrc- Ca *C« ^- * *he:»Lcrd.
No/ii|. *c, v. a pasture.
ErifitXua, ct£, t), atUntion to,

care.
Aepoc. or, v t idle talk, chatter.
Op0aA/iof , or, o t an eye.
Kroof, or, o, Crrus.
'O/iiy }>©♦;. or, o, Homer.
IIar«v:c.\of , or, i, Patrocluf.
TifXf iia\cc» or, u, Telemachus.

*§>r«#o, ofoc. o, Hector.

A\-api9Toft ov, vnthankfuL

IIo.Vr\o7oc t ©a, talkatire.

Ap\- (g.., I gorern.

Arifia~*, I honour not, dis-
honour, despise.

Ejco^m 'd.;, I liken to, com-
pare witt

Srm, I sacrifice.

♦orcr^, I put to death, kill,
murder.

BorAcyuu, I wish, WQL

Tt (enclitic)-
both.

Accordins; to o^ovc *** formed words compounded with
•Jevc, ss o, n /tmiovc, havimg on* Mh, g. fiovoZorro^\ accord-
ing to 7170c* adj«tires in oc, g. arroc, ss 6, if amafiac* tsstar-
dmd, umaarUd, g. avrof.

I pass on to the second great drrision of nouns, and proceed
to speak of

B. Norirs wvick ik thi Gexittti hate a Vowel bstors

TH» TBaXISTATIOX OC.

And her^ f first, I must take up substantiTes which end in
f*?. aZ{, and ore. The stem of these ends in v. The v

Exxxcises. — Grbxk-Escubh.
Oi ,3aei\t(C txiftiXtiav exoret rmv woXtrAr, "H cysXf ry
voful irtrai. 'Exrmp vr 'Ax'iXX<mc pavtvtra*. Oibpcicrmc
Qtoic this Bvovviv. Krpoc s*alc av a7a0w yovtw. O*
axapivroi rovg joveac artpaZovetr. TIuOov, w s-ax, rs«c
yovivmv. TijXf/iaxoc ifr 0^i«o*«**c rlo^- BorXoo ru»c 70VMC
xpo a*avroc tv ripaic ix**"- °* r *»» f 7P a *" ^ayot na strsi
riiponriv. KaX»£ apX«*Ct ** /3aox\fv. Ai 7paff srsAsXeyst
, u<nv. Oi vofulc rqv flcZv aytXrir c<( vo/nf? ayoveiv. 'O^ussec
roi'C 'Hpac opOaXpovf rotg rvv fiovv itmaZu. JlarpocXof fiXsc
nv AxtAAf^c- Krpov, rov rw Uipwv f3ao*iX<a, is*i r» re apery
jeoi ry o*oS4a BavpaZoiuv.

E3COLXSH-GbJ»K.

The flocks follow the shepherd. The king has care of (for)
the citisen. Ears are tired by the idle talk of the ola
woman. An old woman is talkative. The shepherd leads the
herd of oxen to the city. Oxen are sacrificed to the gods by
(va-o with g.) the priests. O priests, sacrifice an ox to the
gods. Children lore their (the) parents. Parents are lored
by their children. It is the business of a good shepherd to
take (hare) care of his herds.

• The rerb ten with a genitiTe, as here,
Any *ft&'* t*«*m{»f m.

it u the

Ir the second place I must ask your attention to nouns end-
ing in 17c* «c ; **c (g. **oc) and «c and w ( g. 00c) in as (g. oocX
oc (g- coc). The stem of these words ends in 9 ; the 9 remains
at the end and before a consonant, but disappears in the

* That ia, x°*"£ ** contracted into xo£r, xcta into yeS,
Xocmv into x°* y * i 11 *! X°* a C mXo X«^C*

LESSONS Itt ITALIAN,

middle between two Towels. In the dative plural one •* dis-
appears, e.g. ,6 0«c, a Jackal, toiq 0w-<n.

Of these words, let us consider, first, those which end in
m£» if- Hie terminations j?g (m. and f.), «c (n.) f belong only
to adjectives, and to proper names terminating in adjective
forms in vjyc, Xi/c, ytvijc, Kparrjg, prjtiijg, xtiBqg, aOtvrjg, and
(«Xfijc) cXifc* The neuter presents the pure stem.

The words of this* class suffer contraction in all the eases,
except the nominative and vocative singular, and 'the dative
plural, after dropping the c\ The words ending in *A«ijc
being contracted into icXifc, again undergo contraction in the
dative singular. Learn both the 'contracted and the uncon-
tracted forms I am about to give of d, tj, rafifr, clear, to 9aftc
and if rptffpitc, a Trireme, or galley with three banks of rowers

'N.
(?.
D.
A.
V.

y.
o.

D.
A.
V.

Singular.

ffcupijc oaftg

(oaf ioq) aafovg
yrafi-Y) 9a fit
(rajt'O.) 9a<prj ea<ptg
aaftg 9a<piQ

Dtnl. N.A.V.

Plural.

!9aft ff)<rae)ctc (aaftajaafij
<ra<pi-(A>i>)(ra$i*v
9a$i9t

(<ra<pt-ag)aa$ug ((7a^i-a)<ra^if
(oa<pi'ig)oa<pug (<Ta$i-a)<Ta<f>q

9aj€-t 9afti

Od). oapt-oiv oafotv

rpiJipifc

(rpiTjpt-og) rpitjpovg
(rp»ifp€-c) rp«|p«
(rpii|p«-«) rpinpn

(rptqpc-fc) rpctipcic
rpitjpc-Av and rpitjpvv
rptrjpi'Oi

(rpeifpe-ac) rptijptig
(rpiijpt-tg) rpinptt£

Dual, rpcifpc-e and rptijpij

rptrjpt'Otv and rpiijpolv.

I subjoin the declension of the proper names XvKpartjg,
Socrates, and TltpucXtijg, Pericles; as strictly proper names, they
are found only in the singular.

JV.
G.
D.
A.
V.

XuHCparng

EwKparovg

EuKpartt

ZvKpaTTj

2«*jepar<c

!TIepiK\iijQ)
UtptKXei-og)
in<pcc\<e-V)
IIipucX<c-a)
ntpueXttg)

TlipucXrjg
TItptxXtovg
(IlcptrXf ti)TI$f *Xf X
ncptxXca
UtpucXng

Mark the contraction in the dual of rpirjpu into rpiijpt, and
not into the usual form in u.

In. adjectives in ijc, f c, when these terminations are pre *eded
by a vowel, ta is commonly contracted into a, as IlcpccXca,
and not into if, as in 9a$ta vcupij ; for example, aKXirjg, un-
renovnud, makes eutXtia into atXta, in the masculine and
feminine accusative singular, and in the neuter nominative,
accusative and vocative; so v^ing forms vyia.

Proper names of this termination, as well as Api/c, Mare, in
the accusative singular, follow the first as well as the third
declension, and are therefore denominated Heteroclite (that
is, of different deeleneione) ; accordingly, we have both £wcparjy
and Swrparqy. But in those ending in kXtjq, the accusative in
ft? is not Attic, and therefore not allowable.

YoCABULaAY.

Acpartjc, tg, immoderate.
AXnBng, cc, true.
Arvxnc* fCt unfortunate.
Afarrjg, ic, unknown, unseen.
'EXmdng, <Ct marshy.
'HpocXifc, ovCt b y Hercules.
ZoetocXtfC, ©t/c, 0, Sophocles.
AovXsta, ac, i?, slavery, servi-
tude.
lyiucn, 17, India.
O/itXta, >/, intercourse (dak)

2*»rijpca, ag, >/, salvation.
Tpayy&a, af, 17 , tragedy.
AvaCayopaCt ov, 6, Anaxagoras.
Erafitivvviac, ov, 0, Epami-

nondas.
2o0i9ri}Ci oy, 0, a sophist.
KaXa/xoc, ov, A, a reed.
Ilora/ioc, ov, 6, a river.
To7toc, ov, d, a place.
Aio'xpoc, At ov, shameful.
EXcaipw, I pity.

Exbbcises.— Qbebk-Ekolish.

Ac SofocXiovc rpaytpdiai coXat ti9tv. Toy Zwcparif «rt ry
eof c? Bav/taXofuy. Swcparct iroXXot fiaOtjrai uoiv. *fl Iyouriy
irapa re rot'c troraftovg kcu rovg kXuhig roirovg ftptt icaXapovg
woXXovg. Atyt ati ra dXrjBtt, u> wai. Avalayopaq, 6 aofiffrrig,
sWaeraXoc nv TltpucXiovg, Q 'Hpa*X<t£, roig arvx*9i ourriptav

it a fi% 1 - £ira/i<4Vwvo k ac warpog yv afavovg. EXfaips rev
arv%fi avQpvwov. OptytaOi, m yiavta, aXriQvv Xoyotv. 01
acpareTf airxpav tovXtiav dovXivov9iv. Mr; o/uAtav fjgc
ajcparci avOpvxy.

Emolish-Obbbx.

Socrates had (in Gieek, fo Soeraiee woe) wonderful wisdom.
Pity unfortunate men. We pity unfortunate men. Many
youths were disciples of Socrates. Socrates had (in Greek,
to Socrates was) much wisdom. They admire the wisdom of
Socrates. The immoderate (man) serves a shameful servitude.
We admire the beautiful tragedies of Sophocles. True words
are believed. I pity the life of immoderate men. Have not
intercourse with immoderate men.

LESSONS IN ITALIAN GRAMMAR.— No. III.

BY CHABLE8 TAU9ENAU, M.D.,

Of the Univertitv of Prria. Professor of the Italian and German Languages
at the Kensington Proprietary Grammar School.

{Continued from page 21.)

Italian, m

Pronounced.

English.

Vtg 9 o
Figai

veg-gof
fld-iee
Od-iee
f6od-jee

I see

Fasten !

099%
Fnggi

To-day
Ply!

Pace

pah-tchai

Peace

Pece

pai-tchai

Pitch

Pino

pee-no

Pine

Poco

pd-ko

Little

Bute

p$o-tai

He has a bad smell

Riparo

ree-paVro

I repair

Impero

im-p6-ro

Empire

Tapino

tah-pee-no

Wretched

Sapone

sah-po-nai

Soap

Impune

im-poo-nai

Unpunished

Pappa

pfehp-pah

Pap for children

Peppe

pOp-pai

Joseph, Joe

Pippo

pip-po
kop-pah

Philip, Phil

Coppa

The occiput, goblet

Zuppa

tsoop-pah

Soup

labc %

t<h.bai

Consumption

Teco

tai-ko

With thee

Tipo

tee-po

Type (a model)

Topo

td-po

Mouse

Tubo

t6o-bo

Tube

Altar e

ahl-tah-rai

Altar

Altero

ahl-t6.ro

Haughty

Allire

ahl-tee-rai

To mount

Alloro

ahl-16-ro

Laurel

Altura

ahl-too-rah

Height

Atto *

uht-to

Act, action

Getto

jet-to
ftt-to

Cast, throw

Fitto

Rent

Cotto

kdt-to

Cooked

lutto

t6ot-to

All, quite

Vano

vah-no

Vain

Voro

vai-ro

True

Vino

vee-no

Wis*

Voto

vo-to

Vow

Avuio

ah-voo-to

Had

Bavaro

b&h-vah-ro

Bavarian

Severo

sai-ye-ro

Severe

Divino

dee-vee-no

Divine

Lavoro

lah-v6-ro

Labour

Dovulo

do-voo-to

Debt, duty

Daw*

dahv-vee

He gives you

Evp%

ev-vee

Is there

Udiwi

oo-div-vee*

He heard you

Dow*

ddv-vee

I give you J
Was there

Fttwi

foov.vee

f When the oft are followed by a, 0, or tf, they are pronounced
\n each syllable like English g big L

THE POPULAR EDUCATOR.

Italian*
Zara
Zero
Zita
Zona
Zttgo
Matata
Oaxera .
Ajtimo
Batote
Asafa
Paw*
Ptzto
Pizzo

Puzzo
Pagato
Ithaca
Agape

Vegeto

Actio

Gaeta

Cedet*

Codies

Egida

Taeito

Vagi to

Rigore

Epocha

Pagode

Jacopo

Aguto

Acuto

Cieuta

Osduto

Apogeo

Capacitaio

Educato

Vocativo

Zebedeo

Tucidide

Abituato

Zodiaco

Agarieo

Idiota

Abigcato

Vegetativo

Decapitate

Decaduto

Agitato

Epicuro

Pedagogia

txah-rah

dzd-ro

tze*e-tah

dzd-iuh

ts6o-go

mah-tsah-rah*

gah-dxai-rah

ah-dzee-mo

bah-ds6*to

ah-tsu-fah

pah-taof

p6»teo

pee-tso

p6*tzo

p6o-tzo

pah-gah-to

ee-tah-kah

ah-gah-pai

ree-kah-mo
vft-jai-to
ah-tchai-to
gah-ai-tah

tchai-dai-tai

kah-dee-tehei

ai-jee-dah

tah- tehee- to

vah-jee-to

ree-g6-rai

epo-ka

p&h-gd-dai

jah-ko-po

ah-g6o-to

ah-k6o-to

tchee-k6o-tah

tchai-doo-to

ah-po-jd-o

kah-pah-tchee»tah*>to

ai-doo-kah-to

vo-kah-tee-vo

tzai-bai-de-o

too- tehee- dee-dai

ah-bec- too- ah-to

dzo-de'e-- ah-ko

ah-gah-ree-ko

ee-dee-6-tah

ah-bee-jai-ah-to

vai-jai-tah-teVro

dai-kah-pee-tah-to

dai-kah-d6o-to

ah-jee-tah-to

ai-pee-k6o-ro

pai- dah- go-je*e->ah

HI.

English.
Zara, a town
Cypher

Girl

Zone, girdle

Omelet

Mazzara in Sicily

Magpie

Unleavened

Half-cooked

He comes to blows

Pool

Piece

Moustache

A well

A bad smell

Paid

Ithaca in Greece

Agape, or Christian
love-feast

Embroidery

Buxom

Vinegar

Town in Naples

Yield!

Cadiz « •

Aegis

Tacitus

Loud wailing

Rigour

Epoch

Pagoda

Jacob

Nail

Acute, ingenious

Water hemlock

Yielded

Apogee

Capacitated

Educated

Vocative

Zebedee

Thucidydes

Habituated

Zodiac

Fungus gt owing on
larches

Ignorant

Stealing of cattle

Growing .

Decapitated

Decayed

Agitated

Epicurus

Education and go-
vernment; of chil-
dren

There are si* semi- vowels in the Italian language, so called
because in their utterance a vowel must be placed before the
consonant. They are not pronounced in one syllable only, as
in the case of the mutes, but require the utterance of two syl-
lables, which syllables are substantially the same though in an
inverse order. The semi- vowels are :

1. F f, named in the alphabet ejfe (pronounced ef-fai).

2. LI, named in the alphabet eUe (pronounced 61-lai). It

♦ In this add a few other cases, I am compelled, for the stke of
completeness of system, to make a slight departure from strict
orthography, rhis word being properly written Mazzara, as well
as the following words gazzera, azzimo, bazaotto, azzitffa.

f There is very little difference between the pronunciation of the
single z and as. The zz, as well as a, may have the sound of tz in
the word rateer, or dz in the word adze. According to modem
'Orthography, the s is generally doubled between two single vowels
in the middle of a word, but not after a consonant and not before
diphthongs the first vowel of which is I: as, for examples, ia, te,
to, where it most remain single, end 4ms tftV* hard sound.

has two sounds—one like the English consonant 1 j the i

is a peculiar sound, of which I shall have occasion to speak im
the pronouncing tables.

3. M m, named in the alphabet emm* (pronounced Im-mai}.
To insure perfect accuracy in the pronunciation, I may remain
that when m is preceded by a vowel with which it forms one
syllable, and a consonant being the next, it mutt be vex*
softly sounded, and the voice must glide, quickly to the next
consonant,' almost as if it formed part of the same syllable)
for^example,«if^t«ofk», ahmT>ee-t£©e-6-nai, ambition; empk %
em-peeo, impious ; ombra, 6m3>rah, a shadow.

4. Nn, named in the alphabet enrne (pronounced en*nai)«
Generally speaking, this letter is pronounced iust as in English f
but- the observation made on the m is equally applicable to »,
In similar circumstances, the voice must glide quickly from the
» to the succeeding consonant ; for example, andare, ahn-dah-
rai, to go ; entrar*, enTtrah-rai, to enter ; onda, 6n^dah, a wave.
After g t n has a peculiar sound, which I shall have occasion
to explain in the pronouncing tables. Often » ia pro-
nounced like m before words commencing with the con-
sonants b, m, and p ; as, gran bestia, pronounced grahm"b6-
steeah, a boorish, insolent fellow, great blockhead, &c. ; sosipire
in marmo, pronounced skol-p6e-rai inTmahrr-mo, to chisel in
marble ; eon poca fatiea, pronounced kompd-kah £ah»tee-kah,
with little effort. This u certainly the finest pronunciation,
because it is the genius of the Italian language* aa in the
classical tongues, particularly Greek, to soften the transition
from one word to another, and often from one syllable to the
other, bychanges of consonants.

6. Rr, named in the alphabet erre (pronounced e"r-ra # ), R,
when it is followed by a consonant, must be vibrated with a
stronger emphasis than in English ; and it is on the other hand
very soft before a vowel ; as, carta, pronounced kahrr-ta, paper,
and soft in cara, pronounced kah-rah, dear.

(7b be continued.)

LESSONS IN FRENC H.— No. LXXX.

By Professor Louis Fabqubllb, LL.D.
} 135.— Remarks on thb Foregoing Rules.

(1.) Although the compound tenses of the reflective or pro*
nominal verbs [$ 43, (6.), \ 46, (2.), § 66] take tore as an
auxiliary, the past participle of those verbs does not follow the
rule (2.) of the preceding section ; but comes under the same
rules with thoee conjugated with avoir. It agrees with the
direct regimen, when that regimen comes before it, and is
invariable when that regimen succeeds : —

Votrc scour a'eut achetk de belles Your eider has bought (hers**/ )

robes. handsome dresses, i. e. , far herself.

Cette femme *'est rendue mal- That woman has rendered herseb

heureuae. unhappy.

Aclute" in the first example does not vary, because #*, placed
before it, is an indirect regimen or dative, while the direct
regimen or accusative, robes, is placed after Che participle.
Rendue in the second example varies, because the word at,
representing femme, is a direct regimen, and precede* the
participle.

We will add a few extracts as examples : —

MFLECT1VB PRONOUNS.

TTsed as indirect Object*.
II nc se rant propose', pour
extraple, que la constitution la
pirn* simple des sneiens.

VOLTAIBE.

They liave proposed to themselves,
as an example, only the most simple
constitution of the ancients.

Used as direct Object*.
Ellettt sont pr o po ee es commsdts
modeles de douceur.

Quoted bt Beschxr,

They have proposed themseih** cm
patterns of gentleness.

• The er like the sound of the syllable «r in the Knghsh wort cns*\

4S8SON8 IN FRENCH*

II est ml, oju'elle et moi nous I
sjmrfe des yens.

Mouses.

ie langue latins et la langue
grscque w Boat loagtemps parUcs.

JS is frue, *A<rt sfc; and I have
spoken to each other with our eyes.

Neanmoins, U rftait conserve'
VmatoAtl prineipale. Bossuet.

i, he hen preserved to
the principal authority.

The Latin, and Greek language*
were long epoken of.

La vie pastorale qui **est conser-
ves dans l'Asia, a'est pas eans opu-
lence. YourAUta.

The pattorat lf^ twttoa mas 00011
preserved in Asta, f$ hot sptfftonf
opulence.

. (2.) "Whet %:onomlnal or reflective Verbs, of which the
second pronoun is an indirect regimen, are Accompanied by
another pronoun, or by a noun, used as a direct regimen, the
.participle agrees with this latter pronoun or noun when it
'la preceded by it, and remains invariable when the re'gime
direct follows. See Rules (4.) (4.) of the preceding sec-
tion i—

Intertable. ,
Noes noes sommee reproche' l*in-

Wt hav e r e pro ac h ed oureesses with
m fodtsereffpii.

Variable.
L'indisefe'tion que nous nons
•eomtoes reproobeV

The f/tutsciettou wuh which tee
have reproached ourselves.

t • Or to render in English the relations the same as in
French:— *

The indiscretion which we have ] We have reproached to oureelvee
reproached to ourselves. \ the indiscretion.

(3.) The participle past conjugated with avoir, and preceded
by a direct regimen, is sometimes followed by an infinitive.
In-such cases, when the direct regimen is under the govern-
ment of the infinitive rather than of the participle, the latter
of course remains unchanged : —

La regie que J'si commend a ear- 1 The nth tchteh I
pliquer. | explain.

(4.) The verb in the infinitive is sometimes understood } yet
the participle must follow the same rule, as if it were
expressed. The participle fait, followed by an infinitive, and
latest', followed by the infinitive of an active verb, are always
invariable : —

Elle a obtenu toutes les fareuM
ev'ella a twain (obtenir).
La maison que j'si fait batir.
Gtt hommes Is s6nt latest battre.

She obtained all the favours which
she wished {to obtain).

The housewhUh I have had built.

These men have suffered them'
selves to be beaten.

(5.) In some cases, it may be difficult to ascertain whether
the regime direct is under the government of the participle or
,of the infinitive.

If the regime direct is to be represented as performing the
action expressed by the infinitive, the participle is made to
apree with that regime in gender and number :—

•JeJatai ves seeourir leurs enne- I I saw them relieving their enemies.
mis. I

In this example it will be seen that les {the re'gime direct) is
represented as actually doing what is expressed by the
infinitive, and that the infinitive itself is translated by the
present participle.

' l£ however, the re'gime direct is to be represented as suffer-
ing the action expressed by the infinitive, then the participle
will remain unchanged, and the infinitive will* be translated as
a passive.. Thus: —
Je let al vM secourir par lean I 1 saw them rctteved by iheir

Further examples :—

Variable.
JeleseA vus reponsser les enne-
mis.
, • I saw them repel {repelling) the

Mnvarwjote.
Je 1st al vu
ennemis.
I saw them repeUedbythe enemies.

par les

Je Us ai vus prendre la fuite.
1 T saw them taking flight.
. Je lee si vus frapper.
. I saw tltem striking.

Les personnes qua j'si entendues
Hifaanter.
1 The persons whom I hcardsW

Je let ai vu prendre tar lefait.
/ saw them taken in the deed.
JelessAvu frapper.
/ saw them struck.
Les chansons qua J'si entenau
chanter.
The songs whhh I heard sung.

(6.) The participle past of neuter verbs, conjugated with
avoir, and those of unipersonal verbs, are always invariable : —

Sow much good has she not done,
during the few days that she reigned .

The excessive heat which we have
had, hat caused much sickness.

Que tie bien n'a-t-elle pas fait,
pendant le pea da jours qn'elle a
rfgni t FlIchier.

U - oheJeurs excesslres qu*il a
/.>/.', out cause* beauooup de mala-
dies. CONDIIiAC.

(7.) The past participle never afcrees with en, because e
can have no other relation to the participle" than that or an

indirect regimen.* The presence of en does not of course prei
rent the agreement of the participle with a direct regimen
preceding the vetf):*-' '

ATez-vous mange* des traits P
JVti «j munge\

Tout Is mend* m*s oflert ties
terricea, et penonne ne m'en a
rendu. Ham. de ILlhttenom.

Have you eaten of thejruttt t

have eaten of them.

tsverybody tendered me services,
and no person rendered me any. ,

Etf, preceded by the Direct Regimen of the Participle.

Casskts, naturally proud and hri-
perlous; sought in the death' of
C<e*cronlyrevens*Meomeinjewiee
which he had reeetped front hint.

Cas-iiiA naturellement fler etira-
l-t'i ii'iix, n> eherehait dans la ptrte
de it'tiar que la vengeance de quel*
quea ifif ant qu'U en arsit reeves.

VEBTOTi

Retidcz graces au ciel qui nous
en. a t+tigira. CORKEILLE.

Render thanks to Heaven, which
has revenged us for it.

(8.) Le pen has in French two meanings : it signifies a small
qymutity, or' the want of-

When it signifies a small quantity, the participle agrees with
the noun which follows le pen : —

Le pen d'affeetion que vous lui I The little affection which you have
iLvtv: ttmtfgnic, lui a rendu le cou- shown him, has restored ins courage.
rage. I

When Upeu is used in the sense of the want of, the participle
remains unaltered : —

Le peu d'affeetion que vous
ares tetn&if/ni, l'a deoouragl.

lui I The want of affection which you
have shown Mm, has discouraged
I atsi.

$ I3s\— Thb Advbeb.— Rules. — IPlacb of the Adverb.

( L) In French the adverb used to modify a verb in a simple
tense Is generally placed after the verb : —

Que de gens prennent hardiment I How many people assume boldly
le mo*que de la vertu I I the mask of virtue I .

ScUDeBi. I

(2.) Adverbs of place, and those used in interrogations, have
the same place in French as in English : —

<>>■• >.-«t votrefrere? IlesttW. I Where ie your brother t He is

(3.) In compound tenses the adverb is placed between the
auxiliary and the participle : —

Vous avesmaJ fait. I You have done wrongs

II nom it bien re^us. | He received us well.

{A.) Adverbs of manner ending in ment f may, in Compound
tenses, be placed before the participle or after it, when they*
are not very long, or followed by other modifying WOrdSi
When, however, they are folio wj&d by such words they must
be placed after the participle : — '

Cats eat heureusement exprime*. \ ,_ . - *.---., .- : ,

Cda e «texprimeAeiir««ew«nl. j That w ncppk\f esnnwed.

Q ret uiu heureusement atempe. | He came Jbriunately in time.

(5.) The adverbs aujourd'hui, to-day; demain, to-mofrow^
hier, yesterday, may be placed before or after the verb, but
never between the auxiliary and the participle. The adverb
diivant ago, more t must always follow the participle :—

* NoC'l *nd Chapsal, pag^ 165. 8everal grammarians cell en it times a'
rfgimen direct. We think with Bescherell* {Dictionnaire national, paps
11 14), that en does not represent the entire direct regimen, but onlj a part
trf it, or rather merely refers to it; the direct regimen being itself under-
ttood. Ex. ATex-voufc des livres? J'en ai. Have you books t I hem
worn** In the latter tentenee, the words quelqaea uns, the direct object, is
u tidentoort after the verb ; J'en ai queigues uns, and en is rather a reiaraaee
to h, than a substitute for it. The literal translation of the sentaase wssV
■how title: I have of them a few.

THE POPULATt EDUCATOR.

Nous soxnmes arrives at/jounf*-
Aw*. m

Yotre ftfcre •'est bless. Ater.

Av jour <T htd 11 fait bean temps ;
" peluvra.

GUtAULT DUVIVTEB.

IPe came to-day %

Tour brother hurt himtetfyette
day.

To-day, it it fine toother; I
saorrcw ft will rain.

§ 137.— OB8EBVi.TIOKg.

1.) The adverbs of comparison, pine, moine, must be repeats
•we every adjective which they modify : —

II est moint paresseux et
. obttfal que son frere.

He If bat idle and obstinate I
hit brother.

(2.) These adverbs, and the adverbs of quantity, need not V
repeated before every noun; but the preposition de, which
must always come between pen, trov, beaueoup, tan!, plus, nunnt
and a noun or an adjective, used substantively, must be repeat*
in every case :—

There would not be muck troubi
and misery in the world, • • •

ThUbookeeUer hat many good an
bad works in hie establishment.

II n'y aurait pas tant de peine
at de misere dans ee monde. . • •

Ce libraire a beaueoup de bons
et de mauvsis ouvrages dans son
nisgisin.

(3.) The adverbs mieuz, letter; pis, worse, must not be
confounded with the adjectives meilleur and pire. See note;
SH(7).

ANSWERS TO CORRESPONDENTS.

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before you begin another set ; reading and conversation will supply you
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faiM, leaven ; the latter again most probably cornea from £«_, to boil.—W.
V. Yates (Orm skirt) : A •• Pupil Teacher's Association" might be formed
with great advantage for the study of the principles of General and Com-
parative Grammar, in relation to all languages but especially the English,
which is now a compound of all languages, taking, as it does, new words
daily from every tongue under the son. This association might take Dr.
Beard'a Lessons in English in the P. E. aa a foundation for its studies and
inquiries. Every word in English should then be traced and silted till its
origin and true meaning are discovered, as well as its various and curious
applications. Thus English Philology would lead to Universal Philology ;
and the study of names or nouns would lead to the study of things, or to
Natural Philosophy ; and these again, to that of Mental Philosophy.

T. Gut (Broomside): The verb cwtcXX_ comee from wv, together, and !
ffTc\A», I set. place, or bring, and therefore siguifies I set together. I place
together, or / bring together. In Acts v. 6, it is applied to the act of wiuding ,
up a dead body, or bringing its limbs together In a winding-eheet or cloak. In
1 Cor. vii. 89, it ia applied to the bringing together, or shortening, of periods j
of time, as the pexioda of life and death, so beautifully expressed in the
Church Burial Service, " in the midst of life we are in death."

E. CaoiSLBT (Littleborcuvh) ; Consult Barlow on the "Strength of

Timber and Iron."— Eta Dilta : If a workman labours twelve or ______

hours a-day, the best part of Physical Education for him is Bathing or
Swimming, if it agrees with him. As to the best plan of learning Geometry
and Euclid, see Cassell's " Self and Class Examiner in Euclid,- price 3d.

J. Crossley (Hadcliffe) : Not quite.— J. Christie (Montrose) : Tow
plan ia good in idea ; but it would involve ue in an amount of labour front
whlch we shrink, seeing what we have already before us. Take oar advice
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Grolle means a rook; our dictionary does not tell at the rest-— SiLV-TAUon;
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Solution of question 17, p. 105. Cassell's Arithmetic; it la stated that the
hound runs 8 rods in the time that the fox rune 5 rode ; call this time It
then, since the hound gains 3 rods every lime called 1, we have 3 rede : 183
rods : : 1 time : 50 times, the hound runs 8 x 50= 400 rods^— IraanooTue
(Southampton) should consult an optician.— Tyro Johnson (kVnaanae):
Telemaoue, a popular French work, will coon be published at this osEsa,
8ee p. 88, vol iv., at the bottom. An edition of the Greek New Testament
may also be expected.— Philo (Nottingham): Thanks; ws renmamial
Cassell's Spelling Book aa the best for a little girt— O. W. A. ftBleejga):
Bead all our articles on the University of London, in vols tt. and itt. of the
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the Psalms into Latin verse is George Buchanan's, and it may be had of any
dealer in old books, from 6d. to 10s. according to the edition.— W. A. G.
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tion 12_*-_-0_-=-1200, the values of * are 31 86 and 3*14, We thiak
that more will be necessary for Matriculation than what is Dkety to be
printed of our Greek lessons, by the time he mentions. He bsk i

under articles to become a barrister. We cannot inspect and give optnioas
on MSB. without a regular fee.— J. B. Boss (Coventry) : We know of at
cheap editions of the Italian poets.— J. Midlxt (Hertford) t _Uedvad_

LITERARY NOTICES

FRENCH.

Now ready, price 4s. in stiff Wrapper, or 5s. strongly bound In eleth,
the First Part complete, consisting of the French and English, of Cab

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Threepenny Numbers, and will form one handsome Volume of eight hundred
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A Comtletb Manual of tor French Language, by P ro fi esor De
Lolme, just published, price 3*. neatly bound. This forme one of the
most simple, practical, and complete Guides to a thorough knowledge of the
French Language which has hitherto been published. The plan opou whisk
I it is conducted Is admirably calculated to accomplish the proposed object.
In the first place, the Grammatical Principles of the language are dearly
laid down, and. recondlv, these Principles are copiously illustrated by suitable
Exercises of English to be turned into French.

I Cassell's Lessons in French, in a neat volume, pries Is. la stiff eoven,
| nr Ss. 6d. neatly bound in cloth.

A Ket to Cassell's Lessons in French, containing Translations of all

the Exercises, with numerous references to the Grammatical Bulcs, pries

Is. paper covers, or Is. 3d. cloth.

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Monthly Parts, is. each.

Cassell's Lessoms in German, price 2s. in stiff covers, or 2s. 3d.
Sloth.

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Cassell's Ket to the Latin Exeecises, now ready, price Is.

The first volume of Cassell's Classical Library is now

rice Is. Cd., containing Latin extracts for translation on the following

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Ancient Geography; with a suitable Dictionary. The second volume,

which is publishing in weekly numbers, prices 2d. each, will ooosjet of

•eful Latin Exercises, or English sentences, to be translatsd into Lsdit,

with numerous references to Andrews and Stoddart's Letta GrajassaT, a

valuable treatise now in the press.

GREEK.

The Third Volume of Cassell's Classical Library will oontaia the

eta of the Apostles in the original Greek, according to the text of Augustas
ftahn; with grammatical, historical, and expository Notes; followed ays
I exicon, explaining the meaning of every word— the whole carefully
revised and corrected. This work Is well adapted for th 3 use of Bshosls,

.lieges, and Theological Seminaries, and will supply our Greek stodsatfs

ith excellent materials for practice in translation*

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is now ready, price Is. in stiff covers, or is. 6d. nsst cloth.

The Self and Class Examiner in Euclid, containing the enuncta-
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of Colleges, Schools, and Private Students, ia now ready, price 3d.

The Answers to all the Questions in Cassell's Arithmetic,
far the use of Private Students, and of Teachers and Professors who use tbJs
I ork in their classes, ii Just issued, price 3d.

LESSONS IN NATURAL PHILOSOPHY.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. IV.
ON GRAVITY AND MOLECULAR ATTRACTION.

GBNB&AL EFFECTS OF GRAVITY.

Universal Attraction and its Laws. — Universal attraction is
that force by which all the material particles of bodies are con-
tinually attracted or drawn towards each other. This force is
considered as a general property inherent in matter. It acts
ipon all bodies, whether at rest or in motion. Its action is always
mutual between bodies; and it operates at all distances, as well
as through all substances.

Universal attraction is called Gravitation, when it operates
among the heavenly bodies ; it is called Gravity, when the attrac-
tion of the earth causes bodies to fall ; and it is called Molecular
Attraction, when applied to the force which unites the particles
of bodies to each other. .

The ancient philosophers, Democritus (360 B.C.) and Epicurus
(300 B.C.), maintained the opinion, that matter was attracted to
common centres in the earth and the heavenly bodies. Kepler
(1600 a.d.) asserted the principle of mutual attraction between
the sun, the earth, and the other planets. Bacon, Galileo, and
Hook, also recognised the fact of the existence of universal attrac-
tion. To Newton (1665 a.d.) was reserved the glory of mathe-
matically demonstrating the laws of Kepler concerning the mo-
tion of the planets, and of proving that gravitation is a general
law of nature. This law is generally expressed in the following
terms : All bodies in the material universe gravitate towards
each other with a force which is directly proportional to their
quantities of matter, or masses, and inversely proportional, to the
squares of their distances.

Since Newton's time, the attraction of matter by matter has
been experimentally demonstrated by Cavendish (1798 a.d.), a
celebrated chemist and natural philosopher. By means of an
apparatus, which is called the Balance of Cavendish, the inventor
not only rendered sensible to the eye the attraction of a large ball
of lead on a small copper bullet, but he ascertained by this
experiment the density of the earth, and found it to be about 6&
times that of water. The apparatus of Cavendish may, therefore, I
be considered as a scale in which the earth, sun, moon, and planets
have been weighed.

Gravity ;—-The force which causes all bodies when left to;
themselves to fall towards the centre of the earth, is called gravity.
This force, which is only a particular case of the law of universal
attraction, exemplifies the mutual attraction which takes place
between the mass of the earth and the mass of the falling body.
The law of gravity is like that of universal gravitation, and
bodies fall to the earth with a force directly proportional to their
mass, and inversely proportional to the square of their distance
from its centre. Gravity acts on all bodies, and in every variety
of condition ; and if some bodies, such as the clouds, smoke, &c,
seem to be freed from its action by their riaing in the atmosphere,
we shall soon see that the cause of this phenomenon must be
referred to gravity itself.

Direction of Gravity; Vertical and Horizontal, — When the par-
ticles of a material sphere act, according to the law of attraction,
in the inverse ratio of the square of the distance, upon a particle
of matter situated without that sphere ; it is demonstrated in I
treatises on Rational Mechanics, that the resultant of the attrac-
tive force of all the particles of the sphere, is the same as if they
were all collected at its centre. It follows from this, that at every
point on the surface of tho globe the attraction of the earth is
directed towards its centre. The depression of the earth at the
poles, the difference in density between the masses of matter of
which it is composed, and the inequalities of its surface as to
mountains, valleys, and plains, are all so many causes which occa-
sion alight deviations in the direction of gravity, but sc slight as
to be sensible only by a very small quantity.

The direction of *he force of gravity is called vertical ; that is,
the straight line in which a body falls to the ground is called a
vertical line. At all points on the surface of the globe, the verti-
cal lines sensibly converge towards the centre— that is, their
directions are not parallel ; but for points which are at a little
distance from each other, such as the particles of the same body, or
of bodies lying near each other, the vertical lines are considered as
strictly parallel. It is obvious that no error can arise from thii
consideration in ordinary cases, when we remember that the mean

TOL. IT.

radius of the earth, or straight line drawn from Us centre to its
length. But when two points on the earth's surface are consi-
derably distant from each other, the angle between the vertical
lines must not be neglected. Thus, in the English measurement
of an arc of the meridian, the angle between the vertical lines at
Dunnose, in the Isle of Wight, and at Clifton near Doncaster,
was found to be 2° 50' 23" 38 ; and in the French measurement
of an arc of the meridian, the angle between the vertical lines at
Paris and at Dunkirk was found to be 2° 12' nearly. These
measurements were both made at the close of the last oentury, at
the expense of the respective governments.

A horizontal line may now be denned as a straight line per-
pendicular to a vertical line; it received its name, however, from
the consideration that it was a straight line which joined any two
diametrically opposite points of the horizon ; or that it was a
tangent at any point on the earth's surface, and therefore coin-
aiding with the horizon at that point.

Plumb-Line, — The vertical line of any place is determined by
the plumb-line. This name is given to a cord, having a small
ball of lead attached to one of its extremities, and having its other
extremity fixed or supported ; when the cord and ball are per-
mitted to hang freely, the former naturally takes the direction of
the vertical line, in consequence of the action of gravity ; for a
body which has only one point of support can only be in equi-
librium when its centre of gravity and the point of support are
situated in the same vertical line, as we shall see when treating
Of the centre of gravity.

The following cut exhibits a drawing of the common mason's
level, in which a plumb-line a c must fall on a certain point b,
in the fiducial line of the instrument, if its two feet are correctly
placed on two points of the level : —

The plumb-line does not indicate whether or not the direction
of gravity in a given place is constant. Thus, if a plumb-line
which is found to be parallel to the wall of a building at a given
period, should be found afterwards to have deviated from this
position, it cannot be inferred, without further observation,
whether gravity has changed its direction, or whether the wall
has departed from the vertical position. In treating of the
properties of liquids, we shall see that their surface can only
remain in the horizontal position, that is, remain level, when that
surface is perpendicular to the direction of gravity. But if this
direction were to change, so would the level of the sea ; the sta-
bility of this level, therefore, is a proof that the direction of
gravity is constant, or invariable. In the vicinity of a large mass
of matter, however, such as a mountain, the plumb-line has been
found to deviate from the true vertical by a sensible quantity, as
has been demonstrated by the experiments of several observers.

ON DENSITY, WEIGHT, CENTRE OF GRAVITY, Ac.

Absolute and Relative Density, — The mass of a body contained
in a certain unit of volume or bulk is called its density. The
absolute density of a body cannot be determined ; that is, we can-
not tell the real quantity of matter which it contains ; but we can
ascertain its relative density, or the quantity of matter which it
'contains, under the same volume, in relation to another body
taken as the unit or standard of comparison. This standard body
for solids and liquids is distilled water taken at a given tempera-
ture. Hence, when the density of zinc, for instance, is said to
be 7, this means that under the same volume or bulk this metal
contains 7 times the quantity of matter that water contains.

If v represents the volume or bulk of a body, M its absolute
mass, and D its quantity of matter under the unit of volume, that
is, its absolute density, it is evident that the quantity of matter con-
tained in the volume V, is V times D; whence, ii=zVD, From

this equation, we have 2) =r — ; that is, the absolute density of a

body is the ratio of its mass to its volume.

Weight. — In every body, weight is considered under three
aspects, viz., the absolute, the relative, and the specific weight.
The absolute weight of a body is the pressure which it exerts on
I any obstacle which prevents it from falling. This pressure is the

THE POPULAR EDUCATOR.

resultant of the flmei by which gravity acta on each of the par
tsetse of a body, and it increases with the quantity of matter in the
tody; thia principle is expressed by saying that the weight of a
body ie pmpcnUu aad to, or increases with, ita mate.

The rHetire weight of a body la tbat which is found by means
of a balance ; it is the ratio of the absolute weight of a body to
tint of another body selected as unity. In our system of weights,
the smallest unit is the grain, which is the seren-thm**rndth pnri
of a larger unit called the pvtnd Aroirdttpois, or th<» Import*?
pound. In Prance, the «nall**t nnit is the grinnu, which is the
weight of a enKc c '•"•■•vfrr cf distilled watpr at its ratiimum
density. Hence, a body whi?h weighs one grnmw, weighs also
15'484 groins, and these are the relators weights of th?s b^dy in
France and England ; bnt if other ur.i^s of weight were adopted
in these countries, the relative weights of the body would bo
altered, bnt the absolute weights of the body would remain the
same.

Lastly, the *pcc : f.c weightf or, as it is often called, the tpecifie
gravity, of a body ?s the ratio of ita relative weight, under a cer-
tain volume to that of an equal volume of distilled water at the
maximum density. Hence, if we say that the specific weight or'
specific gravity of sine is 7, the meaning is, that under an equtl
Tohxme or bulk, sine weigh? 7 times hearier than distilled

The weight of bodies cf equal volume being proportional U
their mass, it follows that if a body contains two or three times the
quantity of matter that water does, its weight must be two or
three times the weight of water ; consequently the ratio between
their weights, or specific gravities, must be the same as the ratio I
between tneir maszc?, or relative densities. Far this reason, the]
expression rela':.-: d>. ,*ily and *jxcific gravity are generally con-*|
sidered as synonj ino-^, or, at least, equivalent to each other. If, [
aowever, the action of gravity were removed, there would be |
neither absolute n->r relative weight in bodies, yet their densities
would remain to be considered. These could not be determined by
the balance ; but ve have seen that the ratio of the masses of
bodies is the same as the ratio of the forces which would com-
municate to these E-.a:scs the eame velocity in the tame ticc.

The weight P of a body being proportional to its mass JT, and to
the intensity of grant y which may be represented by g, the product
JUJrmay be taken as the measure of thu weight, that is PzzzMg.

In many instances, the centre of gravity may be found by trial
This is done by suspending the body by a string successively in
two different positions, and when it is at rest, drawing a straight
line in the body in the direction of the string ; we thus obtain
two straight lines whkh intersect each other in the same point :
this point is the centre of gravity required. For, in each position,
the equilibrium of the body can only take place when ita centre
of gravity is below the point of suspension, and in the direction of
the string produced ; it follows, therefore, that the centre of
gravity must be at the same time on the two different d i recti o ns )
of the string produced, and must consequently be at their point of
int>rs?cti:,::.

In bodies whoso form and homogeneity arc invariable, the
position of the centre of gravity is constant ; but where theeeare
i variable, the position of the centre of gravity changes with them.
The latter is the case in animated beings, their centres of gra v ity
varying with their attitudes, or postures. Thus, the pedestrian
who walks up a hill leans his body forwards; but he reversal
this position when he goes down the hill ; that is, he endeavours
in both cases to preserve the vertical which passes through his
centre of gravity, within the space between his feet, which am
his points of support, as shown in the following cut. The centra
of gravity of a well-proportioned man, when standing firm and
erect, is a point within the body iust about the height of the
navel.

Whence we have Mz

— , a formula for finding the mass when

the weight is known. If in this equation we substitute VD for
Jsf, according to the preceding formula relating to der.sity, we
have PzzzVDjj a second expression for the weight of a hz>ij. In
the case of a body whose weight, densiry, and volume arc repre-
sented by P % /)', and P, we h?.ve, ia like mamvr, Pz=zY'I/g t
Comparirg this result with the former, we have i' : 1" : : VI) :
VD\ VfhenDzzzir, we have P.P :: V . V; and when
-R=P, wc have VD=lYI)' \ whence we have V : V : : If : I).\
From these proportions we infer 1st, that when the densitiea of
bodies are equal, their weights are proportional to their volumes ;
and 2nd, that when their weights are equal, their volumes are
inversely as their densities. We shall soon show the method of
determining the specific gravities of solids and liquids ; but as the
speeifie gravities of gates are determined with relation to the I
atsaoapheric air as unity, their determination must be taken up
after wo have treated of the subject of heat

Centre of Gravity; Determined by Experiment. — The centre of
gravity of a b-.dy is a point through which the resultant of the]
actios* of gravity on all its particles always peases, whatever
position it may assume. It is demonstrated in 8tatice, that every
body has a centre of gravity.

The full investigation of the centre of gravity of any body
belongs to Geometry : but in many ordinary cases it can be
determined at once. Thus, in a homogeneous straight line, the*
centre of gravity is in the middle point ; m a homogeneous circle or
sphere, it is in the centre ; in homogeneous cylinders, it is in the
middle of the axis. In Statics, it is shown that the centre of
gravity of a homogeneous triangle is in the straight line joining
the vertex to the middle of the base, at the distance of two -thirds
of that line from the vertex. In homogeneous pyramids and
cones, the centre of gravity is in the straight line joining the
vertex to the centre of gravity of the base, at the distance of
three* fourths of that lino from the vertex.

Equilibrium of He.icy Bodies. — As gravity ia a single fores
whose direction is vertically downwards, and whose action is applied
at the centre of gravity of all bodies, equilibrium will always be
produced if this force be counteracted by the resistance of a fixed
point through which its direction passes. There are two eases of
equilibrium, according as the heavy body rests on one or severml
points of support. In the first case, the ctntre of gravity must
either coincide with the point of support, or be situated on the
vertical which passes through this point. In the second case, the
vertical drawn though the centre of gravity must peas within tha
base, that is, within the polygon formed by successively joining
all the points of support. In the towers of Pisa and Bologna,
which arc so inclined to the horizon as to seem just ready to mil
upon the passengers in the street, their equilibrium ia still maam*
tained, brcanse their centres of gravity are situated on the verti-
cals which pass through the interior of their bases. A man stands
more firmly in proportion as he extends his feet and widens his
base ; he can thus give to his motions more amplitude, unless bis
centre of gravity is situated without this base. If he stands on
one foot only, his base is diminished and consequently his firm-
ness ; these are diminished still more, it he stands on tiptoe. In
this position, a very alight oscillation will throw his centre of
gravity beyond the base, and destroy his equilibrium.

A man who carrie* a load on his shoulders ia compelled to lean
forwards, lest he should be drawn backwards by the load ; for his
centre of gravity when loaded and standing erect is without the
base ; these different positions may be seen in the foDowing out.

For a similar reason, any one who carries a load in front, as a
nurse with a chOd in her arms, ia obliged to lean backwards. So
bakers and pastrycooks, who carry their loads upon their heads,
require to be as upright as possible.

Difertnt States of £^i/^r*w#».— According to the position of

THE POPULAR EDUCATOR.

balance should be perfectly exact, the following condition* mutt
be fulfilled:—

let. The two arms of the beam, that is, the distances from the
knife-edge at x to the points of suspension of the scales, must
be perfectly equal ; for it is proved in Mechanics, that two equal
forces con only be in equilibrium by means of a lever when the
two arms are equal. Yet there is a method by which the exact
weight of a body can be obtained from a balance although its
arms are unequal.

It cannot be inferred that the two arms of a balance are equal,
by the single circumstance that when the scales are empty the
beam is horizontal ; for it is enough to hang from the longer arm
a lighter scale in order to make it so. To determine whether the ,
arms are equal, place weights in the two scales so that the beam
may take the horizontal position. Make these weights change
places from one basin to another ; the beam will still be horizontal
if the arms are equal ; if not, it will incline to the side of the
longer arm.

2nd. The length of the arms of the beam must remain perfectly
invariable during the oscillations of the balance. For this purpose,
the beam and the scale-hooks must be furnished with very sharp 1
points of support.

3rd. When the beam is horizontal, its centre of gravity must |
be in the vertical passing through the knife-edge and a little
below this edge ; unless this be so, the beam will not assume the
position of stable equilibrium.

4th. The balance must be very sensible, that is, it must oscillate
with a very small difference of weight in the scales ; and this
requires that the beam should be very easily put in motion. For
this purpose, it is made to rest on two supports in agate, or in
well-tempered and polished steel ; this greatly diminishes the
friction. In general, the sensibility of a balance is greater in
proportion to the length of the arms of the beam ; the lightness of
the beam and scales ; the proximity of the centre of gravity of the
beam and the knife-edge, or point of support ; and the length of
the needle which marks the oscillations of the balance.

In order to increase at pleasure the sensibility of a balance, a
button-screw or nut is placed on the beam at c, fig. 10. When
this screw is raised, the centre of gravity of the beam approaches
the knife-edge, and gravity acting on a shorter lever-arm round
the axis of suspension, its effect in opposing the oscillations of the
beam is diminished. If the centre of gravity reaches the knife-
edge, the balance is in a state of indifferent equilibrium ; if it
passes this point, the equilibrium is unstable, and the balance is
then useless.

Mithod of Double Weighing. — This method, due to M. Borda
of Paris, of ascertaining the exact weight of a body by means of
a balance whose arms are unequal, is the following : — Place the
body to be weighed in one of the scales, and make an equilibrium
in the other scale with lead drops or sand ; then, remove from the :
former scale the body to be weighed, and in its place put known
weights of any kind until the equilibrium is again established.
The amount of known weights thus obtained is the exact weight
of the body ; for in the operation, the body and the weights act on I
the same arm of the beam, in order to produce an equilibrium
with the same resistance.

LESSONS IN ENGLISH. —No. LXX.
By John R. Beard, D.D.

SYNTAX.— PREPOSITIONS.

The preposition is intimately connected with two other parts of
speech, the verb and the noun. The relation of the verb to its
object, or of the doer and the doing to the thing done, is often
expressed but imperfectly by the verb. Thus, when I say I go % I
make a merely general statement ; if I wish to give specific informa-
tion, I say, —

I go from the city into the country.
It is not every object, however, which requires a preposition.
When I say,

I pull the boat,
boat stands in immediate dependence on putt, and neither has nor
needs any preposition; but if I add a second object with that
object I (for the most part) employ a preposition; e. g.,

I pull the bo&t from the shore.

Now mark the difference between these two verba, go and
t'uii ; tli/ first, you know, is intransitive, the second is transitive*
The first has an object, but not without the aid of a preposition,
and the business of the preposition is to define the relation of the
verb r-. , to the objects city and country. The second or transitive
verb has one object in immediate dependence on itself, and another
object connected with itself by means of a preposition ; and the
btisiDcsji of the preposition is to define the relation of the verb to
the aecoud object, that is, to the shore.

Hence you learn that transitive verbs in the active voice hove two
object** the immediate and the mediate (or the near and the remote),
the former dependent on themselves exclusively, the latter dependent
on themselves through the link of a preposition.

The verb and preposition may indeed be regarded as one word —
thus, to come- from, to go* to — when by means of the several
suffixes a modification of meaning is in each instance caused.
These intransitive verbs thus supplemented become transitive, that
is, hare an immediate object, for we can say,

I come-from Bath ; I go-to Bath, &c.

The preposition is thus seen to stand between the verb and its
object in order to assist the former in the expression of the latter.
As, however, the object stands in immediate dependence on the
preposition, and only in remote dependence on the verb, so we
may frame the rule thus : —

A ftostt] as an object mag be dependent on a preposition ;
or thus : —

A preposition msy govern a noun as its object ; e. g.,

Ah ! who can tell the triumphs of the mind,

By truth illumin'd, and by taste refin'd ? " — Rogers.

The use of the participle refined here brings this example into
comparison with our model, namely, " a beverage made of wine
and water." By comparing the two together, we see that past
participles take after them a preposition governing an object, and
that the preposition varies with the sense ; it is, indeed, dictated by
the usages of the language. In the usages which determine what
preposition should follow participles, adjectives, and verba, much
of the idiom of our English tongue is involved. Equally does a
regard to a propriety of speech require attention to the exact mean-
ing, and the right application of the several prepositions, that is, to
the syntax of the prepositions.

We have already seen that an infinitive mood may be the object
of a verb in the finite mood ; as,

I love to wander ;

where wander is an infinitive governed by / lore. Now, instead of
to wttttdtr you may supply a noun and say,

I love wandering ; or,
I love a stroll.

The preposition to, you thus see, connects its object with a
transitive verb, when that object is a verb. The preposition In
such cases is a connecting word, but a connecting word which is
essentia I to the import. That it is essential you may learn by
removing it ; thus, I love, wander. Here, too, the object wander
is in. im mediate dependence on to, and only in remote dependence
on 1 love ; consequently, we may say that

The latter of two verbs connected together by the preposition to u
dependent on, or governed by, that preposition.
We may also lay it down as a fact that

77n preposition to stands before a verb when it is used in its most
general application, or in the infinitive mood.

Now a verb so used is in meaning very near to the noun. It is,
indeed, a verbal noun ; e. g.,

To learn to die is the great business of life.
Usage allows the preposition to, thus employed, to be in one kind
of sentence strengthened by another preposition, namely, for,
which, however, has its own object ; e. g.,

1 ' For us to learn to die is the great business of life."

The preposition for thus set at the beginning, followed by an
infinitive, forms a clause or member which is the subject of the
finite verb.

As prepositions govern nouns, so may they govern whatever
stands as , or is used with, the force of a noun, and consequently
propositions may govern

LESSONS IN ENGLISH.

1. A present participle wed as a noun ; as,
He accused the boys of fighting.

2. A present participle and a noun; as,
He accused the soldiers of being cowards.

3. A present combined with a past participle ; as,
He accused the soldiers of having been cowards.

4. A clause of a sentence or a phrase ; as,
He accused the troops of having acted in a cowardly manner.

In the following example, many words, combining to form a sub-
stantive clause, stand as the object to the preposition above;
within the clau«e is a minor clause dependent on the preposi-
tion of: —

" A quick wit and a nice judgment could not raise this man above
being received only tqxrn the foot of contributing to mirth and diversion."

This, however, is a form of a sentence which cannot be recom-
mended for imitation.

Prepositions in general stand before the nouns they govern, but
by poetic license they may be placed after ; e. g.,

" Wild Canon's lonely woods among." — Langhorne.

In verbs used with separable prepositions, the preposition, when
separated, may stand after its object, and even at the end of the
sentence : —

" This you pride yourself upon and this you are ruined by. n
In some phrases the preposition follows the noun ; e. g.,
" Civil and religious liberty all the world over"

An affectation of elegance, which was devoid of a knowledge of
the Teutonic idiom of our language, led Dr. Blair, and has led a
host of blind imitators, to proscribe what that superficial critic
with little accuracy called •' splitting of particles," which he
declares *' is always to be avoided ; " he gives as an instance this
sentence : —

41 Though virtue borrows no assistance from, yet it may often be
accompanied by, the advantages of fortune. ' •

Yet it is certain that sentences so formed are sanctioned by the
highest authority ; e. g.,

" To suppose the zodiac and planets to be efficient of said antecedent
to themselves." — Bent ley.

The sense may require two prepositions used in combination ;
e. g,

44 And from bejbre the lustre of her face
While break the clouds way."— Thompson.

Ellipses of prepositions have given rise to idiomatic j»li rases ;
e.g.,

We rode (over) sixty miles (on) that day.
This looks very like (to) a paradox.

Like, near, next, and other adjectives and adverbs, are used with
an object immediately dependent on them : —

" And earthly power doth then show litest God's
When mercy seasons Justice." — Shakspeare.

Care must be taken not to confound prepositions with adverbs,
especially with regard to the words which are used both ways.
Before is an instance ; e. g.,

Adverb : She entered before.

Preposition : 8he entered before me.

You may ascertain whether in any particular case before (and
similar words) is an adverb or preposition by considering what it
goes with, a verb or a noun; e. g. f

The king came near.

The king came near theciiy.

In the first place, near does no more than qualify came ; in the
second, near governs the city.

The prepositions between and atnong have t^ecific meanings, and
should be used accordingly. Between (twain, two) is by two, that
is, two individuals, or two sets or classes of individuals. Among
denotes distribution to several : —

He divided the apple between his brother and sister.
He divided the apples among the cftiidren.
Among differs from m in this, that while atnong denotes distri-

bution, in denotes presence in a place, and so requires its object
to be one, one individually, or one collectively ; e. g„

In a great nation many are found among whom charity may find
deserving objects.

Among the thousands who live in England there are a few
philosophers.

In differs from into, since while the former denotes rest, the
latter denotes motion : —

Being in a boat, we went into the harbour.

In many phrases, however, in is employed where motion is
signified or employed. In the Bible we find

" rent in twain ; " " cut in pieces ; " " puJed in pieces."

The correct signification has greater influence than the etymo-
logy in determining what preposition shall follow a word.

LESSONS IN GEOMETRY.-No. XXIII.

LECTURES ON EUCLID.

PROPOSITION XVI.— THEOREM.

If one side of a triangle be produced, the exterior angle is greater
than either of the interior opposite angles.

In fig. 16, let abc be a triangle, and let its side b c be pro-
duced to d. The exterior angle a o d is greater than either of the
interior opposite angles gba and bag,

Bisect (I. 10) a c in b, join n e and Pig. IG.

produce it to r. Make e f equal (I. 3) to j^

b e. Join f c.

Because a k is equal (Const.) to a c, and
b ■ (Const.) to b f ; therefore in the tri-
ungles a £ b and cep, the two sides a e
and b b of the one, are equal to the two
sides c b and e f of the other, each to each. I

But the angle abb is equal (I. 15) to the \

angle cbf, because they are vertical angles. c

Therefore the base a u is equal (I. 4) to
the base c f, the triangle akb to the triangle c £ f, and the
remaining angles of the one to the remaining angles of the other,
eaeh to each, viz., those to which the equal sides are opposite.
Wherefore the angle b a b is equal to the angle bcp. But the
angle E c D is greater (Ax. 9) than the angle ecf. Therefore
the angle a c d is greater than the angle bax. In the same
manner, if the side bc be bisected, and a c be produced to g, it
may be demonstrated that the angle b c o is greater than the angle
abc. But the angle acd is equal (I. 15) to the" angle bcg.
Therefore the angle a c d is greater than the angle abc. There-
fore, if one side, &c. Q. E. D.

Scholium. — The student should, for the sake of practice, write
out the demonstration of the second part here alluded to ; other-
wise, the truth of the proposition will not be so completely fixed
in his mind. A new axiom is taken for granted in the demonstra-
tion of this and some subsequent propositions, viz., If two things
be equal to one another, and the one be greater than a third, so is
the other.

EXERCISE TO PROPOSITION XVI.

From a point without a straight line, only one perpendicular can
be drawn to it.

In fig. t, let a be a point without Pig. t.

the straight line b c ; only one per-
pendicular can be drawn from the ,\
point a to the straight line b c.

From the point a, by Prop. XII.,
draw A D perpendicular to b c ; then
no other straight line but a d, drawn
from the point a, can be perpendicular
to bc.

For if possible, let a e drawn from
the point a bc perpendicuL to b c. ** "

Because in the triangle adk, the
straij'..t line ad is perpendicular to

h c, the angle ade is a right angle ; for the same rca&on, the
angle k b b is a right angle ; therefore, by Axiom XI., the angle

THE POPULAR EDUCATOR.

aibU equal to the angle adi, that if, the exterior angle equal t
the interior and opposite angle ; but by Prop. XVI. the exterior
angle is greater than the interior and opposite angle ; therefore
the angle a e b is both equal to, and greater than, the angle adi
which is impossible. Wherefore the straight line a k is not per-
pendicular to b c ; and in the same way it may be gbown that n
other straight line but a b can be perpendicular to » c. Therefore
from a point without a straight line, &c. Q. E. D.*

Corollary 1. — If from any point without a given straight lina
two straight lines be drawn, one perpendicular to it, and the other
not, the perpendicular will be on that side of the straight line which
is not perpendicular, where it makes the acute angle with the given
straight line.

Corollary 2.— The two equal angles of an isosceles triangle ar
both acute angles.

Corollary 3. — Only two equal straight lines can be drawn t<
another straight line from a given point without it.

Corollary 4. — A circle cannot cut a straight line in more points
than two.

PBOPOSITION XVI I.—THKOttfiM.

Any two angles of a triangle are together hss than two right
angles.

In fig. 17, let ab c be any triangle; Fig. 17.

any two of its angles are together less ^

than two right angles.

Produce b c to d. Because a c d is
the exterior angle of the triangle a b c,
the angle a c d is greater (I. 16) than the
interior and opposite angle a b c. To A
each of these unequals, add the angle —

a c b. Therefore the two angles acd and a c b, are greater
{Ax. 4) than the two angles abc and a c b. But the two angles;
acd and a c b are together equal (1.3) to two right angles.
Therefore the two angles abc and b c a are together less than two
right angles. In like manner, it may be demonstrated, that the
two angles b a c and acb, as also the two angles cab and abc,
are together less than two right angles. Therefore, any two angles.
&c. Q. E. D.

EXEBCIBJB 1. TO PBOPOSITION XVII.

The three interior angles of any triangle are together lest than
three right angles.

In fig. 17, let abc be any triangle, its three interior angler
abc, b c a, and cab are together less than three right angles.

For, by Prop. XVII., the two angles abc and bca are
together less than two right angles; the two angles bca and
cab arc together less than two right angles ; and the two angles
cab and abc are together less than two right angles ; therefore,
in all, the three angles abc, bca, and cab taken twice are less
than six right angles; wherefore, the three-angles abc, boa, and
cab taken once are less than three right angles. Therefore, the
three interior angles, &c. Q. E. D.f

Scholium — Here there is evidently a new axiom implied in the
demonstration, namtl\. that the halves of unequals are unequal,
and th t tin iiit-quali:y remains, aftrr halving, on the same bide as
it did b<f.>re halving. Another node of demonstration proposed
by T. Bt-coek, Great \\ arley. i* this: That as every exterior
angle with its corresponding interior is equal to two right angles,
so all the three exterior angles with their corresponding interior 1
angles are together equal to six right angles ; hut by Prop. XVII.
every exterior angle is greater than its opposite interior angle,
therefore all the exterior angles together are greater than all their
corresponding interior angles together. But all the interior angles
together with their corresponding interior angles are equal to six
right angles, therefore all the interior angles are together less than
three right angles, and consequently all the exterior angles are

* This exercise was solved by Non 6utok, Colchester; J. II. Eastwood,
Middlelon; T. Bocock, Great Warley ; E. L. Jones. Pen. broke; C. L.
H\DFitLD and J. Goodfem.ow, IJoIton-le-Moors ; Quintin Princls,
Glasgow ; D. H„ Driffield; E. Buss, I'entonvillc; £. J. Bbemnbb, Car-
lisle ; and others.

+ This exercise was solved by J. H. Eastwood, Middleton ; Quintin
Prinole. Glasgow ; E. J. Bremnbr, Carlisle; E. Buss, Psntonvilte;
H B. N- Boss, Camberwell ; T. Bocock, Great Warley ; and others.

greater than three right angles ; thus the following eserciae is
partially anticipated.

EXEBCI8E II. TO PBOPOSITION XVII.
The two exterior any lee of every triangle are together greater than
two right angles ; and t/ie three exterior any let of every triangle
] are together greater than the three right angles.

In fig. 17, let a b c be any triangle ; any two exterior angles of
this triangle are together greater than two right angles ; and all
the three exterior angles are together greater than three right
1 angles.

For every exterior angle, together with its adjacent interior

angle, is equal to two right angles , therefore, any two exterior

angles, together with their adjacent interior angles, are equal to

four right angles ; but, any two interior angles are together less

than two right angles, by Prop. XVII. ; therefore their two

exterior angles are together greater than two right angles. Again,

. the three exterior angles, together with their adjacent interior

I angles, are together equal to six right angles ; but in the preceding

I exercise it was shown that the three interior angles of any triangle

| are less than three right angles ; therefore, the three exterior angles

are greater than three right angles.

Scholium. — This demonstration depends on the axiom, that if
two unequal quantities are together equal to a given quantity, and
if one of the unequal quantities be less than half of the given
quantity, the other of the unequal quantities must be greater than
half of the given quantity.

PBOPOSITION XVII I.— THEOREM.

The greater side of every triangle is opposite to the greater
angle.

In fig. 18, let a b o be a triangle,
of which the side a o is greater than
the side a b ; the angle abc is
greater than the angle boa.

From a o the greater, cut off by
Prop. III. the part ad equal to the
less ab ; bisect the angle bad, by
Prop. IX., by the straight line a b,
meeting b c in e ; and join e p.

Because, in the two triangles abb
end a d e, the side a d is equal to the
side a b, by construction, and ths side
A e is common to both triangles,

therefore the two sides a b and a b in the triangle A b b, are equal
to the two sides a d and a e in the triangle ade; and the angle
PA e is equal to the angle du, by construction ; therefore, by
Prop. IV., the base b b is equal to the base D b, and the angle
A b e to the angle ade. But, by Prop. XVI., the exterior angle
AD" of the triangle dec is greater than the interior dcb;
wherefore, also, the angle abe is greater than the angle dcb;
therefore, in the triangle abc, the angle a b c is greater than the
angle bca. Wherefore, the greater side of every triangle, &c.
G. E. D.*

Scholium. — This demonstration is different from Euclid's, and
preferable to it, on account of its being more direct, and not
equiring the a fortiori argument.

Corollary — One side of a triangle is greater than, equal to, or
less than another, according as the angle opposite to ihe former
la greater than, equal to, or less than the angle opposite to the
latter.

In Cassell's Euclid this corollary is misplaced, as h is there
attached to the 19th proposition ; and the corollary there attached
to the 18th should be appended to the 19th. This mispleoetneet
f/as pointed out by Mr. G. Williams, Bristol.

Fit. 19.

11 Of curious arts, art thou more fond ? then mark
The mathematic glories of the skies.
In number, weight, and measure, all ordainM.
Wisdom and choice their well-known characters
Here deep impress, and claim it for their own.
Use rivals beauty, art contends with pow'r;
No wanton waste amid effuse expense,
The great Economist adjusting all
To prudent pomp, magnificently wise."

• This exercise wu eoWed by T. Bocock, Great Warlsy; Quintin
famous, Glasgow; J. H. Eastwood, MiddL-too: B. B. N. Boss. Csm-
erwell ; sod others. '

LES80N8 IN FRENCH.

LESSONS IN FRENCH.— No. LXXXI.

By Professor Louis Fasquelle, LL.D.

{ 138.— Advs&bs of Negation.

(1.) The negation is composed of ne placed before the verb,
and pas or point, after it in the simple tenses. The second
negative cornea between the auxiliary and the verb, in the com-
pound tenses : —

Le old sur nos aouhait* ne regie
pas le ehoses. Co»weille.

Komt ^'attache point lo grade a
la noblesM. Corn kills.

I/entirae est It vrai prinoipo de
U consideration, qui n'ost pas tou-
jour* attache aux d ignites

FOWTENELLE.

Lcs rois ne sont point protege's
par les lols. Cne*xiEa.

Heaven does not regulate things
according to out wishes.

Rams does not by any means con-
fine apices to the nobility.

Esteem is the true principle of con-
sideration, which is not always at-
tached to offices

Kings are by no means protected
by laws.

It will be seen in the above examples, that the negative
point is stronger than pas. The meaning of these two words,
which are in fact substantives used adverbially to strengthen
the negative ne, will sufficiently explain this :

N'allez pas means n'alle* un pas, do not go or move one pace
or step. N'ailez point means riallez un point, do not go, or
move a point or dot.

(2.) The second negative may be suppressed after tho verbs
pouvoir, oser, savoir, and cesser : —

Non, decsse j Je ne puis souffrir
qu'mi d« leurs vauaeaux fasie nau-
frage. FInolon.

Dans son appartement, el!e
n'osait rentrcr. Voltaire.

Qui vit hai de tous, ne sauralt
longtemps vivre. Corneille.

La liberte ne cesse d'etre aima-
b'e. Couneille.

No, goddess-, 1 cannot suffer that
a single one of their vessels perish.

Slic dare not reenter her apart-
ment

lie ichj lives hated by all, cannot
exist long.

Liberty cannot cease to be worthy
ofiove.

(3.) Pas ot joint is suppressed, when the verb is modified by
another negative word, such as jamais, guers, nul, nullement,
aucun, per sonne, ni, ne, or followed by que, meaning only, and
plus used negatively : —

Ambition, my lord, has scarcely
any limits.

No one is happy, unless he can
esteem himself.

No one likes to receive advice.

A wiclced man never knows how
to forgive.

1/ ambition, seigneur, n*a guere
de limites. Bouusault.

Nul n'ost heuroux, s'il no Jouit
de «a propre estiino.

J. .1, Rousseau.

/V smtnc u'ajuio ii recevoir do
cou>fci!a. De Scgub.

Va median t nc gait jamais
pariunner. NoeL.

(4.) Ne used Idiomatically.

The negative m is used without any negative sense after the
conjunctions h moins que, unless; de peur que, de crainte que ;
for fear that : —

Unless ycu speak to him.
For fear, or lest you might be de-
ceived.

A moins que vous ne lui parliez.
De peur qu'on ne vous trompe.
L'Acadcmie.

(5.) Ne is used in the same manner after autre, different ;
autrement, ctherwise ; plus, moins, raieux, forming a compari-
son, and after the verbs craindre, avoir peur, trembler, appro*-
header, empecher : —

He is very different from what
he was.

1 le speaks and acts very differently,
lie is more modest than he ap-
pears.

I an almost afraid that {lest) a
dream is deceiving me.

You fear mucli, lest I may change
my mind.

The rain prevented tJicir taking a
walk in the gardens.

11 est tout autre qu'il n'e*tait.

II parle autrement qu'il u'agit.

II est plus modestu qu'il ne le
parait.

Jo crains presqne, jc craios,
qu'ua songe ne ra'abuic.

Racine.

Tons avez bien peur que je ne
change d'avis. Nawvaux.

La pluie empe'eha qu'on ne so
promtnat dans les j <rdiu?.

Racine.

(6.) Remark.— Ne is not used when the verb of the preceding
preposition is accompanied by a negative :

II ne parle Das autrement qu'il He does not speak otherwise than

aglt. he acts.

II nVst pas plus modeste qull He is not more modest than heap-

le parait. pears. •

(7-) After craindre, apprehender, avoir peur, trembler, we put
pae alter the ne when we wish (or the accomplishment cf the
aciion expressed by the second verb :—

Je crains, qu'il ne vienne pas.
J'ai peur, que mon frere n'arrive
pas.

I fear, that he may not come,
lam afraid, that my brother may
not come.

§ 139. —The Preposition.— Regimen op Prepositions and

PREPOSITIONAL Phrases.

(1.) Prepositions may be divided according to their regimen
into three olasses : —

1st. Prepositions governing nouns without the aid of another
preposition. They are:* —
A, at or to
Do, of, from
Dbs, from, as soon as
Apres, after
Attendu, on account of
Avaut, before
Avec, tcith

Chez, with, at the house cj
Concernant, touching
Coutre, against
Dans, in

Depuis, since •

Derricre, behind
De8sus, above
Dessous, under
Devers, towards
Devant, before
Duraut, during
En, in

Entre, between
Envera, toioards
Excepte, except

Hwrais, } "***' ( scc hon Mow )
Malgre, in spite of
Moyennaut, by means of
Joignant, joining
Nonobatant, notwithstanding
Outre, besides
Par, by
Pour, for

Parini, among, amongst
Pendant, during
S us, without
Suuf, safe, save
Selon, acccnll-ig to
i^ou*. under
Suivant, according to
8ur, up'/n
Touohant, touching
A travers, through
Vera, towards
Voici, here is
Voilii, there is
J Vu, consulting

requiring the preposition de after

2nd. Prepositions
them :f —
Auprea, near
*Autour, around
Ensuite, after
Fa u to, /or want
Hon, out of
Loin, far '
Pre*, near
Procbe, near
A cause, on ace unit
A cC'.e, by the side
Acouvcrt, under cover
A fleur, even with
A force, by dint
A la favour, by means
A 1'abri, under slieUcr
A U mode, according to the fashion
A la reserve, reserving
Al'exception, txcepting
A I'exclusiun. excluding
A l'egard, with regard
A I'insu, unknown
A 1 'opposite, contrary
A moins, unless, for less

3rd. The prepositions followed by u are : —

A raison, by reason, at the rale

Au rez, on a level

Au dec-a, this way

Au dela, that way, beyond

Au dessous, under

A u dcfcsus, above

An dedans, within

Au dehors, without

Au devant, before, to mat

Au milieu, in the middle

Au lieu, instead

Au moyen , by means

Au niveau, on a level

Au peril, at the peril

Au prix, at tlie price

Au riaquc at the risk

Au travers, through

Aux depcr.s, at the expense

Aux environs, in the neighbourhood

En depit, in spite of

Le long, along

Yis-k-vU, opposite

Attenant, joining
Jusquc, as far as

Par rapport, tvith regard
Quant, (is to

(2.) Many of the prepositions which govern the re'gime
direct arc formed from active verbs. Almost all the preposi-
tions requiring de before the regimen are formed of a
S reposition and a noun; Those requiring the preposition d
avo a relation of tendency, of aim, Sec.

• Governing the accusative. + Governing tho genitive or ablative.

THE POPULAR EDUCATOR.

{ 140.— Remark.

The rulci which we have given [$ 92, (1.) (2.) note, and
6 133] with regard to the regimen or government of verbs and
adjectives, apply also to prepositions. When two prepositions
require the same regimen, it is useless to repeat this regimen
after each one, but if they require a different regimen, it is
necessary to give to each its proper object. It would, therefore,
be incorrect to say,— Un magistrat doit toujour* juger suivant
et conformement aux lois :— A magistrate should always jutlge
t» accordance with, and conformably to, the laws ; because the pre-
position snicant governs the noun in the rigimc direct, that is
without the aid of another preposition, and conformement
governs the noun in the regime indirect by means of «. We
should say :—

Un magistrat rloit toujour* juger
snicant lea loia, et cnnf.trmcrnent a
ce qu'elles pmcrivent.

Mabmohtel.

A magistrate should always judge
in accordance with the lata and con-
formably to what they pre* m ribe.

$ 111.— Repetition op Piie positions.

1. The prepositions a, de, en, and san\, must be repeated
before every regimen, be it a noun, a pronoun, or a verb : -

Ce monde ci n'eat qu'un lotcric I

a lutt'i-y or

LESSONS IN ITALIAN GRAMMAR.— No. IV.

Ily CHAUI.ES TAl '«EXAU, M.D.,

Of the University of Pa via, and I*rof«»sor of the Gorman and Itatt
Language at the Kttulugton Proprietary Grammar School.

(Continuea from p. 42.)

6. S, named in the alphabet esse (pronounced esvaai
This consonant has considerable variations, and is one of tl
most difficult to pronounce throughout correctly, for even i
Italy there are variations. An irreproachable pronunciatk
of this consonant can only be acquired by closely marking i
utterance in all its shades by Italians who •peak pure!
Speaking generally, there are two leading sounds. One isashar
hissing sound, a* in the English words, sutg, sieve ; the od»
is a much milder sound, as in the English words, eAe**e 9 Jk*
case, pi* as*, &<\ The following general rules will be sumoa
for the present : I shall state the exceptions more fully hereafte

First, the sharp sound of this consonant may be said to I
the ruling sound, because it is heard in the greater number <
syllables and words. I shall invariably mark it by the sing'
letter a ; and n her ever this is used, the reader will reme m b
that it represents the sharp, hissing sound of the letter, thi
avoiding multiplicity of signs, which would be caused by usii
*<. It has always the sharp, hissing sound in the beginning <
; a word before a vowel ; as, for example, sale, pronounced sil

motor*, a soutenir lea loin, ke.

FeHeLon.
Telle e*t la multitude, et sans
frein et sans loia. La IIarpe.

Such is Oh' multitU'h', ic thout rv-
I stiuitU and without liv *.

2. The other prepositions must also be repeated before every
noun, pronoun, or verb, unless the words used as regimens
have a similarity of meaning ; in which case the prepositions
may be placed before the first regimen only, or before all, at
the option of the speaker : —

Je vous donoe ceci pour vous et
pour votre frere.

II perd lajeuaease dans la mol-
l^sseet (dan-) la volupte.

/ give you t/tid for you nndfor
your brother.

1/e wastes his youth in 'ffi minacy
and voluptuous a* a.

$ 142. — Observations os several Preposition**.

( i . i J cant mark* a priority of time and place; — D'-mnt means
simply opposite, in front of; —

i 1 walk brfort you. i e., / walk
J earlier than you, or / haw tfte pre-
( ccdcnce of you in walking.
| I walk in front of you.

e marche avant voni.
Je marche devant vous.

(2.) En, d t dans. — The sense of en is more indefinite, more
extensive than that of dans. En is generally used before the
name of a division of the earth, a kingdom, &c, a before the

menl. It has also the sharp and hissing sound after the eoi
sonamj /, ;/, and r, and I may say a pre-eminently hard an
hissing sound in this cose; as, for example, faao, fahl-a
false ; cono, korr-so, course ; arso, Iihrr-so, burnt ; forse, for
sai, perhaps ; pian*r, peeahn'-ftui, he wept ; rinse, vin-sai, 1
vanquished. In Home, the sharpness of the s after /, n, and
is generally so very audible, that it almost amounts to tl
utterance of a h, as if the example* just given were writtt
with the hard z pronounced with the English sound in tl
word Stcifz'r ; which, however, with all respect for the etern
city and the " l»>c<-a Rnmana," I must pronounce to be.
provincialism.

Secondly, the milder sound of the s occurs generally wni
it is placed between two vowels. As the nearest possib
approach to it, I shall follow the practice of Mr. Walker in h
English pronouncing dictionary, and mark it with as; fore:
ample, a:-ri*o 9 ahv-vce-so, opinion; guisa, gvee-xa, guil
manner; Usoro, tai-zo-ro, treasure; usura, oo-z6-rah, usur
sposa, spo-za, bride ; accusa. ahk-k6o-zah, accusation ; misth
mee-ze-reeah, misery ; i,iU**ra 9 mee-z6o-rah, measure.

This rule is subject to several exceptions, the most import!
of which I must state here.

Many Italian adjectives end in oso and osa, and whener
before these terminations there i* a vowel, the terminations]
has the sharp, hissing sound ; as, for example, glorioso, pi
nounced glo-rec6-so, glorious; virtuoso, virr-tooo-so, virtuou
tortuoso, torr-too6-so, tortuous.

name of a town, and dans before a word restricted by an article i There are many compound words in Italian having the pi

tides dis and mis, and before consonants the final s of the
particles must have the sharp, hissing sound ; as, for examp
disposizione, pronounced dis-po-zee-tseco'-nai, disposition ; 4
misurop dis-mec-z6o-rah, excess; (the reader will note
the two foregoing words, that the * of the particle dis has t
hissing sound, while the next «, placed between two vows
follows the general rule, and has the mild sound) ; dispiscex
dis-pccah-tchcn-tsah, displeasure; discreditars, dis-krai-d<
tah-rai, to discredit.

In the greatest part of compound words, where t begins t
syllable, it has the sharp, hissing sound; as, for examp
proscguire, pro-sai-gwe'e-rai, continue; risolvcrc, ree-sol-vai-i
to dissolve ; vresumcrc, pr{u-s6o-mai-rai, to presume : risorgt
ree sorr-jai-iui, to rise again; trasustanziato, trah-soo-stii
tsecfi-to, transubstantiated.

There are other exceptions which I shuil take occasion
point out as examples occur.

Further, * hos the mild sound when it immediately precec

or a determinative adjective : —

En Europe, en France, a Tari*,
dans ma chambre.

En Amerique ce sont les bisons
qui ont une bosse sur le dos.

Button.
Dans I' Amerique roeridionale le
baeuf etait sbsolument ineonnu.
Bufpon.

In Europe, in /•ranee, m Paris,
in my room

la Ametica the bisons hare a
bunch en thtirback.

In South America the ox tcos m-
tircty unknown.

(3.) Chex might be rendered in English by at the house of,
icith, among, &c. :—

Chez vo»re per* ; chcz vous.

La condition des oomedien* etait
infamc chez les Komains, et hono-
rable chcz les Green.

L\ Bruyciu:.

At your fat Iter's; at your house.

The condition of comedians was
infamous among the Romans, a Ad
honourable with the Greeks.

LESSONS IN ITALIAN.

the consonants b, d, g, I, m, n, r, v ; as, for example, sbarra,
pronounced zbahrr-rah, bar, barrier ; sdirc, zdee-rai, to retract ;
sguarda, zgwahrr-do, look ; slontanare, zlon-tah-nah-rai, to
remove ; smania, zmah-neeah, madness ; snervare, znerr-vah-
iai, to unnerve ; sradicare, zrah-dee-kah-rai, to eradicate ;
svelto, zvel-to, lively, clever, nimble, easy. I have stated that
the particles die and mis before consonants have the sharp, his-
sing sound. There is no deviation from this rule, and these
particles retain the sharp, hissing sound even before the last-
mentioned consonants ; for example, disbandire, pronounced
dis-bahn-dee-rai, to banish ; dwdire, dis-deVrai, to retract ; rfw-
gombrare, dis-gom-brah-rai; to empty ; disleale, dis-laiah-lai,
disloyal; dismettere, dis-met-tai-rai, to dislocate an arm, to
dismiss (an affair); disnervare, dis-nerr-v&h-rai, to unnerve;
disi-adicare, dis-rah-dee-kah-rai, to eradicate ; disvenire, dis-vai-
nee-rai, to swoon; misgradito, mis-grah-dc'e-to, disagreeable;
misUale, mis-laiah-lai, disloyal; misvenire, mis-vai-nee-rai, to
swoon.

When ss is between two vowels, it does not follow the rule
of the single s, but must be sounded with a sharp, hissing
sound; as, for example, fosso, pronounced fds-so. a ditch, a
canal ; 'rosso, r6s-so, red ; posso, p6s-so, I can.

I have not yet spoken of the letter H. It is named in the
alphabet acca (pronounced ah'k-kah). According to its alpha-
betical sound, and because its two syllables are substantially
one, only placed inversely, it might be classed as a semi- vowel ;
but as it is only an auxiliary letter to modify the sounds of c
and g % as I shall have occasion to explain fully hereafter, it is a
mere soundless, written sign, not a letter. It also serves to dis-
tinguish the words ho, I have, from o, or ; hai, thou hast, from
at, dative plural of the article ; ha, ne has, from a, the preposition
to ; and hanuo, they have, from anno, the year. This distinction
is, however, only for the eye, for in pronouncing, the h is quite
mute ; and some purists, headed by Metastasio, instead of an h f
put the grave accent in those first four words.

The Italian has no aspirates, which essentially distinguishes
it from the leading languages of Europe. Only' in the middle,
and at the end of some few interjections, a kind of aspiration
is heard, which is only produced by the prolongation of the
sound of the vowel, or of the transition of the voice from one
vowel to another, principally, however, by a more emphatic
emotion by which such interjections are thrown out ; as, for
example, ah! alii! deh ! ahime ! eh! oh! ehi! ohi ! ohime!
doh!

In the early period of the language, the Italians wrote all
words manifestly of Latin origin with an initial h ; as, for
example, habile, now abile; hinno, now in no; hora, now ora ;
historia, now istoria. This insignificance of the h has given
rise to some proverbial expressions : as, " Quest a ccsa non rale
uri acca" " this is not worth an h ; " or, as an Englishman
would say, " not worth a tig or a farthing ; " or «• Non m'im-
porla un'acca," " I don't care an h for it ; " or, as an Englishman
would say, '* I don't care a straw for it ; " or ** Non ne taper
un' acca, "not to know an h of something; " or, as is often
said in England, " an iota of it." When an Italian has to pro-
nounce the h in another language, it is only with the greatest
difficulty he can master it.

To complete my remarks on the alphabet, I must now say
something of the letters K, W, X, and Y, important letters in
English, but which do not occur in Italian.

Instead of k, the Italians use before consonants and before
the vowels a, o, and u, the letter c ; and before the vowels e and
t, ch. For example, instead of Kalend, the Italians write
Calende.

The English letter to does not occur at all in Italian.

The letter X, which represents properly speaking a com-
pound sound (ks), is unknown in pure Italian words, and the
English sound is never heard. In words of foreign origin,
which would have this sound in English, the Italians place an
• or as, or c; as for the word example (from the Latin
exemplum), the Italians write esempio; for extreme (from
Latin extremus), they write estremo ; for Xenophon, Senofonte ;
for Xerxes, Serte; for Alexander, Alessandro. The letter c
replaces the x in words which are the compounds of the prefix
ex, when c follows it ; for example, for excellent, they write
ecceUenU', for excess, eccesso, &c. Custom has, however,
sanctioned the use of the # in a few words of Greek origin,
for Xaotippe and Xanto (Xanthus, the river in Asia Minor)

are just so written in Italian. They are nevertheless pro-
nounced as if they were written Santippe and Santo. (The
latter word has retained the x principally that it might not bo
confounded in writing with the word Santo, saint).

The letter y is always replaced in Italian by t ; as, for
example, for physics (physical science), the Italians say fisica ;
for stygian, stigio.

SECOND PRONOUNCING TABLE,

8110 WING TUB COMBINATION OF V0WBL8 WITH 8 EM I- VOWELS
IN NATURAL OBDBB.

English.

Beasts, fairs

Thread

Jaws

A monkey

I put to night

A horned owl

Lake

Throat

Hurt

Sun

It is permitted

The heavens

Praise

Delus

Light

Mules

Wild basil

Home

Month

Seed

The sight in artil-
lery, aim

Branches

Manner, mode

Tamed

Wall

I reconsider

Ship

Vein

Negress

Frogs

Berenice, a woman's
name

Thou suppest

Name

Less

Nape of the neck

Cradle

Thin, rare

He gilds

Surrenders (of
towns)

Mr., Master

I laugh

Thou gildest

Property, victuals,
merchandise, robe

A cheat

Rude

Durations

Sarah

Erased

With himself

Italian,

Pronowu

Fere

fd-rai«

Refe

rai-fai

Foce

fd-tchai

Cefo

tchd-fo

Fugo

foo-go

Gu/o

g6o-fo+

Logo

lah-go

Gola

g6-lah

Zeso

lai-zo

Sole

s6-lai

Lice

lee-tchai

Celi

\che-lee

Lode

16-dai

Delo

dS-lo

Lum

16o-mai

Mule

xn6o-lai

Maro

mah-ro

Roma

r6-inah

Mese

mai-zai

Seine

sai-mai

Mira

mee-rah

Rami

rah-mee

Modo

mo-do

Domo

dd-mo

Muro

m6o-ro

Rumo

r6o-mo

Nave

nah-vai

Vena

vai-nah

Nera

nai-rah

Rane

rah-nai

Nice

nee-tchai

Cent

tchai-nee

Nome

n6-mai

Meno

mai-no

Nuca

n6o-kah

Cuna

koo-nah

Rado

rah-do

Dora

d6-rah

Rese

rai-zai

Sere

se-rai

Rido

ree-do

Dori

d6-ree

Roba

ro-bah

Baro

bah-ro

Rude

r6o-dai

Dure

d6o-rai

Sara

sah-rah

Rasa

rah-zah

Seco

sai-ko

• That my pupil readers may thoroughly <
ronunciation, in order to give a com p let

exercise themselves In
pronunciation, in order to give a complete illustration of ihe
junction of vowels and semi-vowels, in natural otder, I have
selected words of two syllables, in which the first syllable of the
first word is the same as the concluding syllable of the second.

f The vowel u in Italian, as a final letter, is only to be found in
monosyllables ; as, tu, thou ; fu, was ; or in those words that have
the grave accent on the last syllable; as, virtu, virtue; Corfu,
Corfu. I am therefore compelled, by the use of the wcrd gnfo, and
others to follow, to depart from the strict system.

THE POPULAB EDUCATOR.

warpvof gifWpQ taXoc, t9Tiv. Opiyov, * vat, riff ailovc,. Ail*c
oyaBotc avipaaiv ixtrcu- Avoiav ixi rip ruBoi tuu x a0€n
BavpaZofUv. Tp cuZot vpoewri to otfiaf. Mif xpo<r£Xixf to
Topyovc, vpoawwov. Q Hgoc, fyvittc. voXXatcu; rove avQpvrovc..
JlavrtQ optyovrai tvtarovc,. TJptTU Tail i koi vtawa adm
t%tiv. JLXtit* tuu Eparm Movvai tiaiv. Iff* /uv Wtu* (kpa-
wivovoiv ot tffTOptfHTpafo*, Ttiv it Eparm oi Xvpnun votirrm.

Ekolish-Gbeex.

Homer sing* (of) the hero Achillea. The hero Achilles is
sung by Homer. The bravery of the hero it wonderful. We
admire the bravery of heroes. Slaves have (say, U> the slaves is)
a sari life. The uncle has (§»T, to the uncle is) a fine garden.
All rejoice at their (the) good condition. Admire, O youth,
with (fUTa and g?n.) modesty the deeds of good men. By
(dat.) the echo we are often deceived .

Noons in ag, aoc, are declined as follows. Only a few
neuters belong to this bead. The terminating o belongs to
the stem : to otXac., a sun-beam • to KptacJUsh.

S.N.A.V.

<r«Xac

otXa-ot

i).

aiXa-i and otXa

r. n.a.v.

(Ttka-a and otXa

otXa-wv

i).

trtXa-oi

D. N.A.V.

oiXa-t

G.D.

tftXa otv

Kptac,

(*p*a-oc)

Upta-t)

Upta-a)

(xpta-wv

(tcpta-tri)

(xpta-t )

[Kpiaoiv)

*p««C

Kpta

KpiUtV

Kpta

Kpt'jiV

After ffiXac decline to tticac,, « gloss or gobLt\ after kotag
decline to ynpag, old ape, and to ytpag, a present. With these
two last may be connected two nouns whose stem ends in r,
namclv to rtpag, a prodigy, and to KtpaQ, a horn, since after
dropping the r they may be contracted in the same manner ;
KtpaQ follows Kptac, throughout, but with the contracted form*.
It has also regular forms with r : thus Ktpac,, Ktparoc,, and
KtpiitQ ; Ktpan and Ktpa, &c. ; rtpav,* howeTer, has the two
forms only in tho plural, the contracted arc the more common,
thus Ttpa, npvv.

Vocabulary.

passed into o:
fame, glory.

A vtpiut, ag, »/» bravery. j

Aiarpo^q, ijc, ')t nourishment.

Evttia (tv and %%u>) at, rj, well-
being, weal.

EXafog, ou, I/, a stag.

Tlpoparov, ov, to, a sheep.

ttyuAfov, ov, ro, a foundation.

Qapfiaicov, (whence pharmacy),
ov, to, medioine, means of
healing.

TLaXiriyi, tyyoc., if, a trumpet.
AvokoXoc,, ov, dissatisfied,

grumbling, harJ.
Uifinw, I send.
npoTpiirbt, I turn towards,

exhort, encourage.
Sif/iatiw, I give a atign (onfia,

a sign), I signify.
'Yirapxw, I exist.

Sin.

Plmr.

Dual

X.A r.

D.
N.A.V.

D.
N.A.V.
G.hD.

e.g., to ytvec,

(7fvf-oc)

(yivt-i)

(ytvt-a)

{ytvt-mv)

ytvt-ci

{ytvt-t)

(yfvf-otv)

raws; ro aAssft

CXJS£

ytwvc.

(<X«-ec)

kXcsvc

ytvu

(cX«-I)

kX&u

ytvn

(kXu-*)

cXf«

ytvwy

(cXti-*r)
kXu-ci

cXf^v

yivil

(cX«-i)
(k\u-ow)

At,

yivoty

K\tO*V

Exibcises.— Grebk-Enolish .

Oi Otoi roiQ avOpuirotc Ttpa irtfiirovotv. Tutv tv yt)pq. kukwv
fapjiaicov o Bavaroc toriv. Ta ytpa tovq arpariwrac uC
av&puav rrporpitru. £| aiywv rat *po(3aruji> yaXa rai Kpta irpoc
ttarpofrjv vicapxti' Ktpaoi icat craXiciyZiv ot arpariwrat
arjfiaivovaiy. UotKtXutv xptwv ytvopiQa. KaXov yrjpwQ Btya-
Xtor iv iraitriv icriv t) rov trojfiaroc fv<£ia. At tXafoi Ktpa
t\ov(T.v. Aw<r«oXoc 6 tv ytfpa flioQ (»c. tortv).

Enolisk-Qrbbk.

Prodigies are sent by (viro with g.) the gods to men.
SoMicrs are delighted witk horns and trumpets. We taste
milk snd flesh. D^ath puU an end to (airoXvn) the evils of
old age. The king sends presents to the soldiers. Presents
encourage soldier*. Soldiers are encouraged by (dat.) presents.

Wo pursuo our taak in the third declension, and offer models
or nouns in oc» g. fog, contracted into ovc. The substantives
of this claas are exclusively neuter, and the terminating a
Wongs to tho stem. In the nominative, the stem- vowel i has

Vocabulary.

r»7» 7 9£t Vt the earth.

Zrjfiia, at, if, disgrace, punish-
ment.

XaX*oc, ov, o, brass.

OKiyroc, 9, ov, mortal* deadly.

nofi|poc t a. ov, wicked.

AefaAifc, tc, firm, sure.

KfMvw (Let. cerno) I separmtc,
decide, judge.

AXXa, but.

AvOoc. to, a flower.

EiBot, ro, a form.

QaXwoc, to, warmth.

♦^Xpc , to, cold.

Kcpcoc, to, gain, in the plural.

KXcoc, to, fame, glory ; in the

plural, honourable deeds.
Mijcoc, to, length.
'T^oc, to, height,
^c tr£oc, to, a lie.
Eap, tapoc, to, the spring.

ExBBcisis. — Grbsk-Enolish.
'H yn KaXot^ avBioiv BaXXti. Mi} aitt\ov ^v%9vc; ctu
OaXtrovc,. To koXov ov ftifcit x9° yov *p*vofUv aXXa opcrf*
Ovk aa+aXtc wav v\poc tv Ovtirtp yivu(*c tortv). M if if*vii
Xtyt. Kxt\ov Tovrjpwv Ktpfotv, Ktptti wovtipa £if/ua»r au
<f>ipii. Karotrrpov tttovg x a ^°C* otvoc it vov (sc. cercy). Ot
avBpwxot kXiovq optyovrai. Oi avtpiQ cXfft x at 9 ovm¥m ®*
aviptiot KXtutv optyovrai. GavpaZofttv ra tw avipw *Xta.

Enolish Geebk.

Keeu from (abstain) wicked gains. Good men keep from
wicked gains. Good men desire honourable deeds. Do not,
O young man, keep from heat and cold, but from wicked men.
Punishment follows a (the) lie. Wo admire the Greeks on
account of their (the) honourable deeds. We avoid wicked
gains. The soldiers rejoice in honourable deeds (4*0*

Our next class of words ends in t</, re, i, v Of these we
take first those words in 7c, vc, namely o «e, g. rt-oc, the com
tcecvil, >/ ovq, (Lat. sus.) a sac, 6 t\0v£, ajfsh.

S. N. tic, out *XP v t

G. n-of ov-ot i\0v-ot

D. ki-i ov-i txBv-i

A. kiv ovv lyfivv

V. kX ov ixOv

P. N. Ki-tt ov-tc, iX^^'C

G. ki-Giv ov-Cjv tyflv-w

D. Ki-oi ov-oi lyfiv-ai

A. ict-ac ov-ag vjfiv-at

V. Ki-tQ ov-tc, *X0v-cc, »X^5c

2). N.A.V. ict-€ ov-t ixfivt

G.D. Ki-olv ov-olv tyflv-oiv

VOCAUULAUY.

horpvg, vott °> a bunch of | Barpaxog, ov, o, a frog.

grapes. Zvpoc ov, 6, a Syrian.

Mi/c, pvoq, 6, a mouse, (Lat. Ayictcrpov, ov, to, a hook.

mut.) Aypioc, a, ov, wild.

Ne<cvc» voq, 6, a dead body, I<roc, », ov, equal.

corpse. Ayptvut, I catch.

'Sraxvt, vo£, 6, an ear of corn. Avaxvicru), I emerge.

Ilaytc, i^oc, >/, a trap. BaaiXtvw, (g.) I am king, I
AfiirtXoc;, ov, 6, a vine. reign.

Exercises. — Greek -En olish.

Ot txBvtQ tt: tov irorapov avaicvirrowriv. 01 9r\ptvrat m

aypiaQ ovag ayptvovoiv. Havrtg tooi vtKvtf ^vx*** & &*&

paeiXtvu. '11 a]iirtXot ftpii poTpvc,. 'H y» $ipti <rraYV{ <«*

I /3orpvc. Toif ftucri paxn *o T * V v *P°£ T °C fiarpaxovc* °*

KEY TO LATIN EXEBCISES.

pvtc fcayuriv ayvivorai. 01 Svpoi mfiovrai tovq i\9vq «c OtovQ.
Ayvurrpotc tvtdptvoptv tovq \%Ovq.

Enolish-Gbebk.

We catch fish with hooks. Fish are caught with hooks.
The hunter lies in wait for wild boars. The bunches of grapes
and ears of corn are beautiful. The vine bears grapes. The
frogs had (to the frogs there teas) once a battle with (against)
the mice. We look on corpses. The earth bears many Tines.
God reigns over fishes and frogs.

A KEY TO THE EXERCISES IN THE

LATIN LESSONS.

By John B. Biakd, D.D.

{Omiinued from page 387, Vol. III.)

Page 383, col. 2, vol. II.— Latin-English.
jfisop, a famous writer, was hump-backed ; the Scythians, war-
like men, were terrible ; the Phoenicians were very skilful sailors ;
Greece was the country of many illustrious men ; the conscious-
ness of a well-spent life (vitae) is pleasant ; the Greek language is
more difficult than the Roman ; the goose, the sheep, and the ass,
seem to be very senseless beasts ; every animal is mortal ; we are
friends [insert a comma after amici], you are enemies ; how great is
jour imbecility ! grammar and music were formerly united ; pity and

Serfidy are beloved in him ; three thousand two hundred of the
amnites were cut to pieces ; folly, rashness, injustice, and intem-
perance, are to be avoided; peace and concord, useful to the
conquered, are honourable to the conquerors ; the captives became
the soldiers' booty ; riches are incitements to evil ; the wall and
the gate were struck with lightning; Cneius and Publius Scipio
were two thunderbolts belonging to the Roman dominion ; Brutus
and Cassius were Caesar's murderers ; Vespasian, when ("appointed)
Quaestor, received by lot as his province Crete and Cyrenae ;
Pompey, deserted by his soldiers, proceeded to Egypt ; philosophy
is the guide of life, the explorer of virtue, the banisher of vice ;
what shall I say of memory, the treasury of all things ?

Page 383, col. 2, vol. II.— English-Latin.

Qui Caesaris fuerunt interfectores ? Brutus et Cassius ; thesaurus
animi est memoria ; vitae dux est religio ; nonne expultrix viti-
orum est religio ? religionis philosophia medicina est animarum :
benignissimae sunt religio et philosophia ; qui imperii Romani
fuerunt fulmina ? duces, imperii Romani fulmina, ad bellum pro-
fecti sunt; in Graecia, magnorum virorum genctrice, vivebant
Solon et Aristides ; caduca sunt divitiae et honores ; vir mulierque
repente sunt mortui ; murus et limen et navis de coelo tacta sunt ;
vos amid, nosinimici sumus ; clarus scriptor fuit iBsopus ?

uEsop's Fables.

The Ass and the Horsb.

An ass called a horse happy because he fed so abundantly, while
not even sufficient straw was supplied to him after the severest
labours. But a war having arisen, the horse is driven to battle,
and being surrounded by foes, at length, after incredible struggles,
sinks on the ground pierced with many wounds. The ass behold-
ing all these things, said : " What a dolt I was to estimate happi-
ness by the condition of the present hour ! "

The Husbandman and his Sons.

When a husbandman, advanced in life, felt that his decease was
at hand, he called together his sons, whom, as is usual, he knew
to disagree sometimes, and ordered a bundle of twigs to be brought.
The twigs being produced, he bade his sons break the bundle.
When they were unable to do so, he gave a twig to each one, and
they being easily broken, he taught his eons how strong a thing is
concord and how weak discord.

Thb Woman and thb Maid-sbbvamt.

A widow woman, who gained her living by weaving, was
accustomed to call up her servants to their work by night as soon
as she heard the first cock-crow. But they, worn out by their
daily toil, resolved to kill the cock. This being done, they began
to be in a worse condition than before ; for their mistress, igno-
rant (incerta) of the time, now often called her slaves even in the
early part of the night.

Page 8, col. 2, vol. III.— Lattn-Enolibh.

An effeminate education unstrings the nerves of both body and
mind ; too much sleep is useful to neither mind nor body ; the
winds bring now rain, now sunshine; he who blends the useful
with the agreeable is approved by all ; credulous hope nourishes
our life, and always declares that to-morrow things will be better ;
Yiriathus had carried on war against the Romans for fourteen
years ; placability and clemency are more praiseworthy than anger:
a great part of our men were wounded or slain ; Gaul takes special
pleasure in beasts of burden, and procures them at a great cost ;
the husband and the father shouted out; the Senate and the
Roman people sanctioned the peace ; the Senate and C. Fabricius
surrendered the deserter to Pyrrhus ; let religion and fidelity be
preferred to friendship : Conon lived (vixit) very much in Cyprus,
Iphicrates in Thrace, Timotheus at Lesbos, Chares at Sigeurn ; nor
has either (aut) Brutus or (aut) Cassius now for the first time
the safety and the liberty of their country the most sacred

Page 8, col. 2, vol. III.— English-Latin.

Magna telorum vis vulnera dabunt; rex cum aliquibus duci-
bus capti sunt ; divitiis et paupertate et morte omnes moventur ;
jus et injuria sunt dissimilia; caetera turba fuserunt; alii urbem,
alii rus petebant ; corporis nervi franguntur molli educatione ; cre-
dula spe alitur nostra vita; civitatis juvenes bellum parant;
jumenta magno parantur impenso; senatus Popult Romani pacem
comprobabit; religio et fides amici tiae antepositae sunt; religio
et fides anteponendae sunt omnibus ; Brutus et Cassius salutem
reipublicae sanctissimam legem judicabunt; reipublicae salus
sanctissima est legum omnium.

Page 18, col. 2, vol. I IT.— Latin-English.

No evil is more oppressive and troublesome than envy ; what
embossed plate, what rich coverlets, what paintings do you think
there are in his house ? the question is, whether one duty is greater
than another ; is there any human being of whom you have a better
opinion ? they spoke to the people, each on his own behalf, with the
greatest authority they severally possessed ; the mind of man is
ignorant of coming fate ; the ancient Germans were not lovers of
letters, but they could endure thirst, cold, and labour ; Africa feeds
herds of wild asses ; Alexander the Great had not control over
his anger ; the ancient Romans were very desirous of glory ; in
summer the days are longer than in winter ; nothing is more divine
than mercy ; the moon is nearer the earth than the sun ; as the
mind is more noble than the body, so virtue is preferable to strength
and external beauty ; how (quanto) preferable [put a note of excla-
mation after potior] is an honourable death to a base life ! how
few philosophers are with you ! the tribunes put forward a law (to
the effect) that one of the two consuls should be chosen from the
people ; we are very numerous ; Themistocles sent to the king by
night the most faithful servant he had : we have come hither to do
thee honour ; Hasdrubal was the son of Giscon ; how many are
you ? (how many are there of you ?) we are few (there are only a
few of us) ; Callisthenes was the most earnest among those Vho
refused (the recusants); Themistocles inflicted on the house of
Xerxes more evils than any other Greek; he is the elder of the
Neros ; I am Deiphftbe, the daughter of Glaucus ; the king's
friends are few; Thales was the wisest of the seven (sages of
Greece) ; the state of the Treviri was by far the most powerful of
all Gaul in cavalry ; to what degree of madness have you gone?
a good friend in a trial lessens the trial one-half; can anything be
more absurd than to seek the means of living the more, the less
the remains of life ? I give you the same advioe as (I give) myself ;
of their benefits some are of that kind that they extend to all the
citizens, some that they affect individuals ; you have an abundance
of wealth; terror and fraud abound ; you have preserved me rather
from love than honour ; he pretended to be in haste on account of
business ; all of them received a military honour on account of their
valour ; that one day on which I returned to my native land, Was
to me as good as an immortality.

Page 18, col. 2, vol. III.— English.Latin.

Regis mulier pulchra est ; regis mulier est pulchrier quam duds
mulier ; uter est sapientior ? sapientissimus mortalium est Socra-
tes ; quid panis est tibi ? eo dementiae est processus at omnes eum
predicent stultum; belli causa venerunt milites; ducis honor!
praemium cuique militum est datum ; librorum aliunde mini est ;
hie unus liber iibrorum omnium mini est instar.

JSeop'i Fables.

Thb Toetoi8B and thb Eagle.

A tortoise earnestly entreated an eagle- to teach her to fly. The
eagle attempted to show her that she asked a thing contrary to he

THE POPULAR EDUCATOR.

SLOANE'S BALANCE.

r~\

Thirteen thirty-sixths of the whole, the Wolf flnish'd,

Twenty-one thirty-sixths, the Tiger diminished,

Leaving only two thirty-sirtks, full to the King,
a The portion eaten up, by himself, at a spring.
* Having found out these answers, apart from ail men,

1 beg to subscribe myself, A. U., Rutherglen.

[This question was also correctly solved by J. W., Reading j W
Parker, Busk ; U. B. R. ; Josephus, Oravesend ; R. Brown, LeVea
H. C. P., Bristol ; and others.]

Sib, — I beg leave to tend you a, sketch of a balance which I have
designed, with a view to bring such an instrument within the reach
of any student of chemistry ; the expense to an ingenious person
would scarcely exreed a shilling. The balance is composed of a
penknife blade, easily procurable at any cutler's for a few pence,
fixed in a stand of wood ; the beam, made of a bit of polished brass
wire, Is formed to rest on the edge of the blade as shewn in the
sketch ; and the pans are watch glasses borne by silk threads* on the
top of the loop in the beam, I have soldered an index which can
be adjusted (the balance being at perfect rest) by a card with a
xero point drawn on it, sliding in a groove on tho top of the wooden
stand. This balanee will be found inexpensive, and sufficiently
sensitive for all usual purposes, weighing grains with accuracy. I
-am, Ac.. John J. Sloan e.

114, Great Britain-street, Dublin.
Sep. 17, 1863.

ANSWERS TO CORRESPONDENTS.

G. A., Jan. (Liverpool): We don't know the French dictionary til spilt pf
Caasell'i French Dictionary has the pronunciation wherever there Is amy
dihlculty.— 8. E. (8henVld) : We think our own lystsm the best.

O. M. (Alderagate) informi ui that quilltd glass may be easily had under
the name of tube glass, and that it may be purchased at Mr. Gibbon's glass
and bottle warehouse. Jerusalem-passage, Clerkenwell, where spirit liiss
and other chemical apparatus may also be had.

A Subscribes (Bromley) recommends such of our subscribers as oat
•pare the money to do themselves the pleasure of presenting vol. L of the
P. E. to some promising, aspirin? jouns friend 1 He seems to think that hy
this means many would be greatly encouraged in the work nf ITrflP Twsmvu

_„, _, _...._ .._. ... ,_....__. ....._ . . . ' I. flsJBSS

SOLUTIONS.

'WntSou a/the Question proposed in No. 75, page 344, Vol III., of
the "Popular Educator,**

Here, the wolf would eat \ of the sheep in 20 minutes, and
the tiger would eat i of the sheep in 10 minutes ; therefore,
both would eat £ of the sheep in 20 minuter. Consequently
there would be \ of the sheep to be eaten together by the wolf,
tiger, and lion.

Now, the wolf would eat 1 sheep in 1 hour ; the tiger would
eat 3 sheep in 1 hour ; and the lion would eat 2 sheep in 1
hour ; therefore, all would eat 6 sheep in 1 hour. In what
time, then, would they eat i of a sheep ? Here we have
•6 sheep : £ sheep : : 1 hour : If minutes for the time taken by
the 3 animals to eat the whole sheep, from the commencement
of the operation.

Lastly, we have 60 minutes : 21 § minutes : : 1 sheep : \h the
part the wolf ate ; 20 minutes : 11 j minutes : : 1 sheep : H, the
part the tiger ate ; 30 minutes : 1} minutes : : 1 sheep : A> the
part the lion ate. Whence, a 1 + § i + &= ? 8=1 sheep, proof.

G. Archbold, St. Peter's.

[The following rythmical answer may please some readers.]

Mister Autodidactos, I've look'd o'er your rhyme,
And propose now to tell you exactly the time
Which the Wolf, with the Tiger and Lion combined,
Took to eat up the Sheep, and leave nothing behind.
Twenty-one and 'wo-thtrds are the minutes, you see,
That the sheep was in esting among them all three.
Then as to the portion to each one allotted,
This may, in the following words, be just noted :

ment, and at the same time be induced to buy the whole

tried the plan himself, and expects good results. — Pbilo (Nottingham)
The instrument! he mentions will be described in future numbers.

Alpha (Thornton I.e Clay) : The term instinct U generally applied to the
reasoning power of the lower anim.il*, and is considered to be an inatanta*
neous faculty of judging of what is right and wrong aa regards their welfare,
conferred on them by God. The term reason is applied to that faculty with
whieh God has endowed man, to enable Aim to judge of what ia right and
wrong as rrgirds his welfare ; conscience ia no other than this faculty properly
instructed, ni made aware ol * hat is right and wrong, and of their conse-
quences. Hence, the man who has received the highest moral and rclirioRS
educa*:-m has the most tender conscious. When the conscience la stared ay
neglecting its warnings, the poflsethor of It becomes worse than the moat
ignorant lavage, and in his actions falls lower than the brute creation. We
recommend all our reader*, by nil meant, to cultivate a tender conscience,
and one Toid of offence towards God and man. The penny edition of the
P. E. mny be exchanged for the three-halfpenny edition, if It be quite clean
and in good condition, on paying the difference in price.

Tom Harrison (Greenwich): We shall discus* the subject of the Bine-:
mial Theorem in the lessons in Algebra as soon aa we cau.— J. 3. (Iiutford)
Go on improving.— F. Kiciiardi (8elby): We don't know it.— W. k.
Edwards (rtwinton-pt.) : Thanks— R. J.lt. : We quite agree with his remarks
on Prop. III. Hook I., but we have dwelt already too long on the initial pro-
position! ; we must now advance with m re (peed.

Omuua : We think that the Latin Die Uo nary by E. A. Andrews, which is
a tianslation of Dr. Freund's Latin Dictionary published in Germany, ia
most likely to be the bat. As to the study of Latin, get all the knowtedce
you can by hook or by crook.— J. E. 8. A. ia too flattering to ne ; we shall
consider his suggestion.

J. E. (Oldham), Student in French (Leeds): Yes.— Jams Joins
(Morriston): Apply and go ahead. — Constant Admirrr (Torquay)
deserves our sincereat thauks ; but many men, many minds.— Warim (Eart
Dereham): Ah ! ray friend, beware 1 there are sad flaws in Legemlra'a Geo-
metry ; don't forsake old Euclid ; he has stood 4,000 years 1 The second caaa
of Prop. VII. won't do, neither will the demonstration of Prop, XVI —
Jsnobia (Brighton): The •• Historical Educator*' is a subatitute for the
lessons in History in the P. E.— J. Thompson (Leicester): We are not
certain.

J. F. Entwistlk (Wigan): His tables for the Oetary Beale are very
ingenious ; many thanks for his kind endeaTours ou our behalf. — E. Hast:
For a list of French books, write to any of the foreign bookeelleia in London,
aa D. Nutt, Strand; Dulan and Co., boho-square, &c. The best library la
London for scientific and all other books ia that of the British Museum;
admission is free, but you must have a recommendatory letter from some
gentleman who la well known, addressed to the chief librarian.— A Subscri-
ber (Westminster) need be under no alarm about omissions of aectloaa in any
branch ; misprints will sometimes happen.— W. O. R. Vrnkrr had batter
make very considerable progress in learning before he thinks of the ndfcls*
try ; mere spouting wou't do.

LITERARY NOTICES.

GEEEK.
The Third Volume of Cassell's Classical Library will contain the

Acta of the Apostles in the original Greek, according to the teat or Augustas
Hahn; with grammatical, historical, and expository Notes ; followed sy a
Lexicon, explaining the meaning of every word— the whole oarsftnly

Hahn ; with grammatical, historical, and expository Notes ; follou
Lexicon, explaining the meaning of every word— the whole

rerlsed and corrected. Thia work ia well adapted for the use of

Colleges, and Theological Seminaries, and will supply our Greek student!
with excellent materials for practice in translation.

The first volume

LATIN,
of Cassell's Classical

Library ia bow ready,

price la. 6d., containing Lathi ex tract j for translation on the foUowiaf
subjects— Easy Fables, Mythology, Biography, The History of Borne, sad
Ancient Geography ; with a suitable Dictionary.' The second
which is publishing in weekly numbers pries 3d. each, will
of uaeful Latin Exercisea, or. English sentences, to be translated iat
with numerous references to Andrews and Stoddart's Latin QtRBsatsr,s
valuable treatise now in the press.

LESSONS HJ NATURAL PHILOSOPHY.

ON PHYSICS OR NATURAL PHILOSOPHY.
No. V.

LAWS OF FALLING BODIES, INTENSITY OF
GRAVITY, &c.

Falling Bodies. — The three laws of Falling Bodies are the
following, which are only strictly accurate when the conside-
ration of the resistance of the air is omitted ; or, in other
words, when the bodies fall in a perfect vacuum.

1st Law : All bodies, large or small, fall with equal rapidity
to the earth's surface, at the same place. This law is proved
by the following experiment, called the guinea and feather expe-
riment. Take a tube of glass of about two yards in length, and
a convenient diameter, fig. 11, closed at one of its extremities,
and furnished at the other with a brass stop-cock; put into this
tube, placed vertically, with the closed end lowest, any two
bodies of different densities, such as lead and cork, gold and
paper, &c, and make a vacuum in it with
Fly. U. an air-pump ; then quickly invert the

tube, by placing the closed end uppermost,
and keep it in the vertical position ; you
will now see the light body and the heavy
body, such as the guinea and the feather,
both fall to the other end of the tube
with the same velocity. Readmit a little
air by opening the stop-cock, invert the
tube in the same manner as before* and I
you will see the light body falling more
slowly than the heavy one, in proportion
to its comparative weight. Lastly, re-
admit the air completely, perform the
same inversion, and you will find that
the light body falls still more slowly than
before, jn consequence of the greater effect
of the resistance of the air when fully
admitted into the tube. The conclusion'
from these experiments is, that if in the I
ordinary circumstances of the atmosphere
bodies fall to the ground with unequal
velocity, the cause of this is the resistance I
of the air, which is more sensibly observed
on the lighter bodies, and not from any
difference in the action of gravity upon
different substances, for it acts alike upon
all substances, making them fall from the
same height in the same time in a vacuum.
Moreover, under equal volume, all bodies
experience the same resistance of the air in
fulling ; but the force with which they are
attracted overcomes this resistance in pro-
portion to their mass.

The resistance of the air to falling
bodies is particularly evident in the case
of liquids. When they fall in the air,
J fl they separate and fall in drops ; but when

;f":i I. they fall in a vacuum, they fall like a solid

mass, without separating into drops. This
phenomena is proved by the apparatus
colled the water-hammer; this is a tube
of glass of about an inch in diameter,
and about a foot or sixteen inches long,
nearly half filled with water and hermeti-
cally sealed, after the air has been expelled
by raising the water to the boiling point.
When this tube is quickly inverted, the
water in falling strikes against its lower end with' a smart
fry sound like that of the collision of two solid bodies.

2nd Law. The velocity acquired by a body falling in a
vacuum is proportional to the time of falling. Thus, at the
end of 2, 3, 4, &c, times a given unit of time, the velocity
acquired will be 2, 3, 4, &c, times the velocity acquired in
that unit.
3rd Law. The spaces described by a body falling in a

!•

1st unit of time is 1, and the spaces described in 2, 3, 4, 5, &c,
units of time, are 4, 9, 16, 25, &c, it follows that the space
described in the 2nd unit of time is 4 less 1, that is, 3 ; in the
3rd unit it is 9 less 4, that is, 5 ; in the 4th unit, 16 less 9, that
is, 7 ; and so on. Hence, the spaces described in the 1st, 2nd,
3rd, 4th, &c, units of time are successively 1, 3, 5, 7, &c,
according to the series of odd numbers. From this it is evident
that the spaces described increase by equal quantities in equal
times, which is in accordance with the definition already given
of uniformly accelerated motion.

The laws of falling bodies are only true when the bodies fall
in a vacuum, and from heights in the atmosphere differing
little from each other in comparison with. ' the radius of the
earth. When the bodies fall in the air, these Jaws are modi-
fied by the resistance of the atmosphere ; and when they fall
from very unequal heights in the atraosphefp, the force of
gravity is not strictly the same.

Galileo, an Italian philosopher and Florentine nobleman,
was the first who made the discovery of tVjese laws, and
announced them to the students of the university of Pisa,
where he was professor of the mathematics in 1611 a.d.

Inclined Plane. — Various apparatus have been invented for
the purpose of proving the laws of falling bodies ; Galileo
employed the inclined plane in an original manner; Atwood
invented the machine known by his name ; a^nd M. Morin,
director of the " Conservatoire des Arts and Metiers" at Paris,
constructed an apparatus first proposed by M. f oncelet.

An inclined plane is one which makes with a horizontal
plane any angle lew than a right angle. In proportion to the
smallness of the angle between these planes, so is the decrease
pf the velocity of a body which descenft alone the inclined
plane. Thus, let a b, fig. 12, represent an inclined plane, a c
the horizontal plane, and u c a perpendicular to the horizontal

Fi?. 19.

vacuum, are proportional to the squares of the times of falling.
Thus, if the time* of falline be 1, 2, 3, 4, 5, &c., times » given
unit of time, the spaces described will be 1,- 4, 9, 16, 25,
fcc. times the space described in th&t unit.
Since, according to the third law, the space described in the

plane drawn from any point it in the inclined plane. If any
body if rest upon this" inclined plane, its weight p acting ver-
tically may be resolved into two forces a and P, the one acting
in a perpendicular and the other in a parallel direction to the
inclined plane a c. The first force, Q, will oe completely
counteracted by the resistance of the inclined plane which acts
in the direction a o, and the other force f only will act on the
mass of the body m in order to make it descend along the plane.
In order to ascertain the value of the force f 9 take on the
line op a length the number of whose units represents the
weight r, and complete the parallelogram dgeh; then the
force p will be represented by the nuifityer of units of length
in on. But the triangles n o h and ABc'are similar, because
their angles are equal (Cassell's Euclid, Book VI., Prop. IV.) ;
whence we have

o h : i> o : : a b : n c, or
p : f :: ab : isc;
that is, the force f will be less than the weight r, in proportion
as the height b c of the inclined plane is less than its length a o.
Thus we can make the force f as small as we please, by
diminishing the height of the plane, or the angle* which, it
makes with the horizon, and thus slacken the motion of tb«>
moveable body m, so as to be able to take account of th*» '
described in one, two, three, &c, seconds, and '*
altering the laws of the motion, since the r
or constant. By such experiments as this
that the spaces described increased as
times.

AticooeCs Machine.— The laws of fal 1
were more clearly demonstrated expe*
a machine invented by Mr. Atwood, r
the University of Cambridge. This n
narrow wooden pillar, about seven t ?

VOL. IV.

THE POPULAR EDUCATOR.

having on the top a gloss case, in which is placed a brass pulley
b, fig. 1 3. Over this puileypasses a silken thread, so fine that it
weight need not be taken into account, and having two equal

weights m and m' bus

r\g. 13.

31'

pended at its extremities.
The axle of the pulley,
instead of resting on two
fixed bearings, is sup-
ported on the circumfe-
rences of four moveable
wheels. By this arrange*,
ment the axle of the
pulley transmits its mo*
tion to the four wheels,
and the Bliding friction
of fixed bearings is con-
verted into the rolling
friction of the wheels, i
contrivance by which the
friction of the axle is very
much diminished.

On the pillar is fixed i
clock-movement h, which
regulates a seconds' pen-
dulum p by means of an
anchor escapement. Thii
escapement is shown on
the dial-plate above the
'swing- wheel which occu-
pies the centre. Thit
escapement oscillates with
the pendulum, and in*
dining to the right and
left alternately at each
oscillation, it allows one
tooth of the swing-wheel
to escape. The axis of
this wheel carries at it*
anterior extremity an in-
dex marking seconds, and
at itB posterior extremity,
behind the dial-plate, an
eccentric, shown at ion
the left of the pillar. Thii
eccentric moves with the
index, and presses on a
lever d, which, by its
motion, overturns a small
platform i, employed to
support the mass m'.

Parallel to the pillar,
and fastened to its base,
is a wooden scale of nearly
the Bame length, divided
into inches and tenths of
an inch, used for the
purpose of measuring the
spaces described by the
falling body. On this
scale are two stages a and b, which by means of tangent
screws can be adjusted to any required height. The stage
a. is intended to receive the weight m' at the end of its course }
and the stage n, which is hollow, allows this weight to pass
through it, and is used only to stop the progress of the addi-
tional weight m which rests upon it at starting. The use of
Atwood's machine is to diminish the velocity of a falling
body, and to produce at pleasure a uniform motion, or a
motion uniformly accelerated.

the weight m to fall by itself, now puts in motion this weight
and the two other weights m and m'. The quantity of motion,
or momentum, will therefore be still the same. If we denote
the velocity of the mass at the end of a second by *, the
momentum will be (m-\-2x)x ; and by putting this equal to the
momentem of m, when it falls alone, we have the equation

(i*+2m)*=«i^ ; whence x =

tng

Thus, if the weights

In order to understand the nature of this machine, suppose
that a small piece of brass m, which in the engraving rests on
the stage b, falls alone ; let its velocity at the end of a second
be denoted by g ; its momentum or quantity of motion wiU
then be denoted by mg. If this piece of brass m be placed on
the weight m', when at the top of the scale, it will descend and
communicate part of its motion to the two weights m and it' ;
for previously to this, the two weights being equal were in
equilibrium, the action of gravity in each being mutually
balanced. It is plain that the same force which would cause |

fw-f-2u
m and m/ were each 16, the weight m being unity or 1, we

should have x = ^ ; that is, the velocity of the mass would

be only one thirty- (bird part of the velocity which it would
have if it fell freely in tfee air. By this means we can more
easily ascertain the nature of the force which causes bodies to
fall, and also render the resistance of the air imperceptible.

The first expeiiment performed by this machine proves that
the spaces described by a falling body increase as the squares
of the times. The pendulum p being at rest, and the second
index being beyond zero, the weight m' is placed on the plat-
form i, and is loaded with the additional weight m, the whole
being kept in the horizontal position by the extremity of the
lever d, and corresponding to zero on the scale. Removing
I then the hollow stage b, and preserving only the final stage a,
I place the latter, by trials, at such a (lib to nee from the zero
point at i, that from this point to the stage a the weights m
and m take only one second in falling, the fall commencing at
I the instant when the pendulum having been put in motion
I the index reaches zero on the dial-plate ; for at this point the
i lever d is put in motion by the eccentric, and the platform i is
overturned, setting the weights m and m at liberty to fall.

Suppose now that we have found the height of the fall, or
the space descended in a second, to be seven divisions of the
scale ; then repeat the experiment as before, but remove the
stage a to a distance from the zero point i, equal to four times
the preceding distance, that is, to the 28th division of the
scale, and it will be seen that this space is described in
exactly two seconds by the two weights m and m'. In like
manner it will be found that at a distance nine times the first,
or at the 63rd division of the scale, the space will be described
in three seconds; and so on. The third law is, therefore,
verified by experiment.'

In order to verify the second law by experiment, it must be
recollected that in accelerated motion the velocity at a given
instant is that of the uniform motion which follows upon the
accelerated motion. Hence, in order to discover according to
what law the velocity of a falling body varies, we have only
to measure the velocity of the uniform motions which imme-
diately follow the accelerated motions successively after one,
two, three, &c, seconds of the fall.

The determination of the uniform motion after the accele-
rated motion is obtained by means of the stage b. This is
placed just at the distance from the zero of the scale which the
two weights m and m' when descending reached in a second, as
in the first experiment; then, the additional weight m being
itopped in its descent by the stage b, the weight m' continues
to descend alone, until it be stopped by ihe stage a, which is
placed below b at such a distance as that the weight it' shall
occupy only one second in passing from b to a. Now, from x
[to b the motion is uniformly accelerated, and from b to a it is
! uniform ; for the weight m being stopped by the stage b,
gravity no longer acts from b to a, and the motion is only
continued in consequence of the inertia of the weight m'. The
number of the divisions of the scale passed over by the weight
M' from the one stage to the other will then represent the
Velocity acquired by the two weights m and m' at the end of
one second.

In repeating this experiment, the stage b is lowered to such
m distance that the two weights m and m' take two seconds to
descend from the point i to the stage b ; the stage ▲ is then
lowered to a distance from b double of that at which it was in
the firBt experiment. Thus, the two weights fall during two
seconds in a state of uniformly accelerated motion ; then reach*
ing the stage b, the weight m' alone passes over the interval
between the stage b and the stage a. The velocity acquired
it the end of two seconds is therefore double of that acquired
at the end of one second. Similar experiments being made foi

LESSONS IN NATURAL PHILOSOPHY.

three, four, &c, seconds, it will be found that the velocities
acquired are three, four, &c, times the velocity acquired at the
end of the first second ; and thus the second law is verified.

M. Moriri$ Apparatus. — In this apparatus, or continued
indicator of mot en, the uniform rotatory motion of a cylinder
covered with paper is combined with the motion of a falling
body, in such a manner that by means of a pencil properly
adjusted for the purpose, it describes on the paper a curve
which represents the law of the motion. In fig. 14, the cylin-
der a, which is covered with paper, is about 9} feet in height,
and about 16 inches in diameter ; this cylinder is set in motion
by a weight p, and this motion is communicated by means of a
cord to the drum b; this drum, by means of two bevelled
wheels, communicates the motion to a rod h and to a wheel
and pinion i and o, which put the cylinder a. in motion.

The weight p having a tendency to accelerate its motion
during its descent, M. Wagner, the maker of the apparatus, cm-

to guide a long wooden ruler which is applied to the cylinder,
and is used to trace on its surface two kinds of equidistant
lines, the one in planes perpendicular to the axis of the
cyl indcr, and the other vertical.

The cast-iron piece, or monkey, m, guided in its descent by
two straight iron wires, r and o, firmly fixed at their extremi-
ties, is placed at first in a catch at d, which can be opened at
pleasure by drawing the wire l. To this monkey m is
fastened at u the pencil which describes, during its descent,
the curve a a on the cylinder as it revolves. From the form
of this curve the laws of motion arc deduced.

For the space passed over by the pencil at the end of any
given time, is at the point in of the curve equal to the portion
am of the vertical traced on the surface of the cylinder. But
the motion of the cylinder being uniform, we can take for the
duration of the fall, when the moveable has descended to w,
the arc h m t between the point in and the vertical which is

Fig. U.

ployed, for the purpose of regulating the motion of the drum b,
a regulator of whicn the mechanism is concealed in the figure.
It is known in mechanics, however, by the name of the difft-
rtntial motion, and it depends both on the motion of a pendulum
o, and of a fly furnished with leaves, which moves with great
rapidity. This fly is contained in a drum t, which rises
or falls according to the velocity of the apparatus. When
the motion is accelerated and the pendulum oscillates too
rapidly, the drum* rises, and the leaves of the fly then meeting
with the resistance of the air, the motion is retarded. On the
ether hand, when the velocity diminishes, the drum is lowered,
and the fly then meeting with less resistance from the air, the
motion is accelerated. Thus a motion sensibly uniform is
obtained ; and for this purpose the descent of the weight p
for about 20 inches is sufficient.
The wheel n, fixed on the axis of the cylinder, is employed

drawn through the point at the origin, or the beginning of the
motion of the pencil. In like manner, at any other point m,
of the curve, the space parsed over is represented by a m"
and the time by K m\ Now, by comparing the lengths a m
and a m with the arcs h m and h' m\ we find that the lengths
or distances a m and a m are to one another as the squares of
their corresponding arcs ; thus it is clearly demonstrated that
the spaces passed over are to one another as the squares of
the tunes of passing over ; and we therefore conclude that
the motion of falling bodies is one uniformly accelerated.

The ratio which is found to subsist between the arcs Am,
h'm\ &c, and the verticals a m, am, &c, show that the curve
s & is a parabola whose axis is Darallel to the generatrix of tho
cylinder ; and this is at once demonstrated by unfolding on a
plane the paper cover of the cylinder gn which the curve is
traced by the pencit

THE POPULAR KDUCATOJt.

LESSONS IN ENGLISH.— No. LXXI.

By John It. Beard, D.D.

SYNTAX.-CONJUNCTIONS.

JojningUs the office of conjunctions. The joining may take place
between two words, between two clauses, and between two proposi-
tions. Properly the conjunction, and, joins two things, — this with
that, and is in consequence required before every second noun,
idjective, verb, &c. The practice of putting and before only the
Mat word of a series is of modern date. As au example of the
merely uniting functions of the conjunction, take this example : —

' " 1st Clause. 1 ?

" Let thero be no strife, I pray thee, between me ond thee, and

3 2nd Claiue.
between my herdmen and thy hcrdmen, for we ire brethren." —
(Gen. xiii. 8.)

The conjunction, and, number one, unites the pair of words, me,
thee ; number two unites the first clause with the second ; the
third and unites " my herdmen' * with " thy herdmen."

As an instance of and uniting propositions, take the fol-
lowing :—

1. And Jesus arose out of the synagogue

2. Ami entered into Simon's house,

3. And Simon's wife's mother was taken with a torer

4. And they besought him for her,
6. And he stood over her

6. And rebuked the fever,

7. yiwUt left her;

8. And immmediately she arose

9. And ministered unto them

Here arc nine successive sentences introduced by and.

While performing the part of joining together, a conjunction
may also show the nature of the union which it effects, assigning,
that is, the logical connexion as well as forming the grammatical
connexion. The logical connexion may be of various kinds.

The conjunction for, as it appears in the above example, gives
an instance of a causal conjunction, or a conjunction which assigns
the ground or reason of what precedes. In the ensuing you have
a specimen of a conditional conjunction in if, and of comparative
conjunctions in as well and than : —

M Ah ! if she lendn not alms ai icell as rules,
What can she more than tell us we are fools."— Pope,

The connecting force of the conjunction that may not appear at
first sight, as in

That mind is not matter, is certain.

Yet analyse the words, and you will find two sentences, of which
that is the link, thus :—

Mind is not matter,
This proposition is certain.
That mind is not matter, is certain.
Conjunctions unite wordi which bear to each other the same gram-
matical relation.

This rule is commonly stated thus : Conjunctions connect the
like tenses of vorbs and the like cases of nouns. The readiest
syntactical guide in the use of conjunctions is the thought. I will
take two instances, one of concord, the other of dependence : —

Concord : You and I are ill.
Dependence: He beat you and me.

In the first proposition, we have I after and, not so much because
tfou is in the nominative case, as because the statement is that I
am ilL This appears by analysis—

You are ill.
I am ill.

In the second proposition, me occurs after and, because me, as
well as you, is dependent on beat; e. g.,

He beaf you ;
He beat me ;

which is shortened into

He beat you and roe.
Aided by these observations, you will have no difficulty in
determining what form your words should assume when united by
conjunctions. You will, for instance, see that of these two proposi-
tions the first is erroneous, and the second correct : —

1. He is wiser than me.

2. He is wiser thau I (am).
So with

a b c

You love him better than I (me).
You love him better than me (I).

These sentences are right or wrong according to the meaning you
intend. If you mean that a loves b better than e lores f, the first
is correct ; in full, the sentence would then stand :

You love him better than I love him ;

but if you mean that a loves b better than a loves c, then the sen-
tence is incorrect, as may appear thus : —

You love him better than you love me.

Similar remarks might be made on the second example. John
Wesley, who was a good scholar, says : —

• 4 Ht hath died to redeem such a rebel as me;'*
and Lord Brougham, whose English is quite idiomatic, writes :—

"That England can spare from her service such men at him. 9 *
Are these high authorities correct ? If me depends on redeem,
Wesley is correct ; if him depends on spare, Brougham is correct.
But Wesley does not say he hath died to redeem me, but to redeem
sttch as. And Brougham does not say England can spare Aim, but
such as. Consequently, these eminent writers are wrong. They
should have said, " such a rebel as I (am) ; '' " such men as
he (is)."

The conjunction, as, carries with it the force of a relative pro-
noun, that is to say, it introduces a second proposition to which it
serves for the subject ; e. g.,

" Bat as many as received him." — (John i. 12.)

As is sometimes used in a manner which involves a grammatical
doubt ; for instance, should we write,

The conditions are as follow ; (or)

The conditions arc as follows.
The phrases are elliptical, and the preference of the one to the
other depends on the way in which the ellipsis should be filled
up; as,

The conditions are as (they) follow.
The conditions are as (it) follows.

I am disposed in favour of the last, thinking that the verb in such
cases is used as an impersonal or unipcrsonal verb.
The employment of the conjunction, that, as in

They affirmed (m?0 he would not come,

is required as indispensable by some grammatical critics with an
emphasis which may be somewhat undue. That the sense does not
require its insertion, i« obvious from its nature and from the sen*
tence just given as an example. If, however, the second membet
of the sentence is separated from the first by several intervening
words, ftri My serve as a point on which the mind may rest,
until it takes up the clause to which it refers, and for which in some
so rt it is a substitute ; e. g.,

Your brother stated that, as he and your cousin i _ r

down High-street, they saw a child fall from the roof of a house. '

Sound, also, has something to do in determining the use or the
non-use of that.

The ease with which conjunctions may be repeated, since they
have no substantive and independent meaning, gives rise to
pleonasms, that is, to forms of speech in which one word or snore
is found than is necessary. In conversation it is common to
bear a sentence introduced with but however, when only but or
however is necessary; the uneducated are especially given to
pleonastic forms of this kind. But we find them in good authors,
as may.be seen by the italicised words in these examplec * —

" When that the poor have cried Caesar hath wept" — Shaksftmre,
" But and if that evil servant say.' 1 — (Matt. xxiv. 4* J

LESSONS IN ITALIAN,

Correspond j >t> Conjunctions.

- Certain conjunctions go In pairs ; that is, the precedence of the
one necessitates the use of the other ; e. g.,

1. To though corresponds yet ; as, " Though he die yet shall he
live. 1 '— fJohn xi. 25.)

2. To uthetJter corresponds or ; as, " }Fhether it be greater or
less.*'— Bishop Butler.

3. To either corresponds or; as, " The indulgence of a declama-
tory manner is not favourable eUJier to good composition or
good delivery."— Blair.

4. To neither corresponds nor : as, '• John the Baptist came neither
eating bread nor drinking wine." — (Luke vii. 33.)

5. To both corresponds and; as, "I am a debtor both to the
Greeks and to the barbarians, both to the wise and unwise." —
(Rom. i. 14.)

6. To such corresponds as ; as, «« An assembly such as earth never
saw." — Cotoper.

7. To such corresponds that ; as, " The difference is sucJi that all
will perceive it."

8. To as corresponds as ; as, " And he went out from his presence
a leper as white as snow." — (2 Kings v. 27.)

9. To as corresponds so ; as. " As two are to four, so are six to
twelve."

10. To so corresponds as; as, " How can you descend to a thing
so base as falsehood."

11. To so corresponds as; as, "No Umb was e'er so mild
as he." — Langhorne.

12. To so corresponds as ; as, " We ought to read blank verse so
as to make every line sensible to the ear." — Blair.

13. To so corresponds that ; as, " No man was so poor that he
could not make restitution." — Alibnan.

14. To not only or not merely corresponds but, but also, but even ;
as, " In heroic times smuggling and piracy were deemed not only
not infamous, but even absolutely honourable." — M divider's Gram-
mar. •■ These are questions not of prudence merely, but of morals
also." — Dymottd** Essays

INTERJECTIONS.

Instead of speaking of a person, you may speak to a person, or
call upon a person ; you may employ the style of direct address.
For such kinds of address our nouns in English have no specific
form ; but exclamations or interjections supply the place of such
forms, and mark the existence of a direct address or appeal. That
address or appeal may have various meaning*, and even various
shades of meaning, corresponding with the state of the feelings at
the moment ; e. g.,

" Ah Dennis I Gildon ah l what ill-starr'd rage
Divides a friendship long conflrra'd by age." — Pope.

" Alas 1 poor Yorick." — ShaJcspeare.

Sometimes interjections, for instance, 01 oh 1 ah ! lo ! merely
call attention, or indicate an appeal or an address ; in such cases
they are followed by the case of the subject or that of the
object; as,

Subject : " O thou unknown, almighty Cause 1 " — Burns.

Object: "Lo! the lilies of the field,

How their leaves instruction yield ! " — Heber.

When deep feeling is intended, the case of the object is used with
a pronoun of the first person ; as,

Ah me 1 O unhappy me 1 woe is me !

that is, ah ! what will become of me ! O what has befallen unhappy
me ! woe is to me ! or, woe is on me !

" Judas said, Hail, master ! and kissed him."— (Matt. xxvi. 49.)
" Hail, Macbeth 1 "Shakspeart.
That Is, Hail be to thee, O master ! Hail (health) be to Macbeth !
In order to distinguish the subject and the object, when used
with exclamations or interjections, from the subject and the object
when employed in the third person singular, the former may be
called the subject of direct address, and the latter the object of
direct address.

The interjection, woe to ! requires the case of the object ; the
object, in reality, is governed by the preposition to : —

" Woe to them that Join honse to house."— (Is. v. 6.)

Theexclamaiion, Ofor / signifies O that I possessed ! as,

" O for that warning voice ! "— Cowper.

but alas for ! simply expresses grief towards ; as,

" Alas for Sicily !"— MiUon.

(t Alas for the day 1 "—(Joel i. 15.)

Instead of Ofor, we sometimes use O that ; e. g.,

" O that my people had hearkened unto me, and Israel had walked in
my ways!"— (Pa. Jxxxi. IS.)

LESSONS IN ITALIAN GRAMMAR.— No. V.

By CHARLES TAUSENAU, M.D.,

Of the University of Pavia, aud Professor of the German and Italian
Languages at the Kensington Proprietary Grammar School.

(Continued from p. 6i. )

IV.

I have now to speak of the diphthongs ; but before entering
into details I may remark that these letters differ materially
?°?u the J^R 1 " 11 ' inasmuch as the two vowels forming a
diphthong do not entirely merge into onesound, but are in Italian
more or less distinctly heard, though only pronounced by due
opening of the mouth, and with one emission of the air or
voice, which gives them the value of one sound. This broad
and general chaiaeterislic, however, prevails among all Italian
diphthongs, that there must be a ruling sound, requiring a
greater stress of the voice and more distinctness of utterance,
which ruling sound is at one time on the first, at another on
the second of the two vowels. In those diphthongs where the
second of the two vowels is the ruling sound, the voice glides
more rapidly from the firs* vowel to the second, and is, as it
were, absorbed by it. The second is on that account heard
with greater distinctness, and such diphthongs present more of
a united sound, while in those diphthongs where the first of
the two vowels is the ruling sound, the second is somewhat
more distinctly heard than the first vowel t>f those diphthongs,
which approach to a united sound, though shortly and quickly
trailed along, as it were, by the first.

The second kind or class may be termed, on this account,
the separated diphthongs ; the first class the united diphthongs,—
though I must caution the reader not to understand these
words in their strictly literal sense ; because, as I have stated
before, in all Italian diphthongs the two vowels are more or
less distinctly heard.

United diphthongs are, for example,

w, as in ftato (feeah-to), breath; biada (beeah-dah), corn;

piano (peeah-no), even, slow.
ie, as iii lieto (leee-to), cheerful ; bieco (bccC-ko), squinting ;

pHqgo (preec-go), request, prayer,
to, as in Jiore (fee6-rai), flower; piove (pcc6-vai), it rains;

brioso (brec-6-so), lively; chioma (keeO-mah) ; head of

hair,
tw, as in piu (peeoo), more; fiume (fefc6o-mai), a river;

schiuma (skce6o-mah), foam, scum.
ua, as in guasto (gwuh-sto), destruction ; qua (kwah), hero,

hither ; quale (kwah-lai), who.
«/?, as in guerra (gwerr-rah), war ; Guelfo (gwel-fo), a Guclph ;

guesto (kwai-sto), this.
mi, as in guisa (gwee-zah), guise, manner; Guido (gwec-do),

Guy ; qui (kwee), here.

as in cuore (kooo-rai), heart;
uomo (ood-mo), man.

suofto (soo6-no), sound;

Separated diphthongs are, for example,

ae, as in acre (ahai-rai), air, gas ; aerimante (ahai-ree-mann-
tai), one who predicts the air, or by aeromancy.

at, as in laido (lahee-do), ugly ; mam (mahec-scV), yes
indeed.

ao, as in Paulo (paho-lo), Paul.

THE roPl'LAlt FJ>UCATOK.

aw»* as in aura (ahoo-rah), a soft breeze ; Umro ilkhoo-ro),
laurel ; fraud* (frahoo-dai), deceit ; fauna (fahoo-no),
faun ; coma (kahoo-zah), a cause (at law;, affair.

##, as in Eolo (eo-lo), Eolus.

au, as in Europa (aioo-ro-pah), Europe ; feudo (feoo-do), a
feud or feoff ; SoUuco (tai-leoo-ko), Seleucus.

The vowel i before any other vowel, and the vowel u before
#, aa they occur in the united diphthongs, make in the pro-
nunciation of Italian precisely the same impression as a grave
or diatonic note in music, slightly but distinctly touched, to
glide otct to the second ruling vowel. They are very easy
transitions, and carry with them a particular charm, giving
to the sound a certain roundness and fulness, thus con-
tributing greatly, by the frequency of the diphthongs in
which they occur, to the musical character of the Italian
tongue.

It must be noted that there are vowels which come together
in words, but are, nevertheless, not diphthong! ; as,
for example, eoagulare (ko-ah-goo-iah-rai), to coagulate;
coerenU (ko-ai-ren-tai), coherent ; coot (kah - oa) f chaos ;
eoincidere (ko-in-tcheVdai-rai), coincide ; raunare (rah-oo-nah-
rai), to assemble ; acmpiere (ah-em-peeai-rai), fulfil ; rtaU (rei-
ah-lai), royal, real, loyal ; rumire (ree-oo-n6e-rai), to reunite;
wiola (vee-o-lah), he violates; viottolo (vee-6t-to-lo), narrow
passage or way, round-about way ; Dione (dee-6-nart, Dion ;
Xhiano (tee-tsee-ah-tio), Titian ; Teodoro (tai-o-do-ro), Theo-
. ore ; riaco (ree-3-sko), I succeed ; reato (tai-ah-to), guilt or
sin ; poet ( pah-ai-xai), country ; reina (rai-6e-nah), queen ;
loom (lai-6-nai), lion ; mantucto (mahn-soo-6-to), tame, gentle,

THIRD PRONOUXCIXO TABLE,

SH0W1XO WORDS WITH VOWELS I* COAXTTIOX.

1. Words the same with regard to their letters, but
with regard to their syllables : —

The reader will have remarked that I have, in the above
examples, separated the two vowels which come together into
syllables, thereby showing that they are not diphthongs, though
they may appear to be such. Indeed, if those sounds were
diphthongs, it is obvious that they could not be used as
separate syllables, as they must in Italian spelling, though
the poets, by their special licence, generally use them as one
syllable.

8ome grammarians are of opinion that in cases of the
coalition of three and sometimes four vowels in the Italian
language, those vowels form one syllable uttered with one and
the same emission of the voice ; and they term the coalition of
three vowels a triphthong, and the coalition of four, a quad-
riphthong t if I may so express it. They have been, perhaps,
led into that belief by the example of the poets, who in the
middle of a verse use the triphthongs like one syllable. It is
certainly allowable for Italian poets to count two or three syl-
lables being mere vowels as one ; but it would be strange to
found grammar on poetical licences, which are, strictly speak-
ing, exceptions to grammatical rule. The following examples,
generally cited as triphthongs, are spelt like words of two syl-
lables, though, as I have already observed, the poets use them
in the middle of a verse like words of one syllable ; and this
is reason enough why thev should not be considered triph-
thongs, i.e., coalitions of three vowels forming one sound and
one syllable ; as, mui (meee-ee), my (pi.) ; tuoi (tood-ee), thy
(pi.) ; tuoi (sood-ec), his (pi.) ; guai (gwah-ee), wailings ;
bitoi (booO-ee), oxen ; vuoi (vooG-ee), thou wilt ; puoi
(pooo-ee), thou canst; appiuolo (ahp-pee 006-I0), a kind of
apple-tree ; etdriuolo (tchai-drce-ood-lo), a cucumber ; mariuolo
(mah-ree-006-lo), a sharper ; vetriuolo (vai-tree-ood-lo), vitriol,
vitrious.

Examples of the so-called quadriphthongs shall be given
and commented on as they occur.

* I hare classed au as a separated diphthong where the first
vowel U the ruling sound. There are, however, words containing
that diphthong, in which t#, the second, is the ruling sound 1 for
esa*nple, paura (pahoo-rah), fear ; baule (bahoo-lai), portmanteau ;
Saulle (sabool-lai), 8aul. flut even in this class of words a and n
must be distinctly heard;, a, as the first of the vowel*, cannot be
ulided over rapidly and absorbed by the u, as would be the case
if a united diphthong. The diphthong au must therefore always
be classed anv>ng lUe separated diphthongs.

Italian.

Pronounced,

Emgiuh.

Baiia

bah-lteah

Nurse •

Balia

bah-lee-ah

Power, ^^-^miftn

Balio

bah-leeo

Huaband of a nurse

Balio

bah-lee-o

Bailiff; steward,

■mm«n

Bacio

bah-tcho«

A kiss, I kiss

Bacio

bah-tchee-o

A northern, sunless

Bugia

boo- j ah

aspect

He boxes a hole, he
lies

Bugia

boo-jee-ah

A lie

Empia

Im-peeah

Impious

Empia (for

entpiia) em-pee-ah

He filled

Lucia

lec-shce-ah

Lie, buck

Lucia

lce-shah

Smooth, sleek

Viola

veeo-lah

Violet

Viola

vce-o-lah

He violates

2. Words

nearly the same aa respects letters, but different

with regard

to syllables : —

Italian,

Pronounced.

English.

Sojia

*6f»feeah

He blows

Sofia

so- fee- ah

Sophia in Bulgaria.
Sophia, a woman's
name

Malvagio

mahl-v&h-jo

Wicked

Malragia

mahl- vah-gee-ah

Malmsey wine

Primizia

prec-mee-tseeah

Firstlings of fruit or
animals in sacrifice

Primazia

pree-mah-tsce-ah

Primacy
Vegetable market

Erbaria

er-bah-rce-ah

Erbario

er-bah-reeo

Herbal

3. General exercises in diphthongs :—

Italian*

Pronounad.

English.

Acre

ahai-rai

Air, gas

Paese

pah-ai-zai
lahee-do

Country

Laido

Ugly

Caino

kah-ee-no

Cain

Traxno

trahee-no

The trot of horses

Traino

trah-ce-no

Sledge

Lima

!ee-nai-ah

A line

Idea

cc-dc-ah

Idea

Idee

ce-dc-ai

Ideas

Lime

l£e-naiai

Lines

Set

tc-ee

Six

(hmi

o-mc-ec

Lamentation

Eolo

eo-lo

Eolus

Leone

lai-6-nai

Lion

Euro

£oo-ro

East wind

Creusa

krai-60'Zah

Creusa, a woman's
name

Biada

beeah-dah

Corn

Diana

dee-ah-nah

Diana

Cielo

tchG-lo

Heaven, horizon,
the air

Lieto

lee-d-to

Cheerful

Paolo

paho-lo
kah-os

Paul

Coos

Chaos

Fauno

fahoo-no

Faun

Paura

pah-6o-rahf

Fear

* For the sake of adhering to system, I am obliged here to
anticipate the use of some combinations I have not yet explained,
but which will be fully explained in the next lesson; as, for
example, do, (pa, tcia, &c.

f I have stated that oil is, strictly speaking, a diphthong, bat
principally in those words where the accent of tone falls on the
t econd of the %owels that compose it. It makes in its pronunciation
the impression as if it were no diphthong at all, because each of
the vowels is distinctly separated in pronunciation. On that
account, I have ventured to place it amongst those words,
with vowels in coalition, that arc not diphthongs.

LESSONS IN FRENCH.

Italittn.

Pronounces

Oiove

jfi-vai

Dio

deVo

Giuda

j6o-dah

JAuto

lec-6o-to

Oibo

Oee-bo

Annoi

ahn-no-ee

Quasi

kwah-zee

Duile

doo-nh-lai

Quete

kwe to

Duello

doo-el-lo

Fluido

fl6oee-do

Luigi

loo-6e-jee

Uomo

Ooo-mo

Luogo

loo- -go

English.
Jove, Jupiter
God
Judas
Lute

Not at all
Thou aunoyest
Almost, as it were
Dual

Quiet, calm
Duel, fray
Fluid
Lewis
Man
Space, spot, locality

LESSONS IN FRENCH.— No. LXXXII.
By Professor Louis Fasquelle, LL.D.

i 143.— Thb Conjunction. — Government op Conjunctions.
[See \ 127.]

(1.) Conjunctions govern the verbs following them in the
infinitive, the indicative, and the subjunctive modes.

1. The infinitive must be put after every conjunction which
is followed by the preposition de, and after all those which
differ from prepositions, only because they are followed by a
verb instead of a noun : —

Etndiez diligemment afin de but- I Study diligently that you may (in
passer vos compagnons. | order to) surpass your companions.

We think with M. Bescherelie, that the words described in
the preceding rule belong more properly to the prepositions
than to the conjunctions.

(2.) The following conjunctions always require the subjunc-
tive after them in French, whatever mode they may take in
English. Those marked with an asterisk require tie before the
verb [§ 138 (4.) :^

Ann que, in order that
•A moini que, unless
Au eas que, if
Avant que, be/bre that
Bien que, although
•De erainte que, for fear
•De peur que, lot
En eas que, in case
Encore que, although
Jnsqu'a ce que, till, until that
Loin que, far from, not that

Quoiqu'a peine a mes maux jo

puisse reaister,
Jaime mienx les souffrir, que de

k*« meritcr. Racine.

En cos que vous persistkz, il fau-
dra que j'allegue an prince ct an
roi memo votre mauvaiae santu.
Fcnclon.

(3.) The following conjunctions: — De maniere que,' de sorte
que, en sorte que, so that; tellement que, in such a manner
that ; si ce n'est que, sinon que, unless that, but that ; govern
the following verb in the indicative or conditional modes, when
the preceding verb expresses a positive assertion ; but they

Sovern the subjunctive, when the preceding verb expresses a
esire or a command : —

Malgre que, although
Konobstant que, notufUhstanding
Non que, not that
Non pas que, not that
Pose que, supposing Uuit
Pour que, that, in order that
Pourvu que, provided that
Quoique, although, though
Sans que, without that
So it que, whether
I Suppose 1 que, suppose that

Although I can scarcely bear my
misfortunes, I would rather suffer
under them, t/uin deserve them.

In case you persist, I must men-
tion your bad health to the prince
and even to (he king.

He behaved very ill, so that he
was obliged to withdraw.

Behave in such a manner that
people may be pleased witli you.

more verbs

II se conduMt trfci raal, de sorte
qa'ilJW con train t de *e retirer.

Faites en sorte qu on soil content
de voas.

(4.) When there are in a sentence two or
governed by a corj unction, que must be placed before the
second and the following verbs, or the conjunction itself may
be repeated : —

Puitquon plaide, qu'on meurt, et Since we plead, we die, and we be-

qu on devieut malade, come sick, we must hare physicians,

II fast dci medecins, il faut det we must have lawyers.
afocaU. La Fowtaine.

Si vous partes et que vous vou- I
lies me prendre avee vous.

Beschebelue.

If you go and wish to take me
witli you.

(5.) The other conjunctions generally govern the same tense
in French as in English :-

Fais du bien aujourd'hui puisque
to vis encore. Villefr^.

Rien n'eblouitles grandes ames,
patceque rien n'est plus haut
qu'elles. Massillon.

(6.) With regard to the conjunction, si, sec § 125,

Do good to-day, since thou yet
llvcst.

Aoilung dazzles great minds, be-
cause nothing is higher titan they.

••)

§ 144.— Collocation of Wohds.

(1.) The place of the different parts of speech has been men-
tioned in the Syntax under their several heads, and in vaiious
other parts of the work. A resume* of the principal rules of
construction may, however, not be unacceptable here.

(2.) The collocation of words is the order according to
which the several words which form a sentence should follow
one another. This order is fixed for the several forms of
sentences, affirmative, negative, and interrogative, by the
genius of the language, and the practice of the best writers,

(3.) The construction of the affirmative sentence is as simple
in French as it is in English. The following is the arrange-
ment of the words : —

1. The Subject. 2. The Verb. 3. T/ie Adverb.

Le raarclianrt est ici.

The merchant is here.

(4) When the subject is accompanied by an adjective, or
another attribute, the order is as follows : —

T/te Subject.
Le marohand
The merchant
Leflls
The son
Le martean
The hammer
Le bateau
The boat

, Its Attribute.*
anglais
English
de votre ami
of your friend
defer
cfiron
a vapeur
steam

3. The Verb.
est

est
is
eat
is

The Adverb.
ici.
here.
la

there.
' id.
here.
Ik.
there.

(5.) When the attribute is placed in apposition with the
subject, the construction is the same in the' two languages : —

1. The Subject. 2. The Verb. 3. The Attribute.
Le marchand eat anglais.

ThemercJiant is English.

(6.) When the verb is in a compound tense, many adverbi
are placed between the auxiliary and the participle : —
1. The Subject. 2. The Auxiliary. 3. The Adverb. 4. The Participle,
Nous a von s sou Tent ta.

We hare often read.

(7.) Long adverbs of manner, ending in meat, other long
adverbs, and the adverbs of lime and place, aujourd'hui, demain,
hier, ici, hi, arc not placed between the auxiliary and the par-
ticiple [§ 130,8.40,5.]:—

Nous avons ccrit aujourd'hui, ll'c hare w/itten to-day .

(8.) When there is a direct regimen in the sentence, it is
placed after the verb :—

I. Subject. 2. Attribute. 3. Verb. 4. Adverb. 5. Regime Direct.
L'ecolier attentif apprend toujour* fa lecon.

Zhcscliolar attentive Uarns always Ids lesson.

(9.) When there are two regimens of equal length, or nearly
so, the direct precedes the indirect: —

1. Subject. 2. Verb, 3. Direct Regimen. 4. Indirect Regimen.
Jean a donnl le livre a mon pere.

John has given the book to my fat/ter.

(10.) Should the direct regimen be followed by a relative
pronoun, or by attributes rendering it longer than the indirect
regimen, the latter is placed first .4fc-

• Some adJectiYet [\ S3 (11.)] are generally placed before the noun,
when uied alone with a noun ; but wlim another adjective comet with
tb*in, they follow the noun :— un petit liomme, a Utile man ; un homtne
petit et gro», a short. stout man; olheis hmc a different m«auiug before the
noun or alter it [\ 85],

THJfc POPULAR KfJUCATOR.

Direct Reg.

4. Verb.

donne.

gtces.

donne.

guvs.

1. Subj. 2. F>r*. 3. Ind. Regimen. 4. DiVwrf Regimen.

Jean a donne A mon pere le livre qa'Il lai avait promts.
John has given to my father tlte book which he had promised him.

(11.) The pronouns representing the direct regimen, and
those representing the indirect regimen, preceded by to,
expressed or understood in English, are placed before the verb
in French : —

1. Subj. 2. Direct Reg. 3. Verb. I 1. Subj. 2. Ind. Reg. 3. Verb.

Nous lea voyone. I Nous leur parlous.

We them ste | We to them speak.

(12.) In the imperative used affirmatively, those pronouns
follow the verb : —

1. Verb. 2. Direct Reg. I 1. Verb. 2. Ind. Reg.
Voyci- les. I Paries- leur.

See t/iem. \ Speak to them.

(13.) "When two personal pronouns are used, as regimens in
a sentence, the indirect, if in the first or second person, pre-
cedes the direct : —

1. Subject. 2. Ind. Reg. 3
Paul nons

Paul to vs

Paul vous

Paul to you

(34.) Should, however, the indirect regimen be in the third
person, it is placed after the direct : —

1. Subject. 2. Direct Reg. 3. Ind. Reg. 4. Verb.
Paul le lui Jonne.

Paul it to him gives.

(15.) In the imperative used affirmatively, tho direct regi-
men precedes always the indirect: —

1 Verb. 2. Dir. Rtg. 3. Ind. Rep.

Donutz- les nous.

Give them to us.

Donnez- les lui.

m Give them to him

(16.) Tho pronoun representing a noun in the oblique cases,
generally preceded in English by a preposition other than to,
is, in French, planed after the verb : —

1. Suy. 2. Verb. 3. Ind. Reg.
Jo ' parle deJul.

/ speak of Mm.

Je parlc avco lui.

I speak with him.

(17.) To render a sentence negative, ne is placed immediately
before the verb, and pie, jamais, rien, &c, after it : —

1. Subj. 2. Negat. 3. Verb. 4. Negat L
Je ne vols pas.

/ not see not.

Je ne lis jamais.

/ not read never.

(18.) When the verb is in a compound tense, the first nega-
tive is placed before the auxiliary, and the second between
that auxiliary and the participle : —

1. Subj. 2. Negat. 3. Reg. 4. Aux. 5. Negat. 6. Part.

Je.

pas

JlOt

him

have

not

seen.

leur

jamais

parle*.

not

to them

have

never

spoken.

leur

rien

donne.

not

to them

have

nothbuj

given.

Je
J

(19.) The pronouns used as direct regimens und as indirect
regimens are placed before the imperative, used negatively.
They are subject to the rules of precedence, (13.) and (14.)

1. Negat. 2. Reg. 3. Reg. 4. Verb. 5. Negat.

[Kale (13.)] Ne nous le donnez pas.

Not tons it give not

pas.
not.

[Rule (14.)] Ne le lui donnez

Not it ♦ to him give

(20.) The construction of an interrogative sentence, which has
a noun for its subject differs in the two languages. The fol-
lowing examples will show the order of the words in
French :—

1. The Subj. 2. Verb.
Le marchand n<;oit-
nceives
ccrit-
writes

The merchant
Mon frcre
My brother

titiplicate Sub. 4. Regime*.

11 . son argent?

he his money}

il des lettres ?

he letters ?

(21.) When the sentence commences with oh, where; que,
what; quel, what, which; combien, how much, how many; the
noun may be placed after the verb : —
Ou est votre ami ? J Where is your friend f

Que dit votre pore ? | What says your father t

(22.) The construction of interrogative sentences, in wnich
the subject of the verb is a pronoun, is very simple. The pro-
noun is placed after the verb in simple tenses, and after the
auxiliary in compound tenses : —

1. Regimen Ind. 2. Verb. 3. Subject.
Nous envoycz- vous

To us send you

1. Reg. Tnd. 2. Aux. 3. Subj. 4. Part.

Leur avez- vous donne*

To them have you given

4. Direct Reg.
notre argent?
our tnoney ?

5. Direct Reg.

oct argent ?
that money?

(23.) The orler of the words in a sentence at once negative
and interrogative is as follows : —

1. lst.Ncg.
No

Not

Reg. Prn. 3. Verb.
nous
tons

envoyet-
send

5. 2nd. Neg. 6. Direct Reg.
pas dc 1' argent *

not money!

(24.) In a compound tense : —

1. 1st Neg. 2. Reg. Prn. 3. Verb.

Subj.

vous

pa*

Ne
Not

4. kuhj.

nous
to us

avez-
huce

5. 2ttd Neg.

pas

not

6. Part.
envoye
sent

you
7. Din Reg.

de l'argent ?
money?

(25.) The first person singular of the present of tne indica-
tive of most verbs, which have in that person only one syllable,
and of a few others having more than one syllable, but ending
in s, cannot admit of the construction mentioned in the 22nd
rule of this Section. To render the sentence interrogative, esU
ce-quc is prefixed to the affirmative form of the verb : —

Kst-ce-qne vous parlor ?
Is it that you speak ?
Do you speak ?

Eat-ce-que Je pretends lui parler ?
Is it that I pretend to speak to him f
Do I pretend to speak to Itim ?

(26.) Every person of a tense susceptible of beiug conjugated
interrogatively, may be rendered so by prefixing est-cc-qus to
the affirmative form : —

Est-ce-que vous lisez ? I

Etst-ce-que votre frere cat arrive ? |

Do you read ?

Is y.ur brother arrived ?

(27.) In poetry and elevated prose, the subject of an affirms,
tive sentence is bometimes placed after the verb : —

Tout-a-coup an jour vif et bril

lant de la zone torride, succede une
nuit univcrselle et profbnde ; a la
parure d'un printempg tkemel, la
nudite dctf plus tristcs hirers.

Raynjll.

Suddenly to the vivid and btU-
liant day of tlte torrid stone, succeeds
a universal and profound night ; to
the attire of an eternal spring, the
nakedness of tlte saddest winters.

(28.) The article, the demonstrative, and the possessive
adjective are repeated before every word which they determine
[S. 85].

1 29.) Pronouns, used as subjects of verbs, may bo repeated
before every verb [§ 99, S. 86].

(30.) Pronouns, used as regimens of verbs, must be repeated
before every verb [§ 105, S. 15],

(31.) Prepositions ore generally repeated before every word
which they govern [§ 1411.

LESSONS IN CHEMISTRY.

Fig. 19.

LESSONS IN CHEMISTRY.—No.IV.

The only tests we have hitherto employed in oar chemical
investigations, are hydro-sulphuric acid, and hydro- sulphate
of ammonia. Let the student now obtain the following : —

1. A solution (saturated; of prussiate of .potash, also called
fcrrocyanide of potassium.

2. Infusion or tincture of gall nuts.

3. Hydro-sulphuret* of ammonia already prepared, by trans-
mitting sulphuretted hydrogen gas through liquor ammonia
(hartshorn), until the latter refuses to dissolve any more.

4. A solutiou of potash procurable at the druggist's, under
the name of liquor potassa*. It must be kept in a glass stop-
pered bottle, and not exposed to the air more than absolutely
necessary.

5. A solution of carbonate of soda (washing soda).

6. A solution of carbonate of ammonia (smelling salts).

7. A solution of ammonia (hartshorn).

The preceding, in addition to hydro-sulphuric-acid gas and
solution, may be regarded as the principal tests for metals.
Others will occasionally come under our notice, but these are
the chief.

Having disposed of the effects developed on the solutions of
manganese and zinc already employed by hydro-sulphuric-acid
and hydro-sulphate of ammonia, let the student next observe
the result of adding to each of these solutions respectively a '
solution of prussiate of potash. He will discover that this!
re-agent determines a while precipitate with either metal ; and
as a general rule it may be remembered, that yellow prussiate
of potash (there is a red prussiate) determines a white preci- ,
pHate with all common or calcigenous metals. To this general |
rule there are very important exceptions, which, however, had
best be fixed in the memory as exceptions : thus, probably,
even in the foregoing testing experiments the '
reader may observe that the precipitate yielded I
by prussiate of potash is tinged bluish ; if so,
this result will depend upon the presence of I
iron, a metal which will scarcely be altogether
absent from the solutions of zinc and man- 1
ganese prepared by a novice in chemical j
operations. Let the student now proceed to I
test portions of zinc solution, and manga-
nese solution, made according to preceding 1
directions, with all the tests mentioned in the '
beginning of this article, and let him make
notes of the results. Most of the tests will i
produce precipitates with both solutions, as
the reader will see ; and the prevailing cha-
racter of the results is whiteness, or a tint ap-
proaching to whiteness. The operation of test-
ing may be performed in conical wine-glasses,
in test tubes, as they are called — instruments
of the following shape, fig. 19, being glass
tubes, open at one end, closed ut the other, and 60 thin that
the flame of A ipirit lamp muy be applied without danger of
causing fracture. A third meihod of conducting test opera-
tions, and Hi! a vciy gbetl one, tunaisti in the employment of
flit strips tit window glass, upon which a single drop of the
solution tdjifc tested is laid, and another drop of the test
solution, fcflabd to it by me ana of a straw, or a glass rod. In
this way teatitig opcratirms may be conducted with great
facility, £ahs must b taken, l.v^cr, when straws are
emplo'vedi pever to tifte >>niw for more than one operation.
Take n*xt tt nolttsinn t mrui;- incite, and * Motion f zinc
prepared (tt nlreajljr described. Add hvdro-SUljmate of am-
monia to either iwlutionYiitid a siityhnret is of course the result.
To either fchlphtiret stdd now, without necessarily decanting
the fluid front which it htft befeh' tHh)w» down, some distilled
vine^ir (arctic acidji and oWfcte that all the sulphuret of
mangencrt U soluble hi tKi* ftutd, wWeas all the stllphuretof
. . . ■ ■ .* lindtnnrbed; Wc We already determined that,
supposing zinc *hd iiiatigatteae f to exist in one and the same

solution, they admit of separation by transmitting through
the solution hydro-sulphuric acid, which throws down all the
zinc, and leaves the manganese, which latter may be subse-
quently wanted, thrown down by means of hydro-sulphate of
ammonia. Another method of separating the two will now
readily occur to the reader. Both may be thrown down at
once by hydrosulphate of ammonia, and the sulphurct of zinc
redissolved by means of acetic acid.

It would be undesirable at this early period of our studies
to describe in greater detail the numerous analytical processes
which may be had recourse to for accomplishing the separa-
tion of zinc and manganese, supposing both to exist in one
solution, and supposing the manganese to be in the condition
of a protosalt.

Recapitulation, — 1. Two solutions yield respectively precipi-
tates with hydro-sulphate of ammonia ; therefore, these solu-
tions contain metals of the calcigenous class.

2. The precipitates are white, therefore the metals in ques-
tion arc either manganese or zinc.

3. One solution yields a white precipitate, with hydro-sul-
phurate of ammonia, though not with hydro-sulphuric acid ;
therefore it must contain manganese.

4. One solution yields a precipitate both with hydro-sul-
phuric and hydro-sulphate of ammonia; therefore it must
contain zinc.

5. Sulphurct of manganese may be separated from sulphuret
of zinc, by the agency of acetic acid (distilled vinegar), in
which sulphurct of zinc is insoluble.

Distinction between the Moist and Dry Processes of Analysis, —
The moist process and the dry process are terms which,
from long use, have become popularly familiar, though they
by no means admit of any precise line of demarcation. There
aro few chemical analyses involving metals which do not
require the agency of fire at some stage of their performance }
again, there are few so called dry processes which do not
require as adjuncts the employment of acids, and other moist
chemical re-agents. As a general rule, it may be stated that
the dry or igneous processes of chemistry are restricted to
operations on the large scale — such* fur example, as the smelt-
ing of metals. To this general rule, however, the blowpipe and its
employment constitute one remarkable exception, all the pro-
cesses conducted by means of this instrument being essentially
small and delicate, sometimes almost microscopic. The blow-
pipe is now invaluable to the chemist, although its employ-
ment in this way dates from very recent periods.

Description of the Blow-pipe. — The greater number of my
readers will have seen a blow-pipe, and probably will have seen
it used, being employed Very extensively by gas-fitters, jewel-
lers, and some other aitisans. The instrument consists in its
simplest form of a bent tube, terminating 4n a fine jet, as
represented in the accompanying diagram, fig. 20, and is

tiff. 20.

RHntr 9 - 1 * Iff* 7 * ^T-Tfrl7« ■ -iWibn^a.

• Still with greater propriety termed hydroaulphuratc.

f The remark applies to manganese in that kind of solution, which
malts from the treatment already described, and others attended with,
m similar result; in other words, iopjctosalis of manganese.

intended to cause the deflexion, by blowing through it, of
a candle or a lamp-flame, as represented in fig. 21. The
flame thus diverted from its upward course is necessarily
limited in extent, but its heat in certain parts is very great,
enabling the operator to obtain (on the small scale) most of
the effects of a furnace.

Generally speaking, artizana who use an instrument in their
trade acquire far more dexteiity in its employment than
philosophers or amateurs. So far as relates to the blow-pipe,
however, there is a remarkable exception to this rule. The
gas-titter and jeweller use the blow-pipe as follows :— Taking
a deep inspiration, they blow as long as the one charge of air
lasts; then stopping, they inspire a fresh draught of air ; after-
wards they set to work again. This' would never do for the
chemist, whose operations demand the solution of the ap-
parently impossible problem : to breathe and to blow uninter-
ruptedly. It is not possible to describe by mere words how
this is accomplished, farther than the description is conveyed
in a general direction, to consider the cheeks as a pair of

7(T

THE POPULAR EDUCATOR-

Fiff. 21.

double bellowi : always blow
ing from the mouth, never from
the lungs.

The facility with which a
good jet can be produced and
maintained, greatly depend/
upon the size of the terminal
orifice, which, if too large, will
require more air than can be
readily supplied by the reser-
voir of the mouth alone. All
delicately made blow-pipet
are supplied with several jets of different sises, but such refine-
ments as these are unnecessary to the novice, who may proceed
to a gas-fitter's shop, and purchase a blow-pipe for sixpence.
II a ring purchased it, let him now determine the distance from
his eye at which vision is most perfect ; which being settled,
let him cut the blow- pipe to correspond. This is a somewhat,
important direction, and should not be neglected.

The Blow-pipe- jet, and its Characteristics.— If a jet of air by
means of the blow-pipe be directed across the flame of a lamp
or candle, just above, or a little on one side of the wick, a jet
will be produced which will have, or should have, the follow-
ing characteristics.

It will be made up of a small central blue conical flame, ex-
tending from a to b, fig. 22, lying within a second and larger
cone, a, e, consisting of a reddish-yellow scarcely perceptible halo.
It is not always that the jet can be obtained so pure as here
described ; but this degree of purity should be always aimed at,
and will sometimes even by a novice be accomplished. The
most heating portion of the flame thus developed corresponds
with the point b ; consequently, if our object be the mere fusion
of a refractory body, to the action of this point should it be
exposed. This portion of the flame, moreover — indeed every
part of the blue cone, possesses a deoxydizing power, that is to
say, it takes away oxygen from any substance which may be
exposed to it. The external faint halo, on the contrary, im-
parts oxygen, and ib therefore called the oxydizing flame.
The blow-pipe is not only useful to the chemist as a means of
effecting the fusion and working of glass tubes, but it enables
him to operate in the dry way on all the metal or minerals
containing them, giving rise to characteristic appearances from
which the existence of any particular substance may be
inferred.

Apparatus necessary to be employed in connexion with the Blow-
pipe. — In the first place, we require a source of flame, and this
varies according to the different purposes for which the blow-
pipe is employed. If used for glass-blowing operations, the
name is usually such as results from the burning of a large
mass of cotton wick, placed in a pan containing tallow, or a
tin dish, and the blow-pipe having a very large jet, is usually
worked by means of a pair of bellows. This, at least, is the
arrangement usually employed by artizans in glass, such as
barometer-makers, thermometer-makers, &c. In laboratories,
gas is sometimes used as the source of flame, being more con-
venient ; but the result is not so good. This bellows blow-pipe
the student need not possess ; all the glass blowing that he will
require may be accomplished by the mouth blow-pipe, as will
be described hereafter. For purposes of mineral analysis, and
to such we are especially directing our attention at present,
the very best flame, according to our opinion, is that of a wax
or spermacetti candle ; but the flame of a common tallow dip
will answer most purposes.

Supports. — Charcoal. — The maximum heat which the blow-pipe
jet can exert results from the contact of the blue apex with a

Siece of well burned charcoal. Of course, some means must be
evised for holding this charcoal, and consequently there are
instruments sold under the name of charcoal-holders ; they arc j
unnecessary, however — a charcoal-holder satisfactory in every j
respect may be constructed for the occasion, by taking a slip of '
tin plate about six inches long by two inches wide, and bending I
one end twice at right angles on itself, in such a manner that J
ic may grasp and fiiraly hold a piece of charcoal. When the !

charcoal has been thus fixed, e little excavation should bemads
at the point by means of a knife, and in this excavation las
substance to be operated upon should be laid.

The Platinum Wire-loop.— In a vast number of blow-pipe a.
periments, the jet is not directed upon the unmixed rabstaact.
but upon a mixture of it and another substance with which
it shall form a glass on fusion, and the nature of the substsaet
is deduced from the colour of the resulting glass. In sad
cases, the support most generally employed, in a loop of plati-
num wire. A portion of the substance to be exam in ed ^"f
fused into the loop, together with a flux, a glees results, SSm
the loop as it would the frame of a window. Various other
blow-pipe supports are known to chemists, but^he two already
' described are the most important, and will answer our i
purpose. J

Blow-pipe examination of Zinc and Manyaneu.'—ln our bun
investigations on zinc and manganese, greet cere was taken to
obtain these metals in certain states of combination : no such
precautions will be necessary in our blow-pipe inquiries on
the same. The zinc specimen may be a piece of the metal
itself; the manganese specimen a portion of black, or binoxide,
otherwise called peroxide ; in other words, the ordinary "■**
manganese-ore of commerce.* Lay a small fragment of me-
tallic zinc (about the size of a barleycorn) upon the charcoal,
and direct upon it the interior blow-pipe flame ; remark how the
zinc burns ; and how a white powder remains : remark too
this white powder is yellow whilst hot. Remember well chest
points, and compare them with the results to be obtai ned here-
after, by treating lead in a similar manner.
I Take the platinum loop, moisten it with the tongue, dip it
into some powdered carbonate of soda : remove it 7 fiusfst
carbonate by directing upon it the apex of the bias eons: let
the fused bead cool : when cool moisten it with the tongue
again, and apply to it a portion of powdered black oxide of
manganese— but a very small portion, just as much ss could be
taken up on the point of a needle. Direct now the outer *—
pf a blow-pipe jet on the loop, and observe the result. lbs
bead fuses, it becomes green when hot, and bluish green when
cold. Repeat the experiment, substituting borax for carbonate
of soda : the bead is now violet red in the external, colourless in
the internal flame. These appearances are characteristic of
manganese, but the appearances lately described ere character-
istic of zinc ; no other metals yielding similar results under
similar treatment: the student may therefore form some
opinion already, concerning the value of the blow-nips as ss
instrument of chemicul analysis.

[The following is a representation^ a Glass Blower's rank
with double bellows worked by the foot, and blow-pipe, '""ft
&c. Such an apparatus can be had in London, complete. &
four guineas.] r

* Commercial black oxulu of manganese, howevtr, fj never pSf*j
always containing iron, lime, and other extraneous materials.

LESSONS IN GREEK.

LESSONS IN GREEK.— No. XL

By John 11. Beard, D.D.

THE THIRD DECLENSION-(Om*fodW).

Continuing the subject, I proceed to words in Xg, X, fig, v.
The Towel of the item remains only in the accusative and
vocative singular, in the other cases it passes into c. In the
genitive singular the masculines and feminines take tag, and
in the genitire plural wv ; e.g., 17 iroXtc, a city : 6 irqxvg, an
ell Neuters end in 00c in the genitive singular ; as ro mvdxi,
mustard ; ro aarv, a city.

S. N.

ToklQ

*nx vc

aivairi

aarv

IToXt-ug

*tixt-»c

oivatrt-og

aart-og

J).

TroXei

*nx"

aivairei

aarti

TToXtV

icn\vv

mvairi

aarv

7T0\l

wijxu

attain

aarv

P.N.

ToXlig

7ri;x«*c

aivairt)

aarrj

iroXt-wv

TTIJXtUV

oivairt'W

atrrt-utv

iroXsot

TWOi

oivairt <rt

a art at

TToXttC.

JTI7X«C

oivairrj

aorti

D. V.

iroXttg

xijx«ic

aivairrj

aorq

iroXi-e

ir 9X «-«

oivairt- 1

aort-i

iroXt-oiv

fnix^'Oiv

oivairt-oiv

aorc-otv

Here belong the adjectives in vg, eta, v, which in declension
depart from that of masculine and feminine substantives in
this only, that the genitive of the masculine singular has
the common form tog, and not ««c, and that the neater plural
has ia : thus, yXvxvg, sweet.

Singular.

N. yXvxvg
G. yXvtt-og
2>. yXi/cc c
A. yXvxw
V. yXvKV

yXvKiia

yXvxeiag

yXvictiQ

yXvictiav

yXvKiia

Dual

yXvKV

Rural*
yXvictig

yXvtt-og yXvKdov
yXvieu yXvKuri
yXvKV yXvKtic
yXvKV yXvKtic

yXvKtt yXvKiia

yXvKtiai

yXvKtiwv

yXvKtiaic

yXviuiac

yXvKtiai

yXvKtt

yXvKta

yXvKew

yXvictai

yXvKia

yXvKta

yXvKtoiv yXvxtiaiv yXvKtoiv

Here also belong the adjectives in vg, v, g., cog, which are
declined as yXvxvg, yXvrv, only that the neuter plural is con-
tracted into 9 like aarrj; as o, >), fairrixyg, to fa**IX v * Ta
inrrjxrj* tw> dl* long.

Some substantives in Xg, as well as the adjectives in tg, t,
ai ifytc, <£p<, skilful, have the regular inflexion, without ony
change of the radical vowel, e.g. 0, rj, iropne. a calf or heifer ;
o t »/» o7c, a sheep ; also (in the singular) rj tyx^vg t an eel.

8. N. iropng *yx*^ vc °*C

(?. iropri-og tyxtXv-oc oiog

D. iropn-i, xoort *7X €Av * °"

A. iroprtv eyx*Xvv o'iv

V. iropri *7X e ^ v °Jt

P. N. iropri-tg, iroprig eyxtXug otic

G. tropn-ntv eyxtXt-utv oiwv

D. iropri' 91 eyx&t-oi 0101

A. iroprt-ag, woprlc tyx& H C °J a C> o7 C

V. iropn-tg, iroprig «7X £ * €, C °'*C

Dual vopn-t tyxiX*-* oU

wopri'Oiy *7X e ^ £ 01V oiotv

VOCABULAUY.

Bpwffif. tug. jy, eating.
Hn/acf, «fc»c, v, acquisition.
Oyirttf , i«c, »/, assistance.
n<xnc> <««C« if* drinking.
UpaKtg, <*»c y), doing, deed.
Xxavig, tmg, »/, want.
Iraaig, tug, »), insurrection, a

ruing.
Yxvtoiq, f*»t, »), understanding.
1'ftwc. ««C '/• pride, arrogance,

insult.
♦t»(Tif, tutg, rj, nature.
QvXaZ, &Kog, 6, a watchman,

guardian.

A PX*»» W* »/» a beginning,
government ; plural, magis-
trates.

Krtifta, arog, ro, a possession.

T«x«ff» 0V Ct ro, a wall.

AffcXyua, ag % ?/, wantonness.

Ev^ta, ac, iii want. ^

£xtdv/iia, ac. >/» desire.

Kapxoc. ov, 6, fruit.

Koapog, ov, o, order, beauty,
the world ; ornament.

No/iogf ov, o, law.

IToXf/toCt or, 6, war.

Uvpyog, ov t o, a tower.

Awpov, ov, ro t a gift.
Bporoc, jj, ov, mortal ; 01 fiooroi,
mortals.

fie/3aioc, a > ov, firm, sure.
Movoc, n. ov, alone, single.
Aiacpopog, ov, different.

EXEHCISES . — G REEK- Ex OL IS II .

AffiXytia TiKTtL vfipiv. Ev iroati tcai fipwact froXXoi itaiv
iraipoi, «v ^£ airovtiaiy irpaypan oXtyoi. 'O xXovroc ffirav««c
cat evdtiag rovg av9pu>irovg Xvti 'Errov ry (pvatt. Ai airo rov
autfiarog eiriOvpiat iroXtpovg xai ara<n:g icai /m\af irapcxovacv.
Ev raig iroXeaiv at apx" ( vo/ttuv ^vXaitt£ ctatv. ATrtx i( *Q** <*>
xoXIrat, vrao^ewv. OpiytcrQe, w av^pec* ^aXaiv rrpa^ewv. Ata-
^opot ctatv at rwv pporutv Qvaug. E£ vflpttag iroWa rara
ytyverai. Karoo avBpog tiutpa ovrjviv ovk t\tt. Aoga cat
xXovrog avev avvcafwc ovc a<r<paXtj Krqpara ttatv. 01 rcov
o'vrwv Kapicoi yXvKiig tiaiv. Aptrqg /3c/3atac titnv at xr^atig
fiovai IloXXa aori; rtix»; fx Ci * ^* rov aareog irvpyoi (3ij3aioi
eto'iv. 01 irvpyot rtp cloth Koapog tioiv.

English-Greek.

Riches free from (Xvu) want. We have friends in eating
and drinking, but not in misfortune. In the city the king is
the guardian of the laws. Obey, O young man, the magis-
trates. O child, strive after honourable deeds. The posses-
sion of virtue is alone sure. The city has (to the city are)
many towers. Good laws bring honour to the city. Follow
nature. The soldiers fight for the deliverance (awrtipta) of
the city. O citizen, avoid insurrection.

There are some nouns of the third declension which cannot
be classified, and the differential points of which must there-
fore be given separately ; they are these

Exceptional Noam of the Third Declension.

1. — Avifp, avepog, a man ; yaXa, yaXcucrog, milk ; yovv, yovarog,

a' knee; 8opv t Soparog, a spear ; ovg, wrog, an ear; gcip,

X'tpoc, a hand; the peculiar forms of which have been

already set forth.
2.— rwiy, if, a married woman, a tcife, G. yvvaiK-og, D. yvvaut-t,

A. yvvauc a } V. yvvat; Pi. yvvaixtg, yvvaucuv, ywai$\ t

yvvaucag.
3. — Zcvg, Zeus, Jupiter, G. Aiog, D. At?, A. Ata, Y. Zev.
4. — 0pt£, ?), hair, G. rptxoc* B. rptx«> &c. D. Pi. 0pt£t.
0. — KXugt >;, a key, G. irXudoc, D. icXu£t, A.cXctv; PI. N.

and D. icXtlg, also ieXct£<f, cXctoag.
6. — Kvuv, 6, i), a dog, G. rvv-op, D. cuv-i, A. rvv-a, V. icvov ; PI.

cvviCi cvvuiv, Kvcrt, Kvvag.
7. — Maprvc, o, a witness (our inartyr), G. ftaprvpog, D.

paprvpi, A. paprvpa, V. paprvg ; D. PI. ftaprvtrt,
8.— Nave (Lat. navis) n, a ship, G. vtutg, D. vtfi, A. vavv;

Dual, G. and D. vcotv (the N. and A. do not occur) ;

PI. vi]tg, vecav, vavei, vavg ; compare ypavg and /Sacri-

Xtvg.
9. — Tewp, ro, icater; G. vSarog, D. vSari, &c.

VOCABULABT.

OiKia, ag, »}, a dwelling.
Krttg, Knvog, 6, a comb.
K.rcvt£w, I comb.

EcicXi7(rta, af , rj, an assembly ;

the New Testament word

for church.
Maprvpia, ag, 1), testimony,
Ilerpa, ag, ?/, a rock, hence

Peter.
(fyeXcta, ag, >), advanUge,

ability.
Kiarif, >/f, 1}, a chest.
Aitrjg, ov, o, Hades, god of the

lower world (Pluto).
JLvfitpwirrig, ov, 6, steersman.
UoXvd(VKtig,ov,6, Polydeukes,

Pollux.
AQqvaiog, ov, 6, an Athenian.
AiaKog, ov, 6, JE&cus.
'IoroCt ov, 6, a loom.
ILvfiog, ov, b, (our cube) a die.
OtKog, ov, b, a house.

Sraywv, ovoc, »/, a drop.

AtOiotf/, oirof, an Ethiopian.

Kaariop, opog. Castor.

Atnaig, twg, tf, a request, en-
treaty.

Airigrog, ov, unfaithful, inad-
missible.

I0vvw, I make straight, I
direct.

KotXatvw, I hollow.

Ko/ugw, I carry, bring.

£u»(oi, I save, rescue.

Yoorrjp, rjpog, 6, a saviour,
deliverer.

A<x°/""> ^ receive.

THE POPULAR EDUCATOR.

EXERCISES. — GkEKK-EnGLISH.

At yvpaiKiQ rtft KocTfUft xainovaw t Oi 'EXXtjvtg otfiovrai Ata
icai llooucui kui AiroXXu) kui aXXovg Qeovg. Tate yvvaiXtv t)
atcujg —ptiru. Oi Kvvtg tuv oikov tpvXarrovcw. 'O KVfifppyjrtig
r;/i/ vavv tOvvu. Ai arayovic tov viarog irtrpav KoiXaivovaiv.
Ti/c. yvyaiKog tan rov oikov vvXarruv. Yuraixag HrGX/jg tart
(Tut^uv oiKiav. Au tv —nrrovai Atoj; Kufiot. Oi kvvtg roig
ai'Oputiroig utQiXitav km »)£oj'//i» wapt\ouaiv. At rwf fiaprvphiV

flClKTlOtUl 7ToXXak'l£ (ITTttTTOI kUTlV. 'llTOl yVVUlKutV tpya k'ttt

ouk tKKXtjtruu (sc. fttrtr). Ko/xt^c, w rrot, ti\v r;yr kigtijc k'Xtlv,
U Zn», f\\ou ri/i' row ar i» # \oi»c itijmv. Kaarwp irai UfAiaciT:*//;
rwv i'*w»> aiorrjptg i/trar. Perrttja iracy Koauov i) ffty// £»*j>it.
Oi A|0fi>7rt<; -//)' rp«x ,f l l *-Xawai' txovau: £2 ) r)\/(, ffiu^t r;/j'
tujeta*'. Ti t o icrtn raj; rj>«\'«c Krti't^o/ttr. Atakvg rag Aifov
»rX«7c ^tAttrrtt.

English Gkklk.

Ornament becomes n woman. Ornament becomes women.
It is the business of women to guard the house. They
bring the keys of the house. The keys of the house uro
brought to the mother. The Athenians had (to the Athe-
nians were) many ships. Jupiter had (to Jupiter were)
many temples. The iibh emerge out of the water. The
steersman guides the ship. The ship is guided by the steers-
man. You worship Jupiter and Apollo.

There are also some

Irrtgnlar Adjectives,

the forms of which I must set before you, as irpaog, irpaua,
irpaov, soft; ttoXvc, jtoXXm, ttoXv, much, pi. vumy; utyag 3
fit yaXij, fitya, great ; as follows : —

awe t\ovaiv. Y.v Aiyvirrtf) iroXXt) airov afOovta qv. "A
BaXarra fnyaXij tart. Mtya native, irpoaayoptvofitv IXtafa
kfiku>i'. KpouTt') >/i' ttoXi'c irXovroc. IIoA\««c U oXtytft ?)co*iig
utya ytyvtrai aXyug. Upatat Xoyoig y'jCtwg cuto/icv. Ta
utyaXa ?u>pa ri\g rv\t\g t\u Qofiov. HoXXtuv avOpwxw t9tj
ton rrpata. Tlovog aptrriv utya o<f>tX\ti. Oi trait ec, rov^ irpaovg
irartpag cat rag irpauag uijrtpag anpyovviv, 'OptXtav *%§ rUg
irpatmv arOpunrotg. A\ yvvaiKtg irpauai tiotv. A\iZar&por 9
rov MaKtioviov (3aatXia, fityav arrayoptvatv o< ~oX\ot.

English-Greek.
Abstain from much wine. Bad men delight in much wine.
Much wine injures men. Kings have great incomes. The
income of the kingdom is great. Egypt has much corn. Many
have much wealth, but little understanding. Strive after
mild manners. The manners of the women are mild. (There)
is beauty in (to) mild manners. Alexander, the king of the
Macedonians, is often called the great.

LESSONS IX GEOLOGY.— No. XLIV.

By Thomas W. Jenkyn, P.D., F.U.G.S., F.G.S., Ac.

CHAPTER IV.

ON THE EFFECTS OF ORGANIC AOENT8 ON TUB EARTH?

CllL'ST.

ON ANIMALCULITE

SECTION 11.
CONTRIBUTIONS TO
OF HOCKS.

THB FOBJCATIOK

7TiJrtqx;

TTpaeia

iroaov

irpaou

irpatiag

rcpaov

irpcHp

rrpatia

irpaoj

Trpaov

Trpattav

irpaov

irpuog, Trpnt

irpaua

irpaov

P. A".

roaot, 7rpaug

Trnattat

rrpata

irpaiojv

TTpauutv

irpatutv

J).

TrnaoiQ, trpaftri

TTpauatg

irpatni

-/.

Trpaovi; irpaflc

trpatiag

rrpata

7".

'.Tnam & 7rp«f»v

irpauai

irpaea

Dual

irpitio

irpaua

irpato

Tpaciv

irpa&iatv

irpaotv

S. A r .

J).

V.
P. \\

TroXvg

TTOXXOV
JTuXXift
TToXw
TToXtt

toXXoi

ToXXlOV

ttoXXj;

TToXXtJC.

TraXXy

TToXXtjl'
7ToXXlf

TroXXai
—oXXioi'

~oXv

7T0XX0l/
7T0XXy
TTuXu
TTOXV

7roXXa

TTtAXwi

\fityug
j fityaXov
utyuXy
' utyai'

\uty.iXvi
IfttyaXtov

1 ptyaXtj '.fitya
\ utyaXijg i ptyaXou
\fityaXg |/tfya\</j
j/tfy«Xi;j' ' fitya
uttyaXti auya
1/ityaXai j/teyaXa
; fieyaXwv | [uXaXtov

The other pnrts arc regular.

r OCABULAUY.

A^Oovta, ag, »/, freedom from
envy (a, not) abundance.

AiyuTrrog, ov, iy, -Ejjypt.

AXtZat'cpog, ov, »*j, Alexander.

KpoHToc, ov, 6, Croesus.

UpavoPog, ov, i), approach, in-
come.

£irog t ov, o f wheat, corn.

4>c/3oj,*, ov,6, tear; fofiov «x fu '»
to have fear, that is, to
cau*e fear.

MaKtBuv, ovog, o, a Macedo-
nian.

lXtac, adog, »), tlie Iliad.
AXyoc. ovg, ro, i>ain, grief.
IWug, ovp, ro, custom ; plural,

manners, morals; hence our

cth ics.
llaQog, oi/j>, ro, suffering.
OXtyoc, »/, ov, small ; pi. few.
0<piX\uj, I nourish, aucmeut,

aid.
II poaayoptvu, 1 name, call.
Mcya, adverb, gieatly, very.

Exercises. — Greek-English.
UoXvv oivov mvtiv Katov eortv, Oi fiaoiXug fityuXag irpovo-

You have seen how the growth, the decay, and the successions
of vegetable life, have contributed to the formation of the
crust of the earth. You ore now invited to examine the contri-
butions which animal life has made to produce some of the rocks
on our globe. There are animal organisms which are really the
spontaneous and hard-working architects of rocks and moun-
tains. This lesson will not refer to those which are piling up
rocky masses by their direct agency, but to those whose
remains contribute to the formation of soil, plains, and hills.

We will begin with the contributions of the smallest and
the minutest animal existences, the majority of which can be
detected only bv powerful microscopes, and with those of some
others that arc just visible to the naked eye. These diminutive
organisms are called animalcules, or little live things. They
are sometimes called Infusoria, on the ground that they are
discovered in all vegetable infusions, in the waters of the seas,
rivers, lakes, pond.-, and puddles, and in liquids used for
domestic purposes.

These agents cannot be seen with the -naked eye. They
belong, as Dr. Mantell has said, to an " invisible world.
They muke their invisible agency to be known by their works.
The Sacred Scriptures teach us that " the things which are
seen were r.ot made of things which do appear." This is
a primary article in the creed of every intelligent geologist
lie applies it to account for the creation of all the worlds of
matter as the results of the power and skill with which the
Supreme Artist combines invisible gases, and says <f let the dry
land appear." The same article can be applied to the large
and innumerable rocks and hills which have been produced,
not of course by one immediate fi.it, but by the slow and
invisible agents which He had created and appointed to execute
the work.

The forms, the structure, and the instincts of these animal-
culites belong to the science of Palaeontology. Our concern now
is, to exhibit them as contributing agents to the formation of
the earth's crust. The science of chemistry, and the microscope,
have shown that some extensive rocks and high mountains ait
nothing but enormous masses of animalculite relics, or im-
mense sepulchres in which their remains are entombed. So
extensively and so abundantly are their relics found in sous
and rocks, that you may well ask, with the poet Yotmo,
44 where is the dust that has not been alive ?" The composi-
tion of several rocks show that the different tribes of these ani*
malculites were countless, that various kinds of them appeared

LESSONS IN GEOLOGY.

on the earth successively, that they lived and worked here for
indefinite periods, and then vanished, and made way for other
kindred generations.

The most distinguished student of animalculitcs is Ehrem-
bero of Berlin, who is the Lord Rossb of the microscope.
These tiny animals exist in ten million times ten millions, and
millions of millions, and are found living in all water and
liquids. Wherever you see a spot of yellow or ochrcous scum
in a pond, or ditch, or any stagnant water, that scum consists
of an aggregation of hosts of animalcule.

The Irving tiling itself that is called an animalculite, or an
infusorial), is a soft, juicy, fleshy, or mucous substance, that,
for the most part, lives in a case which forms its house and
home. This case is sometimes called its shield and sometimes
its shell ; and by technical writers it is called the carapace.
Some, however, exist without such cases, but are naked and
have a flexible skin.

The cases or shields of animalculites differ in different species.
In one class, the shields are calcareous or limy ; in others sili-
ceous or flinty ; in others, ferruginous or irony. Their forms
and shapes are innumerable, but frequently of great beauty and
symmetry. The Xanthidia are a hollow globe of flinty matter.
The Pyxidiculse have a case like a saucer which is filled with
their body. The Bacillarise look like a dozen cards placed in
zigzag row, one touching the other at a point. The Navicular
have a bivalve shell with six openings. Tho Gail lone! 1*
have a bivalve case, but of a cylindrical and half globular form.
You will And the rich and beautiful variety of their shapes
well illustrated in Dr. Mantcll's " Medals of Creation," and
especially in his " Invisible World.

It is these shields or cases of the animalculite, and not the
animalculites themselves, that claim the attention of the geolo-
gist, for it is these shields that he discovers mineralised, and
which, in a fossil state, constitutes vast rocks in the crust of the
earth. Ehrenberg has found them in flint, in opal, in chalk,
and in many other rocks. They are found in vast profusion
in rocks of different periods — such as the tertiary Beries, and in
the chalky and other secondary deposits .

Fossil animalculites are those which had shields ; for the
races that were naked and had a flexible skin had nothing
enduring in their structure. Our lesson will embrace not only
the fossils which belong strictly to the infusoria, but also other
minute organisms with which they are associated. One class
of these are called Polythalamia, because their shells have
many chambers in them, and are not like that of the snail,
which has only one. The other are called Foraminifera,
because their cases or shells are covered with pores, or because
the different chambers of their shell are connected by a pore,
and not by a siphuncle that runs through each.

ANIMALCULITES IX S0IL3 AND SANDS.

At the bottom of many swamps and peat bogs, whether rest-
ing on modern soils or on ancient rocks, there are generally
found layers of white, marly, or flinty paste or clay. This
paste or clay is made up entirely of the shields of infusoria.
'fhey are found in abundance under the bogs of Ireland, in
Lough Island, near Newcastle, and in many parts of North
America.

This statement refers to peat bogs of the present age; but I
when we examine the deposits of the tertiary period, the ani-
raalculite relics far surpass, both in multiplicity of forms and
in extent of distribution, any infusorial strata of modern times.
And even the profusion which is found in the tertiaries of |
England is not to be compared with those of the continent, j
such as France and Germany, and also those of North America.
The rocks of the Paris basin abound with marine sands. These
sands are so full of microscopic animalculites, that a cubic inch
of them — that is, a mass cut and squared like a dice an inch
each way — would contain sixty thousand Foraminifera ,and
Infusoria. This is particularly the case with the sands
brought from Grignon in that neighbourhood. In the district
of BUin, in Northern Germany, there is a rock called ** polish-
ing slate." The rock is of considerable extent, and is fourteen
feet in thickness. It consists entirely of the flinty shields of
Gaillonelle. These shells are so minute, that a cubic inch of
the slate contains forty-one thousand millions, 41,000,000,000 of
animalculites. In Lapland there is a rock of fossil flour, which
is called Bergmohl, or mountain meal. When bread is scarce, |

the inhabitants mingle this fossil meal with the flour of corn,
or with meal made of the bark of trees, ground for food. This
Bergmehl, or fossil flour, is one mass of animalculites. The
same kind of rock is found at San Fioro in Tuscany.

In the neighbourhood of Eyra, in Bohemia, there is dug up a
fine white earth, which lies about three feet under the surface.
When this earth is dry, it has all the appearance of pure mag-
nesia ; but when it is examined by the microscope, it is seen
to be formed entirely of an elegant species of infusorial shells
called Campilodisca.

In North America, one of the most celebrated places for
infusorial rocks, is a district that lies between the cities of
Richmond and Petersburg in Virginia. The city of Rich-
mond is built on a stratum of flinty marls, having a thickness of
more than twenty feet, extending as far as Petersburg, and
spreading out into sterile tracts along the sides of the hills.
1 hese formations are supposed to belong to the older tertiaries,
the meiocene or the eocene. The whole of these deep and
extensive marls are composed of infusorial remains. " When,"
says Dr. Mantell, in "Medals of Creation,'' p. 225, " a few
grains of this marl are prepared, and mounted on a glass,
almost all their varieties will be manifest, so largely is this
earth composed of the skeletons of animalcules : in fact, very
few inorganic particles are intermixed with the organisms.
The merest pellicle or stain, left by the evaporation of a drop
of water in which some of the marl has been mixed, teems
with the most beautiful structures."

ANIMALCULITCS IN CHALK.

Few of the revelations of geology have been more astonish-
ing than the discovery, that a large proportion of the purest white
chalk consists of minute chambered shells and microscopic
corals, all of which are of the most complete and exquisite
structure. If you scrape or brush a piece of chalk in water,
and examine a small patch of the sediment by a microscope,
you will Bee that it consists of a vast abundance of the cases or
shells of Polythalamia, Foraminifera, and Polyparia. Never-
theless, even these microscopic creatures must appear colossal
when you think that these animalcules live upon infusoria more
diminutive than themselves. A cubic inch of white chalk
contains, according to Ehrenberg, more than one million of
I well-preserved shells of animalculites.

This thought is almost overwhelming, when you consider, in
connection with it, the vast extent and the great depth of the
chalk formation on the surface of the globe. All the Chalk
Downs of England, and the cretaceous rocks of the earth, are
only an accumulation of exceedingly minute organisms, which
are 'so closely packed together, that a piece of soft chalk, that
you use in making a mark or drawing a line, has half, its bulk
tormed by fo*ail bodies. This is the case with our English
chalk ; but in the chalk of the South of Europe, the prolusion
of animalculite remains is in much greater proportion.

There is, of course, in every mass of chalk, a quantity of
matter where no animalculite organisms appear in the fleld of
the microscope. This inorganic matter does not owe its ori-
gin to a precipitation of lime that was previoualy held in solu-
tion by the water, but it is the result of the attrition and dis-
integration of the infusiorial organisms into a more pulverized
mass of calcareous particles, which have been afterwards
reunited by crystallisation.

The upper part of the chalk formation abounds in nodules of
flint. Geology has lately shown that these nodules of flints have
originated in an accumulation of the pulverised and ground par-
ticles which have been derived £om the siliceous or flinty shields
of animalculites. The late Dr. Mantell distinguished hi u. self
much by his researches, chemical and geological, among these
infusoria. He says that the most abundant microscopical
forms of animalcule discovered in the chalk and flints of
England are two kinds of Polythalamia, called the Rot alia and
Texituiaria. Associated with these are immense numbers
of the class called Foraminifera.

These animalculite families are found to be most extensively
distributed in the rocks of every part of the globe. In the
East, they have been discovered in the Mount of Olives near
Jerusalem, in the Plains of Damascus, in the Hills of Antili-
banus, and in the rocks about Rcyrout. In the South, it has
been ascertained that a large proportion of the sand of the Lib-
yan desert of Africa consists of microscopic shells. In North

THE POPULAR EDUCATOR.

America, the boundlc** masses of calcareous marls that pre-
ys il in Upper Missouri, and that stretch even to the Rocky
Mountains, are, throughout their en lire depth and extent,
made up of the sheila of infusorial animals.

roiusuxxrKiiA ix nuxmulitie limestone.

Amort g the lower or older scries of tertiary rocks, there are
several lay.rs of limev.cn e which consist of minute, flat, and cir-
cular p:ccta that look as so many Tery diminutive and eren
m:cr r 'V:op:c coin". As Xummulua is the Latin for •* little
c/.jr./* this rxk has been called Xurnmuliiic, as if it consisted
of •• l'*i:\ mor.ey." This calcareous rock consists often of a
*,'/a.yv.\ crystalline marble full of r.ummulitcs, and these
r.-- en*. --!.>* are cr.ly the shells of those extremely minute
i.TS.\ of rr.'/.'.n*co'jj animals called Foraminifcra. Foramini-
f*r» w the Latin for the numerous openings or pores with which
•i* ah:*, is of this zenera are covered.

y.sr.r. zV.:a are no: mil microscopic, though as a genera
v.ey art c.n.:r. „:.v». If you can imazine the sixcofagold
y?z-j. -.r, better s f ili f a soli farthing, you will he helped to
v„s,t*ive '{ the various sizes of this •fossil money" constituting
'jezjvTJk* Kvzr.uLr.i of Limes: --ne. The nummulite varies in

• a* ff.m, a :r.:r.:.te ^o:r.: :o a ci*c of an inch, or an inchanda
ialf .r. i.a=.*-er. Wher. you l> k at it outside, its surface is
T*-*ti..t »—v,tr. *r.i marked with tine undulating lines; hut
.i 'ut -.eot 14 »p'..t transversely, i: is found to consist of several
*-...t. i:.;': it*. 'i.t'.i'A ir.'o very rr. any cells or chambers, by
'.-.. j-* j.irt.:.-,r.s •»:.i^h hi'c no communication with each
v.-er.

T:-e exter.t to which *.;.esc nummulitic rocks spread in
l.3rr*z: j,x:'ji of \:.t e>.b*. has arrested the attention of all
^zv.'sjL jr^ol'.fis'j. In Northern Italy, in a district near Nice,
a a r-xk r*surka*.'.e for its nummuiites. They are also found
:r. \ut \yr.r^-.+u on both flanks of the Pyrenees, and among
t--.e r.-rh Alp*. Tr.ey o:cur in Asia Minor, and may be traced
at .r.'^erraJi alor.z, the wide tract of country which extends
fx'.7L the Mediterranean to the borders of Western India.
Tt.j>'k. cepOftitJ f i the same calcareous nature are found in
<>7**o* a/.d in Egypt. Sir Kcdsrick Mitrchison has lately
shown in a paper read before the Geological Society of London,
that the** r.ummuli::c rocks supply one of the chief connecting
]i/.ks between the deposits of India and those of Europe.
"They extend/' he says, " at intervals through no less than
twenty-five degrees of latitude, and near one hundred degrees
of longitude ; its northernmost ridge on the north flank of the
Carpathians being clearly identifiable with its southernmost
known limb in Cutch, and its western masses in Spain and
Morocco being similar to those of the Bramahpootra " in the
East.

In the United States, a range of mountains near Suggaville,
and which are about three hundred feet high, are entirely
composed of one species of nummuiites.

In our own country, especially in Sussex, the blue clay that
is found at Bracklesham and Stubbington, and the calcareous
sand Atone that is dug up at Ems worth and Bognor, abound in
nummuiites.

The facts which have been briefly stated in this lesson
ithow to you what an important influence the number, the
growth, ar.d the decay of minute bodies and invisible agenta
have had in the slow but progressive formation of our Eaith's
em st. The contribution of each is almost un appreciable even by
the microscope, but the enormous masses produced by their
numerical profusion arc incalculable. Well might Infinite
Power stand over these stupendous operations, and ask "who
hath dcspis.'d the day of small things r" It is by means of
these diminutive agents, that He has brought to pass the most
astounding phenomena and the most magnificent results.
When we think that these minute animalcuUtes have contri-
buted much more material for furnishing the cover of the globe,
than have been supplied by lions, and elephants, and whales,
and leviathans, we cannot but think of the language of the
Psalmist : " O Lord, how manifold arc thy works ! in wisdom
hast thou made them all ; the earth is full of thy riches ; so is
this great and wide sea, wherein are things creeping and innu-
merable, both small and great beasts. These wait all upon
thee, that thou may est give them their meat in due season.
Thou hidest thy face, they arc troubled ; thou takest away
their breath, they die, and return to their dust."

A KEY TO THE EXERCISES IN THE

LATIN LESSONS.

Bj John K. Beard, D.D.

{CXntiHued fi^m page 59, Vol. IV.)

VoL III. p. 72.— Exglish-Lativ.

lleipublicae interest; met refert; illorum interest; omnium
interest ; neminis refrrt ; se domum reversuruin esse certiorem me
fecit filius ; maritum va'.cre certiorem fecit matrem filia tua ; anion*
sum ecnfuAus ; mali saepe coofusi sunt animi ; temporis et neces-
sitatis scnatum regina admonet ; me suscepti negotii taedet ; boni
malorum miserentur : illoa taedet vitoe ; te uxorem habere mibi
venit in mentem ; praeteiitorum reeordatur ; rei miliUria es peri-
tus ; c ^nscianc recti est mens tua ? consilii mei te faciam certiorem ;
literarum appetens puer fiet sapiens ; piscibus scatet mare ; mills
est ingenii sorer tua ; a plurimis divitiae magui arslimantur ; quaati
nunc libiurn emisti : non unius oasis me faciunt ; nostrum est
imperare, tuum obsequi ; proditiouis est accusatus ; capitis damns-
bitur ; clave s urbis potest atis suae fecerunt hostrs.

Vol, III. p. 9-5.— Latin-Ejiqlish.

Caesar said to Damnorix that he pardoned the past misdeeds of
his brother Divitiacus ; the abandoned woman cursed both ; physi-
cian*. while they minister to the whole body, cure not even the
smallest part ; Venus was married to Vulcan ; Gabinius is roiled t
I have reproved Trebatius because he does not regard his health
sufficiently ; the unwilling are not easily persuaded; I am of this
opinion : a good citizen makes to the republic a present of ms

F rival e hatreds; the Germans are given to labour and hardships t
am satisfied that you are worthless ; a good general is present
in dangers ; the physician applied remedies to the wounds ; Caesar
made war on Gaul ; certain signs precede certain things ; father
compares small things with great ; the c onsul preferred the safety
of all to the safety of individuals ; I set before myself all things ;
he esteemed his love for his son less than the public good; Quin-
tius Fabius alone survived the slaughter of his family at Cremers;
the senate bestowed honours on illustrious men ; the virgin mar-
ried him whom Caeeilia had had for a husband ; thy keepers have
given thee the name of madman ; the name of that disease is
avarice ; my name is Arcturus ; I have deliberated and determined;
all things belonging to human life ought to have been investigated,
heard, read, discussed, and handled by the orator ; Alcibiodes had
such sagacity that he could not be deceived, especially when ha
purposely kept his mind on the watch ; majesty and love do not
well agree, nor tarry in one abode ; the father gave his son a dog;
the Rhine approaches the ocean ; you do not know what man you
speak ill of; avoid the dog ; surely these things do not seem to you
suitable to a marriage ? the villas, built along the pleasant plaees
of the river, stand on its margin ; the world obeys God, and the
seas and the lands obey him, and the life of man obeys the com-
mands of the supreme law; I keep constant guard against thee;
it is agreed between Dejotarus and myself [comma after convenill
that he with his troops should be in my camp ; he advised Pompey
to fear my house and be on his guard against me ; but it is agreed
to by all that the Sibyl brought three books to Tarquinius Super*
bus ; it is foolish to allow what you can prevent ; neither the plan
nor the conversation suits me ; an image of victory stood in the
right hand of Ceres : the Parthians had taken the standards from
Crassus; Caesar betrothed the granddaughter of Atticus to
Tiberius Claudius Nero ; it is advantageous to the country itself to
have citixens who perform what they owe to their parents ; no fool
nor dishonest person can be well off; Caesar made to hia country
a piesent of his grudges; Perseus familiarly smiled on persons
whom he scarcely knew ; the praise and the glory of other men are
commonly objects of envy; vou ought to have discerned these
things; who has not heard of the watching* (vigiliae) of Demos-
thenes ?let us alwajs live as if we thought we had to give an account ;
in the school of Pythagoras silence was imposed on disciples for
five years; Aeneas is seen by no one; Julian us and Apollinaris
in thf ir losciviousness and sloth, were like gladiators rather than
generals ; if my son sins at all he sins against me ; we wiah to be
rich not onlv for ourselves but for our children, our relatives, our
friends, an J, above all, for the commonwealth ; I recommended
peace to Pompey and the senate; who is a witness of this thing?
what is Celsus doing, I wonder ? what do you wish ? I do not under-
stand what is the meaning of avarice in old age ; virtue is the only
thing which men can neither give nor receive as a gift; it is base
and nefarious to make a gain of politics ; they blame me greatly
because I bewail the death of my friend; Pausauias went to assist
the inhabitants of Attica ; the Veientes go to aid the 8abinss;
they chose this place as their residence ; Caesar left behind iff

LESSONS IN GERMAN.

cohorts to protect the camp; sleep is Tery like death; a physician
ministers to a sick body ; but who cures the mind ? the lion has a
terrible voice ; Egypt was added to the Roman empire ; he is liberal
who takes from himself what he gives to another ; the genius of
the Oicek poets far excelled the poets of other nations.

Vol. III. p. 95.— English-Latin.

Nomen tibi est Roberto ; filio nomen do Roberto ; simillimus
patris est Alius tuus ; alteri aeris, non tibi ; est mihi ager ; divitias
mini affert ager; mihi auxilio advenerunt amici ; ludos sibi ueprf

dilegerunt ; tibi subrenit medicus, sed mederi non potest ; dorao
mc reliqucrunt praesidio ; vae mihi ! quid facio ? imperio Gal-
4ico Italia est adjects; fratris ingenium longe antccelht meum;
si peccas, tibi peccas ; cate leonem ; porta© liber adjacet ; copiae
fluminis ripao insistunt; mihi convenit liber; hostibut signa
detrahent milites ; iropiis non est bene ; mail malii maledicnnt ;
in doctutn esse con convenit tibi ; prae cnrru eurrit equus ; bona
omnia sibi ipsi proponunt; maximos forti duci honorcs dcferret
senatus; volentibus mult a facile persuadentur ; vulneiibus tuts
remedia . medicus adhibebit ; Angli student laboribus ; est in peri-
culo pater (patri est periculumj ; mulieri supplicanti condonavit{
virginem mini uxorem adjungaro.

LESSONS IN GERMAN.-No.LXX.
Irregular Verbs, continued from p. 33.
S 80. PARADIGM OF A VERB OF THE NEW FORM.

it&tn, to praise.

INDICATIVE.

SUBJUNCTIVE. | CONDITIONAL.

IMPERATIVE.

INFINITIVE.

PABTICIPIJI.

Present Tense.

Present Tense

Present.

ri f 1

d) (obe, I praise.

id) lobe, I may

2. febctu,

Men, to praise.

(obent,

8i«

tu lobefi, thou praisest.

tu lebeft, thou mayst

praise thou

praising.

• Is

rr (cbr, he praises.

ct tcbe, he may

3. U'be er, let

- f 1

mix loben, we praise.

trie (often, we may

him praise.

31 2

i$t tobct, you praise.

i&r tebct, you may

1 . loben nnr,

i U

ic fcben, they praise.

[ic tebeit, they may

let us praise

Imperfect Tent*.

Imperfect Tense.

2. icbet i^r,

nrniftf* v*».

rifi

id) lobte, I praised.

id) Tobete, I might ^

3. loben fie, let

si!

tu tebteft, thou didstpraise.

tu (obetef), thou mightst

them praise

- U

er lobte, be did praise.

er lobete, he might

sf 1

wir tobien, we did praise.

n>it lobeten, we might

3 l!

i$t Ubttt, you did praise.

ifyr lobetct, you might

«• [i

fie bttnt, they did praise.

ftc lobeten, they might

Perfect Tense.

Perfect.

id) babe 1 I have "|
tu $afl j . thou haat j ^

icfr babe "^ I may have

gclcbt ^abci , to

gctcbt, praised.

2 '

tu fabcfl 1 praised, &c.

havepiaised.

cr )at [

2j> he has 1 £

er$abe 1*

wit Baben ' *

% we have | '5

roir £abcn f *c

ir>r 1pUt

w you have J &•

iljr ffubtt 1 °*

He $aben

they have j

fie tyaben J

Pluperfect Tense.

• C 1

id) $atte

I had "]

id) Ij&tte *) I might have

tu r>attcft

thouhadst ^

tu b&tteft

praised, &c.

» (3

ct tyatte l

X he had I §

et ^Itte

* (1

nnr batten

% we had

r 2

mx bvUtcn

2i 2

it>r jottft

w you had

ibr $Attct

fie fatten ^

they had _

fie patten

First Future Tense.

PVr»* Future.

First Future.

« O

id) toerte

I shall -

id) n?crte

(if) I shal

Id) tourte *

(oben nxrtcn, to

5}*

tu totrft

thou wilt

tu toertejt

praise, &c.

tu nuirtcft

be about tc

S (3

ex njtrt
n>ic nerten

, g he will
1 ' ;§ we shall

er rocrte
toxx werten

er tvurte
nix nmrtcn

.1 S *

praise.

i&r hKrtct

you will

ibr iocrtet

i\)x tvurtet

*l3

fie wcrtcn

J they nal^

fie ivcrtcn

fie tourtcn ^

■

Second Future Tense.

SecondFuture Tense.

Second Future

^ t\

id) tocrtc

' ^ I shall -

id) njerte

(if) I shall

id) tourtt

* (8

tauurft

£ thou wilt

«5

tu n?ertc|l

5 have praised

tu tvurtefl

J5*

er toirt

, 2. he will

er tvcite

•I &c -

er toflrtc

>£2?

\
at fl

nriruxrten

* £ we shall

• p

- wttteerben

toir teuiten

«D g.5

3 2

tyt tDCTtCt

>§ you will

i^r irertct

i^r tourtct

i-s £

ftenxrten

* they will j

Tie toerten -)

o»

fie nmrtcn j

$ 81. The Mixed Conjugation
{Embracing the Irregular Verbs properly so called).

There are a few verbs (sixteen in all), which have a sort of
mixed conjugation : partaking of the Old Form, in that they
t their radical vowels to form the Imperfect Tense and the

Perfect Participle, and at the same time, partaking of the New
Form, in that they assume, in the same parts, the tense sign
te and the participial ending t. These are they which, strictly
■peaking, are the irregular verbs of the language, and accord-
ingly, they are here ao classed. They will be found, also,
in the geneial List of (so called) "irregular" verba, which,
for the sake of convenience, we have inserted.

THfi POPULAR EDUCATOR.

S 82. VERBS OF THE MIXED CONJUGATION.

INFINITIVE.

itfrcnncn, to burn,
Sflrinqcn, to bring,
£cnlcn, to think,
Turfcn, to be per-
mittcd,
£afccit, to have,

.(teitiicn, to know,
»<?pnnfn,tobcable,

ran,
Wtycn. to be al-
lowed, may,
ft'iufTcn. to be
obliged, must,
?icnuen, to name,
ffienren, to run,
2cntfn, to Rend
'£cftcn, to be
obliged, shall,
SBcntcn, to turn,
25ij[cn, to know,

SBotrcn, to be wil-
ling,

IMPEI'.FECT.

of the Indicative

! Jndicat.

Subjunct

tapt
r a un-
ci rut.

— — iA'frraRntc^ditrrnutCiqfbrduitt

— — jtrfi brarfitc :itfc brad^tci^fbrndt

— — icf tad.itc Jidi Hcttc ^itartt
icfjtarf, tu tcirffl. lUhturfie itcfr ttirftc

cr rarf | |

id* Tmbc, tu Mil cr id* Kittc id» Mttc
Hi ! | I

— - - is lanntf ,u* fennte j,j;f.:n:;t
ufclann, ti: fniiKtl, trf» finite id» K-iir.tc 'jfliMtnt

cr fa mi I j j

icf» mag, t;i r.M*.»t. i»' ku'-'M* 'id; nn*<fle Ljruiixtt

cr 111*3 | | |

irh nm*. tit niuj?, :•*(? nuStc : id; niujltc \jcntupt

cr imifj I | i

— — 'iip liamuc id' ncitnu tjcnannt

— — ii!' raiuife ;i,T) rennte -grramit

— — lift faiittc i»i; fentetc l^cuiirt
id? fett, tu foflft, |' — , - - —

rrfrfl ! I !

— — ! idnv.intte!i(f i h>cntrtrjijm«.iiiti
id; ireifi, tu lvcijit/id) ivuptc ! id; wit fire l^tmupt

cr u?eiji
id; will, tu luillrt.
[ cr will

frrenne

M'C

rciffc

$ 83. Paradigms ok irrkgui.ar vkmis.

(1) In order to a better display of the irregularities of some
of these verbs, we append the following paradigms. They will
be found exceedingly convenient for ready reference. Some of
these verbs, also have certain peculiar uses, which require spe-
cial attention. For this reason we have, immediately after the
paradigms, added a series of explanatory remarks, with copious
examples illustrating the several ways in which they arc
employed.

ANSWERS TO CORRESPONDENTS.

I'.v Etudiant: The letter v is put at the end of words ending- i» a vowel
and coming b«f(»r«« a word beginning- with a vowel, whether a CMnma inter-
venes or not; but it may be omitted. The correction suggested was made
in answer to another correspondent, vol. iii., p. 311, where the meaning of
X«ip«(l rejoice) is given. The following is the translation of the lints of
Homer:—

" For thero Is not anjwhere a more miserable Ivinar than man anions h)\
the creature* that breathe and crawl upon the earth." " And when the
early io*y-Hnjrered dawn appeared."

J.\i-<)i:ks Ks X : Wo cairwt answer the first query satisfActorily, but can
only conjecture there may be some reasons of a loral character lor using a
feminine noun to designate a man. The word den is used with a nominative
ca«c in a partitive or indi fi'.ilc rense to express nomr, any; as, des pommes,
sime apples, or limply apples. See vol. i., pp. 32 and U3. Wo do not know
which a in the word arnann our correspondent mean*.

A Constant Sunsouin^n : "Which is the better of the two?" U
undoubtedly correct, and best i«, strictly spcakim*, wrong; but it may be
questioned "whether usa;;e, which i? the only guide in language, doe* not
afford the latter sanction enough to rer.dcr it allowable.

Trktian : We have not room for the complete parkins of the sentence
referred to, nor do we see any difficulty in It.

Aquila Pulchra: The preposition ab is indispensable before names of
lining agent*, but U not nsed before those of lifeless instruments, which arc
simply put in the ablative. Ad insulam could not bo changed to insula, the
dative case. The word to, afrcr a word signifying motion, must generally
be translated by ad, followed by an nccus alive, though the preposition is
omitted before the namo of a town or small island. The French books
mentioned are good and cheap.

II. Style : We are now preparing an easy German reading book, which will
be published soon, under the title of •• Le.*»ons in German Pronunciation."
We have already published an •* Eclectic German Header , n containing select
and varied extract* from German authors. Both these works have a dic-
tionary of all the words at the end.

Raoinr( Manchester) : All right.— Saloviak (Shrewsbury): We do not
know.— lu * okamu* (Amble) : Not.

Zig.zao (Spalding): His geometrical tri«ection of an angle won't do; his
other queries are exceedingly small.— G. n. (Manchester) In right; he will find
tl.o mutter put rijrht at p. 81) of the same volume. Rce the 1st No. or vet
iv.— W. R. C. (Stepney) : l he Stadium differ* in different places and with
different aneient writ-rs.— J. (.'. C. : We really cannot well advise without
more definite information; if in town, a personal interview would sat*
Immense trouble.— An An Mill? n : See pi«t Notices to Correspondents.—
X. \. /.. i Liverpool'.: Sruiy I.miii well i*.r*t, and then Greek. Ux ELITE
iHirmingham; : Here i» a Freiu-h t-mg f<ir you :—

1)oih'.'ai.o«ui: DE I/AMITltf.
l r n ami tu techniMra*
Sans tc prr«S'-r MnMinenoent.
Fcmhlalilc a toi tu le voti.lras
D'aie, di* L'oilts, de sentimeiit.
A t'aimer tu l>> ronvieras
Kn viv:»:it charit'iblemeut.
Ton roapc t tu lui prouverus
F.n lc reprenant tranchement.
Janiidu nil tieu tu no voudr.m
Qm'iI i»rr\ N r»- ton jugeiiicut.
An lie^nin tu le d^'eudra*
("outre tons intrejiiderncut.
A s-a piiole tti croiras
('ninme :\ son i-utier drvoueineiit.
li-'uicvuh lu lui p.inlounvras
8-ui vouloir <iu'il t'en Jas;e autant.
Si:s peiiies tu devineras
I'our le.* c 'iijoli-r ^euleml'nt l
T.«> tlenues tu ne lui dira*
(i-i? ft* s I y jieut Koula?ement.
S.i femme lu re«pccteras
Kt l.i tienno paroillement.
Avec lui tu part age ras
Tons tes bien>< fraternellement.
Ft laisant ainsi tu seras
Sur d'Ore aimo Men tendretnent.

F. TI. .1. ,;!.o:i<lon) and J. K. II. (Kidderminster): Thanks. — J. Dowiu.
^liirminghaiu): Thanks; the cau^c for a standing army Is to keep the
b-ildiiin- df power iu I'urope. as well a% for national defeuce. T*ie second
question i* nbiurd.— CnkTi's : We don't know the •• lieir-at'LawSociety.**—
J. r.i'THRRFORn ( l)i:ckd( n) : The correct answer to a question implying an
afiiniMtion is yir.t: and to one iinplyinjr a negative, is no. — NilDb>H-
iiandcm asks too much of us.— W. U. Hudson (Lincoln): 8erie$ is both
singmur and plural ; hence we can say both this series aud thes* series.—
W. W. }\. (Taunton j and A 1'atiikr (Uurnlcy) : We cannot undertake to
iiConiTinnd one As-furance Poclety more than another. — C, THOMAS (St.
Au^trli): liitrlit.— J. Thomas (Sheffield): We never undertake to answer
Helling questions.— J. c. Juhnstonk: We mean that the whole Hew
Testament in French enn be hail for Gd. The specific gravity of silver, flat
and not hammered, i* 10474, and hanrnered, 10 511; of tin, pure and not
hardened, T'SOl, and hardened, 7"J9y ; Uiatoi water being l'OOtt.

Alpha (Farringdon) : To differentiate y= (1 +s 2 ) s (l+*)*,
apply the formula (hjz=zd{jn')-=zttdv~\-vdit t thus :

^/=(l+^(l+/)'+(l+i)',/(l+.ry = .
(l+^) ; 4ri+.r) >/•+ l+i-)»3(l+^)V(l+^)=

(i+^s(l+i-) ■ { t+.i.*+Gx+W J dx=z

IJTIvilARY NOTICES.

FRKNCIi

New re.-tdy, price Is. i:i stiiT Wrapper, or 5«. strongly boond in eloth,
the First Part complete, consisting ol the French and English, of Cass Rt.i.*fl
Fki'.ncii Dictionaky: the entire woik will be completed in Twenty-sis
Threepenny Number*, and « ill form one handsome Volume of eight hundred
and thirty-two pa?es. Trice 8s. 6d. bound m cloth, or the Two Division*
may be had separate.

A Complete Manual op the Frbnou Lanoi aqb, by Professor De
Lolme, jiut published, price 3s. neatly bound. This forms one of the
most simple, practical, and complete Guides to a thorough knowledge of the
French Language which has hitherto been published. The plan upon which
it is conducted is admiral!) calculated to accomplish the proposed object.
In the first place, the Grammatical Principles of the Lauruage are clearty
laid down, and, secondly, thc-e Principles are copiously illustrated by suitable,
£xerr ; ses of English to be turned into French.

Casskll's Lessons in French, in a neat volume, price 8s. in stiff covers
or 2j. 6d. m atly bound in cloth.

A Key toCabskll'8 Lessons in French, containing Translations of sli
the. Exercises, with numerous references to the Grammatical Jlliles, price
Is. paper covers, or Is. 6d. cloth.

GERMAN.

Carsbxl's Gbrman Dictionary is now issuing in Numbers, at 3d. each
Monthly Parts, Is. each.

Cassell's Lessons in German, price 3s. in stiff covers, or 2s. W.
cloth.

Cassell's Lessons in Latin, price 2s. in stiff covers, or 2s. 6d. cloth.

Cassell's Key to the Latin Exercises, now ready, price Is. in slllf
covers, or Is. 6d. cloth.

LESSONS IN CHEMISTRY.

LESSONS IN CHEMISTRY.— No. V.
ON HYDROGEN.

Thb student will remember that in the first lesson he was told
to prepare a certain combination of tobacco-pipes, corks, and
large-mouthed bottles. They hare not been employed hitherto,
and the learner may consequently think I hare forgotten all
about them: not so.

It has been my especial object to arrange these lessons in
such a manner that manipulative details, or the directions
for conducting the mechanical part of operations (and che-
mistry is full of such), may be interspersed with a due pro-
portion of thinking philosophy. I shall continue to hold this
object in view, and therefore ahall not set off the manipulative
part of chemistry by itself, but describe the manufacture of
every instrument when wanted.

Perhaps the operative student may have observed — at any
rate, he ought to have observed, for no phenomenon occurring
during the performance of a chemical operation and appertain-
ing to it should remain unnoticed,— I say he may have observed,
that during the act of solution of the sine in dilute sulphuric
acid a certain gas was evolved. Now this gas is termed
hydrogen ; it is the lightest ponderable body m nature, and
the common method of procuring it is really that which the
student has already followed, namely, by the operation of
dilute sulphuric acid upon the metal sine : iron will answer
nearly as well. Perhaps, moreover, the student may hare
observed that the hydrogen gas thus developed had a peculiar
smell : this, however, is a casualty — pure hydrogen is almost
devoid of smelL I need not describe on what the smell de-
pends just at this time, further than stating that the cause is
a sort of oil generated during the process of dissolving sino in
dilute sulphuric acid.

Let us now learn a few properties of this gas by experiment,
generalising these properties hereafter. For this purpose,
repeat the act of solution, — using zinc and dilute sulphuric j
acid as before,— only let the solution be performed in the bottle
instead of an open dish, and stop its mouth with the perforated
cork, armed with its tobacco-pipe shank, immediately after
the sino and dilute acid have been poured into it. It is
scarcely necessary to intimate that the mixture of sulphuric
acid with the predetermined quantity of water can scarcely,
with safety, be attempted in the bottle itself, on account of the
heat developed. It requires to be effected in an earthenware
basin, jug, cup, or something of that sort.

Having generated hydrogen in this way, we shall soon learn
one of its most prominent qualities: causing a flame to
approach the end of the tobacco-pipe shank, the hydrogen
which escapes will immediately take fire, proving that it is
combustible. In performing this experiment, it will be well
for the operator to place himself at some little distance from
the apparatus, because if the light be caused to approach the
extremity of the tobacco-pipe shank before the generated
hydrogen has forced out all the atmospheric air which the
bottle originally contained, an explosion will be the result :
not dangerous in itself, but it may be destructive to the clothes
by the diffusion of the dilute acid in spray. Every pheno-
menon, as I have before remarked, occurring during the
performance of a chemical experiment is important, and should
never be passed unchallenged. In the present case, we do
not stipulate for an explosion ; we will effect that purposely,
and by a convenient process, hereafter. Nevertheless, should
an explosion occur, it would only serve to anticipate a com-
munication of the fact, that hydrogen gas forms an explosive
mixture when mingled with air in certain proportions. If
an explosion occur, replace the stopper, and wait this time
before applying the flame until all the atmospheric air has been
expelled. This period may be readily guessed at, or may be
insured, by giving the operation a little more time. Applying
now the flame, the jet of hydrogen will burn tranquilly.

The next experiment we will perform shall have reference
to the extreme lightness of hydrogen. It is this : —Attach
to one end of a thin slip of deal, a drinking- tumbler, or
other similar vessel, as indicated in the accompanying dia-
gram at f, fig. 23, and to the other end of the same slip of deal
any pan-like contrivance for the suspension of a counterpoise
st ; next, support the slip by a fulcrum/ (an upright board,

I terminating above in a sharp edge, will do). These prelimi-
naries being arranged, place under the suspended and inverted
tumbler the tobacco-pipe stem delivering hydrogen gas. If

Fig. S8.

the apparatus be sufficiently delicate, the tumbler t will be
raised, thus proving the levity of hydrogen gas. There
are many processes of demonstration more elegant than this :
several will be mentioned hereafter. There are none, how-
ever, of equal simplicity, as they require the use of apparatus
not yet described.

The next experiment to be mentioned shall have reference
to the products of the combustion of hydrogen gas. For
this purpose, ignite a jet of such gas as it emerges from
the shank of the tobacco-pipe, and hold over the flame a wide-
mouthed bottle or tumbler, as represented in the following
diagram, fig. 24 : —

Fif.24.

YOL. IT.

After the lapse of a few seconds, the vessel, previously dry, will
be bedewed with moisture. Where does the student believe
the moisture comes from ? His first idea, perhaps, might be,
that it comes from little particles blown out, as it were, from
the liquid in the bottle. In our rough experiment, probably
a little is attributable to that source ; but if every care be taken
to dry the gas, still its combustion yields water— nothing but
water. Hence hydrogen derives its name from vflwp, water,
and yiwaut, I form ; hydrogen, then, means the water-former.

If, instead of a tumbler, the student uses a large-mouthed
bottle (a soda-water bottle answers remarkably well}, he will
generally succeed in eliciting a roaring or singing noise, attri-
butable to vibrations set up in the contained air by means of
the burning hydrogen.

The chemistry of gases is very delicate; I shall, therefore,
when describing these bodies (the term sounds oddly to an un-
chemical ear, though it is correct) frequently require to men-
tion instruments that the student neither has nor requires to
have, a mero description of their form and mode of operation
being sufficiently instructive. Of this kind is Cavendish's
Eudiometer, the instrument by which the truth that hydrogen
by combustion with oxygen (for that is essential) yields water,
nothing but water, was first determined. In the experiment
which we have performed, the hydrogen supplied itself with
oxygen from the atmospheric air : but it would have been com-

THE POPULAR EDUCATOR.

potent for the operator to have mixed it with oxygen previous
to combustion : and this is what the chemist Cavendish did.
Having effected a mixture of oxygen and hydrogen, and filled
with this mixture a thick glass vessel, as represented in the
accompanying diagram, fig. 26, and since known as Cavendish's

Eudiometer, he then caused an electric discharge to traverse
a pair of wires a b, penetrating the glass stopper t, so that an
electric spark should pass through the space «': by this
elegant contrivance the gas was ignited) and the sides of the
vessel became bedewed with moisture, which on being examined
was found to be water. As the experiment adverted to will
scarcely be performed by any chemical novice, it would be a
waste of time to describe in detail the construction and use of
this beautiful instrument. I shall merely content myself,
therefore, with observing that the stopper is screwed tightly
down by means of a contrivance indicated in our diagram ; and
the foot m of brass is not permanent, but admits of being
screwed off at m\ and the instrument attached to this point of
junction to the receiver of an air-pump. The student will
easily understand, that the air originally contained in the vessel
being pumped out, a vacuum will ensue, and the stop-cock e
being screwed on to a vessel containing gas, the latter will
rush in. The method here described is not the usual one by
which vessels are filled with gas; chemists accomplish the
object far more readily by what is called the pneumatic trough,
to be described presently. In the experiment of Cavendish,
however, water would have been inadmissible as the filling
agent, and mercury scarcely more eligible.

Methods of Collecting Gas, — Two methods of collecting gases
have already come under our notice. Firstly, we collected
hydrogen by simply inverting a tumbler over a jet, through
which the gas was escaping. This method is usually called
that of a displacement, and is sometimes had recourse to,

although not very correct in its results. The second method
is by exhaustion, as we have seen in the instance of Cavendish's
Eudiometer. The third method, now to be described, is by far
the most usual and most important,— collection by the pneu-
matic trough. If a bottle be taken, filled with water, and held
thus inverted over water, I need hardly say the water which it
contains will not escape; but if a jet of gas be liberated under
the mouth of the bottle, it follows, from a consideration of
seme ordinary laws of hydrostatics, that gas being lighter than
water, the former will ascend and the latter will descend, until
ultimately the bottle becomes quite filled with gas, but empty
of water. For this elegant contrivance we are indebted to the in-
genuity of Dr. Priestley. In my sketch, fig. 26, 1 have represented

a common basin as the vessel in which the bottle is inverted, sad
I have represented the bottle as supported by the hand. I
need not say this way of proceding is inconvenient; to rive
full effect to the operation one requires that the bottle shall
stand without support, and that the vessel shall be large— one,
in fact rather like a tub than a basin; a vessel thus modified
becomes the pneumatic trough.

As relates to the bottle or jar in which the gas fa to be col-
lected, it will stand quite well without any support provided
its mouth be sufficiently wide ; if circumstances of any kind
require the use of a narrow-mouthed bottle, it may be supported
in dozens of ways, readily occurring to the operator. The
student need not expend one penny in the purchase of a pneu-
matic trough, except he has to deliver public lectures, sad
requires display. The first wash-bowl, kitchen-tub, loot-pan,
or slop-basin he can lay hands on will answer sufficiently weQ;
and as for the support, I will now just mention one that in
many cases answers even better than a shelf. It is this.

Taking a piece of tin or iron, or other metal plate, fold it i

Fif. 28.

LESSONS IN ENGLISH.

the shape of a cone, the apex of which is truncated; next cut
a notch in the lower or base edge of the cone, and the stand is
made. The use of it will be evident from an examination of
the diagram, fig. 28. The notch admits the gas delivering
tube, the truncated apex delivers the gas into the bottle, which
rests supported on the sides.

If the student were not told of these contrivances he might
think me remiss ; but I want to create a feeling of independence
in his mind, to impress him with the conviction, that in
the majority of chemical operations involving the use of
mechanical contrivances, many different methods admit of
being followed, each equally good. The support just described
is useful, and not inelegant, but I shall not quarrel with a
student who tells me that two bricks set edgeways in a pan of
water, fig. 29, furnish a support which is nearly as good.

Fig. ».

The great fault of most books which treat of c h emical ma-
nipulations is this : — they represent the apparatus which is
not intrinsically best for gaining any particular result, but the
apparatus which makes the prettiest engraving. This, in my
opinion, is but a questionable benefit to the pictorial art, and
a vast disadvantage to the student of chemistry.

LESSONS IN ENGLISH.— No. LXXH.

By John R. Beard, D.D.

COMPOUND 8ENTENCES.

Wb have already learnt that a subject may comprise a noon or
nouns standing in apposition to the principal noun ; as,
Principal Norn. Apposition. Predict*.

Victoria, Queen of England, conquered Burmah.

This appositions! clause or member proves when analysed to be a
sentence of itself; e.g.,

Street. Sentence, Predicate.

Victoria, who is Queen of England, conquered Burmah.
Stmflar accessaries may be made to the subject, which may be
called

Subject- Accessaries.

f being Queen of England \
Vl.** hXST,^ gained rep....
\ while Queen of England ;
These accessaries are denominated subject accessaries, because
they qualify the subject. Accessaries may qualify the object

also; eg.,

Object-Aceessartee.

Sby her Yirtues.
for the good laws she sanctioned,
in consequence of her burin.

These accessaries, whether they attach to the subject or the
object, may be characterised as

Adverbial Accessaries
The essential quality of the adverb is to declare the quality of
an affirmation, thus :

He writes well.
But the quality of an act may be assigned by an adverbial phrase
s» wen m by a simple adverb; eg.,

In great concern he ran to bear the sad tidings.

Hie words printed in italics form an adverbial phrase. Adverbial
phrases involve what may be called an adverbial object ; thus, in
great concern is an adverbial object. Adverbial objects may be
various; as,

1. Of time : On arriving kemu I hastened to bed.

2. Of place : He slew his foe in the dell

3. Of manner : The father begged his fife with many supplications.

An object, then, may be not only single or compound*
Single : He launched the ship ;
Compound: The waves overwhelmed the boat and the crews

near or remote ; as,

Neart He sold his desk ;

Bemote: He sold his desk to his ebrft;

but also adverbial, and that of three kinds,-— of tune, of place, of

A simple sentence is a sentence which hat one subject and one
affirmation or predicate ; and a compound sentence n a sentence
that has more than one subject and more than one predicate.
The component parts of a compound sentence are called its mem-
bers. These members may be two or more; they may also each
form a separate sentence :—

Compound Sente n ce s of two M m h t re .
1 2

He will perish who loves unrighteousness.

1 2

The lark sang his matins and sank into his nest

The first sentence is equivalent to these two propositions :—

1. Some one will perish.

2. The lover of unrighteousness will perish.

The second sentence is equivalent to these two statements i —

1. The lark sang his matins.

2. The lark sank into his nest.

Compound Sentences of three Members.

1 2 8

When the Queen arrived, the fleet had weighed anchor and sailed.

1. The Queen arrived.

2. Before then the fleet had weighed anchor.

3. Before then the fleet had sailed.

Thus what in the compound sentence stands ss three members,
becomes in the analysis three individual sentences. , . . .

It is easy to see that the members may be increased almost at
pleasure : —

The sick and all but dying man drinks water and revives.

Compound sentences have members of two kinds, the principal
and the accessary. The principal member is that which «*uiicWes
the leading thought, the accessary member is that which enunciates
the subordinate thought :—

Principal Member. ACOTMABY MWMH,

The man drinks (and) U refreshed.

The accessary member (or members) may be of two kinds,
namely, interposed or appended. An accessary member ismter-
posed when itTappears in the body of a sentence, being mtroduced
by a relative pronoun, a relative adverb, or a conjunction ; e. g.,

Principal Accessabt PrmciswL

Intbufosbd.
Ed. Pron. : The msn who drinks ii refres hed

ltd. Ad.: The man when he drinks ""^^

Conjee.: The man ifhedrinks is refreshed

Appended members are added by means of conjmictionfc,

adverbs, and pronouns:—

Accessabt
Principal. Afpbkdmd.

Adv. : The man is refreshed •*■» «** •»*■.

THE POPULAR EDUCATOR.

The principal member may be expanded ; e. g.,
Principal Member Expanded.

The accessary member may also be expanded ; e. g.,
Interposed Accessary.

"—-{StoSKLd drink. }••*•*•*•*.
The appended member, too, may be expanded ; e. g.
Appended Accessary Expanded.

The man drinks (and) j jj

is refreshed,
refreshed and strengthened.

Sentences may be farther divided into the direct and the inverted.
A sentence is direct when the principal member precedes the
accessary; e. g.,

Direct Sentence.

Principal. Accessary.

The man drinks (and) is refreshed.

A sentence is inverted when the accessary sentence precedes the
principal: —

Inverted Sentence.

Accessary.

Principal.
(if he drinks.

The man is refreshed I when he drinks.
( should he dxink.

Relative pronouns are such pronouns as relate to some pre-
ceding noun, called the antecedent ; that is, the foregoing word ;
e. g.,

Relatives and Antecedents.

Antecedent.

The man
The men

Relative,
who drinks water
whom he met

Predicate.
is wise,
he struck.

Subject.

Object.

The relative must agree with its antecedent in person, gender,
and number; e. g.,

Antecedent. Relative. Predicate.

1.
2

I
He

who
who

read,
reflects.

In number one, who is of the first person, because J is of the
first person ; who is of the singular number, because / is of the
singular number. The effect of the relative on the verb is more
clearly seen in the second instance, where an * is added to the verb,
which accordingly appears as reflects.

As the language is now written and spoken by the best authori-
ties, the relative who has one change of form in the nominative,
namely, in which ; which is commonly applied to things. Who,
however, has a genitive and an objective, as well as a nominative
case, and may be declined or inflected thus : —

Wno Declined.

Singular and Plural. Masculine. Fembdne. Neuter

Singular J Atai. who who which

whose of which (whose)

and >
Plural. )

Oenit. whose
Object, whom

whom which

Instead of whose and which we sometimes find whereof.

That, which is without any inflexional change, may be used
in lieu of who or which, being applied to both persons and
things ; e. g.,

" He that reproacheth a acorner, getteth to himself shame."—
(Prov. ix 7.

The word « is also used with the force of a relative after such,
to many, the sums ; t. g.,

" The malcontents made such demands at none but a tyrant eoali
refuse." — DoHnbroke.

What is a relative which performs the double function of a ab-
ject and an object, being equivalent to that which, and used In only
the neuter gender ; e. g.,

" My master wotteth not what is with me."— (Gen. xxxix. 8.)

As a subject for exemplifying the doctrines laid down in regard
to the structure of sentences, I shall take some sentences from
Daniel Defoe, a writer of idiomatic English.

Compound Sentence.

" Oxford makes by much the best outward appearance of any
city I have seen, being visible for several miles round on all sides
in a most delightful plain ; and adorned with the steeples of the
several colleges and churches, which make a glorious show."

Here I must premise that the form " the best outward appear-
ance of any city," &c, is incorrect, and should have been "the
best outward appearance of all the cities I," &c. This compound
sentence may be reduced into these simple sentences : —

1. Oxford makes a very good appearance.

2. Oxford makes an appearance better than many cities.

3. I have never seen a city with a better appearance than
Oxford.

4. Oxford is visible for several miles round.
6. Oxford is visible from all sides.

6. Oxford stands in a most delightful plain.

7. Oxford is adorned with the steeples of several colleges.

8. Oxford is adorned with the steeples of several churches.

9. The architectural decorations of Oxford make a glorious show.

The resolution of this long sentence into the several slslimt
propositions which it contains, has, by showing the meaning of tat
several parts, prepared the way for our exhibiting the logical rela-
tions which those parts sustain to each other, thus : —

Logical Relations of the Sentence.

1. Oxford

2. makes

3. the best outward appearance

4. of any city

5. that I have seen

6. being visible

7. for several miles round

8. on all sides

9. in a most delightful plain

10. and adorned

11. with the steeples, &c.

the subject to 2

makes together with 3 the predi-
cate to 1
the object to 2
adverbial object to 2
appended accessary to 2
accessary to the subject 1
adverbial object to 6

second accessary to 1
adverbial object to 10
12. which makes a glorious show appended accessary to 10

Several of these parts may be analysed or explained ; e. g.,
Number three consists of the definite article the, the superlative
adjective best, the adjective outward in the positive degree, and
the common noun appearance, which is the object to the verb
makes.

Number six presents a case of explanatory apposition, sines
being visible is subjoined to the subject Oxford in order to stats
some additional facts respecting it ; number ten stands to
ber one in the same relation.

Number twelve presents an appended relative t
of which these are the components ; namely, which, a i
noun agreeing with its antecedent steeples ; make, a verb in the
indicative mood, third person, plural number, agreeing with its
subject which ; a, the indefinite article limiting show ; glorious, sa
adjective qualifying show ; show, a common noun dependent on
or the object to the verb make. Viewed structurally, tail
appendage stands thus :

Subject. Predicate.

Verb. Object.

Which make a glorious show.

By way of applying what you have learnt, tako portions of any
good prose author, mark the logical relations of the sentences
after you have resolved each into the simple propositions of width
it consists, and explain by grammatical analysis (that is, "nana")

LESSONS IN NATURAL PHILOSOPHY.

the several component*. In other termi, convert each of these
compound sentences into simple sentences. Distribute each simple
sentence into subject and predicate, distinguishing the verb (the
copula) and the attribute. Next, exhibit each compound
sentence in its several members, showing what are principal, what
accessary, and what appended, what interposed; together with
the accessaries to the subjects and objects, and the adverbial
objects. Finally, give the grammatical analysis of the whole.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. VI.

LAWS OP GRAVITY; PENDULUM.

(Continued from page 63.)

Formula relating to Falling Bodies, — The second and third laws
of falling bodies may be respectively represented by the formulae
v=zgt, and *=\g&. For, let g be the velocity acquired at the end
of a second by a body falling in a vacuum, and v its velocity
after t seconds; then, the velocities being proportional to the
times, we have g : v : : 1 : t ; whence v=gt (I). Again, a body
which falls during t seconds by a motion uniformly accelerated,
with an initial velocity equal to zero or 0, and a final velocity
equal to gt, will describe the same space as if it fell during the
wnole time t by a uniform motion, with a mean velocity between
and gt, that is, with the velocity \gt. Now, in the latter case,
the motion being uniform, the space described is equal to the
product of the velocity and the time ; whence, denoting this space
by «, we have s-=z\gt X < = \9* (2). The demonstration of
these theorems is given mathematically in treatises on Dynamics;
see WheweU's Mechanical Euclid, and other elementary works
of the same description*

If in the formula (2) we make *=r 1, we have «=£?, whence
g =z 2*; that is, the velocity acquired at the end of a unit of time
is double the space described in that unit of time. This value of
g is called the measure of gravity. Thus, in the latitude of Lon-
don, it has been found that a body falling near the surface of the
earth, in a vacuum, describes about 16^r fc*t in the first second
of its fall; hence, the measure of gravity of London is about 32$
feet ; in other words, after a body has fallen 16^ feet in 1 second,
by tie force of gravity, it would, if the attraction of the earth were
removed or counteracted, continue to mil ever after with a
uniform velocity of 32} feet per second.

In formula (1) the velocity v is expressed in * function of the
time; that is, an expression involving the number denoting the
time ; but we can likewise express it in a function of the space
described, by eliminating t from the two formulae (1) and (2).

For, from the first, we have f =-f^ whence <» = — ; now substi-
9 9 2

toting this value of** in formula (2), we have*=4^X — =

_L; and multiplying both sides of this equation by 2y, we have

v-=z2g»; and extracting the root, we have finally, vz=.\/2gs\

hence, we conclude that, when a body mils in a vacuum, the

velocity acquired at any given instant is proportional to the

square root of the height of the fall.

The formulae v=.gt, and * = 1 gt 2 , having been determined by
considering gravity as an accelerating force, and consequently in
a ease where motion is uniformly accelerated, they may be con-
sidered as general formulas for this kind of motion. But it
must be observed, that as g denotes the acceleration of the
velocity imparted in each second by the accelerating force, the
value of g will vary with the intensity of the force.

Causes which Modify the Intensity of Gravity.— Three causes
have an effect in making the intensity of gravity vary ; 1st, the
elevation of the place above the ground, or general level of the
earth's surface; 2nd, the centrifugal force due to the earth's
rotation on her axis ; 3rd, the depression of the earth's surface
near the poles.

1. Since terrestrial attraction acts upon bodies as if the whole
mass of the globe were collected at its centre, and this attraction
acts upon them in the inverse ratio of the square of their distance

from that centre, it follows that the intensity of gravity will
increase or decrease, according as the bodies approach to, or
recede from, the general level of the earth's surface. This varia-
tion, however, is not apparent in the ordinary phenomena which
are observed at the surface of the globe, because, its 'radius
being nearly 4,000 miles, the distance from the centre is sensibly
the same when a body is elevated by a few hundred yards.
But when the heights of bodies above the earth's surface are very
considerable, gravity can no longer be considered as having the
same intensity. It is necessary, therefore, to remember that the
laws of falling bodies already explained are only true for heights
within certain appreciable limits.

2. The second cause which modifies the intensity of gravity is
the centrifugal force. A force which produces a curvilinear motion,
and which gives to bodies under the influence of this motion a
tendency to fly off from the axis of rotation, is called centrifugal.
It is demonstrated in treatises on Bational Mechanics, that the
centrifugal force is proportional to the square of the velocity of
rotation ; whence it follows that, under the same meridian, it
increases as we approach the equator, where it reaches its maxi-
mum, because there the greatest velocity takes place. At the
poles the centrifugal force is zero. At the equator, the centrifu-
gal force is directly opposed to gravity, and is equal to jt? of its
intensity. Now 289 being the square of 1 7, it follows that, if the
motion of rotation in the earth were 17 times slower than it is, the
centrifugal force at the equator would be equal to that of gravity,
and all bodies on its surface in this latitude would be on the
point of being projected into space.

As we proceed from the equator towards the poles, gravity is
less and less affected by the centrifugal force. This happens chiefly
because the centrifugal force decreases in proportion as we recede
from the equator, and also because that, at the equator, the cen-
trifugal force is directly opposite to that of gravity, whereas, in
proceeding towards the poles, its direction becomes more and
more inclined to that of gravity, and thus loses intensity. Thus,
in fig. 15, in which pq represents the axis of the earth, and if the

Tig. 15.

equator, at any point a, the centrifugal force is represented by
the straight fine a b perpendicular to the axis at x ; now the
force of gravity which acts in the direction of the radius c d, is
diminished by a quantity represented not bv ab, but by ad,
which is the composant of the centrifugal force acting in the
direction a d.

3. The intensity of gravity is also modified by the depression
of the earth at the poles ; for, in the vicinity, and at these points,
bodies are nearer to the centre of the earth, and consequently
more subject to its attraction.

Measure of the Intensity of Gravity. — After the preceding con-
siderations, gravity may be considered in the same place, and in
cases where the heights of the fall are inconsiderable, as a con-
stantly accelerating force ; and that the measure of its intensity
is the velocity imparted in one second of its fall to a body falling
in a vacuum, without regard to its mass, seeing that in a vacuum
all bodies fall in the same time. This velocity is represented in
general by 2g : it increases from the equator to the pole, and at
London it is 32$ feet

The Pendulum. — The general name of pendulum is given to
every Bolid body suspended atone point on a horizontal axis,
around which it oscillates. There are two kinds of pendulum ;
the simple and the compound.

The simple pendulum (which exists only in idea) is that which
would ta fanned by a heavy material point suspended by a per-

TEE IWULAB EDUCATOR.

fectly rigid rod, msxtcnaible and without weight, at a pob t that is, that they are seaaibly equal in the same time, so long at
round which it freely oscillates. Of course this pendulum cam* their am p litu des do not exceed a oertain limit, namely 2° or •*
he pat in actual practice, because it is purely tneoretkad, and is of the circle.

aployed only to determine by cnlonlatimr the laws of to
oscillations of the pendulum.

The comp oun d pendul u m may be nried in its form in any
manner whatever, but it is generally made of a metallio lens or
bob, suspended by an iron or wooden rod, and moveable round a

horizontal axis, such as the pendulum of a dock, the pendulum tions are the same, whaterer be the substances of which they am
*, in flg. 13 of the preceding lesson, or that exhibited in the composed. Thus, simple pendulums of which the material posat
following cut, where o is the point of suspension, and o the point is composed of cork, lead, or gold, perform the same number of
of oscillation ; in other words, o is the pom —-"—•—- *- *■*- ^ — - M ^ * « ■ - - -*

Galileo was the tot who established the mobhroniam of ths
small oscillations of the pendulum. It is said tha^ when a young
man, he first made this discovery by obserrimg the motions oft
lamp suspended in the dome of the cathedral atPisa.

2. In pendulums of the same length, the duration of thc<

where a simple pendulum would produce th
same oscillations as the compound pendulum
Compound pendulums are suspended eithe
on a Imife-edge, on the same principle as ths
of balances, or by means of a thin and flexibl
steel soring, which is bent slightly at eveq
oscillation.

In order to explain the oscillatory motioi
of the pendulum, we shall first notice th
simple pendulum tic, flg. 10. When th<
material point m is below the point of suspen
sion c on the Tertical passing through that
point, the action of gravity is destroyed, or
rather counteracted; but if the point h
transferred to st, its weight r will be deoom
posed into two forces, the direction of the on<
being in the straight line * m produced to b
and that of the other in the tangent stntc
the arc m m *• The c ompo e ant m b is coun-
teracted by the resistance of the point *, but
the eonrposant st d urges the material point to descend from
m to m. When it reaches this point, the pendulum does not
■top; for, in consequence of its inertia, it proceed s in the

Fif . 16.

point oscillations in the same tune, if they are of equal length.

direction mm. Now, if the same construction be made at any
point of the arc mm, it wul be found that the gravity which
acted from m to x with an accelerating force will now act
from m to n with a retarding force. It will take away, there-
fore, successively from the moveable the velocity acquired in
iti descent, so that, when it reaches the point a at a height
equal to that of the point m, the velocity will become aero, as
it was at the latter point. Whence it follows, that the
same series of phenomena win be repeated, and the pendulum
will continually oscillate. In practice, this result is prevented
by the resistance of the air, and the rigidity of the cord, obstacles
which can never be completely annihilated in compound pen-
dulums.

Laws of the Oscillation of the Pendulum.— The passage of the
pendulum from one extreme position or point m to the other is n
called an oscillation or swing. The arc m n is called the amplitude
of the oscillation; and the length of the simple pendulum is
the distance of the point of suspension o from the material:
point m.

In treatises on Eational Mechanics, it is demonstrated that the i
oscillations of the simple pendulum arc regulated by the four
following laws.

1. In the same pendulum, the small oscillations are isochronous ;

In pendulums of unequal length, the durations of their
! oscillations are proportional to the square roots of their 1«ng*%.
Thus, if the lengths of pendulums be respectively 4, 9, 16, Ac,
times that of a given pendulum, the duration of their oecOlatioos
will be respectively 2, 8, 4, ecc times that of the oscillation of the
given pendulum.

4. At different places of the earth's surface, the derations of ths
oscillations of a pendulum of the same length are in the inverse
ratio of the square roots of the intensities of gravity.

These laws are deduced from the formula *=*V--, which is

derived from the application of the calculus to the motion of ths
I rimnle pendulum. In this formula, * denotes the duration of an
osoillstion ; /, the length of the pendulum ; 2a, the intensity of
gravity, that is, the velocity acquired at the end of the 1st second
by a body falling in a vacuum. Also, w is a constant quantiiy
which denotes the ratio of the circuraferenoe of a circle to its
diameter, which is equal to 3141692.
The first two laws of the pendulum are deduced at once from

the formula f==wt/—-; for this formula contains the values

neither of the amplitude of the oscillation, nor of the density of
he substance of which the pendulum is coiapoeed. the value off
being independent of the values of these Quantities. As to the
bird and fourth laws, they are also comprehended under the for-
mula, since, in the radical expression, / is the numerator, and 2a
the denominator of the fraction.

Lenath of the Compound Pendu l um , T he preceding laws and
formula) are applicable also to the oompound pendulum; but in this
ease it is necessary to define what is meant by the length of the
pendulum. Every compound pendulum is formed of a heavy rod
te rmin a ting in a laraer or smaller mass, according to ita form and
purpose ; now, all the different points oftsuoh a pendulum tend,
according to the third law of pendulum motion, to describe their
os cill s t ions in times differing from each other, and increasing in
duration in proportion to the square roots of their distances from
the point of suspension. But all these points being invariably
connected together, their oscillations are necessarily performed in
the same time. Hence, it is evident that the motion of the
points nearer to the axis of suspension is retarded, and that of the
points more remote from that axis is accelerated. Between
these two extremes there are some points which are neither
accelerated nor retarded, and which oscillate as if they were not
connected with the rest of the mass. These points being all at
be same distance from the axis of suspension, form together sn
sie of oscillation parallel to the former ; now the distance of the
axis of oscillatio n is called the length of the oompound pendulum.
Hence, the length of a oompound pendulum is the same as the
length of a simple pendulum which performs its o scillat i o ns in
the same time. Thus in the preceding figure of the oompound
pendulum, the point o is the centre or place of the axis ofsmpom-
a*ew, and op the length of the compound mass ; all the points of
lis mass between o and c are retarded, and all the pointa
etween p and c are accelerated ; but all the points at o are
■either accelerated nor retarded, and therefore the point o If the
centre or place of the axis of oscillation.
The axis of oscillation possesses the property of reciprocity with
ie axis of suspension ; that is, if we suspend the pendulum by
Its axis of oscillation, the duration of the oscillations will be the
same as before; in other words, the axis of suspension will then
become the axis of oscillation. By means of this property, the
length of the oompound pendulum can be found experimentally.
This is done by inverting the pendulum and suspending it by
leans of a moveable axis, which is placed, after several trials, in
fuoh a manner that the number of oscillations performed in the

LESSONS IN ITALIAN.

lame time may be exactly the lame aa they were before ite
inversion. When this object has been attained, then the distance
between the second axis of suspension and the first, is the true
length required. If we now substitute the value thus obtained,
instead of J, in the formula relating to the simple pendulum, this
formula becomes applicable to the compound pendulum, and the
laws of oscillation are the same as those belonging to the simple
pendulum.

The length of the seoonds pendulum, that is, the pendulum
which beats 60 times in a minute, varies at every place, aooord-
ing to the intensity of the force of gravity at that place: thus,

at the Equator, it is 39*0137
at London, it is 39*1303

at 10° from the Pole, it is 89*2106

Ver&oation of the Lowe of the Pendtdum^The laws of the
simple pendulum can only be verified by means of the oompound
pendulum ; and this is best done by constructing the latter in
such a manner that it may fulfil, as much as possible, the condi-
tions of the former ; as, for instance, by suspending at the end of a
very fine thread, a small sphere of an extremely dense substance,
anon as lead or platinum. A pendulum of this construction
fljffffl«ia«i almost exactly like a simple pendulum, whose length is
equal to the distance between the point of suspension ana the
centre of the small sphere.

In order to verify the law of the isochronism of small oscilla-
tions, a pendulum of the preceding construction is made to oscil-
late, and the number of oscillations which it performs in equal
i is noted when the amplitude is 3°, 2°. or 1°. By this
i it is asoertsined that the number of oscillations is in these
i exactly the same.
In order to prove the second law, several pendulums b, d, o,
fig. 17, are constructed as suggested above ; that is, having their

Tig. 17.

lengths in fine thread, equal and terminated in spheres of the
t^m^ diameter, but of different substances, as lead, ivory, or
brass. Neglecting the resistance of the sir, it is found that all
these pendulums make the same number of oscillations in the
same tune; whence it is inferred that gravity acta on all sub-
stances with the same intensity — a foot which has been formerly
proved to the student.

The thir d law is verified by making pendulums oscillate, whose
lengths are to one another respectively as the numbers 1 , 4, 9, <fcc;
when it is found that the oscillations of these pendulums are to
one another respectively as the numbers 1, 2, 3, &c.

The fourth law, relating to the oscillations of pendulums, cannot
be correctly proved by experiment.

Urn of the Pendulum.— The oscillations of the pendulum show, I

as we have seen above, that gravity acts upon all bodies with the
same intensity. They also enable us to determine the intensity
of gravity at different points of the earth's surface, and conse-
quently the true form of the earth itself. The isochronism of
the oscillations renders it applicable as a regulator of timepieces.
Lastly, M. Foucaud has recently employed it in the experimental
demonstration of the diurnal rotation of the earth.

In order to measure the intensity of gravity by means of the pen-
dulum, we ascertain the value of fy, from the equation t = w |/~

By squaring both sides of this equation, we have &—* *__.

mA I

whence, by reduction, we have 2? s 2- — . Thus, we see that,

In order to find the value of 2a at any place, we must measure the
length of the compound pendulum at that place, and then the
duration of its osculations ; this may be found by ascertaining
how many oscillations it makes in a given number of seconds,
and dividing the latter number by the number of oscillations.

By such experiments the value of 2a has been determined at
different points on the earth's surface. Hence, by calculation, we
deduce from the value of 2g at each place, the distance of that place
from the centre of the earth, and consequently the form of the
earth itself.

Huygens, a Butch philosopher, was the first who applied the
pendulum as a clock-regulator, in 1657, and the spiral spring to
watches in 1675. When the pendulum is employed as a regula-
tor, it is furnished with an anchor escapement, as explained in
the description of Atwood's Machine.

LESSONS IN ITALIAN GRAMMAR— No. VI.

By CHABLE8 TAU8ENAU, M.D.,

Of the University of Pavta, and Professor of the German and Italian
Language* at the Kensington Proprietary Grammar 8chooL

FOUBTH PRONOUNCING TABLE,

FOR ADDITIONAL XXSROI8B IK TSUI VOWBLS.

1. Words that contain a, e % t, o, or repeated «:—

Italia*.
Calafatata
Abbacmata
Aecanalata
Salemandra
Abbraeiava
Cavaleava
Pereevererete
Dependentemente
Pretenderete
EceeUentemenie
Insipidissitni
Vicinusimi
Inimieieeimi

Mirifici

Dietmtieeimi

DifficUienmi

Odoroeo

Doioroeo

Pomoeotogno*

TutntUtuo

Ouccurucu

Ueufruttuo

Pronounced,
kah-lah-mh-tahtah
ahb-bah-tohee-nah-tah
ahk-kah-nah-lah-tah
sah-lah-mahn-drah
ahb-brah-tchah-vah
kah-vaM-kah-vah

Ser-sai-vai-rai-rai-tai
ai-pen-den-tai-men-tai
prai-ten-dai-rai-tai
et-tchel-len-tai-men-tai
in-see-pee-dis-see-mee
vee-tchee-niB-see-mee
ec-nee-mee-tchis-see-mee

moe-r6e-fee-tchee

dee-stin-tis-see-mee

dif-fee-tchee-lis-see-mee

o-do-r6-so

do-lo-r6-so

po-mo-ko-ton-nyo

too-m6ol-too-o

kook-koo-roo-koo

oo-xoo-fr6ot-too-o

Bnglitk.

Calked

Blinded

Channelled(colnmn)

Salamander

I kindled

I rode

Yon will persevere

Dependent

You will pretend

Excellently

Most insipid

Very near or vicinal

Verjr hostile or in-
imical

Wonderful, mira-
culous

Very clearer distinct

Very difficult

Fragrant, odorous

Painful, dolorous

Quince

I excite a tumult

A word imitating
the cock-crowing

I have or enjoy the
temporary use

2. Words comprising the five vowels :—
Italian. Pronounced. English.

Afettuoti ahf-fet-too-6-si Kind, affectionate

Communicare kom-moo-nee-k&h-rai To communicate

• The sound of the pi will be explained in another lesson

THE POPULAB EDUCATOR.

Delieatuzzo

JBntusiasmo

lulminatore

Lutmghertumo

Procuratrice

RepubUeano

Saluberrimo

Pronounced,
dai-lee-kah-too-tso

en-too-zee-ah-zmo

fool-mee-nah-t6-rai

loo-zin-gai-rahn-no

pro-koo-rah-tree-tchai

rai-poo-blee-kah-no

sah-loo-b$rr-ree-mo

Speculated epai-koo-lah-t6-ree

Bubordinare soo-bor-dee-nah-rai
Superlativo soo-per-lah-tee-vo

English.

Over-refined, deli-
cate

Enthusiasm

One who fulminate!

They will natter

A solicitor's wife

Republican

Very wholesome oi
salubrious

Thinkers, specula-
tors

To subordinate

Highest, superla-
tive

It is necessary that I should now explain with some degree]
of minuteness certain peculiarities of the most frequent occur-
rence, and consequently of the highest importance in the
pronunciation of the letters e, g, and *, when they enter into
certain combinations with other letters.

With regard to the letters e and g, I have already stated and
illustrated by examples in the first pronouncing table, that
when c and g are placed before the rowels a, o, and u, c is
sounded like k, and g like the English g in the words game, go,
and gull. But suppose that it should be necessary in the
declension of nouns, the conjugation of verbs, &c, to give to
the e and g before the vowels e and t the same sound that c and
g have before a, o, and u ; it is obvious that some sign must be
used to mark that pronunciation of the e and g 9 and avoid con-
fusion. This sign is no other than the letter h, which, as has
been remarked, is a mere soundless, written sign, and on that
account pre-eminently suited to the purpose. In this way we
arrive at the combinations eh and gh ; and from what has been
said, it is obvious that the sound of eh before e and i can be
no other than the sound of h ; and the sound of gh before e and
t, that of g in the English words game, go, and gull. And,
indeed, it is a fundamental rule of Italian grammar, which
cannot be too strongly impressed on the mind of the reader,
that whenever a grammatical necessity arises in the inflexions
or terminational changes of a word, for retaining the sound
of the e which in the root sounded like h, and the sound of g
which in the root sounded like g in game, go, and gull, before the
vowels e and t ; h must be placed between c and g, and the vowels
$ and i, and the combinations thus resulting will be the, chi, and
ghc t ghi, pronounced kai or ke\ kee ; yai or yh6, ghee. For
example, banehe (pronounced bahn-kai), banks, offices; stecchil
(Rt6k-kee), thorns, prickles ; Tedesehi (tai-dai-skee), Germans ;
Turchi (to6rr-kee), Turks ; oche (d-kai), geese ; vecchio (vek-
keeo) ; an old man; perchk (per-kai), why ; Jianc hi (feeahn-
kee), flanks, sides; Gherardo (gai-rahrr-do), Gerard; ghetto
(irhet-to), a Jewry; ghirlanda (ghirr - l&hn - dah), garland;
Ghibeilino (chibel-fee-no), Ghibellin ; alberghi (ahl-berr-ghee),
hotels ; maghe (mah-gai), sorceresses ; impieghi (im-peee-ghee),
employments.

But suppose a necessity arises for giving to the letter e before |
a, o, and u the sound of e in the word church, and to g before
a, u, and o the sound of g in ginger. Evidently a sign must be
used to indicate that, or else c would be sounded like k, and g
like g in game. Now this sign is the vowel ». In common
conversation this i is scarcely heard, serving the purpose only
of a mere soundless, written sign ; but in the more measured or
studied pronunciation of the pulpit, the stage, public assemblies,
and even frequently in the conversation of cultivated persons,
the i is slightly touched in the enunciation, while the voice
rapidly glides to the pronunciation of the vowels a, o, and u.
Hence another fundamental rule of Italian, which goes side by
side with the one above stated, that whenever a necessity
arises for giving to the c before a, o, and u the compressed sound
of c in the English word church, and to g before a, o, and u the
compressed sound of g in ginger, the letter t (an auxiliary letter
«n this case) must be placed between e and the vowels a, o, and
u, and between g and the vowels a, o, and u, and the combina-
tions thus arising will be cia, do, ciu, and gia, gio, giu,
pronounced tchah, tcho, tchoo, and jan, jo, joo. For example,
ciascuno (tchah-sk6o-no), every body ; ciancia (tchahn-tchah),
foolery ; eio (tchfi), that, what ; dot (tchoe), that is to say ;
braedo (braht-tcho), arm ; dufi (tchoof-fo), I catch, I snap ;

durma ftchoorr-mah), a mob, a crew of galley slaves ; ^_
(jahl-lo), yellow ; giorno (j6rr-no), day ; giudice 06o-dee-tchai),
judge ; giustizia (joo-stee-tzeeah), justice ; giubilo (joo-bee-k),
joy, jubilee.

When e follows the letter *, thus forming the combination se,
and when at the same time it precedes the vowel a, a, and u, or
I thft consonants / and r, it will be clearly apparent that the e m this
case will follow the general rule, and be sounded like h ; as, tea,
eco, ecu, eela, &c, eeri, &c, pronounced skah, sko, skoo, sklah, Jke^
skree, &c. When, however, the combination ee immediately
precedes the vowels e and t, the sound of the e is leas com-
pressed than without the * before it ; and ee in such cases is
sounded like ah in English words. The combinations ace and
ad will be, therefore, pronounced shai, or she" and shee. But
when c with an s before it, and with e or » to follow, is to retain
the sound of k just as before a, o, and «, recourse is had to the
same auxiliary letter h to indicate the preservation of the sound
of e like k ; and the combinations ache and echi are pronounced
skai, or ske" and skee. When on the other hand e with an a
before it, and with the vowels a, o, and u to follow, is to be
pronounced not like skah, sko, skoo, but like ah, recourse
must be had to the letter t", which is interposed between ee and
a, o, and u, just as in those cases where, as we have seen, #
standing by itself, is to have the compressed sound of e in
church before a, 0, and u ; and the combinations thus arising
acia, ado, and aciu, will be pronounced shah, sho, and shoo.
The previous observation holds good in this case likewise, that
in more studied pronunciation the letter t is in these combina-
tions slightly touched, though the voice must rapidly glide to
the enunciation of the vowels a, 0, and u. Examples : — storpa
(skahrr-pah), shoe ; acoppiarc (skop-pdeah-rai), to burst, crack;
ecuffia (sk6of-feeah), a woman's cap; acherno (skerr-no)
mockery ; achifare (skee-fah-rai), to avoid, to have an aversion
for; telamare (sklah-m&h-rai), to exclaim ; ecrwere (skree- vai-
rai), to write; scclto (shdl-to), selected; acevro (shai-vro),
separated ; adame (shah-mai), a swarm of bees ; coedm (ko-
ihah), thigh ; sciolto (shdl-to), ungirded ; tdoceo (shdk-ko),
stupid ; aaciutto (ah-sh6ot-to), dry.

The combinations gl, gn, and some others, I shall explain by
notes, as they occur in the next pronouncing table.

SKETCHES FOR YOUNG THINKERS.

{Continued from page 55.)
CHAPTER II.

MORAL EXCELLENCE.

It is the object of this chapter to show that Goodness is bete
than Greatness, and to define the meaning of true wisdom. w*t
have already seen how men can overcome difficulties in mteOeetud
pursuits, and rise superior to social circumstances ; we now tarn
to inquire, whether moral excellence is dependent or independent
>f the influences by which we are surrounded. In the outset,
one or two explanatory observations may be necessary to shorten
the ground, and show the position which we occupy. Mental
and moral excellence are by no means antagonistic or incompatible.
In thousands of instances they have been found in the n»pf
individual, brightening, strengthening, and regulating each other.
Too frequently have ability and dee been associated, as if they
were almost inseparable. No mistake can be more egregious.
Pacts bear out the statement, that many of the brightest orns-
nents of the race have been among the most virtuous, godly, sad
exemplary characters. Without further introductory remark, we
proceed to substantiate this proposition. The cases referred to will
pe treated with much the same brevity as in the former nhtstsr,
since they are quoted as corroborative and illustrative, rather *****
as biographiea of the persons whose names are recorded.

Of Cyrus, the Lord said : — " He is my shepherd and «h»n per-
form all my pleasure." He is universally regarded as the most
accomplished prince whose name profane history has handed down
to us. His intellect was gigantic, and his skill in controversy only
equalled by his power in execution. The Almighty chose him as
he Instrument of punishing wicked nations, and carrying oat

SKETCHES FOB YOUNG THINKERS.

His own inscrutable designs. We will not follow him through
all the devious way along which he walked, but will come to his
deathbed, and hear his dying words. History tells us that he
convened his children, and the chief officers of state, and gave
expression to many excellent observations. He appointed his son
Oambyses to be his successor, and observed "that the chief
strength and support of the throne were not vast extent of country,
number of forces, nor immense riches, but just veneration towards
God, good understanding between brethren, and the acquisition
of true and faithful friends." These sentiments were highly
, honourable to the mind and heart of this magnanimous Persian
king. It would be unfair to judge him by the standard of the
nineteenth century, but if we carefully collate the history of the
times in which he lived, and minutely watch his extraordinary
career, we must be satisfied that he combined, in no ordinary
degree, a cultivated mind and a heart steadfastly fixed on the
purposes of God.

Confucius, the renowned philosopher of China, is always
pointed to as an example of the union of intellectual and moral
excellence, and, we think, with some fair show of propriety.
Judging him by the light of the New Testament, our estimate of
his character might be comparatively low ; but when we remem-
ber that he was born upwards of 550 years before the incarnation
of Christ, we are amazed at the beauty of many of his maxims,
and applaud much of his wonderful philosophy. In his childhood
he is said to have been grave, affectionate, and obedient, and
always to have offered his food to the " Supreme Lord of heaven,"
before venturing to partake of it himself. To his relations he
ever paid the most patriotic regard ; he commenced at twenty-three
years of age to introduce a general reformation of manners. An
elegant writer has well said of Confucius, that " he was every-
where known ; his integrity and the splendour of his virtues made
him beloved. Songs were governed by his counsels, and the people
reverenced him as a saint/ 1 Be his tenets what they may, his
historians have not failed to chronicle one fact which will ever
redound to his credit. He was no hypocrite ; what he taught to
others he invariably practised himself. His sincerity was trans-
parent ; his countrymen had implicit confidence in his fidelity,
and many of them courageously avowed themselves his disciples,
and walked according to his laws. He expired in the seventy-
third year of his age, greatly lamented by thousands of survivors.
Let this Chinese philosopher be fairly judged in a spirit of candour,
and few will be the men who will deny that he was the wonder
of his age, and worthy of more praise than some are willing to
render.

Turning from China to Greece, we find there Socrates, who has
been justly designated the greatest of the ancient heathen philo-
sophers. Socrates was pre-eminently a practical man. He
possessed wonderful natural talents, and a most extraordinary
amount of knowledge. He was at once a profound philosopher,
an honourable citizen, and a popular instructor. He looked at
philosophy, however, as a means rather than an end ; hence he
lived out his learning in his everyday transactions. He was not
fond of wasting his energies in abstruse speculations and learned
refinements ; ho sought rather to be useful, to elevate his species,
and to dignify philosophy, by showing how applicable it was to all
the affairs of practical life. His benevolence was as remarkable
as his learning was extraordinary. To all who applied, he com-
municated his knowledge freely ; in house, market, or prison, he
was alike ready to instruct, encourage, and bless his fellow-men.
It is even recorded of him, that he •• instructed his pupils without
any gratuity/' The chief men of Athens were his stewards ;
they sent him provisions as they apprehended he wanted them.
He took what his present necessities required, and returned the
rest. Observing at a particular time the numerous articles of
luxury which were exposed to sale at Athens, he exclaimed

'How many things are here which I do not want !' Good man!
he fell a victim to the wounded pride and villany of some of his
countrymen, and was condemned to die ! In these circumstances
we will presently see one of the most overwhelming proofs that
moral excellence is independent of eocial position, and superior to
the fear of death. One of his most violent persecutors privately
informed him, that if he would desist from censuring his conduct,
that steps should be immediately taken to prevent his execution.
How did the philosopher now act ? Did his cowardly heart quail
at the prospect of death? "No!" Socrates replied, with the
dignity of a philosopher and the confidence of injured innocence ;

wise than my duty requires.'' Ha bravely suffered, he drank the
hemlock, and died in the possession of perfect peace.

These instances, quoted from the history of heathen philosophy,
abundantly testify that mental and moral excellence can exist in
the same individual. Others might be quoted in profusion, but
if those already given tend to arouse the inquisitiveness of the
young thinker, and lead him to examine the historical records
himself, the object of the writer will be completely answered.
If these men, living in barbarous ages, were distinguished for
learning and virtue, does it not become a serious question, what
manner of persons ought we to be ? They lived early in the
morning, with no light but the feeble glimmering of the stars,
and that light often obscured by the murky gloom and vapour of
superstition and folly ; and we live at a time when the sun of
intelligence and virtue is bathing the world in a flood of meri-
dian splendour! True, at that period there were many learned
and noble men, there were also numerous resorts of learning ; but
no man of moderate intelligence will contend that the same
facilities existed then as do now. They had the Academy, the
Lyceum, and various schools of learning, but they had no
Mechanics' Institutes, no peoples' reading rooms, they had not
that free and mighty press which causes learning to " flow as a
river," and popular intelligent "as the waves of the sea."
Learning was then the privilege of the few ; Pythagoras was con-
tent to lecture behind a curtain, without condescending to appear
before his disciples. But now we live in a different age ; the
oligarchy of literature is abolished, the curtain is removed, the
press is at full work, and no man need be ignorant who has the
perseverance to acquire knowledge. Men must be tried according
to the advantages which they have possessed. The law is in*
violable, that *' to whom much is given, of him shall much be
required." According to this law, and it is a just one, how (Treat
is the condemnation of those who are content to dwell in the low-
lands of ignorance, narrow-mindedness, and bigotry, instead of
rising to the mountain-top of knowledge, magnanimity, and large-
heartedness. A cheap literature, an instructive lecture-room, and
a liberal education are among the chief glories of the century in
which we live. It is an age of progress, not of power; of learning,
not of fighting ; of schools, art, and union, not of soldiers, arms,
and discord. The young thinker has much to do with this state
of society ; it is from his ranks that all vacancies are to be sup-
plied, that all offices in civil, political, and religious society are to
be discharged, therefore his mind must be filled with information,
and strengthened by severe and searching discipline.

We now come to the Christian era, and briefly refer to a few
more, examples bearing out the subject under discussion. The
first name which meets our eye, as particularly worthy of observa-
tion, is that of Ignatius, who was born in Syria, and afterwards
became Bishop of Antiooh. History represents him as having
been brought up under the supervision of the Apostle John, and
occupying the biahoprie of Antioch for upwards of forty years.
Such a man of eminent piety and learning was not to be tolerated
in that age of ferocity and persecution. The Emperor Trajan
knew him, and had cruelly designed to put him to death. He was
ordered to be thrown among wild beasts, to be devoured by them.
Did his moral excellence desert him in the prospect of this cruel
fate ? Far from it. Instead of cooling his zeal, it only tended to
increase the fervour of his love, and in the fulness of his heart he
blessed his God that he had been found worthy of such a death.
He joyfully undertook his voyage to Rome ; he begged the prayers
of nis fellow-Christians, and before being thrown to the savage
beasts that were to destroy him, he cheeringly said : " Now indeed
I begin to be a disciple ; I weigh neither visible nor invisible
things in comparison of an interest in Jesus Christ." He met
his antagonists, and exchanged mortality for life.

Immediately following Ignatius is the name of the venerable
Polycajip. He succeeded Ignatius in Antiooh, and discharged
every duty with characteristic fidelity and apostolic seal. He
lived in troublous times. In 167, Smyrna was raging with per-
secution, and the bloodthirsty opponents of Christianity cried for
vengeance on Polycarp. He was brought in old age before the
tribunal of the proconsul, and with unfaltering confidence avowed
his attachment to Christian truth. On being requested to deny
the truth and disavow the Lord Jesus, he boldly answered:—
" Eighty and six years have I served Christ, and he has never
deserted me ; how then can I blaspheme my King and Saviour r"
Trembling with age, he was brought to the stake ; he poured out

w whilst X Eye I will never disguise the troth, nor speak other- 1 hie heart in fervent prayer, and hit ransomed soul rode into ,

THE POPULAR EDUCATOft.

UZKWXJ& TO CORRESPONDENTS.

A ur \m Wt ^jf 4Ltf -Aft Tut /arieswoeos m the first Volume of CeaseU's
'-.mbcm .we*'* *i4 m. *»uuiow« tu»c fet*<dard's Latin Grammar, which ii

w.i »W«Mwi mas* «u* frg» the roughly-drawn MB. characters,
L* .vi««*t^r «u Uattf eaaa ie iaoa rt a >- «*, *, av, u«, f § *r, v, B ( C> They arc
i*-# <w* „. j* im«: e*iu u ujC mmu, TLe German letter « may be written

,;»«>■ 1 v 4 ^mimt. lOfO^mtM to overact exercises.

*«• „ » i4m/ 3 u» • ^^tuwlw um4 only be learnt 00c after the other,

* i * )wtfi r^i '. ^1 }w a»jpp*#*.tlon.

r /. . *j*.:tM 1 ut »w< 4 ^cufc4*4 f'/f «#ti. You mlstranslsto the other
•1.J4M.. «*iusi cuvim m /tucr#«4 ifcus : M J jii)»/,oour/e^ot»e wickedness."
- ■* +*•.&* \f u* u>k>k -v xi* f«f*it4»« rii «/ ■ofnettuies be omitted, bat

*.*J* ty..t*>Mf wt w*A »UAU Urfr fctltfjl.ll definite article OCCUrS. The
«4»^ • (*:•»* ^vuV^^^C t*ft, LeSSOftS 111 •locution WlU 11101117

, j «- ,<«•• !.'■• ;>!**■■■ :•. '/btuiiiiry !■ couieiued In Put XVI., No-
o , A* -vi »*. ;# rf** '^« t WkUr r»n never rUe higher than ite

.-4 •. M y '•,**>" V* />*•, MMN Hi* f'/f'lllg-pUUJp l>U employed.— ElN

p - «.»"* '%.»**$* /-. .« ,M»f^««ii»i« t« ull wltUh country dm produced

I* «..»* I.*'**** «M4. *• KtotitytmA Willi III* JHI {filiation, unlets you tit

<"**-<<-/ «•>»* t** »*a •<.« «.*ii»ii« «f a el»*n period In tlm one hand, and a
t^ y .... «*t.*4*« m^4. -•.<,!.».« fli^jrui««<l within that period in the other,
< ( ...^i -«« m<*mmi v* »*#* v*9M**$ with iii« ihiiiiImm iif tlio latter, for Eng-
•,./ >,<.«4 M 4l«.«Mii Is^nu* h1 Ilia •m«lltt«Mor Ilia iiopuUtion, end
k« /,#«... u<wmvw v* «•*. ».*#*• M.«N "»!**« Iiav« aitMli tit IfcMptieiid, w« fUeil,
m »» >*-/ v -u*, w^. u« ««ooii «*r U*a M#Mi|<eji»iiii would be In favour of

« ,m9.»^^**d *0ifg* k) *il Mi»*n« iiu'ly 'Hir l,««KiUi In (Jeomatry
« v+ f >- *i-» ; » u* m,«** « m»im« «#l/i«ii. U«un«iT»a Amii in ( J>rst>) :
> .^* tjjuis imi #.^i#« a<#«#ot *4mi «.«|n.u*a oMi^iHiiliiir a olrll eiifUiear.
J /..#• /V» *4 uwL»i4 vf *U* #»<|MUtla ■India* Mrt«ul4 Ull « VulUlllf. The

l^V u«.d^.% «tA.*irt ^ai« u ci/buuiffcil In Ilia i»r(*eraMin«t uf the '* Keule
'.'j4j^ 0-« /.ju «,i jfaWAti'iiaa/' att . al r , arla t I*. I'Mgreinme dea
^..i.. ^ m* 4 t«.-*-«\- ^<i* *4mU9ii*n k l't.K*Am i;aiilrala ; »". I'lOflremmo iUa
Crfj t.i.i..«i(/iwk; J^y*>Aw« at 'iiulalCiua Aiilrfr, fen.— AMATBUa :
ii.mtJht l* *•*« iaa^u, wl a |M«Ubla lAliuiali/iy ; Iba flrat ebamUU have
]l«<! vui^ «) lt» iX..i^« i^:iuu4 ihi a4t old tae*lray.-(iaiiMiiH 11. (Old
Jruu-ftlrt.t.i, feul/i. Jj».aj«i'» lAaawiia hi Ki«ajlUh In lha I*. K.

r * . Uk»bhki <lfo«d)jj(fUld|(Kj . W« altall ba limit haji|»y to ba favoured
waL « /u/tb«f «<ul«oait^u of bu Idaei on the inoUoiis of tna earth aud the
auoou, viUirr b> dlagreui t,i luMblnary j ■•» euoual rotatory of the earth on en
axis yer\».udic\iUi in lint plane of l (a urtill, ami e new eiplanetien of the
uiuwii'a monthly rotaiiou, aia coxUiuly uovaiUae worth* of our attention.

fuu.u (NoUin«beui); Ilia •.ornaUoiia on the hey bi OaaaeH'e Arlth*
luallcarv ull liylit; aKwuf iba eiiawira in llie Kay were taken from the
auawera publlabvd U> Ilia oileiual eulbork nf lha work, t nil tlnf that they
were con «ct i but wlnlliur ibu criura hv baa diaruveied aro«e from mla*
briuU, or ceideMiicail in the ralcululnia, It la dllttcuU now to eay.—
\V'. Wai.kaa (buuilip.iiij : 1 •• the laei itilitlnu o( " Keith on the Clloba*,** in
185 1, >wu will find the uuinliei uf ib« cuuatalUtuma atated at W. ee taken
from the U.iyul Aatroiinniioal Huoiet)'* catalogue ; and V more are added M
given b> foreign matin uitlicUna.

W. JoNKa(8tttrk|Miri) : The l^«»oni in Arlthmetio are not completed;
your writing li rather i>tirT. and your • filing U very b^d.— R. Blomilit :
Hit auggeMtioii at 10 training-achoi^i will be borne in mind.— J. Mabjhau.
f Hurneld) *. llymer'a ** Thyaieal Astronomy ;*• but the grand book U Laplaeet
'* Meeanique Celeste ; " there it a oollection of table* ealled the ** BequUtU
Tablra" to be ueed with the " Nautical Almanac."— Am old SrascaiBim

itfhrew*bury) : We should be flad to pleate him by ineerting hie letter : but
t U contrary to our rule to lend our page* to puff or pralae any worka of
which we do not know the value.

W. W. W. : To the exprci«e appended to Prop. II., Book IV. of Caa-
eell'e Euclid, add the wordt "only in the caie of the equilateral triawrle."—
John Davibs fPontypaol) ahould get a copy of CaaeeU'B "Emignnra
Almanac," price od.

S.OBKT(Sutton-in-Aahfleld): Hie method of calculating diaeount ia do
doubt the true one; but if if netvr eiaei in praehet; we must therefore
follow the cuetomarr method, which we have done.— A. P. B. (Hoxtoo):
The beet proof of elasticity is the rebound of the elastic substance ; but
according to his theory Way would be elastic.— S. G. J. (Drogheda} : The
study of two language* together it very likely to lead to confnrion ; we would
therefore recommend that of a language and a science together.— W. P. P.
(lAmdon) : •• A former had £100 to buy oxen, tbeep, and geese, so that he
should have 100 ammala In all, the oxen being £5 a-plece, the sheep £1
a-piece. and the goes* It. a-piece. How many of each did he buy ? Here,
let x, y. and s denote the numbert of each sort of animal ; then by the
qurtium we have thetr two equations >-(!.) Jr+g+srsl00, and (9.)
IO0x+^0y+s^M00; lubtractiug (1.) from (1) we have Wjr+l^T^lWO,

and therefore * - : — ^ » 100— &r + — - ; now, as theie can be no

•I*
fraction*, y— must be a whole number; In order that this may be the case,

4* must be divisible by 19 ; and therefore « «19; whence jr=l, and r^W
Tne anewer is. therefore, 19 oxen, 1 •hvep, and 80 geete. The other
quettion it usele**. and so plain that it nceda no eaplanation.

J. li. iKiddermintter): Thank* for hit cor re* t lorn; if any teetioni seem
to be omitted, it ran only be by mi»ukea In the numlH>ring.— (.Uvtikb
(Hn»t.il> : •• I'ncle Torn'* Cabin " in French, »n I the M Kr> " in thf aanie, ma>
be obtained at our office.— P. II. : We would revommrnd theatudy of Kroneb
and I aim together to tluxe mho hat* lime at thru- diatioaal. - A Hbaiibb
In Uleertone, whote tl^uature *»o rauuot read, 1m retvrred to Metar*.
Berne, Thornthwalte and Co., 1M, Newiiaie-etrett, for the price of dsguer-

apfjaratus. Ws would scarcely advisa any one to

B, Biiaoir * Sis plan ia excellent— Wm. Jonbb ahould study the Lsesoas
from the W. M. F. first— B. W. (Greenwich): Bight— J. Batbs (Halifax)
Is wrong about the formula to which he refers at p. 10a", vol. li.. and eta ere

right- —....« -. .. r: .„.—...

was alj^

BOLTOMIAM I

brother; we < „ „

readers as require It a Hat of the wJtolss. and we think that thoytnrhsss
the AaUecf j this list is taken eertofim from an edition of the Bible, printed
and published by royal authority at Edinburgh, in the year that Qaeea
Victoria was crowned (1838) :—

" A Tablb op Kiwdebd and Apfikitt, wherein w h osoever arerelaisd
are forbidden hi Scripture, and by our Laws, to marry together.

A mam way not starry his

1. Grandmother
1 S. Grandfather's wife

3. Win's grandmother
! 4. Father's sister

6. If other's sister

6. Father's brothtrt wife

7. Mother's brother's win
B. Win's father's sister

9. Wife's mother's sister

10. Mother

11. Step-mother
19. Wife's mother

13. Daughter

14. Wlfe'e daughter

15. Son'* wife

16. Sitter

17. Wife's amUr

18. Brother's wife
IV. Bon** daughter

•JO. Daughter's daughter

31. Hon't son's wife

34. Daughter'* eon's wife

9.1. Wife's son's daughter

94. Wife'* daughter*! daughter

3ft. Brother's daughter

98. Meter's daughter
97. Brother's son'* wife
3M. Hlstcr*s son** wife

99. Wife's brother's daughter
30. Wife's sitter's daughter

1. Grandfather

3. Husband's grandfather

4. Father** brother

5. Mother's brother

6. Father's titter's husband

7. Mother's sister's husband

8. Husband's father** toother

9. Husband's mother's brotber

10. Father

11. Stop-father'

19. Husband's father

u! Husband's son

15. Daughter's husband

16. Brother

17. Husband's brother

18. Sister's husband

19. Son's son

90. Daughter's son

91. 8on's daughter's hu+ fr a M

99. Daughter's daughter** husband

93. Husband'* son's son

94. Husband's daughter's son

95. Brother's son

96. Sister'* son

97. Brother's daughter's inwbsnd

98. BitteT's daughter's husband

99. Husband's brother'! son
30. Husband's sister's son

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rirst six, and the Ele\ enth and Twelfth Books of Euclid. Edited by PiofSfor
Wallace, A.M., price Is. in stiff covers, or It. fid. neat cloth.— KEY. 3d*

i , as»Ki.L t s Kikments op ALOBBEA (onifbrui with CajJtll's XVOUB%
price Is. in sUff covers, or Is. fid. neat deth.

LESSONS IN INSTRUMENTAL ARITHMETIC.

INSTRUMENTAL ARITHMETIC— No. III.

THE PLANE SCALE AND PROTRACTOR.

{Continued from page 13.)

Ik order to giro our students some idea of the other lines
flrawn on the Plane Scale, we must explain some of the terms
employed in Trigonometry. The definition of an angle has
been given in the Lessons on Geometry ; but in Trigonometry
this definition is greatly altered and extended. Angular mag-
nitude in general is the space generated by the revolution of
a straight line about one of its extremities which remains
fixed; and an angle is the space between the initial and
terminal positions of the straight line, whatever be the quan-
tity of revolution. Thus, in fig. 1, let ox be a straight line
Which revolves about the fixed extremity o, and let o ▲ be its
Initial position in general ; then, if o m be its first terminal
position, a o M is an angle in what is called the first quadrant,
and is less than a right angle.
In order to explain the different quadrants, it will be suffi-

quadrant, the angle boa' the second quadrant, the angle a' o B
the third quadrant, and the angle b' o a the fourth quadrant'*
the initial position of the revolving line being always o a.

Fig. 1.

s. ~7*

»' \.

«• \

Now, if the terminal position of o A be in the first quadrant,
as o m, the angle a o m is said to be less than a right angle ; if
the terminal position of o a lie in the second quadrant, as o m',
the angle a o m' is said to be less than two right angles, and

Fig. 2.

wtt*ir?7ftrs

dent to remark, that by the 2nd corollary to Prop. XIII., I greater than one right angle; if the terminal position of oa
CaaselTs Euclid, all the angles about a point are equal to four lie in the third quadrant, as o n', the angle is said to be
light angles ; and if a a' and b b' be two straight lines drawn | greater than two right angles, and less than three right

Fig. 3.

at right angles to each other, they form four right angles, viz.,
A ob, bo a, a ob', and b'o a. Here, each of these angles is
^.fourth, or a quadrant, of the entire angular space about the

angles ; and if the termina position of o a lie in the fourth
quadrant, as o n, the angle is said to be greater than three
right angles, and less than four right angles. Moreover, it

point o ; and by convention, the angle a o b is called the first the terminal position of o a be such that it has passed or.ee
VOL. IV. 85

THE P0FTLA2* El>UCATO£.

liit lan-rent* '.*:' mari e * beyond "i* : and the tangent of M** it
inxxnii* -.<.. wiin ou: enc.

- tnuf : ^y an
. trie trectrt tt- ■

tn« *-:■!: ".n* u: :u*r sircicri:: imet eaten rtmr iron. trie trectrt tt- tin
xaufr*r::> o: tracr. Deere*: a tu'.*v«*-i ■«.. or. txit fr-.'hie xl b Btraicti:

11%'. 2'... %:-■» Wi.. iaav- tZi« Liu- 0' >-7f//"-. WlllCI. b^glXlfr

wu-.tl lue Li*. & St»*t ieriuiiiaie-

Tut i:u' ix;arkec i:: i-jz liBTKB^ i* the ixm of the t'nnrd?-
of tht r J'3'fT-fJi' iM:::'f L-f :u*. cuiu-jii*--. ai.u it , ..iJiiutru»..-;ed thu* :
d'.Titi* •:,. xjr*: ijujiuraii:^. an iilv. 3l e-:;u;&. par ». , taei. craw
c:iuru<» inm. vu* u: :i.t es:ireu::tiv; of ii»» ijiiuaruuta. utl n
w.-i. tr-'siu: . n«.*r:: m* djwi. their i-np-n* ox. tin sea it xi. b
fttraiCir i:ii» iinxi. i:t v.-fe and y»L will i-.a'V: lh». 2- mi *}* llhum**.
a* iuu-Ked :n *.ne vjoj*. . ;ii«_ huxuik! o: pon::» :l l quaurux:'
■xi on:y t. wim-r. art xuu:ket, :rou. 1 u fc »i. tht inuf. bu:
every quart*;: ji iiir u hm m univi. uiliiousL no: nuniueret. ;
ant. r pmiir iiiij;- v- uu^rier poiint*.

Tut ^w n/ Zrayurz. market ix. if only t tea-it of equal
yrsn- : u:.l *. n- in*. ii««* m.irKe'- £. >'. : ;m hr*-: rimaiui. uf
wjl ue:ii«: uxviued nu*.. :«;.:/w. Tin hut u 4 Sn»:izahun:u
xuarket E T. t u uit-rejy a in** {/ Tannmu l/ Ba:/ :/« _d~-e*.axa;.
it t-uustruvteu iiiuis : ciivmt iht fir-h*. uuacirai.iu. art a> i*f:»rt.
and irjXL :ht remote ez,ireni::y oi -.-ft bet-one ouadruxital axi
that u. Hit p'Mn: ui :in b"niickr>jii xiiari.eL* IH 4L . ora*
vtraigh: lxii«f i :'ru ■UE.".-^nh. > t uecr*?efr u: *.Lt Mjn.iciri:i(..
bfcfuiTiuij: a*. I 1 - \u>ji. *c? l-»x :nt" d^ta- »_■» tirmeei. mt
ceixirt uf t'l.. •:a'_i* i;!*^ *.:.i jn.:x.:s- uf *.Lt- n.:er>ecti-jr. uf liiefct
BtraifEix: iiu*t t;;i ;iit perptiitii?ular i: Hit rucLuf of tii»
quaorauta. art vni'.i. jjn*hf f tiirjupi. (*. ol tin urai*-. ix. a
airaigh: iixit. auc ti»u wL. iiort tut i»m nf Semaanp+t,:* at
marked ol Hit f»caA . LafJr,

Tiit LtM ui LoM.i'uo: .« , marked ll. if canFtrurtei tLui d-i^iit
out of tut radi: o: iin- quaurauiu. art niit 01 etuul j.trit ; t»iet.
tiirougL eaci- uf iiit>t diviKrjM cruw |»erpexiCiri:.ur!' *: u u:
rudiuK interfct'jLiijj: Uit uuauru«ial art il at ihui.t ji:i;x.ia. ui.t
XiUXXib^T '.iieix. iiyix. 1 il (if i>»'£;ixiT.ixic xtjxl u-a: i.irxne- :-t
the perjniiUii'u'.ax ueures: :iit t ex.trt ." xxtzt. drtw t:.:»raf t":
these puiiitb Ituxx. :hut estr«ii::r of tut quaLran'.a. arc xaarLei
CO ; lasiJT. iur down ii. a mrnr!.: liiit. ox, ihi hviu*. *iit
le&gthc of thet»t chorda, axid vou wil. hert the i.."*- c#/ x ■!./■! -«fl» ■
ah x&aikt'» ox. Hit sL-iiit.

ITit ui»t of these vuriout i:iie* or. ili J' ' p»t yisn. aiii iht
appIicatioL of the 1'rv+w.x.n il t^t b.iluiioL ..f Pru:>iexxi£. xcuf:
be deferred till wt pivt uxuiher Lefct-jXi it. lx.Kruiiifs.ial
Axithmeuc .

LESSONS IN CHEMlSTIiy.— No. VI.

!>■ ixjr preoecixip k>6bciL I i-ji: uff wiui a g*Tiertl deacriptiot of
the xiatiut auc uma tif tht jjueumaiiL Tmu^'r ; tjit Htiidtuai wil.
now proceed to uet thit truu^L abtjrdixif it iiiBa-uiiUJiit. Th*
object to be aimed a: it tht cullbdioii of hTorupeL cae : wLiui
ol tourst vi iiur. xnakt htdurt we ccl collect, and tht pro»je» uf
inakiii£ it LtAlpj bita. gout iLrjngL airaacj. recuna n4-/-i*#
deacriplijiL Ail tht variolic pieow of apparatus neueesLrr ii ^Lu
oolietti'jxL, aav t out, h^Tt i^^^ Hieniioued. Tii* taanertianet
oiit it a bexxt tubt t-f soiut- t*jrt ijr tranan-iitiDp the car /•■:»» tht-
generator r^ tht Koring botut or jar • act ft P:

Fif. M'.

I can: ▼err iittie of wbmi Ibe i

metal paa pnit. x&dia-rubber.

BBtflha. wxuti net — iij or rafautxrr xan

aXKitc ia. the tut tube ■nail x* wr-tight :"

point Sxior: lencniif of metal f ■ jiijm me i

ttit laborstorr for efiedmir coxtimiiiiixxUm»22&lxn« :

xx. fomiexiin. witi. bucl tube* the ataneni will i

d< no: eaaijr admit of ii c riuMi CgxtrT tieiri

xx. corka. NerertiMrieai tnii mar be i

retaxxi-c rnr cart. Ai>rrr t eL thxnpi the

pnnc tht portidL of tube exrvelopad by "the bbb; a i

at lr produce a diaturuob. of wimi fie. ~"

Tit

\ V

1: if ea*y u TmnawtTid tha: nob a tvml xtomf gxra, tbi
oricmal air-tx|rxitirir. However parfiocL ■ HgnmtfiwA deatrojed. Wt
na^t now pn«ridt*c tl the naoemary apjiaialiB Sat ftiflwITng tbt
caa. but the atorxxif of i: require* a trifiinf mWrrini m tbe mat
of diaa or piata .if piaaa. ' Ftaif prl— if mvrnr dmm eommm
xjapwz. clam, a* bexnr mare ■ccuntteJy plain ; bet tke ktser, mv
dervc iimi 17 prmdzne an a atant or miather piece of f^ma akaf
witi. emery* anc water, ■newea perfBOtxr w«2L Ikt tnaft a
these dxaut x&cy xk- either square or abrniar. Tncy my be at
either by mean* of a ciamor'f diamnnd, or born mmttf m well,
tiit rounc onei nidged bene?, by a common pair of tmmoa mei
nor**. A juiit af cima ibaf u — le d doea xwtadait of
xitmr nr. like a tiit of aiik or ronar 1 admit, n*Tertheleaa, tmt
a rarefiu peranx. may. afier aomt pr e! irn'maM Hum, trim phmi «f
culm by tLif meant u- aimoat any ahmpe be den. Well, went
?t:>w reacy t: c:ixxjnenat opecstiana.

. Apply the clam Last an:-?eaaivehr to tlhe montb of e*A
t.DtLu uxider wnte: . rcmort tht bode ani dme xnmi tkewsfar, tai
t>ee. ai y:»t eaaliy can. whether caxaacs belveeatJwflmatmimDaoi
'.>f the b.itut takflf piaat- all round : if not, grind tbe moata ortkt
:ih.tt at nefseaairy may inquire with emery or aiHar maa aai
wa:*.:r, ttntll i-.Ttic* u perfect.

I*ry tbt fane of the brcuea' mosxna, altotbe awoi; aatv
eaii wr^i. a IrJe p .n^aruxc.

I . r^l a Km*, at witl. water ; invert it ovm tiae
trou^i : tranax-uit hydrogen caixniczi: sot mvjxaaraaf; to <
gat m-mt dix.it :y 1: if oeveioped, but waiting a abort '
you are oertaix. thr,* all the a^moepbtsnt air origimUiT
-x trie generL*.^.g h:ituc- has been expelled. As soon at tbe Mdi
hai :»ec:ixxit f-l_ .if gaa. i.e M n^.> r.r" tro^r, slide aaasr ioiJaoaa
vine of the :>Sed and accxa^^^-szang glam pesma (fig. 33).

rjf. as.

. Next pluie the bottle to stand oa a taass «bb1 wM
; taking the pre.au tins to lay some sort of weight apoa oe) ajpami
| plate to prt^e^t iu being raised up by tae probable exnesaeaa

Tbiatabe is indicated in the preceding diagram by the letter t.

— ga«. R&vi^g thuf c Ejected a lew boCUes of ajdroeaa, J*

• ct-c prx>rt-l t: make yonratlf aoquainted vita its xanana**
i qualitief.

I (5. Jktta^abitofwaxtJ|iertoaitjB«ei > arin

LESSONS IN CHEMISTRY.

the wire into the wax, light the taper and plunge it
an inverted bottle of hydrogen gas, as represented in fig. 34.
Particularly observe two phenomena: — (a)
Pig. 83. The gas itself burns where it comes into contact
with the atmosphere. (6) The taper when
ft plunged up into the gas is extinguished.

S] Deductions, Therefore hydrogen gas is lighter

than air, otherwise it would come out of the
inverted pottle. It is a combustible but not a
supporter of combustion.

(6.) Repeat the experiment, having reversed
the conditions of the bottle, i.e. place it to stand
mouth upward; remove the glass plate, and
plunge into the bottle the ignited taper. The
latter now continues to burn as it did in the
naked atmosphere, proving again the extreme
lightness of hydrogen, by showing that it has
escaped. !

(7.) Pour some lime water very rapidly into

a bottle containing hydrogen; replace the glass

» before all the' hydrogen has escaped, agitate the bottle, and

irk that no change is perceptible.

Fig. 34.

,B. Lime water is prepared by soaking a piece of quicklime
iatilled water ; atmospheric contact not being permitted, i.e.,
arm the operation in a bottle filled to the stopper with water.

transparent portion of the resulting liquid is called lime
it, the turbid sediment cream of lime,

l.) Moisten a piece of blue litmus paper with distilled water,
hold it in an inverted bottle-full of hydrogen gas. Remark

no change takes place. N. B. Litmus paper and tincture of
Hi are general tests of acidity. Acids turn these materials

Deduction. Hydrogen gas is not acid.
I.) Tinge a moistened slip of litmus paper red, by holding it
a few instants over the mouth of a bottle containing any
tile acid, such as spirit of salt (hydrochloric or muriatic
). Immerse this moistened slip in a bottle containing h j drogen
as before. Remark that no change ensues, the redness of the
or remaining unimpaired. N.B. Litmus paper thus reddened
test for alkalies generally, which class of bodies cause the
j n»1 blue colour to return. Deduction. Hydrogen gas is not
line. Instead of litmus paper reddened, yellow turmeric paper
it have been used; alkalies change the colour of this to
rn.

0.) Partly fill a bottle with hydrogen gas ; apply the glass
i ; agitate ; reimmerse in water ; remove the glass plate, and
irklhat no fresh portion of water rushes into the bottle ; thus
ing that hydrogen gas is not perceptibly absorbable by

IT.

1.) Finally, remember the following recapitulation of pro-

les as characteristic of hydrogen gas. It is —

avoid of smell (when pure).

ghter than air.

ivisible ; therefore colourless.

tmbustible.

ja supporter of combustion.

at absorbed by water.

ot affecting lime water,

>6S not redden litmus ; therefore is not acid.

Does not restore reddened litmus to its original blue ; therefore
is not alkaline.

General Remarks concerning the Nature of Flame. — Perhaps you
observed, when the jet of hydrogen was ignited, that it burned
with a pale and scarcely perceptible name. From that circum-
stance you might have inferred that very little heat is developed
by such flame. This idea is incorrect ; the flame produced by the
burning of hydrogen gas is really very powerful as to heat, and
generally, let it be remembered, that the heating power of a flame is
in an inverse ratio to its illuminating power. The most violent
flame, as to heating and firing effects, results from the combustion
of two measures of hydrogen gas and one measure of oxygen gas ;
but the light of this flame is scarcely perceptible.

The reader will here do well to again develope some hydrogen
gas in the tobacco-pipe bottle apparatus, and set the gas on fire
as it escapes. Whilst burning, if some powdered charcoal, or
magnesia, or lime, or indeed almost any powder, be sifted into the
flame, its illuminative property will greatly increase. The sifting
can be best effected by attaching a screw to the end of a stick ;
placing the powder to be sifted in the sieve, and striking the end
of the stick with a mallet, fig. 35. *

rig. 35.

From the result of this experiment it may be deduced, firstly,
that red-hot hydrogen is not very luminous ; secondly, that red-
hot solid particles are more luminous ; and it may be suspected
that red-hot solid particles exist in the flame of candle-lamps, coal
gas, and other similar illuminative sources. The suspicion is
just : every person is aware that an object immersed in a flame
of this kind becomes sooty or black. On what then does this
sootiness depend? On charcoal, this being the solid matter
which nature designs to become red-hot in an illuminative flame.
The student will not forget, then, the fact that coal-gas, oil, tal-
low, &c, contain, as one of these elements, charcoal, or, in
chemical language, carbon ; indeed, generally any substance that
during combustion covers an object immersed in it with a sooty
coat contains charcoal or carbon. The student will not fail to
see, moreover, that charcoal, when burned, becomes invisible ;
which invisible product must be a gas. It is called carbonic acid
gas.

It shall be the object of a future lesson to teach something
more about this gas; meantime it is proper that the learner
should be made acquainted with the theory of the changes which
ensue when sulphuric acid and water are added to zinc. He will
say, perhaps. I already know what these changes are ; the liquid
result is a solution of sulphate of zinc, and the gaseous result is
hydrogen gas ; what more can I want to know ? Yes, you
require to know a little more than this, and the best way of
imparting this further knowledge will be by means of a diagram
as follows : —

fl Hydrogen escapes

|8 Oxygen

9 water

32 Zinc-

40 Oxide of Zino

40 Sulphuric Acid ■ ' 80 Sulphate of

Oxide of Zinc.

It will appear, then, from an examination of the preceding
diagram, that the hydrogen comes* from the water used, and its
evolution is proximately determined by the formation of oxide of

THE POPULAR EDUCATOR.

sino, to oombine in its turn with sulphuric acid. The reader
-will moreover observe that what we call, for shortness, sulphate
of sine is really sulphate of the oxide of sine. Acids never oom-
bine with metals, but with acids.

"With respect to the diagram just given, I advise the student,
whenever he is in doubt as to the changes which ensue during
ohemieal composition or decomposition, to have recourse to a dia-
gram. First put down all the substances employed, then divide
them into three components, then join the elements together by
lines or brackets in a manner that shall be accordant with actual
results.

One point connected with the preceding diagram requires fur-
ther explanation ; I mean the numbers there given* . My first
intention was to have omitted them, because the general explana-
tion of what took place would have been equally comprehensible
without them. Further reflection caused me to alter this deter-
mination ) let the reader, then, consider them as the shadow of a
coming doctrine— the atomio theory and doctrine of definite pro-
portions.

I shall not say more about it at present, but shall simply
tent myself by remarking, that chemical combination* do net
take place in proportions a little more or a little leas, but they
are fixed, unvarying, definite, and therefore capable of i

tion by numbers, which latter are called the atomio equivalents
or proportional numbers of the bodies concerned. Thus 8 .is
the atomic number for oxygen, and 1 for hydrogen, con-
sequently the atomic number of water must be 9. .Ton
must learn the atomio numbers of simple bodies, but do not
attempt too much at a time. Remeniber on this occasion the
atomic numbers of hydrogen, oxygen, and sine— 1, 8, and SI;
this is surely no difficult matter. If you choose to remember
the atomio weight of sulphurio aoid to be 40, well and good; here-
after you will get at this information through another channel—
you will be told that sulphurio acid is a oompound of three equi-
valents of oxygen and one of sulphur ; now the equivalent number
of sulphur being 16 and of oxygen 8, it follows that 164-(3x8)=
40; or, in the symbols of chemical algebra, 8O 3 =S+30, S
standing for sulphur and for oxygen*

LESSONS IN GERM A N.-No. LXXII.

Irregular Verbs, continued from p. 87.
(4) SMoijcn, to be allowed, to have liberty. (Sec Remark 11.)

INDICATIVE.

SUBJUNCTIVE.

CONDITIONAL.

1MPKRAT1VB. I INFINITIVE.

PARTICIPLE.

Present Tense.

Wanting.

Present Tense.

Present.

O i 1

i$ mag, I am allowed

id) mcge, I may "|

megen, to be

mogent, being

8 2

tu magfl. thou art allowed.

tu ntogcfl, thou mayst ! *|

allowed.

2 (3

er mag, he is allowed.

er moge, he may ! 1
t»ir mijgen, we may j ^

• I 1

wir megen, wc arc allowed.

5 2

u)r meget, you are allowed.

ifjr midget, you may *
Tie mogen, they may J

£ (3

fie megen, they are allowed.

Imperfect Tense. 1 Imperfect Tense.

icfc incite, I was allowed. ' ity mc$te, I might "1
tu moo)teft, thou wast allowed, tu modjtefi, thou mightst "8
« ntod)te, he was allowed. 1 er m«$te, he might ! §

SJ2

5 (3

i\\

u»ir molten, we were allowed. tcir moa)ten, we might [ =3

U)r mo$tet, you were allowed.) i$r meo)tet, you might g
fie mod)ten, they were allowed, fie mdo)ten, they might J

2 (3

Perfect Tense. Perfect Tense.

Perfect Tense.

Perfect.

ri /l

io) f»aU gemcctyt, t have been io) fabc ] I may have

grmoe>t ffaltn,

genMK

1 »

2 {2

tu $ajt gemed)t, allowed, &c

tu ^abefl ] ^ been allowed,

to have been

allowed.

• (3

er $at gemod)t.

cr ffabc \% &c.

allowed.

* 1

2 <2

trie tyaben gemeo)t,

roir babeu | |

u)r tyabet gnnoctyt,

i&rbabet °»
fie babeit J

M 1 "
* (3

fie $aben gemw$t,

Pluperfect Tense.

^ f J

s 2

* (3

fi (3

ic$ $atte gemwbt, I had been

to) fyatte "

I might have

tu batteft gemwbt, allowed, &c.

tu r)attefl

^ been allowed

er batte gemod)t,

er bdtte

l! &c.

tvir batten gem«$t,

ivir batten

ibr ^attct gemoa)t,

ibr $attet

«n

fie fatten gemoo)t,

fie fatten ^

First Future Tense.

First FtttureTense.

First Future.

6 P

i$ luerte migen, I shall be

id) toette

(i0 1 shall be

to) twurte "

M 2

tu tuiril megen, allowed, &c.

tu iverteft

allowed, &c.

tu lourtefl

■°*&

5 1 3

er nrirt mpgen,

er toerte

er nmrte

.11'

5i 2

roir mertcn mogen,
ibr toertet mogen,

ivir iverten
ibr ivertet

toirmurten
ibr n>urtet

■.egg

S 1.3

fie iverten mogen,

fte iverten

fte luurten ^

•^ Ti

Second Future Tense.

Second Future Tense,

Second Future.

idb tuerte "^ B - 1 shall havel i$ toerte ^

tf (if) I shall

id) toiirte "1 ^

21 2

tu n?irft

.» been allowed,

tu toertefi

£ have been al-

tu teurtefl

or ■ jc

7: — fc

s [3

er toirb

**• &c.

er lverte

*- lowed, &c.

er njflrte

S I 1

loir toerteu

ivir iverten

ivirteurten

'f'l^

§ 2

u)r ivertet

i$r ivertet

ibr toutbet

l p i b

* 3

fie iverten -)

fie iverten w

fte luurten

S3 <u

LESSONS IN GEOLOGY.

(11) Remark* on mug en.

9tytn marks pottibility under allowance or concession from
another : as, fft mag latyn, he may laugh ; that is, he has per-
mission to laugh, no one hinders him. <5r mag tin Braver SDtann
fruLhemay (I grant) be a brave man ; where the possibility of his
being a brave man is a thing conceded. Kindred to this are the
other significations (eAanee, inclination, with, &c.) usually attri-
buted to this verb: thus, rt mo$te rcgnen, it might rain ; that is,
the causes that seem to forbid, are likely not to operate ; i$
mjtytc ti kjttcifeltt, I am ditpottd or inclined to doubt it, that is,
I might doubt it altogether, but for certain circumstances
seeming to forbid : mdge tf fcer $immel geben, may heaven grant it;
ty mag ti ni$t tyun, I do not like to do it, that is, I am not per-
mitted by my feelings to do it cheerfully, &c.

LESSONS IN GEOLOGY.— No. XLV.
By Thos. W. Jbnxyn, D.D., F.R.G.S., F.G.S., &c.

CHAPTER IV.

ON THE EFFECTS OF ORGANIC AGENTS UPON THE

EARTH'S CRUST.

SECTION III.

ON THrf AGBNOY OF CORAL INSECTS IN TUB PRODUCTION OF
R0CX8.

In almost every district on the surface of the globe, and at
almost every depth in the earth's crust, calcareous strata ire
found, which have all the appearance of being the work and
product of living agents — agents that knew how to secrete
atoms of carbonate of lime out of sea water, and had skill to
unite those particles into beautiful structures, which were to
form stony habitations for their own safety and comfort.

This class of animals is constantly called coral. This is not
their appropriate name, for coral is the name of the rock that
is built, and not of the animal that constructs it. They are
sometimes called Zoophytes, a Greek term which means
animal plants, on account of their resemblance in form to
growing plants. At other times they are called Polyparia,
and Polypifera. These and others are only names for the
coral insect, or the animal that constructs the coral rock. The
coral insect consists of a little oblong bag of jelly, which is
closed at one end but open at the other. The mouth of the
bag is surrounded by the insect's tentacles or feelers, which
are generally about six or eight in number, and dart in all
directions like the rays of a star.

Myriads of these minute animals live close together, and
unite to form a common stony skeleton called coral, in the
minute openings of which they live. When they are under
water, they protrude their mouths and tentacles to seize and
receive their calcareous food ; but the moment they are appre-
hensive of danger, they withdraw into their holes. These cal-
careous abodes form, over the bottom of the sea, stony cases,
called coral banks or coral reefs, which they build up from a
moderate depth, not much exceeding a hundred feet. It is
found that at different depths, and in different areas, corals of
different species develope themselves. Their range extends
on each side the equator between 32° north latitude and 28°
south latitude.

The amount of coral rocks in different oceans is enormous ;
hut not so enormous as was at first apprehended by the earlier
navigators. The scientific men, who accompanied exploring
expeditions, found the Indian and Pacific Oceans studded
everywhere with the products of these polyparia. As the
seas in the immediate neighbourhoods of coral rocks were
always well-nigh unfathomable, it was conjectured that the
coral insects had built up their masonry from a sea bottom at
immense depths. In the coral rocks which appeared above
the surface of the sea, the insects had finished their work and
died ; but it was conjectured that other zoophytes were, in
the meantime, just commencing their architecture at the
bottom of deep seas, were spreading their sheets of coral
rock over a vast area of sea bottom, and that they, in their turn,
would work up their rocky structure* to the surface of the
ocean.

MM. Quoy and Gainard were the first to show that the
coral insects had not built up their masses of rock from great
depths, but had merely produced stony incrustations a few
fathoms deep, and that these incrustations rested upon some
underlying rocks. They also remarked that wherever land
I was cut into have with shallow and quiet water, and exposed
to the intense heat of the sun, there the polyparia abounded
most, and there they in crusted the rock the most extensively.
From circumstances of this character it was conjectured that
the coral reefs and coral islands took their form and shape
from the forms and the inequalities of the rocks on which
they were built, and that circular or oval islands owed their
form to the underlying crusts of the craters of submarine vol-
canoes. All these hypotheses have been long ago exploded,
partly by Sir Charles Lyell, but chiefly by Mr. Charles
Darwin, the most distinguished and the most successful
student of coral formations.

Coral rocks are divided into three great classes, called
respectively Atolls, Barrier Reefs, and Fringing Reefs.

Atolls used to be called Lagoon Islands, and consist of
rings of land in the midst of the ocean. The ring of land,
sometimes oval or egg-shaped, is a few hundred yards in
breadth. These ring islands or atolls are sometimes only a
mile in diameter, but sometimes as much as thirty miles. Land
of this description is generally low, rising but little above the
level of high water, but covered with cocoa-nut trees and
pan dan us of great height (see illustration, fig. 102, at the close
of this lesson). Within these rings of land U a bed of calm,
clear, and shallow water. It is this sheet of water that is called
a lagoon. In this water the more minute and the more
delicate kinds of coral insects find a tranquil abode, while the
stronger and the larger live and work on the outer margin of
the ring among the waves and breakers. Every such atoll has
an opening at one part of it, which allows a ship of any burden
to pass from the ocean into the lagoon.

The second class of coral rocks consist of Barrier Reefs.
These are coral rocks which either extend in straight lines in
the front of a continent or of a large island, or encircle smaller
islands. In both cases, as they arc separated from the land
by a broad and rather deep channel of water, they are analo-
gous to the lagoon within the atoll.

The annexed illustration (fig. 99) represents a part of the bar-
rier that encircles an island. It is a true sketch of the Island
of Bolabola, as seen from one of the central peak*. You see
that the coral reef is covered with palm trees, and you must
imagine that the reef completely encircles the island, in the
centre of which you see that peaked rock. That reef was all
worked beneath the sea, but by a volcanic upheaval, sudden
or gradual, it has become dry land.

The extent and dimensions of these barrier reefs vary from
three miles to more than forty miles in diameter. There is
near New Caledonia a reef, fronting one side and encircling
| both ends of the island, that is 400 miles long.

Fig 99.— The hland of Bolabola in the Pacific, surrounded by
a Coral Reef overgrown with Palms.

The third class of coral rocks ate Fringing Retfs. Where

THE POPULAR EDUCATOR.

the land slopes abruptly under water, these reefs are only a few
yards in breadth, and they form a kind of stony ribbon or
fringe round the shore. In places where the land slopes gently
under the water, the reef always extends farther seaward,
sometimes even as much as a mile from the land. From the
circumstance that corals always grow more vigorously on the
outside amid the breakers, and that the sediments washed
within the reefs have a noxious effect upon the insects, the
outer edge of the reef is always the highest part.

In accounting for the architecture of coral reefs, there are
three things to be assumed as well-established facts : first,
that no coral insects can live at a depth below 20 or 30
fathoms — that is, below 120 or 180 feet; secondly, that their

stony masonry must have a foundation to rest upon; and
thirdly, that as soon as the corals build up their reef to such a
height as to be left dry at low water, they cease to work.

For the sake of understanding the formation of coral rocks,
let us look again at the figure which represents the Island
of Bolabola. We have supposed that the reef which sur-
rounds it became dry land, through being upheaved by a
sudden or gradual volcanic action. But now, let us imagine
that that peak and that yonder reef are subsiding and sinking
under the waters of the ocean. The island, with its present
reef, represented by the unbroken lines in the next diagram
subsides slowly.

Fig. 100.— Growth of Coral on a subsiding Island.

In this illustration (fig. 100) a a represents the outer edges
of the fringing reef at the present sea level, b b are the present
shores of the island. As gradually as the island continues to
sink, so progressively do the corals work upward ; and a' a'
represent the outer edges of the reef after its upward growth,
during a period of subsidence, has been completed, and even-
tually converted into a barrier with islets on it. b' b' are the
new shores of the now encircled island ; and c c represents the
lagoon between the fringing reef and the island, after a subsi-
dence of several hundred feet, is given by the dotted lines

aa'b'. You can now see why certain encircling reefs stand
so far from the shores which they form.

The same facts would come out, if, instead of an island, we
had supposed .the shore of a continent fringed with reels to
have subsided."

You must again imagine that the island of Bolabola has
continued to subside for thousands of years, until there was
formed around it a new barrier reef, represented by the broken
lines in fig. 101.

J£

Fig* 101. — A Section through Bolabola during a Period of supposed Subsidence.

a' a' represent the outer edges of the barrier reef at the level
of the sea, with islets on it. b' b' the shores of the included
island of Bolabola. c c, the lagoon channel between the reef
and the land. On our supposition, as the barrier reef continues
to sink down slowly, the coral insects go on working vigor-
ously upwards. As the island sinks, the water gains inch by
inch on the shore, and the two peaks, x t, form separate
islands within one great encircling reef ; and, finally, x the
highest disappears. As soon as this takes place, a perfect
atoll is formed, and a" a" represent the outer edges of the
reef, now converted into an atoll, and c' is the lagoon in which
a ship rides at anchor.

11 We can now," says Mr. Darwin, M perceive how it comes
that atolls, having sprung from encircling barrier reefs, re-
semble them in general size, form, in the manner in which
they are grouped together, and in their arrangements in single
or double lines ; for they may be called rude outline charts of
the sunken islands over which they stand. We can, farther see
how it arises that atolls in the Pacific and Indian Oceans extend
on lines parallel to the generally prevailing strike of the high
lands and great coast lines of those oceans. I venture,
therefore, to affirm that, on the theory of the upward growth
of the corals during the sinking of the land, all the leading
features in those wonderful structures, the lagoon island or

atolls, as well as in the no less wonderful barrier reefs,
whether encircling small islands or stretching for hundreds of
miles along the shores of a continent, are simply explained."—
Darwin* s Naturalist's Journal^ p. 474.

The preceding figure represented to you the gradual forma-
tion of lagoon islands or atolls by subsidence. Fig. 102 will
give you the appearance of an atoll when so formed.

This engraving, after all, gives but a faint idea of the
singular aspect of an atoll. Whitsunday Island is one of the
smallest size, and has its narrow islets united together in
a ring. "The immensity of the ocean, the fury of the
breakers, contrasted with the lowness of the land and the
smoothness of the bright green water within the lagoon, can
hardly be imagined without having been seen."

The rocks produced by coral insects are of immense extent.
Coral reefs are scattered in the oceans, as if in certain lines of
enormous length. On the eastern coast of Australia a coral
reef stretches that is 350 miles long. In the Pacific there are
two groups of islands, the one called the Disappointment
Islands, and the other the Duff group. These two groups are
500 miles apart, but they are connected by coral reefs over
which the natives can travel from one island to another. Also
between New Guinea and Australia there is a line of coral
ret is 700 miles long, in which there are no gaps wider than

LESSONS IN GREEK.

thirty miles. In the Indian Ocean, to the west of Malabar,
there is a chain of coral islets and coral reefs, called the Mal-
divas, that is 480 geographical miles long. "This chain consists
of a series of innumerable atolls, between which no soundings
could be found at 150 fathoms.

The study of coral formations is of importance in geology,
as it tends to explain the production of coralline rocks formed
at earlier epochs in the history of the globe. Geologists find

of the Danish islands, however, the flinty chalk is covered
by coral limestone.

The oolite beds abound in corals, and their limestones are
nothing but coral reefs consolidated. Indeed, the coral rag,
in this formation has all the characters of the reefs now
forming in the Pacific. Rocks constructed by corals form the
principal part of the vast range of the Jura in Switzerland.

In the carboniferous system are deep and extensive strata

Fig, 102. — Whitsunday Islatul, an Atoll in the Pacific Ocean,

that in very remote periods in the earth's history, and in
much higher latitudes than at present, these coral insects were
among some of the most efficient architects employed by the
Creator in the structure of the earth's crust, ana that both
the architects and the architecture in the ancient hills were the
same as in the present day.

All the tertiary formation, especially the coralline crag,
supplies numerous specimens of cargophylliae, spongiae, &c,
while the eocene deposits contain astrea, meandrina, and
mugenera, inhabitants of tropical seas.

In the chalk formation corals are abundant in certain
localities, as in the sandy strata of Maestricht ; but in the
white chalk of England there is no appearance of coral reefs,
though corals of a small and delicate species are found in it.
It is evident that the white chalk was deposited in a profound
ocean. As, therefore, the corals can only live at a moderate
depth, coral reefs could not have been produced in the chalk
sea, except in shallows or near the sea-shore. In some

called the mountain limestone, which abounds in various forms
of corals. The silurian system also teems with peculiar kinds
of corals.

From these facts we learn, as Dr. Mantell says, "that
an atom of living jelly floating in the ocean, at length be-
coming fixed to a rock, may be the first link in a chain of
events, which, after the lapse of ages, may produce important
modifications in the physical geography of our globe. When
we bring the knowledge thus acquired to bear on the natural
records of our planet, and examine the rocks and mountains
around us, we find that, in periods so remote as to exceed our
powers of calculation, similar effects were produced by beings
of the same type of organization as those whose labours " are
carried on at this day. " We are thus enabled to read the
history of the past, and to trace the succession of events, each
of such duration as to defy all attempts to determine, with
any approach to probability, the period required for its deve-
lopment." — Wonders of Geology, p. 657.

LESSONS IN GREEK.— No. XII.
By John R. Beard, D.D.
A deviation from the usual form of the Second Declension
may here claim the student's attention.

The Second Declension contracted.

A small number of substantives in which an o or an t stands
before the case-endings undergo contraction. By contraction
is meant the blending of two vowels into a diphthong, or some
other equivalent. The student must learn both the uncon-
tracted and the contracted forms, first horizontally, as irXoog,
wXovc, ; irXow irXov, &c. ; and then perpendicularly, as 7rXooc,
tXoov, irXotp, uncontracted ; and 7rXoi>c, irXov, nXtp, con-
tracted. Thus are declined 6 irXoog, a sailing or voyage ; 6 7r«pe-
jtXooc, a tailing round or circumnavigation ; and to oareov, a bone.

Examples of Contracted Nouns ; Second Declension.

S.N.

V.
P.N.

D.iV.A; V.

G.kD.

After

rrXoov

irXoy

ttXoov

irXoe

ttXooi

rcXooiv

irXooig.

itXoovq

irXooi

irXout

UiicontlContr JJncont. Contrac.

irXooc. \irXovg irepiirXoog irtpurXovg

trXov ireptirXoov irtpnrXov

7rXy \TrepnrXo(i> irepiirXy

wXovv lirepiirXoov TrepnrXovv

irXov 7rtpi7rXo€ ireonrXov

ttXoX \7rtpiirXoot irep+irXvi

irX&V \TTtpLirX0UiV TClplTcXtUV

irXolg irepiirXootg lirepiirXoig
irXovg irepnrXoovg lirepiirXovg
irepiirXooi ] ire pnrXoi
ireptirXout |7T6pi7rXu>
ireptirXootv \ireptirXoiv

irXot
irXtit

irXooiv ,irXotv

Uncon.
oareov
oareov

OOTtlp

oareov

OGTIOV

ojrea

OffTZlOP

ovreoig

oarea

otrrea^

OCTTtdJ

oortoiv

Contrc,

OffTOUV
OOTOV

oartp

oorovv

oarovv

oara

oarwv

qotoIq

oara

oorw

OOTOiV

this manner^ decline the multiplicative adjectiv

ending in oog (ovc), on (jjj), oov (oDv), as airXov, anXij, airXovv,
single or simple; also adjectives of two terminations in oog (ovg)
and oov (ovv) formed from the substantive voog{vovc), the mind,
as 6, t) evvovq, to evvovv, well-minded, that is, well disposed ; and
from the substantive wXoog (nXovg) 6, >) tvirXovg, to evirXovv,
voyaging successfully. These differ from their substantives
only in this, that in the neuter plural they suffer no contrac-
tion, ending in -voa and -Xoa. Decline in the same
manner adjectives ending in ooc, and denoting that of which a
thing is made, as \pvatog (xpvoovc), xpt/roa (xP v<r v)t Xp v<Tl0V
(xpvaovv), golden. In the neuter plural ea is contracted into a.
When the feminine termination ea is preceded by a vowel or
p, the ea is contracted, not into i/» hut into a, as

ept'eog (epeovg), epe ea (epea), eptov (tpeovv), woollen.

apyvp eog (apyvpovg), apyvp-ea (apyvpa), apyvp-tov (apyop-
ovv), of silver.

Examples of Contracted Adjectives ; Second Declension.

i M .

\\pvaovg
\Xpvaov
jXpveV
^Xpvoovv
Xpvaovg
Xpvaoi
Xpvawv
XpvToZc
'Xpuffovc
\\pvao\
D.N. & V. xpvtrte)
G.D. \xpvaoXv

S.N,

V.
P.N.

, N.

Xpvtrn

Xpvaovv

airXovg

a7rX>j

airXovv

Xpvtnjg

Xpvaov

cnrXov

airXrjg.

airXov

Xpvag

Xpvay

airX<p
airXovv

ctirXy

airXtp

Xpvaijv

Xpvaovv

atrXrjv

airXovv

Xpvari

Xpvaovv

airXovg

aicXri

airXovv

Xpvvai

Xpvaa

airXol

atrXae

airXa

Xpva&v

Xpva&v \aTrXwv

airX&v

Xpvaaig

Xpvaotg a7rXo7c \airXalg

airXolg

Xpvcag

Xpvaa '«7rXoDc

a7rXag

airXa

Xpvaal Ixpufra , curXot

airXal

cnrXa

Xpvad \X9 V<J ^ airXw

airXa

awXut

Xpvaaiv

Xpvooiv

axXoTv

airXatv

aaXoty

THE POPULAR EDUCATOR

VoCABULAEY.

Nooc, ov, 6, the understanding,
the mind, the soul.

Kavtov, ov, ro, a small basket.

Evvooc, ovv, well-disposed, be-
nevolent.

Avoog, ovv (a not and woe),
unintelligent, senseless.

XaXictog, €a, eov, brazen, made
of brass.

AXrjOua, ag, 1), truth.

OcpaTrau'a, rjg, »}, a female ser-
vant.

pyi> 9C» ») anger.

^wxi (K n 9* Psyche), >jc, »/» the
soul.

Ttyta, ag, >/, Tegea, a city in
Arcadia.

OpioTijg, ov, 6, Orestes.

Apro$, ov, 6, bread.

6, a multitude,

O^Xoc, OV,

crowd.
'Yirvoc, ov, o, sleep.
XaXtvoc, ov, 6, a bridle, rein.
Karoirrpov, ov, ro, a mirror.
KvireXXoy, ov, to, a goblet.
T«jciw, ov, to, a child.
Ar/Xoc, i], ov, known, evident,

clear.
ActjXog, ov, unknown.
OXtyoe, tj, ov, few.
EfeeaXvirrw, I uncover,
Erurov4t(<ii, I lighten.
Eptfri, I contend, I am in strife

with some one.
Aiy«, I say, I name.
Ilpo<r<f>tpw, I carry, I bring to,
Kcu-— cat, both.
5Jvi>, with.

Exercises. — Grebk-Ehoush.

AoyOC KCLTOTTTOOV UTTl TOV V0V, TOV KOVV t\ 0V9lV °* CtvBpmWOi

tii8aaica\ov. Tov ivvovv^ikovQipa-mut. Oi ayaOoi QtXot tchttov
vovv t\ovaiv. 'O 7rXouc earn' a^Aoc roic. vavraic. 2vv vy rov
/3tov ay€. 'O o^Xoc ov* tyti vovv. M^ *pt£« rote avoig. 01 ayaOoi
roic ayaflotc evvoi €tartv. Op«yov ^iXwv ivviov. Ta Op«orov oorra
<v Ttyf ^ ijv. Ai 0epairatvat tv Kavaiig tov aprov irpoafipovaiv.
Oi 9tot kcli kclKov Kai kokov ttXovv toiq vavraig irapi\ov<Jiv.
"VvXHQ X a ^ tV0 C avOpunrotg 6 vovg iojtiv. XloXXajrtc opyi; avOput-
irutv vovv tKKaXvTrrti. 'AwXovf tariv 6 r»/c aXrjQtiag Xoyog.
Aoyoc tvvovg tirucovfiZtt Xvvijv. To kvxiXXov eanv apy vpovv.
'O Bavarog Xtytrat xaXitovc vxvog,

English-Greek.

The understanding is a teacher to men. The well-disposed
friend is honoured (Qtpairtvto). Well-disposed friends are
honoured. To the well-disposed are many friends (that is, the
well-disposed have many friends). Abstain from the senseless.
Strive after benevolent friends. Bring the broad in a basket.
Avoid senseless youths. Senseless youths are avoided. The
goblet is golden. Silver goblets are beautiful. Pass life {Qiov
ayttv) with understanding. Contend ye not with the senseless.

Remark that as a general rule the subject (or what is com-
monly called the nominative) has the article, the predicate being
without it. Thus if, as in the last Greek sentence, you meet
with a sentence having two nouns connected by the verb eivai,
take first, that is, take as the subject, that which has the
article before it, as

Subject.

Bavarog

Death

Predicate,
Xtyirai xaXjeovc virvog
is called a brazen sleep.

THE THREE DECLENSIONS {review).

With the nouns of the first and second declension, the stu-
dent, if he has thoroughly mastered the foregoing lessons,
will find no difficulty in any attempt he may make to construe
classical Greek. It is somewhat different with nouns of the
.third declension, the discovery of the nominative of which is
necessary in order to consult a Greek lexicon with ease and
effect. I therefore subjoin the following, which will enable
him from the genitive case to find the nominative ; in which
form substantives and adjectives appear in dictionaries. I
give the genitive, because the genitive is, as it were, the key
to the remaining oblique cases. Thus, if you meet with avdpa,
you know the genitive must have two of these letters, namely,
cp ; if you meet with xa/xcuvEc, you know the genitive will
have the letters x n V Liav » ** y° u meet w * tn ptkavtc, you know
the genitive will have the letters jxeXav. Now, from the
genitive you may get to the nominative, and you may do so
by the aid of what has already been said. But for this jrou
must bear in mind that the v in piXav, though belonging

to the stem, does not appear in the nominative. In the follow*
ing table, however, you will find that a genitive having a v,
as in dvog, comes from a noun in ag ; fUkag, therefore, is the
word which you have to look for in the lexicon, and uika£
you find to mean black. Thus, you see* if the genitive is
given, the word is easily ascertained. In general, then, the
genitive in

doc

Bog
y«f

KOf

are*

Y7°V
pog

WOf

VTOf

comes from a nominative in a

conies from a nominative in £

}

comes from a nominative in
comes from a nominative in
comet from a nominative in

and in particular

avof

O.VT0Q

aog

evog

tvrog

tog

tpog

iiit£
10Q

irog
ivog

VOQ

ovog

ovrog

oog

opog

pog

Tpog

vvroQ

vog

v$og

vQog

wvog "i

wvrog J

woe )

wroe /

comes from a nominative in ag, av

comes from a nominative in ag

come from a nominative in

comes from a nominative in

comes from a nominative in v

co me 8 from a nominative in utv

comes from a nominative in w, ovq

comes from a nominative in w, we, ore

oomes from a nominative in wp. op

comes from a nominative in lye, og, tag

comes from a nominative in p

comes from a nominative in rr/p

comes from a nominative in vg

avg, ag

r\v

ttg

h v, vg, tvg
i, v, ic

comes from a nominative in
comes from a nominative in

u>e

I wish you, with the aid of this table, to review the ground
over which we have gone. With it you should possess the
utmost familiarity before you pass on to the next topic. In
order to assist you, and at once to ground you in wnat you
have learnt, and to enlarge your acquirements, I subjoin
exercises bearing on the three declensions These exercises
are taken from the best Greek authors, and from the Sacred
Scriptures. When you have mastered them, you will feel that
already you have made some progress.

I premise a few syntactical remarks. In Greek, as in
Latin, adjectives, adjective pronouns, and participle*, agree
with their nouns in gender, number, and case, That is, if the
noun is in the accusative singular, in the accusative singular
must the adjective, &c, be. If the noun is in the genitive
plural, the adjective must be in the genitive plural. If the
noun is of the neuter gender, put the adjective in the neuter
gender : and so in all other cases, the adjective, the adjective
pronoun, and the participle, when they agree in sense, must
agree also in form, both being in the same gender, number,
and case. Thus we say ayaVog avrjp, a pood man: but if we
use yvvti instead of avtjp, we must change ayaOog into ayaOq.
Also we write ay Spa ayaBov Qavpafa, I admire a good man;
but yvvauca ayaOtjv Bavpafat I admire a good woman — where

LESSONS IN GKEEK.

ayaBog becomes ayaQov to agree with av&pa, and ayaBnv to
agrcfl with yvvauca. Compare the declensions of adjectives
and ooufls combined in the fourth and sixth lesson.

As a general rule, a transitive verb, ox a verb which has an
object after it, has that object in the accusative case, as in the
sentence just given — avSpa ayaQov Bavpa£n>. Many verbg, how-
ever, put.their object in some other case ; some require the geni-
tive, and some the dative. Examples have already appeared.

When two nouns come together in a state of dependence,
the dependent noun is put in the genitive case : e. g., 'O AAcg-
av&pog tov QiXtirirov nv v\og, Alexander was the son of Philip ;
where ♦tAnrarov is in the genitive case because it is in sense
dependent on vlog.

When two verbs come together in a state of dependence,
the dependent verb is put in the infinitive mood: e.g.,
fiovXopai vtiwo invttv, I wish to drink water ; where mvtiv is
governed in tne infinitive mood by flovXopat, the former being
in tense dependent on the latter.

Recapitulatory Exercises from the Greek Classics.

1. Mia %EXt£<tfP tap ov irotti. 2. Itavra oxpovogirpog 0a>c
aytt. 3. HiXom vtoi ntrav Arptvg cat Qvtarng. 4. IloXXa
avBpuxoig Trap* tXirttia yiyvtrat. 5. TvvaiZi Koapog 6 rpoirog
(to- tativ) ov ra xpvata. 6. Oi rtTTiysg tvfwvoi Xtyovrat
eivai. 7. MvpfinKwv kui ptXiGatov fliog icoXvtrovog tori. 8.
TlyvtotTKti $(op rov <f>iopa Kat XvKog Xvkov. 9. Ov icrnoig aXX* if
XPW l Q rwv fiifSXuav opyavov rrjg iraiStiag toriv. 10. 'VLptv
}voig avtv ua&notutg rvfXov, if £t paOnoig di\a Qvottog tXXiirtg.
11. /O gpovoc rw T^P? icpoonBti Ttfv tmorifpnv. 12. IloXXat
naap al rng flovictpu love *Xavai. 13. Avrjp avSpa xai iroXig
iroXiv <rw£et. 14. "Eirapivtttvdag wg aXnBug tv avSpaaiv avnp
nv. 15. Ttputv ytpovn yXuttraav ifdiornv «x £e » nnig vaiii, icai
yvvaiKi Tcpoofopov yvvn. 16. Tlavrtg ot rutv apionav Htpoutv
waiZtg iwi raig fiaaiXtutg Bvpaig Traititvovrai. 17. Eupog
rirpv9KH vvfia, tov c*t vow Xoyog. 18. 'H fpovnotg ptyiorov
tortv ayaBov. 19. HoXecjg y\>v\n oi vopot- 20. 'H rvpavvig
atueiag unrnp toriv. 21. 'O dtiXog rrjg irarpitiog rrpocoTijg
tori v. 22. Oi ayaBoi avtipeg Bttov tiicovcg tioiv. 23. Oi
"Nopatitg rutv At/3i/wv ov raig nptpaig, aXXa raig vv%iv apiB-
uovoiv. 24. XaXtvov ton Xtyttv irpog yaortpa, <ara ovk
Igotxrav. 25. 'Hfaiffrog rw iro&t x w ^°C nv. 26. *H Mn£aa
ypaftrai rw rratde etivov vwofiXtirovoa. 27. HBovg fiatravog
tortv avQpwiroig \povog. 28. Oi oftig top iov tv roig odovoiv
cvovfftv. 29. 'O Tlapvatraog peya *ai vvgkiov opog evriv. 30^
Bv pouorta £vo tonv tirioniia oprj, to \itv 'EXikiov KaXovfitvov t
trtpov it KtOaipwv. 31. 'O NtiXoc «x €t itowroia yevq ixBvutv.
32. Ttpa rovg yovtlg. 33. Avaxapffig Tt\v afnrtXov nice Tpetg
fipuv porpvg' rov wpcurov, rjdovijg' rov tiivripov, fitQr^g' tov
rptrov, antitag. 34. Uovog tvtcXuag 7rari/p (sc. lonv), 35.
Qrtavov rat TtjBvog naig r\v \vaxog. 36. Ot rirriytg oirovvrai
tiiv Spoaov. 87. KXtavQng apn rovg aicaidtvrovg povy ry
poppy Tuv Btjpiiov SiaQtpuv. 38. Kvaxapotg ovtidiZoptvog on
^KvBrjg fjv, tint, ry ytwi. aXX* ov rtp rpoinv. 39. Ko\a£ovrat
tv $£ov icavrtg o\ kcikoi, paatXtig, dovXot, aarpairai, 7T6v//r«c,
rXovaiot, irTti>xoi. 40. At Qopicov Bvyartptg ypaiai tjaav tK
ytvtrtig, 41. Zqviov f0»;, $tiv rag iroXttg Kooptiv ovk avaOtj-
paciv, aXXa raig rwv oiicovvrutv aptraig.

In giving the vocabulary of these recapitulatory exercises,
I shall take each sentence in the order in which it stands,
because the learner will here need more aid than he has
hitherto received.

Vocabulary to the Exercises from the Classics.

1. Mca, one, from the numeral tig, pia, iv, one; YeXttiuv,
nom. sing., fera., agreeing with fjtia ; x l ^ (OV t X £ ^ 0, '°C> a
wallow.

2. See note. 9

• This sentence contains nothing that the student ought not to
know. 1 therefore leave him to the knowledge he has, or may
nave, already attained, and so in future shall I do without giving
notice thereof.

3. lUAoirtfrom IIcXo^, UtXoirog, a proper name, governed
in the dative case by ijcrav; to Felop* there were, that is,
Pelope had; ATptvg (g. t»g), Atreus; evtirrrfc (g. ov), Thyestee.
Observe that the English y represents the Greek v.

4. irap for rrapa, against, vap' iXirt^a, contrary to their expec-
tations ; tXm&a, ace sing., from rf eXtrig (g. eXirtdog), hope ;
why has the plural adjective woXXa the verb in the singular ?

5. rpoirog, ov, 6, a turning, disposition ; xpwia, neut., pi.,
from xpvmov, a diminutive of X9 v °OQ* 9°Mt and so denoting
golden ornaments, jewels.

6. rerriyec, grasshopper*, from 6 rern£ (g. nrrlyoc) J tvfwvoi,
pleasing in sound, nom. pi., from tvfwvog (tv and Qwvn, a
voice), an adjective of two terminations ; \«yoi>rai, are said,
the third person plural, passive voice, present tense, from Xiyw,
J say ; it governs arai, to be, in the infinitive mood.

7. pvpfinicujv, gen. pi. governed by frog, from 6 pvppnl,
pvpfinicoc, an ant; ptXiaevv, gen. pi. governed by (3iog % from
ptXiaaa, ng, »/, a bee; noXvicovog, ov (from iroXvg and icovog),
laborious.

8. yiyvcjoncti (from yiyvut9Kut,I know), indicative mood, active
voice, third person singular agreeing with its subject, ox
nominative <Jxop ; <f>top, Qtapog, b, a thief, Xvnog, ov, 6, a wolf

9« X9 n<Tl Ct ttog, tj, use ; opyavov, ov, to, a means, our organ.

10. avtv, without; rvfXov, from rvfXog, n, ov, blind; the
adjective is in the neuter gender, denoting disparagement, a
blind thing ; dixa, separate from ; tXXiirtg, from AAttrtyc, tg ,
defective (from X«7ru>, I leave),

11. irpoaTiBti, adds, from TrpoariOnpi, I add; ttriarnpn, ng, »},
understanding.

12. povKtput, having the horns of an ox, from fiovKtpwg, w, and
that from fiovg and Ktpa ; lovg, lo, from Ioi, ovg, irXavai, wan-
dtrings, from trXavn, ng, »/.

14. aXijOutg, truly ; tog aXtjButg, very truly.

15. i)$i<jrt)v> sweetmt, the superlative degree of r/dvg, sweet;
icpootyopov, pleasant, from irpoafopog, ov, conducive to (vpog and
<ptpu)).

16. aptoruiv, the best, that is, noble, from apiarog, a superla-
tive of ayaflof.

17. Eifog, ovg, to, a sword; nrpfaxncee, wounds, from rtTpuxjKio,
I wound.

18. ptyiaTov, the greatest, superlative from ptyag, great,

20. rvpavvig, Xdog, »), usurped power, tyranny; aSuctag, of
injustice (a privative, and ducn, right, justice).

21. dttXog, n, ov, cowardly, 6 StiXog, the coward; rrpo^orng,
ov, 6, a betrayer, traitor.

22. tiKovtg, images ; tucwv, ovog, 6, an image.

23. Houadtg, the nomads, or wandering tribes, from vopag,
aiog, and that from vtpto already explained ; apiBpovoiv, they
number, from apiQptw, I inunber, our arithmetic.

24. txovoav, having, present participle from <x<u, I have; it
agrees with yaortpa.

25. 'H0a«rroc, Vulcan ; \oj\oq, n, ov, lame.

26. Mq&ta, ag, »), Medea ; vTrofiXtfrovaa, scowling at, from biro,
under, and pXtma, I look.

27. nBovg, of character, from to nBog ; paaavog, ov, if, a touch-
stone, test.

28. o$ig, o$t<ag, o, a serpent ; tog, ov, a dart, sting.

29. Tlapvavoog, Parnassus, a mountain of Phocis, on which
was Delphi ; avuKiog, ov, overhung with clouds t from ovv, with,
and <TKia, a shade.

30. tmoTjpog, op, distinguished, remarkable, from tin, on
(here an intensive), and anpa, a sign, whence our semaphore,
that is, a telegraph ; 'EXikuv, Helicon ; KiBaiptov, CUhaeron ;
KoXovfjuvov, called, named, pirticiple agreeing with to, that is,
opog ; inpog, a, ov, other, the other.

33. Avaxaptrtg, Anaeharsis; tint, said; rifiovng depends on
fiorpvg ; ueBij, ng, »), intoxication ; anfoa (from a, not, and qdvg,
sweet), disgust.

34. tincXtta, ag, y, glory, distinction.

35. Qictavog, ov, 6, Oce&nus, Ocean considered as a divinity ;
TnBvg, og, n, Tethys, a sea- goddess.

36. aiTtopai, I feed on ; tpovog, ov, if, detc.

37. KXtavOng, Cteanthes ; i<pn, said ; airaititvrog, ov, untaught,
uneducated; uopfn, ng, if % form; iiaftpia, I differ.

38. ovitttfa, I reproach, Anacharsis being reproached; ^KvBng,
a Scythian.

100

THE POPULAR EDUCATOR.

89. KoXagw, I punish; iv a*iov, Sofiqt is understood, in the
abode of Hades, in hell ; aarpaTrng, ov, 6, a satrap or governor
of a province ; irivnc,, nroc, poor ; irr«x<>c, n, o"> begging ;
oi WTiox 01 * beggars,

40. vpata, r), old, an oW woman, grey-haired.

41, ctiv, that it was necessary, proper ; avaOnpa, toq, to, an
offering, public monument, from ava, up, and riOnpi, I place ;
rwv otKovvrutv of their inhabitants, from oikiw, I inhabit, com-
pare oiKog and ourta.

(lb fc continued).

ON PHYSICS OR NATURAL PHILOSOPHY.
No. VH.

MOLECULAR FORCES.

Nature of Molecular Forces — The phenomena which bodies
constantly exhibit lead to the conclusion that their particles
are always under the action of two opposite forces, one of
which tends to make them attract, and the other to repel, one
another. The first, which is called molecular attraction, varies
in the same body only with the distance of the particles ; the
second, which is produced by heat, varies with the inten-
sity of the agent and with the distance of the particles. From
the mutual relation of these forces, and from the disposition
and arrangement which they give to the particles, arise the
different states of bodies, namely, solid, liquid, and gaseous.

Molecular attraction only acts at distances incalculably
small. Its effect is nothing at any sensible distance, a property
which distinguishes it from gravity and universal gravitation,
which act at all distances. We are ignorant of the precise
laws according to which molecular attraction operates.
According to the manner in which it is viewed, it receives the
different names of cohesion, Affinity, and adhesion.

Cohesion is the force which unites similar particles of matter
to each other, that is, matter of the same kind, as for instance
two particles of water, or two particles of iron. This force is
almost nothing in gases, sensible in liquids, and very great in
solids. Its intensity is diminished when the temperature of a
body is raised, while the repulsive force arising from heat is
increased. Hence, when solid bodies are heated, they ulti-
mately become liquid, and even pass from this state into the
aeriform or gaseous state.

Cohesion varies not only with the nature of the bodies, but
also with the arrangement of their particles. To the modifica-
tions which cohesion undergoes in different circumstances are
to be attributed the. different qualities of tenacity, ductility,
and hardness.

In liquids, taken in large quantity, gravity oveicomes
cohesion. Hence liquids, constantly yielding to the action of
gravity, and assuming no particular form of their own, take
always that of the vessels in which they are contained. In small
drops of liquids, however, cohesion overcomes gravity, and
they assume the spherical or spheroidal form. This may be
seen in the drops of dew suspended on the leaves of plants ;
and the same phenomenon is observed when a liquid is poured
on a plane horizontal surface and does not wet it, as mercury
upon wood. The same experiment can be made with water,
if the surface be previously rubbed or sprinkled with a light
powder, such as lamp-black, &c.

Affinity is the attraction which takes place between hetero-
geneous substsnces ; in water, for instance, which is composed
of two atoms of hydrogen to one of oxygen, it is affinity which
unites these two bodies ; but it is cohesion which unites two
particles of water. Hence, it is evident that in compound
bodies cohesion and affinity act together, while in simple
bodies it is only cohesion that unites the particles. Affinity is
the form of attraction to which we refer all the combinations
and decompositions of chemistry.

Every cause which tends to weaken cohesion increases
affinity. The latter is, in fact, increased by the state of
division in a body ; it is also increased by the liquid or the
gaseous state of a body. This force is particularly developed
by a body when it is disengaged from combination with
another body and isolated or left free to yield itself to the
action of other bodies for which it may have an affinity. Ihis

force also exhibits very variable effects, according to the eleva-
tion of the temperature of bodies. In certain cases, by separa-
ting the particles and diminishing cohesion, heat produces
combinations. For example, between sulphur and oxygen
the affinity is without effect at the ordinary temperature,
while at a high temperature these bodies combine and produce
a fixed compound called sulphurous acid. In other cases, on
the contrary, heat destroys combinations, by communicating
to their elements unequal expansibility. Hence many metallic
oxides are decomposed by the action of heat.

Adhesion is the molecular attraction exhibited in bodies
which stick together by contact. Two plates of glass, for
example, when placed in contact with a weight upon them,
adhere so strongly that they cannot be separated without
breaking, after the weight is removed. The force of adhesion
acts between solids and liquids, and between solids and gases.

Adhesion between solids is not merely the effect of atmo-
spheric pressure, for its action is exhibited in a vacuum. This
force increases in proportion to the degree of the smoothness
of the surfaces in contact, and to the length of the duration
of contact ; for the resistance to their separation is greater in
proportion to the time that their contact has continued. More-
over, adhesion between solid bodies is independent of their
thickness — a fact which indicates that the molecular attraction
acts at indefinitely small distances.

When solid bodies are immersed in water, alcohol, and most
other liquids, they are found covered with a coat of the liquid
when taken out of it ; and this is simply the effect of adhesion.

Adhesion is produced between solids and gases, similar to
that between solids and liquids. Thus, if we immerse a plate
of glass or of metal in water, we perceive air-bubbles floating
on the surface. Now, in this case the water does not pene-
trate the pores of the plate, but the air-bubbles arise only
from the expulsion of the air which surrounded the plate like
the coating of a liquid. A series of phenomena proceeding
from molecular attraction, under the names capillary attrac-
tion, endosmose, absorption, and imbibition, shall be brought under
our notice in the sequel.

PARTICULAR PROPERTIES OF SOLIDS.

Having explained to the student the principal properties of
matter common to solids, liquids, and gases, we shall in this
lesson treat of some particular properties of solids ; such as
the elasticity of traction, the elasticity of torsion, the elasticity of
flexure, tenacity \ ductility, and hardness.

Elasticity of Traction. — In our second lesson we explained
the nature of elasticity in general, and referred chiefly to that
developed by pressure. In solids, however, elasticity is deve-
loped also by traction or extension, by twisting or torsion, and
by flexure or bending.

In ascertaining the laws of the elasticity of traction, M.
Savart employed an apparatus represented in fig. 18. This

Fi*. 18.

LESSONS IN NATURAL PHILOSOPHY.

101

apparatus consists of a wooden stand, from the top of which
are suspended the rods or wires on which the experiments are
made. At their lower extremity is fixed a scale-pan for hold-
ing the weights used in determining the force of traction, and
two points a, b, are marked, between which the exact distance
is measured, by means of a cathetometer, before the scale-pan |
is loaded.

A cathetometer or vertical measurer, as the derivation from the
Greek implies, is a brass scale divided into inches and fractions '
of an inch, placed upon a stand which is brought exactly into
the vertical position by adjusting screws at the bottom. On this
scale there is placed a sliding telescope sight, exactly at right
angles to the vertical, which carries a vernier capable of
measuring to fractions of an inch, each one hundredth part of
the former. By fixing this telescope sight successively at the
points a and b, as seen in the figure, we obtain by means of
the graduated scale the exact distance between these two
points. Now by loading the scale-pan with weights, and
again measuring the distance between the points a and b, we
ascertain the amount of elongation or extension arising from
the traction of the weights.

By experiments conducted in this manner, it has been found
so long as the limit of elasticity has not been exceeded, that
the traction or extension of rods and wires is regulated by the
three following laws : —

1st. Metal rods and wires have their elasticity of extension
perfect ; that is, they resume exactly their original length as
soon as the force of traction ceases.

2nd. In the same substance, and having the same diameter,
the extension or elongation is proportional to the force of
traction and to the length. *

3rd. In rods or wires of the same length and of the same
material, but of unequal diameter, the extensions or elonga-
tions are in the inverse ratio of the squares of the diameters.

Both calculation and experiment prove, that when bodies
are extended by traction, their volume or bulk is increased.

Elasticity of Torsion. — The laws of the torsion of metal wires
and threads of various substances were first ascertained by
M. Coulomb, a French philosopher, who died in 1806. In his
researches on this subject he employed an apparatus called the
balance of torsion ; this is composed of a fine metallic wire or
thread, fastened to a stand at its upper extremity, and
stretched vertically by a weight, to the centre of which is
attached a horizontal pointer or index. Below this is placed
a graduated circle or dial-plate, attached to the stand by a
sliding piece and tangent-screw ; the centre of this circle, which
is exactly under the centre of the index, is so adjusted as to
be exactly under the direction of the wire or thread produced
when it is in the vertical position. Now, if the index be
turned round, out of its position of equilibrium, by the amount
of a certain angle, which is called the angle of torsion, the force
necessary to put the index in this new position is called the
force of torsion. When this turning round of the index takes
place, the particles of the wire or thread which were before
situated in the straight line parallel to its length or axis, are
now situated in a spiral round it. If the limit of elasticity
has not been exceeded, the particles have a tendency to return
to their original position, and this tendency is verified by their
actual return to it, as soon as the force of torsion is removed ;
bat they do not remain in this position. For, in consequence
of their acquired velocity, they pass this position, and produce
torsion in a contrary direction ; thus the equilibrium is again
disturbed, and the wire revolving now on itself, the index does
not point to zero on the dial-plate until after a certain num-
ber of oscillations on both sides of this point.

By means of this apparatus Coulomb proved that when the
amplitudes of the oscillations do not exceed a certain number
of degrees, these oscillations are regulated by the following
laws:—

1 1st. They are very sensibly isochronous, that is, performed
in equal times.

2nd. In the same wire the angle of torsion is proportional
to the force of torsion.

3rd. In wires of the same diameter, and with the same force
of torsion, the angle of torsion is proportional to their length.

4th. In wires of the same length, and with the same force,

the angle of torsio n is inversely proportional to the fourth
powers of the diamet^p.

Elasticity of flexure. — All solids cut into thin lamin» or
plates, and fixed at one of their extremities, when more or less
bent from their natural position, return to that position as soon
as the force which bent them is removed. This property is very
evident in tempered steel, caoutchouc, wood, and paper. Cer-
tain bodies can be bent only at a very small angle, unless they
be extended to a very great length, or be made extremely
thin. For example, glass cannot be bent unless it be formed
of very thin lamina; about a foot in length, or be reduced to a
very fine thread. In the latter state it becomes so flexible,
that it can be formed into waving plumes, or woven into
cloth.

Numerous applications of the elasticity- of torsion are to be
seen in the construction of bows, cross-bows, watch-springs,
carriage-springs, spring-balances, and dynamometers, or instru-
ments for measuring the intensity of forces, chiefly of animal
power. The elasticity of hair, wool, and feathers is employed
in the construction of mattresses, cushions, and other pieces of
domestic furniture.

^ "Whatever may be the species of elasticity under considera-
tion, as we have formerly remarked, there is always « limit to
its action ; that is, a degree of molecular displacement beyond
which the elastic bodies are fractured, or rendered incapable
of reassuming their original form. Owing to several causes,
this limit is variable. For instance, the elasticity of several
metals is increased by hardening them ; that is, by bringing
their particles more closely together, as in wire-drawing,
plate-rolling, or hammering. Some substances, as steel,
cast iron, glass, &c, become more elastic and at the same time
harder by the process of tempering, which consists in cooling
a metal suddenly after it has been raised to a high tempera-
ture.

Elasticity, on the contrary, is diminished by the process of
annealing, which consists in bringing bodies to a lower tempera-
ture than that required for tempering, and then slowly cooling
them. It is by this process that the elasticity of springs is
graduated at pleasure.

In the operation of tempering, steel and cast iron acquire a
great degree of hardness, and it is chiefly for this purpose that
tempering is employed. All cutting instruments are made of
tempered steel. But there are some bodies upon which tem-
pering produces an entirely opposite effect. Thus the combi-
nation of metals called tam-tam, which is composed of one part
of tin to four parts of copper, becomes ductile and malleable
when it is suddenly cooled ; on the contrary it becomes hard
and brittle like glass when slowly cooled. Sulphur exhibits
the same phenomenon ; when cooled slowly, it is hard and
brittle ; but when cooled suddenly, it becomes soft and ductile
like wax ; but it does not continue in this state.

Glass presents a curious phenomenon of tempering in what
are called Dutch tears or Prince Rupert's drops y names given to
small globules of glass, in the shape of tears, which in a state
of fusion are dropped into cold water. Glass being a bad
conductor of heat, the central parts of these globules are still
in a state of fusion when the parts in contact with the water
have become solid. From this, it follows that their molecular
forces being unable to resume the state of stable equilibrium,
the globules become so brittle that fracture at a single point of
their surface is sufficient to make them burst in pieces with a
loud noise, and at once fall into powder. As glass undergoes
the real process of tempering when too suddenly cooled, the
brittlenes8 of newly-made articles is diminished by annealing
them over a fire, from which they are very slowly withdrawn.

Tenacity is the resistance which bodies oppose to their
extension by traction. In order to determine the amount of
this force in different bodies, they are formed into cylindric
or prismatic rods, and subjected, in the direction of their
length, to the traction of a weight of so many pounds as are
sufficient to determine the force of rupture or separation of
their particles.

Tenacity is directly proportional to the force which produces
the rupture, and inversely proportional to the area of the
transverse section of the rods or prisms employed in resisting
the strain. According to numerous experiments upon metals,
the force necessary to produce rupture is nearly triple of that

tt>2

THE POPULAR ^EDUCATOR.

which corresponds to the limit of elasticity. Tenacity
diminishes with the duration of tradA. Jt is found that,
after a certain period, metallic and other rods give way under
smaller loads than those which would produce immediate
rupture ; and in all cases, the resistance of bodies to traction
is less than their resistance to pressure.

Tenacity varies not only in different bodies, but also in those
which are composed of the same matter, and in equal quantity
according to their difference in form. In rods ot equal sec-
tional area, the prismatic form possesses less power of resistance
than the cylindric. In a given quantity of matter, the hollow
cylinder possesses a greater power of resistance than the solid
cylinder ; and the maximum of tenacity in the former takes
place when the outer diameter is to the inner one in the rati<
of 11 to 6.

In the same body, the form has the same influence on the
resistance to pressure that it has on the resistance to traction
Hence, a hollow cylinder, of equal matter and altitude, has i
greater power of resistance to pressure than a solid one;
whence it follows that the bones of animals, the feathers of
birds, the stalks of grass and of a great number of plants, being
hollow, present a greater resistance to rupture by pressure
or traction than if they were solid, the mass of matter being
the same.

Tenacity, as well as elasticity, varies in the same body
according to the direction in which force is applied. In wood,
for example, the tenacity and elasticity are greater in the
direction of the fibres than in any crossing direction. This
difference is, in general, manifested in all bodies whose contex-
ture is not the same in all directions. Yet M. Savart dis-
covered, by means of ingenious experiments on the sonorous
vibrations of bodies, that a difference in this respect existed in
a number of bodies whose contexture was completely homo-
geneous ; such as zinc, lead, brass, glass, resinous bodies, &c
He also discovered this difference in certain directions perpen-
dicular to es_h other, which he called axes of stronger am
weaker elasticity. M. Savart attributed this modification of
these properties to a symmetrical arrangement which the
particles ot bodies tend always to assume when they are slowly
cooled. It is of the greatest importance, in the arts of con*
struct ion, to take into consideration the limits of the tenacity
and compressibility of materials. In suspension-bridges, for
instance, the stability of the structure chiefly depends on the
tenacity of the rods which support the road- way. The follow-
ing table exhibits the weights in tons on the square inch
which certain bodies can support in vertical traction before
rupture, or in other words, the limit of direct cohesion o]
tenacity.

Metals.
Wrought iron wire, from A to A I

inch diameter J

Ditto, -Ay inch diameter

Wrought iron bars

Ditto, hammered

Wrought iron, rolled

Wrought iron chains

Cast iron

Cast steel

Ditto, tilted

Steel blistered and hammered

Shear steel

Raw steel

Damascus steel

Copper cast

Copper hammered

Sheet copper

Copper wire

Platinum wire

Silver wire

Cast silver

Gold wire

Cast Gold

Brass

Gun metal

Tin wire

Sheet lead, milled

Weights.

from 60

to 91 tone

„ 36

» 43 „

25*

»»

from 14

to 18 „

21*

„ 25 „

» 9? »

59*

from 31

to 44 „

»»

• 21

»»

27*

>»

»»

t»

_ tt

i>.

»♦

Woods*

Box 9

Ash 8 „

Teak 7 „

Beech 5 f ,

Oak 5 M

Fir 5 „

Pear 4* „

Mahogany , 3* „

Elm 6 „

American Pine • 6 „

White Deal 6

Ductility. — This is a property which many bodies possess, and
it consists in their power to change their form under various
degrees of pressure or traction. In some bodies, as clay and
wax, a very slight force is sufficient to produce a change in their
form ; in others, as glass and rosin, it is necessary to add heat ;
but in metals, strong force is required^ as in hammering, wire-
drawing, and laminating or reducing to plates. Ductility is
denominated malleability when it is produced by the operation
of the hammer. The most malleable metal is lead ; the most
ductile in laminating is gold ; and in wire-drawing, is plati-
num. The great ductility of platinum enabled Wallas ton to
produce wires of this metal not exceeding the thirty-thou-
sandth part of an inch in diameter. This was effected by cover-
ing a platinum wire of about one-hundredth of an inch in
diameter with a coating of silver until the diameter of the
compound wire was about & of an inch in thickness ; then by
drawing this wire until its diameter was as fine as possible, the
two metals were equally extended by the process ; and lastly,
by dipping the wire in nitric acid, the silver was dissolved
and the platinum wire remained; exhibiting the extraordi-
nary degree of fineness above mentioned. A thousand yards of
this wire would weigh only about three-quarters of a grain ;
and a quantity equal in bulk to a common die would reach
from London to Vienna.

Hardness. — This property of matter is the resistance which
bodies present to scratching' or abrasion by other bodies.
This property is only relative, that is, a substance may be
hard with reference to one body and soft with regard to
another. The relative hardness then consists in this, that one
body can be made to scratch or abrade another without being
itself capable of being scratched or abraded by the other. The
hardest of all bodies is the diamond, for it will scratch all
bodies, but cannot be scratched by any. * After the diamond
in hardness follow the sapphire, the ruby, the rock-crystal,
the flint, the stone, &c. Metals in a state of purity are gene-
rally soft. Lead can be scratched with the nail. The processes
which increase their elasticity also increase their hardness ; such
as tempering, annealing, &c. Alloys or mixtures are harder
than metale. Thus in jewellery and in coining, the hardness
of gold and silver is increased by alloying them with copper.
The hardness of bodies does not increase in proportion to
their resistance to pressure. Glass and the diamond are much
harder than wood, but they present less resistance to the blow
of a hammer. The hardness of bodies is usefully employed in
polish ing-powders, such as emery, pumice-stone, and tripoli.
The diamond, which is the hardest of all bodies, can only be
ground or polished by means of a powder which is merely
pulverized diamond.

Case-Hardening is a process by which the surface of arti-
cles made of wrought iron is converted into steel. The articles
to be case-hardened having been prepared in wrought iron,
they are placed in an iron box in layers, in order to receive
that degree of hardening on the surface which will prepare
them for receiving a final polish. A layer of animal carbon
(horns, hoofs, skins, or leather), at first so burned as to be
capable of reduction to powder, is spread over each; the box,
then carefully covered and luted with an equal mixture of
clay and sand, is kept at a slight heat for half an hour, and its
contents are then emptied into water. By this means, a surface
of hardened steel is obtained over the whole of the article, of
a thickness depending on the duration of the time in which
he;it has been applied. This process is particularly applicable
to articles wanting external hardness and polish, as fire-irons ;
but it is not applicable to cutting instruments.

• In the direction of their fibre*.

LESSONS IN ITALIAN.

103

LESSONS IN ITALIAN GRAMMAR.— No. Vll.

BY CHARLES TAUSEJtAtT, M.D.,

Of the University of Pavla, and Professor of the Italian and German
Languages at the Kensington Proprietary Grammar School.

(Continued from page 84.)
FIFTH PRONOUNCING TABLE,

IIAUSTRATINQ 8BVBRAL COMBINATIONS OF THB LBTTBRS C, ff,
AND 9.

1. Che, Chi, Ghi, Ghi*

Italian*

Ch$to

Chino

Ghetto

Qhiro

Rachels

Arehimede

Vogherd

Beghino

Fichi
1*9**
Lmghi

Hditm*
Ckiaro
Chieem
Chiodo

Pronounced*

kai-to

kee-no

gh6t-to

ghee-ro

rah-ke-lal

ahrr-kee-m6-dai

vo-gai-rah

bai-ghee-no

ffc-kai

fee-kee

lai-gal

lan-ghee

English,

Quiet

Descent, bent

Jewry

Dormouse

Rachel

Archimedes

He will row

Biggin, a child's cap

Sea-calves

Fig-trees

Leagues, alliances

Lakes

2, Chia, Chie, Ohio, Chit*.*

M$khiorr$

Rmfhiar*
zYtgmsersi

Vnghie

Pronounced.
keeah-ro
keeai-zah
keed-do
kee6o-so
tabrr-keeah-to
bahn-keed-rai
mel-kee6rr-rai
kon-keeoo-so
Tdk-keeab
slk-keeai
so6k-keeo
skee6o-mab

8. Ghia, Ghie,

Pronounced*

gheeah-yah

gheed-rah

gheed-vah

rin-gheeah-rai

prai-eheed-rah

sin-ghee6-Uo;

tchfa-gheeah

06n-gheeai

nn-gheeo

English.
Clear, bright
Church
Nail, I nail
Inclosed, inclosure
Flump, fat
Banker
Melchior
Concluded
An old woman
Buckets
Auger, juice
Froth, scum

Ghio.f

English*

Gravel, sand

A ferrule

Clod, turf

To grin

Prayer, desire

Sob, sigh, hiccough

Girth

Nails, hoofs

I grin, grinding the teeth

• I hart explained the combination ohi to be sounded like kee.
When one of the five vowels follows this syllable, it is so
Intimately blended with the following vowel, that a kind of
soneeied sound of ohi is the result, the voice sliding, as it were,
Jrosn.OBi to the next vowel with great rapidity.

t The remark made with respect to the syllable cAt, fol-
lowed by any of the five vowels, is equully applicable to the
syllable ghi followed by a vowel : here, likewise, the syllable ghi is,
as it were, squeezed, and the voice mntt slide into the pronuncia-
tion of the vowels that follow ghi with great rapidity.

X The double tar, as well as the single z, may have the mild
stand of the word aam (with which, by-the-bye, the ds in the word
Windsor corresponds), or the hard sound of tz in Switzerland.
According to modern orthography, the letter a is generally doubled
fat the middle of words between two vowels, and the pronunciation
of this tz scarcely differs from that of the single e. However,
before diphthongs,— as, for example, ia, te, and to,— * must remain
single, and has always, in such a case, the sharp sound. For
•sample, rtmgradar* (rin-grah-tsseah-rsi), to thank ; pigruna (pee-
giee-teeeab), idleness; tamo (ee-n#*tseeai), follies; BonUMo (Bo-
net-fah-tseeo), Boniface.

4. Cia t die, dt* Cio, Cm, Gia, Gie, Gii, Gio t Giu,

Italian*

Ciano

Ciera

Ciofo

Ciueo

Giara

Gielo

Gioi-e

Giuda

Baciare

Areiere

Ar clone

Acciuga

Fagiano

Eugiero

Jnginsto

Pancia

Specie

Lercio

Ciuffo

Eegia

Giulio

Pronounced*

tch ah -no

tchai-rah}

tchd-fo

tch6o-ko

jah-rah

jUo|

jo-vai

j6o-dah

bah-tchah-rai

ahrr-tche-rai

ahrr-tch6*nai

aht-tch6o-gah$

fah-jah-no

roo-j6-ro

in-j6o-8to

pahn-tchah

spe-tchai

lerr-tcho

tch6of-fo

r6-jah

r6od-jo

j6o-leeo

English*

Bluebottle (plant)

The look, face

A mean fellow

An ass

Cup or glass

Ice, frost, cold

Jove, Jupiter

Judah

To kiss, salute

Bowman, archer

Saddle-bow, saddle

Anchovy

Pheasant

Roger

Unjust

Belly, paunch, body

Kind, species

Dirty, foul

I catch or snap

Royal palace

Roaring

A Roman coin, July

6. Gua t Cue, Gui, Guo, Qua, Que, Qui, Quo.

Italian*

Guado
Guelfo

Guida
Seyuo
Quasi
Questo
Quito

Pronounced.

gw&h-do
gwdl-fo

gwee-dah

sS-gwo

kwah-zee

kvai-sto

kwee-to

English.

A ford

A Guelph, an ancient
coin of Florence
Leader, guide
I follow or pursue
Almost, as if
This
I receipt

X The vowel i before e, when both follow the consonant e t are
pronounced as though the i was not there, and the whole combina-
tion only ce. The same remark, however, made with regard to
the combinations da, cio, "and c#*— that in a more measured
enunciation the vowel i in these cases is slightly touched —
holds good here also.

J The observation just made in the foregoing note with respect to
de is strictly applicable to the syllable gie. It & always pronounced
as though the i was not there ; unless slightly touched in measured
pronunciation.

} No observation has yet been made in reference to the pro-
nunciation of the double c (ce). This depends, as well as the
pronunciation of double g (gg), on the vowel that follows the
latter c. If that vowel is o, o, or «, the ce is sounded like a double
* (U)orcfe. For example, oocea (bdk-kah), mouth; 00000 (b4k-ko),
beak ; aocusare (ahk-koo-sah-rai), to accuse. If, however, that
vowel which follows the latter e is e or l t the double c (00) is sounded
something like tch in the English word match, only perhaps
stronger, and with vibration. On that account, I have tried to
imitate the stronger sound of the oe by the letters ffcA, placing the
first t in the first syllable, and tch at the beginning of the second,
just ks I hare attempted to imitate the sound of the gg by placing
d in one syllable, and j at the beginning of the next, in such words
as paggi (pahd-jee), pages, attendants. The remark with respect
to the pronunciation of the gg, however, holds good of cc ; the
voice must not pause too long on the t of the syllable where the
first e occurs, and glide as quickly as possible to the pronunciation
of the second c, which must be very much vibrated. In this way
a more equal distribution of the sound tch between the two sylla-
bles will be effected, which will produce the correct sound of
the ce ; and my imitation of that sound by tick has no other object
than to indicate to the^ reader the necessity of giving a stronger
vibration to the cc. It is obvious that when 00 is followed by con-
sonants, it must be pronounced like k, just as the single c in the
like case must be so pronounced. For example, acdamare (ahk-
klah-mah-rai), to elect by acclamation, to ..pplaudf ; accresoere (ahk-
krai-shai-rai), to increase, &c. When between the cc and the
vowels e or i the letter h is interposed, the 00 is also sounded like Jr,
as well as the single c in such cases and for the same reasons ; the
A being a mere auxiliary letter to indicate that cc before e and i is
not to have the sound of Uch. but of kk, as in cMcchera (kfk-kai-rah),
a tea-cup ; chiacchiera (keeaok-keeai-rah), chit-chat.

104

THE POPULAR EDUCATOK.

Ilatian.

Pronounced.

Quojo

kwd-yo

Reguate

aai-gwah-tch&i

Jnsegus

in-sg-gwai

Inguine

in-gwee-nai

Liguori

lee-gwd-ree

Aquarh

ah-kwah-reeo

Loquela

lo-kwe-lah

Aquila

ah-qwee-lah

Aquoso

ah-qw6-*o

Lingua

lin-gwah

Rangue

sahn-gwai

Pmgui

pin- g wee

Pasqua

pah.sk wah

Cinque

tchin-kwai

Iniquo

ee-nce-kwo

Adequi

ah-de-kwee

English.

Leather, skin

Follower, disciple

He pursues

Groin

Liguori

Aquarius

Tongue, language

Eagle

Aqueous, watery

Tongue, language

Blood

Fat, plump

Easter

Five

Unjust, iniquitous

Thou comparest

6. Cla, Ck, Cli, Clo t Clu, Gla, Gle, Gli, Glo, Glu.

Italian.

Pronounced,

English.

Clava

klah.Tah

Club

Clero

kJd.ro

aergy

Clima

klee'-mah

Climate

Cloto

kld-to

Clotho, one of the Fates

Clusio

kloo.zeeo

Clusium, a town

Gladio

ghth-deeo*

Knife, poniard

GUba

glg.bah

Clod of earth

Glifo

gli-fo

Glyph (in architecture)
Globe

Globe

glO-bo

Gluma

glo6>mah

Chaff

JUclatno

rai-klah-mo

Reclamation

• This is the first occurrence in these lesions of the important
combination gl. It has two different sounds. When it is not fol-
lowed by the letter i it has the sound of gl in gland, glebe, glory,
gkte ; and this sound can offer no difficulty. But when the com-
bination gl is followed by the letter i and one of the vowels a, e, o,
and u, it is pronounced precisely as the double / (//) in the French
words bouUh, fills, gresiUer, grenouille, bouillon, btilard, biUet t brouuTon,
JtuuTu, and, generally speaking, in all those words where the 11 has
after the vowel I a squeezed sound in the French language. They
who are unacquainted with French may form a notion of this
sound by separating and inverting the gl in the enunciation, i.e., by
pronouncing U before the g, and changing the latter into y. Only
the first I must go to one syllable, and the second I along with the
y, and with a squeezed sound to the beginning of the next, while
care must be taken that the ▼oice should glide rapidly from one

2 liable to the other, by which means a more equal distribution of,
e squeezed sound Uy will be produced, and a correct pronunciation •
of the gl effected. An approximation to this sound may be found
in the English words million, miliary, biliary, billiards, seraglio, in»
tagUo, and aglio. The letter t, between the combination gl and the
vowels a, e, o, and sj, is (as well as in the combinations eta, do, clu,
and gia, gto, giu) a mere auxiliary letter* i.e. f a mere soundless,
written sign, to indicate that gl before a, e f o, and u is not to have
the sound of gl in gland, glebe, glory, and give, but that squeezed
sound, the imitation and description of which I have here
attempted.

For example : vaglio (vahl-lyo), a sieve ; meglio (mel-lyo), better ;
pigldo (pfl-lyo), I take, seize; miscuglio (mis-kdol-lyo), mixture;
svegliare (zvel-lyah-rai), to awake; togUere (t6Myai-rai). to take
away ; scegliere (shll-lyai-rai), to choose ; doglia (ddl-lyah), sorrows ;
bfgUardo (bil-lyahrr-do), billiards ; biglietto (bil-ly£t-to), note, bill ;
imbroglione (im-brol-lydnai), a meddling fellow ; JbgHulo (fol-lyod-
to), full of leaves. EgU, he, eglino, they, quegli, that one, gli (the
plural of the article or the pronoun), with its numerous composi-
tions, and gli, the final inflexion or terroinational syllable of nouns
and verbs, hare always the squeezed sound ttyee ; while the mere
syllable y#, at the commencement and in the middle of words, always
has the sound of gl in gland, glebe, Ac The only exception is
AngH, Englishmen, pronounced ahn-glee. For example : figU
(fil-lyee), sons ; jbgU (fftl-lyee). leaves of paper ; gigli (jil-lyee),
lilies ; negUgere (nai-gleC-jai-rai), to neglect ; negligente (nai-
glee-jen-te), negligent; negligent (nai-glee-jAn-tsah), negligence ;
negligentare (nai-glee-jen-tah-rai), to neglect.

ANSWERS TO CORRESPONDENTS.

Civis f Dublin): We recommend him to take up Part I. of the French
Lesions from the P. E. to follow the Lessons from the W. M. F. Part II.
of the former will be ready in about three weeks. — Ambition (CopthalL.
conrt) will see the stadies thit it will be necessary for him to take up.
If be withe* to matriculate at the Univeraity of London, in voL iL of the
P. E., p. 137.

Eipsellio (Leicester', : Right — Cabmoney (Belfast) will see by the solu-
tion we hare inserted that his is wrong. Thanks for his other communica-
tions.— SriUDB B radios (Fetter-lane): His conjecture about the Greek
extract Is rig ht : but that about the Greek lesson is wrong. There Is a rery
considerable difference between the ancient and the modern Greek. We be-
lieve that old Homer would not be understood in his own country. — J. Mills
.(Tewkesbury) : His poetry is good, but not sufficiently measured ; that is,
put into the proper number of syllables in each line ; some lines hare ten
•> liable* , some twelve, and so on. Were we to correct it, we would begin
thus:

u Ah, dost thou gase upon that little child,

And smile with admiration at its form ?

Scarcely as yet unfolded, helpless thins;.

What is there In its features so divine,

Or in Its wondrous structure so profound ?

This is but one of Nature's lovely works.

With which earth teems throughout her wide domain.

Behold the smallest insects far surpass.

In texture delicate, this blooming child !

Their microscopic organs how minute.

Their mechaniqoe, how wonderfully fine I

But ah, within that infant form there lies

A soul divine ; a young Immortal soul !

A soul of worth so infinitely great.

That all the powers of Mathematie tore

Its value cannot calculate or weigh."

A. Richardson (Newcastle) and E. Evans (Ashby-de-la-Zonch): We
regret that we cannot give them the information they require. — W. X.
(Manchester) and Parallax: We advise them to write to If essrs. Watkins
and Hill, 5, Chartng-cross, London, who will furnish them with a catalogue
of their telescopes, achromatic and reflecting, with their sizes, powers,
and prices. They can also have information from the same firm about magic
lanterns, sliders, and diagrams or atlases of the heavens.

C. B. C. (Hull) must study our Lessons in Penmanship, vol. ii., P. E*—
T. aIuxlow (Sheffield) : Get an old copy of Barrow's Euclid (which you may
at any old book-stall for Is.), and you will see all the books of Euclid from the
1st to the 16th inclusive.— W. Ha dpi eld (Hayfield): We know of no paper
in which excise vacancies are advertised^— W. J. Osborni (Soho) : We
think that the courtesy is due to any clergyman who does not wish bis
sermon taken down in short-hand, to refrain from so doing ; he is the beat
judge of thevalneof his own productions.— J. Addrr (Grandtully): The
rule for finding the index of the quotient is this : Subtract the index of the
dividend from that of the divisor, and the remainder is the Index of the
quotient : now this being done for the first term in every step of the opera-
tion for finding the greatest common measure, there can be no difficulty at
the end, for the remainder will take the indices of its terms from those
which correspond to them in the dividend, supposing them, of course, to be
in arithmetical progression proceeding from that of the first term.

directions given in No. 3G, vol •
tendent of the docks where he
(Gray's-inn-road) and A 8ubscklbrk
are informed that Mr.Cassell has published the rery book they want, M Tne
People's Biographical Dictionary," compiled by Dr. Beard, and that It may
be had at thi* office for 2s. 4d. in paper covers. The Atlas is progressing in
the P. E. Lord Byron swam the Hellespont. Don't bind the '* Magazine of
Art," or any other periodical, too soon ; sell your copy and buy another,
taking more care next time.— J. Bbwlry (Langrigg) : His verses are very
good, but not up to our mark. — A Tbocblbsomb subscriber will find an
artie'eon shell-cleaning in the P. E. " Latin ward*," col. 2, p. 288, vol. ii.,
should be " Latin tcoraV' certainly.— Student of Anqlbsbi : In the pas-
sage "si eupis placere magistro," the " si" means only if; " cu pis" means
you desire, as shown by the termination " is ; " " placere/' to please, accord-
ing to the Latin idiom, requires the dative ••migistro," to the master, to
follow it ; but we cannot literally say in English, to please to the master',
yet, as to please means to give pleasure, we can say to give pleasure to the
master. Death would be the consequence of the stopping up the pores of
the body; but the neglect of washing the body, which is a great sin,
besides being a great evil, is compensated for, in strong and healthy persons,
by copious and heavy perspiration, which literally washes the body Itself,
and clears the pores for a time. Still this Is an unhealthy state, and cannot
be long continued with impunity.— C hemic us (Falkirk): Mr. Cassell U
about to publish a work on Botsny.

T. Ta it (Glasgow) should attend to the direction
ii. — X. P. P. should apply to the superintendent c
wishes to be admitted.— W. B. E. (Gray's-inn-rosx

LITERARY NOTICES.

GERMAN.

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or Parts, Is. each. The entire work will be issued at 8s. 6d. in strong
binding.

Cassell's Lbssons in G REMAN. Part I., price 3s: in paper covert, or
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covers, or 2s. neat cloth, will shortly be issued.

Cassbll's Eclectic German Rbadrr, price 2s. in paper covers, or
2s. 6d. neat cloth.

Cassell's Elements op Arithmetic (uniform with Caasell's Euclid)
is now ready, price Is. in stiff covers, or Is. 6d. neat cloth.— Kit, 3d.

NATURAL PHILOSOPHY.

10.0

ON PHYSICS OR NATURAL PHILOSOPHY—

No. VIII.

HYDROSTATICS.

The Science of Liquids at Rest. — Hydrostatics is that part of
natural philosophy which has for its object the investigation
of the conditions of equilibrium in liquids, and of the pressures
which they produce, either in mass, or on the sides of the
Teasels which contain them. The science which treats of the
motion of liquids is called Hydrodynamics ; and the application
of its principles to the art of conveying and raising water is
particularly denominated Hydraulics.

General Character of Liquids. — It has been already stated
that liquids are bodies of which the particles, in consequence
of their extreme mobility, yield to the slightest effort made to
displace them. Their fluidity, however, is not perfect ; for
among their particles there always exists an adherence which
constitutes a greater or less degree of viscosity (stickiness).

The fluidity of liquids is manifest, but in a higher degree, in
the gases ; the distinction between liquids and gases being,
that the former possess the property of compressibility in a very
alight degree, whereas the latter arc highly compressible and
elastic

The fluidity of liquids is shown by the facility with which
they take all kinds of shapes ; their small compressibility is
proved by the following experiment.

Compressibility 'of Liquids. — Subsequently to the experiment
of the academicians of Florence formerly mentioned, liquids
were for a long time considered to be incompressible. After-
wards, experiments were made on this subject, in England 6y
Canton in 1761, and by Perkins in 1819; at Copenhagen, by
(Ersted in 1823, and again by Colladon and Sturm in 1827.
From these various experiments, it has been concluded as a
fact that liquids are really compressible.

The apparatus employed in measuring the compressibility of
liquids are called Piesometers, that is (from the Greek), Pres-
sure-measurers. The following is a description of that of (Ersted,
with the improvements of M. Desprctz. This piesometer, fig.
19, is composed of a very strong glass cylinder, about 3 J inches

Fig. 19.

in diameter. This cylinder, which is completely filled with
•iter, is terminated at the bottom by a wooden stand, in which
it is firmly cemented ; and at the top a copper cylinder is fixed
10 ^ by means of a plate, which can be uuscrewed at pleasure,

VOL. IV.

This plate is furnished with a funnel-pipe at it, by which the
water is admitted into the cylinder, and with an air-tight
pump-body and piston, the latter being moved up or down by
means of a screw p. In the interior of the apparatus is con-
tained a glass reservoir a, filled vith the liquid whose com-
pressibility is to be ascertained. This reservoir terminates in
a bent capillary tube, the lower end of which is immersed in a
mercurial bath at o. This tube is previously divided into
parts of equal capacity, it having been ascertained how many
of these parts the reservoir a contains ; this is found by deter-
mining the weight r of the mercury contained in the reser-
voir a, and the weighty of the mercury contained in a certain
number n of the divisions of the capillary tube ; then, denot-
ing the number of the divisions of the small tube contained in
the reservoir by n, we have the following proportion p : P : :
w : K\ whence, the value of N can bo easily deduced.

In the interior of the cylinder is contained a Manometer
{rarity measurer) of compressed air. This is a glass tube b,
closed at the upper extremity, and open at the lower extre-
mity, which is also immersed in the mercurial bath o. When
no pressure is applied to the water which fills the cylinder,
the tube Bis completely full of air; but when pressure is
applied to the water in the cylinder, by means of the screw v
and the piston to which it is attached, this pressure is com-
municated to the mercury, which then rises in the tube n by
compressing the air contained in it. A graduated scale c,
placed alongside of the tube, indicates the quantity by which
the volume of air is diminished ; it is by means of the quantity
of diminution in the volume of air that the pressure on the
liquid contained in the cylinder is determined, as will be
afterwards shown.

In making experiments with this apparatus, the reservoir a
is first filled with the liquid whose compressibility is to be
found ; the cylinder is then filled with water by means of
the funnel-pipe b. The screw r is then turned so as to make
the piston descend and produce a pressure on the water and
the mercury contained in the cylinder ; this pressure not only
raises tho mercury in the tube b, but also in the capillary tube
fastened to the reservoir a, as shown in the figure. The rise
of the mercury in the capillary tube shows that the liquid con-
tained in the reservoir has diminished in volume, the measure
of its diminution being indicated on the tube itself, as above
mentioned.

In his experiments, (Ersted supposed that the capacity of
the reservoir remained invariable, and that the sides of it were
equally acted upon by the liquid both in the interior and on
the exterior. Mathematical investigation has proved that this
capacity is diminished by both pressures. In their experi-
ments, Colladon and Sturm took this change of capacity into
account ; and they have proved that for a pressure equal to
that of the atmosphere, and at the temperature of 32° Fahren-
heit, the parts of the original volume by which certain liquids
were contracted, are as follows :—

Mercury * 000005 = roiA}ou

Distilled water -000049 = »»} ffw

Ditto, freed from air -000054 = T¥ W*

Sulphuric ether -000133 = ?iVfr

They also observed that in the case of water and mercury,
within certain limits, the diminution of volume is proportional
to the pressure.

Principle of Equality of Pressure. — On the supposition that
liquids are incompressible and possess perfect fluidity, and are
freed from the action of gravity, the following principle, called
the principle of equality of pressure in every direction, universally
holds good : liquids communicate in all directions, with tho
same intensity, the pressures applied to any point of their
mass. This principle was first announced to the world by the
celebrated Pascal, who died in 1C62, and is sometimes called
the principle of Pascal.

In order to have a proper idea of this principle, suppose a
vessel, fig. 20, of any shape whatever, to be filled with water,
aud that in its sides at different places cylindrical openings
a, b, c, d, and b are made, to which there are applied moveable
pistons exactly fitting them. If to any, piston a, an external
pressure be applied, say of 20 pounds this pressure is instan-
taneously communicated to the internal surfaces of the pistons

106

THE POPULAR EDUCATOR.

b, c, d and b, and they will be pushed outwardly with a pres-
sure of 20 pounds, if their surfaces be each equal to that of the

Fig. 20.

piston a ; but if their surfaces be twice, thrice, or four times
that, of the piston a, the pressure communicated will be 40, 60,
or 80 pounds accordingly ; that is, the pressure communicated
increases proportionally to the surface.

The principle of equality of pressure is generally considered
as a consequence of the constitution of liquids. It can be
proved by the following experiment that the pressure is
roally communicated in all directions ; but it does not prove
that it is equally so. A cylinder, fig. 21, in which a piston

Fi*. 91.

moves, is fixed to a hollow globe on which are placed a num-
ber of small cylindric pipes, all perpendicular to the surface.
The globe and the. cylinder being filled with water, if the pis-
ton be pushed inwards the water will spout through all the
orifices or pipes, and not through that only which is opposite
to the piston. The reason why the principle of equality of
pressure, or, as it has been elegantly termed, the Quaquavertal
Pressure, cannot be perfectly proved, is that in our experiments
wa cannot take away weight from the liquids, nor friction from
the pistons which communicate pressure to them.

Direction of the Surface of Liquid*. — When a liquid is acted
on by the force of gravity only, its surface always tends to
take a direction perpendicular to the direction of that force,
fhus, suppose that the surface of a liquid, as water, takes for
an instant the direction b a, fig. 22, inclined to the horizon, the

Fig. S3.

action of gravity p on any particle m of this surface having

the direction m p, may be decomposed into two forces, the one
q, acting in the direction m a perpendicular to the surface ▲ b,
and the other f, acting in the direction wpotba. The first
force q will be counteracted by the resistance of the liquid
mass, and the second f will urge the particle m in the direction
m f. The same reasoning being applicable to every particle of
the liquid surface, it is evident that this surface cannot remain
at rest in the direction b a inclined to the horizon, but must
assume the horizontal direction, when the force acting in the
direction b a becomes zero.

If the liquid be acted upon by other forces besides that of
gravity, its surface will tend to take a direction perpendicular
to that of the resultant of all these forces, as will be seen in
the case of the phenomena of capillary attraction. According
to the principle explained above, when a liquid is contained
in a vessel or basin of small extent, its free surface is plane and
horizontal, seeing that at every point of that surface the direc-
tion of gravity is then the same. This is not the case, how-
ever, in the surface of a liquid of great extent, such as that of
the sea. For the surface of the sea being everywhere perpen-
dicular to the direction of gravity, and this direction varying
in different places considerably apart from each other, it is
plain that the surface of the sea changes its direction with
that of gravity ; and the latter being constantly directed to
the centre of the earth, the former causes the sea sensibly to
assume a spherical form, as may be observed in the phenomena
of a ship approaching to, or receding from, the shore.

PRESSURE IN LIQUIDS RESULTING FROM THE
ACTION OF GRAVITY.

Laws of Vertical Pressure Downwards. — If we suppose a
liquid to be in a state of rest in a vessel, and imagine it to be
divided into horizontal layers of equal thickness, it is plain
that each of these supports the weight of all the layers which
are above it. Throughout the liquid mass, therefore, we see
that gravity gives rise to pressures which vary from layer to
layer, and from point to point. These pressures, which come
under our consideration in their effects on the bottom and
sides of* vessels, are subject to the following general laws :—

1st. The pressure on every layer is proportional to its
depth.

2nd. The pressure is the' same on all points of the same
horizontal layer.

3rd. At the same depth, in different liquids, the pressure is
proportional to the density of the liquid.

4 th, In the same liquid, the pressure on any layer is inde-

Sendent of the form of the vessel, and only depends on the
epth of that layer.

Three of these laws may be considered as self-evident ; the
proof of the fourth will be seen when we come to the con-
sideration of the pressure on the bottom of vessels.

Vertical Pressure Upwards.— The downward pressure of the
upper layers of a liquid upon those which are below them,
produces in the latter a reaction which is equal and contrary,
in consequence of the principlo of the communication of
pressure in all directions. This upward pressure is denomi-
nated the resistance of liquids. It is very sensible when we
push our hand into a liquid, especially if it be one of great
density, such as mercury.

Fi*. 23.

NATURAL PHILOSOPHY.

107

To proxe this fact by experiment, we employ a glass tube
open at both ends, fig. 23. To the lower end of this tube is
Applied a disk of glass b, which serves as a stopper, and which
is supported in its position by means of a thread a which is
fastened to it. This apparatus being immersed in a glass
Teasel nearly full of water, the hand is removed from the
thread and the disk is left free. This disk then remains as a
stopper applied to the tube, indicating that it is supported by
the upward pressure of the water, which is greater than the
downward pressure of its weight. Now, if water be slowly
poured into the tube, the disk will continue to support this
water until the level of the water within the tube is nearly
the same as that without, when the disk will fall to the bot-
tom of the vessel. This experiment proves that the downward
pressure on the disk is equal to a column of water having for
its base the interior section of the tube, and for its height the
distance of the disk from the upper surface of the water in
which the tube is immersed. Hence, the resistance or upward
pressure of liquids, as well as their downward pressure, is
proportional to their depth.

Pressure on the Bottom of Vessels. — The pressure of a liquid
on the bottom of the vessel which contains it, is regulated by
the same laws as the pressure on any layer of that liquid ;
that is, it depends only on the density of the liquid and on its
depth, and not on the form of the vessel. That the pressure
on the bottom of vessels is independent of their form is proved
by the following experiment, the apparatus for which was
invented by M. de Haldat.

This apparatus is composed of a bent tube a c n, fig. 2*, on

the quantity of liquid which it contains As to the bottom
of the vessel, it is evidently the same in the two cases, that is,
the surface of the mercury in the tube a c.

From this law, it Is evident that by means of a very small
quantity of water very considerable pressures may be obtained.
For this purpose, wc have only to fix in the side of a closed
vessel full of water a tube of very small diameter and of great
height ; this tube being filled with water, the pressure com-
municated to the side of the vessel is equal to the weight of
the column of water which has this side for its base, and whose
height is equal to the height of tho tube, 'thus the pressure
of the water on the side of the vessel may be indefinitely
increased. In this manner, a narrow pipe of water of the
height of 33 feet has burst a strong and well- constructed
cask.

On the principle just proved, the pressure of water which
exists at the bouom of the sea may be determined. It is
known, and will soon be proved, that the pressure of the
atmosphere is equivalent to that of a column of water of 33
feet. Now navigators have often observed that the sounding
lead does not reach the bottom of the sea at a depth of about
13,200 feet. There is therefore a pressure equal to 400 times
that of the atmosphere at the bottom of a sea of the depth of
2£ miles.

Lateral Pressure of 'Liquids, — The pressure which arises from

gravity in the mass of a liquid is communicated in all directions

according to the quaquaversal principle; hence, it follows

J that tho pressures which take place perpendicularly to the

I vertical sides of vessels are included in the laws of vertical

Fig. si.

which, st a, two vessels u and p can be screwed in succession,

of the same depth, but of different form and capacity, the first

being conical and the second cylindrical. The experiment is

made by pouring mercury into the tube a c, until its level

Marly reaches tho cock a. The vessel u is then screwed on

the tube and filled with water ; the water by its weight forces

the mercury back and causes it to rise in the tube at c u, and

its level is marked by means of a slide n, which moves along

the part of the tube cd. The level of the water in the

vessel k is marked by means of a moveable rod placed

*bove it. These levels being noted, the vessel m is emptied by

the cock at a ; it is then unsciewed, and replaced by the vessel

>. Now, on pouring water into this vessel, the mercury which

had resumed its original level in the tube at a, is again raised

m the tube at c ; and as soon as the water reaches the samo

level in the vessel p, which it had in the vessel m (which is

preset ved by the position- of the rod above it), the mercury

takes exactly the same level in tho tube at h, as it did before,

{Ms Wng indicated by the slide h. This pressure is therefore

"dependent of tho shapo of tho vessel, and consequently of

pressure. It has been proved both by analysis and by experi-
ment, that the pressure on a given side of a vessel is equal to
tho weight of a column of water which has that side for its
base, and for its height the vertical distance of its centre of
gravity from the surface of tho water. As to the point of
application of this pressure, it is always a little below the
centre of gravity. This point is in fact called the centre of
pressure ; and its position is determined by calculations of
which the following are some rcsulte : 1st. Ihe centre of pres-
sure of a rectangular side, of which the upper edge is level
with the water, is situated downwards from that edge at two-
thirds of the straight line which joins the middle of its hori-
z »ntal edges. 2nd. The centre of pressure of a triangular side
of which the base is level with the upper 'surface of the water,
is in the middle of the straight line which joins the vertex of
the triangle with the middle of the base. 3rd. The centre of
pressure of a triangle whose vertex is at the level of the water,
and base horizontal, is at the distance of three-fourths of the
straight line joining the vertex and the middle of the base
from that vertex.

108

THE POPULAR EDUCATOR.

T>4 Hydraulic Tourniquet. — When a liquid is in equilibrium
in a vessel, it produces on the opposite sides along each hori-
zontal layer pressures equal and contrary in pairs, which
counteract each other, so that the existence of these pressure*
is not manifest ; they are, however, proved by the Hydraulic
Tourniquet. This apparatus is composed of a glass vessel, fig.
25, which, resting on a pivot, revolves freely round a vertical

Fig. 2*

principle of Pascal, the upward pressure of the liquid column,
whose section is ii e f o, on the annular side of which r o f a is
a section, is equal to the weight of a column of water which
would fill the spuce of which o p o ii e f n i is a section. The
effective pressure of the liquid on the body supporting the

axis. On this vessel, at its lower end. is fixed, perpendicular
to its axis, a copper tube bent horizontally at its two ends and
in opposite directions, the bottom of the vessel being fixed in
the middle of the tube. If the apparatus be filled with water,
and the tube quite closed at both ends, the interior pressures
on the sides of the tube counteract each other, and no morion
ensues. But if the tube be open at both ends, the liquid
escape?, and then the pressure no longer acts on the sides at
the orifices r, but onlv on the opposite sides at A, as men in
the sketch on the right of the figure. The pressure which
takes place at a being no longer balanced by the pressure on
the opposite point at n, acts upon the tube and on the whole
vesM'l so as to produce a motion of rotation in the direction of
the ..rrow, in the sketch to the right of the figure ; this motion
being more or less rapid in proportion to the height of the
liquid in the vessel, and to the section of the orifices from
which the water issues. The motion produced in this appara-
tus, is similar to that exhibited in the machine known by the
name of Barker* t mill. The lateral pressure of water is applied
in a useful and important manner in the construction of the
hydraulic machines called Wheels of Reaction.

Hydrostatic Paradox. — We have already seen that the pres-
sure on the bottom of a vessel full of liquid depends neither
on the form of the vessel nor on the quantity of the liquid,
but only on the height of the level of the liquid above the
bottom. Now, the pressure on the bottom of the vessel must
not be confounded with that of the vessel itself on the body
which supports it. The latter is always equal to the whole
weight of the vessel and of the liquid which it contains ; while
the former may be greater than this, less than this, or equal
to it, according to the form of the vessel. This curiout i-.-.H i»
commonly known under the name of the Hydrostatic Paradox,
because tnat, at first sight, it seems to bo paradoxical, that is,
contrary to received notions.

To explain this paradox, let k f p n, fig. 26, be the vertical
section of a vessel formed of two cylindrical parts in one piece,
but of unequal diameter. Let it be filled with water ; then as
the horizontal pressures balance each other on all its aides,
these may be left out of consideration. The vertical pressure
upon the bottom u n, is equal to the weight of a column of the
liquid which has this bottom for its base, and the height o u
for its altitude ; that is, this pressure is the same as If the
vessel had xxio for its vertical section, and was completely
filled with water. This pressure is not wholly communicated
to the body which supports the vessel ; for according to the

base, is therefore the weight of the volume of water which fills
the space whose section is ox n i, diminished by that of the
water which would be contained in the space whose section is
opohbfri, that is, in fact, the weight of water actually con-
tained in the given vessel.

If the vessel has the same diameter throughout, the water
presses with the same force both on the bottom and on the
supporting body ; if the vessel has a greater diameter at the
top than at the bottom, the pressure on the bottom is less than
on the supporting body.

LESSONS IN BOOKKEEPING.— No. VII.

HOME TRADE.

{Continued from page 341, Vol. III.)

When you see in a city, such as London, a space of ground
dug up to a certain depth, and surrounded by a hoard, that is,
an enclosure formed of a collection of boards fastened to posts
driven into the ground, you then begin to think that a build-
ing is about to commence, that a superstructure is about to be
raised, and that its foundation is in the process of preparation.
Tou are still more convinced of the fact, when you see cart-
loads of stone, brick, and lime deposited within the hoard, and
workmen proceeding to prepare the mortar and stones or
bricks for the foundation. So it is in the system of Book-
keeping by Double Entry, which we are about to lay before
you. We must begin with a series of Transactions in Business,
which are arranged in the exact order of their occurrence, as
the materials to be employed in forming a system or super-
structure which shall constitute a model for your guidance in
keeping the books of any Mercantile house in which you may
hereafter be engaged. We have selected the supposed trans-
actions of a particular branch of Home Trade, namely, that of a
Cotton Merchant, as one well adapted, from its simplicity and
generality, to exemplify the principles which we have ex-
plained in former Lessons. We have arranged these
transactions in order from January, when we suppose the
business to be commenced, till June, when we suppose a
Balance to be struck, and the Merchant's Heal Worth ascer-
tained. These six months' transactions in the Cotton trade
are interspersed with various Banking, Bitty and Cash trans-
actions, such as might be supposed to occur in the business
of a Cotton. Merchant resident in the metropolis ; and the
whole is afterwards entered in the various subsidiary books which
belong to such a business ; then into the Journal ; and, lastly,
into the ledger. The General Balance is then taken, and the
difference between the Assets and Liabilities, or the Heal
Worth of the Merchant, is ascertained from the Ledger alone.
The remarks which it will be necessary to make concerning
the method of Balancing the Books, a process equivalent to the
taking of stock among tradesmen ana others, who only use
Single Entry, we must postpone until we have shown how to
i make up the Subsidiary Books of our system.

LESSONS IN BOOKKEEPING.

109

MEMORANDA OF TRANSACTIONS.
— January 1st, 1853.

Began business with a capital of

3rd.

Lodged my Capital in the London and West-
minster Bank

£1200

5th.

Drew out of the London and Westminster Bank
5th.

Took from Cash for Petty Cash

7th. =

Bought of Osmond and Co., London,
22 bags of Berbice Cotton (on credit)
Net 7280 lbs. at 9Ad. per lb. ..."

10th.

Took from Cash for Petty Cash

12th.

Bought of Andrews and Co., London,
80 bags of Grenada Cotton (on credit)
Net 9240 lbs. at 8 id. per lb.

17th.

£10

£5

£288 3 4

£327 5 0.

Brew out of the London and Westminster Bank £985
17th.

Bought £1000 of Stock in the Three Per Cents.
Consols, at 98| percent. ... ... £985

. 2lst. •

Accepted a Bill drawn by Osmond and Co., London,
No. ] , Payable to their Order, due at 3 months £288 3

22nd. —

Drew out of the London and Westminster Bank
22nd.

Took out of Cash for my Private Account
2 # 6th.

£10

Bought of Andrews and Co., London,
14 bags of Maranham Cotton (on credit)
Net 4350 lbs. at 7*d. per lb.

£135 18 9

• 31st.

Accepted two Bills drawn by Andrews and Co., London
No. 2, Payable to their Order, due at 3 mos. £327 5
„ 3, „ Smith and Co. „ 4 mos. 135 18 9

■ February 1st.

8old to Brown and Smith, London,
22 bags of Berbice Cotton (at 1 mo. credit)

Net 7280 lbs. at I0}d. per lb. ...
Discount at 1| per cent

- 5th.

£318 10
4 15

£313 11

£100

Drew out of the London and Westminster Bank

5th.

Lent to Thomas Watson, London ... £100

10th.

Bought of White and Co., London,
24 bags of West India Cotton (at 1 mo. credit)

Net 7460 lbs. at 6jd. per lb. ... £202 10

Discount at 1} per cent. ... ... 3 7

• 14th.

Sold to Williams and Co., London,
14 bags of Orenada Cotton (at 1 mo. credit)

Net 4312 lbs. at 9Jd. per lb.
Discount at liper cent. ... ...

£170
2

13 8
11 2

£168 2 6

17th.

Bought of White and Co., London,
24 bags of West India Cotton (at 1 mo. credit)
Net 8476 lbs. at 6Jd. per lb. ... ... £229

Discount at l£ per cent. ... ... 3

11 2
8 10

£226 2 4

■ 21st.

Sold to Williams and Co., London,

16 bags of Grenada Cotton (at 1 mo. credit)

Net 4928 lbs. at 9jd. per lb. ... £195

Discount at 1* per cent. ... .. 2

1 4
18 6

- 22nd.

Received of Thomas Watson, London,
My Loan of the 5th instant

£192 2 10

£100

- 22nd. •

Deposited in the London and Westminster Bank £100

25 th.

Bought of the East India Company,

10 Lots of Madras Cotton (prompt April 25th), viz.,

. 1. containing

12bal

es, net 43201b*

j. at 4d. per

Lb. £72

4260

4132

68 17

4084

68 1

3976

66 5

4092

68 4

4300

80 12

4184

78 9

3896

73 1

10.

4004

>»

75 1

■ 25th.

Due to James Manning, London,
For his Brokerage on £721 12s. at J per cent.

-26th. ■

Drew out of the London and Westminster Bank
26th.

Lent to Darling and Co., of London,

28th.

Paid the East India Company their Deposit on
10 Lots of Cotton at £6 per Lot

28th.

Took out of Cash for Petty Cash

March 1st.

Received of Brown and Smith, London,
For Cotton sold to them February 1st

1st.

Deposited in the London and Westminster Bank £300
2nd.

Paid James Manning, London,
For his Brokerage on the purchase of Cotton

£721 12

£3 12 2

14 6

£3 12 2

£120

£50

£60

£10

£313

3rd.

£199

■ Sold £1000 of Stock in the Three Per Cents.
3 | Consols, at 99£ per cent

£997 10

110

THE POPULAR EDUCATOR.

•3rJ.

Deposited in the London and Westminster Bank £1000

5th.

Received of Darling and Co., of London,
My Loan of the 2Gth ult.

5th.

£50
£50

Lodged in the London and Westminster Bank

10th.

Drew out of the London and Westminster Bank £200

10th.

Paid White and Co., London,
For Cotton bought of them February 10th ...

13th.

Sold to Spencer and Co., London,

14 bags of Maranham Cotton (at 1 mo. credit)

Net 13501bs. at 9d. per lb. ...
Discount 1} per cent.

£199 3

£163 2 6
2 8 11

14th.

Received of Williams and Co., London,
For Cotton sold to them 14th February
Hth.

Lodged in the I«ondon and Westminster Bank

-* 16th.

Sold to Thompson and 'Co., London,
24 bags of West India Cotton, for Cash,

Net 74601b*. at 8Jd. per lb

Discount 2} per cent.

£160 13 7

£168 2 6
£170

£264 4 2
6 12 1

16th.

Received of Thompson and Co., London,
For Cotton sold to them this day,

17th.

Paid to White and Co., London,
For Cotton bought of them 17th February

18th.

Took from Cash for Private Account

21st.

Received of Williams and Co., London,
For Cotton sold to them 21st February

21st.

Net 4240 lbs. at 8d. per lb.
■ 24th.

Bought of Baring, Smith and Co., London,
30 bags of Dcmerara Cotton (on credit),
Net 92181bs. at 7Jd. per lb. ...

26th.

LESSONS IN ITALIAN GRAMMAR.— No. VIII.

By CHAELE3 TAU8ENAU. M.D.,

Of the University of Pa*ia, and Professor of the German and Italian
Language* at the Kensington Proprietary Grammar School.

{Continued from p. 104.)

7. Gna, Gnc, Gni, Gno, Gnu.

Italian.
Gnao
Gneo
Gnido
Gnome
Gnuno
Bag no
Segno
Cigno
Sogno
Pugro
Coguato
Piynere
Cognito
Signore
Ognuno

Pronounced.
nyuh-o*
nyfi-o
nyee-do
nyO-mai
ny6o-no
bahn-nyo
scn-nyo
tchin-nyo
s6n-nyo
poon-nyo
kon-nyah-to
pin-nyai-rai
* kon-nyee-to
sin-ny6-rai
on-ny6o-no

English.
Mewing of cats
Gnejus

Qniaus, a town of Caria
A gnome
Nobody, not one
Bathing-place
Sign

Swan, cygnet
Dream

Fist, cuff, I fight
Brother-in-law
To push
Known
Sir
Everybody

£257 12 1
£257 12 1

£226 2 4
£20

£192 2 10

Deposited in tho London and Westminster Bank £200

22nd.

Sold to Althorpe and Co., London,

12 bags of West India Cotton (for cash in a week),

£141 6 8

£288 1 3

Drew out of the Lon don and Westminster Bank £000

26th.

Lent White and Co., London, ... ... £600

29th

Received of Althorpe and Co., London,
For Cotton sold to them on the 22nd inst.

30th.

Received of White and Co., London.
My Loan of the 26th inst.

_ 30th.

£141 6 8

£600

Deposited in tho London and Westminster Bank £740

31st.

Accepted a Bill drawn by Baring, Snvth and Co., London,
No. 1, TayaWc to their Order, due at 3 mos. £288 1 3

♦ On is a combination almost as important as gl. before n
must never be omitted to be sounded, as in the English words
gnaw, gnat. Sue., but Englishmen arc apt to forget this, and to
sound the combination gn in several foreign languages as if no a
was before the n. The combination gn must, likewise, never be
sounded as gn in the English words signify, maUgnity, assignation,
physiognomy, cognisance, and so on. Those who know French will
be able to sound gn at once by bearing in mind the correct pro-
nunciation of gn in the French words mtgnon, mignard, peigner,
oignon, fcc, with which the Italian pronunciation of gn exactly
agrees. Those who do not understand French may form a notion
of the sound, by the same operation pointed out in my explanation
of the sound of gl. They must, as it were, sound the n before the
g, and change the latter into y ; only taking care that the voice
should glide lapidly from n to y, and squeeze, as it were, these
two letters into one very mild enunciation. Indeed this very mild
enunciation of the squeezed sound gn is a peculiarity of the Italian
language, and among foreigners, Germans, who have no corre-
sponding sound, rarely arrive at a correct pronunciaUon of the gn.
The English have words, the pronunciation of which may be said
to be an approximation to the tyalian sound; as, for example,
bagnio, seignior, poignant, poignard, champignon, Spaniard, and,
perhaps, most of all, in the word cognac ; and therefore English-
men may, without much difficulty, arrive at a correct pronunciation,
never losing sight of the peculiar squeezed and mild aound of the
Italian gn.

I shall try to imitate the sound gn by the letters nny in a similar
way to that m which I haveiraitated the sound?! before t and another
vowel by the letters Uy ; and where in Italian words the gn occurs in
the middle and at the end, the first n must go in some respect to one
syllable, and the second n along with the y to the next : the voice
rapidly gliding from one of those syllables to the other m the way
I hare already stated. For example: campagna (pronounced
kahm-pahn-nyah), country ; vegnente (ren-nyln-tai), future, next ;
Gingno (joon-nyo), June; gnocchi fnyOk-kee), small dumplings,
clowns; scrigno (okim-nyno), hunch, a coffer ; Spammoh (Spafin-
nyood- o), a Spaniard. I must not omit the remark that foreigners,
in Iuli an pronunciation, are apt to confound the two combinations
gn and ng as though they were the same. This is not the case. In
uttering gn, the g must be converted into y and sounded after n ;
while in uttering ng, the g retains the natural sound depending on
the vowel that follows. In uttering gn, the n, which is heard
before the g, has its natural sound ; while in uttering ng, n has a
kind of nasal sound. Further, the combination gn always retains
its peculiar sound irrespective of the vowels that may follow, which
is illustrated in the pronouncing table above ; while in the com-
bination ng, g has the sound of the English g in get before the
vowels a, o, andti, and the sound of the English j before the
vowels e and i. For example: gingno (jodn-nyo) t June, and
gitmgo (jo6n-go), I arrive. I join; agnolo (a
angelo (ahn-jai-lo), angel ; pugno (podn-nvo),
pungo (po6n-go), I sting. As a last remark on the gn, J
not) that when gn is followed by the lettrr i, it is a sign that gni is
to form a syllable by itself; and the t in such cases is neve* a
mere auxiliary letter — never a mere soundless, written sign to
indicate that gn is to have a squeezed sound, because, as I have

> (joon-nyo). June, and
(ahn-nyo-lo), angel, and
ro), fist, cuff, I fight, and
lark on the gn, I have to

LESSONS IN ITALIAN.

Italian.
Seabro
Pesea

P«fM

Sctmo

Bisee
Grip*
Fkeei

ScogHo

Botco

Seueio

Scuro

Sehiatta

Schic^o

JFUehi

Schioppo

Schiuma

Seiamo

Scienxa

Sciocco

Sciupa

Seranna

Seresio

Serigno

Serofa

Scruto

Sgarro

Sgkerro

Sghigno

Bgorbio

Sgvsto

Sguseio

Squadra

Squero

Sqivllo

Squoja

Fasgnale

PasqUino

8. Sea, See,
Pronounced.
skah-bro
pai-skah
pd-skah
shai-mo

bee-shai

shSe-pah

fah-shee

sk&l-lyo

bo-sko

skoo-tcho

sk6o-ro
Sch, Scia, Seie, Scio,
skeeaht-tah

skeeet-to

fec-skee

skeeOp-po

skee6o-mah

shah-mai

shen-tsah

shOk-ko

shoo-pah

skrahn-nah

skre-tseeo

skrin-nyo

skrd-fah

skr6o-to

zgahrr-ro

zgh6rr.ro

zghin-nyo

zg6rr-beeo

zg6o-sto

zg6o-sho •

skwah-drahf

skw€-ro

skwil-lo

skwd-yah

pjh-skw&h-lai

pah-skwee-no

Sri, Sco, Sou.

English.

Rough

Fishing, fishery

Peach

Diminution, diminished
I diminish

Snakes

An ignorant man

Bundles, fasces

Shell, rock, danger

Forest, wood

I undo something sown,
I rip

Obscure
Seiu, Ser, Sg, Sgh, Sq.

Issue, progeny, genera-
tion, race

Pure, unmixed, polished,
nimble, ingenuous

Whistlings

Gun

Froth, scum
Swarm of bees
Science

Stupid, a fool
He tears, spoils
Camp - chair, folding -

chair
Discord, spite
Hunch, coffer
A sow
I scrutinise
Error

A bravo, bully
Smile

Spot of ink
I get tired of
I shell, shell-work
A square (instrument),

squadron
Wharf, dock-yard
Sound, gimlet
He flays
Paschal
Pasquin}

Tnelito

in-klee-to

Ciciope

tchee-kld-pai

Rccluta

rai-klo6-tah

Inglese

in-glai-zai

Anglico

ah'n-glee-ko

Egloga

e-g-o-gah

higluvic

in-glo6-veeai

Tecla

te-klah

Cicli

tched-klee

Siclo

s6e-klo

Egla

e-glah

Egle

6-glai

Angli

ahn-glee

Anglo

ahn-glo

Qlutine

glo6-tee-nai

stated, gn has naturally, and without any exception, a squeezed
sound. This was quite different in the combination gl, and makes
the essential difference between the combinations gl and gn. The
reader will not have forgotten my remarks in the preceding note,
that when gl is followed by the rowels a, e, o, and u, and the letter
i is interposed between these vowels and the gl, i is a mere auxiliary
letter, and denotes the squeezed sound of gl somewhat similar to
that of gl in the English word seraglio. For example, compagnia
(pronounced kom-pahn-nye^-ah), company, certainly differing from
the word campagna above stated.

f I hare repeatedly in these lessons marked the combinations gva,
guLgui, guo, and the combinations qua, que, qui, quo, with " gwah . . . •"

and " qwah " I must, however, warn the reader not to give to

the tcr in these cases the full and legitimate sound of the English id,
which is peculiar to the English language. I might have marked
these combinations "gvah...." and "qvah....," and so
they are marked by the distinguished grammarian, Abate Flario
Casarotti, and other writers on Italian grammar; but the Italian
• is a softer sound than the English — a kind of medium sound
between the to and the English v. On this account I have thought
it more advisable to mark these combinations with to instead of t\
and if the reader will avoid the peculiarity of the pronunciation of
the English to (pronounced with a forward motion and instant
withdrawal of the lips), pronouncing it more like a softer v, he will
approach the true sound.

X A mutilated statue of a gladiator at Rome, where satires and
libels, sometimes of historical celebrity, against popery, cardinals,
the government, prominent persons and events, have been for
centuries, and are still affixed : Pasquin, therefore, may be said to
represent the fourth estate of Rome. The statue derived its name ,
* i one Pasquino, a Roman tailor, remarkable for his lampoons, I

Italian. Pronounced. English.

Risquoto ree-skw6-to I exact, I redeem, I

shudder
ltenowned
Cyclops
Recruiting
Englishman
Anglian
Eclogue
Voracity

Thecla (a wom/m's name)
Cycles

Sheckle (a Hebrew coin
and weight)
Egla, a name
Egla, a name
Englishmen
Englishman
Glue, birdlime •

10. Glia, Glie, Glio, Glu

to-vahl-lyah Table-cloth, towel

O-nel-lyah Oneglia, a town in Sar-
dinia

fah-mil-lyah Family

in-vdl-lyah Wrapper

ah-go61-lyah Eagle, needle, pyramid

pahl-lyai Straws

vail-lyai Vigils, evening parties

fil-lyai Daughters

m61-lyai Wife

go61-lyai Obelisks

vahl-lyo Sieve, I sift

vfil-lyo An old man

'il-lyo Lily

61-lyo Cockle-weed

lo6l-lyo July

rahl-lyee Rays

Vegli v&l-lyee Old men

Tigli til-lyee Linden-trees

Sogli sttt-lyee Thrones

fkgli fo61-lyee Was to him

In the previous pronouncing table, the reader will havo
remarked that two vowels, when t is the first, may come
together in one syllable without constituting a diphthong.
The reason of this is, that in such cases the t is not heard, or
scarcely perceptibly touched in more measured enunciation,
ind only serves the purposes of an auxiliary letter, to denote to
the eye that the preceding consonants c, g, or gl, in such combina -
tions as eia, eio, ciu, &c, gia, gio, giu, &c, glia, glio, gliu, &c, are
to have what may be termed the squeezed sound. The letter t is
not heard, or scarcelv heard, and why should it form a diph-
thong simply because in j ux taposition with another vowel ? The
lame observation is applicable to such combinations as scia 9 ado,
iciu, &c, pronounced shah, sho, shoo, &c. In all these cases
ft diphthong is seen, but not heard, or scarcely heard. And
even three vowels in combination, when % is the first, may
meet in one syllable, without constituting triphthongs ; be-
cause in such cases as well, i is preceded by the letters e, g,
and gl, not being pronounced, and only serving to denote the
Squeezed sound of these consonants. For example : libricciuolo
(pronounced lee-brit-tchoou-lo), a small book; muriecimlo
(moo-rit-tchood-lo), a small wall; uomicciuolo (ooo-mit-tchooo-
to), a little man ; giuoco (jood-ko), a game ; Jigliuolo (fil-lyooo-
lo), a child, son ; cavigliuolo (kah-vil-lyooO-lo), a little peg or
pin. In these examples, the three vowel combinations, or,
more correctly speaking, associations, are diphthongs and not
triphthongs ; and it is only by confusion of signs written for
the eye, with literal representations of sound, that has led
grammarians to class them as triphthongs. In taking this
view, I venture to differ from many authorities ; but I think I
aave shown reason for so doing.

Tovaglia
Oneglia

Famiglia

Invoglia

Aguglia

Paglie

Veglie

Figlie

Moglie

Guglie

Yaglio

Veglio

Giglio

Loglio

Luglio

I have now explained the elements of Italian pronunciation.
Exceptions, philosophical reasons, delicacies, and refinements,
[ shall on future occasions explain in " additional remarks" on
tad who was wont to satirise his neighbours and the passers-by of I pronunciation ; and any necessary further remarks that may
Ms shop. I be considered elementary, I shall likewise from tune to tune add

112

THE POPULAR EDUCATOR.

The remark that these explanations only contain the ele-
mentary principles of Italian pronunciation, will serve to show
the student really desirous of acquiring a knowledge, and not
a smattering, of Italian, the importance and necessity of fol-
lowing me closely and carefully throughout. The pace may be
tiresome, but, if taken now, will spare much labour for the
future. The ingenious reader cannot fail to have noted that
the tables I have given are not expanded examples of words,
but systematic exercises, illustrating in natural order all vocal
combinations, and thus giving an insight, from the very first,
into the structure of the language.

It may tffe here seasonably remarked, that many persons in
England learn Italian for musical purposes only. The system
of pronunciation here given will be of peculiar advantage to
them ; for in singing Italian airs, and in reading the scores of
Italian opetas, nothing is so puzzling as the necessity of giving to
one note what to the eye seems two, and sometimes even three

syllables ; and nothing is so hideous as to hear Mozart's or
Rossini's music distorted by a failure to vibrate double con-
sonants, by the neglect of the two e's and the two o's t by hard
enunciation of the gn and gl, by improper syllabic distribution
of vowels and diphthongs, &c.

Two more tables will finish my lessons on pronunciation,
and satisfactorily initiate the student into the difficulties of
this part of the language. In the concluding table, I shall
give a general mirror of the pronunciation, to which the stu-
dent who may have a doubt as to the proper pronunciation of a
word may always refer, and thus obviate the necessity of con-
stantly imitating the pronunciation of 'words by signs through-
out the grammar.

I have already explained the importance of mastering the
difficulty to foreigners of giving the proper vibrated sound
to double consonants.

LESSONS IN GERMAN.— No. LXXIII.
Irregular Verbs, continued from p. 95.

(5j jtyiitjfen, to be obliged ; must. (See Remark 12.)

1 INDICATIVE.

BUBJO'CTIYE.

CONDITIONAL. j IMPERATIVE.

INFINITIVE.

PARTICIPLE.

Present Tense.

Present Tense

Present.

3 [3
»• (.3

i$ muy, I am *1
tu mufit, thou art | ^
cr roup, he is I g
njir miiffcn, we are f g
il;r muifct, you are | o
fie miiffcn, they are J

id) miiffc, I may
tu muffeft, thou niayst
er muffc, he may
uric muffen, we may
i$r muffer, you may
fie muffen, they may ^

•is

mflffen, to be
obliged.

muffent, being
obliged.

Imperfect Tense.

fc < 2

* ri

8 J*
* (.3

id) imifftc, I was
tu mutjtfft, thou wast
cr mujitc, he was
mir muitcit, we were
iOr mujitet, you were
fie mugtcn, they were„

id) mufte, I might
tu mu§tcft, thou mightst
cr muptc, he might
loir mufiteu,we might
i$r ntuptct you might
fie muf ten, they might „

i
i

•

Perfect Tense.

Perfect.

>. <{ 2

* P

* 1 3

id) fra&c gemufit, I have been
tu tyaft gemupr, obliged, &c.
cr Imt gemufit,
wit fraben gemufit,
il;r Isifrct gemufit,
fie fufren gcinujit,

Pluperfect Tense.

id) Mc gemufit I may have
tu f)aUfi gemufit, been obliged,
er \)<\U gemufit, &c.
teir y afcen gemuft,
tyr Jfabtt gemufit,
fie $abcn gemupr,

Pluperfect Tense.

•

gemuft ^abci-,
to have been
obliged.

gemuft,
obliged.

•

3 (3

id) battc gemufit, I had been
tu fcattcfl gemufit, obliged, &c.
cr (nittc gemufit,
njir fatten gemufit,
ibr tyattct gemupt,
Tic fatten gemufit,

First Future Tense.

id) b&ttc gemufit, I might have
tu $Atteft gemujjt, been
er tyattc gemufit, obliged, &c.
urit fatten gemufj t,
if;r Htttt gemufit,
fie tyittten gemufit,

First Future Tense.

First Future.

S (3

* u

id) u>erte miiffcn, I shall be
tu ivirft muffen. obliged, &c.
cr nrirb miiffcn,
rcir tocctcn muffen,
it?x* ivcrtct miiffcn,
fie totttcn miiffcn,

id) tverte muffen, (if) I shall be
tu tecttcfl muffen, obliged, &c
er werte muffen,
»ir njerten muffen,
ir>r roettet muffen,
fie iverten mujfen,

id) touvte "
tu teiirtcft
er tvurte
»ir hjurtcn
i\)x tourtct
w njuvten ^

***

iJS)

Second Future Tense.

Second Future.

t 2

« (3

« ( ]
5 2

* (8|

id) tocxU ""
tu teirfl
cr n>irb
wir luertcn
tyr iwrtct
ftc Jverten

c - I shall have
<§ been obliged,

r OiL

3
£

ic$tt?erte "1 c - (if) I shall
tu wcttcft I »g have been
er hxrte 1 £- obliged, &c.

tor tuertct | g
fie trcrtcn J **

id) tourte
du hjuttcfl
cr toutte
sir mOitcn
^r tefirtet
te toflrten ^

£5-2

it* 3 O

c ° a

(12) Remarks on muffen.
The German miiffcn, and the English must, are very nearly equi-
valents. The predominant power of the word is everywhere
that of obligation or necessity, and this being kept in mind, it

will often be convenient to employ in translating it such words
as, be obliged, am to, lave need to, and the like. Often an
infinitive is understood with it : as, i$ mup jutucf, I must (70)
back.

LESSONS IN CHEMISTRY.

113

LESSONS IN CHEMISTRY.— No. VII.

Lst us now contrast the properties of the two gases which
have already come under our notice. You will remember
that although hydrogen gas is the one alone to which our
direct attention has been given, sulphuretted hydrogen, other-
wise called hydrosulphuric acid, has also come before our
notice as an agent for distinguishing one metal from another,
and effecting their separation. Let the operator now study
the characteristics of the two gases by contrast. For this
purpose, fill some bottles with these two gases respectively ; a

Eneumatic trough may be used, and water employed as the
quid ; for although hydrosulphuric acid gas be absorbable by
water, nevertheless, if we avoid agitation, and if we apply the
water. a little warm, the gas will not be absorbed to an extent
sufficient to interfere with our collecting a competent portion.

Referring to the preceding lesson, you will remember I!
therein described certain tests or trials to be made on hydro-
gen. I need not repeat the instructions, but I want the reader
to repeat the experiments, and arrive at his own deductions.
Let him pay especial attention to the heaviness or lightness of
sulphuretted hydrogen, (he will soon see which). Let him
observe its action on blue turmeric paper. Let him observe
whether it be a supporter of combustion, or a combustible ;
and whether it be absorbable by water.

Having gone through these experiments, the young chemist
will scarcely fail in the recognition of this gas, wherever it may
exist. Rut the most remarkable test still remains. Reader,
what do you think it is ? Perhaps you think the test in ques-
tion is the result, — the white precipitate which ensues when
sulphuretted hydrogen is brought into contact with a solution
of zinc. This supposition would be in the right direction, but
you will not fail to observe that the result would have been
much more easily seen had the precipitate been black instead
of white.

Now by far the greater number of metals do yield a black
precipitate with this gas — amongst them lead. If, then, we
immerse a slip of paper in any solution of lead, say the acetate
of lead for example, such paper becomes a test for sulphuretted
hydrogen gas, which it immediately affects with blackness,
and no other gas will accomplish this. The blackening of
white paint is due to the same agent. The atmosphere con-
tains sulphuretted hydrogen derived from various sources,
especially animal emanations, and the products of the combus-
tion of coal ; hence the blackening of the paint. Harrogate
water, and many other medicinal springs, contain this gas
dissolved ; hence the danger of a lady bathing in such waters
if her skin be covered with certain mineral cosmetics. Her
akin from pure white becomes black. This gas is evolved from
the hair, and on a knowledge of this fact depends the opera-
tions of hair dye, the best of which is made by adding liquor
potassse to sugar of lead solution, until the precipitate at first
formed becomes dissolved. A lead solution thus results, with
which if the hair be bathed, a black tinge is the result.

Perform now these experiments. Take a bottle filled with
hydrosulphuiic acid, agitate it thus, fig. 36, in some cold water,
and observe how the water gradually rises on account of the

Fig. 86.

Repeat the same experiments with hydrogen, and observe
jhat no absorption takes place. Next, mix hydrogen ard
aulphuretted hydrogen together in any proportions you muy
lease, and effect their separation by

(1.) Agitation with water.

(2. ) Agitation with lime water or cream of lime.

(3.) Or, with a metallic solution, say acetate of lead.

Now I will suppose you to be applying this knowledge, or

omething like it, to a case of ordinary life. A bottle lull of

gas — an empty bottle as you might have called it before you

egan the study of chemistry— is brought to you, with a request

that you will determine whether sulphuretted hydrogen gas

he present or the contrary. After our preceding investigations,

you now know that if sulphuretted hydrogen be present, the

as will blacken a slip of paper dipped in sugar of (acetate of)

»ad, and you would find that the result which holds good for

mixtures of hydrogen with sulphuretted hydrogen, also holds

good for mixtures of carburetted hydrogen (coal gas) with

sulphuretted hydrogen ; viz., all the latter admits of separation

y being agitated.

(1.) With cold water ; or better
?2.) With cream of lime,

(3.) Or, with a metallic solution (acetate of lead).
One experiment more with sulphuretted hydrogen. Gene-
rate some in a bottle with cork and tobacco-pipe stem ; ignite
he jet which escapes, and hold over it a glass tube thus, fig. 37.

Fiy. 37.

absorption of the gas. Repeat the experiment with lime
water, or rather cream of lime or solution of sugar of lead
and remark that the solution is still more rapid.

Now apply the nose to the other end of the tube, as near as
you may find agreeable, and remark how totally the original
odour of hydrosulphuric acid gas has been altered by combus-
tion. The smell now is exactly like that of a burning sulphur
match. Now apply a slip of blue litmus paper moistened
with water, to the cool end of the tube, and remark that
although the smell has changed, the result is still acid.
Remark that the acid will no longer blacken lead paper, and
that it will bleach a red rose, llencc the acid gas resulting
from the combustion of sulphuretted hydrogen is sulphurous
acid, because no other gas bleaches red roses and smells like
burning sulphur. Sec how readily substances are known by
the application of chemical deductions. Again, observe that
the interior of the glass tube employed in the preceding
experiment is probably at the commencement of the operation
bedewed wiih moisture ; at any rate, if the jet be caused to
burn under an inverted tumbler, moisture is seen ; hence the
presence of hydrogen in sulphuretted hydrogen would be
demonstrated, even had we not been aware of its existence
there. A diagram represents the change still moro clearly : —

17 Hydrosul-

phuric acid or

Sulphuretted

hydrogen

1 Hydrogen-
16 Sulphur-

-9 Water

■32 Sulphurous acid

120

/ 1G Oxygen
The atmosphere ! 8 Oxygen
(96 Nitrogen
In this diagram, I have avoided all fractional numbers for
[the take of greater clearness; and the student having seen

114

THE POPULAR EDUCATOR.

thus, much of diagrams, is requested to make a diagram
(I do not insist upon atomic figures) of the decomposition
which takes place on the addition of dilute sulphuric acid
to the sulphuret of iron. All the elements of this decom-
position have been discussed directly or collaterally, so that I
have no doubt my students will be able to frame the diagram.
Resumption of the Metals. . Having commenced these lessons
with a sketch of the chemical relations of zinc and manganese,
more especially as relates to the reagency of hydrosulphuric
acid ana hydrosulphate of ammonia, we then branched off
collaterally into a discussion concerning the properties of these
two gases ; which discussion being brought to a conclusion,
for the time at least, back we return to the metals once more.
Notwithstanding the digression, we have not wandered so far
from the study of metals as the reader may have supposed.
This light and invisible gas — hydrogen — has many of the pro-
perties of a metal ; indeed by certain chemists it is considered
to be a metal ; at any rate, it has the singular property of com-
bining with two metals in a marked degree, and with a third
to a less extent. These metals are arsenic, tellurium, and
antimony, This circumstance furnishes us with a sufficient
link of connexion to lead us at once to arsenic as being the
most important metal of the three ; but there is another con-
necting link. Arsenic, as I have mentioned already, is one of
the few calcigenous metals (don't pass the term calci-
genous without understanding it, I have explained its meaning
once) — one of the calcigenous metals which does not yield a
black precipitate with hydrosulphuric acid ; so let arsenic be
our present theme.

The student has heard of arsenic frequently enough ; he
has perhaps, however, never seen it, for the true arsenic, i.e. the
metal arsenic, is rare. What people usually call arsenic is
really a white powder, a combination of arsenic with oxygen ;
in like manner, the substance usually called manganese is
really an oxide of the true manganese, which is a brittle metal
something like steel in aspect. Arsenic is also a resplendent
brittle metal, as will be evident hereafter.

The substance I wish you to take for the purpose of study-
ing the general properties of arsenic, is the white arsenic of
the shops. There will be some difficulty in procuring this,
however, druggists not being allowed to sell it, except dis-
guised by the mixture of other substances ; perhaps, therefore,
the easier, and certainly the safer plan, will consist in the
purchase of about a drachm of a very weak solution of white
arsenic, used in medical practice under the denomination of
liquor arsenicalis. The strength of this solution is one
grain of white arsenic in fluid ounces ; a very weak solution
consequently, but strong enough for our purposes.

The experiments about to be performed are not theoretically
interesting merely; they will comprehend one of the processes,
and perhaps the best of a J, followed in the process of extracting
arsenic from bodies which contain it. The objects I shall have
in view are — firstly, the extraction of arsenic from the liquor
arsenicalis ; secondly, the examination by tests of the arsenic
thus extracted.

Experiment 1. Take a bottle with tobacco-pipe shank and
perforated cork. Pour into the bottle, the usual fngre-

Fi ? . 38. •

ric acid ; replace the cork, and ignite the escaping jet. Hold
over the latter firstly, a white plate in such a manner that the
jet of hydrogen flame may play against the plate, fig. 38. If
all the materials be freed of arsenic, the hydrogen will leave
no stain.

Secondly, repeat the experiment, substituting for the plate
a piece of glass tube open at either extremity, and about a foot
long ; the diameter of the tube may be about the fourth or the
third of an inch. Again, if arsenic be absent from the materials
employed, the burning flame will impress no stain.

Remove now the cork, pour into the bottle a small portion
of liquor arsenicalis, and repeat the experiments with plate
and tube as before.

The flame will now be recognised to evolve a dense smoke,
which may be white or black according to circumstances. If
collected from within the flame thus, fig. 39, the stain is black,

rigr. 39.

being composed of particles of metallic arsenic ; if collecte 1
without or above the flame, thus, fig. 40, the deposition >s

Pigr. 40.

white, being in this case white arsenic, otherwise called
arsenious acid or oxide of arsenic. The conversion of
me tall ; c arsenic into its oxide is most readily observed
in the tube experiment, wherein the black crust of me-
tallic arsenic which extends a certain way up, hmj to

Fi*. 41.

changes to white arsenic, say at b, and eventually
escapes. Whilst operating with the tube, do not forget to smekT^
the garlic-like odour produced by the metal arsenic whe
volatilizing. This smell is an important indication of t*^

presence ri the metal. I need not direct the learner's atten
„ _„ -- _- _. f .... „ — _ «.„.*v™ r ~«. to the curious fact, that the peculiarity of hydrogen gas, wi

LESSONS IN GREEK.

115

we have just been investigating, namely, its property of com-
bining with arsenic and carrying this metal away in the form
of gas, presents us with an elegant and a powerful agent of
analysis. Supposing arsenic to exist in the contents of a
stomach, it may be extracted in this way ; or supposing a
compound to exist of the three metals already examined, i,e m
sine, manganese and arsenic, and supposing it desired to remove
the arsenic, this might easily be done by adding to the mixture
dilute sulphuric acid, and thus driving the arsenic away in
the form of arseniretted hydrogen gas. finally, the zinc and
manganese might be separated, as already described at p. 78.
Having thus indicated the general method of obtaining —
eslrmettng — arsenic from liquor arsenicalis, we will in our next
lesson resume the subject, with the special view of obtaining
from the fluid in question a sufficient amount of arsenic in
the form of arsenious acid to prosecute our experiments upon.

LESSONS IN GREEK.— No. XIII.

By John R. Beard, D.D.

(Continued from page 100.)

Exercises from the Book of Proverbs.

1. Yioc owpog tvfpaivtt irartpa, v'tog ft a<j>pu>v Xvirn ry pnrpt.
2. Tlivia ait pa rairttvdi, x"P'£ ^ c avfpttiov irXovrt£ov*tv. 3.
BvXoyia Kvptov cirt KtfaXifV fixatov. 4. Mvrjfirj fiKaitov
fur tyxupnov (sc. tari), ovoua fe aatpovg afitvvvrai. 5.
Miaog tytpti »'«*<>£. 6. 'Oe (k x^Xtutv irpoaftptt aoftav, pafiftp
rmcrti avfpa aKapfiov. 7. Avnp ciyXioaaog airoKaXvrrrti
fiovXag tv avvtfpup, iriarog ft rrvog Kpvrrru irpaypara. 8.
IVvif avfptia ortfavog ry avfpt. 0. Aoyov afiKov ptrrtt
fixaiog, aatftng ft ai9\v%>trai. 10. "Ztfnpog aiftjpov oKvi'tt,
avnp ft irapolwu irpoawirov traipov, 11. 'Qarirep fpoaog tv
ap^ra, gat wairtp vtrog tv Btptt, ovrwg ovk tanv a<pnovi rtpn
12. AnavQai tpvovrai tv x (l P l p&vouov, foitXtta ft tv %api rwi>
afpovw. 13. "2o<pia Kai tvvota ayaBn tv irvXaig aofwv (sc.
tunv)' tftyot ovk tKKXivovatv ik orouarog Kvpiov. 14. Airo-
BvtjtrKti *ajp<ov tv apapnaig. 15. M17 \aipt tin KaKOirototg,
ftnft ZnXov apapriaXovg. 1G. Qofiov rov Of or, vie, Kai (3a<ji\ea.
17. Aoyoig aoftov irapafiaXXt oov ovg, Kai aKovt tfiov \oyov. 18.
VXtnpoavvt) cat aXtOtia (pvXaKTj fiaatXti. 19. Koapog vtavtatg
aofif, 8o£a ft irptafivrtpuv iroXtai. 20. Ila? avrjp Qatvtrai
iavrift fueatog, KartvBvvtt ft Kapfiag Kvpiog. 21. XicoXavrov
woe, rat vfipiGTiKov ptBn, irag ft a<f>nwv toiovtoiq avpirXtKtrat.

Vocabulary to the Fassages prom the Proverbs.

1. tvfpaivta, I rejoice (transitively) ; Xi»tij, ng, 1), grief.

2. irtvta, ag, >/, poverty; rairttvow, / lower, degrade ;
avfpttog, a, ov, wanly, excellent ; irXovn^ut, I make rich (from
what noun is the verb dcriied r)

3. tvXoyta, ag, »/, a blaming (what nre the components of the
noun ?) ; Kvptog, ov, b. lord, matter, the Lord, that is, the Al-
mighty, in the Old Testament ; fiKaiov for rov ftxatov, the
article is often omitted in the Greek version of the Hebrew
Scriptures : this version is called the Septuaginf, sometimes
"the Seventy," because said to have been made by that
number of learned Jews at Alexandria in Egypt ; the transla-
tion was completed in the second century before Christ.

4. nvnpn, ng, 1), memory, the memory ; tyKtapiov, ov, to,
JwotM, eulogy, our word encomium ; avtfing, ovg, impiou*, com-
ptrt 0t0opat, Itcorehip ; fffitvvvfii, I extinguish ; vptvvvrat, is
extingviihcd, that is, destroyed.

5. /luroc* ovg t to, hatred, connected with fin?tu>, I hate;
mueoc, ouc, to, strife ; here is exemplified the remark that the
Seventy are given to the omission of the article, for in Attic
Greek this proposition would be to piaog tytpii to vetKog.

6. oc, the relative pronoun he who ; x l &°€* °^C> T0 * a l*P »
pa&itv, 9v, to, a stick, staff; axapfiog, ov (from a, not, and
copftto, the heart), heartless, senseless.

7. fiyXwtrtrog (from fig, twice, and yXwrra, ng, 7), a tonoue)$
double tongucd ; airoKaXvimo (airo t from, and KaXvirno, J hide)
I conceal; ovvtfptov, on*, to, an assembly, hence our word sanJ«>~
drim, the name of the Jewish Parliament ; rrvoii, ng, t), a
breathing, breath; marog here would in classical Greek be

6 WlflTOC.

8. artfawc, ov, 6, aeroim, hence our proper name Stephen.

9. aivxvvopat, lam asha med 9 from aurgoc, ovc, hatefulness,
shame.

10. atfnpog, ov, 6, iron ; o£ii'w, I sharpen ; in irapognvci, tlie
preposition rrapa sirengthens the force of the verb ; eratpoc,
ov, 6, a companion, friend.

11. aptjrog^ (from apaw, I bind in bundles), harvest time;
vtrog (from vttv, Lat. phiere, to rain), rain; Btpog, ovg, to,
summer.

12. arai'Oa, ng, >/, a thorn ; 0t/w, I prodwc (Lat. fui, I was),
(pvofxai, I am prwlueed, I am bom, I spring up.; ptOvapog (from
pt9v, wine, strong drink), drunken; a<ppwy, ovog (from a and
fpnv), senseless, foots.

13. tvvota, ag, 1), sense (from tv, in, and vovg, the mind),
trvXn t i|ff,>), a gate; uckXivw (tx,from, and kXivui, I bend), I turn
away.

14. airo9v7j<TKt*> (aico,from, and QvnaKio, I die), I die ; apap-
ria, ag, »), sin ; consult aftapTavta, already explained.

15. xaipoi, I rejoice; Kaicotroiog, ov, b (tcaKog, evil, and
rroietoy I do), an evil-doer ; ZnXota, I desire, envy ; ajiaprotXo^
(afiapravui), a sinner.

16. foptopat, I fear, reverence.

17. irapapaXXta (irapa, near, paXXw, I throw), I apply to ;
o-oc, thy, here the personal pronoun is used for the article,
ordinary Greek giving to ovg ; tpog, my.

18. tXtnpoavvn (from tXtog, pity), mercy; hence our word
eleemosynary, which, through the old En*glish almcsse, is con-
tracted into alms.

19. wpeafivTnp (our presbyter, whence our priest), an old
man ; rroXtog, a, ov, bald, grey ; woXtai, grey hairs (sc. rpix*li,
hair).

20. faivofiai, I appear; lavTtp, to himself; KartvQvvw, I
direct, guide.

21. aKoXaarog, ov (a not, and KoXaZto, I punish, restrict), wi-
restrainab/e, riotous; vpptariicog, ov, insulting : ptBn, tjc, >/,
drunkenness: roiovrog, such ; roiovreig, such things; avpirXtKtt
(ffvv, with, nd irXerw, I weave), I bind together ; avfitrXtxtrat, ii
entangled in, is chained to.

EXEUCISE3 FROM THE NEW TESTAMENT.

1. Maicapiog (sc. tartv) avnp og virofitvti Trtipaapov. 2.
'EKaoroc irtipaltrat viro rng if tag tiriBvptag. 3. '11 trrtOvpia
TiKTti afiapnav, 1) ft afiupna aieoKvtt Oavarov. 4. JIaaa fomg
ayaOi] Kai irav ftapnpa rtXtiov avtaOiv ««m Karaftaivov amt
rov ITarpoc riav ipuruv. 6. Opyn avfpog fiKaioevvr,v Ocou ov
Kartpyafarat. 6. TivtaOt voinrai Xoyov, rat pn povov aKpoarat m
7. QpncrKCia tcaBapa Kai apiavrog irapa Tip i)np Kai Uarpi avrn
tonv, treiaKtiertaOai opfavovg Kai XWC lv T 9 9Xi^/ti avrwv,
atnriXov lavrov rnptiv awo rov KOtruov. 8. "H avwBtv aofia
rrpiarov fttv ayvrj tanv, tirtiTa tipnriicn, tmtiKtjg, tvmt9nr
ptarn tXtov Kai Kapirwv aya9wv, aciaKpiTog, avviroKpiTog
KapTTog ft fiKaioavvng tv tipnvg airtiptrai Toig irotovaiv tipqvrjv.

9. UoBtv iroXtpoi Kai iroOtv pa\ai tv vptv ; ovk tvrtvBtv, tK

TtJV t)f0VMV i'fllOV, TbiV GTpaTtVOptVU)V tV TOUJ ptXtaiV VpttiV.

10. Mocx'ot Kai poixaXiftg, ovk oifart ort >/ <piXia rov Koapov
t\9pa rov B«ow tariv. 11. 'O Qtog virtpttfavoig avriraoatrai,
rantivoig ft fiftaai x a n '' 12. £«C tartv b vopoBtrng Kai Kptrng,
6 fvvaptvog ataaai xat aroXtaat. — The Epistle General of James.

Vocabulary to the Extracts from the New Testament.

" 1. MaKaptog, a, ov, happy, blessed; viraptvu (viro, under, and
utvta, I rtmain), I endure; frtipaauog, ov, 6 (irtipafa, I try,
tempt) trial.

2. iKaarog, n, ov, each, every ; if tog, a, ov, one's own.

116

THE POPULAR EDUCATOR.

3. airoKvtw (euro, from, and Kvta, J conceive, am pregnant), I
bear, I bring forth; Qavarog, ov, 6, death.

4. Soaig, eug, i), a giving ; Btaonua, arog, to, a gift ; TtXuog,
a, ov, perfect ; avtoBtv (ava),from above, the termination Qtv
gives the idea of frotn, [ compare in Number IX., rroOiv and
tvrevBiv; Karafiaivu) Uara, down, and fiaivu>, I go), I come
down, tan Kar, literally, w coming dotcn, is constantly com-
ing down — a beautiful description of the constancy of the
Heavenly Father's goodness ; 0<uc, fwrog, to, light.

6. opyn, ng, t) (the root of opeyouai), desire, effort, a strong
emotion, anger ; Siicaioavvn, ng, i/, justice, just designs ; rarep-
yaZopai (icara, down, thoroughly, and tpyov, a work), I accom-
plish.

6. yivouai (the old form of ytyvofiai, compare yivog, a race*
a kind), 1 become ; iroinTng, ov, 6, a doer, a maker, hence our

,poet, the great maker, that is, inventor; atcpoarng, ov, &, a
hearer* *

7. Qpnaicua, ag, »/, service, God's service, religion ; icaOapog,
a, ov, pure; auiavrog (uiaivta, I spot), unspotted; cat, even,
that is, ovTog, avrn, tovto, this; nriaiceirrouai (tiri, over, and
ffKiicTOfiai, I survey) I overlook ; from the same root is our
bishop, that is, an overlooker, a superintendent; opfavog, ov,
6, our word orphan; \npa, ag, t), a widow; G\i\ptg, nag, t),
affliction ; avrutv, of them, their ; aairtXog, ov, unstained {tririXog,
a stain), rnptw, I keep, preserve.

8. ayvog, n t ov, chaste, holy ; nptorov, in the first place,
trrtiTa, then, in the second place ; ttptjviKog (upnvn, peace), peace'
ful; tKULKtjg, mild; ivwuOng (ireiOta, I persuade), easy to be
entreated; uiarog, n, ov,full; aSiaicpiTog (a, not, 8ia, through,
koivu), I distinguish), without partiality ; avviroKptrog (a, not,
the v is interposed between the two vowels for the sake of
euphony ; vrro, under, and Kpivta, hence our word hypocrite),
without hypocrisy ; <nrtipio } I sow ; roic iroiovaiv, for those doing,
that is, those who do or pursue.

9. iroOtv, whence; ivrtvQtv, thence; vuuiv, of you, your;
orpaTtvopai, I war; rwv vrpar, which make war; utXog, ovg,
to, a limb, member ; vuiv, in yon*

10. Moixoft ov, 6, an adulterer ; uoixctXig, l8og % //, an adul-
teress ; ovk oiCaTf, know ye not ? cx#pa, ag, y), hatred.

11. virtpntyavog (virep, above, high, too much, and <paivu>, I
show), haughty ; avriraaaouai (avrt, against, and raaaut, I set),
I array myself in opposition to; ranttvog, n, ov, low, lowly,
humble ; £tcWc, he gives.

12. vopoOirng (vopog, a law, and Ti9njii, I place), a lawgiver ;
tivvapcu, I am able;. 6 dvvau. who ts able; ooj£<jj, I save;
airoXXvui, J destroy; auxrai and airoXtoai are infinitives
governed by 6 tivvautvog.

LESSONS IN ALGEBRA.— No. VIII.
REDUCTION OF FRACTIONS.

129. To reduce fractions of different denominators to fractions
having a common denominator.

Multiply together each numerator and all the denominators
except its own, and the product will be the required numerator of
each fraction ; next, multiply together all the denominators, and the
product will be the required denominator of each fraction ; these
properly arranged in order will give the answer.
Examples.

1. Reduce — . — , and — to fractions having a common de-

b d* y °

nominator. .

Here, aXd*y=ady, } ^

<?X by. y=xby, rare the three numerators,
and, mXbXd=mbd,J
Also, bXdXyzzbdy, is the common denominator.

Hence, the reduced fractions are -r-r-, -t?-. and -rr— . Ana.

bdy bdy bdy

The reason of this rule is plain, for the reduction consista in
multiplying the numerator and denominator of each fraction into
all the other denominators, a process which does not alter the
value of the fractions ; see Art. 120.

ft _ , dr 2h . 6c

2. Reduce — — , — , and — to fractions having a common

om g y °

denominator.

An 8.

An.. ±~± r% «nd -,—5

dgry 6hmy IScgm
3gmy ' 'dgmy * Zgmy *

2 a r4-l

3. Reduce --, — -, and -~-r to fractions having a common

denominator.

A 2(fje +M * 3ff</+3aA 3r^c+3j;

AM ' Zdx+Mjf 3^+3/1^' Md Mx+Mx

4. Reduce — t-t, and - — -- to fractions having a common de-

a-f-o a—b

nominator.

a+b
a 3 -* 3 *

130. An integer and a fraction are easily reduced to fractions
having a common denominator, by making the former a fraction :
see Art. 121.

5. Reduce a and — to fractions having a common denominator.

c •

Here, a and — are equal to — and — , which are equivalent to
c \ c

ae b

-—■ »ad •— the fractions having a common denominator.

6. Reduce a, b, — and — to fractions having a common de-
nominator.

. amy bmy hy , dm

Ans. , — ^-, —^-, and .

my my my my

7. Reduce --, -—■, and — to fractions having a common de-

nominator. Ans. ^L, 1* and —. '
tdf' bdf b<tf %

a _ . Zx y 1

8. Reduce — , jt, and — to fractions having a common de-

nominator.

9. Reduce
nominator.

10. Reduce
denominator.

11. Reduce
nominator.

12. Reduce
denominator.

30&r lay bah

An9 ' Toll 1 iQaT> and 10^'

b, — and - to fractions having a common dc-
9 *

. Iby 2x , cy

Ana. -—-, --, and --.

2y ' 2y 7y

* o 3c , 1

"T» ~» -~t *nd -— to factions having a common

t* s y j

Zxyz 3aby 9acz , ayz

Ans. r , — —, , and — - — •

Zayz Sayz Sayz 3ayz

Sx b x

~j -r-% and — to fractions having a common de-

60&c 6ab -iacx
An§ -50^'20i7» 1,ld 20^

a 5 8a 1 " .

■t-> -yt — » and —- to fractions having a common

. 28arv UOby 224bx Iby

LESSONS IN ALGEBRA.

117

13. Reduce — . 17, — , *, and — to fractions having a com-
x c 4a

\6a*c GSocx 4axy 4aex 2 , c*x

Ana. —. , — , , — , and .

4acx 4aex Aacx 4acx -4acx

14. Reduce -rr? and -777 to fractions haying a common de-
a*b* a*b* °

0. Reduce ax-\ — — to an improper fraction. Ans. — •

a a

c bd — by^-c

7. Reduce £— -j— to an improper fraction. Ans. — .

8. Reduce x*-t-a#-}-a s -| to an improper fraction.

a 9 b* a a b 9

16. Reduce -. . fl , — r-r and — r to fractions having a

1 denominator.

x*+x*+x+l

ax — a

Ans. — 1 — r v**
x*—l

* 4 -l

16, Reduce -r : — rr and — r— to fractions having a corn-
s'— os+a 11 a?+a

men denominator.

xt—ax+a 1

Ans.

* 3 +a J

and

*»+a 3

Ans.

9. Reduce 2*— 4a+

7a 3

x+2a

to an improper fraction.
Ans.

2* fl — a*

10. Reduce 3a— 4.r-|- , * ■ to an improper fraction.

<r+2a *

4a— 3s

Ans*

12a 9

4a— 3*'

2 3

17 - **«* "5P "5P -5P ■i" - F to fractionf

fearing a common denominator.

ZOedef 40adef 45abef 48abcf bOabcd

Ani# Wabcdef' Mabcdef 60abcdef GOabcdef ** 60abcdef'
131* To reduce an improper fraction to a whole or mixed
quantity.

Divide the numerator by the denominator, the quotient uith the
remainder in a fractional form is the answer : see Art 105.

Examples.

1. Reduce a0 ~T°' n ~K , to a whole or mixed quantity.

Ans. «+m+ —

2. Reduce **— *Wy— **' to a whole or mixed quantity,

Ans. M-l+ay- J Z

132. To reduce a mixed quantity to an improper fraction.

Multiply the integer by the given denominator, and add the given

numerator to the product ; see Art. 121. The sum wilt be the

ne mir t d numerator ; and this placed over the given denominator will

pm the improper fraction required.

If the sign before the dividing line is — , all the signs in the
Buneratormustbe changed ; see Art 123.

Examples.

1. Reduce a-4- — to an improper fraction. Ans. V*

If Qc—b

2. Reduce a to an improper fraction. Ans. .

c c

a—c abx—a^c

3. Reduce ah to an improper fraction. Ans. — .

x x

r *

4. Reduce m4-d— - — - to an improper fraction.

h — a

11. Reduce 1 — - — - to an improper fraction. Ans. -—
x+a x+a'

133. To reduce a compound fraction to a simple one.

Multiply all the numerators together for a new numerator and
all the denominators for a neio denominator.

Example.

2 a 2a

1. Reduce —of -. ,— to a simple fraction. Ans. r-r-: — ■•

7 b+2 r 7b+li

2 4 b-\-h

2. Reduce ~ of — of -r~- — to a simple fraction.

3 6 2a — m r

Ans.-J*±^_
30a— 15m '

a fl c a e A aW '

3. Reduce — of —- of — to a simple fraction. Ans. -———-.

b rf* p r wy*

a 2 b* c* a*b*c*

4. Reduce — of -=• of -r? to a simple fraction. Ans.

b c % d %

d 9 '

, ^ * x 2 —ax-\-a 2 ,x+x A . . # .

5. Reduce -=-r — -7—7 of to a simple fraction.

ar+a.i'+a' 1 x — a

Ans.

*"-a"

6. Reduce ?flzt?±! of **+*, to a simple fraction.

^+4*— 3

. tnh +dh — md^rd 2

5. Reduce x 2— to an improper fraction. Ans,

A-d

or— a — b

a- 9^-13x+4
*»_19;r+l2 •

7. Reduce — of — of -— . to a simple fraction.
7 3 8— a

Ans.

108— 21a

Examples for Practicb.

1. What is the value of r^ ? Ans. 4.

3oxy

. aalbceddff . . ' , . .

2. What is the value of — ^ JJ ? Ans. abedf.

S. What is the xaluo of — X4 ? Ans. 44.
a

4. What is the value of -H* ? Ans. 4y.

£. What is the value of -^ when the denominator is multiplied
fry A} Ans. 2x.

118

THE POPULAR EDUCATOR.

6. What ti the value of-—? when the denominator u divided by

24ax
3
Ciix? Ans. — axy.

Mabx

7. What is the value of — — — when both numerator and de-

o4a

nominator are X,2d} Ans. — bx,

8. Reduce —. to a whole or mixed number.

2ab

Ans. Zc-\-6z.

9. Reduce =-tt to a whole number. Ans. 4a — 2y.

12*

10.

i. Reduce /**■*» — 'T <tx 'T a — ^ a wno ] e or mixed number.

Ans. b-\-x-\-m-\*
Reduce the four next examples to their lowest terms.

e+dx

H. J*. Ans. A. 12.
oae a

^-.Ans.- 1 -. 13.
12*yy 4y

4*+oy

Ans. £+2 14. — »—« » Ans. f3£"L,

15. Reduce — and -j to a common denominator. I
yd \

Ans. -^and^.
dy dy '

o f

16. Reduce ~, ~, — , and — to a common denominator.
b d g y

AnM adgy begy bdfy bdgx

•A 118 * tt— • 77-.» T7ZT' and hj„.'

bdgy bdgy bdgy

bdgy*

b+c

17. Reduce a— —-*— to an improper fraction.

Ans.

ax—b

=*.!

18. Reduce a+& j-^ to an Improper fraction.

Ans. 4aa> -Hfa»-Hy

2oav

2 a c x * **<&

1 9. Reduce ^ of — of — of — to a simple fraction. Ans. — -.

2 2x „ 4ab m 2e m 4dx , abc .

20. Reduce y of ^ of — - of — of — of -^- to a simple

fraction. Ans.

abc*x

ADDITION OF FRACTIONS.

To add fractional quantities together.

134. Rule.— Reduce the given fraction* to fractions having
a common denominator if necessary ; then add their numerators,
.-, ml place the sum over the common denominator,

EXAMPLE8.

2 4 2-4-4 6 3

1. Add — and — of a pound. Ans. -^j- or ^ = -g- of a

pound.

2. Add L and L together.

b d *

Here, reducing them to a common denominator, they become

od , be . . . a d-\-be

— and —, whence their sum is — =3- . Ans.

la oa ■ oa

3. Find the sum of -r and ^ — .

3Ai»-2r</— rf 3
Zdh

m «. , , * * . *— * w * ay—bd+md

4. Fmd the sum of -r and . Ans. r- 1 .

a y dy

a d am — dy

5. Find the sum of — and . Ans.

~ « » «• , . a 2 -X~b"

C. Find the sum of — n and - L . Ans. — = — r a .

a-\-b a—b a* — b £

y — n

— a — A . ar — am — dh

7. Add —j- to Ans. — — .

8. Add ^=i- to ^i?. Ans. -G.

9. Add y,—, and —together. Ans. ^

. « . , , 2**/ hx . ax , 2

10. Add—^-, —.and together.

2 ' y' c ^ a

flcy •

11. Add a+ —, ^ , xy and -^- together.

i x 4

Ans. o^+^^figlll.

12. Add 42- -,<*— ^-, and *+ ^- together.

Ans. 42+2*—

"•Aaig-^^^-^-^-r.

Ans. y+
6

4a+4q*— 2*+2y

14. Add *+*, *±1° and - -5*j±L together.

Ans. 2«— 36+5j?+9;

135. For many purposes, it is sufficient to add fractions in the
same manner as integers are added, by writing them one after
another with their proper signs.

15. Find the sum of -r-, — and 5-—.

a 3 d

Here, the sum is simply -^- -| r— . Ans.

136. To add fractions and integers together.

Write them one after another with their signs; or convert the
integers into fractions, reduce the fractions to a common denominator,
and then add as before,

. o . . . b amA-b

1. What is the sum of a and - ? Ans. a-\ or — .

m 'mm

2. What is the sum of 3rfand —2— ?

m — u

An.. Sd+ ■J±J„y^»W*,

m—y

w— y

3. What is the sum of 5a* und — — ?

An..5,+ g±gor 5 »-Kgfr.

KEY TO LATIN EXERCISES.

119

A KEY TO THE EXERCISES IN THE
LATIN LESSONS.

By John R. Beard, D.D.

{Continued from page 75, Vol, IV.)

Vol. III., p. 113.— Latin-English.

How gieat your labour 1 alas I how wretched I am! O the
deceptive hope of men, and their frail fortune and our empty
strifes ; by the faith of gods and men ! what great undertaking,
sacred Jupiter, was ever accomplished not only in this city but in
all lands ! alas ! my labours have been undertaken in vain ! O my
fallacious hopes, and empty thoughts ! lo ! here is the reason why
the law was passed ; aha ! you have a talent of silver ! I write a
letter; I whip a dog; the son loves his father; the Romans
conquered the Carthaginians ; Scipio destroyed Carthage ; the
very swift foot-soldiers were able in running to keep up with the
cavalry; serene peace befits men, fierce rage (befits) wild beasts ;
red hair is no discredit to a man among the Germans ; let prudence
never fail [in the note for infinitive read imperative] the orator;
Themistocles did not escape from envy on the part of ,his fellow-
citizens ; Ulysses wished to withdraw from warfare ; fortune assists
the brave ; you think that I am a rival of Agamemnon ; glory, like
a shadow, follows valour ; brave and wise men are not accustomed
to seek to much the rewards of good deeds as good deeds' them-
selves ; Marius commanded in that part ; ho had formerly played
a similar game ; I dreamed a wonderful dream ; I am of opinion
that your fathers are alive ; I enjoy that kind of life which alone
deserves the name ; I have sworn a very certain ana very imposing
oath ; Siccius Dentatus had nine triumphs ; I cannot make the
same boast ; that I doubt not ; in that I agree with you ; Pytha-
goras visited the magi of the Persians; the consuls entered on
their consulship ; Pythagoras went to many barbarous regions
on foot ; I met no one>; all fates surround us on every side ; soon
the Roman legions besieged Carthage ; Scipio did not refuse a
conference ; history ought not to depart from truth ; the best plans
art forming ; this town is under siege ; a very large inheritance
comes into (your) possession ; they declare that cither by a letter
or a messenger they are approaching him as if king; Caesar went to
the colonies of his country; he wished to visit, and become
acquainted with those nations also ; with great hope I enter on
the remainder of my speech ; the mother called her son a brother-
slayer; Eunius has well said that anger is the beginning of
madness ; he named Sicily the nurse of the Roman populace ; the
recollection of pleasures we have enjoyed makes life happy;
cupidity and avarice make men blind ; the Carthaginians appointed
Hamilear their commander-in-chief; the people created Anous
Martius king ; Apollo judged Socrates to be the wisest of men ;
Socrates accounted himself an inhabitant and citizen of the whole
world* Ariovistus replied to Caesar that he should consider him
not sis a friend but as an enemy ; what is more foolish than to
account unoertain things certain, and false things true ? Cato, by
himself, is as good to me as a hundred thousand men ; Artaxerxes
asked the Athenians to let him have Iphicrates as a general ; do
you consider that nothing ? the Achaeans sought aid from Philip;
Verres (capital V) demanded from parents money to be allowed
to bury their chi'dren ; Caesar daily required corn from the Acdui ;
who taught Epaminondas music ? I have not concealed the con-
versation from thee ; know that my opinion has not been asked ;
Marina had learnt all military arts ; am I even now to be taught
to speak either Greek or Latin ? in that you give me excellent
advice ; this one counsel I give my pupiU ; Apollo is asked to
supply words ; you must inquire your way ; Epaminondas is taught
music ; Cato was asked his opinion ; the legions were conveyed
through Italy, Rhegium, and Sicily, and then from Sicily across
into Africa ; Miltiades reached the Chersonesus ; all hurry together
Into thehouses ; Mithridatcs sent ambassadors as far as Spain to
Cneius Pompey ; Caesar's soldiers go up under the mountain ; he
tent his forces across the Hellespont ; he commanded the army to
pass over the Rhine ; they pass the river on a bridge ; we con-
versed from eight o'clock till eveniug ; he will sleep till sunrise ;
he walked seventy miles; Arijvisus proceeded from his own
boundaries three days* march ; the plain of Marathon is distant
from tho town of the Athenians about ten miles ; the towers stand
eighty feet apart ; the Arabians have their swords about four ells
{JJJJSj »• ■oldicrs raised a mound three hundred and thirty feet
woaa, and eighty feet high ; Atticus for thirty years wanted no
medicine ; Appi Us waa manv years blind; Saguntum has now
Zj, Xh ™ years in the power of tho enemy ; the name of Pytha-
5JJLJ Houn *ned for many ages; Nestor had outlived two
S5J-T T" of men ; I 4m in my eighty-fourth year ; I sleep the
*w ttrough ; like Mercury in all things, both voice and com-

Vol. III., p. 113.— English-Latin.

Canem verberant ; Alius patrem amat ; epistolam scribis ; AngK
vincent hostes ; hostes victl sunt ab Anglis ; Carthago a Scipicne
deleta est ; pax fortes decet ; duccin Vcllingtonum feccrunt Angli ;
Napoleoneni nominarunt impcratorom Gilli ; vigentesimum ago
annum ; tricesimum annum ago [instead of age read ago] ; frater
multos menses caecus fuit; fossa decern pedes est lata; exercitum
transduxit flumen; somnium somuiavit Josephus ; alca ludunt;
illud dubitas ? illud uuhi concedunt ; regem adeo ; boni veritatem
nunquam egrediuntur; avnratia caecos reddit homines ; Socrates
sapiens est habitus; consul sentcntiam rogatus est; puellas
musicam docent ; Latinam docendi sunt pueri ; eheu me miserum !
vae tibi, maritc !

Vol. III., p. 130.— Latin-English.

Conon for the most part lived at Cyprus, Iphicrates in Thrace,
Timotheus at Lesbos; we were detained seven days at* Corcyra ;
Miltiadcs tarried in the Chersonesus; the Gauls went to their
homes ; great things were carried on abroad in those times ; M.
Drusus was killed at his own house ; I spoke those same things at
my house ; they carry gold and silver into the palace ; they invite
each other to their homes ; I am not at my ease in another person's
house ; at the house of Caesar there are no friends : many persons
assemble at his house ; the victory was announced at Corinth, at
Athens, and at Laccdeinon ; he was brought over from Apollonia,
a city of Pontus; the Romans came to the town Cirta; the
strangers are in the town of Citium ; Archiaa was born at Antioch,
formerly a celebrated city ; the soldiers stopped at Alba, a fortified
city that was near ; when I was directing my way to Mutina; there
was a look-down from Gergovia into the camp (castra) ; I intended
to go from Athens ; ambassadors came from Ardea to Rome ; a
vessel is ready for us at Cajcta; Socrates introduced philosophy
even into homes ; Antony committed impure deeds even in a chaste
family ; discipline flourished in that house ; Alcibiades was educated
in the house of Pericles ; he was said to celebrate mysterious rites
in his own house; they went to their own rural properties ; Pompey
being conquered by Caesar hastened to Alexandria ; the emperor
G alii en us was slain at Milan; Caius Marius betook himself to
Praeneste ; many famous Romans are said to have gone to Rhodes;
the Romans were brave at home and abroad ; at Delphi there was
a very famous temple of Apollo ; wherefore both kings and peoples
were accustomed to send ambassadors to Delphi, or to seek
oracular responses from Delphi ; the Romans sent ambassadors to
Athens; Demaratus had fled from Corinth to Tarquinii in Etruria;
we are punished by negligence in many things ; they arc in fault
who desert their duties through weakness of mind ; I beg you to
think that I write to you more rarely than I was accustomed, not
through forgetfulness of you, but through my bad health ; anxiety
had taken possession of -the senators lest the people through fear
and anger should appoint military tribunes ; I almost lost my
senses through excessive joy; the pilot's art is praised for its
utility ; one ought to grieve for a misdeed, and to rejoice at correc-
tion ; I am wont to rejoice in nothing so much as in a consciousness
of performing my duties; being glad at your lot you will live
wisely ; the Campanians were always proud of the excellence of
their fields ; Greece formerly flourished in opulence, dominion and
glory ; the Roman state laboured under two vices, avarice and
luxury ; oxen protect themselves bv horns, boars by tusks, lions by
jaws (bites); Lycurgus confirmed his laws by the authority of the
Delphian Apollo ; Atticus gratuitously supplied all the Athenians
with corn ; we are supplied and adorned with the gifts of the gods ;
it is the duty of the senate to assist the state by its counsel; many
old men have found pleasure in cultivating the land; being
oppressed with food and wine, we, in the hours of rest, see troubled
and confused things ; Varus (dele comma) is a man possessed of
the highest religion and the highest authority ; that belongs to
each person which each enjoys and uses ; the Helots among the
Spartans performed the office of slaves ; Caesar obtained the com-
mand of all Gaul ; the Numidians for the most part lived on milk
and the flesh of wild beasts ; the crocodile is protected by his skin,
which is very hard, against all blows ; elephants breathe, drink,
and smell by means of their trunk ; some people eat locusts ; the
teeth are worn away by use, but arc not burnt with fire ; in silence
he led his forces out of the camp; Miltiades restored order in
Chersonesus with the greatest equity ; let us always venerate tho
gods with a pure, sound and uncorrupt mind and voice ; they went
over fhe forests of the Alps not without loss ; Dolabella (not Dola-
bellam) provided a fleet with the intention of going to Italy ; allow
me to day so ; the stars accomplish their courses with the greatest
speed ; Iphicrates had a great soul ; Caesar is reported to have
been tall, light-complexioned, slender of limb, with a mouth some-
what large, black and brilliant eyes, and excellent health; all the
Britons colour themselves with woad (blue), and on that account
they have a more frightful appearance in battle, they also have

120

THE POPULAR EDUCATOR.

long hair, being shaved in every part of the body except the head
and upper lip ; Cato in all things possessed singular foresight an
Industry ; Dionysius ordered boys of rare beauty to stand at hi*
table ; Caesar sent to Ariovistus Valerius Procillus, a youth of
very high virtue and humanity ; there was between Labienus and
the enemy a river difficult to be passed and with broken banks t
Chrysogonus purchased a Corinthian vase at a great price ; Caesar
shows the soldiers how much a victory must cost; the conquered
purchased peace at a great cost ; peace of mind is purchasable for
neither gold nor gems ; of old, dots were immolated to the god* at
Carthage; Alexander died at Babylon; Pindar flourished at
Thebes, Theocritus at Syracuse ; in winter bosrs sleep in caves |
no mortal is wise on all occasion*; Iphigenia, the daughter of
Agamemnon, was slain at Aulis; Dione was put to death (inter
fecta est) at Syracuse; Dionysius got possession of Syracuse again j

I Measure having dominion (dominante) all virtues of necessity lie
ow fare necessarily depressed), if all things were lost, yet virtue
could uphold itself; calling Uod to witness, he promised many
thingi ; in the civil w*r nothing happened which I did not foretell ;
it is not advantageous to quit the banks of the Rhine, when now
hostile nations are about to make irruptions.

Ayrshire; and
by a plane

SOLUTIONS.

Solution of J. F. Wilson's question, page 300, col. 1, Vol. III., by
John Bates, White-gate Terrace, near Halifax,

Lit a b f d be a section of the globe, w a l the wall, and c
the place of the lighted taper. Let c a be drawn through the
centre o, and c w and ci tangents to the section aefd at d
and b. Join db and do, and let db meet ca in o. Then
w ir is the diameter of the shadow of the globe on the wall,
and d p b is a central section of the segment of the globe
whose surface is enlightened, and of is its height. Let
the radius a o or fo = «, and the distance c a = * ; then

o = x — a. Now, by the similar triangles, cod and
d o o, we have co:oc::od:oo, or x — a : a : : a : o Q ;

whence o o equals J??_ and fo = of — oo equals j

sr— a
a — ° 2 — ax — la- But the area of the sur f ace f the

*— a x — a

enlightened segment, whose arc is e f d, is by mensuration,

2 ir { ***— u * \ that is, the product of its height by the

circumference of the globe, ir being 3141592, &c. Again, we
have, by the 47th Prop, of Euclid, Bookl., c d =t/(s 9 — 2ax);
and by the similar triangles cdo and caw, c d : d o : : c a :

A w ; or y/{x* — 2ax) : a : x : a w ; whence a wrr.—SL—^
and the area of the shadow on the wall = ir ( ** V

— tr( a * x V Consequently, we have, by the question,
\x— 2a/

V *— a / \x — 2a/

This quadratic gives us x = iL f 7 + ^yj Y Now, since a =

1 inch, we have, by taking the upper sign, # = 5'56155, &c.
inches, the distance of the taper from the wall. We hope some
of our correspondents will give us an explanation of the case
when the under sign is taken, thai is, when x = 1*4384. &c.

This question was also solved by T. F,
X plus Y.

Answer to D.F. F.-C. H.'s query, to bisect a com
parallel to its base.
If a cone be divided by a plane parallel to its base, the upper
I part will be a cone similar to the whole ; and similar solids
[are to each other as the cubes of their like dimensions.
I Hence, in the case proposed, wc have this rule.

Cube any given dimension (either slant height, perpen-
I dicular height, or base) of the whole cone ; divide this cube
by 2, and the quotient will be the cube of the like dimension
of the upper cone, or half. X plus Y.

This question was solved also by Peter Simple, Fleet-street,
and others.

CORRESPONDENCE.

THE GIFT OF ORATORY.

" Though I speak with the tongues of men and of angels ! ! '— 1 Cor. zlii. 1.

Dear Sib, — As one of your pupils, allow me to ask your advice,
through the medium of the P.K., viz. : What course of study must
I pursue in order to become an orator, beginning at the very first
rudiments of the art ?

I am confident that I might be the means of doing much public
good in, this manner, fori possess (I am not writing under any
egotistical disposition, but simply telling the truth) many rare
talents, being about the mid lie stature, of commanding and
pleasing features, a fine yet powerful voice, with perfect command
over it, having studied singing for the last six years with that
object in view ; and from what little experience I have had, I have
discovered that I possess that great secret of success in oratory —
bower to sway the multitude. Yet with all these talents I lack
knowledge ; you will, therefore, confer a great boon upon one of
your earnest pupils by giving the advice he earnestly seeks.

Yours, &c. Respicb Finbm.

[The author of the preceding letter having sent us his real name
and address, we cannot but insert it as a specimen of many which
We receive, and to give our subscribers an idea of the labour which
we have to undergo as the Editor of the Popular Edtjcatoe.
How truly does the letter show, as he confesses himself, that the
author lacks knowledge, the best of all knowledge, namely,-

knowledge! We would strongly recommend to his perusal Mason's

' Treatise on Self-Knowledge/' and to his reflections the celebrated

adage of antiquity, uttered by Solon, yvw9t veavrov, nosce teip-

fum, know thyself. We would also recommend the perusal of the

look once printed separately from the Bible, and used as a class*

book in the parochial schools of Scotland, namely, " The Proverbs

f Solomon.' 1 who was even wiser than Solon. Lastly, we would

recommend him to begin at the first volume of the P.K., and study

very word of it, in order to gain that knowledge which he himself

eems to fe$l the want of. We give him a year to make himself

master of it. After that the second volume awaits him ; then the

ttird snd the fourth. Having thus got something into his

raniura, he may try to spout or make an oration to the public,

with advantage to himself and instruction to his hearers.]

ANSWERS TO CORRESPONDENTS.

W. Follett (Bognor) thould study well all Mr. Cassell's publications,

ipecially the Popular Educator, vole. 1, 2 and 3 ; and 4 as far as published.

—J. Lovett (Ashfordby) and A Wrll-wishkr (Grahamston) are right.—

T.Hill (Manchester): Lessons on Elocution are almost ready.— Bans:

Wrong on the wolf question, and right on the taper question. — F. Qold-

so (Abingdon): Received, and under consideration.— A 8TUDSKr op

Kixo's : The omission ha* been noticed.— Subscriber (Wlgtonshlre) : If a

tell be thrown at an angle of 45° it will have the greatest range. The stature

of an individual has nothing to do with the angle of elevation. W. Taylor

(Cowbridge): We roust defer the subject of annuities for some time. Lingua

1 Latin means both the instrument of speech, the tongue, and that which

Is spoken by it, language. In French, this word becomes La Langue, and

leans the same two things ; but the- French have a word, Le Langage,

erived from this, which signifies only that which is spoken, language,

the English word tongue, like the Latin Lingua and the French La Langue,

Weans both the instrument of speech, and that which is spoken by it, lam-

uage. The English word language, borrowed from the French, has the same

leaning, namely, that which is spoken by the tongue. Hence, it appears

tiat tongue and language are synonymous when applied to that which is

9oken, but that the latter cannot be applied to the instrument of speech.

3-J. W. Tapper (Kilkenny) ; Covers for the P. E. may be bad at this office.

1. common. Is. 6d. fine edition. The cheapest cases of Mathematical

ostruments are said to be sold at the " Society of Arts, " Adelphi, London,

-Indootos (Lubenhatn): Spirit-Umpa may be had at all prices, from ls.94.

nd upwards according to their uses; see Knight and Bon's Catalogue

(Foster-lane. London), where you will also get Manganese, and a vast

variety of other chemicals. Here also you will get chemical apparatus of

very description.— Warin (East Dereham) . Received.

NATURAL PHILOSOPHY.

Ill

ON PHYSICS OK NATURAL PHILOSOPHY.

No. IX.

ON THE EQUILIBRIUM OF LIQUIDS.

S m di ik 'i m n of a Liquid in a tingle Vestek— In order that *
Ua^ should reniain m equilibrium in a vessel of any shape, the
two following condition! are necessary :

lit Iti surface at every point mmt be perpendicular to the
dilution of the foroo which attracts the particles of the liquid.

Sad. Ereyperticle of themiamnftinaUdirectiongbennder
the aetion of equal and contrary fbroet

The firrt condition has already been considered, when treating of
tile inttnenoe of gravity on the direction of the free surface of a
IfaafcL The second condition is self-evident; for, if the preaiurei
which urged, a particle in two opposite directions were not equal
sad contrary, it would be urged in the direction of the greater pres-
sure, and the equflibrium would be destroyed, seeing that motion
would ensue. This condition is, besides, a consequence of the prin-
ciple of the equality of the pressure and reaction which erery
force produces when applied to a liquid.

The Bqu&brimm of a Liquid in Vessels which commumocU with
ems anefasr.-^When several vessels of different forms oontsin the
same liquid and communicate with one another, equilibrium can
only take place in each Teasel when the preceding conditions are
satisfied, and when the free surfaces of this liquid in all the
TBssnls are situated in the same horizontal plane. Thus, let the
different Teasels in fig. 27, communicate with each other, and be

Fijr. 2S

potassa, alcohol coloured red, and oil of naphtha. When the vial
is shaken, the four liquids are mixed together ; but when it is at
rest, the mercury, which is the densest, links to the bottom ; then
above the mercury, the water will place itself; above the water,
the alcohol ; and above the alcohol, the oil of naphtha. Such is
the order of these bodies aooording to their decreasing densities.
The water in this experiment is saturated with carbonate of
potassa, in order that it may not be mixed with the alcohol, in
which this salt is not soluble.

The separation of the liquids in the preceding experiment, is
referable to the same cause which makes solid bodies immersed
in a liquid more dense than they are, rise and float on its surface.

In consequence of this principle of hydrostatics, we find that
the fresh waters at the mouths of rivers float to a considerable
distance above the salt water of the ocean into which, they fall.
For the same reason,' cream, which is lighter than milk, separates
from the latter by degrees and is found floating on its surface.

Equilibrium ofjtwo Heterogeneous Liquid*, in two Vends which
communicate with each other.— When two liquids of different
densities, and incapable of chemical action on each other, are
contained in two communicating vessels, to the conditions of
equilibrium already stated, must be added the following: that
the hei ghts of the columns of the liquids which are in equi-
librium, sre in the inverse ratio of their densities.

In order to prove this principle by experiment, we take a bent
tube, fix it on a board placed vertically, fig. 28, and pour mercury

Fig. 28.

,.,. , I to a certain height with water; and suppose that a vertical
lays* of the liquid in the tube of communication is under our
eosttidcration. This layer canno t remain in equilibrium unless
the pressures which set upon it in the directions from m towards
w, and fitmi w towards m, are equal and oontrary. But we have
atan in our last lesson, that these pressures sre equivalent to the
weight of a column of water which has for its base the layer
mnder consideration, and for height the vertical distance of its
centre of gravity from the surface of the liquid. Now if we sup-
pose a honaontal plane mk drawn through this centre of gravity,
ttis plain that flic equilibrium cannot take place unless the
hrisAtofthe liquid above this plane is the same in each Teasel;
therefore, the surfooe of the water in the different vessels must
be in the same horizontal plane.

Equilibrium of Supernatant Liquid*.— When several hetero-
geneous liquids float above one another in the same vessel, stable
equilibrium cannot take place, unless each satisfies the conditions
already stated regarding a smale liquid ; snd, in sddition to this,
ii i iliiss the liquids sre arranged above each other in the order of
their densities, that is, diminishing in their densities -upwards.
Tnk condition is dearly proved by the experiment with the vud
*1Mo Jour elements. This name if given to a long and narrow

"' " saturated with carbonate of

TOL. XT,

into it ; we then pour water into one of the branches of the tube*
Now, the column of water a b pressing on the mercury at b, the
level of the mercury 4 in the tube is lowered in the branch a b,
and raised in the other branch by a quantity [od; when the
equilibrium takes place, if we suppose a horizontal plane bo to
pass through the point b, then the column of water ab balances
the column of mercury on. Measuring the altitudes on and a b.
by means of two equally graduated scales fixed to each vertical
branch of the tube, we find that the ratio of a b to od is 13£ to
1. Hence, we infer that the density of mercury is 13$ times that
of water ; consequently the altitudes of the columns of mercury
snd water, above the horixontal plane, are to one another in the
inverse ratio of their densities. The reason of this is plain; for
as the pressures on the same horizontal plane b c are the same,
the equilibrium can only be established by any column gaining
in altitude what is lost in density.

The preceding principle may be deduced from a very simple
calculation. Let d and eT be the densities of water and mercury
respectively ; and let h and h' be the altitudes of the columns of
these liquids respectively, when they are in a state of equili-
brium ; and let g denote the intensity of gravity. The pressure
at b, being proportional to the density of the liquid above it, to
its height, and to the intensity of gravity, has for its measure the
product dhg. For the same reason, the pressure at o has for its
measure the product eT h' g. But in a state of equilibrium these
pressures are equal; therefore, we have dhgzzith'g; whence,
suppressing the common factory, we have d A = <fA', or diet
: : V : h ; which is the algebraic expression of the principle to be
proved.

This h y d rost a tic principle may be employed in determining
the density of s liquid. Thus, supposing that one of the f— •-—

THE POPULAR EDUCATOR,

of the tube in fig. 28, contained water, and the other ether, the
respective altitudes of the liquid columns, when they balance each
other, are to one another as 7 of ether to B of water, or as 1 to
"H4 ; whence, if the density of water be taken as unity, the
density of ether is 'T14 ; and so of other liquid*.

- AWWATIOWS Q7 TUB PR3CBDIN0 H1ML08TATIQ PBTJICOTiBS,

The Hydraulic Frets. — The principle of the quaquaversal pres-
sure of liquids was applied in a very important manner in the
invention of the Hydraulic Prats, til* principle was, as we have
aeea, discovered by Pascal, but was first applied by Bramah to
this Invention, at London, in 1706 ; hence, it is frequently celled
Bramah' s picas. This apparatus, by means of which enormous
pressure can be produced, m composed of two cylinders or pumps
▲ and ■, fig. 29, communicating with each other, the one of very

compressed by the press. The orifice o is intended, by
a stop-cock below, to withdrew the water from the i
when the pressure is to be removed.

apparatus

Now, in consequence of the quaquaversal principle, the down-
ward pressure of the piston a is oommunioated upwards to the
piston b, with a force proportional to the surface of the latter,
as compared with that of the former. Thus, if the suriaee ct* the
piston n be 10 or 20 times greaser than that of the piston s» the
pressure communicated to the piston n will be 10 or 10 tunes
greater than that of the piston a. From the piston b, the pres-
sure is oommunicsUd by the piston«*odto the body it, which is
thus compressed between^the moveable plate, raised by this piston,
and the fixed plate d. The figure represents a model of the
hydraulic press, intended for the illustration of the urinciple of
operation. The pump cylinder* are made of glass, in order to
render the action of the apparatus visible, But in actual practice,

rig. 29.

small diameter andytfee other of large diameter. In the small
cylinder, a piston is sands to move up and down by means of a
lever ; in its ascent, this piston draws water from the reservoir
h, and thus the lower part of the body of this pump is filled. In
the descent of the same piston, a valve fixed on the orifice of the
pipe ■, at the bottom of the body of the pump, is closed; the
water driven back by the piston is forced into the body of the
large pump, by a pipe communicating between the two pumps
(shown In the figure by dotted Hnes), and terminating in a valve
opening upwards. Whenever a fresh quantity of water is forced
into the body of the pump b, this valve is opened ; but it is

the cylinders of the pumps are made of strong cast-iron, on
account of their besM geqnsatty subjected to enormous pressures.
It is necessary sknfhet the dtfbrence of the diameters of the
cylinders be much more than that exhibited in the figure, for on
this depends the great power of the machine. In some applications
of the hydraulic press, pressures a mo un ti n g to that of 100,000
pounds on the base of Urn laager piston, are frequently
employed.

This remarkable invention la In constant use in all cases where
very great pressure is required, and where time is not an immediate
object ; as in packing goods, extracting juices, oils, &c. It is

Fig. ao.

closed by its own weight as soon as the piston a is made to I also employed in testing the strength of guns, stesm-bxalei^anet
second, and the water introduced into the pump b is prevented chains for various purposes..

from returning into the body of the small pump a. lastly, in JTcfcr-ZttW, The instrument called the water-level Is aim
the cylinder n is contained a piston intended to communicate of the applications of the principles of equilibrium in v ess el s en
uha pressure to other bodies, for this purpose, the piston-rod tubes communicating with eacn other. It is constructed of g k
iscsjUiron plat* on which is placed the bodies to he I long tin or brass tube bent at both e*ds*aad tonuses* thee*

NATURAL PHILOSOPHY

•^WfthtWoehMttbesof j^ttnend m,fig. *). In net
Hi nfbs ia tu s it li plated horiitentally on a three-legged stand or
•afltort, with the bent ends toned upwards, and ooloured water is
Jfttjfed into thttthe till it ritee to a certain height in both ends in
tht tits* tube*. A§ soon m tht water is aft rati. Its level, that is,
thntwrtfttof tke water in thtte tubes, is &t side; or in other
WMlt, * horbonftal plane will pass through tht two surfaces of
ft* Wnttr at ft and *. This instrument u employed in taking

r point a, we place a graduated levelling staff at the point
A. In the present instance, this staff k formed of two vertical
w tt i tn tods, sliding on each other in a groom and terminated at
the top by a piece of tin m, which has a martin the ntiddle of it.
IMt ttaff being adjusted vertically at a, an observer at the level
ftt d, directs hit sight along the surface of the water at d and s,
to the ttaff, and makes signs to hit assistant who holds it, to
lengthen or shorten it, until the central mark m be fomnd in the
ansrifaraatlon of the horizontal line d e. By measuring then the
height a fc, and subtracting (tarn it the height of the level above
the gvtnnd, the observer ascertains at once the difference of level
ht t wttn A and s, that is, hew much the point b is above the
point a. The following enlarged view of the water-level and
levelling staff, with their adjusting apparatus, will give our stu-
dent! a better idea of these instruments. The figures f and o

J I. E

H, O. I.

show the level and its support, h and i two different forms of the
ItvtDmg staff, tht following figure * shews the mode of apply-

ing the instrument to the practice of levelling. We have seen
that the deferences in the vertical distances on the staff show the
differences of the levels ; now by the addition of these consecutive
distances when the ground is ascending, and by their subtrac-
tion when it is descending, we ascertain the respective positions
of any number of points on the ground with reference to
any assumed horizontal plane. The level fbtaid by this
instrument is only the apparent level, that is, the level which
corresponds to the points contained in a plane touching the sur-
face of the globe, supposing it perfectly sphcTioal The true
level is that Which corresponds to points equally distant from the
centre of the earth. In the case of short distances, the apparent
level may be taken for the true level ; at the distance tf one mile,
the difference between them it only 8 inches; the general
appro rim tit rule for finding the difference of level between two
points on the earth's surface being to square their distance m
mile<t y and lake two-thirds of this square for their difference of
level in feet,

Air-Level. — The air-level is more sensible and more accurate
than the water-level. It consists of a tube of glass, fig. 31, very

Fisj. 31.

, filled with water, hermetically sealed at both ends,
w a small bubble of adr which tends always to occupy
elevated part of it. This tube is enclosed in a metal
otet D. and fixed lengthwise on a stand, which is so carefully
adjusted, that when at rest on a horizontal plane, the air- bubble
u is always found in the middle between two points marked on
the case ; and part of the case is left open, so that the oscillations
of the air-bubble may be observed until it Anally- settles in the
true horizontal position. In taking levels with this instrument,
a telescope is fixed on it for the more accurate determination of
the horizontal positions. The following ngure l shows the

mode of adjtistfag the teletoope to the lord, and fte mode of
bringing the air-bubble to the centre of the level, and under the
midSeof the telescope, by means of adjusting screws.

The &Oj^Z*KK,intemtedby M. Che*zy, it adjusted « a similar
manner. But on the right of the figure there is placed a small
hole intended for the eye-piece ; and on the loft, a moveable sight
with diaphragm, for the more accurate determination of the slope-
line. To this sight theft k attached a graduated vertical scale,
for —<M>r»«iTimj the degree of the slope or inclination of any lint

1*4

THE POPULAR EDUCATOR.

measured on the ground, at so many inches or fractions of an
inch par yard. The stand or auppart for this instrument, o, is

vied alio in the air-level, and aimilar instruments employed in
surveying.

greater or leas extant, below which are found two strata imper-
meable to water, as ▲▲ and bb,
o. and having between them a

permeable stratum mm. Sup-
pose also, that the latter commu-
nicates with a more elevated stra-
tum, through which rain-water
passes. This water, following
the natural declivity of the
ground along the permeable
stratum, is found below the
topographical basin which we
have supposed to exist, with-
out being able to communicate
with it, in consequence of the
interposition of the imper-
meable stratum jljl. But if, in
the surface of the ground, we
sink a shaft which goes through
this stratum, then the waters,
which seek always to find their
level, will rise in this shaft to
greater or less height, in

Fig. 3*.

Rmntaitu and Artesian Wells.— Like*, seas, fountains and
rivers, are so many vessels communicating with each other, in
which the waters are incessantly endeavouring to find a new
level. To these may be added Artesian wells, so called because
they were first discovered in the province of Artois in France.
The origin of some of these wells £oes back to the end of the
twelfth century. At a period much earlier than that just
mentioned, wells of this kind were constructed in China and

hese wells are very narrow shafts sunk in the ground and of
very variable depths. Their waters are generally of the nature
of a continued spring or fountain. Their theory is the following :
the strata of which tine exterior covering of the earth is composed,
are chiefly of two kinds ; the one permeable to water, as sand and
and the other impermeable, as clay, &c Now, suppose
: represents a local valley or topographical basin of

Svel; s
t fig.

proportion as they communicate with a stratum of greater or leai
elevation.

The water which supplies the Artesian wells often comes from
the distance of 60 or 100 miles. Their depth varies with the
localities in which they are found. The Artesian well of Grenelle
in Paris, is 1,794 feet deep, and the temperature of its water is
82° Fahrenheit. It yields about 660 Imperial gallons of water
per minute, being one of the most abundant in supply, and one
of the deepest which have hitherto been sunk, though surpassed by
that of Mondorf in Prussia, the depth of which is 2,202 feet, and
the temperature of its water 93° Fahrenheit. According to the
law of the increase of temperature in the terrestrial strata, it
would be necessary that the depth of an Artesian well should be
about 600 feet, in order that its water should be, during the
whole year, of the temperature of our oommon baths, vis. 90°
Fahrenheit, or blood-heat.

LESSONS IN GREEK.— No. XIV.

By Jomr B. Beamd, D J).

COMPARISON OF ADJECTIVES.

SajMristtt* (from super, above, beyond, and latus, carried) it
In pammar applied to adjectives when they are in that form
which signifies the greatest degree or amount of the quality
described by them. The degree below, or an inferior degree
of the quality, is called the comparative ; and the simple state
of the adjective is named the positive ; thus sweet is the posi-
tive, *vwt*er the comparative, and sweeUest the superlative.

The Gveek language has two forms of comparison. The
first, and by far the most common, adds to the positive rtpoc,
rtpa, rtpov for the comparative, and raroc, rarti, rarov for
the superlative ; the second adds for the comparative Z<wv, lov,
or e*y, ov, and for the superlative iotoc, lory, ictov. The ter-

minations oc, a, ov, &c, respectively point out the masculine,
the feminine, and the neuter gender.

As in Latin and English, the superlative in Greek denotes
either the highest degree of a quality, or a very high degree.

Instead of these ordinary forms the comparative may be
indicated by pxXXov, more, and the superlative by jioXurro,
most, put before the adjective.

Let us consider

The First Form of Comparison*

m. f. y.

Comparative rtpoQ rtpd rtpov

Superlative raroe rani rarov

Adjectives in oc, «j (d), ov.
Most of the adjectives of this class add the forma ef
I comparison to the stem by means of the connecting rowel

LESSONS IN GHEEK

i»

• or m, The connecting vowel is o when a long syllable
precedes j if a short syllable precedes, the connecting Towel
is «. A short syllable is a syllable the Towel of which
is short : a long syllable is a syllable the Towel of which
is long. Diphthongs are long, and a Towel followed by
two consonants, or one double consonant, is long. A long
Towel or a diphthong is said to be long by nature ; a vowel made
long by standing before two consonants, or one double conso-
nant, is said to be long by position. The rule is exemplified in
these words : —

Positive. Comparative. Superlative.

uov4-og, light cov^-o-rcpoc, lighter Kovf-o-rarog, lightest
«oXvp-o£» strong iffxvp-o-rcpoftitronger «r%vp-o-raroc,stronge8t
Xtwr-oc, thin Xftrr-o-rtpog, thinner Xticr'-o~rarog, thinnest
etftvec, wise e^-u-rfpoc, wiser oof-v-rarog, wisest
ejfip-og, secure cxvp-w-repoc, Becurer cgi/p-M- raroc, securest

Contracted words in coc, ovg, and ooq, ovg, undergo con-
tractions also in the comparative and superlative; the former
blend < and a» into to, the latter assume the connecting syllable
a*, and blend it with the foregoing o ; thus —

Pumple.

mpfvp'tog, irop+vp-ovg.

wopfvp-fA»-r<poc> *opfvp~v-rtpog.
Top+vp-tu-rarog *-opfwp-oi-rarot.

Simple.

avXoog,

a.wXo-to-rtpog,

bfcXo'ta-raroQ,

a,icXovg,

arX-ovo-rtpog.

airX-ove , -raroc.

Here belong also contracted adjectives of two terminations
in eve *nd ow, as tv-voog, ev-vovg (well disposed), tv~voov,
tv-veer} comparative, two-to-npog, tv-vova-rtpog ; superla-
tive, two- «<r- raroc, «v-vov<r-raroc.

The ensuing four adjectives in aiog, namely, ytoaiog, old ;
rmXawf, of old, ancient ; xfpoioc, belonging to the other side (of
the river); o%oXawg,idle\ take the endings repoc and raroc,
without any connecting vowel, as

P. yspai-og. C. ytpai-rtpog. & yipac- raroc-

Note that ^iXoc, loving, commonly has in the comparative
uaXXov fiXog, and in the superlative ftXrarog.

The f olio win? eight adjectives in oc, namely tvhog,fair (wea-
ther), tfovxoe (o and 17), quiet, toog, &fo, rcapaTrXnoiog, similar,
eefytoft Mr/y (in the morning), otf/ioc, /ate, irpwtoc* m *fe dawn,
append the connecting syllable at to the stem, so that the
comparative and superlative exactly correspond to the forms
if the preceding, as

P. ut<r-og. C. uto-ai-rtpog. S. uto-ai-rarog.

Two adjectives in oc, namely tppwptvog, strong, and ojrparoct
mmixed, append the connecting syllable to to the stem, as
tppwusv-to-rtpog, tpptautv-to- raroc ; acpar-£0--r€poc» aicpaT-tv
raroc. So atoococ* a, ov, modest, has in the superlative atooc-
to-rarog.

The following four adjectives in oc, namely XaXoc, talkative,
uovofayog, eating alone, orj/ofayog, fond of good eating, and
*ru%oQ, poor, begging ; take ic for their connecting syllable,
as XaX-0C) XaX-ta-rtpoc, XaX-t<r-raroc.

Adjectives in ijc (g. ov), after dropping the ng, take the con-
necting syllable ur, as
P. cX«rr-i|Ct thievish. C. xXticT-io-rtpog. 8. sXtirr-to-rarog,

80 also one in 17c of the third declension, namely, ^evirjCt
<C (g* *°C» ovg), false, makes yj/tvSiortpog, ittvtiiorarog.

Vocabulary.

AipcroC) n, ov, chosen.
Biatoc, a, ov, violent.
Aicatoc. a, ov, just.
Ti/uoc, a, ov, honoured,
d, valuable.

I Xprjoiuog, n, ov, useful.
S7rapriaricoc» n, ov, Spartan.
*Lu*irn, ng, rj t silence.
KoXXtac, ov, 6, Callias, a pro-
per name.

Iv£oc» ov, 6, Indian.
AaKttaiuovwg, ov, 6, a Lace-

dsemonian.
ApwruBng, ov, 6, Aristides.
Ovfotc, cvoct no one; ovfcv,

nothing.
IIarptc» tooct Vy one's mother

country.

KvcXfc^r, *»xoc, A, Cyclops.

E0voc, ovg, ro 9 a people, na-
tion.

AyaXXw, I adorn; in the mid-
dle voice with the dative, I
am proud of,

No/u£« (vojcoc), I think, I
hold as true.

The English adverb of comparison, than, is represented by
» (Latin quam) ; thus, the eon is wiser than the father, is in
Greek, 6 vioc oofartpog toriv n 6 varrjp. Another form of
comparison drops the n, and instead, as in the previous in-
stance, of having the same case after the n t than, as before it,
puts the second noun in the genitive, as vioc *o*<wrepoc rov
varpog toriv.

EXXBCI8S8. — Grbex-English.

Apiorttdng irr^xiorarog nv, aXXa Sucawrarog. Oi KvcXwvcf
puuoraroi noav. KaXXtac irXovoutrarog nv AOtjvclhov. Ovofv
OMvng eon xffloipuripov. 2tyj| ror* sortv alptrvrepa Xoyov.
Ovtev tori oofiag riputrtpov. So^ca irXovrov Krn/ta ripturtpav
fortv. *H Aaxtiaifiovtav £catra nv atrXovorarn. Oi 7<paircpoi
rate Tbiv vtiav ri/iatg ayaXXovrat. 'H trarptg rotg avBpvwoic
QtXrarn toriv. Oc Ivtiot iraXairarov tOvog vofutovrai. O
iraifcg, tort ^ov%atraroi. Oc 2iraprtarucot vtavuu tppet/w
vtortpoi noav rtov AOnvauev. HoXXoi rutv x<AJ&>tw tioi
XaXioTtpot. 01 do vXot voXXaxtg y^tvdioraroi cat cXcwrioraroi
no IV.

English-Greek.

The father is wiser than the son. The mother is more talk-
ative than the daughter. Virtue is the most valuable posses-
sion. Socrates was the wisest Athenian. The Athenians
were wiser than the Lacedaemonians. No one of the ancient
Greeks was wiser than Aristides. Men are quieter than boys.
The Lacedaemonians were very strong, Swallows are very
chattering. The raven is very thievish. Socrates' manner of
life was very simple.

In adjectives of the third declension, the comparison-forms
are added to the adjective stem, either immediately or by
means of the connecting syllable to or i*. The adjective stem
appears in either the neuter or in the genitive, after the
removal of the termination oc*

The adjectives in vg, eta, v; in ng, tg ; in ac, av, as well as
ficLKop blessed, affix the c<j..i orison-forms immediately to the
stem; as

Superlative.

yXvKv-rarog
a\nOto-raro
ictvto-rarog
utXav-rarog
fiaxap-rarog

The adjectives rjtvg, sweet, rayyg, noift, and iroXvc, much,
take the second comparison-forms, namely those in iuv and
toy.

The adjectives in w, ov (g. ovog), assume the connecting
syllable to ; e. g., evdaiuwv (n. ov), fortunate, happy.

Positive.

Neuter.

Comparative.

yXvievg, sweet.

yXvKV'Ttpog,

aXnOng, true,

«C

aXnBto-rtpog

*tvng,poor,

«C

Ttvto»rtpog

utXag, black,

utXav-rtpog

uaxap, blessed

uaicap-Ttpog

P. cv£ac/*wv.

2f. fvoVuftov. C. tv&a*uov-to-r%Qog. 8. evdatuov*
to-rarog.

Adjectives in i{ take as their connecting syllable partly to
partly to, as

a$nXiS,

ap*aZ t

Genitive,

Comparative,

Superlative,

Genitive,
Comparative,

afnXUog, growing old.

a$nXuc-to-rtpog.

afnXuc-to-rarog.

apvay-og, robbing.

apway-ta-rtpof.

aoirar-t*vrare£.

THE POPULAR KWCATQR

The adjectives in etc, «\ whose stem ends in rr, append the
termination* ripo$ ana rarog immediately to the etosa ; but in
the coming together of two r'sthe first changes into 0, whereon
the foregoing v is dropped ; the procesa and the result stay be
pjeseatea thus

P- X<HM«£, tfv, G, xoquvt-o^ pltcumg.

XOQUVT-TipOQ.
%CLpUV9'TtpOQ,

Camp. xaQua-rtpof* 6hg>. xapu<r*wef>
Compounds of x^'C interpose a», as
•A f*»x«pi£, »i

0. e*-tx<ipir-oc, pleating .
C fjrtxaptr-w-rtpoc. S.

eir«)fap«r*«-TOfr©^.

VOCABULABT,

Ba0vg, tux, v, deep. {some.
Bapt/Ci eux, v, heavy, burden-

besides the nam. are ace.

vptafiw, and voc. iroi<rpv ;

In the ptur. trpeirfkicjt old,

an. old man.
Q«VC* «4t v, swift
Ac&vug, <c. powerless* weak.
Eyjcparqg, «& self-controlled,

abstinent.
Evtr«/3Sff , fc, pious.
Europe* • (e\ lroc>, attwmtiT*
OmW» s> «sv straight, tight
Airvrjy Tjs, r) ./Etna.

Atvxul, oci ih misfortune.

AQpwSirTj, t)q> r), Aphrodite*
fVenuiO.

'H/Jg, ijc, ij, youth.

'Op/xr/, i}c, rj, impulse, eager-
ness, seal.

Xpert*?, *v, d, Otitis*.

Mwanrc, *ro$» 9» the middle*
moderation*

Noq/ta, aro£» ro, a thought
(something in the vovc>
mind).

II«p«px#^, I pea* by.

4*4^ suddenly,

Ovtfe, nor.

EXSHCI8B8. — GrBBX-EnOLISH.

Am/mu «* *•*)/*«, waetpxsroi 4l^>eV ^ ***** oaji* ytyvm*
uMNfcpa. To mpac jdayvrtpev ww -*irv*c» '© Aafarof »•*
/fata/raty dirvy irapairXij<w»>raroi; e<mv. (H veoi to*q rtv
TrpofivTtQuv evmivote xa ( f 0vffiv - wtXiac £uc«ia£ *Tfff<£ sot**
asVatoffwri}. *H fm^or^s *» wow a<r*t«XMr<pa caw. Oi
yepovrec a<r0€V€<rr«pot «<ri rwv vea>v. BovXiye op&yc onflev «mr
aff^aXeorepov. Oi xopaxtc fuXavrarot «<riv. Swcparqc ryrpa-
r**)r*40£ »jp eoi <ft»t)ptv««r«raf. Bv rot^ aruxtatc voAAawc
<4 avQfuyirot at*ff«ais<rrspot £i<rt*v 9 *» WMf ««tvx«i**. gfertaf
ijy <kpwtryt*raro£. A*de£«rif ijv x«pt«rr«n| ranw 0sw*i

English-*© *xxx.

. Old a** u Ter T burdensome. Nothing is swifter than thought.
Moderation is the safest. No bird is blacker than the raven.
The boy is swift, the man is swifter, the horse is swiftest.
The host* i» awif ter than, the man ; the* men is swifts* ten
the boy. Youth is more attractive than old age. The
Ethiopiana. age very btftok. No one of the Athenians waa
more aelfncontrnlled than Socrates. Critte s was more given
to pander (fobbing) than Alexander. Nothing isr more
pleasing than, \teautiml flowers.

LBS80MS IN BGOSLKEBPINa^N^ VIL
HOME TRADE.

^^' Apwi ith. ■■ . i ■■«■■«

Bought of Osmond and Co., London,

* If bags of Ba^ic^ Cotton (at aiortnight'aaredU>

Net 4960 lbs. at 9d. per lb.
Discount 1} per cent.

£186 %
2 15

£183

4 3

-April nth.

Aocepted a Bill drawn by Andrews and Co., London,
No, 5, payable to Ford and Co., due at a mos. £*3* 17

■12th.

Sold to Allison and Co«» of London,
12 bags of Weat India Cotton (on credit)
N«4mt».atWUpiBrlb,

13th.

Prew a Bill on Alttsem and Co., Londesi,
No. h Payabk to my Order, due at 2 mot,

•13th.

Recenred of Spencer and Co., London,
For Cotton sold to them on the lttfe Marsh

£150 6

4150 6

£\m 1* f

14th. •

I^wwtofthALonx^aiidWa^imiwteiBank £170

ltttu

Paid the East India Company a moiety of the
amount due for Cotton bougkt on the 25th
February ... •, ... M «> £330 16

.jfth.

Took out of Cash for Petty Cash

18th.

Sold at LiTerpool, by tha egemey of Thomae Ionea,
24 bales of MaeSsns Cotton

Net 85801bs at 6|d. per lb £232

Pis Commission arid other expense* ... 5

£20

• 18th. •

• 20th. •

Sold Lloyd and Co., of Manchester,
24 bales of Madras Cotton (on credit)

Net 9216&D8. at 0*d. per lb.
Incidental expenses

• 22nd. •

Bought of Ovington and Co., London,
94 bags of Demerara Cotton
Net 73621b*. at 8d. per lb.

-24th.-

£229 11 4

Deewoutofth«I^doMan4 WeAtWWterBank £190

18th,

Paid Osmond and Co., of London,
For Cotton bought of them on the 4th inst. ... £183 4 3

£222 10
10

£223 9 10

4244 8

Drew out of the London and Westminster Bank £290

_ 24th.

Paid BUI No. 1, drawn by Osmond and Co. £288 3 4

25th.

Receired of Lloyd and Co., of Liverpool,
Xhe ioj lowing remittances in Bills,
No. 2, drawn on Warwick and Co., due May 15th £120 Mr

Nb. 8, drawn on Thiaelton and Co., due
25th.

25th 102 19 10

7th..

Bought of Andrews and Co., London,
22 bags of Maranham Cotton (on eredtfr}
Net 7l661be. at 8d; ner lb.

£238 17 4

Drew out of the London and Westminster Bank £330

25th.

Paid the East India Company,
Tfre> ram wining moiety of the amount due for Cotton
Bought on the 2ftb February ... ... £330 10 §

L1S80NB IN BOOKKEEPING.

127

-April 26th.

Received of Thomas Jones, oflLWerpooi,

The following remittances in Bills,

No. 4, drawn on Parker and Co., due May 11th £190 10 6
, No. 6, », fl Baring and Co,, „ June 3rd 56 10

27th

typld at Liverpool, by Thomas Jones,
24 bales Madras Cotton (on credit)

Net 80681b*. at 6id. per lb,
His Commission and other i

£218 10
6 9

£213 1

-29th..

Accepted a Bill drawn by Ovington and Co.,
: ' No. 6, payable to Spicer and Co., due at 3 mos. £245 8

- 30th.

Sold at Liverpool, by Thomas Jones,
30 bags ofSDemerara Cotton
Net 92181bs. at 9d. per lb.
His Commissieti and other expenses

May 12th.-

Received of Thomas Jones, of Liverpool,
The following remittances in Bills,
No. 9, drawn on Lubbock and Co., due June 16th £300
No. 10, „ „ Payne and Co., „ „ 18th 37

13th. .

Bought of Stevenson and Co., of Liverpool,
On account of Perkins and Co., of London,
30 bags of New Orleans Cotton, value ,

My Commission and other expenses <

£212
6

14th.

Received of Thomas Jones, of Liverpool,
The following remittances in Bills,
No. 11, drawn on Smith and Co., due June 12th £200
No. 12, „ „ Baring and Co., „ „ 2Ut 41

30th.

Took out of Cash for Private Account

- May 2nd.

Sola tolioyd and Co., of Manchester,
16 bags of Berbice Cotton (an credit)

Net 49601bs. at 10}d. per lb.
Incidental expenses

£345 13 6
8 12 10

£337

£9

16th. •

Received of Powell and Co., of Manchester,
The following remittances in Bills,
No. 13, drawn on Wagnall and Co., due

June 26th.. ...
No. 14, drawn on Margetson and Co., due
June 30 ...

£100 d
£199 17 2

15th.

3rd.-

D*W 0e* of the London and Westminster Bank

3rd.

MdB9, Ho. % drawn by Andrews and Co.

■ 4th,

Sold at Liverpool, by Thomas Jones,
24 bags of Madras Cotton (on credit)

Net 8484lbs. at 7d. per lb.
jTia ComnsJssion and other expenses ...

£217
18

£217 18 10

£340

£327

£247
6

9
3

Received in Cash for Bill No. 2, Warwick add Co. £120 10

15th.

Deposited mth6 London and Westminster Bank £120

16th.

Bought of 8tewart and Co., of Liverpool,
On account of Perkins and Co., or London,
40 bags of Sea-island Cotton, fine
My Commission and other expenses . . .

£610 10
15 19

20th.

£241 6 2

5th.-

Sold to Powtll and Co., of Manchester,
22 bags of Maraaham Cotton (on credit)

Net 71«b*. at lOd. per lb.
Incidental expenses ... ...

£298 11
1 6

£299 17 2

• 6th.

Drew out of the London and Westminster Bank £210

« 20th. ■ ■ —

Remitted in Cash to Stevenson and Co., Liverpool,

On account of Perkins and Co., London,

For Cotton bought on the 13th inst £212 6 8

25th.

Received in Cash for Bill No. 3, Thiselton and Co. £102 19 10

26th.

Discounted and received in Cash for Bills,
No. 8, Barclay and Co., due June 1st
No. 9, Lubbock and Co., ,, „ 16th
Paid for discount on the Bills

£217 18 10

300

1 2 3

Received of lHomas Jones, of Liverpool,
The followfag remittances in Bilk,
No. sVdraMca Abrahssna and Go., doe

Jtm#6th ... ~- —

No. 7, arawn on Welch and Co., due May 29th

0th.

Received of Lloyd and. Co., of Manchester,
Bm No. S, drawn on Barclay ao4 Co., dm*
June 1st ... —

£113
100

25th.

-10th J-

Becsivsd ik Cash fox BUI No. 4, Parks* and Co.

11th. —

Took eut el Cash for Petty Cash

Htn.

£219 18 10

£190 10 6

£10

l)epositsdmtheX4Dn^nai^dWi»^ins^r^aB^ *W *.

Remitted in Cash to Stewart and Co., Liverpool,
On account of Perkins and Co., London,
For Cotton bought on the 16th inst

-27th.

Sold Brown and Smith, London,

12 bales Madras Cotton, for Cash in hand,
Net 38961b*. at 6d. per lb.

£610 19 4

£97 * *

-29th..

Deposited in the London and Westminster Bank £100

29th.

Received m cash for Bffl No. 7, Welch and Co., £100 _

30th.

Deposited in the London and Westminster Bank £100

128

THE POPULAR SDoGATOR.

. May 31st.

Beceired of Perkins and Co., London, 4 Bills, via.,
No. 15 drawn on Warner and Co., due June 7th £200
„ 16 „ Russell and Co. „ 10th £200

17 Payne and Co. „ 15th £375 10

18 Alexander and Co. „ 28th £47 16

-June 1st. •

Sold to Powell and Co., of Manchester,
24 bags of Demerara Cotton (on credit)

Net 73621bs. at lOd. per lb.
Incidental expenses

£306 15
1 10

- June 21st. -

Deposited in the London and Westminster Bank
26th. *-

Received in Cash for Bill No. 13, Wagnall and Co. £100
26th.

Deposited in the London and Westminster Bank. £100
28th.

Received in Cash for Bill No. 18, Alexander
and Co.

£50

£47 16

3rd..

Received in Cash for Bill No. 5, Baring and Co.

3rd.

Drew out of the London and Westminster Bank

3rd.

Paid Bill No. 3, Smith and Co.

5th.

Took out of Cash for Petty Cash Account
6th.

£308 5
£36 10

£100

£135 18 9

£10

• 30th.

Received in Cash for Bill No. 14, Margetton
and Co., ... ... ••• ••

30th.

Deposited in the London and Wesm. ster Bank £250

30th.

Made up the account of Petty Cash from Jan.
till this day

Received in Cash for Bill No. 6, Abrahams and Co. £113

6th.

Deposited in the London and Westminster Bank £100

-7th. •

Received in Cash far Bill No. 15, Warner and Co., £200

7th.

Deposited in the London and Westminster Bank £200

10th.

Received in Cash far Bill No. 16, Russell and Co., £200

10th.

Deposited in the London and Westminster Bank £200

11th.

Received from Powell and Co., Manchester, 2 Bills, vis.,
No 19, drawn on Payne, Smith and Co., due

July 10th £150

„ 20, ,, Lloyd and Co. July 20th £158

12th.

Received in Cash for Bill No. 11, Smith and Co., £200

12th

Deposited in the London and Westminster Bank £200

£199 17 3

£57 8 9

•30th.

Estimated my unsold Cotton at prime cost, aa
follows, on taking a General Baton* this day,
12 bags of Madras Cotton
Net40041bs. at4ld.perlb £75

1 •.

LESSONS IN CHEMISTRY.— No. VUL

Whtti arsenic (arsenious acid) is not very soluble in water, but
it readily dissolves in potash solution: add, therefore, about
fifteen or twenty drops of liquor potass* to about a wine-glassful
of distilled water, and place the fluid in a widish-mouthed bottle,
capable of holding about four wine-glasses full-— that is to say, a
bottle having a capacity of about six fluid ounces. Instead of a
bottle of this kind, a clean Florence flask may be employed, sal
probably it will be the better of the two. Assuming a Florence
flask to be needy I shall oonstructmy diagram accordingly, fig. 42.

rit>42.

-15th.

Received in Cash for Bill No. 1 7, Payne and Co., £375 10

15th

Took out of Cash for Private Account ... £20

16th.

Deposited in the London and;Westminster Bank £360

16th.

Received in Cash for Bill No. 1, Allison and Co., £150 6

. 16th

Deposited in the London and Westminster Bank £150

18th

Received in Cash for Bill No. 10, Payne and Co., £87 8

18th. ,

Deposited in the London and Westminster Bank £40

21st

Received in C*«h {or Bill No. 1?, Blaring and Co., 441 5 2

b is the bottle in which the arseninretted hydrogen gas is to ob
generated by mixing together sine, dilate sulphuric acid, tad
liquor srsenicalis ; t the tobaceo-pipe shank, and / the flame
produced by the burning gasj t is a thin bent glass tube, through
which the products of combustion (water and arsenical teus)
pass into the Florence flask f. The tube bends downwards in the
flask until it nearly touches, but not quite, the potash solution.
By this arrangement most of the arsenic enters the bent tube in
the state of arsenious acid, passes along the tube, comes in contact
with the potash solution, and is by the latter eventually absorbed*
During the progress of the operation it will be welL from time to
time, to agitate the Florenoe flask in order to facilitate absorp-
tion of the gas.

The student must not imagine that by the arrangement ef

LESSONS IN CHEMISTRY.

1»

apparatus just described all the arsenio contained in the liquor
arsenicalis will be collected. Some portion will inevitably escape
Were it our object to collect absolutely all, other methods muat bt
had recourse to. I wish the reader, however, to understand that
these le ss ons involve qualitative, not quantitative chemistry— thi
latter department of the soienoe beinga subject for ratore consider,
ation. It so happens, howerer, that a great number of the prac-
tical chemi c al operations haying reference to arsenic involve
qualitative rather than quantitative questions— the question being j
not so much to determine the exact quantity of arsenic present at
whether it exists at all. The operator will soon see how every
particle of anenio might be collected and estimated if desired.

Before passing on* to a further consideration of our arsenical
solution, just reflect for an instant on the elegant power of analysis;
with which the property of arsenic to oombine with hydrogen and
form a pas furnishes us. Hereafter a few other instances of the
separation of solid bodies from each other, by converting one into
a gas, will be made known, Flint is one of these. This hard, I
heavy, apparently untraotable substanoe, can be readily made to
assume the form of a gas.

Bsp en mm t s with Me Arsenical Solution.-- However much wo
have been discursively beating about since we first commenced
these lessons with the examination of a metal, I trust you have
not forgotten two or three red-letter rules mentioned some time
bade. I will repeat them : they are as foUowB :—
Metals are divided into

Kaligenous,
Terrigenous,
Calcigenous.

The latter class oontsins all the substances we commonly term
metals.

AH calcigenous metallic solutions yield a precipitate, either
with hydxoeulphurio add, hydrosulphate of ammonia, or yellow
prusaiste of potash— generally with all these.

Tie normal colour of precipitate with hydrosulphuric acid or
hytasulphnrate of ammonia is black ; but two metals yield a
white, and four a yellow precipitate.

Solutions of all calcigenous metals, save five, yield precipitates
with hydrosulphuric acid alone.

Kve do not ; but they yield a precipitate with hydrosulphate
of «—«"'*■ They are iron, manganese, uranium, cobalt, and
nickel.

Now commence the operation of testing. Transfer the arseni-
cal solution from the Florence flask to a tall wine-glass or a bottle,
and transmit (through it sulphuretted hydrogen gas. Most probably
you will have no precipitate ; and possibly you will infer that
hrdrosulphurio acid is incapable of furnishing a precipitate with
an arsenical solution. Do not arrive at any such hasty conclu-
sion : we will proceed to examine the conditions of this liquid.
In the first place, is it alkaline ? Try it by means of a piece of
reddened litmus paper, or a pieoe of yellow tissue-paper,— you
have been already instructed as to the changes on these which
alkalinites would produce. Do not, however, dip the paper into the
liquid! — that is a dirty plan, only followed by slovenly people.
Lay the slip of paper, previously moistened with distilled water,
upon a little slip of dean window-glass ; then dip the enoVof a
glass rod into the fluid, from which withdraw a small quantity,
and apply it to the paper.

This is the proper way to conduct the operation. Well, if the
solution be alkaline, we have a sufficient explanation of the reason
why no p re cipi t at e ensued ; for sulphuret of arsenic, like most
other sulphurets, refuses to fell in the presence of alkalies : the
greater number of acids also prevent its felling, but aoetio acid is
an exception to this rule : therefore add aoetio acid to the arseni-
cal solution until the liquid, on being tested with blue litmus-
paper, manifests distinct signs of acidity. Now transmit through
tta current of hydrosulphurio acid gas, as already directed, and
yon will have a result, but the kind of result will depend upon
circumstances. If the amount of arsenio oontained in the solution
be less than a oertain amount, precipitation does not immediately
ensue, but the fluid is tinged yellow. Now, why is this ? The
explanation has already been given. I have already said, that
sulphuret of arsenic is soluble in the greater number of acids.
Well, oven hydrosulphurio add gas is not an exception to this rule.
A oertain definite portion of this add throws down the arsenic in
an insoluble form, but an excess redissdves that predpitate. If,
m , jon obtain a solution which is merdy tinged yellow,

although acetic add in distinct excess should have been added,
boil the liquid for a few seconds in a shallow vesssL when a pre-
dpitate will oertainly ensue. The proper vessel for conducting
the boiling operation is a noroelsin evaporating dish, fig. 43 ; but
an enamelled saucepan wall answer perfectly well.

Fig. 43.

I stated a short time since that the method of obtaining every
portion of arsenio from a liquid containing it would soon be made
evident. This it the method. The arsenical solution being brought
to the proper condition, that is to say, perfectly neutral, or else
acidulated with acetic add, hydrosulphuric add is passed through
it; the liquid boiled and filtered ; all the arsenic is obtained in the
condition of sulphuret upon the Alter. Instead of filtration, decan-
tation may, in many instances, be profitably adopted. Decantation
oonsists in the pouring away of a liquid from a sediment, and is
best conducted by means of what chemists term a Phillips' a test-
glass— a vessd of this form, fig. 44. Owing to its peculiar con-
struction,

Fig. 44.

being widest below, the deposition of a precipitate takes place
With great facility. Even the operation of pouring requires some
practioe— that is to say, pouring without disturbing the deposited
predpitate. First dip a glass rod into the fluid, then do as repre-
sented below, fig. 45. In this manner the major portion of a
fluid may be drawn off from a predpitate.

Fif. 45.

I need hardly say that no predpitate can bo considered pure
until it has been frequently washed by distilled water, and the
water separated, either by decantation or filtering.

If the process of filtering be adopted, and cirenmstances make
fVrequirite to separate the predpitate from the filter, it may be
effected by holding the unfolded Alter lightly between the thumb
and finger over an evaporating dish, and directing against the
Alter a powerful but minute jet of water by means of an apparatus
dready detailed, and here represented, fig. 46. The nature of the
combination is such, that air being foroed by the mouth down
the tube t, water emerges throughthe jet f against the filter.

In the greater number of operations, however, we do not

1»

THE POPULAR EDUCATOR.

require to effect the separation of a precipitate from its filter.
Our operations being qualitative, a sufficient quantity of ike pre-

cipitate for our future purposes oould have been separated
the filter by mere scraping. I would strongly advise the student,
however, not to neglect the practice of learning how to remove the
precipitate from the paper in the manner detailed ; of course the
sulphuret will be found in the evaporating dish, mixed with a
great deal of water. As much as convenient of the water is now
to be poured off, and the remainder dissipated by gentle evapora-
tion over a steam or water-bath ; the sulphuret will then be
obtained dry and pure. It is almost superfluous to state, that the
steam or water bath may be a saucepan containing water, over
the mouth of which the basin or evaporating dish is laid, as repre-
sented in the accompanying diagram, fig. 47.

Fig. 47.

If the basin or evaporating dish touch the water contained in
the saucepan, it is said to be heated by a water bath ; if it only
come into contact with steam, it it said to be heated by a steam

bath.

Reduction of Sulphuret s/ Anenic (orptment) into Metallic Arsenic.
—Take a piece of quilled glass febe, about ten inches long, and one-
1 ourth of an inch in diameter, and applying the flame of a spirit-

Fif.S8.

JLX.

lamp, fig. 48, fuse it at the point L revolving it all the time heat it
applied. Separate the two ends by gentle extension, then twist
the tubes in reverse directions, so as to obliterate the capilary orifice
at t ; break the filament, and continuing to apply the point of a
spirit-lamp flame, finish by making a tube like that represented
in dse following diagram, fig. 49, about the diameter there given,
but almost twiee the length. In all probability you will not
be abet to finish, off the tube so neatly aa represented— most
likely you will have a head of glass at the closed and like

Wf.4*.

this. To get rid of this bead entirely requires tamo
and arrets: take no heed of it, therefore. I sheJ
after give more specific directions As? working Cmee*
attending to which the disfigurement may be ptovonecd; ins
time, the tube you have succeeded in forming will ana _
the purposes intended. Incorporate by a pestle and mortar, or on
a piece of paper wish a knife, the sulphuret of arsenic yon have
made, and dried, with about its own weight of a mixture of new*
dered okarcoei and carbonate of soda (washing soda) in, sqael
proportions; then carefully throw the mixture into the elsasd
tube thus prepared, in such a manner that its sides may not remain
soiled — to remove which soiling, a feather may be used — but what*
ever be the plan adopted, the sideaof the tube must be made quite
clean.

Fig. 90.

If now the flame of a sftnt-lamp be applied to the tube con*
taining the mixture of sulphuret, carbonate of soda, and eharoosi
--the tube being held by a slip of thick pasmr wound round in—
2* *?£&* *** * * e •™ lllti « cf watery vapour, which, onris-
teg, willdhntiietubc,fig.50. The operator sno^Ueninfsdlyremove
it by means lof a strip, of blotting-paper, othsrwsm ft saigh* trickle
ba^k,siMi,fiUHng on the hottest part of the tnba» hrcakk The
next effect will be the deoomposition of the sufehuxat of arsenic
into r--*-»"- — — ■ -> * -•« #. • - f • . - -

kinp fiesae esoefully i __

timed, and. uartmUw sssmsVdTtf

_,_ ^.^^^^ oxygen, into srsasuoueaeid; and

by repeating the operation smaosssUy often, t»e total oonvnt-
p sion of the metal into the arid or oxide (white ananas ) any be
reedUyseeomphshed. * '^

T hfavolat ffityof the crust of metalfaarseaioiaa nharssiarnf
tact nvportence, distinguishing arsenic from everythin g eta* I
mawa re that boo ks es p e cial ly medfe^legml liiijilitasji mat
tartons states wMcn occur in the suTiamium of gian% umiaav

ItBSSOKfr m GERMAN;

1*1

sgrflmony, afford crusts which may be confounded with that arising
flm sjceenic. So far as the objection applies to antimony, you
■hill form your own opinion hereafter ; aa regards stains ii the
aubstanoe of glass, yon may form an opinion presently. It is
■otivBttp jtiasfble for a beginner to Awe a glaaa tube in a spirit-
lsss^fkasje without giving rise to a dark stain in the gkaa— tMa
•lain depends upon the change of oxide of lead, an ingredient of
ftmt-gls**, mto nwtallao lead, ft instead el a smUftmn tome,
that of an oil lamp be employed, then, in addition to the lead
stains, others are apt to be produced by the imbedding of char-
coal in the fused class. These stains, it is said, may beamftoBtiied
with tha azaenical crust ; but if the remark apply in any degree,

it can only apply to the moat careless of observers. An arsenical
crust may be volatilised, and caused to deposit further on towards
the mouth of the tube : lead and charcoal stains are fixed, at least
so far as locality is concern edr. By dexterous manipulation they
may sometimes be altogether removed ; but the operation of
removing them causes no fresh stain. Remark well the appear-
sasse of em arsenical crust, and news* feat you will misfmsjn it for
anything else. A very simple plan of avoiding lead stains consists
in the use of glass which is totally free from lead.

The glass known as German or Bohemian is of this kind. I
have not recommended it to the beginner, on account of its extreme
infaaibility, and the difficulty with which it is worked.

tESSONS IN GERMAN.— No. LXXIV.

Irregular Verbs, continued /rem p. 112.
(6) ©oOen, to be obliged. (See Remark 13.)

HTJ>IOAtivj£.

BTTBJXOfCTTVE.

COHDIWOHAi. IMrnkTrVE. 1AJTUUX1VJ. PABUCIMJJ.

•.(3

Present Tense.

Present Tenee.

i^foH,
bu fottft,

wir fatten,
i$t foflet,
fie fatten,

I am obliged,
thou art obiged .
he is obliged,
we are obliged,
you are obliged,
they are obliged.

tefbOtfc

er fatte ,
toir fatten,
$t fattet,
fie fatten,

I may
thou mayst
he may
we may
you may
they may

*|%nlMrttfr,

fbOtc,

jefottten,

|\i%t fsOtct,

3|flt{euten.

Imperfect Tense.

I was obliged,
thou wast obliged,
he was obliged,
we were obliged,
you were obliged,
they were obliged.

Imperfect Tenee.

ty fottte,
bu fatttefi,
er fottte,
tore fattten,
u)r fottten,
fie fottten,

ill
111

- c 1
HI

2(3

Perfect Tense.

id)faoe "^ I have
tmfrft J thou hast

15 he has
•gwe have
you have
they have ^

Pluperfect Tense.

t^lorte ") I had
tttyattefk thouhadst
et^otte I g he had
totr fatten ^ we had
i$t Joitet * you had
fU fatten J they had ^

First Future Tense.

I shall '
thou wilt
t? he will

I might
thou mightst
he might
we might

Sou might
ley might

Perfect Tense.

Prmtsti Tsmse.

fatten, to be
•bhejed.

Present.
obliged

\d) $a6e
bu fabeft
er $abe
toir baben
i$r ^aoet
fie $aben

I may have
been obliged,
3 &c.

Perfect Ti

tfWi&aben,
to have
obliged.

Perfect.

*f*t
obliged.

5(3

a a

i$ toerte
fcti nrirfl
er arirb
roic toetten
t$t toertet
{U »ctben ^

Second Future Tense.

. I shall "
5 thou wilt
She will

» we shall
**" you will
they will^

y l

i$ toetbe
bn XBtcft
er nrirfe
nrir toerben
i^rtterbtt
fie toerben

*g we shall
£ you will
* they will

Pluperfect Turn.

I might
been obliged,

\Q y atte
bu fatteft
er $dtte
tore patten
ibr bdttet
fie fatten

First Future Tmm.

FirHPuture.

x$ toerbe ~) (if ) I shall be||s) *«We
bu toerbeft ^ oblige*, fte.

er toerbe J if
toir toerben t %
ifa toerbet
fie toerben J

taftftrttfl

er tourbe ■
tot? tourben
tfr toftrbet
sje tourben

Second Future Tense.

tc& toerbe
bu tocrbeft
et tserbf
wit toerben
i$r teerbet
fietoertcu

14
21

Second Future.

(if) I shall ty toiirbe "
have been * u tturteft
obliged, &c. cr tourbe

!»lr tourben
■ibr tourbet
kit tourben m

ill

(1») Juwsrfa ea ft U • a | must be kept in view. The following examples will be sufficient

... ... .. : to show this:

The prjmarvand prevalent use of fatten is to indicate Mm ; ^ f ^ w ^ j,^ ^
or necessity. What Particular word or phrase shall be employed • • »

to tranalate U, ia aty «ven ease, mi* be determined b, cir- ■ ^ fott ^^en he tt to (i e.
cumatai««.lliie^iUe^^aiyHi^ ^ adfce* to. tibe/^n- €5oa UJ et ¥ aki f am / to
' M 1 1 for in whatever way expressed, that primary sense I to) have fti

to (i. e. art *Mfcf«Tte» do that :

is bidden to) go :

(L e. emltound or am I permitted

TOR POPULAR EDUCATOE.

9k Wetufe* pftfcps notara fan, tke fleet a? mU or rqperfc*?

U (L e. seat/, awarding to report) be beaten.
€fc f*&a ft)* aid? sdaaiat jaitn, yog axe iii/mirf or aaaatted

act to (that is, yoo teal* act of necessity, hi an/ opiaioa)

the (L «• "■**

Oaf Ml tar «at? what i
j oT the) bat?

8n «*aaara fsfk. ***** cf I
fLt should be eNyas* by
fteJUriaiao.
80 with aa infiaitiv* aaaVtatood: aef ftft a*?what*as/i»
(*)/ aeffaSief? what s»«^«j to ? <L<l gsffryisg^aAaf
uthmtUbtT)
tri^B^iMvcrt^af^keiloesDotkaoarwhMto^o.

(7) Siffrn,tokncnr.

ijcdicatttb.

euajuacTive.

COWMTlOlfAL.

UmVlTlYB

PABTXCEPLB.

Present Tense.

id) vetf , I know,

bsacifi thou knowest-

crttetf, he knows.

vtr toiffes, we know.

tyr ariffct, yon know.

fbacfjea, thryknow.

Imperfect Tense.

Present ivMf*
id)*«fe, I may

he may
we may
yon may
they may

id)****,

batoeftcft

crwsftc,

tofewefftca,

tyrtofiffteft,

fUtsfifftcn,

I knew.

then didst know,
he knew,
we knew,
yon knew,
they knew.

S (3
* >2

Perfect Tense.

id) $abe gcteitft, I hare known,
bn $ojt gfleiift, dec.

cr $aft getouf ft,
toir ^aben gearoft,
i$r frabeft gramft,
fir $abeii gctouf ft,

Pluperfect Tense.
id) $*ttc enoiift, I had known,
feu lottrft gctonf ft, Ao.
cr tyofttc gcamfft,
toir fatten grtouft,
tyr ^atlrt gctottf t,
fU fatten grtouft,

.Ffov* Future Tense,

id) wcrbe tutffen, I shall know,
tu nrirft totfTen, Ao.

cr totrb toiffcit,
loir tocrbcii toifftn,
i$r tocrbeft toiffcit,
flc tocrbca toiffcit,

Second Future Tense.

id) toerbe
bit toirp
cr toirb
toir tocrben
i$r tocrbeft
fit tocrben

^I shall have
»| known, Ac.

ba wtffr&

«**
totr tot^ea,
•v* •wj»*#
F* wiffc^

jjnpcrTcct Accuse.

id) teafftc, I might
be wufuft, thoamightet
a teafftc, he might
toirtoefftcn, we might
ifr toaftct, yon might
fktoafftca, they might a

Perfect Teem.

id) job geweft, I may hare
ba fobeft geweft, known, Ac
or frabe geweft,
totr yuocn gctovfft,
t$r tyabeft gctottft,
fie faoen aetoeff,

Pluperfect Tense.

id) Joftfte gctoef ft, I might hare
btt fj&tuft octonfft, known, Ac*
cr jftftfte gctonfft,
toir ^Aitcn gctoafft,
u)r ^Atftcft gctotift,
fie ^Aftftcn gciwfft,

J^r#< JFWtortf Tense.

id) *i*rb< totfftn,
bu tocrbefi kDiffen,
cr tocrbc totffcnv
ten tverbcu t&iffcn,
t^r tocrbeft tviffen,
fu tverbcit toiffen,

Second Fntmre Tense.

Of) I
hare known.
Ac

PresmtTense.

2 atffcba.

knawthoo.
3. lotffccr, let

him know.
1. *tffcs»fx,kt

nsknow.
2* aiffci t^r,

know ye.
3. wi^ca fa let

•tiffta, to
know.

(if)Ishall
know, Ac.

id)tt«rbc ^
bu tocrbefi
cr iocrbc
toir tocrben
i^r tocrbeft
flc tocrben m

First PtOmre,

ieftaarbe
bvMrbefi
cr toflrbe
toir tottrbcii
t$r ojttrbcft
fie tburben -

Second Fetnre.

id)iefirbe

f-sS

«J3

Perfect Tense,
qaouft tyrixn,
to have
known.

emefefaiow*

ba toArbe^
cr tofirbc
toir tourbcB
i^r tourbeft
Ik

It*

LOOK ALOFT.

In tha tempest of lift, when the wave and the gale
Are around end above, if thy footing should fail,
If thine eye should grow dim, and thy caution depart,
11 Look aloft ! " and be firm, and be fearless of heart.

If the friend who embraced in prosperity's alow,
With a smile for each joy and a tear for each woe,
Should betray tkee when sorrows like clouds are arrayed
" Look aloft ! " to the friendship which never shall fade.

Should the visions which hope spreads in light to thine eye,
like the tints of the rainbow, bat brighten to fly,

Then tarn, and through tears of repentant regret,
"Look aloft ! M to the Bun that is never to set.

Should they who are dearest, the son of thy heart,
The wife of thy bosom, in sorrow depart,
" Look aloft " from the darkness and dust of the tomb,
To that soil where affection is ever in bloom.

And oh ! when death comes in his terrors, to cast
His fears on the future, his pall on the past,
In that moment of darkness, with hope in thy heart,
And a «nBe in thine eye, " look aloft " and depart

lessons in Italian.

183

LB880N8 IN ITALIAN GRAMMAR.— No. IX.

By CHABLE8 TAU8ENAU, M.D.,

Of the tTnlTtnity of Pavia, and Profeaaor of the German and Italian
1 at the Kensington Proprietary Grammar BchooL

A* the proper vibrated sound of double consonants can
only be acquired by much steady practice, I have to request
my pupil readers frequently to read aloud the following table,
in which I have selected a series of words showing the differ-
ence of pronunciation, and, at the same time, of meaning,
caused by the doubling of consonants in words, but for this
change, identical :—

SIXTH PRONOUNCING TABLE,

THB PRONUNCIATION 07 SINGLB AND DOUBLE
CONSONANTS.

Ala

am*

Arm

Cmn§
Cmro

Cmm

F*to
Wwca

IfNfc

Mfcsls
Tropa
Trtppo
Pen*

tteeo

Steno

Abate

hmto
heiito

Pronounced,
ah-lah
ahl-lah
ah-rah
ahr-rah
kah-nai
kahn-nai
kah-ro
kahr-ro
kih-sa
kahs-sa
fah-to
faht-to
feed-ko
feedk-ko
fo6-mo
fo6m-mo
gd-tah
g6t-tah
mo6-lo
mo61-lo
tr6-po
trdp-po
p&i-nah
pen-nah
sai-tah
set-tah
r6-so
r6s-so
sai-co
sek-ko
sai-no
sen-no
aai-rah
sdr-rah
sai-tai
s&t-tai
s6~no
sdn-no
bah-zai
b&hs-sai
m&i-zai
mes-sai
rd-zah
r6s-sah
stai-zo
stes-so
ah-ba-tai
ahb-bat-tai

in-sd-to

in-set-to

in-vee-to

in-vit-to

aht-tchai-zo

aht-tches-so

kon-tai-zah

kon-tes-sah

Englith.
Wing

To the (fern.)
Altar

Earnest-money
Dog

Canes, reeds, tubes
Dear

Car, cart, waggon
House
Chest, box
Fate

Done, made, fact, deed
Hoarse
Flake
Smoke
We were
Cheek
Gout
Mule

Barb (a fish)
Trope
Too much
Pain, punishment
Pen
Silk
Sect
Gnawed
Red

With himself
Dryness, dry
Bosom

Good sense, intelligence
Erening
Defile, hothouse
Thira*.
Seven
lam
Sleep

Foundations
Low, vile, base
Month
Harvest
Rose

Red (fern.)
Extended
The same
Abbot
He batters down, he

abates
Ingrafting
Insect
Invitation
Invincible
Inflamed, kindled
Admittance,
Dispute, contest
Countess

Italian.

Jronounced,

English

• One of the exceptional words, where the < must be pronounced
w»ha sharp, hissing sound, though it is placed between two

Maple

Acerra, a town in Naples

I pant, panting

Ring

Anus (in anatomy)

Year

Worm, silkworar

Bacchus

Dominions

Beak

Cheese

I chase, expel

Hair

Hat

Lady of rank

Doe

Ebb, he grows weak,

blunt
He had
Torch
Faces (pi)
Honeycombs
He does or makes there
He looks
Myrrh
Tender
They held
You sell

Acts of vengeance
Vinegar
I accept
Tonic medicines
Thou knockest down
Scab, scald, achor
Thou runnest hither or

helpest

Admittance, access
Devoted, obliged
Withered, thin
Entirely, quite
Winged, bird, beside
I suckle
Alecto, one of the three

furies
I allure
Dill, a plan
I annex
Ring-finger
To abolish, annul
Asylum
Horse-fly
Athens

He kept his word
Comet

He may commit (a crime)
Facetious, droll (fern.)
Facet (on cut atones)
Rose-garden, hedge of

rosea
Reddish

I shall now proceed to an explanation of the Italian
accents as they are used in Italian writing and printing ; for I
have already remarked on the accent of tone (an accent not
marked in Italian writing and printing), and its primary
importance in the enunciation of each word. This is, properly
speaking, rather a part of orthography than of pronunciation :
but I speak of it here because it is so intimately connected
with the rules of pronunciation, and, indeed, with the whole
grammar, that I prefer to explain it at the beginning of these
grammatical instructions, instead of at the end of them, as
generally grammarians do

Strictly speaking, there is only one Italian accent, which is
the grave accent, marked with a stroke from the left to the
right, thus r). Its use is not left to the discretion of the
writer, but is^zegulated by invariable rules: its omission is

AcCTa

ah-tchai-rah

Acerra

ah-tch&rr-rah

Anelo

ah-nd-lo

AneUo

ah-nel-lo

ah-no

Anno

ahn-no

Bmco

bah-ko

JSaeeo

bahk-ko

Beeo

b§-ko

Beeeo

bfik-ko

Cacio

kah-tcho

Caceio

kaht-tcho

QapeUo

kah-pei-lo

CappeOo

kahp-pgl-lo

Datna

dah-mah

Damma

dahm-mah

Ebe

e-bai

Ebb*

ftb-bai

Face

iah-tchai

Faeee

faht-tchai

Fart

fah-vee

Faw%

fahv-vee

Mira

me&rah

Mirra

mirr-rah

Ttnero

t3-nai-ro

Tennero

ten-nai-ro

Vendete

ven-dai-tai

VendetU

ven-de't-tai

Actio

ah-tchai-to

Aecetto ]

aht-tchet-to

Aeopt

ah-kd-pee

Accoppt

ahk-kdp-pee

Acori

ah-kd-ree

Accorri

ahk-k6r-ree

Adito

ah-dee-to

AddiUo

ahd-dit-to

Afato

ah-fah-to

Affatto
AUio

ahf-faht-to

ah-lah-to

AUatto

ahl-lah t- to

Aletto

ah-ldt-to

AUetto

ahl-ldt-to

Aneto

ah-n&-to

Annetto

ahn-ndt-to

Anuiare

ah-noo-l&h-rai

Anntdlare

ahn-nool-l&h-rai

Asilo

ah-zee-lo

AseiUo

ahs-sil-lo

Atene

ah-td-nai

AtUmne

aht-ten-nai

Cometa

ko-m&i-tah

Commeia

kom-me't-tah

Fateta

fah-tche-tah

Femetta

faht-tch6t-tah

Roseto

ro-zai-to

Roeeetto

ros-set-to

*«*

THE *0#flLAfc BDUCAVOB.

therefore an in fraction of grammatical laws. A characteristic
of this accent is, that only final letters of Italian words can be
marked with it. It is placed—

1st. On the last rowel of those words of aaore than one syl-
lable, the pronunciation of which require* a very emphatic *&§*§
to be laid on that Towel ; as, for example, field (peeuUt&lt)**
piety, pity ; bontd (bon-tu), goodness J tiborid (lee-birr-teh),
liberty; earitd (kah-ree-tah), charity; virt& (virr-to6), virtue ;
giovcntu (jo-ven-too), youth; pero (pai-r6), for that remaon,
still; amd (ah-md), he loved; crede (krsi-dai), he believed;
udi (oo-dee), he heard ; amero (ah-mai-rd), I shall low \ eetti
(ko-ste€), here ; cosid (ko-stah), there; eoei (ko-see),f thus.

2nd. On some monosyllables, where, to avoid ambiguity and
confusion, the grave accent is used as a means of indicating the
difference of signification. For example :

With the Grave Assent. Withosst ike Grave Accmi*

d (ah), has (for ha) a (ah), to (preposition)

ehe (kaij, to the end that, or in ehe (kai), who, which , what;

order that ; for (conjunction) that (conjunction)
dd (dah), gives, five da (dak), from, toy

di (doe), day di (dee), of

die (deed), he gave (for iiede) die (dee-ai), day
I (S). is e (ai), end

fe (fai). faith (for>eV) /#* (fai), he did (for feee)

gid ( jah), already, inaeed gia (jee-eh), he went (i r vita)

Id (lah), li (lee), there la (lah), U (lee), articles and

pronouns
tie (n£), nor ne (nai), a pronoun

6 (6), I have (for As) o ( , or

j>ie (peed), foot ( for jttWfe) jris (perf-ei), pious

«e (aai), a pronoun ** (sai), if

si (see), yea, eo si (see), a pronoun

3rd. It is placed on those monosyllables which have more
than one vowel as termination, to indicate the necessity of
pronouncing them as monosyllables ; as* for example : cu
(tend), that, what; pud (pood), he can; pto (peeo6), more; gin
(joo), below; qtd (kwee), here; *& (seefi), he is seated (for
siede).

Other monosyllables offer no ambiguity, and must there-
fore be considered as naturally unaccented, as they can neither
be confounded with other words of the same spelling, nor can
their pronunciation offer any difficulty. To mark these, as Is
sometimes done, with a grave accent, merely because they are
monosyllables, is not only a grammatical fault, but useless,
serving no purpose whatever, and encumbering Italian writing
with superfluous signs; for example: re (rai), king; fu
(foo), was ; gru (groo), crane ; eu (soo), above; ee (tchai), us,
here; ma (mah), but; mo (md), now; no (no), not; so (s6),
I know ; me (mai), me; &c.

Of the monosyllable qua (kwah), here, it may be remarked
that it is mote frequently written without than with the g?*re
accent, and of eU (stl), he stood (for oteMe), that being an
abbreviated word, it is always written with the grave accent,

I shall terminate these remarks on the grave accent with
two important rules, of very frequent application in I Uiisn
grammar.

1. When any monosyllable, written with the grave accent
or unaccented, or when any word of more syllables than one,
having the grave accent on its final vowel, is joined to another
word so as to make a compound with it, the initial consanant
of the latter word (unless an s with another consonant to fol-
low) must be , strongly vibrated in pronunciation, arid there-
fore doubted in writing, and the grave accent of the first word
taken off. For example :

• Fot the sake of consistency of system, I shall net deviate,
m these cases, from my useal practice of marking evert ly I ubk
whieh has the accent of tone- ey the acute of etrstuasV \ sign.
The readsr wiiL, of course, understand that these are mere arbitrary
signs used for the purpose of instruction, and which most aot be
imitated when he may huve occasion to write words requiring the
grave accent.

f This is another of those exceptional words where the s must
be pronounced with a sharp, hksiag eeund, though it is placed
i. l»efewten two vowels. It ss •bvious,frora its sseaarnsj, that, like cmu
(kd-sah), thing, it is of the most frequent occurrence.

e (e), is, and vi (ya«) theres=#etrf (dv-*ee), there is.

piu (peeoo), more, and toeto (t6-sto) # waazzpiuttosto (peeoo-
td-sto), sooner, rather.

gid (jah), indeed, and mai (mahee), neverz^ismmei (jahm-
mahee), never.

dd (dah), give, and mi (mee), to me=dammi (dafcsn-mee),
give me.

I fa (lah), do, and mt (mee), to me=r/bm*ti (fahm^mee),
do me.

amd (ah«mo) t he loved, and la (lah), her==*molfc* (ah-mSl-
lah), he loved her.

faro (fah-rd), I shall do, and lo (lo), itszfaroOo (fah-rol-io),
I shall do it.

fra (frah), between, and tanto (tfhn-to), so much ot SO kssg
a time= frattanto (fraht-t&hn-to), in the mean time.

da (dah), from, end lo (lo), therafoto (dahl-lo), from the.

eu (soo), upon, and lo (lo), the=sullo (sool-lo), upon the.

2. Monosyllables, though naturally unaccented, must be
marked with, the grave accent, when as last syllables ef a
compound they are joined to particles ox other words. Fer
example s

per (per), through, and ehe (kai), whietes^psrefe? (perr-ka*),
why, because.

a (ah), to, and do (do), I giverrarfid (shbVdd), I apply flay*
self to.

eonfra (k6n-trah), against, and fo (f&), I make=xontr*fl
(kon-trahi-f8), I counterfeit.

ri (ree), a particle, and ho (hd), I havez=riAo or ri6 (ree-6),
% have or get again.

ri (ree), a particle, and so (so), I knjow==mi» (ree-sd), I know
by hearsay, I learn*

eopra (so-prah), upon, and sto (std), I stand==sqpra*tS' (se»
pra-st6), I am above*

tras (trahs), a particle, and vo (vO), t goezfrosfd (trsh*"v6),
X pass beyond or exceed.

qua (kwah), here, and su (soo), aboTer=yiaM«» (kwahs-so6),
up here.

mai (mahee), never, and no (n6), not=maino (manee-nd), no,
not at all.

oi (oee), ah ! aUsl end me (mai), me=xmi (oee-mai), alas !
unhappy me !

vice (vee^tohai), ernes titute, and re (rai), kmgzrviceri (vee-
tchai-rai), viosroy.

And so all the numerous and similar compounds of chc, Ac
compounds of su, and of the verbs do t fb t ho, so, sto, vo, &c.

The acute accent has been adopted by modern authors ss the
mark to show the difference of meaning in some words of the
same spelling, though differently pronounced, which weeds,
without the acute sign, might occasion confusion and ambiguitr,
particularly in the case where words of more than one syllable
terminate in the dinhtoongs ia t ie, • and io, and from the use ef
the acute sign over the t, and the necessary stress laid on tfre
syllable thus accented, acquire a different signification. Bat
even in words ending in io and ia t and presenting no ambiguitf ,
the acute sign is not nnfrequently pieced merely to indicate
that the letter t does not make the two terminating voweleo
and a in conjunction with the » diphthongs, but that they ate
separate syllables. It is a characteristic of the acute sign that
it can never be used in final letters, as the grave accent is used.
But the use of this accent is, generally speaking, not regulated
by invariable rules, and is frequently left to the discretion of
the writer. I need not say that the acute sign, which X have
adopted in these azsmmatical instructions, exactly answers the
purpose for which it has been introduced by Italian writes,
with this dUfferac* only, that I shall use it throughout &e
whole course oi the grammar, .while they place it merely on
some words to avoid ambiguity.

I shall eawy give atfstof words where It is snore generally used,
some of which I haw already quoted in the preceding fMb-
nouncing tables : natio (nah - tec* - o)> natta (nan - te$ - ah),
natal, native; reeilo (rai-stee-o), restive. stubborn; stantto (stahn-
tee'-oj, old, rancid, fruitless ; Upgio (Ied-je^-o), rrnrlinjg deak.
a painter's easel ; ubbia 'oob-beC-ah), bad presage ; ' sas^i

KEY TO LATIN EXERCISES.

185

(mah-lee*-ah), sorcery, enchantment; kutia (ba-stee'-ah),
bastion ; ttrofinio (stro-fee-nee-o), Bcouring, rubbing ; mormerio
(marr-mo-ree-o), buzzing, murmur ; rovinio (ro-vee-nee-o ,
great noise ; A6cine (feed-tchee-nai), skin of Taisin-stones ;
dtfoio (tsoo-fo-Io), flute, whistling ; margin* (muhrr-jee-nai),
t oar, edge, margin.

With the Acute Sign. Without the Amis Sign*

balia (bah-lee-ah), nurse
gid (jah), already, indeed
net (nai-ee), in tne (pi.)

bmli* (bah-lee-ah), power
fU ftetf-sh), he went

«sY (nt-ee), moles, patches _

dmoorm (ahn-ko-rah), anchor aneora (ahn-k6-rah)7 again
strepiech (stro - pit - tehee - o), etropiecio (stro-pit-tcho), I rub
friction, rubbing

The circumflex accent is of more recent use, particularly
among poets, to distinguish words of the same ferm, but
of different signification ; as, for example :

With the CircuinJUx Sign. Without the dreum/ee} Sif*.

Mere (t6r-rai), to take, seise torn (tor-rai), tower

(fox tCfUere) .
esViw (kdr-rai), to gather (for oorre (kor-rai), he runs

sssdre (eh-mah-ro), they loyed amoro (ah-mah-ro), bitter
(for mm eron o)
"" "*" fero (f&-ro}, fierce, wild

era (6-rah), now
'alloro aUorm (ahl-16-rah), then
gr offers)
issV (oo-defa), they heard (for udire (oo-de£-rai), to hear

Tfce reader will have remarked that the circumflexed 6 in
4*» above examples has the open sound; and thus this mark-
ka* of those words on the part of modern Italian authors agrees
witk the sign that I have uniformly adopted to mark the open
1 sound of o.

K Ul TO THE EXERCISES IN THE
LATIN LESSONS.

By John B. Beard, DJ).

{Continued from page 120, Vol. IV.)

Yol. III., p. 130.— English-Latin.

▲taenia vixit soror mea ; Athcnas frater tuus ivit; ab Athenis
ivit Consul t a Gallia in Angliam venirt legatus ; domine est mater ?
ewoite korA dotni erit; Corinttium proficisitur rcgina ; apud Regi-
assn saulram tt.t arjrenti ct auri ; eo rus; rur esc pater; rure
quando Timet soror? belli dumique fortes sunt Angli ; plectitur
lfgUgentia; vulupiitis causa juvenes oflieia d< serent ; tribuni
'tis metu atqu^ iia creati Hunt; esne Porte t-iA laetus ? beneficiis
tonuati; instrucli sum pueri libris ; Unguis tutantur se feminae ;
ke libria donavit me pater ; juvenes ludo delectantur; Deum
pus mente venerati sunt; est homo excelss stature; singulari
asjestiludine eat soror tua ; prisci Britanni borrido dieuntnr fuisse
l; erat Caesar dux summtt virtute; flumen difficile est
b; haec domus auro non est venabst Homeri poemata
sis non mercantur ; aestate cautant axes, ludunt pueri ; inter-
> duee, fugerunt milites ; sole orientc, nox abit; non semper
sapient sapientes.

YoL III., p. 147.— Latin-English.

1 fears nothing to write respecting the commonwealth ; these are

lis things which I have to say; O Hannibal, thou kno west how to

esaquer, but how to pioiitby a conquest thou dost not know;

Fdopidas aid not hesitate to join battle as soon as he beheld the

•assay ; they proceed to go to Soguntum ; all who desire to per-

*~~ ", great things are wont to reflect long : Miltiades compelled

"to return to their duty ; the office of seeing that the

■1th received no damage was assigned to Posthomias ;

took means for restoring the libraries destroyed (ab-

Swptts) by fire ; they have begun to contend in arms ; I prefer

teat well to being rich; for poets to be unpolished is a sign of

H|hgence ; I have the power to be happy ; I forbid thee to be at

nst; I allow thee to hold thy peace ; they may be timid and

"\j I have not time to be ill ; men do no&allow poets to

r merit ; to a learned mind thought is life ; the faith-

ful learning of the liberal arts softens the character; but we
consider to trip, to err, to be ignorant, to be deceived, both an evil
and a disgrace ; do not wish that which cannot be [dele the comma
after fieri] ; do not forget that you are Cicero ; arrange so as to
postpone (the matter) to another day ; I will let you know if any-
thing new takes place ; I wish I could avoid not only the blame but
also the suspicion ; I wish I could find the true as easily as I can
confute the raise ; I wish the occasion had not offered in which yon
might ascertain how much I value Pompey, how much Brutus ;
would that you would pardon me ; I wish you to write whatever
comes into your mind : the senate voted that the consuls should
take care that the republic received no injury ; you should love me,
not mine ; man must die ; your diction should flower forth from a
familiarity with your matter; I pass the fact that he chose this
abode as his home ; it is the time for making greater efforts ; he
formed the plan of thoroughly destroying the fortunes of his neigh-
bours ; I am ready to sail ; they are prepared to endure all things ;
they say that Demosthenes was accustomed to declaim before the
sounding billows ; we shall be in a better moral condition when
we have learnt what nature requires ; Plato, if only I can interpret
him, uses pretty nearly these words ; I will be as thou wishest me
to be i he took steps for having very many houses built.

Vol III., p. 148.— English-Latin.

De fratre tuo nihil habeoquod scribam ; Deum esse eognovimus *
plurima protuliase verba constat Demosthenemt quid dices sdo;
auid dieturus sis scio ; quid dices seism ; id quod dixit pirate rex
damnavit ; ea quae dixisti damnavit pater mens ; esse quern videri
bonus malim; illis pecuniam colligere non vacat; videri doeta
vult soror tua; eloqueatem esse TuUionem scio; abisse patrem
sciunt ; qusndo rediturae sint sorores ignorant ; quando rediturae
eseent eoreres ignoraoant; ejuid agas vident; nemo tarn eaeeue
erat qmim quid ageres videret.

YoL UUt p. IleWLaixx-EjroLiSK.

No one knows what the late evening may bring y go, create
consuls from the common people ; the patricians raging say that
they were going and creating consuls from the people : he will
know this when he breathes his last ; he said that he would know
this when he breathed his last ; I will do what the consul com-
manded ; he says that he will do what the consul commands ; he
said that he would do what the consul commanded (he said) that
you ought not to deal with him as with a citizen who had formed
the hope of gaining a crown ; it is announced to Caesar that the
Bulmonenses are desirous to do what he wished ; the soldiers send
ambassadors to Caesar (saying) that they are ready to open the
gates, and to do whatever he commands ; that he might punish
the guilty, that he would pardon those who had erred, and that he
would lead them against the enemy ; while I wan absent, as often
as I thought of my country, all these things occurred to me — the
hills, the plains, and the Tiber, and these skies under which I was
born and brought up ; it is a custom at Athens to eulogise in a
public assembly such as have been slain in battle ; Themistoclee
walked abroad by night, because he was unable to sleep ; no cha-
racter appears more suitable to speak of old age; no human sight
has power to penetrate into heaven ; innocence is that affection
which iiijures no one ; we must take care to use that liberality
which may benefit friends and injure no one ; no race of men is so
brutish as not to have some idea of God ; the Campanians com-
mitted faults too great for pardon ; I am the person to hold* that
it is better to yield to Caesar what he demands than to join battle ;
it is more easy to find those who of their own accord offer them-
selves to death than those who bear pain patiently,; there is no one
who does not prefer having all the integral parts of his body unin-
jured; who is there but discerns how great is the power in the
senses ; there is nothing which may not be injured by being badly
told ; there is nothing that does not perish ; acquit him who con-
fesses tnat he took possession of the gr< atest sums of money to the
vry great injury of our allies; that kind of utterance is to be
chosen which may chiefly hold the attention of the auditors ; who
art thou ? I know not who I am ; there will be runny to whom you
may properly give a letter ; there is no living being except man
which has any notion of God; the shining of* the* sun is more
brilliant than (that) of any Arc, since it shines so far and so wide in
the measureless universe.

Vol. III., p. 166.— Enqlish-Lxtin.

Quid afferat eras nescio ; hostem esse venturum dicit ; quando
sit moriturus nemo cognoscit; scisne quando sint redituri qui
venerint ? vos non ridere quuni ipai sa spectamini, miror ; me non
ridere te spectanum miiaxi dixit pater; ahume aptior est qui
Greccaoa doceat ? qui pueros bonos ac duigentes faciat neminem
aptiorem scio; noctu ambulabo quia somnum capere nequeoi
virtue nmlli aoeet; sapiuai qui vlrtnum null! notere eonfirment ;

186

THE POPULAR KDUOATOfL

non is sum qui religiouem noeere hominibns oonfirmam ; quia est
quin quanta in religione vis tit videat ?

Vol III., p. 173.— Latik-English.

That power overcame all the blandishments of pleasure and
ease ; there is disturbance by tea and land ; Nnma had imbued all
breast* with such piety that faith and oaths governed the state ; to
repel force by force reason has prescribed to the taught, and neces-
sity to barbarians, and custom to nations, and nature itself to wild
beasts ; the world is the begetter, and originator, andparent, and,
so to say, the nurse and educator of all things ; Hortenius re-
membered both what was said against (him) ana what he himself
said ; that can neither be kept unsaid nor oe said as a regard to
dignity demands ; no animal can be found which was never born
and will always live; therefore, both promises are sometimes not
to be made, and deposits are not always to be restored ; Caesar pos-
Besses a certain splendid method of speaking, in voice, in gesture,
also in a magnificent and noble form ; if right, justice also ; the best
man (most readily) confesses that he is ignorant of many things,
and that he must learn [read discendaj many things again and
again ; the fruit of leisure is not effort but relaxation of mind ; he
is on the side not of enemies but of friends; I have gained this,
that not only thy whole house but all the city may know me to be
very friendly ; I am persuaded that a man ought not to admire, or
wish for, or desire anything except what is honourable ; nothing is
so correspondent to nature, whether for prosperity or adversity, as
friendship ; distinguished men, whether they do well or ill, excel
in both ; the laws of the Cretans, which, whether Jupiter or Minos !
enacted them, instruct youth in labours.

VoL III., p. 173.— English-Latin.

Hand operantur ; idciroo quum erit opus, nihil habebunt ; id
quod dicis vix credibile videtur ; sed sic est : deos omnes etiam
atque etiam, invocavit Cicero ; nullum nisi homo inveniri potest
animal quod rationis sit compos ; illud et bonum est et malum ;
hoc neque bonum neque malum; patri et filii civitas decrevit
statuam ; filiaeque datum est praemium ; divitiae non modo eom-
parandae sunt sed etiam fruendae; aut discs aut discede; quae
dicis aut vera aut falsa sunt.

Vol. III., p. 192.— Latin-English.

It happened very conveniently for me that you came to hear
Antony ; they aim at appearing good men ; I admonish you daily
to reflect that anger should be resisted ; if the good put down
tyrants, as often happens, the state is created anew ; in pro-

—e, so that I may then (in old age) live happily ; the sun makes
all things flourish ; I advise you carefully to read not only my
orations, but also these books on philosophy ; we are impelled by
nature to wish to benefit as many persons ss possible : it happened

nature 10 wisn to oeneni mm many yvtauua ■» pwiw, *• «-i»jj«««~*
very inconveniently that you never saw him ; besides he is de-
lighted with superior minds; this is a common thought in great
and free states (namely), that envy is the companion of glory;
hence it is proved, not that pleasure is not pleasure, but that
pleasure is not the highest good ; I cannot help sending a letter to
you every day ; do not hesitate to trust all these things to this one
man ; since I have spoken of the nature of the war, now I will say a
few things respecting its magnitude ; since neither the authority of
the senate nor my age avails with thee ; speak, since we have sat
down on the soft herb ; who neglect aU right and honourable things
while they pursue power ; the sick man is said to have hope while
there is life ; I have stopped longer than was allowed ; as long as
there was war with the citisens, he was quiet at home ; from the
angry, those are to bo removed on whom they try to make an
attack, until they have recovered themselves; I have considered
everything secondary, provided I could obey the commands of my
lather ; diligent preparation is to be employed in all business
before you take it in hand ; since you have hope not even on the
part of the Romans, I bring you peace; since nothing was written
to me of your arrival, I fear lest that may so happen ; as soon as I
reached Borne, I considered I ought to do nothing before I con-
gratulated thee while absent on our return ; when the army had
been drawn up, the spear-bearers first of all went into battle ;
because nature cannot be changed, therefore friendships are ever-
lasting ; you should eat to live, not live to eat; nothing is wanting
to make me most miserable ; he almost slew Varus -, they jnay so
withstand as to prevent external things from being effected; if all
things take place by fate, nothing can admonish us to be more
cautious; if you wisely bear troubled circumstances, you will bear
the more tranquil joyfully ; the day would fail me if I wished to
defend the cause of poverty; if we could always keep the best, we
should certainly not need counsel ; had not counsel, reason, Judg-
ment, been in old men our ancestors would not hare called the

highest tribunal (by the name of) senate (the counsel of the elders) ;
I should not have come unless the fates had given a place and an
abode ; I could remember the tune if possessed of the words ; very
good men do what is right, what is honourable, although they see
that no emolument will follow; man does not admire what he sees
frequently, although he knows not why it takes place ; there are
those who, through the fear of hatred, dare not say what they
think, although it is excellent; in certain commendable men,
though their talents were not very great, yet was there praiseworthy
industry ; although every virtue attracts us to itself, and makes us
love those in whom it appears to exist, yet justice and liberality
does that pre-eminently; though Aristides excelled in self-con-
trol, yet was he punished with a ten years' exile ; that which is
base, though concealed, can yet in no way be honourable.

ANSWER8 TO CORRESPONDENTS.

J. Twiidaxk (Manchester) : The treat labour attending the getting up
of the numbers of the French Dictionary is the cause of the occasional
Irregularity in the Issue.— C. FosTia (Nottingham): |The choice of words
in the second part of the French Dictionary is a great advantage, for by
turning to the first pert you can see the different shades of meaning in the
different words, and thus select the most suitable for your purpose.—
Thomas B. (Sutton in Ashneld) wants some young subscriber to the P. E.
to solve him the following quesUon taken from " Poor Richard's Almanac *
for 1847 : '* A man had a certain number of apples which he divided among
three boys as follows : to the 1st boy, he gave half .the whole number and
half an apple; to the 2nd boy, be gave half of what remained and half aa
apple; and to the 3rd boy, half of the residue and half an apple. What
number of apples bad he to make this division without cutting any apple
and without having any apple remaining/'

E. Edwards (Paris): We regret our inability to give him directions in
medical studies. We would advise him to procure programmes of the
different medical lectures delivered in Paris, as these would answer his
purpose better than any directions we could give ; the lecturers themselves

German Pronouncing Dictionaries.— Youth op 17 (M
straight lines placed in a circle bisect each other, it may be inferred either
from the 4th or the 9th of the 3rd Book of Euclid, that the point of bisec-
tion is the centre. As to the the studies for Holy Ordtrt. we recommend
him to apply to the rector or curate of his parish. The study of Latin
and French might go together.— L. F. O. (Sheffield): His proposal for a
People's College in London is a very good one ; we think that the authorities
of the University of London should allow such colleges to be affiliated to
the university, in order to encourage the working classes to aim at its
honours, and thus to raise the standard of morality and intelligence ; for
when men are studying the languages and philosophy in the evening,
instead of lounging in the beer shop, they are surely more out of the way
of temptation.— W. M. (Norwood): Uymnie a I'Angleterre received.

J. Holland: The best English Grammar is of course the Lessons in
English in the P. E.— W. L. M. (Islington) : A letter of recommendation
to blr Henry Ellis from a well known character, is the best mode of obtain-
ing a ticket to the Reading-room of the British Museum.— A. Baows:
Very iugenious, but too flattering.— Self-taught (Ouke-sreet) : The best
edition of the P. E. sells at 4s. 6d. per vol. The eases for binding them in,
are Is. 3d. per vol. best edition, and Is. per vol. common edition. A binder
can scarcely charge less than 6d. for putting the book in the ease in a

E roper manner.— Kaimist had better apply to Messrs. Cocks and Co., New
iurllngton-street, on the subject of musical instruments and instruction
books.— O. Williams (Bristol) : The double Webster is surely better than
the single one.— J. F. C. is perfectly right ; the correction has escaped the
printer's notice.— J. Cora (Manchester) Is right; they have been corrected.

LITERARY NOTICES.

JJOHN CASSELL'S DICTIONARIES;

IN NUMBERS, AT 3d. ; PARTS, AT la.

NOTICE.

rmsxrcK dictiova&t.

In consequence of the serious Illness of the principal Editor of the FaiHOM
Dictiomasy. the regular weekly issue of tnis work has unfortunately been
interfered with No. 21 is now ready, and every effort will be made to
continue it weekly until completed.

os:

DXCXIOVA&V.

The Third Part of this Dictionary is now ready, aa also the first Thirteen
Numbers; and it will be regularly issued fortnightly, or eftensr if ftossJate,
till completed.

TBS UkXTM DXCTXOVA&Y.

The First Number of this Work, edited by J. B, Baaap, aXD* arise *i,
will be rsadv Jan. 7, and will appear weekly.

NATURAL PHILOSOPHY.

1ST

ON PHYSICS OR NATURAL PHILOSOPHY.

No.X.
BODIES IMMERSED IN LIQUIDS.

Present* en Bodies immersed in Liquids .— When a solid body
it wholly immersed in a liquid, pressures take place at every
mint of its surface, perpendicularly to that surface, and
isereasmg with the depth. If we stippose these pressures to
be divided into horiaontal and vertical pressures, then the for-
mer act on each horiaontal layer of the solid, with intensities
which are equal and contrary to each other, and therefore
destroy each other's effects; but the vertical pressures are
unequal, and tend to make the body move upwards. Thus,
suppose that a cube is immersed in a vessel of water, fig. 34,

Tig. 34

mud that, lor the soke of simplification, four of its sides are
sd vertically. The vertical sides presenting the same
i to Iks liquid and being immersed to the same depth,

however, to the pressures which act vertically on the horiaon-
tal sides a and b, it is evident that the downward pressure on
a is equal to that of the weight of a column of water having
the side a for its base, and a d for its height ; also, that the
upward pressure on b, is equal to that of the weight of a
column of water having the side b for its base, and b d for its
height. The cube, therefore, tends to rise under the pressure
of a force equal to the difference of these pressures, which is
evidently equal to the weight of a column of water having the
same base, and the same height as the cube ; consequently
this pressure is equivalent to the weight of the water dis-
placed by the body immersed ; and such is the force which
tends to push a body upwards when it is immersed in a liquid.

Principle of Archimedes.— "From the previous considerations,
it is now evident that every body immersed in a liquid, is
acted on by two opposite forces ; 1st, that of gravity, which
tends to make it descend ; and 2nd, that of the upward pres-
sure of the liquid, which tends to make it ascend with a force
equal to that of the weight of the liquid which is displaced by
the body. The weight of the body itself, therefore, is either
partially or wholly destroyed or counteracted by this upward

f>ressure ; whence, we conclude, that a body immersed in :
iquid loses a part of its weight equal to the weight of tLe
liquid displaced by the body. This principle, which constitutes
the foundation of the theory relating to immersed end floating
bodies, is known by the name of the Principle of Archimedes
because it was discovered by that celebrated geometrician at
Syracuse, about 220 b.c.

This principle is experimentally proved by means of the
Eydrostatie Balance. This apparatus is only a common balance
having the scales furnished with hooka", and the beam so
adjusted that it can be raised or lowered at pleasure by meacr
of a rack, moved by a pinion at c, fig. 35. A. catch d holds
the rack when it is raised. When the beam is raised, a hollow
copper cylinder a is hung under one of the scales, and below
that a solid cylinder b, whose volume is exactly the same as
the interior of the former ; in the other scale, are then placed
weights sufficient to balance the whole. If now the cylinder

Fig. 35.

**perieaee equal pressures ; and the sides being opposite to each
*ber, two and two, it is plain that those preasuresare equal
*■* contrary; hence, they are in equilibrium. W*th regard

fOL.IT.

a be filled with water, the equilibrium is destroyed ; but if
the beam be lowered at the sane time, to that the cylinder b
is entirely immersed in a vessel of water placed below it, the

THE POPULAB EDUCATOR.

3uilibrium will be restored. The cylinder b therefore, loses,
er its immersion, a pert of its weight equal to the weight of
the water poured into the cylinder x. Thus, the principle of
Archimedes is proved, since the internal capacity of the Utter
cylinder is exactly equal to the volume of the cylinder b.

Determination of the volume of a Body. — The principle of
Archimedes supplies us with the means of finding with exact*
ness the volume of a body of the most irregular form, when it
is not soluble in water. For this purpose, we hang the body
by a fine thread to the hook of the scale of a hydrostatic
balance, and weigh it first in air of a given temperature ; we
then weigh it in distilled water at the same temperature ; and
the loss of weight which h experiences in the latter case, is
the weight of the water displaced. From the weight of this
water we ascertain its volume, and consequently mat of the
body immersed, which is evidently the same. For example,
suppose the loss of weight in a body to be 2jlbs. Avoirdupois,
the temperature of the water and air being 02° Fahrenheit ; it
is plain, since* an Imperial gallon of water, at this tem-
perature, weighs 10 pounds, and that its volume is 277274
cubic inches, that the volume of the body in question must be
omufourth of that of an Imperial gallon of water, or 69318
cubic inches.

Equilibrium of imme n e d <md fhetmg JMUm.— From the
theoretic considerations which led us to the principle of Archi-
medes, we see that, if a body be immersed in a liquid of the
same density as itself, the upward pressure which ten to
raise the body is equal to its weight ; the body will therefore,
remain suspended m the liquid wherever it is placed. If the
body has a greater density than the liquid, it will sink; because
the pressure of its weight is greater than the upward pressure
of the liquid. If the body has a less density than the liquid,
the upward pressure of the latter will predominate over that of
its weight, and the body will float at the surface, having dis-
placed only a quantity of the liquid of the same volume as itself.
Wax, wood, cork, and all other bodies lighter than water,
therefore, float on its surface.

The laws of stable equilibrium relating to bodies immersed
or floating in a liquid, are : 1st, that they displace a quantity
of the liquid whose weight is equal to theirs ; 2nd, that their
centre of gravity must be below the centre of pressure and in
the same vertical line.

In theoretical mechanics, however, it is proved that stable
equilibrium may take place although the centre of pressure be
found below the centre of gravity, provided that a certain
point called the Metacentric be situated above the centre of
gravity. The determination of this point belongs to geometry ;
and its knowledge is of the greatest importance in the stowage
of vessels, for it is upon the relative position of the centre of
gravity, and the metacentre, that their stability depends.

According to the principle of Archimedes, bodies float with
greater facility upon the surfaces of liquids in proportion to
their density relatively to that of the floating bodies. For
example, an egg sinks m common pump or river water, because
it weighs heavier than an equal volume of water ; but it swim*
in water saturated with salt. A piece of oak floats on water;
but it sinks in oil. A mass of iron floats on mercury; but it
instantly sinks in water and most other liquids. In floating
bodies, the volume of the part immersed in the liquid, is in the
inverse ratio of the density of the liquid, and in the direct
ratio of that of the floating body.

The different effects of floatation, suspension, and sinking in
a liquid, are ingeniously illustrated by the following apparatus,
fig. 36, which consists of a tall glass jar, or similar vessel,
nearly filled with water, and closely covered at the top with a
piece of bladder or other air-tight membrane. In the vessel is
placed a small figure made of glass, metal or enamel, having a
hollow ball of glass at the top containing air and water, and
floating at the surface of the water in the vessel. In this ball,
at the lower part, there is a small aperture through which
water is made to flow inwardly or outwardly, according as the
air within it is more or less^ compressed. The quantity of
water previously introduced into the ball is such, that the
figure requires only a very slight additional weight to make it
jmk to the bottom of the vessel. If then we press lightlv with
the thumb, on the air-tight membrane, the air immediately

under it is c omp res s ed, and transmits the force of the pressure
to the water in the vessel, and thus within the ball. In con-
sequence of the compression which the air within the ball now
undergoes, a certain additional quantity of water is forced into
the ball, and the floating figure, becoming more heavy, instantly
sinks. If the pressure on the membrane be removed, the air

Fig. 86.

in the ball expands, the additional water is forced out of the
ball, the figure becomes lighter, and rises to the surface to
float as before. Thus, by varying the pressure, the figure can
be made to remain atfche top, in the middle, or at the bottom
of the vessel, at the pleasure of the experimenter.

A great many kinds of fish are furnished interiorly under
the back-bone with a thin membraneous vessel full of air,
called the twist. These fishes, by compressing or expanding
this vessel by a muscular effort, cause its volume to vary, and
produce effects similar to that which we have described in the
preceding experiment ; so that by this means they can rise or
sink, or remain in the middle of the water, according as instinct
directs their motions.

SunmminQ.— The human body is lighter than a quantity of
fresh water equal to it in volume. Hence, it will naturally
float on fresh water, such as rivers, ponds, &c; and still more
on salt water, such as the sea, the latter being a heavier liquid.
The difficulty of swimming, therefore, arises less from the ina-
bility of the swimmer to keep near the surface of the water, than
from his inability to keep his head above water in order to
have free respiration ; for his head, being heavier than the
other members of his body, has a tendency to sink. Hence
the necessity of human beings learning to swim, and of culti-
vating it as an art. On the contrary, the heads of quadrupeds
being lighter than the other members of their body, they can
remain for a considerable time in the water without sinking,
and can swim naturally without effort.

SPECIFIC GRAVITY.

Specific Weight or Qramty.— We have seen, in Lesson IV. p.
46, that the specific weight or gravity of a body, whether solid
or liquid, is a number which expresses the ratio of the relative
weight of a body of a given volume, to that of an equal volume
of distilled water at the maximum density. In order, therefore,
to determine the specific weight of a body, we must find its
relative weight and that of an equal volume of water, at the
same temperature, and divide the former weight by the latter,
when the quotient will be the specific weight required, that of
water being taken for unity.

Various methods are employed in the determination of the
specifio weights of solids and liquids ; the most useful of these
methods will be explained in the following paragraphs.

Specific Weight of Solid*, — In order to determine the specific
weight of a solid, by means of the hydrostatic balance, fig. &,
we weigh it first in air, and then suspending it by the hook of
the balance we weigh it in water \ the loss of weaght which «
experiences in the latter case k is» according to the prMpleof

LESSONS IN GEOLOGY.

1S9

( Arphime4es, the weight of a volume of wafer equal to that
of the body ; we "have only now to divide' the weight of the
podj in air by the weight which it ban lost in water/ and the
quotient is the specific weight required. Thus, if p repre-
sents the weight of the oody in air, jf its weight in
prater, and d its specific weight, the weight of the water dis-
placed being p—p\ we have d=z JL— t

• J%$ Areometer* of Nicholson.— -The term areometer (from Gr.
araios, thin, and matron, measure) literally signifies rerity-
l i i essa i i , and is applied to a floating apparatus employed in
ftrternrinmg the specific weights of soUqs. The areometer of
Nicholson » composed of a hollow cylinder b made of tin,
fig. 97, to which is applied a cone c, filled with lead ; the use

Fig. 37.

small iron-wire grating to- coyer the body and prevent its
rising to the surface of the water in the vessel. This beinc
done, the process of determining its specific weight' is thej
conducted in the same manner as in the preceding framplW *

of this eons being to ballast the apparatus in a vessel of water,
in Such a manner as that its centre of gravity shall be placed
.below the centre of pressure, the condition, as before remarked,
necessary fi>r stable equilibrium. This apparatus is furnished
at the Upper part with a stem and a scale-pan a, for the re-
ceptfon of the weights and the bodies whose specific weights
are to he determined. On the stem a mark is placed, called
pie iemtetymari or point of water-Uvel % which is used to de-
termine when the apparatus sinks to tfie same level in the
vessel of water,' when loaded with a weight or with a body. In
using this instrument, we first ascertain the weight which it
[is n ece ssa r y to put into the scale a, in order to make the
areometer sink to the water-mark in the vessel ; for, when this
scale is empty, the instrument floats above the level of the
water.' Now, supposing that this weight is 2,000 grains, and
* we wish to find the specific gravity or weight of any substance,
say sulphur ; we remove this weight ; we take a piece of sul-
phur of less weight than 2,000 grains, and we place it in the
' scale A ; we then add as many grains as are necessary to make
. the areometer sink to the water-mark. Supposing that these
; additional grains are 880, it is plain that the weight of the

Siece'of sulphur in this scale is 1,120 grains. Having thus
etermined the weight of the sulphur in sir, we must now find
the weight of an equal volume of water. For this purpose,
we lift the areometer out of the vessel of water, and wo trans-
fer the piece of sulphur from the scale a to the cone c, as
shown in the figure. The total weight of the apparatus is not
changed by this change of position in the place of the sulphur,
\ and yef on its re-immersion in the vessel of water, it no longer
sinks to the water-mark. This arises from the fact of the
\ sulphur, when immersed, logins actually a part of its weight
equal to that of the water which it displaces. If we now put
* into the upper plate a, weights sufficient to bring the instru-
ment down to the water-mark, say, in this instance, 551
grains, this number will represent the weight of the volume of
' water displaced ; that is, of the volume of water equal to that
of the sulphur. We have, therefore, only to divide 1,120
grains, the weight of the sulphur in air, by 651 grains, its
' weight lost in water, and we have for the quotient 2*03, the
specific weight or specific gravity of sulphur.

If the substance whose specific weight is required is lighter
then water, it will have a tendency to float, and will not
'loathe base of t the eoneo. In this case, we employ a

LESSORS IN GE0LQPY.— No. XL.VL
By Thos. W. Jhxxyn, D.D., F.R.G.S., F.GkS., &c

CHAPTER IV.
ON THE EFFECTS OF ORGANIC AGENTS ON THE
EARTH'S CRUST.

SECTION IV.

THE RESULTS OF THH AGKTCY OF MAN.

Though man comes into the world as a creature subject to the
laws of nature, it is yet evident that he is endowed with an
agtney that can re-act upon nature, so far as not only to trans-
form her aspects, but even to prescribe new laws to her opera-
tions. Han has not been so long upon the face of the earth as
plants and animals have been, nor has his race been so exten-
sively distributed as the flora and the fauna of the globe have
been, and therefore he has had neither the time nor the space
which they have had, for exerting deep and signal influence
on the earth's crust. Yet, wherever mankind have established
themselves and promoted rivflixationV' there they hare pro-
duced great geological changes m the surface of the globe.

You have often heard the line quoted "God made the
country, and man made the* town." There is muoh poetical
truth, and some physical truth, expressed in this verse : but
ft is not •• all truth, and nothing but the truth." Geology
robs it, not of the beautiful poetry which it breathes, but of
the physical fact which it asserts. Kan has not only made
the town, but his agency* and especially his advancement
in civilisation, has made the country muoh what it is, You
will, very likely, change your mind about the fact on which
thispoetry is founded, if you will attend to this lesson.

Where 'man is found in a savage state, employed merely in
hunting or fishing, his influence in changing the aspects ot
nature is very slight. In this state, the population is compara-
tively scanty, and its activity is very limited. He may extir-
pate a few animals for food, and he may destroy a few forests
tor fuel, but the change which he produces on the earth's
surface is very trivial.

When man becomes a shepherd and herdsman, and leads a
nomadic life, his influence on the earth becomes more exten-
sive and permanent. Particular animals are, by his agency,
appropriated, tamed and domesticated. These animals increase
in number and multiply. The very process of taming them
produces great and decided changes in their habits and aspects,
until they appear as if they were altered and become new animals
on the earth's surface. In the mean time, the wild animals that
are destructive to the tamed breed, are attacked and even-
tually exterminated. To find pasture for the multiplied
domesticated animals, heaths, prairies, and forests are destroyed
by fire; and the ashes which result from the conflagration
give rise to a more luxuriant vegetation.

It is when man becomes a tiller of the ground, an agricuL
turist, that he exerts the greatest influence in producing
geological changes. He now putt forth his energy to root out
immense forests, in order to form arable land ; or, from his
knowledge of agricultural chemistry, he may burn down the
forests, that the ashes may manure the soil and increase the
amount of the crop. It is well known to travellers and readers
that this process of burning large forests, for agricultural pur-
poses, is carried on upon a gigantic scale in North America,
in Brazil, in Java, and in many tropical countries, where vast
forests have been completely extirpated.

As man advances to be an agriculturist, he comes to apply
his agency to all manner of soils on the earth's surface. He
finds land that is too wet either to produce pasture or to grow
corn. He then proceeds to drain the marsh and the moor.
The water is drawn away towards rills and streamlets. The
beds of brooks and rivers become narrowed, another direction
is given to their course, and a new power given to their abrad-
ing (action. Kan can raise effectual barriers against the pro-

140

THE POPULAR EDUCATOR.

great even of the iea itself Han in a civilised state pro-
tects the ooatti of his country, bj raising dikes sgsinst thi
encroachments of the ocean. He dams in many bays of the
sea by artificial embankments, and in this manner abridges the
dominion of the sea, and changes the bottom of the ocean, first
into pasture land, and then into arable soil. Look to Holt
land. Kan has rescued that co un try , and is still continuing to
rescue it from the ocean. At this very day, man is altering it,
and enlarging it by draining immense lakes, and by dredging
up fresh soil from the bottom of rivers and seas.

It is not likely that the human race, living amid the geologi-
cal changes which its civilisation produces on the surface of the
earth, will be able to form an adequate conception either of
their physical importance, or of their scientific value. If you I
imagine that the continents of our globe were once more, ss
thev have been frequently before, submerged under the waves
of the ocean, and that the geologist of some future millennium
would be investigating these very complicated phenomena,—
then, to Asm, the particulars recorded in the geological works
of the present sge would be of incalculable value* They
would give him new light in his inquiries and new power in
his proofs, as he descanted upon the fossil flora and fossil
fauna of the rocks which were deposited in, what would then
be called, the human epoch.

The agency of man, by means of agriculture and by the
progress of civilisation, exerted upon plants and animals, is
developed in three ways : first, by the removal and extinction
of one class : secondly, by the introduction and extension of
s second : and thirdly, by the modification of others.

In every country where man settles, some classes of plants
belonging to the district are allowed to continue to clothe the
soil, and others are displaced and exterminated. In his migra-
tions, man carries with him foreign plants which he conreys
from other and distant regions, and sows in his adopted land.
This we find to be the case in Europe. All of our corn plants,
most ot our fruit trees and kitchen vegetables, have been
derived from Asia. The potato and tobacco were brought
from America. Cotton has been conveyed from India to
North America and Brasil. Coffee has been transplanted from
Abyssinia and Arabia to Java, to the West Indies, and to South
America.

There are innumerable instances in which the plants, thst
were first introduced by human settlers, have, without his
will, and sometimes even against his will, multiplied and
diffused themselves so widely, ss even to displace the original
vegetation of the country. For instance, in St. Helena, the
original flora of the island has been almost driven out by the
foreign plants which were brought there since it became
inhabited by Europeans. Also, in the pampas of South
America, in New England, in Australia, in South Africa, the
European species of plants, which have been brought thither
by man, exceed in number all the other species which have
been wafted from any other region and by any other agency.

Some of the facts connected with the transmission of plants
sre full of interest. It is well known that in modern times,
armies have been known to carry, in all directions, grains anal
vegetables from one extremity of the earth to another. This
fact throws light upon the diffusion of vegetation, and shows'
that in more ancient times, the conquests of Alexander, the 1
distant expeditions of the Romans, and the marches of the
Crusaders, have transported many plants from one region to
another. Where man introduces corn, he introduces corres-
ponding weeds also. In our own corn-fields, both the grain
and the weeds that grow with it are from Asia. In the south
of France, where the farmers are in the habit of sowing Bar-
bery wheat, there also the weeds of Algiers and Tunis continue
to grow. Even the wools and the cottons which are brought,
to France from the East, have borne with them the grains of
exotic plants which have naturalized themselves near Mont-
pellier. Outside one of the gates of that town, is a meadow
which is set apart for drying foreign wool after it haa been
washed. Now, in that drying-ground, there is scarcely a
year in which some foreign plants are not found growing and
naturalising themselves in the soil. This interesting fact
illustrates how seeds are borne from one region to another, in
the woolly or hairy coats of wild animals. It is hence obvious
that man, partly by direct and positive agency, or by the.

I undesigned contributions of his auxiliaries has done much to
change the face of nature.

What man haa done for plants, he has accomp Mahed for
animals. When Europeans landed in America, they fond
the New World to be quite destitute of every one of our
domestic animals. Innumerable species of them are now
found in all parts of North and South America. This is also
the esse with South Africa, Australia, Yen Diemen's Land*
New Zealand, and the islands of the Pacific You must not
allow this met to pass unobserved, for in consequence of this
transportation of new animals, great revolutions have taken
place both in the physical aspects of the country, and in the
activity of human life on the globe. As man has on the esse
hand extended the animal kingdom, he has, on the other,
exterminated or expelled many entire races of snima la. This
[is the esse with the elk and the beaver in Northern Europe,
the furred animals of North America, the hippopotamus ami
crocodile in Egypt, the lion in Greece, and the wild boar and
wolf in Britain.

One of the most remarkable facts in the results of man's
reaction upon nature is, that, by studying and obeying her laws,
he has compelled her to bring forth new creations which did
not previously exist— creations which are daily increasing and
multiplying. This refers to the modified forms of beings,
to the nch varieties and to the diversified races of plants and
animals which have been produced by man's skill in combina-
tions. The infinite number in the races of dogs would never
have existed unless man had studied and mastered the wolf
and the jackal. The same endless variety of races might be
instanced in the horse and the ox. The case is precisely
the same with plants. If nature had not been acted upon by
the genius of man, we, instead of the 1,400 or 1,600 different
kinds of apples which now adorn our orchards, would have
had nothing but the wild crab ; and instead of the innumerable
varieties of roses which now fill the air with their fragence, we
would have had only the wild rose. This power of man over
vegetative nature is singularly illustrated in the history of the
dahlia. At first the dahlia was a simple flower ; now, this
one plant can boast of fifteen hundred double varieties.

One circumstance that gives great importance to the agency
of man on the earth's surface, is the fact that it exerts an
influence on the formations of climates. The removal of
extensive forests, especially in the mountsinous districts of
warm countries, produces a great and lasting cha nge in the
condition of the humidity of the atmosphere.Under ' ^ r frr 1 *
of forests, the earth and the air always become oooled.
This cooling causes a condensation of vapours in the atmos-
phere. The condensed vapours fall on the earth as dew or
drain, which produce springs in the soil. These spri ng s com-
bine rills, Btreamleta, brooks and rivers. The felling of forests,
.therefore, by giving free play to the winds, affect the waterahed
of a country. The drainage of marshes, the drying up of
•lakes, and the deepening of river beds, diminish evaporation*
iand consequently lessen the moisture of the atmoaphere.

As an illustration of the influence of human ageney upon
climates, it may be stated that scientific men consid er the
climate of Europe to be much warmer now than it was in the
•days of the Romana, and that this improvement is due to the
clearing away of the ancient forests. Though this has been
disputed by the late M. Araoo, there can be no doubt that, by
the extermination of the forests, the climate of the different
■tates of North America have been very much modified.

The mining operations of man have had some email share in
producing geological changes in the superficial crust of the
earth. These mines are to be distinguished from the quarries
which he has opened in the face of mountains, whether for
dislodging any vein of ore that has its outcrop at the surface.
or for removing freestone and elate for building purposes.
By mining, he digs a perpendicular shaft many fathotna deep
into the bowels of the earth, or opens a horisontal s^Alery,
called a level, which enters into the side of a mountain and
may penetrate the rock for many furlongs and miles. In this
manner immense seams of coal and beds of salt are extracted
from their place amid the deposits of the globe, and extensile
veins of the ores of iron, lead and copper and other metals are
removed from beneath the earth'a surface. These «^*r*f
operations tend to produce irregulsxities in the earth's sur-
face. He brings upwards from the depths below an rmmm

LESSONS IN CHEMISTRY.

141

quantity of clays and atone*, which he piles in heapa upon the
•oil. By the wide excavations and the empty apaeea which hia
adita have left in the rocka beneath, certain extenta of the
earth's surface fall in and form hollowa. Compared with the
magnitude of the globe, and the depth of the aemidiameter of*
the earth, all these minings are mere burrowinga and ecratoh-
ings : still they hare not been without their influence in the
geological changes of the earth's crust

The lest instance to be mentioned in this leaaon, of man's
agency in affecting the cruet of the earth, is the contribution
which he makes of particular fossil remains to the various
rocka that are now being deposited both on land and at the
bottom of the aea. In the vast hollows which man's mining
operations have produced in the rocks, an immense quantity
of timber ia introduced, to prop up the top of other rocka and
prevent them from falling in. It haa been calculated that, in
So Cornish mines alone, it would require one hundred and forty
aquare miles of Norwegian forest, to afford the due supply of
timber for the works.

Many of the soils and rocka that are now forming, abound
with the various productions of man's art, the remains of
buried towns, the wrecks of ships containing human bones, the
nine of machinery, pottery, and a great variety of coins, trin-
kets, &c. The skeletons of the human frame are also daily

eontributing a large amount of fossils to the deposited rocks,
a burying grounds ------

i or in battle fields, and in the depths of the

from the facts and statements contained in this article, you
will see that man haa contributed something to make the
oosmtry as well as to make the town.

The aeries of lessons to which you have hitherto attended,
have been arranged in such a manner aa to make you
acqoaintort with the various agencies which, under the auper-
mtendence of the Supreme and Benevolent Architect of the
world, have been employed in constructing the crust of the earth.
Tom have seen that fire, water, atmospheric agents, winds,
aleuta and living organisms have co-operated in the production
of the shell of the globe.

Oar aext series of lessons wQl be on the classification of the
joafa that compose the eerth'acrust.

LESSONS IN CHEMISTRY.— No. IX.

Tjraeelence of such vast extent and seeming complexity as
ehsamiatry is, great care should be taken to present each sub-
ject under its simplest possible aspect, and never, on any
occasion, to loae the thread which ia to conduct us through
oar labyrinth. Now, I am aware that objection may be taken
to these lessons, of the following kind. It may be argued that
I have omitted many important testa ; that I have not taken
eogniaance of numerous oxides ; not even to the extent of
aa—rtonlnft their name — that I, on some occasions, have not
asjsnlnjnil the term or designation which chemists have proved
to M most correct; aa, for example, I have simply used the
tana aulphuret of arsenic, instead of the more precise term
§mfm%ulphui'tt, indicative of the amount of sulphur which this
pertioulsT aulphuret contains. I will not apologise for this
plan of treating the subject, inasmuch as I know it to be the
Mat plan, but will simply assure the student that the propriety
of all these omissions has been well observed in my mind.
Again, I have, in a previous lecture, asserted roundly that
the salt aulphuret of sine is a compound of sulphuric acid and
oxide of atno, — and that generally metallic ealta are com-
pounds of acids and oxides ; yet I am well aware that the
expiession is by no means universally correct. In a word, it
la my intention to avoid theory altogether in these lessons —
not that I undervalue theory, but I consider that it ia treated
of with the greatest propriety alone.

Besuming the consideration of arsenic, you will aee that
two distinct properties have been brought into requisition :—
two distinct lines of action for effecting the separation of
c. If combined with lino or manganese, the only two
i which, in addition to itself, have hitherto come under

our notice, it may be separated, as we have seen, by the agency
of hydrogen : this is one power. If combined with manganese
asome, it may be separated, as is here seen, by hydrosulphurie
jead, which, as we have proved, throws down arsenic, but not
You are not to assume that these are the only

means by which the separation could be effected, but they are
the4nost evident, and the means immediately deducible from
the evidence before us. Aa regards the separation of arsenic
by means of hydrogen, the operation may be said to apply to
aficaaes whatever; its value will therefore be easily recognised,
arsenic being a very important metal, and frequently coming
under the notice of a chemist in esses of .poisoning by it. I
shall now pass on to the performance of other experiments
having reference to its separation from matters which contain
it. I shall, firstly, rely on the two prime agents of analysis
(hydrogen and sulphuretted hydrogen), and snail then proceed
to mention some processes which may be required aa supple-
mentary.

£xp*rimmt.--'Mx3L together a little arsenious acid in the form
of liquor araenicalia, with about a wine-glassful of milk, and
proceed to extract the arsenic How would you act about it ?
Doubtless, our two agents will occur to you. You will either
determine to throw down the arsenic at once from the milk
by means of a current of hydrosulphurie acid, or you will
determine to pour the mixture into the proper apparatus, and
with the proper materials for generating araeniuretted hydro-
sen gaa. All very well in theory; but in practice it will not
do. You will soon find, on trial, that sulphuretted hydrogen
does not well act in milk, — hence that plan ia ineligible; —
you will aa soon discover that the milk causes such a bubbling
m the bottle for generating araeniuretted hydrogen, that
instead of more gaa escaping, as it ought, the liquid comes out
in a jet. You must therefore commence by getting rid of a
certain portion at least of the animal particles of the milk. A
definite object ia thus presented to us. Now most people
know that the portion of milk termed caeeine ia coagulated
by the operation of acids ;— acetic acid (distilled vinegar will
do) ;— if, then, a portion of acetic acid be added, and the milk
be heated, coagulation will ensue ; filter through gauae, and
waah the coagulum— you obtain most of the arsenic. Another
portion of muk is rendered insoluble by high drying ; hence if
the fluid which haa run through the gauae be evaporated, not
only to perfect dryness, but until a small slip of deal wood *,

pushed quite down to the bottom of the dish, and there
caused to remain during the operation, become tU^kUy
browned, you will find that the residue being allowed to cool,
and water added, the resulting solution will be still further
diaembarassed from animal particles. The fluid will now, in
the case of milk, be sufficiently pure to admit of working
satisfactorily, or by the araeniuretted hydrogen plan, and
will even afford a eatiafaetory result with hydrosulphurie acid.
The process of coagulation by an acid only applies to such an
organic matter aa milk ; but the process of high drying is
applicable universally to all kinds of organic mixtures. In
order to ensure the total separation of organic matter, other
measures should be adopted ; but those described should bo
firstly tried, and are generally efficient.

Iiirlhtr Tetts for Artmie.— Prepare a clear, weak solution
of white arsenic (chemical term arsenious acid) in water and
potash, either by the process already described, or by the
more direct process of boiling a little white arsenic with
potaah solution. When prepared, acidify a portion of this
solution, and apply the following tests :—

(1.) Ammowacal Nitrate of Silver.— Take a bit of lunar
causae (nitrate of silver), or the same salt in a crystalline
state, if you can obtain it, and add to it a tablespoonful of
water : a solution will thus result, which should be Kept in a
glass-stoppered bottle ; — very frequently, hereafter, we shall
require this solution, nitrate of ailver, as a test.

(2.) Add a few drops of this solution to a small portion of
arsenical solution, placed in a wine-glass, or some other con-
venient vessel. If the solution have been duly acidulated with
acetic acid, as directed, no precipitat* will ensue. Add now
very minute quantities of liquor ammonia) (hartshorn) by
means of a glass rod ; — a yellow precipitate will now imme-
diately form; hence a combination of nitrate of silver and am-
monia, used as directed, becomes a test of the presence of arsenic.

(3.) Add now more ainmonia, and you will observe the

.xfeKl^tjiJLifei)tJfcik«)fe.

precipitate just formed to. dissolve entirely ;-r-thua p
Sf necessity of attending to the conditions of success. At a
t<mo when the indications of this test were more valuable
then tjiej now are, it waa usual to keep ready-made in tfre
laboratory* a mixture of nitrate of ailver and ammonia in due
proportion,— under the name of Ammonia-nitrate of tike r. It
may be mad© by adding to a solution of nitrate of silver su0).
oient ammonia to precipitate all the oxide of ailver, and
dissolve it nearly, though not quite.

N.B. — Particularly remark that no precipitation occurs in
such a solution aa above described, until a certain quantity of
ammonia has been added.

Conversion of Armniovn into Amnio Acid. — Hitherto I have
designedly employed the term arsenic in a somewhat loose
sense : sometimes meaning by it metallic arsenic, sometimes
white arsenic, or arsenious acid. Inasmuch aa metallic arsenic
does not dissolve as such — and arsenious acid is that alone
which hsa entered into all our solutions hitherto,— no great
precision of language has been called for. We shall presently »
however, discover that arsenioia acid is not the only com-
pound of the metal which can enter into solution : — there
being also an arsenic acid, the study of which substance in-
volves some important points.

'What is the difference between arsentstu and amenta' or,
more generally speaking, what is the distinction intended to
be conveyed by appending out and ie respectively to any

Erefix } The explanation u simply this. lue greater nuav
er of acids contain oxygen, and one substance frequently
combines with oxygen in two or more proportions to form two
different acids. Provided the number of combinations be no
more than two, the acid containing the smallest quantity of
oxygen is designated by the termination out, the other by the
termination ie. The former makes salts called " iUt" the
latter those called " atet " Thus, in the present case, wc have
arsenious and arsenic acids ; arsenite and arseniate of potash,
Composition of arsenisiM and arsents acids : —

Arsenic.

Oxygen.

Ports by wt.

Parts by wi.

38
88

12
20

Arsenioia acid ...
Arsenic acid

Experiment (I.)— By fracturing a Florence flask almost at
random, curved stripes and spicules will be obtained, which
are very useful in many chemical operations. Place upon a
thin, curved atrip of this kind, a little of a mixture of aneniawr
acid and nitre (saltpetre), otherwise called nitrate of potaah,
and fuse the mixture by the heat of a spirit-lamp flame.
Maintain the mixture in fusion during two or three minutes,
then remove the source of heat, and allow the mixture, glass
and all, to cooL When it has become quite cold, break the
gloss with its fused coat into little pieces, if necessary ; put
them into a test-tube, pour water into the tube, and appl y heat,

By following these directions, a solution will be obtained,
in which the arsenic exists — but not as arsenious acid. It will
now have acquired oxygen from the nitre, and become arsenic
acid.

Experiment (2.) — Test a little of this solution with nitrate of
silver, and remark thar, even without the addition of ammonia,
a precipitate falls : not a y< Ho <, but a dirty black red pre-
cipitate however. It is the aise iate of silver.

Experiment i3.) -P.i>a a current of hydrosulphuric acid
throusgh another portion of the same solution, and observe that
a ye low precipitate fills ss it would have done in a solution
of arsen -.om* acid. The precipitate, however, although similar
in c lour and behaviour, is different in the mutual relation of
i s component*.

Experiment (4.) — Mix a little charcoal powder with a little
more ih.tii iin own weight of nitre : — place the mixture on a
blip ••!' uU-s himilar t • the lust. an<l apply heat as befure. If
Miffi i> nt ui re nave b en u«e<I, the charcoal will altogether
diMtppear, hy the opera ion of cause*, hereafter to be explained.

Nov*, it no huppoiis that all animal and vegetable substances.
< ontain a large quantity of charcoal carbon, although veiled.
If, therefore, animal or vegetable bodies be mixed with nitre —
the mixture dried and ignited — that result which we have seen
to occur with charcoal alone will occur with them— -the carton

! will, be burned awsjr; and if the Animal or vegetable eoraV
feound should have chanced to contain arsenic, the lattct
would have been simultaneously converted into arsenic add.
I n Experiment (5.)— Mix a little arsenious acid, In any state of
mixture, with some milk, porter, cabbage, or, in snort, maf
animal or vegetable substance :—add nitre to the mixture;
evaporate, dry, and ignite in the beat way you can. The
operation should be conducted in a platinum crucible ; it may
be exacted to a sufficient extent for demonstration on a slip of
thin glass. Jfceiissolve, filter,— precipitate by hydroaulphurio
acid, and reduce the precipitate to the condition of metallic
arsenic, u before described. The process of extracting arsenic
from animal and vegetable mixtures, after previous conversion
into arsenic acid, baa been frequently had recourse to in Judicial
inquiries. The late Professor Orflla first taught medico-
legal inquirers that, in many cases, it waa not enough to seek
i for 1 ptrseniq in the contents of a stomach, inasmuch as the
poisonous agent might have by chance become absorbed into
the liver or other tissues. This being the esse, the process of
incineration with nitre becomes especially advantageous:
occasionally, however, the same ultimate result may be ac-
j compliehed by the use of even better substances than nitre.
Such variations of the process, however, need not be discussed
just at present.

JDetokionof.Artenic by Sulphuret of Copper and Ammom*.—-
It would not be proper, under the need of arsenic, to omit
all mention of this test. — which is one of considerable j4eli-
cacy, — although far inferior to sulphuretted hydrogen, and the
process of extraction by hydrogen.

Experiment (I.)— Into a portion of liquid containing anenious
acid, drop a few drops of solution of sulphate of copper : — no
precipitate will ensue, provided tfo arsenical solution be not
alkaline — immediately, howey ex, mat liquor ammonias is added,
with the precautions already detailed under the head of test-
ing with nitrate of ailver, a green precipitate occurs. This
green precipitate is used as a pigment, being purohaaeable under
tne name of Scheele's green. Perhaps you have observed a
sort of very brilliant green paper, employed .for the ^urpoae of
labelling bottles of rum, whiskey, &c. ; generally, if npt in-
variably, this tint in question is imparted by Scheele's green.'

If you can procure a few fragments of this paper, the
presence of araenio in it adntltp of^easy recognition by several
tests. In the first place, if a. piece of paper of this aort ba
ignited, and. the flame, blown out, the smoke will be found to
smell like garlic— this in itself is a presumptive indicatttjh of
arsenic. But the most certain and satisfactory method of
assuring yourself that arsenic really exists in it, will be either—

1. By boiling the paper in water, and adding the result
to a mixture of dilute sulphuric acid and water. In the
apparatus so frequently applied, and proceeding aa already
mentioned.

2. By cutting the paper in fine shreds,— mixing it with a
little washing soda, and heating in a tube : charcoal here is
unnecessary, the paper containing charcoal enough of its own.

3. By incinerating with nitre, redissoMng and proceeding
as before.

. I may here mention, in connexion with the mixture of
charcoal and carbonate of soda (a* directed to be prepared
some time ago by the process of direct incorporation J,
a substance termed by chemists black flux is couuuonly
employed. Now, black flux is a mixture, not of charcoal and
corponate of soda, but charcoal and carbonate of Uiitaoh ; not
prepared by the process of direct mingling, but indirectly. The
method of preparing black flux is thus : intimately mix in a
mortar two parts of cream of tartar with one part of nitre ;
project the mixture into a red-hot crucible; ^wiver ihe
crucible, and allow the whole to cool. As the result oi tins
treatment, you will eventually obtain an intimate uuxturo of
| carbon I charcoal and carbonate of potash). Where does the
charcoal come from, you perhaps may inquire? Not Irony the
nitre, certainly ; this we all know. It must come, then, from
the cream of tartar ; but how or why, you arc not in a position
to understand until we shall have, at a future period, detailed
the nature and the relations of carbon. One conuaiiction,
however, may probably occur to you ; seeing that in a previous
operation wc have availed ourselves of nitre tor the. purpose
of burning away carbon. Why, you may ask, does .it not do
so in the present case t Simply because we hale not usee s

SKETCHES PQB tOIING. frUNXERS.

•ufficient amount of nitre to produce this result :— if we had,
the carbon would have been entirely removed ; the resulting
product would hare been altogether white, and we should
, hnre had a preparation, sometimes made and employed by the
Chemists, under the name of white flux.

SKETCHES FOR YOUNG THINKEBS.

Oontimted from page 86.
i Unwilling to multiply illustrations beyond the bounds of pro-
priety, we leave the age of martyrdom, and now present a few
- more from other sources.

Louis IX., King of France (in the year 1226), holds a conspi-
cuous plaoe in the annals of history,, ss a wise and virtuous
monarch. From all that we gather, he combined both intellec-
tual and mXn-al ; excellence In himself. We are told, that his
reputation for uprightness, Denotation and candour, was so great,
that All the English barons, and even Henry II L, " consented to
make him umpire of the differences which subsisted between
them." Fenelon, ss quoted by Murray, has given this long a most
safoeflent character. He says :— " He was distinguished by the
nobleness of his sentiments; he was without haughtiness, £resumjH
Hon, or severity. In every respect, he attended to the real inte-
rests of his country, of which he wss as truly the father as the
kam>" His farewell words to his son Philip, are highly devout
and affecting: — " God grant you grace, my son, to do his will]
continually \ so that he may be glorified by your means, and that]
we may be with him after this life, and praise him eternally ."
Hie following letter to his daughter Isabella, queen of Navarre,
we have mucn pleasure in quoting :— " My dear daughter, I con*
iefte won to love our Lord with all your might ; for this is the
fcmwrtifln of all. goodness. No one is so worthy to be loved.!
10*11 may we say, ' Lord, thou art our God, and our. goods are
nothing to thee.' It was the Lord who sent his Son upon earth,
and delivered him over to death for our salvation. If you love
" 'Bit, my daughter, the advantage will be yours ; and be assured
that you can never love and serve him too much. He has well
osesrved that we should love him ; for ho first loved us. I wish
yea could comprehend what the Son of God has done for out
- redemption. My daughter, be very desirous to know how you
■ay best please the Lord : and bestow all your care to avoid |
everything that may displease him. But, particularly, never be
guilty of any deliberate sin, though it were to save your life. Tak '
jfleajtrre in hearing God reverently spoken of, both in sermons an
. in private conversation. Shun too familiar discourse, except with
vary virtuous persons. Obey, my daughter, tout husband, your
lather and your mother in the Lord : you are bound to do so both
for their saxes and the sake of him who has commanded it. In
what is contrary to the glory of God, you owe obedience to none.
Endeavour, my daughter, to be an example of goodness to all who
may see, and to all who may hear of you. fie not too nice about
dress : if *you have too many clothes, give them away in charity.
Beware, also, of having an excessive osre of your furniture.
Aspire after a disposition to do the will of God purely for
his sake, independently of the hope of reward, or tho fear of
punishment.' 1 What a noble letter from a king to a daughter!
it comprehends the loftiest, and the most minute duties of life j
if the principles contained in this admirable epistle were full y
wrought out, the world would be transformed at once. Hens
then, we have an example quite to the point On the one hand,
we have longs and barons asking his counsel, so great was h
wisdom : and on the other, we hear him pouring out the mo
pious exhortations to his children. What a combination of wisdom
and goodness ! The wisdom gives a dignity and effect to the
goodness, and the goodness renders the wisdom more exalted
and attractive.

France has not been altogether destitute of good men, althouf
its history is one of the most lamentable in the world. Fren< I =
fickleness, caprice, and restlessness are known throughout civilize*
society. One example has, however, been given of a wise and
virtuous prince ; we have another instance, of a somewhat diffe-
rent character, but quite in keeping with the subject. It shows
* the truth of our opening sentence, that goodness is better than
greatness. We refer to Salmasius, who is well known to have
been one of the most extraordinary men of his oira or any subs
qoent age. A modern writer, speaking of this man, says : — *' He
was knowing in almost everything ; in school divinity, in law, in
philosophy, in criticism; and he was so consummate a lingui

that there was scarcely a language in which he had not attained
a considerable proficiency. He was perfect in Greek and Latin ;
he understood the Hebrew, Arabic, and Persian, Egyptian, Chi-
ase, &c, and he wss well acquainted with all the European
languages," Here, then, is intdUctutl excellence. Europe rung
with his praises. We will turn, and converse with this literary
Titan, when he had nearly run his race, and " drunk every cup
of fame/' .When his friends were gathered around him, he ex-
aimed, with penitential earnestness: — "Oh! I have lost an
fyiwianaft portion of time— time, that most precious thing in the
world I Sad I but one year more, it should be spent in studying
isvid's Malms and Paul's epistles. Oh ! sirs, mind the world less,
and God. mpre: 'The fear of the Lord, that is wisdom; and to
depart from evil that is understanding/ " There is something
remarkable in this confession. Here wss a man of vast and mul-
tifarious learning; one who had sat and heard the Grecian sages
philosophise, pd her poets strike the lyre and wake the praises
1 a world ; a man who had made himself acquainted with all
nowledge, and for whose society emperors and nobles contended,
oming down with the simplicity of a child, and wishing for ano-
ther year, that he might read David's psalms and Paul's epistles !
There was a sound in that Hebrew lyre, which no other instru-
ment could produce ; and a power in the writings of the Jewish
covert, which made all otnor literature shrivel into insignin-
ejance ! The evening of life, and an approaching eternity, are the
test teachers of serious truths. Men look at things'then in their
roper light. All parade and glitter are taken away, and things
ire left in their naked and unadorned reality. We- would, that
he testimony of Salmasius were engraved on every heart, and
contemplated by every understanding.

Another case, illustrative of the same point, is that of Cesser
Borgia, son of -Pope Alexander VI. D' Aubigne, speaking of him,
ays : — " Caesar wss the handsomest and strongest man of his age.
Six wild bulls fell easily beneath his blows, in single combat,
fivery morning, some new victim was found, which had been assas-
sinated during the night, in the Boman streets. Cesar Borgia
was the hero of crime?' Testing him by the same standard ■■

that of Salmasius, via- the death-bed, we have the following ex-
pressive confession :— " I had provided, in the course of my life,
lor everything except death ; and now, alas ! I am to die, altnough
entirely unprepared.' 1 This man was a secularist. His whole
attention was confined to this world ;— to his excesses there was
no end ; whatever he wished, he obtained ; and after a most ex-
traordinary career, be -left the foregoing confession, as a voice
from the death-bed to succeeding generations.

Again recurring to France, we are filled with amazement at the
prodigious literary acquisitions of Pascal. If ever there was a
great man on earth, Blaise Pascal was the man. In him, mental
and moral excellence may almost be said to have reached their
consummation. Bayle has paid him the following lofty tribute-.?—
" A hundred volumes of religious discourses are not of so much
avail, to confound the impious, as a simple account of the life pf
Pascal. His humility and his devotion mortify the libertines
more than if they were attacked by a deaen missionaries. They
can no longer assert that piety is confined to men of little minds,
when they behold the highest degree of it in a geometrician of
the first rank, the most acute metaphysician, and one of the mOst
penetrating minds that ever existed.' 1 Notwithstanding his bril-
liant talents, and all but unrivalled learning, he was as meek
and gentle as a little child. His case might have been appropri-
ately quoted in the former chapter, as a proof that intellectual
excellence does not minister to vanity and pedantry. Such men
are living commentaries on the word of God. Ihey confound
the gainaayer by their learning ; the dissolute by. their purity ;
and the hypocrite by their manifest sincerity. Such men are
more noble than kings ; they shed a radiance upon the woi Id, and
by their "walk and conversation" recommend tho practice of
justice, truth, and virtue. We have by no means presented all
the illustrations which French biography supplies, of the truth
and importance of the subject, — no reference has been made to
Benezet, Moulin, Kenti, or JbUchelieu ; but the youthful reader will
add to his knowledge of men and things, by reading such memoirs
of these men as he may be able to procure. Thus we leave
France, thankful that amidst all its bloodshed, revolutionising,
and mutability, there aro registered in its archives the names of
many who have contributed largely to our best literature, who
have added lustre to humanity, and have not been ashamed to add
the graces of piety to the laurels of learning.

144

THE POPULAR EDUCATOR.

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LBSSQNS IN ITALIAN.

147

LESSONS IN ITALIAN GRAMMAR.— No. X.

BT CHAELE8 TAU8ENAT7, M.D.,

Of the University of Pavia. and Profetior of the Italian and German
Languages at the Kensington Proprietary Grammar School.

I cannot begin my exposition of the grammar of the
language without first offering some remarks on the use of tl |
apostrophe in Italian, which, with the general table, will coi
elude for the present my lessons on pronunciation. Some
supplementary and important pronouncing tables will be given
at the end of the grammar.

The apostrophe is essentially different from accent, an
indicates that the word on which it is placed has been d<
prived of a Towel or of a syllable. Where, therefore, for it
take of harmony, at the beginning or end of a word, a rowel !■
omitted because the preceding word terminates with a rows}
or the subsequent word begins with one, the apostrophe mutt
be placed. It can never l>e used in the middle, and a
omissions and contractions in the middle of words must be
written without this sign. For example : t amors (pronounced
lah-mo-rai), lore (for io amore) ; deWanima (del-lah-nee-mah),
of the soul (for deUa anima) ; dalTuomo (dahl-lood-mo), from
man (for' dallo uomo) ; capo d 'opera (kah-po dd-pai-rah), %
masterpiece, an odd man (for capo di opera) j t'io poeeo (aee-o
pds-so), if I can (for « io poteo) ; pms'io (pen-see-o), I think
(to peneo io) ; topra 7 leito (so-prahllet-to), upon the bed (for
eopra U letto) ; totto H eield fs6t-toltch&-lo), under the Sky ffc
totto il eielo) ; e'n questo, /n gueih (en qwai-sto, en qWel-lo'
as well in the latter as the former (for e in questo, $ t
qneOo) ; tra'ltl$'l no (trahl see el nd), beween yes and nc
*>., hesitating (for trail si eUno).

I may here remark, that the use of the apostrophe at th
beginning of a word is more frequent in poetry than in prose.

: It is necessary to bear in mind the distinction between the

foHrophe as a sign of elision, and the abbreviation of words

where letters are omitted without the use of this sign. I con* I

ai4sr it necessary to state some elementary rules with respect

to the abbreviation of words.
• *

1. The final vowel of any Italian word may be, and

always without the use of the apostrophe, omitted, if it i

immediately preceded by one of these four consonants l 3 m, n

sod r, the so-called liquid consonants or liquids, and if, at the

same time, the subsequent word should commence with a con

sonant, except the « impure, as the Italians call it ; that is, t

followed by another consonant ; as, spirit o, spirit ; tcettro

sceptre. For example : il cameval passato (il kahrr-nai-vah

pehs-sah-to), the last carnival (for il camevale paeeeto) ; a man

Intra (ah mahn dfe-strah), on the right hand (for a man*

deetra) ; ogni uom taeea (6n-nyee oodm tah-tchai-ah), everyone

was silent (for ogni uomo taeea) ; vuol far questo (voodl fahi

kwai-ato\ he wants to do this (for vuolefare queeto).

2. In words ending with Ho, and having the accent of tone
on the ayllable preceding to, it is customary to omit the whole
of the syllable lo, if the subsequent word begins with a con-
sonant which is not the * impure. For example : Bit for HUo,
beautiful ; quel for quelle, that, the former ; vol for voile, valley ;
eapdl for eavdllo, horse; ueeil for ueoHlo, bird; fratil for
JratSUo, brother ; tranquil for tranquttlo, tranquil ; cervH for
eervillo, brains ; ruecil for rueeillo, brook, &c.

3. The abbreviations or omissions of the final vowels men*
tioned in the two preceding rules can never take place in that
part of a sentence which requires a pause, i.e., before a comma,

olon, or period. It is, therefore, not allowable to say Ella ha
una beUa man, she has a fine hand, but mono ; not chi & quel
Signer ? who is that gentleman ? but Signore, &c.

Other important rules with respect to abbreviation I shall
state and comment upon as examples occur in the course of
the grammar, and I snail now content myself with this con-
cluding remark, that all abbreviations in the Italian language,
whether made with or without the apostrophe, are made merely
for the sake of harmony and to avoid hiatus, i.e., a pro-
longed opening of the mouth by the recurrence of vowels.
But as perspicuity is of greater importance than harmony, this
general rule may be safely laid down, that abbreviations should I

not be used without absolute necessity, and that those should
be specially avoided which would tend to ambiguity,

I will here give a general and concluding pronouncing
table, showing the most complicated combinations of vowels
with consonants of the whole of the Italian language :—

Italian,

Ca
Co
Ou
Ce

Che
Chi
Oia

t*
c*>

Chia

Chie

Ohio

Chiu

Qhe

Ghi

Gia

Gie

Gio

Giu

Gla

Gle

Oli

Glo

Glu

Glia

Glie

Glio

Italian*

Pronounced.

kah

Gliu

Uyoo

koor k6

Gna

nnyah

koo

Gne

nnyaiornnyd

tchaior tche*

Qni

nnyee

tehee

Gno

nnyo or nnyd

kaiorke

Gnu

nnyoo

kee

Qua

gwah

tchah

Que

gwai or gw§

tchai, or tchfe

Qui

gwee

tcho or tend

Quo

gwo or gwd

tchoo

yah

keeah

yai or yd

keeai or keet

yo or yd

keeo or keed

TOO

kwah

keeoo

Qua

gah

Que

kwai or kwe*

go or gd

Qui

kwee

goo

Quo

kwo or kwd

jai or jS

Sea

skah

jee

Sco

sko or skd

ghai or ghg

Sou

skoo

ghee

8ee

shai or shd

jah

Act

shee

jai or^e

Sehe

skai or ske"

joorjd

Schi

skee

joo

8eia

shah

glah

Scie

shai or sh6

glai or gl6

Seio

sho or sho

gli or llvee
glo or gld

Seiu

shoo

Schia

skeeah

gloo
flyah

Sehie

skeeaiorskeee'

Sehio

skeeo or skeed

llyaiorllye*

Schiu

skeeoo

llyo or 11yd

I now enter on the grammar proper, of the Italian language.
In fulfilment of my promise to follow the natural method to
teach, as it were, the language as it is formed in the mind,
>| shall first speak of nouns, and other kinds of words
allied to nouns, and then proceed to explain the verbs
and their various inflexions. Two methods are open to choice,
each of which has its sealous advocates in tuition. Some
would confine themselves strictly to theory in grammatical
teaching ; others as exclusively to practice in the earlier stages
of the instruction. If we adhere strictly to theoretical exposition,
file progress of the pupil is sure, but slow; if we are merely prac-
tical, the pace may be rapid, but the attainments are superficial.

shall endeavour to blend the two, and while I, as concisely as
I can, explain all the principles and rules of the language, I

hall constantly strive to impress them on the minds of my
pupil readers by practical exercises on each rule as it occurs.
I snail, in this part of my labour, endeavour to improve on a
modern invention of Germany, the country, perhaps, most
> ] istinguished for scientific method in education. It should
be the aim of every educator so to teach, that his pupils may re-
gard the instruction as relating to a living language to be acquired
by the tongue, and not merely as dead writing to be compre-
hended only by the head. From the very outset of these
grammatical lessons my pupils will learn to form sentences,
so that as the head acquires knowledge of its principles, the
tongue will grow familiar in the practice of the language. In
i lus uniting practice with theory, I shall, of course, be obliged
in one class of the exercises to anticipate the systematic exposi-
tion of principles, but I shaU only do so with strict regard to
the progressive knowledge of the student, and I shall specially
i iapt the exercises to that end, and perhaps thereby succeed
in more firmly impressing even the rules anticipated, on the
mind. The pupil must bear in mind that he is now about
to learn to speak as well as to read the language of Italy.

"With regard to the selection of exercises, I shall not scruple,

148

THfc POPULAH KDUCAtOR.

in addition to my own, to make a free use of example* whicl
hare pawed the test of years of experience in the beat tehoolf
of Italy and Germany. lam more anxious to serve the interests
of my pupils than gratify a literary vanity ; and eren were I to
make an effort at originality, by the preparation of exclusively
new exercises, one man could hardly hope to excel the
united labours of many grammarians in this direction.

The exercises ought to be read over frequently, and always
aloud ; and if committed to memory, so much the better lor
the knowledge of the student.

As I haye so yery fully explained the elementary principles of
pronunciation, eyen at a length which may haye damped the
ardour of more impatient readers, it will not henceforth
be necessary to give the pronunciation of each Italian word
used. Should any doubt occur, the student can always refer
to the pronouncing lessons or to the general table which pre-
cedes these remarks. As it is, however, most desirable that
the reader should have as much assistance as possible, I shall
aid him by a new, and, I believe, a most effective method,
namely, by dividing each Italian word used, into syllables, for
the most part, as the words are divided in Italian spelling and
writing. I shall not omit to mark the accent of tone with the
acute sign or with the circumflex sign over the • and e ; signs,
be it remembered, not used in Italian writing or printing, with
the exception of the words commented on in my remarks on
the use of the accent. The grave accent will, henceforth,
always be placed where the usage of writing requires it, and
in such cases it will serve, likewise, to denote the accent of
tone. I am induced, by three reasons, to adopt this method
of dividing words into syllables : —

First, to correct the great fault of Englishmen in pronouncing
Italian by slurring over words, the component sounds of which
are unfamiliar to the ear. By this means, the learner will be
in some measure compelled to do justice to each syllable.

Secondly, it will be a practical aid to the memory. This
dwelling on the ingredients of the word will impress the word
itself better on the memory.

Thirdly, it will be useful in the case of compound words, in
indica t ing at once the elementary constitution of the words.

ANSWERS TO CORRESPONDENTS.

CasMismY.— F. M., S. J. B., a Diliftat Pupil, s Younf Chemist, and a
Dance, hmy« experienced difficulty in generating lulpharet of iron according
to directions g Wen.— The iron bar mutt be whit* hot ; a piece of iron as large
at a kitchen poker cannot be heated to whiteness in a common open fire.
Those who can have access to a smith's forge, may avail themselves of it.

H. DcmcuT : Hydrotulphate of ammonia, and hydroeulphuret of am-
monia, are terms commonly employed to indicate one and the same substance,
nor can any ambiguity arise from their indiscriminate use. H. Dunkley,
however, is right in assuming that, viewed in relation to their analogies,
these two expressions should indicate two different bodice. The most recent
term for the liquid in question is tulphurtt of ammonium; but ammonium
Is a hypothetical compound— It may exist or it may not. It has never been
separately obtained.— Pharmaden, H. Hud, and a Novice— will receive
answers to their questions next week.— P. S. (Trafalgar-road): Is respect-
fully Informed that we cannot And room for his article, which will.be
returned on application for it.

J. Jonas (Royal Marinas): We should have been happy to insert his
poetical communication oa the question of Auiodiiaetai, 'but it Is too
late. We love to encourage the Welehv— W. N. Banana (Islington) and ,
another friend have apprised us that a list of eleven or twelve students
passed m CZasifcf at the last matriculation examination of the University
of London. The omission of the three names is our fruit; ws concluded too
hastily that there were none, the paper ami u$ not containing them. We
must atone for this another time— H. wabdimolby (Leeds): The wolf
and the tiger did not eat eo long as twenty minuUa toosthbsu— Battue
(Liverpool) : It is oot legal to acknowledge ths parnmmti of a debt by a bill
by poet without the Id. receipt stamp.— E. A. Uotbe (Portsmouth): The
•• History of England,*' by Dr. Ferguson, at 3s., 3r . 64., or 4s.

J. H. Eastwood (Middleton) : Beeeived.— D. A. B. (Forfar) : The trans- 1
lation of M Non sum ita hebes ut isthuc diosm," it I am not to dull a* I soy '
in that maiUr ; or Snotties), lam net so blind at lam Mecr-eyed.— J. E. H, ,
(Kidderminster): Many thanks for his corrections.— U. Williams (Btlstol) :
Prop. VII. Book II. might be mads a Corollary to Prop. IV. but the advan-
tage would be too small to compensate for the disarrangement of the proposi- ,
ttons. As to the exereieo appended to Prop. XV. Book III., the term chord
as defined in Ua»sell*s Euclid Is opposed to the term diameter t and of course
cannot pees through the centre. By joining o l in toe figure to Prop. II
Book I., it can be proved that D o L is an equilateral triangle, but not till I
vou come to Prop. XXX11.

H.Oaeextt (Derby;: French is the esslest languags to learn. With
ordinary care, the maps will not wear out; but they may be strengthened
si the folds with narrow strips of thin paper of strong texture and a little

paste As to colouring mape.it to the simplest thing in the world; you have
on|v to make every country a different colour from those that are around it,
taking ears to keep the colour within the dotted boundary line, and to lay it
on very lightly indeed. Some taste may of course be shown in the selec-
tion and the arrangement of the colours of adjoining countries.— Anxious,
must free himself of his incog, if he wishes us to answer him.— a 8omool-
KASTBB (Wolverhampton), should apply to Henry Dunn, Esq. Secretary to
the British and Foreign School Society, Borough Bond, London, for

the Pamphlet entitled "The Normal 8chooU, fcc.," which will give him sll
the information be wante.— J. B. Smith ( 8toke-Newington): We cannot
promise to publish any latter till we see it, and can Judge of its contents.
The regulations relating to the desrees at the University of London, are
contained In vol. Ik p. 213, and p. 137; and for the rest, he should st ones
apply to the University Almanac We give the same advice to Anni
Sbftbndbcim : Doneaater.— J. Maboh (Merrick): 8ee p. 60, col. 1, vol.
iv.— Un Gaboon Qauois (Aberystwith): His French letter to us is very
well done ; but it is too flattering to be inserted ; besides If we inserted his
letter we should be completely deluged with French letters from all parte
of the Empire.— T. Powsll. will find a key to the Latin Exercises in the
P. E., and a correction of the errata in various parts of the subsequent
volumes.— K. T. N» (Beech Lane) : His suggestion is good and will be eon-
lidered.— SarTBNnaouc (Louth), in a very well written letter to us, adverts
to the** Law of the Association of Ideas.* and says that in the study of
Latin, ho learned the vocabulary prefixed to each exercise, and that in the
Very next book which he took op for casual reading, he often found several
norde derived from those that he had thus learned. He adds that in etudy-
ing the French in connection with the Latin, he recalls to mind the words of
the latter, which have the same meaning as those of the former, and thus
Ixes both in his memory.

Our correspondents give us more credit for knowledge of their affairs,
their mental capacities, their physical capabilities , and their general babi-
and respective positions in life, than they themselvee possess ; they
take us for ths greatest conjurer that ever was known. Thus : M. A. C.

must . m w .

Hudderefield). asks us " what are the best studies hs should pursue to be a
rosily practical man, like Franklin It 1 *— Leo (Brompton), asks us "how
many numbers of the Popular Educator make a volume 1 !'* Sooius asks as
for " a ummweal rule for placing Latin words in a sentence 11" C. D. Bao-
bme asks us *' whether the students of Greek are to do their beet, without
knowing whether they are right or not!!" J. T bo mas (Halifax), asks as

•if the phrase If i$ cold, be grammatical ! 1" In Logo (Birmingham),
Earnestly asks us " where Cain's wife came from II" C. Y. Pabtbioob
(North Molton), asks us to give the Chemical analysis of the North Molton
time-stone, ss its properties are unknown to ths residents 1!" W. Towa-
ibmo asks us " if a wife can be put in a Lunatic Asylum because she doubts
the fidelity of her husband 1 ! I** A Constant Subsoeibbe (SpUsby), asks
us '* whether the letter A is silent or not in the word Ckobham," see p. SB,
tins M from the bottom !! J. Edwabbs (Lancaster), saks us for M Mr. Bell's
address,*' which was given before ; vis. 13, Hope-street, Charlotte-square,
Edinburgh 1 1 G. Jackson (Leicester), accuses us of not fulfilling our
jsngagement as to Music. and asks ne for •* the name of a work teaching it by
Mr. Curwen's system ;" sse Mr. Curwen's " Grammar of Vocal Music,*'
price fts. 6d«— ** The Pupil's Manual of the Tonie Sol-Fa Method of 8ineing,
and Sol-Fa School Music," price Is.—" The School Course of 8ol-Fa-Exer-
eJses," pries 4d.— •• The Sol-Fa edition of the People's service of song,"
price Is. fid. fcc, and especially ths M Tonie 8oUFa Beporter, and Magsaas
pf Vocal Musts for ths People, price Id. each number 1 1 ! J. 8. M. (Norfolk),
isas us to give the Analysis of Bice and Wheat 11 J.T.(Nim!er-strect),snES
is to •• inform him of the cheapest class where our English Lessons ere
itudied 1 !** F. B. (Buckley), sake us, " what is ths cure for disease brought
mi by hard study 1 1" H. Jean (Norwich), asks us when we think of introduc-
ing the Hebrew Language in the P. E. !•! And lastly, Sblf-tauokt, with
i thousand others, asks us if his style of writing or penmanship will do for a
dark's situation ! 1 ! 1

I T. T. is right.— B. Tobbinoton (Bolton-le-Mooro): We'requestaimto
exercise a litus patience, the agent is not in fault ; no one can help the
Illness of an editor.— J. Dowbll (Birmingham) : The word ocer comes from
the French pair, thus defined in Boniface's Dictionary ; •• anoiennement
litre de dignltd ; l'un dee dues ou cotntes qui avaient seance au parlement
de Paris ; membre de la ehambre dee seigneurs d'Angleterre ; vaaeal qui*a
droit ds juger avee le seigneur du lieu."— T. T. Kiblt ; pocket compasses
may be had from 3s. to 3gs. according to mounting, at Knight and Sons,
roster Lane, Cheapeide. Back numbers of both editions of vols. U f ana
f, of the P. £., may he had on demand.— C. J. Hoseins (Winchester) : An
English sovereign can neither legally marry a subject nor a foreigner who is
pot a Protestant. Ths rain falls because the pressure »f the atmosphere Is
diminished, and consequently ths barometer sinks. Dr. Black's oalance,
svhich you have described in his own words as follows, may bo useful to our
chemical students:—** A thin piece of fir-wood of the thickness of a shilling
is divided into 20 parts, tVe. 10 on each* side of the middle ; being altogether
a foot long, and half an inch broad. These are the principal divisions, and
these are subdivided into halves and quarters. Across the axis is fixed
a very small needle, which Is fitted to its place by sealing-wax. The
fulcrum is a piece ot brass plate, the middle of which lies flat upon
the table; the two ends are bent at right angles so aa to stand upright.
These two ends are ground at the earns time on a flat hone. A grain
weight ie placed on one division of the balance, and the object to
to weighed on another; the position of the two will indicate the weight of
the latter.** The mode of calculating the weight by this balance is this :
suppose for instance that half a grain weight on division 10'of one end of
the beam, was balanced by an object on division 6] of the opposite end,
what is the weight 1 It Is shown in Mechanics, that ths distances of tan
ireighU from the fulcrum are to one another, inversely as the weights taeasv
iclves; therefore, we have 6} : 10 : : « : f?, hence, the weight of the oh j e et ;
m I? of a grain.— A Tbaobbb (Torquay) : Ths publication of the tr e ati ssm
from the P. E.ie only a question of time and demand.— T. Maces* (Dublin) a
Hie suggestion has been often made, but it would be a serious undertaking^.
The vendor can legally refuse to exchange old numbers for new ones even oa
paying the diflerence.— Isbabl (Glasgow) : No one requires to study Dsr-
Stoddard and Andrews* Latin Grammar unless he likes { but the snare*
knowledge he can get the better.

THE POPULAR EDUCATOR.

node (from Lat. nodus, a knot) or an eaoJ (from Lat. ovum,
i mv), For the sake of some mathematical reader* we
lay just add the equation belonging to the conchoid, via.

«V=(*^-y") («±*)".

where the double sign indicates that phte ia to be taken when
the properties of the superior conchoid are investigated ; and
that wunue is to be taken when those of the inferior conchoid are
under consideration. This equation shows that the conchoid
Ss a eurre of the fourth order, because, when expanded, it
becomes an equation of the /art* degree. Of the figures here
shown, the first was drawn exactly according to the method
•bote described, but the second and third figure* were copied,
merely to give an idea of their form, and their perfect accuracy
l* doubtful We would therefore advise our Btudents to draw
these figures for themselves ; the process will form an interest-
ing and amusing exercise.

The common Hyperbela, one of the conic sections, described
in the Lessons in Drawing, fig. 86, p. 226, vol. II* la another
curve which has asymptotes, as shore defined. In order to
explain the nature of these asymptotes in the easiest manner*
enppoeethafcin fig. 4, between the two axes a* and Ay of the

Fig. 4.

hyperbola, two straight lines h h' and xi' are drawn through
the centre a, in such a manner that a h and a k', the hypotenuses
of the two right-angled triangles abh and a c x', are at dis-
tances from the centre each equal respectively to the distances
a r and a f' from that point to either of the/oa f and f' of the
curve ; then, these two strain ht lines, indefinitely produced,
are the aeytnptotee of the hyperbola, and possess the property
of continually approaching the four branches of the curve in
as many different directions, without ever meeting them, though
both were continued to infinity. In like manner, if n b be
the traneveree axis of another hyperbola, having the two foci f
and/', the same asymptotes h h and x x' are the asymptotes
of this hyperbola. In speaking thus of these hyperbolas, we
hare considered the two opposite curves passing through the
vertices b and o, as one hyperbola ; and the two opposite
curves, which pass through the vertices d and b, as another
hyperbola; but, the former are frequently called opposite
hyperbolae, and the latter conjugate hyperbolae.

The equation belonging to the hyperbola, is of the following
form, via.,

*«*«_ a a y a =a9da .

a form which is very similar to the equation belonging to the
ellipse, another conic section, viz.,

If in the latter equation, b becomes equal to a, the equation
is changed into that belonging to the circle, via,,

These three equations may also be exhibited in the following
curious forms, by which they are moat likely to be more easily
remembered, via.,

(1.) (— ) + f—J = l, equation to the circle.
(2). (— ) + (j\ = 1, equation to the ellipse.

(3.) f — ) — (~ J = 1, equation to the hyperbola.

The equation to the conic sections, generally, ia of the sol*
lowing form :—

y a z=jiig | a w* ;

and this equation includes all the curves known by this name,
viz., the parabola, the ellipse, and the hyperbola; but we
must stop here till we take up the subject in our mathematical
course.

In reference to the paaaage above quoted, which gave rise to
our preceding remarks, we may join m the language of Zophar
the Naamathite, and say, " Canst thou by searching find out
God? Canst thou find out the Almighty unto perfection?
High as heaven, what canst thou do r Deeper than hell,
what canst thou know ?" And to this we may add the words
of Elihu the Buxite : " Touching the Almighty, we cannot
find him out; he is excellent in power and in judgment."
Nevertheless we are permitted to illustrate spiritual and eter-
nal things by material and visible objects. Hence, in Scrip-
ture, we find that God is spoken of as having eyes and hands,
which are with him, and to us, the emblems of knowledge and
power. With this example before us, we may reverently com-
pare the existence of the Eternal, which is " from everlasting
to everlasting," to a straight line which had no beginning, anc
which has no end ; and we may, in the same spirit, liken thf
infinite and unbending rectitude, truth and justice of the area
Creator, to the directrix or axis of a curve which extends bot
ways to infinity, without ever deviating to one side or to tl
the other ; for with him " one day is as a thousand years, si
a thousand years as one day ;" and with him, there ia "
variableness, neither shadow of turning."

How different from all this is the condition of man ! Ti
may he be compared to the curve line, of which the direc
is continually changing ; the curve line, which depends fc
direction at every point, upon its relation to the grea*
invariable axis ; the curve line which, even in a state of
parative approach to that axis, can only become paralW
at an infinite distance. Hence, it is that even whe
borrow a simile from the curve and jits asymptote*, the
phorical comparison between God and man falls inf
short of the real ttate of the case ; for, although it r
admitted that, during the endless agec of eternity, the j
and saved soul of man shall be continually drawing
and nearer unto God, through the contemplation of hi
and ineffable glory, yet there will be such an incoo
great distance between the Creator and the created,
comparison dwindles down to that of continually apj
ing parallels, as infinite in their mutual distance aa
endless in their mutual approach, and everlasting
asymptotic relation to one another. Yet the apo
speaking to believers, saya, " we shall be like him, £
see him as he is ;" true, we shall be like him in kind
degree. His greatness, his goodness and his holin/
the universe ; ours, although similar in kind,
infinitesimal only in magnitude, and shall fill only
to which he shall appoint us. Our respective 1
enlarge as eternal ages roll on, but the mighty f
Eternal is as unlimited as his duration, and aa or
as that infinite awoe which he ever continue* tr
own glory*

LESSGM8 IN BOO&UBPDTG.

161

LESSONS IN BOOKKEEPING.— No. IX.

(Continued from page 146).

Iv the following Day-Book, the entries of the Purchases and
8ales of Cotton, detailed in the Memoranda of Transaction!, *re
here entered in the proper Dr. and Ca. form, and in business they
irould constitute the original record of these transactions. ' The
original do c ument s relating to these transactions would, of
course, be found in the Inyoice Book ; those relating to Pur-

cTiases, in the Invoice Book inward i and those relating to Sales,
in the Invoice Book outward; the former consisting of the
actual invoice* sent in with the goo-i^, which are usually posted
in a Blue Paper Book; the latter consisting of exact copies
of the actual invoices sent out with goods.

(i)

DAY BOOK.

(1)

January 7th,- 1853.

Dr.

Cb.

Cotton Account Dr. to Osmond and Co.

Bought 22 bags of Berbice Cotton, Net 7280 lbs., at 9}d per lb. ...

12th.

Cotton Account Dr. to Andrews and Co.-

Bought 30 bags of Grenada Cotton, Net. 93*0 U»*t at *tt» 9* lb « •••

26th.

. Cotton Account Dr. to Andrews and Co.

Bought 14 bags of Myrtii^ Cotton, Net 4350 lbs., at 7£d. per lb.

£288
827
135

3
6

£288
327
135

£751,

£751

February 1st

813
4

199
3

14
15

3
7

318
202

10
.0

Brown and Smith Dr. to Cotton Account

Sold 22 bags of Berbice Cotton, Net 7280 lbs. at 10£d. per lb.
Discount at l{ per cent.

10th.

Cotton Account, Dr. to White and Co.

Bought 24 bags of West India Cotton, Net 7160 lbs. at 6jd. per lb.
| Discount at 1& per cent.

DAY BOOK.

(2)

February 14th.

Williams and Co. Dr. to Cotton Account

Sold 14 bags of Grenada Cotton, Net 4312 lbs., at 9£d. per lb.
Discount at 1& per cent. ... '

17th. * —

Cotton Account Dr. to White and Co.

Bought 24 bags of West India Cotton, Net 8476 lbs. at 6$d. per lb.
Discount at lj per cent. ... **

• 21st.

Williams and Co. Dr. to Cotton Account

Sold 16 bags of Grenada Cotton, Net 4928 lbs., at 9fcL per lb.
Discount H to* cent

■25th.-

Charges Account Dr. to James Manning

For his Brokerage ou £721 12s. 0d\ at $ per cent.

Dr.

£168

226

192

6
2

4
10

10
6

£170

Cm.

229 11

195

152

THE POPULAR EDUCATOR.

(3)

DAY BOOK.

(3)

-February 26th.

Dr.

Cb.

Cotton Account Dr. to Bast India Company ...

Bought 10 Lots of Madras Cotton

(prompt, April 25th), fix.,
Lot No. 1, containing 12 Bales, Net 4820 lbs. at 4d. per lb.

£721 12

it 2 ,

» 12

4260

at „

t. 3 ,

4132

at „

•• *

4084

»t „

» 5 ,

t»

3976

at „

» 6 ,

• 12

4092

at „

»» 7

t 12

4300

at4tf.

•> 8 ,

4184

•*».

,» 9 ,

3896

at „

>• 10 ,

t 12

4004

•t„

March 13th.

£1841

I £72
71
68
68
66
68
80
78
73
75

1841

17
1

5
4
12
9
1
1

Spencer and Co. Dr. to Cotton Account

Sold 14 bags of Maranham Cotton, Net 4360 lbs. at 94. per lb, ,
Discount 1} per cent.

•16th.

Thompson and Co. Dr. to Cotton Account

Sold 24 bags of West India Cotton, Net 7460 lbs. at 8}d. per lb.
Discount 2} per cent

Althorpe and Co. Dr. to Cotton Account

Sold 12 bags of West India Cotton, Net 4240 lbs at 8d. per lb . .

£160
2

267

141

-24th.

Cotton Account Dr. to Baring, Smith and Co.

Bought 30 bags of Demerara Cotton, Net 9218 lbs. at 7}d* per lb.

£866

18
8

12
12

163

264

141

288

£856

DAY BOOK.

(4)

• April 4th.

Cotton Account Dr. to Osmond and Co.

Bought 16 bags of Berbice Cotton, Net 4960 lbs at 9d. per lb. ...
Discount at 1J per cent.

7th..

Cotton Account Dr. to Andrews and Co.

Bought 22 bags Maranhara Cotton, Net 7166 lbs at 8d. per lb.

• 12th.

Allison and Co. Dr. to Cotter i Account

Sold 12 bags West India < Cotton, Net 4236 lbs. at 8fl. per lb. ...

-18th..

Thomas Jones Dr. to Cotton Account

For 24 bales of Madras G wton, Net 8680 lbs at 6±d. per lb. ...
His Commission and other e: rpenses

-20th.

Lloyd send Co. Dr. to Cotton Account
Sold!

24 bales of Madras (Cotton, Net 8216 lbs at 6jd. per lb. ...
Incidental expanses

£183
2

238
160

226

223

'i<.

Ca.

£186

238

150

232

222

10
19

LESSONS IN BOOKKEEPING.

DAY BOOK.

(«;

April 22nd.

Dr.

Cr.

Cotton Account Dr. to Ovington and Co.

Bought 24 bags of Demerara Cotton, Net 7362 lbs. at 8d. per lb.

£245

213
6

337
8

1
9

8
10

£246
218

345

8
10

Thomas Jones Dr. to Cotton Account ... ... ... ...

For 24 bales of Madras Cotton, Net 8068 lbs. at 6}d. per lb.
His Commission and other expenses ••• ... ••• ...

30th.

Thomas Jones Dr. to Cotton Account ... ... ••• ...

For 30 bags of Demerara Cotton, Net 9218 lbs. at 9d. per lb.
His Commission and other expenses

1840

£1840

£217

241
6

5
3

2
10

£217

247

Llovd and Co. Dr. to Cotton Account

Sold 16 bags of Berbice Cotton, Net 4960 lbs. at 10£d. per lb.
Incidental expenses ... ... ... ... ...

4th.

Thomas Jones Dr. to Cotton Account ... ...

For 24 bags of Madras Cotton, Net 8484 lbs. at 7d. per lb.
His Commission and other expenses ... ... , ..

(•)

DAY BOOK.

(«)

Minr 1th .i.i

T\w

■LIB.

UK.

Powell and Co. Dr. to Cotton Account ... ... ... ...

Sold 22 bags of Maranham Cotton, Net 7166 lbs. at lOd. per lb.
Incidental expenses

13th.

Perkins and Co. Dr. to Charges Account

For Commission &c. on the purchase of Cotton amounting to
£212 6 8

16th.

Perkins and Co. Dr. to Charges Account

For Commission &c. on the purchase of Cotton amounting to
£610 19 4

27th.

Brown and Smith Dr. to Cotton Account

Sold 12 bales Madras Cotton, for Cash, Net 3896 lbs. at 9d. per lb.

£299

17
6

19
8

2
8
2

£298

19
8

8
6

£883

T- ,_

£308
57

£306
1

Powell and ^Jo. Dr. to Cotton Account

Sold 24 bags of Demerara Cotton, Net 7362 lbs. at 10 per lb.
Incidental expenses

30th.

Charges Account Dr. to Petty Cash Account

For Petty expenses paid from January 1st till this day, as per
Petty Cash Book ...

£365

£165

1*4

u . "

THE POPULAR EDUCATOR.

LESSONS IN GERMAN.— No. LXXV.
Ir regu l ar Verfa, continued from p* 18S,

(8) aBoJfai, to be willing. (See Remark 14.;

M-_

DcraoufWi

BUBJ Ufltri iv JS.

COTWITlUXAIi.

fyvittiTTra

nrrDrnrra.

FABTICEPIjI,

Present Tense.

i 1 ™***** 7>**e.

i¥eKai TVnjff

Present,

i^ tpitt. I *i!l.

t(* ipoUr. 1 may ^

turiif ji to be

tisofLtw,

■

t» ixnCIft, thou wilt.

tu nwfleft thou m&yst

willLog.

wUling*

ee roiU, he will.

et njotte, he may

' i

wit irrflfn, we will.

toir h; tun. we may

5 i

iljt nutlet you will.

ifcr TwJti-t, you may

;-i

fit nrilcsi. they will

(ie loctfcn, they may

Imperfect Tense.

r i

\$ tawftte, I wms

id? n?cHte, I might

£ <

tu uwtttcfl, thou wist

tu UKiIbeft thou mi^' t*t

fr ir.?! 1 tt .. he was

rt tocTItc, he might

nrir TOaJUea we were

1 -

wir reottteiw we might

►

3 J

u)e wtittttt, you were

int njrllitt, you might

-i

Tit uwUirn f Sbey were ^

fit ttnjlltoi H they might 4

F*r/*e* Taw.

Perfect Tense.

Perftet Tente.

Perfect

* [i

idi batrt

I have *

H J

ut laic 1 I may have

cii &-.ikfi ' bfeo willing.

qtwctlt Fubfi-, to

getoollt

* -{2

tu 0a|t

thou hut

have willing.

willed.

3 ^3

« lot '

3 he has

* f '

t&Lt bAt*t1

h we have

&ir 6»ifct n [ S

5<U

iIit &atrt

* you have

■^

ifcr $aUt 9

fc U

fie bafcen d

they havc^

fle^ibai J

Pluperfect Tense.

* o

t$ tartt n

Xhad

^r.

' tdi fldtt* "

I might have

t)U i- latfl

tbonhadst

tu fedtttit

t been willing,

£ (3

ti- biire

3 he bad

er tdttt

,i Ac.

i5*

tcrc tottta

g we had

' *

n?tr fidrten

ibrfrattet

*y0U had

ifit Bottct

£?S

fw ^atttn J they had _,

fi« fatten ^

First Future Ten**.

Jlrtl Jwltar* IV««,

.Rritl ^fnre.

o f 1

t4 totrtt ") I shall *

ift Jocrtt ^

rif . J hhallhr

lit? ftiirtt *

t]2

til mirft thou wilt

bu iBertefi

willing, &c

ba wflttitfl

3 U

er tcttt £ J he will
tuir tttrten | * we Ahull
ifer werbet you will
fie jwrten J they will J

rr tuctte

re roue*!

111*

l{J

ntit werten

jcie tourfeen

w ^

it*r ftftfcrt

tt!x ivurt ft

*> Ls

fit KDcr^tn j

fie toutotn u

^- ^1

Second JFWur* IVmm.

Second Fntttre Tense.

Second jfoture.

z hi

t<$ ftWte

1 j. 1 shall have
1 been wil

■J3> liugi &c.

idj UJttte

1 rf {iO I thall

M todxtt "

t .1 si'i:ft

t u ire 1 1 c»t

y. have been

tu tv kkrt r ft

ill

« [3

«t wit b

ei n. ■:rt l

^ *»■ willing, &c

rx fDUTte

*9 ^=

1 ; •S K

tf [

irir inert en

UOTtWrttn

mil- iviincti

5 2

ifcr totrtei

iftr m*rts«

iUr tour1«t

* (a

ftc IMfSC|

fie icctten

■■131

fit i^iittna J

^«^

(14) Remarks on tooUetu

SBotlni implies future purpose: thus, t$ kwiS ge^en, I will (to) go,
i. e. my purpose is to go. The expression of mere futurity would
be, t<$ vocttt gtfceit. Kindred to this is another signification of
tooOtn: as, re wntl bk^ grfe^en ^oben, he wills to have seen you,
that is, he wltt hate it or affirms, that he saw you.

Examples,

further illustrating the uses of the preceding verbs.

I am allowed to do it.
It might perhaps be true.
It might easily happen.

3$ barf H t^tm.

ffi turfte vieuetyt toa^r fcin.

<&B turfte rocM gefdjeben.

XDu barffl efl nur forfcem.

9x fann tortrr lefen no# f^reiBm.

3<^ fann mid> irren.

3^ fonntt i^n nk^t vrtfn$nt.

jt&Bnm €5te 9«utr jn mfar Ipnunes ?

You need only ask for it.

He can neither read nor write.

I may be mistaken.

I could not understand him.

Can you cone to me to-day f

3$ mag bat nt$t.

3^ mbtyt gem toifirs, toicvirl Ityc

rtifl.
3(^ mbd)U teo^I tttoat bavon ^abrn.

<Bl mag fetn.

3Q mo^te tteBct.

9»dge rr langt (ebm !

3^ rntrf el t^un.

Qrr atufte ity fdnrt aSetraaenl fd^A*

men.
0Jhi§te e6 nt^t fo fommen ?
SBenn ic^ fietBrn miif te, f nmtbe i<^

e« ni$t t^un.
3<9 mottte getne ge$m

3c^ »{a ju gufe ge^m.

3(^ toottte, taf tote getyen follten.

I do not tike that

I should like to know wbat

o'clock it is.
I should like to have some of

it.
It may be.

I had rather ; I would rather.
Long may he live !
I must do it
He should be ashamed of bis

conduct.
Should it not so hare happened?
If I should die, I would not do

it.
I would willingly (i.e. would

like to) go.
I will go on foot.
I was for our going.

LESSONS IN CHEMISTRY.

366

9$ m ffe) aagetraatu *•&•*■
Star Jtesnj fall asgrfsennea feat.
ftai« cr suefce fterbs* foOtr.

SBenn to* fo fein follte.

You should write ; you are to

write.
What doe* that mean?
It it said to have happened.
The king is amd to have arrived.
If he should die to-morrow.
If that should be so.

ft 94. PaSSITB VxUTO.

(1) The passive voice is formed by adding to the auxiliary
ttcftcs, to become, through all its moods and tenses, the perfect
participle of the main verb, thus :

Iicdic. Active.
Prat, ty toBc, I praise,
Imp. ty hbu, I praised,
Per/, hf, $o»e gelrit,

I have praised,
Fhtp. ty fatte gttset,

I had praised,
'.. JW. ty ttote lo&a,

I shall praise,
2 JW. t$ tperbe gcloBt $o&tt,

I shall have praised,

Indic. Passive.
ty toote gelrit, I am praised,
in) wttH jrfofo, I was praised,
in) bin geiofct uvrfcfit,

I have been praised,
u} tear qdofe toocbes,

X had been praised,
in) tt*tb< 9<tofct sxrteo,

I shall be praised.
t$ tt*rt>e grtoBt nwrbca ftin,

I shall have been praised, &a

l2) It will be noted, that wherever the perfect participle of
the main verb (as gelcbt above) is joined with the participle of
the auxiliary, the latter is written uwrtfn, not graorfcen, whereby
an effensive repetition (of the syDahle gc) is avoided. Some*
timet nwrben is altogether omitted fcu the past teases, but this
should be avoided.

(S) The German, by confining nxrbtn with the past participle
to the expression oipastvomess and using fein, when the participle
is to he taken as a mere adjective, has a manifest advantage
over the English passive. Thus, if we wish to nay, in German,
he is feared, it will be, cr totrb gefur$tct ! if the intention, how*
« ver, be merely to mark the state or character of the person as
one who is feared, that is, whose character or conduct inspires
fear generally, the German will be, cr ijt gefur$tet, he is (
1 (man). The form of expression in English, it will be
, is the same for both ideas : " he U feared."

(4) The Germans, however, employ the passive form far less
frequently than the English. They prefer other methods:
thus, man fagt, one says, i.e. it is $aid; fcer €tyftfft( ffat fty gefunben,
the key has been found.

LESSONS IN CHEMISTRY.— No. X.

Pbbhaps you will think we have had enough of arsenic, and
that it is time to proceed to another metal. Presently we will do
so, hut before taking leave of arsenic altogether, we must not fail
to notice a very elegant method of separating it, under certain cir-
cumstances, by the process of a German named Iteinsch, iieinsch's
process consists in adding to an arsenical liquid a few drops of
nv.imrii? aoid, immersiug a few slips of clear bright copper, and

boiling in a glass or p^celain vessel. By this treatment, if any
arsenic be present, it wiil, except under certain peculiar conditions,
be thrown down upon the copper in the form of a crust. The
copper thus coated being then removed, thrown into the hydrogen
generator, and the gas whi< h escapes tested, the distinctive cha-
racteristics of arsenic will be observed. In bidding arsenic fare-
well, let me impress upon your memory the fact of there being no
antidote to this poison. By the expression antidote, we mean
some body which has the property of counteracting the effects of a
poison. For the most part, antidotes act by rendering the poison
in question insoluble ; for it is an *ixi nn in medicine that che-
mical bodies only act on in.» animal system in virtue of their in-
solubility. 1 am awo ihut yon will find in certain books a
statenent snmcwluit ..'„ vaiiam .• witii this remark of mine: you
will find ch.inu.al mentioned as ore antidote to the effects of
arsenio, magnesia ano-.^r antidote, an*! the hydrated peroxide of
iron, a th ; rd. As c r.o rna the two former, they have not the
slightest pretence to efficacy ; the third U efficacious, but it will
not keep, it must bo prepared when wanted, therefore for all prao-
taaal purposes it does not exist We wiU now take up another.

Chemical Characteristics of Cadmium.— Bj this time the student
is aware that nearly all the operations of chemists are prosecuted
on solutionis We shall require, therefore, a solution of ^"i"",
Now cadmium is a scarce metal ; a Tory interesting metal, never-
theless, consequently we must not noajisot it

In order to obtain the solution on which future experiments are
'to he conducted, you may either select as a basis the metal cad-
mium itself, or the oxide of cadmium. Country readers may send
each a letter to Messrs. Bland and Long, of Fleet-street, asking
them to forward a few grains of ondmjum, the expense of which
will he Tory trifling. Cadmium is a soft white metal, in appear-
ance very much like tin ; it is frequently associated wish ore of
sine, in a preparation of which metal, oxide of sine, it wee fisst
discovered by Professor Btromeyer, in 1817. Cadmium readily
dissolves in sulphuric acid (oil of vitriol), also in Irydioaajoaia or
muri atio aeid (spirit of seh) ; perhaps the latter will best seat our
purposes. Let the acid he dilute (four or Ave by me as ur e of water
to one of aeid), and aid the solution by heat Ascertain when the
process of solution is complete that a little free aoid is seesent,
for on this acidity hinges a curious point in analysis. I need
scarcely say this determination of acidity is accomplished by
litmus paper in the usual manner.

And now let me recall to year memory a certain fact If hydro-
sulphuric aoid gas be transmitted through a solution of sine in
either sulphuric or hydrochloric aeid, no presspitate mils if either
of the solution acids be m excess. On trying the experiment,
however, with a solution of cadmium, we get a precipitate at once.
This precipitate, you will remark, is yellow — so very much resem-
bling the sulphuret of arsenic in appearance, that it is impossible
by mere ocular inspection to discriminate between them.
Their chemical characteristics soon point out distinctions ; thus, for
example, sulphuret of arsenic is soluble in ammonia, whilst sul-
phuret of cadmium is not ; and still more conclusive is the result
of heating with charcoal and carbonate of potash or soda in a tube.
In the case of arsenio we get the well-known crust; in the case
of cadmium we do not. The history of cadmium is very curious,
and demands the attentive study of every chemist, as showing the
necessity of extreme care in following out investigations. It is
the custom throughout Germany for a government commission to
examine druggists' shone from time to time, with the object of
determining whether the drugs and chemicals are pure, in the
year 1817, a certain commissioner, having examined a specimen of
oxide of sine, held by s very respectable druggist, pronoun ued it
to contain arsenio. The commissioner wss deceived by tne ap-
pearance developed on the ad d i t ion of sulphuretted hydrogen.
Against his decision the druggist appealed. Professor Stsomeyer
was called on to investigate the subject, and the result of his
labours wss the discovery of the new metal cadmium. Nothing can
be more easy than the process adopted by Stromeyer for the sepa-
ration of cadmium from the associated zinc. He dissolved both
in hydrochloric acid, taking care that the acid remained in excess.
He then transmitted a current of hydrosulphuric acid gas, and the
cadmium was thrown down in the form of yellow sulphuret. The
latter he collected, washed, mixed with black flux, and exposed to
red heat in a crucible. The sulphuret was reduced, and metallic
cadmium obtained. In other words, he pursued the exact course
to obtain metallio cadmium, that you have pur*u*>d on many
occasions now to obtain metallio nrwnic, with the sole exception
that he employed a higher temperature. The general theory
of the routine for obtaining a metal from its sulphuret is prvtty
nearly the same ; only arsenical sulphureta, however, are capable
of being reduced to the metal bo state, and the metal volatilised
by the mere heat of a spirit-lamp flame.

Chemical Characteristics of Antimony.— The metal antimony
being one of those which, in certain states of solution, precipitate
hydrosulphuric acid, yellow (we call it yellow by courtesy ; its
true colour is orange), it forms a continuation of that thread we
have laid hold of to conduct us through the labyrinth of che-
mistry.

Antimony is in many respects a very peculiar metal. The
learner would And it a difficult task to make s solution of this
I metal, therefore he will do well to procure ten or eleven grains of
] tartar emetic, a substance which contains antimony, and which
I readily dissolves in water. Ten grains of tartar emetic, and about
I two wine glasses full of distilled water, will form a very proper
1 solution for our future experiments. He must not omit, however,
] to make himself acquainted with the metal antimony as waBL If

106

THE POPULAR EDUCATOR.

he live in the country, he had better procure a small quantity in a
bottle. Probably the Tillage druggist will say he keeps antimony.
He keeps that which is commonly sold by his trade under the
name of antimony, but the substance is really a sulphuret of that
metal If the druggist chance to have real metallic antimony, he
will know it by the name of Regulus of antimony.

Haying procured a little of the metal, observe well its general
characteristics — its hardness, its steel-grey appearance, and its
brittleness.

Exper i me n t 1. — Haying put a fragment of the metal into a glass
tube closed at one end, and surrounded the tube with a strip of
stout paper in order to protect the fingers against heat, fig. 51, apply
* spirit-lamp flame, and remark whether any portion of the metal
be yolatilised, as was the case with arsenic. You will find that
antimony, although a volatile metal (as indeed all metals are, the
difference being purely one of degree), is totally incapable of
volatilisation by the mere flame of the spirit-lamp. Hence, what-
ever legal theorists may say, there can be no danger of confound-
ing this substance with arsenic.

Fig. 51.

occurred in our experiments. All the metallic antimony has been
rendsOT by this means insoluble ; hence it follows that given the
problem of separating antimony from an alloy, or mixture of anti-
mony with another metal or other metals soluble in nitric acid,
the separation may be effected in this simple manner. Now
only one other metal exists which is rendered insoluble by nitrio
acid, that metal is tin.

Experiment 4.— Fuse together, in atobacoo pipe or iron spoon,
equal parts of antimony and sine. Break the mass into small
fragments by hammering, and pour upon the fragments nitric
acid ; wait until the action has ceased, wash the residue copiously
with distilled water and you will have effected the separation of
the two metals — the zino will be obtained in solution, and the
antimony will remain in the condition of white powder.

Experiment 6, — I desired you a short time since to remark the
orange-coloured gas which escaped on the addition of nitric acid
to antimony. I shall have a great deal to state about that gas
and its components hereafter ; meantime I wish you to repeat tha
experiment with slight variations. Instead of conducting tie
operation in a closed vessel, use by preference a little flask, as
shown in fig. 52 , if you have it (a Florence flask would be loo
large) ; if not, a large test tube, t. e. t a glass tube closed at one
end, as in fig. 58.

Flf. 63.

Experiment 2. — Lay a fragment of antimony upon a piece of
charcoal, and direct upon it the blowpipe flame. Treated thus
the metal is readily volatilised, but the greater portion of it de-
posits again on the charcoal in concentric rings. Remark the
difference of effect between the inside and the outaide blowpipe
flame. Remember tho appearance developed by the same treat-
ment on sine,«and, if you please, repeat the experiment with that
metal, in order that the results developed by it may be com-
pared with those of antimony.

Experiment 3. — Place a little powdered antimony in a watch
glass, or something of that sort. Pour on it a little nitric acid
uiquafortis), and remark the violent action which takes place.
Observe the orange fumes which are developed, and particularly

Fig. 53.

The object in the experiment about to be described, is to collect
the gas developed ; therefore the flask or other closed generating
vessel will require to be fitted up with perforated cork snd bast
tube in the following manner, see fig. 54.

Fig. 54.

observe, when all action has oeased, that a white powder insoluble
in water remains. Nothing similar to this action has hitherto

Having projected some roughly powdered antimony into the
flask, pour upon it some nitric acid, rapidly replace the cork, and
insert the delivery end of the bent glass tube under the mouth of
the collecting bottle. These arrangements beins; made, the
evolved gas will be collected. Remark, however, it is now no
longer orange-coloured, but totally devoid of all colour. "When
the bottle becomes about half filled with the colourless gas,
remove the delivery tube, or, what is still better, collect the gsj
which still comes over in a separate bottle.

Experiment 6.— Agitate, by a sort of underhanded motion, the
gaseous contents, and remark that no absorption takes place,
there were absorption, the water-level of the bottle would rise.

Experiment 7. — Place the half-filled bottle on the shelf of
pneumatic trough, and measure into it an amount of
air about equal to the amount of gas it already contains.

NATURAL PHILOSOPHY.

157

now ho v the colour changes, and how absoiption takes place. I
•hall hereafter, in the proper time and place, explain the reason
of these phenomena ; meantime a sufficient number of nets hare

Fig. W.

teen shown to enable you to arrive at just conclusions. Suppose
the phenomena, instead of being known and understood, were
observed by you as the first, and that you desired to publish your
discoveries, what inferences would you have arrived at? I shall
rt.ume the examination of antimony in our next lesson.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. XL

SPECIFIC GRAVITY:

{Continued from page 139.)

8fec$o Weight of Solids.— When solid bodies can be had
only m the state of powder, their specific weight is determined
ha the following manner. Take a small glass bottle with a
lane mouth and a ground stopper or top exactly fitted to it ;
weigh the powder of the substance whose specific gravity is
required, and place it in one of the scales of a balance, along-
side of the glass bottle completely filled to the top with water,
tad carefully closed and wiped ; next, put as much shot or grains
n the other scale as will produce equilibrium ; when this is
obtained, take the glass bottle up and pour the powder into it ;
a certain quantity of water will now be forced out of the
bottle, which must be carefully wiped and closed as before,
and replaced on the scale whence it was taken. The equili-
brium will no longer exist, seeing that the powder^ has taken
the place of the water forced out of the bottle ; weights must
therefore be put on the scale alongside of the bottle until the
equilibrium be restored ; then, these weights will represent
the weight of the water equal in volume to that of the pow-
der. This being obtained, you have only to find the specific
weight by a calculation exactly similar to that explained in
our last lesson. It is necessary to observe that, in making this
experiment, the air must be carefully excluded from the glass
bottle, such as naturally adheres to the particles of a commi-
nuted bodyjand occasions them to displace a sensible quantity
of water. This exclusion of the air is effected by placing the
bottle, after the powder has been poured into it, under the
receiver of an air-pump, and exhausting it of the air it con-
tains ; or, by boiling the water into which the powder has
been poured. It is necessary also that the powder be insoluble
in water, or incapable of chemical affinity.

Rodin Soluble in Water.— If a body be soluble in water,
neither of the methods of finding the specific weight of a body,
which we have explained, will be available for this purpose.
We moat then find its specific weight relatively to a liquid in
which it is not soluble, as for example, alcohol. Haying
found, by a process about to be explained, the specific weight
of alcohol relatively to water, we find the specific weight of
the given substance, by multiplying its specific weight rela-
tively to alcohol by the specific weight of alcohol relatively to
water. Thus, if under equal volumes, p be the weight of the

substance, p' that of alcohol, and p" that of water ; then *L will

be the specific weight of the substance relatively to alcohol, and
*L that of alcohol relatively to water. Now, the product of
these two fractions in which p' is eliminated being a common

factor, is-**., which represents the specific weight of the given

P"
substance relatively to water.

TABLE

Of the Specific Weights or Specific Gravities of Solids, at the Tem-
perature of 32° Fahrenheit, as compared with that of distilled
water at the maximum density, taken as unity.

Solids.

Specific Weights.

(Metals.)
Platinum, rolled

22*069

Platinum, hammered ...

...

20337

Gold, hammered

...

19-362

Gold, melted, but not hammered

19*258

Lead, melted ...

...

11-362

Silver, melted

...

10-474

Bismuth, melted

...

9'822

Copper, wire drawn

...

8-878

Copper, not hammered ...

...

8*788

Steel, tempered, but not hardened

7-816

Iron, in bars ...

...

7*788

Iron, cast

...

7*207

Tin, melted ...

...

7*291

Zinc, melted ...

...

6-861

Antimony, melted

...

6*712

(Stones, &c.)

Diamond, the heavier

...

3*531

Diamond, the lighter ...

...

3501

Flint Glass ...

...

3-329

Marble, Parian

...

2-837

Rock Crystal ...

...

2-653

Glass, cast (St. Gobain)

fc ...

2-488

Porcelain, Chinese

2-385

Porcelain, Sevres

...

2*146

Sulphur, native

...

2033

Ivory

...

1-917

Anthracite

...

1-800

Coal, compact ...

•••

1-329

Amber, yellow transparent

...

1-078

Ice, melting ...

...

0*930

(Woods, &c.)

Beech

...

0-852

Oak ...

...

0-845

Yew

0*807

Elm ... !!'.

...

0-800

Apple-tree

...

0-733

Fur, yellow

...

0-657

Poplar, white Spanish ...

...

0*527

Poplar, common

...

0*389

Cork

...

0-240

Specific Weight of Liquids.-- -The specific weight of liquids
may be determined,.^**, by the Hydrostatic Balance. Thus, to
the hook of one of the scales of the balance, attach a body on
which the liquid has no chemical action, as, for example, a
ball of platinum. Weigh this ball successively in air, in dis-
tilled water at the maximum density, and in the given HqwVd,
and observe the loss of weight which it suffers in water and in
the given liquid ; you will thus obtain two numbers, which
represent the weight of equal volumes of water and of the
given liquid ; you have then only to divide the second weight
by the first, and the quotient will be the specific weight or
specific gravity of the given liquid. Thus, let p be the weight
of the ball ef platinum in air, p* its weight in water, and p' its
weight in the given liquid, d being put for the specific weight;
then, the weight of the water displaced by the ball of platinum
is p—p\ the weight of the given liquid displaced by the same is

p—p" ; therefore, we have d — **""** .
P—p'
The specific weight of a liquid may be determined, secondly ',
by Fahrenheit's Areometer. This areometer, fig. 38, is similar
to Nicholson's, but it is made of glass, so as to be capable of
immersion in all kinds of liquid, and it wants the under plate

TBE POPULAR EDUCATOH.

Or inverted cone. The stem is marked like the former with a
point of level, to indicate the immersion of the instrument to
the same constant depth. It is also ballasted at the lower end
by a glass bulb filled with mercury.

Fif.38.

In performing experiments with this areometer, its weight
must De carefully ascertained ; it is then made to float in a
vessel full of water, and weights are put into the upper scale
or cup, until the fixed mark on the stem reaches the level of
the water. In this state, the weight of the areometer, added
to the weights in the cup, represents the weight of a volume

of water equal to that of the part of the apparatus immersed, _ ,

according to the first condition of the equilibrium of floating hollow cube whose length, breadth and thickness are each
bodies formerly mentioned. Now, having determined in the one foot, is very nearly 1000 ounces Avoirdupois, when taken

liquids. Specific Weights.

Madeira wine ... ... 1*038

Port wine ... ... ... 0*997

Bordeaux wine ... ... 0*994

Distilled water at 39° F. or the \ . §000

maximum density )

Distilled water at 32° P. ... 0*999

Ammoniac, liquid .. ... 0*875

Olive oil ... ... ... 0*915

Linseed oil ... ... ... 0*940

Whale oil ... ... ... 0*923

Hempseed oil ... ... 0*926

Rapeseedoil ... ... .„ 0*919

Turpentine (essenee) ... ... 0*870

Oil of naphtha ... .., 0*847

Alcohol (absolute) ... .„ 0*792

Sulphuric ether ... 9M 0*716

Hydrocloric ether ... ... 0*846

Nitric ether ... ... 0*886

Acetic ether ... ... ... 0*866

Use of tke Table* of Sheep* Weights.— The tables of the
speeifio weights or specific gravities of bodies, are capable of
numerous and useful applications. In mineralogy, they fur-
nish a distinctive character by which different kinds of mine-
rals may be recognised according to their density. In chemis-
try, their use is indispensable, as will be seen in the lessons in
that science. In the practical arts, they also serve two very
important purposes ; 1st, to determine the weight of a body
whose volume is known j and .2nd, to determine the volume
when the weight is known. .

It has been long known that the weight of a cubic foot of
water, that is, the weight of a volume of water contained in a

same manner "the weight of an equal volume of the given
liquid, we have only to divide this weight by the former, and
we obtain the specific weight required.

The specific weight of a liquid may be determined, thirdly*
by means of a glass bottle such as we described in finding the
specific weight of a solid in powder. This bottle is first

weighed when empty, then when full of water and lastly ^ prece d1ng tables of the specific weights of
when full of the given liquid. If we now subtract the weight ti pi/ e achnumber by 1,000, that is, if we rem
of the bottle from its weight when respectively full of water US •Iftrartl^w. hW *£ vervTeLlv

and of the given liquid, we have under equal volume the
weight of water and of the given liquid; whence we can
deduce, as before, the specific weight required*

Temperature when Specific Weights are determined.— As the
volume of bodies increases with their temperature, and as this
increase varies in cUfferent bodies, it is plain that the specific
weight of any substance is not strictly the same at different
temperatures. Hence the necessity of selecting a constant or
fixed temperature for the determination of specific weights.
The temperature selected for water is 39° Fahrenheit, or
according to Stampfer 38°* 76, because this is the temperature
at which it is found to have its maximum or greatest density.
p\e general temperature selected both for solids and liquids,
is that of 32° Fahrenheit, or, the temperature of freezing
water.

' When we come to treat of the subject of heat, directions
will be given for the reduction of experiments to these tem-
peratures.

TABLE

Of the Specific Weights of Liquids at 32

Fahrenheit^ as compared

with that of distilled water at the maximum

density, taken as

unity.

Liquids.

Specific weights.

Mercury or Quicksilver

...

13*578

Sulphuric acid

...

1*841

Hydrochloric acid

...

1-240

Nitric acid

...

1*271

Acetic acid

...

10G3

Phosphoric acid

...

1*558

Aquafortis, double

...

1*300

Ditto, single

•••

1*200

Milk

...

1030

Sea- water

•••

1-026

at the maximum density; the difference being such, that
according to the experiments made by order of the Legislature,
this weight is exactly 999*2777 ounces Avoirdupois. Suppos-
ing now that this weight is for all practical purposes 1000
ounces, we have at once a relation between the volume of the
cubic foot of water and its weight, which will solve the two
problems just mentioned in a very easy manner. For, if in

a of bodies, we mul-
. , . . remove the decimal

point altogether, we have then very nearly the number of
ounces which a cubic foot of each body will weigh, for
example, a cubic foot of bar iron will on this principle weigh
7,788 ounces Avoirdupois, or 4 owts. 1 qr. 10 lbs. 12oxs.; and
2,000 cubic inches of the same substance will weigh 5 cwts.
3 lbs. 5 oss. nearly ; for, a cubic foot being 1,728 cubic inches,
we have 1,728 : 2,000 : : 7,788 : 9,013 nearly; and 9,013 ounces
Avoirdupois are equivalent to the weight just stated. In like
manner, on the same principle, 6 cwts. 3 qrs. of a bar of iron
are equal in volume to 2,68$ cubic inches of that material, or
to 1 cubic foot and 955$ cubic inches ; for, 6 cwts. 3 qrs.=12 t 096
ounces ; and 7,788 : 12,09$ : : 1,-728 : 2,683} cubic inches.

Generally, if we represent the number of cubic feet in the
volume of a body by F, the specific weight in chiliads (thou-
sands) of ounces Avoirdupois by 2), and the relative weight of
a body by P, we shall have P=zV D ; that is, according to this
notation, the relative weight of a body is equal to the product
of its volume by its specific weight. Conversely, since from

the preceding equation we have V— ;

we shall, therefore,

have this rule, that the volume of a body is equal to the quo-
tient of its relative weight divided by its specific weight.
1 As an application of the formula J=*c= FA we may here
show how to calculate the interior diameter of a capillary tube.
First, introduce into the tube a column of mercury, aeoerfun-
ing with accuracy its length and its weight. Next, supposing
the column of mercury to be cylindrical, we have, according to
the rule for finding the solid content of a cylinder, F=a*i*H
where r is the radius of the circular section of the cylinder,
liifk length, and it =3*141*3. Substituting this value of Fin
the equation PsTD, we have i*=7rr«/D ; whence r*=»

\/ . In the same manner, tine diameter of a vary
, metallic wire may be calculated.

LESSONS IN ITALIAN.

LESSONS IN ITALIAN GRAMMAR.— No. XL

By GHABLES TAUSENAU, M.D.,

Of tbe University of Pavia, and Professor of the German and Iiattan
Languages at the Kensington Proprietary Grammar SehooL

Thsre are three articles in the Italian language, U and lo
for the masculine, and la fqr the feminine gender, equivalent
to the English definite article the.

The artitle il can only be used before those masculine words
which begin with a consonant, excepting always s impure ;
i.e., 9 followed by a consonant. The plural is t. For ex-
ample :

Ilgiar-dt-no, the garden I H ei-gno-re, the gentleman
1 giar dl-ni, the gardens | I si-gn6-ri 9 the gentlemen

The article lo, without the apostrophe, can only be used
before those masculine words which begin with the t impure ;
t.#., an * followed by another consonant. The plural of lo is
gli.* For example :

Many grammarians of great authority have even emphatically
proscribed the use of per il in the place of per lo. As, however,
cultivated persons and the best writers have never ceased oc-
casionally to use the combination per il, its correctness and
allowableness will at once be admitted, for the usage of a language
is a safer guide han the caprice of grammarians.

Lo qpi-ri-to, the spirit I Lo ttra-nM-re, the stranger

Gli spi-r+-ti, the spirits | Gli ttra-nie-ri, the strangers

The article lo is also used before all masculine words that
begin with a vowel ; but in such a oase the apostrophe must
be used thus, t. For example :

L* tin-pii-go, the office or em-
ployment

X' an-gt~b t the angel
Gli dn-ge-li, the angels

le d-ni-me, the souls ; le in+et-gne, the banners, signs ; Is 4-p#-
re, the works ; le u-sdn-ce, the usages.

It is obvious that the six words above mentioned, con-
stituting the three articles in the singular and plural, s7, lo, la, t,
gli, and k, must frequently meet monosyllables, and therefore
occasion dissonance. As harmony is a marked characteristic of
the language, some means must be found to. correct this. This
is effected by contractions, in which letters are changed, omitted
or added according to laws dictated! by the conveniences of
pronunciation, by custom, and by harmony. The monosyllables
referred to are di, of ; a, to j sis, from, by ; eon, with ; per, for
through; *u, upon; and the important contractions (to be
committed to memory) to which they are subject, when in
combination with the articles il> h, la, i, gH, and h, are the
following : —

G? im-pti-ghi, the offices or
employments

The tender will remark that I have placed no apostrophe
after f% the plural of lo, before dn-ge-li, while I have used the
apostrophe on gV before im-pie-ghi. The reason of this is,
tut the plural gli only requires the apostrophe before words
eomneneing with the vowel t, and never before words com-
mencing with the Towels a, e, o, and u; which is clearly a
necessary usage to maintain the squeezed sound of the word
gl* (flyee) in these cases. For, otherwise, gP dn-ge-li would be
pronounced, according to tho rules explained in the fifth pro-
nouncing table, glahn-jai-lee. Even Italians themselves are
occasionally lUble to commit the fault of placing the apostro-
phe on the gV before a, e, 0, and u ; but the difference caused
in the pronunciation manifestly snows the grossness of this
blunder.

The aiticle la can only be used before words of the feminine
gender which begin with consonants. The plural is le. For
example:
Latd-vo U, the table I La md-dre, the mother

Le td-vo-le, the tables | Le md-dri, the mothers

The article la must have the apostrophe V when it comes
before words of the feminine gender commencing with a vowel.
For example s
V a-ni-ma, the soul I V eV-fla, the herb or grass

£# d-ni-me, the souls | V er-be, the herbs or grasses

The reader will have observed that I have not placed an
apostrophe on the le before the plural a-ni-me, while the le
has the apostrophe before the plural fr-be. The reason is, that
it is a common usage to place the apostrophe on the plural le
before woTds of the feminine gender commencing with the
vowel e. For example :

L' es-pe-rien-zs, the experiences; f e-re»sUe 9 the heresies.
But before feminine words commencing with the other vowels,
the le is not commonly used with an apostrophe. For example :

♦ The only exception to this rule is the very frequent use of
the article lo after the preposition per, for, through, before words
not beginning with the s impure ; as, for ex raj>le, per lomdn-do,
for the world: per lo giar-di-no, for or through the garden ; per lo
o, for the past.

Instead of diil

write eHl

Instead of m i write n4ik

t»

dii

»»

dti*

into

neVlo

dilo

del-lo

int

ndW

diV

»»

dell'

in gli

ne-gli

>•

di gli

»i

dd-gli

in la

nel-la

»»

dila

del-la

conil

col

dilc

dtl-le

con i

cot

ail

con lo

col-lo

a i

»•

«t

conV

cUt

alo

al-lo

con gli

co-gli

»»

ml'

alt

eon la

oil-la

a gli

»»

ag-li

con I*

c6Ule

a la

al-la

*M U

eul

ale

al-lo

tu i

sui

daU

dal

euh

suLlo

t»

da i

!•

dai%

eul'

suit

dalo

ddl-lo

augli

sii-gli

daV

datf

su la

fill, la

da gli

dd-gH

tu le

tid-le

data

ddl~la

peril

pkl

dale

•t

uuw

per i

•t

9*W\

»!

in il

net

per gli

pe-gli

Tho reader will remark that I only give three contractions
of the word per. For this reason, that per, generally speaking,
is not contracted with an article commencing with the letter
/, and in suoh cases it is customary to place per and such an
article separately ; as, per lo pes-sd-to, for the past ; per la cd-
*a,\\ for the house ; per le eo-ril-U, for the sisters.

With regard to the word w», with, it may be remarked, that
when it comes in connexion with an article commencing with
/, it is optional to contract it ; it being equally correct to say
eon lo 1 or eol-lo ece't-tro, with the awptre ; e*l or con Vin-gdn-
tto, with the deceit ; eon la or col-la si-gnc-ra, with the lady ;
con le or c6l-lc brdc-cia*b with the arms.

Two important prepositions, tra and/ra, between and under,
can likewise be contracted with the article, but in a special
way, and with modifications which must be stated separately.

If tra and fra are to be contracted with an article commen-
cing with I, the letter / must be doubled, U ; as, for example,
fHd-U tnon-td-ane, between the mountains ; trdl~U du-e 90-rel-

* It is useful, with regard to pronunc ation and orthognptiy, to
bear in mind the diff- ren<e between ttie»e three words: dtt, -M the
(pi ), t^-i, God* (the pluxal of Di-o), aud De.\, Dty (of the Baxbary
States).

f It is, for the reasons stated in the previous note, useful to
mind the difference between di, to the (pl.)> and d-j, tutors.

% Mind tho difference between ddi, from or by the (pi.), and
dd-i } thou givest

§ Mind, also, the difference between nH, in the (pi.), and nt-i,
moles (upon the body), patches (on the face).

H The letter in this word, although placed between two vowels,
has the sharp, hissing sound, as well as in the words c6sa, thing,
and 00-M, thus, before commented on.

U Once for all, being obliged for the greatest part to divide the
syllables as they are divided in Italian spelling, I must em-
phatically warn the reader not to read the combination cc (when
not followed by h) as though the first c was a k (the English-
man would naturally do so), but to read the whole combina-
tion as though it was ttch, gliding with great rapidity from one
syllable to the other. I must refer, on this point, to my remarks
and tables on pronunciation

160

THE POPULAR EDUCATOR.

le, between the two sisters ; frdUo seri-gno $ la sS-dia, between
the ride-board and the chair.

Whenever tra or fra is to be joined to the article t, the
Utter is omitted, and an apostrophe placed in its stead. For
example : fra* cu-gi-m, between the cousins ; tra* fra-til-li,
between the brothers.

The words tra and fra are nerer contracted with the article
gli. For example : fra gli a-ml-ei, between the friends ; tra
§V in-fe-U-ei, between the unfortunate.

When fra or tra stands before il, the letter t of the article
is commonly not heard in pronunciation and in writing, the
apostrophe is used in its place. For example : fra f l s6n-no,
during the sleep ; tra 'I si e'l n6, between yes and no,
hesitating.

The so-called indefinite article uno, masculine, and una,
feminine, will be hereafter explained.

In Italian, as in English, the nouns hare no terminations!
alteration in either number; that is to say, all cases are
alike. Strictly speaking, therefore, they cannot be said to
hare any declensions. All changes in Italian nouns denote
only a difference in gender or in number. For example : pds-
se-ro, sparrow, not only denotes the object sparrow, but also
that it is a male ; and pds-se-re (female) sparrows, not only
denotes the feminine but the plurality of number. The article
in Italian, as in French, Spanish, and English, does not in
itself denote the case, but is a word that distinguishes one
noun as a determined object from another noun of the same
class. It is on this account a fixed principle of the language
nerer to place the article before a noun, when the latter is
used in its general and indeterminate signification. The
articles il, lo, and la, are in themselves as indeclinable as the
noun itself. They only change according to the gender and
number of the noun ; and when the Italians desire to denote
cases, they must, on this account, like the English, place be-
fore the articles certain words, which are the substitutes of
those inflexions by whieh, in the Greek, Latin, and German
languages, the cases are expressed. The English have only
two such signs of cases ; the words of and to. The Italians
have three ; di, for the second case, or genitive ; a, for the
third case, or dative ; and da, for the sixth case, or ablative.
These three words, di, a, and da, are used in the singular as
well as in the plural, before masculine nouns as well as femi-
nine. In the first case, or nominative, and in the fourth case,
or accusative, the Italian noun has, as well as the English, no
case sign before it, and both these cases are sufficiently dis-
tinguishable by the place which they take before or after the
verb, for which reason they require no special distinguishing
mark. For example :

A-les-sdn-dro vin>se Dd-rio> Alexander conquered Darius ;
Cdr-lo per-euo-te il cd-ne, Charles strikes the dog ; il prin-ci-pe
a- ma la cde-eia, the prince likes the chase; Pii-tro lig-ge* le
gaz-tit-te, Peter reads the newspapers.

I shall now subjoin two tables illustrating the declensions of
Italian nouns : I. with and without an article ; and, II. with some
important words frequently preceding them. These tables are
so important that they must be committed to memory. But
let me first remark, that it will be sufficient for our present
purpose to lay down this fundamental rule with regard to the
formation of the plural of Italian nouns :

All Italian nouns, masculine and feminine, change their final
vowel into i in the plural ; as, il pd-dre, the father ; i pd-dri,
the fathers ; il po-e-ta, the poet ; i po-i-ti, the poets ; il cer-vo,
the stag ; i cer-vi, the stags ; la md-dre, the mother; le md-dri,
the mothers ; la md-no, the hand ; le md-ni, the hands.

The most important exceptions from this rule are feminine nouns
terminating in a, whieh form their plural by changing A into a ; as,
la so-ril-la, the sister ; le so-ril-le, the sisters.

I.
Singular.

Nominative :

li-bro

U li-bro

the book

Genitive:

li-bro

del li-bro

of the book

Dative :

li-bro

alU-bro

to the book

Accusative :

li-bro

il li-bro

the book

Ablative :

li-bro

dal li-bro

from the books

li-bro

ml li-bro

in the book

eon

li-bro

col li-bro

with the book

Nominative :
Genitive :
Dative t
Accusative :
Ablative :

• I must once for all, and emphatically, warn the reader, be-
cause I am oblicred, in the case of the double g (gg), to place the
first g in one syllable, and the second g in the next, not to read
''when the gg is not followed by h) the first g like g in the
English word get, to which mistake many readers will be naturally
liable ; but I must refer with regard to the pronunciation of the g
(gg) to the lessons on pronunciation.

Nominative :
Genitive :
Dative :
Accusative :
Ablative :

Nominative :
Genitive :
Dative:
Accusative :
Ablative:

Nominative :
Genitive:
Dative :
Accusative :
Ablative :

con

per

di
a

da
in
eon
per

con

per

li-bro
li-bro

li-bri
li-bri
li-bri
li-bri
li-bri
li-bri
li-bri
li-bri
li-bri

pel li-bro
sul li-bro

Plural,

il<-bri»
dei(de % )li-brit
ai (a*) li-bri
i li-bri

dai (da*) li-bri
nei (ne*) li-bri
coi [co') li-bri
pet (pe*) li-bri
sui (su*) libri

for the book
on the book

the books
of the books
to the books
the books
from the books
in the books
with the books
for the books
on the books

Singular.

sehiop-po lo schidp-po the gun

schiop-po de'l-lo schidp-po of the gun

schiop-po dl-lo schidp-po to the gun

schidp-po lo schiop-po the gun

schiop-po ddl-lo schiop-po from the gun

schiop-po nil-lo schiop-po in the gun

schiop-po c6l-lo schiop-po with the gun

schiop-po per lo schidp-po for the gun

schi6p-po sid-lo schiop-po on the gun

Plural.

schiop-pi glCschiop-pi the guns

schiop-pi di-gli schiop.pi of the guns

schiop-pi d-gli schiop-pi to the guns

schiop-pi gli schiop-pi the guns

schiop-pi dd-gli schiop-pi from tine guns

schidp-pi ni-gli schiop-pi in the guns

schiop-pi c6-gli schiop-pi with the guns

schiop-pi pi-gli schiop-pi for the guns

schiop-pi su-gli schiop-pi on the guns

ad
da

a-nU-lo
a-nil-lo

a-nil-lot

a-nil-lo

V a-nil-lo the ring

delT a-nil-lo of the ring

alT a-nU-lo to the ring

F a-nil-lo the ring

dalT a-nil-lo from the ring

netf a-nil-lo in the ring

colT a-nil-lo with the ring

per V a-nil-lo for the ring

sulT a-nil-lo on the ring

• Instead of the plurals i, del, cd, dai, some old writers used the
plurals U, dsflf, out, daBi ; but this is no longer usual.

f The plurals dei, ai, dai, nei, coi, pet, sui, axe frequently marked
with the apostrophe for the sake of harmony, thus : de\ a\ da\ %€,
oo*, pf, su\ especially when coming before several words all of
which terminate in t. For example : a ca-cuUne def me%H svd-ipec-
od-Uy on account of his many sins.

% Harmony, which has had so much influence on the formation
and pronunciation of Italian words, requires that to the case-sign
a, when it comes before a vowel, frequently the letter d is added:
as, ad o+nt-re, to honour ; ad a-nd-eo, to the friend ; for a onore and
a amico.

The laws of harmony, likewise, frequently require the mark of
the apostrophe on the case-sign di, when it comes before words
commencing with a Towel ; as, cdpo d* 6-pe-ra> masterpiece ; si-gno
<T u-miUa, si£n of humility.

The case-sign da, on the other hand, is nerer marked with the
apostrophe, but always written in full, in order to avoid the
inevitable ambiguity of confounding the case-sign di with it when-
erer it is marked with the apostrophe, and the dissonance of two
vowels in this case coming together mupt be tolerated ; because, as
I have already rcm*rkc»l, perspicuity is a more urgent law than
harmony in these contractions.

GREEK EXERCISES.

161

Plural.

Nominative :
Genitive:
Dative:
Accusative :
Ablative:

Nominative :
Genitive:
Dative:
Accusative :
Ablative :

di
ad

eon

per

di
a

da
in
eon
per

a-nil-li
a-nil-li
a-nil-li
a-nil-li
a-nil-li
a-nil-li
a-nil-li
a-nil-li
a-nil-li

gli a-nil4i
d&gli a-nil-li
d-gli a-nil-li
gli a-nil-li
dd-gli a-nil-li
ni-gli a-nil-li
co- gli a nil-li
pi-gli a-nil-li
eit-gli a-nil-li

Singular.

cd-sa
ed-ea
cd-sa
cd-ea
cd-sa
ed-ea
ed-ea
ed-ea
ed-ea

Nominative :
Genitive :
Dative:
Accusative :
Ablative:

ed-ee
di ed-ee
a ed-ee

cd-ee
da ed-ee
in ed-ee
con cd-ee
per ed-ee
eu ed-ee

Nominative:

Genitive:

Dative:

Accusative:

Ablative:

di
ad

con

per

sue

Nominative :
Genitive : di

Dative : ad

Accusative:
Ablative: da
in
eon
per
eu

dr-te
dr-te
dr-te
dr-te
dr-te
dr-te
dr-te
dr-U
dr-te

dr-ti
dr-ti
dr-ti
dr-ti
dr-ti
dr-ti
dr-ti
drti
dr-ti

Nominative :
Genitive:
Dative:
Accusative :
Ablative :

Nominative :
Genitive :
Dative :
Accusative :
Ablative :

da
in
con
per

di
ad

da
in
con
P"

la ed-ea
dH-la ed-ea
dl-la ed-ea
la cd-sa
ddl-la ed-ea
ne%la cd-sa
col-la ed-ea
per la ed-ea
eUl'la cd-sa

Plural.

le ed-ee
dO-le ed-ee
dl-le cd-ee
le ed-ee
ddl-le cd-ee
nH-le ed-ee
cU-le cd-ee
per le cd-ee
eid-U ed-ee

Singular.

Vdr-U
deU dr-te
alT dr-U
Vdr-U
daWdr-U
nelTdr-U
coif dr-U
per F dr-U
euUdr-U

Plural.

le dr-ti
dil-U dr-ti
dl-le dr-ti
le dr-ti
ddl-le dr-ti
nel-le dr-ti
eol-le drti
per le dr-ti
eid-le dr-ti

Singular.

Zdn-dra
Zdn-dra
ltm-dra
Zdn-dra
Zdn-dra
Z6n-dra
Zdn-dra
Zdn-dra

Al-bdr-to
Al-Mr-U
Al-bdr-to
AUbdr-U
Al-bdr-to
Al-bdr-U
Al-bdr-U
Al-bdr-to

therinfrs
of the rings
to the rings
the rings
from the rings
in the rings
with the rings
for the rings
on the rings

the house
of the house
to the house
the house
from the house
in the house
with the house
for the house
on the house

the houses
of the houses
to the houses
the houses
from the houses
in the houses
with the houses
for the houses
on the houses

thwart
of the art
to the art
the art
from the art
in the art
with the art
for the art
on the art

the arts
of the arts
to the arts
the arts
from the arts
in the arts
with the arts
for the arts
on the arts

London*
of London
to London
London
from London
in London
with London
for London

Albert
of Albert
to Albert
Albert
from Albert
in Albert
with Albert
for Albert

Nominative :
Genitive :
Dative :
Accusative :
Ablative :

Nominative :
Genitive :
Dative :
Accusative :
Ablative.

Nominative :
Genitive :
Dative :
Accusative
Ablative :

di
a

da
in

con
per

per

da
in
eon
per

Vit-to-ria
Vit-to-ria
Vit-td-ria
VU-td-ria
Vit-td-ria
Vit-t6-ria
Vittd-ria
Vit-to-ria

Gid-ve
Qid-ve
Gid-ve
Gi6-ve
Qid-ve
Gid-ve
Gid-ve
Gid-ve

Di-o

Di-o
Di-o
Di-o
Di-o
Di-o
Di-o
Di-o

Victoria
of Victoria
to Victoria
Victoria
from Victoria
in Victoria
with Victoria
for Victoria

Jupiter
of J upiter
to Jupiter
Jupiter
from Jupiter
in Jupiter
with Jupiter
for Jupiter

God
of God
to God
God

from God
in God
with God
for God

KEY TO THE LESSONS IN GREEK.

By John R. Biajld, D.D.

Vol. HI., p. 227— Grbxx-Enqlm.

Always be true. Rejoice ye (xcupat, I rejoice). Follow.
Do not complain. I live -pleasantly. I am well educated.
Thou writestb eautifully . If thou writest ill, thou art blamed.
He hastens. He fights bravely. If you flatter, you are not true.
If thou flatterest, thou art not believed. We flee. If we flee,
we are pursued. Vou flee badly (like cowards). If you
flatter, you are blamed. If you fight bravely, you are ad*
mired. If they flatter, they are not true. It is not well to
flee. It is well to fight bravely. If thou art pursued, do not
flee. Fight bravely. If they natter, they are blamed. If
thou speakest the truth, thou art believed. Always excel.
Eat and drink, and play, moderately.

Enqlish-Gbxbx.

AXifOcvw. AXj}0ct/£if. AXnQtvti. AXnOivofitv. A\tj9evtrt,
AXnOivovot. Ei aXrjQtvw iriorivofiai. Mij fiaxtoQe. Maxovrai.
'E-rrtaOt. 'Eiry. 'EicioQt. Haidevti. Qtvy overt (flee). E*
ftvyovoi duiticovai. OavfiaZofiai. QavpaZovrat. Ei pXatctvovai
ov OavfiaZovrai, Ev t%u avdotiug jiaxioBai. Mcrpiwg todu
Koi irtve. Ov OTrtvdovai. Et KoXaKtvug ov tiavfiaZy. KaXttg
ypafu. Toafovai kokhq. Ev t%ti an aptortvtiv. Mcrptwf
piortvtrt. Ayav toOiovei.

Vol. HI., p. 308.— Gbsxx-Exglish.

Yield not to force. The lyre dissipates cares. Friendship
promises refuge and aid. Care corrodes the heart. Worship
(cultivate) the Muses. Do not believe false accusations.
Justice often yields to injustice. We are often worn down by
hard ("severe) poverty. Flee from (avoid) talkativeness.
Wickeoness brings erief. Luxury begets injustice and avarice.
Avoid luxury as a shame Tor a bane). True friendship arises
through (from) virtue ana intercourse.

Englisk-Grsbx.

Atrtxov rnc. {Stag* Airtxtrai rnc j&af . Ov* arexcrat rng
fiiac.. Airixovrai rnc (Stag, fevye rnv aSuuav. Qevytrt rnv

• It is obvious that proper names of gods, persons, towns, and
other localities, require no article in the singular, because their
individual aignincatton renders any other more precise determine*
tion or distinction by meant of the article superfluous. ,

ite

THE PGPULAft 1DU0ATOR.

miuciav. +*vy*t nf* a&auav a)g ftartav. *H /8ta Xwnt*
as-ayei. Aux &i«|f TiYwrcu ifeeiny. AX^Otvcu £<Xuu out apenjc
ytyvovra*. "H suplia wtvif ruptrw. Al fupipvai Xvovrai ra
Xvp?.

Td. HL, p. 319. — Gbuk-English.

Dishonour follows vice. Bear poverty easily. Thunder
arises from shining lightning. Virtue has excellent repute.
Regard to law sets right wrong judgments. Justice begets
justice, and injury injury. Pursue a good manner of living.
Restrain your tongue. Fortune often has (brings) changes.
Bear ye poverty. Splendid fortunes easily fall. Bear then for-
tunes (changes of fortune). Virtue yields not to misfortunes
(fortunes). Abstain from hard (severe) cares. The queen
nas a splendid kingdom.* The robe is beautiful. We have
beautiful robes.

English -Grbex.

Qtvyire roc psptuvac. 'H Kcuua rurru arifuav. *H apery
ioly itrirai. 'Pao'uoc; tytpovoi rrjv iciviav. 'H vivta feptrcu
f>ain»>Q. Qiptrt rrjv irtvtav paSiiag. B%iig fiiTafloXaf. Aire-
%ov rijc KaKiaQ. KaXqv <rro\rjv t\ ov9i ' Mn uki ry rv%y-
*Pa£ta*c tucovoi ry rvxV* Karfjren r»v yXwrrav. 2/coXiai
tiuccu tvBvvovrai.

Vol. HI., p. 820.— Grbbk-Bwoush.

Learn wisdom, O young man. Politeness becomes a citizen.
We blame the talkativeness of a youth. Avoid injustice,
citizen. We admire the art of the bird-catcher. It is proper
for auditors and spectators to keep silent. O sailors, avoid
the north wind. The north-wind (compare our Boreas) often
injures sailors. O citizens, strive after virtue. The Sybsrites
were voluptuaries. Sailors have to do with the sea. Flee, O
Persian. The Spartans have an honourable reputation. I
avoid a youth (who is) a voluptuary, (or a Voluptuous youth,
ojr a youth given to pleasure). Abstain from chatterers. Hear,
O master (sovereign lord).

Shqlish-Grbhl.

♦evyrrf,* Utpoai. noXirenc. frptwu rj aptny. Ts/f tt*v%iav
dyav irpoarjKU TroXiry. Mcrv&rvtrc, w nartai, nr* etyutv,
Ttjv oofiav fiavBavovoi. Trjv aoQiav pavQavtrt. ftp oxyftav
pavQavio. "H oo<pta pavOaverai. Vtavujt irpticti ?} tvKOOfiitu
Mn pXatrTtt w Boppa, roue vavrag. 4cvye, u> vavra, rov
fioppav, 'O fioppag ^cvycrat. Optyov, <*/ Swaprurra, rtfC folifg.
'Uavxiav aytrt, u> afoXioxat. AfoXiffgov airt\trt.

Gbbbx- English.

The bravery of the Spartans was admirable. Flee, O young
man. Do you flee, O lovers. Thieves are avoided. Justice
becomes judges. It is the duty of soldiers to fight for the
citizens. Avoid liars. It is the part of a master to take care
of his domestics. Do not trust a liar. Art supports the
artist. From liars thieves are produced. The Spartans were
lovers of glory and honour. Shipwreck often arises from the
north-wind. We admire the skill of Hermes (Mercury).

Exgli»h-Gbbkk.

Oi riff £o£ijc tpaarai ov fykvyovrcu. 01 \ptvarai ri/c aXtjOtiag
owe tin tpaorat. 'H rov Swapriarov apcrtf Oatpaorn qv. Mj
ifMfrevm, •# Sirapriarai, roic ifavoratf . *U rov 'Bppov nxrj
T)v Oavfiaarij. Tnv rmv 'Siraptiarutvaptrrfv QdvpaKofUv. *fvys
\f/tv(TTi)v f u> XirapTiara. Eoti h<nroTov, or Attnrorovttrri ciriftt*
XttoBat rov oiKtrov, 'OiKtrtov fori tirifuXiioDai rwv lioiroTujv.

• In the Greek, the distinction between the words for
queen and kingdom is made merely by the accentuation, thus,
9*#<n, Pafftkua, ha* the accent on the autepenuH (the last
syllable but two, reckoning from the end), whereas BaetXtUt,
( r m $ dtm f hae the aeeent on the penult, or the last syllable ^uf

Tigwraf rpt+ovet at nxvai. Totf arparimraiQ Tpov^KH
juttfifrflo* w-«p* rwv xoXirutv. , H<rwx«^»' «y<i *» Poppa. Toy
'Eppqv OavpuxZu.

Vol. EH., p. 337-8,— Gmbx-Enqlibh.

Pursue honourable deeds, O beloved youth. Obey the
words of thy teacher. Thou leanest excellent things from the
excellent. A faithful friend partakes of (your) good and
(yoni) W things (fortunes). The gods (Qtoi) care for men.
Men worship (Oipawtvovatv) the gods. DangeT attends many
works. Good things are mixed with bad. Hie bad man is
hostile to (at enmity with) gods and men. Men rejoice in
good (men or things). O God, grant good fortune (happi-
nesi) to our friends. O slave, bear the wine to the young
tTiim. Wine (6 otyog) does not dissipate, but begets
Glory follows a difficult achievement.

EWGLXSH-G&ZBK.

0* ayaBoi rip 9fy irtiBovrai. Ov xtiBovrai rip Qi<p * <
Unburst, w maXoi vtavuu, r^ ddaaicaXtp. Oi razoi rocc ayaQotQ
fX^p«i tiviv. Taiv kokvv aictxov. Ol ujQXm rutv *adi*y
tKiptXevvTat ($povTi£ov<n). Mjj Tip tyivoTov Koytp ir«rrevc,
u* <fnXi wai. UoWoig Xoyoic iirirai Kivdwof. Ol toOXot
t'nii'un rovg itiavKaXovc Qtpwxtvovoiv.

Gxxex-Bnolish.

Virtue, not time, is the measure of life. Death libe-
rates men from labours and evils. Wine rejoices the
iiLLtidb ■■! men. With ten thousand trials honourable things
arise (are produced). The divinity conducts the bad to judg-
ment* A faithful friend in a difficult division (strife) is
worth silver and gold. There are many diseases among men.
Counsel leads to good. Silence brings honour to a youth.
The door is shut by bars. Art nourishes men. O beloved
disciples (scholars), strive after wisdom and virtue.

Bnoxish»G&eek.

Ttp Qavartp airoXvovTcu tu>p kcikujv oi avBpiatroi. Tsf P*f
rryXAoi wovo* iwovrai. *U rov Ouov ao<f>ta icpog tvSatuanar
rai'-; tuBXovQ ayti. Touq rov Kpirov XoyoiQ iirov, Oi rovreov
Xayat um kavot. 'H Xvpa raQ tov Bvtiov nipipvag Xva.
'Sup -jic^Kti ij rjovx ia - Tovc ayaOovz rpt^H q Tixvq* *0
^o\Xoq jcXeut r jjv Ovpav.

G&bsx-Emolish .

Temples are built to the gods (0co<c). It is not easy to
walk on ropes. We hunt hares. Androgeus was the son of
Minos. Hares are hunted by huntsmen. Pray to the merci-
ful God. Eagles capture hares. Reverence the merciful
divinities. The brave receive deathless praise. Pray that you
may have (find) God merciful. The gods are propitious to
the £0©d T Pleasures lead away most people as captive. The
Samians support beautiful peacocks in honour of J uno. The
peacock has beautiful wings.

Englibh-Gmek.

Tote @totc vcsjc *rt£cic. KriCovrcu vttp rocc 0*oi£. Kcwv Tip
Btip fti£w. Ewi koXuv paivovai. Tovc Xayutc Qffptvofuv. Oi
Xayip Orjpevovrai. Ot Eafitoi koXovq rauig <ri/d#vrtt4. Toy
tXiwv 9tov otfiovrai* 'O Qeog iXiutg iotc roic aya(hn£, Ol
BtipivTai Bnptvowi rovg Xayutg. *0 MevtXttag Xafiflavu aytipw

G&bbk-Emolish.

Peacocks were sacred to Hera (JTuno). We admire MLenelaos
Ivt 'h\r valour. The poets call the morning rosy-angered.
Truth I tf aXrjBiia) often does not satisfy the people. Helen
was the wife ot Menelaos. Babylon produces many peacocks.
In - h. • temples of the gods are many pillars. Hares are
timid unimals. *£he voyage round t Mount) Athos was dan-
gflcous* the palace has fine chamber*,

LATIN EXERCISES.

ica

Enolish-Grbbx.

MevcXcwg Qavua&rai tri ry aptry. Qavpa£ofuv rav
pododacruXov t/«*. IIoXAot rtup cv fiafiiXutvup tiktovtcu* Bv
ra» r»c 'Hpac vup cart koXoq tclujq. 01 Ofjpivrat rauig **«-
Bpivovm. Oi ray evcfyfvovrm viro raw Otfpivrwy. Oi ayaflot
woXirai rov avoqrov Xtaiv 0£t/yov«i.

Vol. III., p. 374.— Gkbhx-English.

Avoid wild beasts. A hand washes a hand. Keep from
the wasp. The meadow* bloom. The soldiers sing their war
song. W<* know (try) gold and silver in (by) fire. Many
become friends at the goblet (over their cups), but most (a
peater number become) enemies [put a comma after *cXoiJ.
Men are delighted with the harp and banqueting and Glances
and songs of victory. The Greeks worship Apollo and
Poseidon (Neptune). Industrious scholars read the works of
Xonophon with pleasure.

Bnglibh-Gbbbx.
vfttyt rove 0»0«£. Qrjpa ftvyovou Tag X ct P a £ *"&•
Air<x«a0< rwv typHav. Zrparwrng ra» iraiavi ripirtrai. *0
r*tav rote, orpartmrag rfpwft. O owovdatoi paftfrat, ra rov
JsVvofW vroc /3i/3\ia avaytyvwretrs. Ta rov XtvoftvroQ pifiXia
avayiyvwoKOvrat vwo rwv <rirov9aiu>v /uxfliyrwv. Tcpwofwtfa
ro«f tornXoig \ttpu<n, Oi \fi/M*yfc daXXovct. 01 wotnra* rov
AwoXXt* ctpovrau Tov UotTtidv aifStrat 6 wottfrifC*

Tol. III., p. 376.— -Grebjl-Ekolish.

Pay respect to the old man. Worship the divinities. Shep-
herds guard flocks. Avoid the bad man as a perilous harbour.
Without the Divinity man is not happy. God dwells in the
•pper air. Often severe cares waste away the minds of men.
Allow good leaders, O beloved (O friend). O young man, get
out of the way of the aged. Often the people have an unjust
disposition (as their) leader. God is the punisher of those
who are too elated. Have a sound mind. O God, bestow
good Attune on old men. Huntsmen capture lions.

Bmolish-Grmjl.

(M oyoOot iratftec. rove ytpo*ntc Otpairtvovei. Oi yssovrsg
Qtpmwivovrai vwo rmv ayaBvv ira*oW. Oi evQpovtg viavtai
ttxevov rife Wot* rotg ytpewi* *Birw0€, » <fn\oi y ayatiy qytpovi.
£gsp*v ayaOovg rfyifiovug *0 \ttog woXXcucig ivtrat KaKoig
jfytfiOGi. 'O Otoe raptx* 1 tvrv%tav rotg trvfpoei* Oi XMovrtg
stye voyrut vtco rmv flifptvrmv. Tt 6«iev *t/3opc0a.
Gbbbx-Emoush.

Love your father and your mother. Be not thou a, slave to
the belly. Rejoice, O dear youth, in thy good father and thy
good mother. Consult not with a bad man. There were
many beautiful temples to (in honour of) De meter (Ceres).
The good daughter willingly obeys her dear mother. Good men
are admired. Often a bad son is born of a good father. I hate
the bad man. Shining glory follows good men. Persephone'
(Proserpine) was the daughter of Demeter (Ceres). O dear
daughter [comma after Qvyartp], love thy mother. Virtue is
an honourable prize for a wise (skilful) man. Good sons love
their fathers and their mothers. The Greeks worship Demeter.
dear youths, obey your fathers and your mothers. dear
father, gratify thy beloved daughter,

Ewglish-Gxxbx.

A KEY TO THE BXEKClSfcS IN THE

LATIN LESSONS.

By John R. Bbajld, D J).

(Qmtmmdfrom page 120, Vol. IV.)

Page 193.— English-Latin.

Culpo te quod patri non opitularis ; hoc aero ut bonus vrdear
liuus ; tarn bene didicit discipulus ut maximaio consecutus esset
Ifiidem ; quam bene hunc sub t In u it laborem ; tit omnia viridescant
faoit ver ; ut liberis prosit natura impellitur pater } ewse non potest
quod simul domi et foris ee ; ne animum perdu* te hortor : quando-
quidem considimus colloquaraur ; dura haec fiunt in urbem abito
et illic mane doneo veniat pater; non antequam totam videro
domum apud me ero ; sapientes ut vivant eilunt, non vivunt ut
edant ; nihil abest quin felioissimi sint ; tantum abest me doctum
esse ut Latins scribere non poisim ; si diligent us, eris felix ; si
diligens esses, esses felix ; si diligens fuisses, fuisses felix.

Page 202. — Latin-English.

In the very senate-house there are enemies ; some proficiency has
been made in our authority and eloquence i the people are accusto-
med to pass over the worthy ; he who places death among evils can-
not avoid fearing it ; the mind cannot avoid doing something ; the
state which now has no existence ; there is no friendship when one
is unwilling to hear the truth, and the other is read? to lie ; you
are aware that he both has courage and is not without wisdom ; do
not think that when I have departed and left you, I shall either be
nowhere or (aut) have no existence i we are able to adduce scarcely
a few men who excelled in speaking ; you seem to admire a thing
certainly not difficult j who art thou ? I am Pamphilus ; whence
was Cinna cast ? out of the city : whose book is this ? mine ; in.
what city are we ? Rome ; whom does this concern ? us ; what did
you give for the house ? a large sum ; what are y ou doing ? I am
coining silver ; did no one announce that to you ? no one \ did
your brother announce that to you ? yes, that ; was it your brother
that announced that to you ? yes, it was ; was it to you that your
brother announced that r yes, to me ; was it your father he dia not
please ? yes, my father; do you not think that was done by heaven ?
certainly, by heaven it was done ; has not one's native country a
claim superior to all (other) duties ? undoubtedly ; is it probable I
should be unwilling to see thee ? much rather have I been unwill-
ing to be seen (videri) by tbee ; is it not base for philosophers to
question these things ? it is base ; do you remember my speaking
in the Senate ? i remember it ; is it enough that we should be
compelled to fear you ? yes ; am I not coining silver ? yes j do you
not observe ? I do ; is not a dog like a wolf ? ne is; surely you do
not require richer witnesses ? O no ; do we then seem to thee to
be angry when in pleading we say anything sharp and strong ? no \
does pleasure make a man better or worse ? am I a slave to thee,
or thou to me ; I ask whether or not thy brother would come ; he
had inquired of me whether I did not think that he was bad ; we
confess that it does not depend on ourselves whether we are acute
or dull in intellect; this point should be considered, whether friend-
ship was desired on account of human weakness, or there was
some more honourable cause ; Aleaaudt-r asked the oracle whether
his father by fate intended for him (sibi) the dominion of the world;
if virtue is to be estimated in and for itself, I doubt whether I should
place Thrasybuius first of all ; we certainly must die ; this is the
uncertain point, whether we have to die this very day ; the govern-
ment of which state I should prefer to (that of) Greece, and I am
inclined to think to (that of) all nations ; a great affair was trans-
acted on that day, and perhaps the greatest iu that war; a very
wise, and I think a very excellent man, would rather confess his
fault 1 1 am inclined to think that honours so great as you received,
were never bestowed on any one ; I question if anything better
than friendship has been bestowed by the immortal gods on man*
excepting wisdom.

O vssryuM, erfpytre rov irartpm teat rqv sinrcpa. Af ayaQai
Oryarcpcc toiq warpa&i ecu rcuc /inrpatft iruBovrai. 01 ireXirai
tjjv Ar//i7jrtpa <r«/3ovrat. Tn Atjfitfrpi tirirat if Ilipert^svt;.
Tov aortoa 9avpa£ofUv. U0sjpevrac. /xn covXtvtrt Ty yaarpi,
XyaBti **ri|p ayatiqv dvyartoa orioyti. U /inrip kcu icarif
ertpytrt ro»c wmiiag. 'O avifp cx^u/sena. Tov av^pdt ^
txOatpovai. Tote aofoig avdpaoi xuOovrai. Ty An/ii}rpf j£
fcrojiai. noAXacif tf 070*0* wwrpeff aw* /ft*rpog ytyvovrai|a

A 8HOET Diaxooub. Cersswt.— j

Mencdemus, you seem to me to work too hard, you are now

sixty years of age.
Why do you meddle with other people's business P I am used

to it.
Can use require a man to tot tore himself ?
It does me (he sheds tears).
Dont Weep, and let me know (sclam) your private tatflfj*

lit Why do you wish to know that?

164

THE POPULAR EDUCATOR.

CL On this account, that I aaey be able to console yom, or i

(jovare) yon with advice or money.
JC I wffl tell y on alL

€7. Bat netawbfle lay down your rake ; itop working.
J£ Certainly not ; let me alone ; I do not want rest.
C. I wfil not let yon alone ; now speak.
JC I hare an only son ; ah ! what did I say ? I hare ? nay, I ha

whether I hare now or not is uncertain.
CL What then?
it YonahaUknow.

Page 20£— ExGLiSH-LaTix.

Ofesrone es ? non Tero, ted Lentnlns; nam Cicero es ? mini-
me; viz eredam patrem jam nollom erne; nnllns est; nbi est ?
nnsqnam non est ; ha nbi ? com Deo ; qms es ? Johannes snm ;
nonne Jaeobns ? non Tero, Jaeobus sbiit domam ; atrnm Jaeobns
ant Johannes sis me* non refert ; lane veait pater ; ne pater Teniat
metno; veniet neene? venturas neene sit sorer ignoro; ntmm
gandeam neene, nihil tni refert ; domam abis, ant alio ? unde
venitavis? iode: qnoTolat avis? eo; nbt es (art)? hie; nbi est
fatter ? fllic ; nbi est rex ibi regina.

Page 216. — Lativ-Exglish.

Cato whom when an old man I knew; neither the spears nor the '
very long swords which they use with both hands, were of service
to the Sarmatians ; I take pleasure in moderate feasts with men of
mr own age, very few ox whom however remain; Agamemnon,
when he had to devote to Diana the most beautiful product of his
kingdom, immolated Ipbigenia ; examples, and those not ancient
ones, are sought after ; the enemy were cut to pieces in one battle,
and that an easy one ; the Gauls despised the legion not having
its complement of men, on account of the small number of it*
soldiers; I knew Crassus as being, and that from his boyhood,
given to the best studies; I alone saw thy friend ; I did not eon-
verse with him ; we are not born for ourselves only ; Hannibal was
the first to go into battle, and when the conflict came, he was the
last to leave it ; the wolf prowls by night about the flocks ; I first
read and then copied that oration ; you see me to-day for the last
time ; Sylla was constantly present at the works, in the main body of
the army, and with the sentries ; in no way did Sextus lay down his
arms (retire from the army.)

Page 216. — English-La Tin.

Beligione delete, in tenebris est mundns ; mortua uxor tua tibi
attulit magnum moestum ; ad legendum Ciceronem venerunt dis-
ci puli ; hoc legendo libro doetus no ; bibliis sacris legendis sapien-
tes fiunt homines ; sd mini domum aedificandam fratrem conduxi
tuum (or domam aedificandam loeavi frstri tuo) ; nihil sine deo oriri
mini est exploratum ( or exploratum habeo) ; Bomam visurus eo
Testes aliquas misi ; to ridentem viderant; libros legentes discipu-
los vidit paedsgogus ; puer urbem intravit, senex renquit.

Page 285.— Latin -En o lis h.

Jugurtha will be obedient to your commands ; envy arose from
opulence ; Numa Pompilius was appointed king ; the Tynans
inquired whether Alexander was greater than Neptune ; we saw

ANSWERS TO CORRESPONDENTS.

*Wi H. P." tbonld not be impatient. If be really wants to acquire the
lui^jjLge, be matt master the principles of prcmimrisrinn The k**o» in
Qr nsnssa r proper commeacc witb the article in Somber 11. Yenexoni** and
Zolta** are old grammars, which were much need in their dsy. They are
dt Actcnt in practical utility, grammatical tuition in foreign lanrnarr* hariLg
raid* rrevt pi o g Te as since they were written. The lesaocu in the " Popular
I Educator" are intended for two dasee* of readers. 1. Per those who desire a
! tnc r- 'j^h scientific knowledge. 2. For those who only desire to know enough
to he able to read and sneak readily. The practical exereUe* in the gram-
mar proper will not fsil fully to satisfy the second dam of readers as well,
*:. ; H'.is * - -

engraver. Your writing does jou great

Flaccus coming from Asia entered Macedonia ; it is certain that
the man who breathes, is alive, and that he who lives, breathes ;
the poet errs when he ascribes a good speech to a bad man ; Zeno
is of opinion that the natural law is divine; the human figure;
excels the form of all living beings ; abundance of matter begets
abundance of words ; the inventions of necessity are older than,
those of pleasure; I seek from philosophers a remedy for grief;
by concord small things grow, by discord the greatest waste away ;
friendship makes prosperity more shining and adversity more light;
cruelty is very adverse to human nature, which we ought to follow;
I will teach thee the other appointments of life.

Page 235.— English-Latin.

Yerhum mini dixit ; tibi ? non vero, sed patri ; patri verbum
dixit ; unum ? non vero. sed duo ; duo verba dixit patri meo ;
nonne sorori locutus est r minime, suae uxori ; utilia loqui melius
est quam silere ; post hominum memoriam maxima haeo est con-
flagratio ; cum metu semper loqui se inoipere dicit Cicero ; religio
sola ad beats vivendum sufflcit; sufficluntne divitiae ad beate
vivendumr pexgite, discipuli, inquit magister, et discite quam
plurima.

Dodiealomu
UoaiomudeTA

K really good Italian dictionary is a desideratum in this conn try. Barett?*
and Ptironps are the best, bat expensive. GramUefs Pocket Dictionary
maj perhaps serre the purposes of *• W. H. P.**

AsWi: ZTpaTwmr and ev<veXc*tW are the correct forma. Tbe conjectures
*-|> b regard to the geography of Greece axe also correct. The nnmbers of
Engliih salles appended to the scale of the map of Greece are ten times too
g reit, owing to a mistake of ;the engrarer. To

CTWlfL.

l'\ Elkvs (Birmingham): San should be sans.
Twn • ■ Laws oi^Bula, and in every two lines of the Dodecaiojue de rAwtilie\
p. 76., f ou will find a new role, making twelve in alL Gazans Jleuris means
parterre*, or g nen plot* covered with Jtceeers^-W.G. B. (Lincoln):
. . Life of Mary, Qneen of 8coU, by Allan Cunningham, price Is. 6d.
— Eta Dslta (LWerpool) : Do with solid food as Solomon advises every
one to do with honem, tee Proverbs xxv. 16.— EsraaaKCi (Dublin): If
you -.nd any contribution as an author to a Magazine, the Editor will surely
publub it, if it be found welTwritten (composed), and worthy of the subject
of which it pr of ess e s to treat. Every gentlemanly Editor would, of course,
te-.i'i ; tn private notice of his approbation or disapprobation of the article
jou eent him, and not keep you in unnecessary suspense. We only hope
that your laudable ambition to be an author is well founded. You should
coup lit l some accomplished literary friend on this point before you subject
yourself to the pain of a disappointment.

M c &IC-— There remain only two articles to complete the course on vocal
music. The last lesson on the common '* notation " gives a fuller account
of tiuit subject than is usual in elementary works, and supplies answers to
most of our correspondents, whose queries arose from difficulties in connec-
tion with notation. Had space permitted, we should have been glad to deal
f uLJ y with the many interesting letters we hare received, chiefly from work-
l ■ r "an n, on the subject of the Monoehord and the structure of the scale,
indicating a love for mechanical contrivances in connection with scientific
stud j, greater than even see had anticipated. 8ome, however, have made
tbe strange mistake of measuring their monoehord by the " scale of fifty-
three degrees. The proportionate lengths of string had been given dis-
tinctly (see the lesson) in our previous column. It had also been stated
that the number of vibrations to each note was in sneers* proportion to the
I . r. j'j.i of the strings. In other words, the higher the note the shorter the
Spring , and the more numerous the vibrations by which it is produced. Bat
it is plain that, while this length of string and number of vibrations can be
acftmfly measured or counttd, the difference of pitch between one sound and
it d other is not a thing that we can reaUe measure or count. The teals of
fifty-three degrees, or more correctly (tee the article) of 474 dtflrc acst,is
an arit hmetical abstraction, arising oat of the proportionate lengths of suing
on Uj

in reality (the degrees of pitch), but still an abstraction.
comparative shades of colour cannot be UteraUa measured or numbered,
but it might be very useful to represent these differences of shade by a
scale of numbers, the truth |of that scale being founded on the relauvs
quant) ties of the pigments compounded, while in physical reality it has no
eili te nee, and is only a useful abstraction. The letter of Opi/ex (who says,
be tet to study our lessons "in earnest, obedient as a slave, and docile as a
little chUd," and immediately gets angry with us for not •• squaring "
etactly with his own preconceived and superficial notions of music), we did
not notice at the time, thinking it insincere. It may have sprung, however,
from x more innocent weakness. A Lover of Music can obtain au Mr. Cur-
wen' a works at Messrs. Ward and Co.'e, Paternoster Bow, and from Mr.
Hubert Griffiths, Plaistow, Essex, he can obtain a list of all the teachers and
class 1 1 in the metropolis connected with our "method." .These are very
numerous, and increasing in number. Orito should study the chapter on
"Mvio'ly " in the Grammar of Vocal Music (2*. 6d. Ward and Co.), or** Hamil-
ton ' ■ Catechism of Counterpoint Melody and Composition " (2: Cocks and Co.)
H e «ho>uld learn to adapt the accent of his music to that of his poetry. We
httve been greatly interested in the case of a lady, now sixty years of age,
once not undistinguished on the stage, who has for many years maintained
htrsnlf by street singing, and whose chief pleasure even now is the study
of languages and science. She pursues these studies while singing mechani-
cal ty before the mansions of the nobility. She wss some numbers behind in
her <' Popular Educator." We know this to be a true case. Will any one
help her I To a number of correspondents we have sent private replies, in
order to save space and repetition here. Not a few ask us questions which
they lhould rather put to some musical instrument maker or music seller,
whose business and pleasure it would be to reply. Mr. Curwen will welcome
cc-rreflpondenee from the students of his lessons in the P. E. addressed to
htm et Plaistow, Essex. He will reply to them as fully as time sad oppor-
'. 'in 1 1 y may permit.

Erbjlta.

v. ] , I V. p. 45, col 9, after line 1, insert droumferenct is about 4,000m
and that the distemcecf such pee^Us ism nothina t wkm <
pared with;
p. 47, col. 1, line 11, after casmat insert but.

on the one hand, and the proportionate vibrations on the other,- _ .

ery useful in giving a clear and true idea of what cannot be measured
,i ...._ » _■* _,._,.. t ^ «,,* _*_*___..,__ i n the same way,

p.«i, cut. a, unc it, «wr iwmmn insert m
p. 81, col. 2, line 25.fcT«Jceoer tosA faster,
p. 81, col. 9, line 8 from bottom, for ty read f.
p. 8s,eoL 2, art 4, also for ty read e.

.»4>J 4

LESSONS IN GEOLOGY.

16*

LESSONS IN GEOLOGY.- No. XLVH.
By Thos. W. Jbhxyx, DJ)., F.E.G.S., F.GJ3* Jfce,
CHAPTER V.
ON THE CLASSIFICATION OF THE BOCKS IN THE EARTH'S CRUST.

SECTION I.

▲ TABULAE YMW OF BOCXfl IN THB VBKTIOAX OBDSB IN WHICH TEXT OOO0B.

NiametqfQrovpt

" fJoLYSLL.

1. Recent.

3. Post-Pleistocene.

ft. Pleistocene, or
r Pleiocene.

IFkiooene.
sVMefoecne.

Upper Eocene.

Middle Eocene.

Lower Eocene.

L THB SYSTEM OF MODERN BOCKS.
Lttholooical Chabaohul

The depotiU of preient riven, coniiiting of sand, mud,

and tilt ; banks formed in the sea, at the mouths of

riven ; peat moitea, shelly marl; banks of shingle

thrown up by the sea; coral reefs, fee. ; sand dunes

. thrown up by winds.

The clays, marls, and volcanic tufas of the Isle of
Ischia, in Italy.
- The Loess, or the ancient sediment of the Rhine.

The newer parts of the boulder formation, with erratic

. blocks.

BrWth LocalitiM *kenft*md.

Banks of streams; bottom of lake*
and livers; the Goodwin sands;
the dunes of Cornwall, Lancashire,
and Norfolk.

Scotland, and the North of England.

H. THE TERTIARY SYSTEM OF BOCKS.

"The boulder formation or northern drift

Cavern deposits, and osseous or bony breccias.

The Norwich crag, being sands and marls formed by
river-water and the sea.

Limestone of Girgenti, in Sicily.

Sands, clays, and gravels, consisting of fragments of
earlier strata drifted from the neighbourhood and from
a distance.

r The red crag, and the coralline crag of Suffolk, con-
sisting of sands, clays, and marls, imbedding shells
and corals, and remains of land animals.

The Sub-Appenine rocks in Italy.

"The Faluns of Touraine.

Some of the beds at Bourdeaux, in France.

Part of the molasse of Switzerland.

The upper marine beds of Paris Basin, and the sand-
stones of Fontainebleau.

The millstone rocks of the same place.

The tile-clays, near Berlin.

The tertiary beds about Mayence.

The gypsum of Paris.

Fresh water limestone, and beds of clays and sands,
formed by rivers and by sea water, containing shells
of fresh water and marine animals.

The Barton beds.

The Calcaire Grossier of Paris.

Sands, sandstones, gravel of flint pebbles, with beds of
. clay, called Bagshot sands, and Bracklesham beds.

London clay — properly so called-— found at Highgate,
and in the Isle of Sheppey, of a blue or lead colour,
containing nodules of septaria or cement stone.

Sables inferieurs of Paria.

Mottled and plastic clays, with flint pebbles.

Nuoomuiitic limestone of the Alps.

Coast of Norfolk.

At the bottoms of every valley, on the
sides of hills; all about London,
Bath,Bristol, Gloucester, Liverpool,

Coasts of Suffolk, Norfolk, and
Essex.

Headon-hill, and other places in the
Isle of Wight.

Hampshire.

Bagshot Heath, in Hampshire ; High-
gate, near London; Bracklesham
Bay, in Sussex.

London, Highgate, Isle of Sheppey,
Richmond -hill, coast of Hampshire,
and Folkstone.

Woolwich, Reading, Poole, in Dorset-
shire, and Alum Bay, in Isle of
Wight.

III. THE SECONDARY SYSTEM OF ROCK8.

7 The Maastricht Beds.
& Upper White Chalk.

9. Lower Chalk.
▼©L,IY.

§ i. The Cretaceous, or Chalky.

'A limestone of a yellowish-white colour, about Mae-

stricht, in Belgium.
A bed of coralline limestone at Faxoe, in Denmark.

Soft and marking white chalk, with flints, both in>
nodules and in beds.

Chalk without flints, and harder thin the upper chalk.

Chalk marl, or malm, or clunch, a clayey gray chalk,
hardening into gray sand and marl.

The Downs of Surrey and Sussex,
Marlborough Downs, Salisbury
Plain, the Cfiffs of Dover, Rams-
gate, Brighton, &c.

Flamborough Head, 8hakspeare s
Cliff at Dover, Warminster, Maid-
stone. , , . _

Tale of Pewsey. in Wiltshire; Ben-
* son. in Oxfordshire; Guildford, in
Surrey.
- 90

106

THE POPULAR EDUCATOR.

oocordi^ (o Ltell.
f

LlTBOfcOeKJAI, Chabaotbb.

/" Loose sand, with bright green particles, and sandstone
Upper Greenup j b^TSMSS

\ Marly stone, with layers of chert.
Q an i t f Dark-blue clay, or marl, with small oonaretians of atone,

• 1 and many fossils.

Sands with green parties, and sandstones with beds of
chert.
Lower Greensand. •{ Sands white, yellowish, and ferruginous ox irony, with
concretions of limestone.
A limestone, called the Kenfiah rag.

Warminster ; Devizes ; Wantage ; Shafts*

bury.
Merstnam, in Surrey ; Kent.

bury.

>rstnam, in Surrey;
South of the Isle of Wight.

Folkstone ; Maidstone ; Isle of Wight ;

Devises.
Black Down, $•▼*&, $c.

Atherfield, Isle of Wight.

Maidstone, in Kent.

11. Wealden Clay.
13. PuibeckBeds.

14. Upper Oolite.

16. Middle Oolite.

16. Lower Oolite.

17. lias.

{ n. Thb Wbaldb*.

Clays, with occasional bands of limestone.
J Sands, with calciferous or limy grits and olays.
Limestones, and limy flags or slates, and beds of marl.

§ in. Thb Oolite.

Portland stone, a gritty limestone, with beds and nodules

of chert.
Portland sands.
Kimmeridge clay, a blue shaly clay, with nodules of

septaria or cement stone.
Coral rag, imperfect limestone, or a limy freestone,

abounding with shells and fossil corals.
Calcareous grit, a silicious and shelly sandstone. •
Oxford clay, a blue and yellow clay, with Melbury

marble, turtle stone, or septaria.
Kelloway rock, a coarse and sandy limestone, with many

fossils.
Cornbrash, an imperfect limestone, sometimes blue and

sandy.
Forest marble, a coarse, slaty limestone, full of shells.
Bradford clay, a tenacious, brown day, sometimes shaly,

full of shells and corals.
Great oolite, a yellow freestone, with fragments of shells.

The Bath stone.
Stonesfield slate, a kind of slate partly limy, partly

flinty, passing sometimes into sand with shale.
Fuller's earth, a brown clay.
Inferior oolite, a coarse, limy freestone, and yellow

sands and marl.

} iv. Thb Lias.

/"White lias limestone, often blue.
< A blue slaty marl and day.
(.The limestone full of fossil bones of reptiles.

Wealds of Kent, Sussex, and Surrey.
Hastings, in Sussex, and Ouekfield, in

Kent: Tilgate Forest.
Isle of Purbeck.

Isle of Portland, Swindon, Aylesbury.

Kimmeridge, in Wiltshire ; Shotover-hill,

near Oxford ; Isle of Purbeck.
Colne, in Wiltshire; Kirbey Moor, in

Yorkshire.
Abingdon ; Weymouth.
Oxford; Bedford; Yale of Blackmoor, in

Dorsetshire.
Kelloway near Chippenham, Wiltshire,

and Scarborough.
Malmsbury; Trowbridge.

Hinton, near Bath; Frome.
Bradford, Wilts. ; Cirencester.

Bath: Farley Downs; Combe Downs;

and Bathford-hm.
Stonesfield, near Woodstock ; Stamford ;

Stevenhampton j Cleaveland Hills.
Sides of the hills round Bath.
Bath; Mendip Hills; Dundry Down;

Cotswold Hills; YeoviL

Lyme Regis ; Whitby ; Yale of Bath.

} v. Thb Trias.

18. Upper Trias.

19. Middle Trias.

20. Lower Trias.

21. Opper Permian.

22. Lower Permian.

The keuper of Germany ; variegated marbles, red, gray,

blue, green ; white sandstones with gypsum.
The bone bed of Axmouth. Axmouth, Dorset.

!A limestone, compact and grayish, sometimes called
muschelkalk, with beds of dolomite and gypsum,
wanting in England*
f Burner sandstein, or variegated sandstone of Germany.
I The sandstone spotted red and white, with gypsum
"t and rock salt.

1 Part of the new red sandstone, and the rock salt beds ; Cheshire ; Worcestershire.
(^ red clays and marls.

IV. THE PRIMARY SYSTEM OF ROCKS.

N.B.— Not the Primitive Rocks.

§ i. Thb Pbbmxan.

r Yellow magnesian limestone, sub-crystalline. Nottingham; Mansfield; Knaresborough;

I The zechstcin ofThuringia. Sunderland; Exeter.

(Marl slate. Durham.

Lower new red sandstone of the north of England, and Durham ; Warwickshire ; Staffordshire*
the Rothliegendes of Germany

LESSONS IN GEOLOGY.

Iff

§ ii. Thb Carboniferous, or Coax Formation.

Mum* of Groups
oc c o i xiia y to Lyblx.

23, Goal Measures.

LlTHOLOGlOAX CHARACTER.

BrUuhLocaUiie^whm^J^md.

24. Upper Devonian.

25. Lower Devonian.

91 Upper Silurian.

27. Lower Silurian.

Beds of sandstone and shale, with seams of coal and beds Northumberland and South Wales.

of culm, grit stone, and sometimes limestone.
Millstone grit, a coarse, flinty sandstone, with beds of From Derbyshire up to Northumberland.

flagstones and of grindstones.
Mountain limestone, compact, clue, or reddish, con- Mendip jCliftonJby Bristol; South Wales;

taming sometimes ores of lead and calamine of tin, banks of the Wye ; Derbyshire ; T

full of shells and corals. The secondary marble of shire, &c.

Derbyshire.
k Beds oi the Mendip Hills.

} in. The Devonian, or Old Brd Sajtdmorr.

'A yellow sandstone.

Sandstones and conglomerates of pebbles ; a limestone
called cornstone ; marls alternatins; with slaty beds of
sandstones ; paving and roofing stipes.
w Upper parts of the Devonian beds of South Devon.
Gray sandstones and gray slates that used to be called
grauwacke, with slaty limestones ; secondary marble,
and green ehloritic slates.

Dura Den, in Fifeshire.
Monmouth ; Herefordshire ; Shropshire ;
Cumberland; Forfarshire, in Scotland.

South Devon.

Caithness, Cromarty, in Scotland; Bs>
moor, Ilfracombe, in Devonshire ; $t.
Columb and Truro, in Cornwall ; Fly-
mouth and Torquay, in South Devon.

§ it. Thr Silurian.

fTilestones.

Clayey limestones, of blue and gray colour
and flagstones, foil of marine shells.

A crystalline blue and gray limestone, called the Wen-
lock or Dudley limestone.

t A dark-gray shale, with nodules of limestone.
''A shelly limestone, called the Caradoc limestone, and a
greenish sandstone, abounding wit^L shells a^nd corals,
called the Caradoc sandstone.

Llandeilo flags ; limy schists or slates ; freestone grits
and limestone ; dark-coloured flagstones, &c.

Brecon and Carmarthen,
dark shales Ludlow Castle ; Aymestry ; WooHhorpe.

Dudley Castle; Wenlock Edge, in Shrop.
shire.

Wenlock.

Caer Caradoc, Shropshire: North and
South Wales; May Hill, Gloucester-
shire.

Llandeilo Fawr, Carmarthenshire; Builth,
Breconshire; Landrindod, Radnorshire.

28. Cambrian Rooks.

29. Chlorite Schist.

30. Mica Schist

SL Granite.

ft Trap Rocks.

§ v. Thr Cambria* or Professor Srdowiox.

N.B.— Now most generally referred to the Silurian.

f Ply nlimmon Rooks, slates with beds of conglomerate. Plynlimmon Mountains, in Cardiganshire.
| Bala limestone, beds of dark limestone, and slates with Bala, Merionethshire.
< a few fossils.

I Snowdon slates, blue and fine grained, with a few Snowdon Hills, North Wales.
L fossils.

§ vi. Thr Cumbrian op Professor Sbdowick.

Slaty rocks, void of organio remains*

About the Cumberland lakes ; Longmynd
Hill, in Shropshire; Barmouth, in
North Wales ; the Mull of Galloway,
and Lammermuir.

V. TUB CRYSTALLINE SYSTEM OF ROCKS.
§ i. Thr Stratified.

Composed of quartz and chlorite, laminated.

Benlomond, in Scotland.

f Composed principally of quarts and mica, granular and Benlomond, Loch Awe ; Mull of Can tire,

( laminated. in Scotland.

A rock laminated and granular, and composed of quartz, The Grampian Hills, and the Western

feldspar, and miea ; that is, of the ruins of granite, Isles of Scotland.

often much contorted, have crystallized limestones

and hornblende slate associated.

§ ii. Thr Urstraitfird.

A rock composed of crystalline grains of Quarts, feldspar,
and mica, or sometimes hornblende, in colour, gray,
red, and white.

'TJnstratified and crystalline rooks, which, in a molten
state, have upraised, penetrated, and fractured many
stratified rocks of different ages, and have thereby pro-
duced faults and dykes. Tnese are called porphyry,
greenstone, basalt, toadstone, compact feldspar,
tycur to, serpentine, &e

Aberdeen; Dartmoor; Land's End.

168

THE POPULAK EDUCATOR.

The following diagram will assist you in learning the position
and the order of different formations, from the surface soil down
to the crystalline and granite rocks, which are supposed to be
below the strata marked v in the diagram.
Fig. 103.

▲. Alluvial SoiL

B. Erratic Blocks, and Till.
0. The Pleistocene.

d. The Pleiocene.

b. TheMeiocene.

f. The Eocene.

'X"»%S J 5rAfcV£SS- o. The Chalk Formation.

h. The Qnadersandstein.
i. The Neocomien.
J. TheWealden.
x. The Oolite.

l. The Lias.
m. The Keeper.

n. The Mnschelkalk.

\ o. The Buntersandstein*

p. The Zechstein.

q. New Bed Sandstone, or
Rothliegendes

R. The Coal Measures.

s. The Mountain Limestone.
t. The Devonian, or Old
Bed Sandstone.

u. The Silurian.

t. The Cambrian.

An ideal S<c'ion of (he Stratified Bocks,
in thdr vertical order oj position.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. XII.

AREOMETERS OF VARIABLE VOLUME.

Different hinds of Areometers. — The areometers of Nicholson
and Fahrenheit, described in our last lesson, may be defined as
those which have a constant volume and a variable weighty because
they are always immersed to the same depth in the liquid,
and" weights are placed on their scale or cup, evecordin^ to the
weight of the solid or the liquid whose specific weight is to be
determined. Areometers are also constructed having a
variable volume and a constant weight ; that is, having no fixed
point of immersion level on the stem, and prcaerving always
the same weight. These apparatus, known under the names
of hydrometers, scale-areometers, or liquor-tests, are not
intended to ascertain the specific weights of. liquids, but to
determine the strength of saline solutions, acitfis, and alcohols.

The Areometer of '2tewm*\— This areometer, which was invented
by M. Baume^ of Paris, is one of those having a constant
weight, and is very extensively used. It consists of a glass
bulb full of air having a graduated stem, with a smaller bulb
below it full of mercury to ballast the apparatus when floating
in a liquid, fig. 39. This instrument is differently graduated

Fig. 39.

according as it is intended for liquids denser than water, or for
liquids lighter than water. In the former case the weight is
so regulated that in distilled water, at the maximum density, it
sinks nearly to the upper extremity of the stem, and is in
equilibrium at a point marked zero. In order to graduate the
stem, fill a Teasel with a solution consisting of 85 parts ot
water by weight, and 15 parts of sea salt. This solution being
denser than pure water, the instrument will sink in it only as
far as the point b, which is then marked 15. Next, dividing
the interval between the points a and b into fifteen equal
parts, and continuing the divisions to the bottom of the stem,
the instrument is graduated. The divisions are marked on a
small slip of paper placed in the interior of the glass stem.

The areometer thus constructed can be employed only fat
liquids denser than water, such as acids and saline solutions,
being both an acid-test and a salt- test. For liquids not so
dense as water, the zero being; placed at the bottom of the rod,
the graduation is reversed. . Baume' determined the zero point
of the instrument by its immersion in a solution of 90 parts of
water by weight with 10 parts of sea-salt, the point marked
10 on the scale being that which indicated its depth in distilled
water. Dividing then the interval between these two points
into 10 equal parts, and continuing the divisions to the top of
the stem, the instrument is graduated, and becomes a liquor-
test.

• These areometers being graduated in a manner entirely
arbitrary, indicate neither the densities of the liquids, nor the
quantities of salt held in solution. Yet they are usefully
employed in ascertaining when a saline or acid solution has
been brought to a point of fixed concentration, or a certain
degree of strength. The graduation of these instruments
assists much in the rapid formation of mixtures and solutions
in given proportions, not with very great precision, but with
a sufficient approximation in a great number of practical cases.
For example, in the manufacture of common syrups, it has
been found that the salt-test of Baume* should stand at the
mark 35 on the scale as the point of level, in a syrup of
proper strength when cooL Thus the manufacturer is fur-
nished with an instrument with which he can readily test
the degree of concentration in his syrups. In like manner, in
sea- water at the temperature of 82° F., the hydrometer of
Baume' stands at the mark 3 on the scale, indicating that the
water is of that degree of strength proper for saline baths
ordered to patients in certain diseases. The solutions of sea-
salt and water, which physicians prescribe, are in general
much weaker than that indicated by the proper degree on the
instrument ; that is, the artificial saline baths have not that
degree of ssltness which the natural sea- water has, and are nofe
therefore sufficiently efficacious in producing a cure.

NATURAL PHILOSOPHY.

169

The alcohol-test or measure, invented by M. Gay-Lussac, is
exactly similar in form to the areometer of Baume' ; it differs
only in the mode of graduation, this being such that the
instrument indicates not only the strength of an alcoholic
mixture, but it also shows how much per cent, it contains of
water, and how much per cent, of absolute alcohol, that is, of,
alcohol at its maximum strength. It is graduated in the fol-
lowing manner : The instrument is first immersed in absolute
alcohol, and the point or level at which it stands is marked !
100, care being taken to ballast it so that this point is always j
found near the top of the stem. Mixtures are then formed j
containing 100 parts in volume of 95, 90, 85, 80, &c, of absolute
alcohol, and 5, 10, 15, 20, &c, respectively of water. The j
instrument is successively immersed in these mixtures, and !
the points or levels at which it stands are respectively marked ;
96, 90, 85, 80, &c, accordingly. In order to complete the ;
graduation, it is necessary only to divide each interval into 5
equal parts.

If the instrument thus graduated should sink, for example,
to 58 in an alcoholic mixture, this would indicate that in 100
parts of volume, it contains 58 parts of absolute alcohol and
42 parts of water. It is, moreover, necessary to take the tem-
perature into account ; for when this increases or diminishes,
the density of the alcohol conversely diminishes or increases
accordingly, and the instrument consequently sinks more or
less in the same alcoholic mixture. To meet this case, Gay-
Lussac constructed for his alcohol-test-tables of correction, by
means of which the indications of the instrument may be recti-
fied, according to the temperature of the mixture as shown by
the thermometer.

Saline-tests or measures are also graduated, on the principle .
of the preceding instrument, to show the quantity of salt Dy
weight contained in different solutions. The zero of these
instruments answers to pure water, and they are graduated
by dissolving 5, 10, 15, 20, &c, equal parts by weight of a given
salt in 95, 90, 85, 80, &c, equal parts oy weight respectively of
pure water, taking care that in the different solutions the salt
and the water are thoroughly mixed. Immersing the instru-
ment successively in these solutions, and marking the numbers
5, 10, 15, 20, &c, respectively at the points where the instru-
ment stands in equilibrium, and dividing the intervals into 5
equal parts, the apparatus is completed. Such instruments
have thi« inconvenience, that every separate kind of salt requires
a special saline- test. That, for instance, which has been gra-
duated for the nitrate of potassa, would give indications
entirely wrong in a solution of carbonate of potassa.

On the same principle are constructed milk-tests, wine-
tests, and spirit-tests, all called by the general name of hydro-
meters (from the Greek, and signifying water-measures) ; these
instruments are employed in determining the quantity of water
which may have Seen introduced into these liquids for the

Surposes of fraud. But such instruments are not to be wholly ;
epended upon, since the densities of milk and of wine, for
example, are very variable, even when they are in a perfectly
natural state ; hence, fraud might be attributed to indications
which were due rather to the naturally bad qualities of these,
liquids. Similar test instruments are used by medical men for
the liquids found in the human body.

Instruments called densimeters (a Latin-Greek compound,
signifying density measure) have been invented for the purpose
of showing the relative density of a liquid according to the
degree to which they sink therein. The densimeter of Gay-
Lussac is exactly similar to the areometer of Baume', represented
in fig. 89. It only differs from it in the principle of its gra-
duation, which varies according as it is intended to be used 1
for liquids more or less dense tnan water. In the former of
these cases, the instrument is ballasted, when immersed in
pure water, so that it shall sink to the point a at the top of
the stem. Taking a liquid of which the density is known,'
and greater than that of water, say in the ratio of 4 to 3, we
immerse the instrument in it, and find that it stands at the
level of the point b on the stem. Now, if we represent by v
and a 7 the volumes of the parts of the instrument respectively,
immersed in water and in the given liquid, these volumes are^
to one another in the inverse ratio of the densities of that*
liquids, according to a former lesson: we have therefore
9 iv : ; 4 : 3 ; whence, «*=}*.

If, therefore, we represent the volume v by 100, the volume v'
will be 75. We then mark respectively at the points a and b
the numbers 100 and 75. The volume of a b being, according
to the value of v', the fourth part of v t we divide the space a b
into 25 equal parts, and each of these parts is A- of a b or yfo
of v t that is, of the volume immersed in pure water. We next
continue the division to the lower part of the stem, on the
supposition that it is constructed bo as to be of exactly the
same diameter throughout, that is, wherever a horizontal
section may be taken.

The instrument being now graduated, suppose that the
density of another liquid, say that of sulphuric acid, is required ;
immerse the instrument in the liquid, and if it sinks to the
level or point marked 54 on the stem, this indicates that the
Volume of the liquid displaced is represented by 54, that of the
volume of water v being represented by 100. Now, as every
floating body displaces a weight of the liquid in which it is
immersed equal to its own, it follows that the volume of water
p or 100, and the volume of sulphuric acid 54, have the same
weight ; but the volumes of bodies of equal weights are in the
inverse ratio of their densities. Consequently, if we represent
the density of sulphuric acid by x, that of water being unity,
we have x : 1 : : 180 : 54 ; whence z=z*$h=. 1*85, which is the
density of sulphuric acid.

If the densimeter is intended to measure the density of liquids
lighter than water, the instrument must be ballasted so that
the point marked 100, corresponding to pure water, may be
placed at the bottom of the stem. At its upper extremity is
then placed a weight equal to the fourth of that of the instru-
ment. Now, the weight of the instrument alone being repre-
sented by 100, its weight will then be represented by 125.
This number 125 being marked on the stem, as another point
pf level, we divide the interval between the points marked 100
and 125 into 25 equal parts, and continue the divisions to the
top of the stem.

j The application of the densimeter of Gay-Lussac requires
a quantity of liquid sufficient to fill a vessel of considerable
capacity. In certain cases, however, especially in physiology,
when experimenting on animal liquids, it often happens that
we can only obtain a few grains of the animal matter. This led
to the invention of the densimeter of M. Rousseau, wHich ac-
complishes the object in view. This instrument is of the form
Of the areometer of Baume', fig. 40 ; but the top of the stem is

Fit/. 40.

furnished with a small cup for the reception of the liquid
whose density is required. We shall here show how the
'inventor graduated his instrument, according to the French
{system of weights. On the sides of the cup is placed a mark
indicating a capacity a c, equal to that of a cubic centimetre (or
•06103 of a cubic inch, whicn is rather less than ^ of a cubic
I inch). In order to graduate the instrument,^ is ballasted in
I such a manner that in distilled water at the maximum density
jit sinks to the point b at the bottom of the stem, and this is
I the zero point of the instrument, The cup is then filled with

THE POPULAR EDUCATOR,

a%tiUed water of the marTnrwm iUmKj ay to the point a, that
fc, to the capacity of a cubic centimetre, or, which » the tame
thine , equal to the weight of a §im mm t (or 15*440 troy grains).
At the point to which the instrument now rinks the number
20 is marked. The interval from to 20 is then divided into
20 equal parts, and the divisions are continued to the top of
the stem. The stem being exactly of the same diameter
throughout, each division now corresponds to ^ or *05 of a
gramme (•>., 772 of a troy grain). This graduation being
made, if we wish to find the density of a liquid, say bile, we
fill the cup a c with it, up to the mark formerly mentioned,
and if the instrument sinks to the division marked 20}, we
find that the weight of the bile bi the cup is equal to *05
gramme + 20*5, or 102£ gramme; that is, the weight of water
being 1, the weight of bile is 1*025, a number which represents
the density of bile, that of water being unity ; for the weights
of bodies of the same volume are in the same ratio as their
densities.

LESSONS IN GREEK.— No. XV.
By Jon* R. Bbakd, D.D.

Adjective* in uov {or w) and tarog.

Tnasa forms are taken by rfBvg, tweet, and ra%og, swift, the
termination vg being removed; rarvg, however, has in the
com p ar ative Barrmv [9ao<n*v is another form of the same word)
thus:

P. ifi-vg. C. rfi-vuv* N. t)Z-iov. 8, Ti$-i9rog.
rax'VC- Barrwv. Barrov. rax-t*rog.

The other adjectives in vg, as Qapvg, heavy, fiaBvg, deep,
0pa\VQ 9 short, iaevg, thick, tvpvg, oroad, o£i/c, thorp, Tp*.Q$vg\
old, uticvg, twift, take the forms iu rtpog, rarog, thus :

P. fiaBvg. N. pa9v. C. fiaBvrtpog. 8. fiaQv- rarog.

Tho forms iusv and terog are taken also by two adjectives
ending in poc, namely aiovpog, hateful, shameful, and «xfy°£»
hostile ; the termination oc being cut off; as

P. atffgpoc. 0. aia \-tu>v. N ai9%-iov, S. ai9%'urrog.

VOCABULAEY.

Oapn, ng, t), smell.

Kmpoc, ov, 6, season, time

generally.
Zwov, to, a living being, an

animal.
0<big, ewe, 6 and rj, a serpent.
AXXot, at, a, others.

Oi axparug, the intemperate.

Aoiirog, n, ov, the remainder,
the rest.

Mcra0£pu>,lbear away, change.

Hapixv, I afford, communi-
cate ; (middle voice), yield,
give.

Exercises. — GrBBBlt-ENGLiSH.

*0 paBvrarog virvog rjtitorog «mv. XloXXa avBn rjiiarnv
ofTfitiv rraptxiTai. Ovdiv Oarrov tan rng rfprjg. Tijv aioxiarnv
ScvXtiav oi cucparug SovXevovnv. Uavrutv ifiivrov tonv 17
Xia. Ovliv aiaxiov earnv n aXXa pev iv vip ex av > «^Xa St
Xiyuv (to think one thing and tap another). Oi otyug roig Xouroig
Zutoig txQioroi iimv. Ovdiv rtp avOpioirtp txBtov tanv n 6
avBpwirog. Taxiora 6 Katpog /uraftpu ra irpaypara.

English- Gaiii.

Nothing is sweeter than deep sleep. Sleep is very sweet.
Nothing is more disgraceful than slavery. Slavery is a ver^
bhtiT thing. Horses are very swift. Nothing is more hostile
( unfriendly) than bad ad vie*. It is sharaetul to think one
thing nnd say another. Bad men think one thing and say
another. Nothing is sweeter than a faithful friend.

1. ayaBog good osavwr. 3. as***** mftmrog, 9,

fitXrtmc „

tpUTTwr (cyorvwr) Kparisrog „
V^wr Xt-wra? „

2. mcoc bad kouomv mtnaerog „

Xttp~* Xfiourrvc,

rirrmv (vf*vw* inferior tfatrra (adv.) „

3. nrAoc beaatifaljcaAAM#y axXkurrog „

4. akyuvoc painful a\yti » i rtf%, aXf tm n a r m Q „

nXytwr cXyurroc t»

fUZKporarog'X

ajfewrroc J "

lUMforarog „

tXaxurroe „

oXxyurros n

ptyimc „

r-XuaroQ „

W9TOQ „

mratrarog „
Tiorarog „

Several adjectives which express the idea of order or suc-
cession appear in the comparative and superlative only, since
from their import they cannot denote an absolute quality, and
may be used only in comparison. Their root will be found
in a preposition, or adverb of place ; e. g.

Adjectives without a Positive.

(from rpo, before) wpcripog, prior, -rpwroc, first,
(from av<tt, up) avwrcpoc, upper, mvmrarog, upmost,
(from virtp, over) va-iprcpoc, higher, vwiprarog, highest,
(from biro : under) vortpoq, posterior, vcrraroc, most behind,
(from it, from) ctrxarof, last, most from,

most remote,
(from xXrjowv, near, in Homer xXtftrtoc) rXnciairtpoc, nearer.

TrXtjotairarog, nearest,
(from wpockf, forwards) wpocunpog, further, more in advance,

xpoxrvraTOQi furthest,

VOCABULABT.

5. fuupoc

long

paxportpoc

6. fuxpoc

small

auaperfooc
ikarrttv (iXaowr)

7. oXtyoc

few

fuuev

8. fityat

great

ptoTjmt

9, toXvc

much

tXumv (xXmtv)

10. paZu*

easy

pq**

11. irtirtv

ripe

irvreurtpoc

12. xitav

fat

inortooQ

Avayien, ng, if, necessity.

Avayxatog, a, ov, necessary.

Avapxia, ag, )), absence of
government, anarchy.

Mirpov, ov, ro, measure, mo-
deration.

Ifinpia, ag, i), Spain.

KoXaKtia, ag, r/, flattery.

Eotfpoavvn, ng, 17, Bound-mind-
edness.

BXcv0fpoc, a, ov, free.
MaXaxog, n, ov, soft.
EfifvTog, ov, inborn.
Evrvxyg, «c, fortunate.
laxvto, I am strong.
KtXiw, I ord6r.
2/cw7rrw, I jeef.
2rtpyu), I love, I am satisfied

with, I put up with.
Bviore, sometimes.
17, n, either, or.

A number of adjectives not being reducible to either of
these forms, are called irregular. I subjoin a list of

Xv/ipovKog, ov, 6, an adviser.
VtiTiav, ovog, 6, a neighbour.

*Qc» with a superlative, adds strength to it, as qumn ia Latin,
*?• £•» vc raxiorog, quam celerrimus, as swift as possible.

EX£RGXSB8. — GbBBK-EnOLISK.

Ovx fiaxporarog fiteg apiorog toriv, aXXa b eirovtiaiorarog,
Mirpov tin, icaoiv etpiorov (sc. cortv). Tvvpcu rwv ytpairtpwv
afutvovg turiv. XvpfiovXog ovditg tort fitXritav xpo* *' B
Xcyi oiyng nparrova, n oxynv «*< ( * ^ ei fpartcrrov ten to
aoyctXterrecrov. Sirtuirrctc, w Xtpvrt. BtXnovwv xaKtovg (viort
cvrvxtartpoi ei<nv, Ovk ten Xvirqg x ll 9 0V fLvBpbur^ kokov.
HoXoKtta rmv aXktav anavrwv caccov xetptcrrov eotiv. Anjp
fiaXaieoc rnv ^vxnv (as to his soul, mind) kcu (even) xpif/Aarwv
ifTTfAv. Tone ywcuZiv $ out^povwii KaXXtorn aptrn ctrrtv*
Owr tern Knfpa KaXXtov <f>t\ov. *H SovXtta rtp (XtvBtptp aXyivrti
eoriv. 'H oSog fitjKiarjj toriv. 'O KpOKoSeiXog cf (Xaxiorov
yiyvtrai fuytarog. *tt ytj iXarrtov tori row ijXwv. ^rtpyt kcu.
ra fteiw. OXiytoroi avQpwiroi ivSaipoveg *my f OvStig vo/toQ

LESSONS IN GREEK.

171

ioyyu puZov rng avaytng. Mdrp£ cepdif icoXXazig jU£c(ovac
pXaflag 0£p£t. Avapx ia ff puKov ovk tern kclkov. 'O iroXtpog
xXfurra Kaica Qtptt. Epipvrog tart roig avBpwxovg if rov
irXiiovog tmOvfita. Twn to9Xn nXuora ayaOa r<p ouetp 0cpa.
T«k avayxaia rov /3tou 0£pe d>f patrra (as easily as you can). To
KtXevtivpaov ton rov trparrtiv. 01 rijc aoQtjg Kapiroi irtiraira*
rot turi. Ev rtp rov irarpoQ Ktjirtp o\ rijc ajiwtXov fiorpvtg
wtxairtpoi ucriVj n tv rtp rov ytirovog. Iptjpta rpupu iriorara
irpofiara.

Englibh-Grbbk.

There is nothing better than a very diligent life. The
opinion of the anoienta is very good. Time is the best
adviser. The safest is the best. Grief is a very great evil.
Nothing is worse than flattery. The intemperate man is the
slave of pleasures. Women have nothing more beautiful than
wisdom. To a free man nothing is worse than slavery. The
crocodile is very long. The son is less than the father. The
bad often have more property than the good. War brings
very great evils. It is easy to command, it is hard to obey.
We enjoy most (superlative neat, of ntvg) the ripest fruits.
My father's sheep are fatter than those of {the article ra)
his neighbour.

In order to assist you in mastering the subject, I here put
together the different terminations of adjectives. I add those
of die participles, because the participle and the adjective are
declined alike ; remember that both adjective and participle
are also declined like nouns of the same terminations. You
will also call to mind that adjectives are divided into three
classes: 1, those of three terminations ; 2, those of two ter-
minations ; 3, those of one termination.

GENERAL VlBW OP THE TERMINATIONS OP ADJECTIVES.

1. Adjectives of Three Terminations.

<*t 9> ov,

oc, a, ov,

Contracted in
$og t td, covf

JN r . aya9og, aya9rj, aya9ov, good

G. aya9ov, aya9rjg, ayaOov
N.P. aya9oi, ayaOai, ayaQa

G. aya9utv, aya9u>v, aya9(av

N. oy doog, oySorj, oyooov, eight
G.P. oySowv, oySotav, oySoutv

N. ypa<pop.tvog, ypa<pofitvij, ypa&ofitvov,

written
G.P. ypafo/xtvuv, ypa$Ofizvu)v, ypa<pop.tv<jJV.

AT. Sucaiog, Sitcata, dixaiov, just

G, Sucaiov, BiKaiag, diicaiov
G.P. diKdnov, dueaiuv, dacaiajv

N. €x9pog, tx®P a * *X®P 0V * hostile

G. ex®P° v > *X®P a C* l X®P ov

N. a9poog, aOpoa, aOpoov, crowded, dense

G. ad poo v, a9poag, aOpoov
G.P. a9powv, avpowv, aOpowv.

golden

N. xpvtreog, xpv<T£a, xpvatov )
Xpwovg, xP v9 *i* XP v<ro ^ v i
G. X9 v< *°v* XP U(T *iCt XP V(T °v
N.P. gpv<roi, xpucraT, xpv<xa
N. epttog,tpnd,tpttov\ wooUy
tptovg, sped, tptovv ) J

G. tpioi'y tptdg, tptov.

2. in vg,tta, v, N. yXvitvg, yXvKtia, yXvicv, sweet

G. yXvKtog, yXvKtiag, yXvKtog
G.P. yXvKttov, yXvicttwv, yXvictuv.

3. in vg y vow, vv 9 N, Swcvvg, otutvvoa, dwcvuv, showing

G. StiKvvvrog, deuevvfTTjg, Stixvvvrog
N, $vg 9 <pv<ra t <pvv, born, arisen
G. <puvrog, (pvcnjg, Qvvrog.

4. in «c, aroa, tv, N. x«P*«c X a P l * <r(rrt » x a P uv * ^zceivkl

G. xapi£vroc, x a P u<riTr H:* X a P UVT0 £
ContTteted N. Tifirjtig, nfijfiaaa, rtfintv i nonoure d
» *. >± rt /*f C» r rifiriqaa, rifit)v ) - -

" • ' t». Tifinvfog, rtjiiiacrijg, rifJLrjvTog

K. fieXiro'iig, fitXiv-tava, pt- \

Xiro-tv t honeyish
peXtrovg, iLtXiTovooa, fuXi- i
rovv )
G. fuXirovvrog, ptXiTovavrjg, peXiTOvvrog.
6. €tf, Mffa, tv, K. Xu<f>9Hg t XshPOeioci, Xei<f>Otv, left
G. XuipQivrog, Xu<p9tiot]g t Xei<p9tvrog
X. riOug, Ti9naa t ri9tv % placing
G. Ti9tvrog, ri9uang, riQevrog.

6. ag, aiva, av, N. peXag, ptXaiva^ pcXav, black

G. fuXavog, inXaivrjg, fuXavog.

7. fie, aim, dv t N. irag, rraora, irav, all, every

G. iravrog, iraaTjg, rravrog
N.P. irapreg, navai, -navra
G. iravTtov, iraawv % iravroiv.

8. ag, aaa, av, N. Xeixj/dg. \ti\p arret, Xeixf/av, having left

G. Xtiij/avrog, Xu\parr^g f \tt\pavTog.
9 nv, ttva, £v, iV, reprjv, repttva, reptv

G. repivog, Tipuvijg, reptvog.

10. Dvc, ovffa, ov, N. didovg, didovoa, Sidov, giving

G. SidovTog, SiSovoijq, SiBovrog,

11. *>v, o$oa t ov, N. tKutv, titovoa, ikov, willing

G. tKovrog, tKoveng, exovrog.

12. (av, ovad, ov, N. Xtiirwv, Xwrrovaa, Xmtov, leaving

G. XuirovTog, Xwcovang, Xwkovtoq
Contracted, N. rip&v, ripL&aa, rtpCbv, honotirhlg
G. rtpiuvTog, rtuwang, TuiGtvrog
N. 0tXwv, <pi\ovaa, ftXovv, loving
G. QiXovvrog, ipLXovtTTjg, (piXovvrog.

13. <og, via, oq, N. rtrvfvg, rervfifia, rtrvpog, having struck

G. Tvrvtyorog, rtrvipviag t rrrvforoQ.

2. Adjectives of Two Terminations..

og, ov,

2. ovg, ovv,

3. u>g, wv t

mv, ov,

6. ng, eg,

6. nv, tv,

7. top, op,

8. tf, i,

9. vg, v,

10. ovg, ov,

N.
G.

N.
G.
N.
G.
N.
G.
N.
G.
N.
G.
N.
G.
N.
G.
N.
G.
N.
G.

M. and F.

aXoyog
aXoyov

evvovg

twov

\Xtcjg

l\£6>

auxpoujv

<r<i)ippovog

aXn9ng

aXn9ovg

apprjv

apptvog

airarutp

aicaropog

tdptg

idpiog

atiaicpvg

adatepvog

povoSovg

fiovoSovrog

aXoyov
aXoyov

tvvow

evvov

IXtutv

unreasonable
well-disposed
propitious

oruxppov

sound-minde

aoxppovog

aXn9tg

true

a\rj9ovg

apptv

male

apptvog

arrarop

fatherless

aicaropog

icpi

expert

iCpLOQ

atiaxpv

tearless

adaxpvog

fiovodov

having one

fjovodovrog

tooth.

3. Adjectives of One Termination.

1. ag, G. ov, N. o, fioviag, G. poviov, lonely

2. ag, G. avrog, N. 6, y), axapag, G. aicaftavrog, unwearied

3. ag, G. aSog, N. 6,r),<pvya£, G. Qvyadog, fleeing, an

exile.

4. op, G. apog, N. 6, t) , paicap, also 17 uaxaipa, blessed

5. rjg, G. ov, N. 6, t9tXovrrjg, G. efcXovrov, willing,

spontaneous

N. 6, 1), apytjg, G. apytjrog, white
-V. o, 7), arrrtjVi G. airrfjvog, unfeathered
N. 6, ry, ayvwg. G. ayv&rog, unknown
N. 6, »/, avaXtig, G. avaXtitiog, powerleAi
X. 6, >/, venXvg, G. verfXidog, recently

come
A r . a, 1) apxaZ, G. dprrdyog, plundering
N. 6, 1), 7/\i$, G. yXiKoc, of the same age

6. ng, G. 7)rog %

7. rjv, G. ijvog,

8. tog, G. GtTog,

9. ig, G. idog,
10. vg, G. vcoc.

11.

G. yog
G. Kog
G. XOQ

N. b, t), fiuvvS, G. fiUfvvxog,

having one
hoot

172

THE POPULAR EDUCATOR.

LE8SON8 IN GERMAN.-No. LXXVL
Irregular Verb, eontimed from p. 156.

S 85 PARADIGM OF A PASSIVE VERB.
©etoBt roerben, to be praised.

INDICATIVE.

SUBJUNCTIVE.

CONDITIONAL.

XMPBSATrVB.

INFINITIVE.

PAJLTICH»LB.

Present Tense.

PresentTensc

6 f 1

i<$ toerbe ""J lam
bu toirft j thou art

i<9 toerbe

I maybe

2* toerbebu

gebtttoecoe*,to

£ {2

bu toerbeft

praised, &c

3. toerbe ct

be praised.

• (3

g i 1

cr toirb, 1 ^he is
toir toerben, f *£ we are

et toerbe
toit toerben

1. toerben
toir

•?"

5 2

i$r tocrbet, you are

tyr toerbet

2. toerbet

* (3

fie toerben J they are -

fie toerben u

Imperfect Ton*.

Imperfect Tense,

3 toerben
fie J

6 P

u$ tourbe "| I was "

i$ tourbe ^

I might be

be thou

2 {2

bu tourbeft ] thou wast

•ri

bu tofirbefi

praised, &c.

• (3

er tourbe l^hewas

er tourbe

« P

air tourben f *§ we were

toir tourben

►3

S 2

tyttourbet 1 you were

p«

i$r tourbet

* (3

fie tourben J they were,

fie tourbeu ^

Per/bet Tense.

Perfect Tense.

Perfect*

6 (1
5 2
• (3

tf (I
" >2

i<$ Hit

.1 have
1 thou hast
fc |hehas

i<$ fei

j. I may have

ge loot toerben fcin,

««IpH

bufctft

bufeiefl

I been praised,

to have been

praised.

er ift

.'2

erfri

praised.

toit flnb

* ^ we hare

• O.

toir fcien

i^r feib

a you have

tyrfeiet

•* 1 *
* (3

flefinb J w theyhave >

fie feien

Pluperfect Tense.

Pluperfect Tense. T

i<$ toot

^Ihad

•d

tytodre "

.g I might have

s f J

butoorfi

2 thouhadst
J he had

bu todrefi

2 been praised,
| Ac.

2 {2

ct tear

er toore

* (3

toit toaren

* ~ we had

■p.

toir to&ren

s i\

t$r toaret

!§ you had

tyt tootet

* IS

fie toaren -|

& they have^

fie toAren -

Jfrrf Future Tense.

First FutureTense.

JYrrf Future.

Future Tense.

ri
2
3

id) toerbe
bu toirft
et toirb

e I shall be
i praised, &c.

i^ toerbe
bu toerbcfl
er toerbe

-. (ii) I shall be
£ praised, &c.

ic}toutre "
bu toutbefi
er tourbe

toerben getofct
toerben, to be
about to be

1
2

toir toerben
i$r nerbet

toit toerben
tyr toertet

nnttourben
i$r tourbet

- 1

*o jj -2

praised.

lie toerben <J

a»

fie toerben -

fie tourben -

coi-t a

Second Future Tense.

fi^eoful JWftwv. '

* r 1

xdf toerbe

j. I shall have
? been praised,

id^ toerbe "

c (if) I shall

d) tourbe

bu trtrft

bu toerbefi

.g have been

bu tofirbefi

et toirb

er toerbe

2 c praised, Ac.

et tourbe

B D M

<• f 1

loir toerben

totr toerben

"J*

unrtourben

5 2

i$t toetbet

tyr toerbet

t^r tourbet

?l|

fie toerben ^

fie toerben

<3>

fie tourben j

l«J

S 86. Rbflxxivx Verbs.

(1) A verb is said to be reflexive, when it represents the
subject as acting upon itself. We have several such in English :
he deports himself well; he bethought himself; they betook
themselves to the woods ; where the subject and the object, in
each case, being identical, the verb is made reflexive. It is
manifest, that any active transitive verb may thus become a
reflexive verb.

(2) Strictly speaking, however, those only are accounted
reflexives that cannot otherwise be used. The number of these
in German is much larger than in English. Some of them
require the reciprocal pronoun to be in the Dative, but most of
them govern the Accusative : thus, (with the Dative), i$ titte
mir ntyt tin, I do not imagine ; (with the Accusative,) i$ ftydme
atty, I am ashamed. Further examples are the following :

WITH THB DATIVE.

G&9 onmofen, to presume;
usurp.
€%$ muBebtttflen, to make a con-
dition.
&id> einoUben, to imagine.
ei$ flrtrauen, to be confident.
@i<$'f<$meufceUt, to flatter one's
self.
6te$ »orne$men, to propose to
one's self.
€ic$ vecfteuen, to represent to
one's self.
€&$ toiberftwec^en, to contradict.

WITH THE ACCUSATIVE

ety onf^tden, to prepare.

GiQ oaferit, to intimate.

©t^Bebanfen, to be thankful for.
ei^ Bebenten, to pause, to think.
C&9 ocgeoen, to repair to; to

happea.
wiS; to

©t^i oe^tftn, to put up wit] .

make do.
eity freuen, to rejoice.

6tc^ toibetfe^etti to resist*

(3) Since the action of these rerbs is confined to the agsnt

LESSONS IN CHEMISTRY.

(key we rightly regarded as tntntntitwe$; for the verb and the
pronoun under its government, are to be taken together as *
single expression for intransitive action ; thus, \a) fcene mty, I
rejoice my*?, that is, I rpetetf, or <fe%M m.

(4) In like manner, reflexives often become the equivalent
of pa$twet: as, ter eipftffel $<tt fty otfiroKn, the key has /own
ftssft that is, the key tt found or tow been found, &c

(5) In some instances a verb is found to have, both in th
simple and in the reflexive form, the same signification: a>
teres and fa iron, to err; to be mistaken.

(6) It is worthy of remark, also, that some transitive*, upor
passing into the reflexive form, undergo some change of signifi
cation : thus, from Bcrafen, to call, comes fa krafen, to appeal t
It is generally easy, however, in these cases, to account for suck |
changes. The following are additional examples

u»

ftomfoi, to think upon ;
Ocftyrifccn, to assign;

tfsbcn, to find;

gita$tat, to fear;
$4t«t, to guard ;
9tQ/ajn, to make ;

CKtflfli, to place ;
Sersitnwtten, to answer for ;

Screen, to pass away ;
$crfaffrn, to leave ;

fa bebcnfen, to pause to think.
fa Beftyriten, to be contented
with,
fa finben (in ettaxil), to accommo
date one's self to a thing
fa fftr$tcn, to be afraid of.
fty $fitcn, to beware.
fa mac^en (an tttoai), to set
about a thing.
fa flctlen, to feign, pretend.
fa verannwrten, to defend one's
self,
fa ftcrge^en, to commit a fault
fa Bcrlaffen, to rely upon.

LESSONS IN CHEMISTRY.— No. XI.

Having made yourself acquainted with the physical aspects
and chemical relations of metallic antimony, I purpose now
directing your attention to a solution of that metal, for which
pur pose we will select a soluble preparation of antimony : the
tartrate of antimony and potash— commonly known as tartar-
tmetie, under which name it is procurable at any druggist's
shop.

Tartrate of antimony and potash is a very convenient pre-
paration for our present wants, inasmuch as it is perfectly
soluble in water ; a remark which applies to very few antimony
salts. A proper solution for our experiments will result from
the mixture of about ten grains of tartar-emetic and two
wine-glasses full of distilled water. ,

Certainly the most characteristic test for this substance, and
I may say for antimony in solution generally (there are some
exceptions), is hydrosulphuric acid or hydrosulphate of ammo- 1
nia— whicn of the two is immaterial ; either of these tests
throws down an orange-red precipitate, which under some cir-
cumstances, such as particular states of dilution, &c, may appear
yellow. The truth is, however, that the so-called yellow of the
sulphuret of antimony, is yellow by courtesy thus to express
oneself; however, by calling it yellow without qualification or
circumlocution, one avoids the necessity of splitting up facts
into detail. Once more let me call to your mind, that although
we have not met hitherto with one metal that affects hydro-
sulphuric acid and hydrosulphate of ammonia black, never-
theless black is the normal colour of the precipitates yielded
by these reagents on metals; hence, when all the precipitates
which are not black shall have come under our notice, the
remaining ones may be allowed to take care of themselves.

Having prepared this orange sulphuret of antimony, termed
by chemists the eeoquitulphuret, for a reason that will be evident
by and bye, observe well the general appearance of the sub-
stance in order that you may be sure of never confounding it with
yellow sulphuret of arsenic. Generally speaking, the difference
between the appearance of the two will be a sufficient ajpde,
but the surest test consists in reducing it in a glass tube by means
of heat and black flux, or else a mixture of charcoal and carbonate
of potassa or soda. To this end, mix a few grains of the orange
or sesquisulphuret of antimony with twice its weight of the
black flux, oi for want of this, a mixture of charcoal and car-
bonate of soda (washing soda and charcoal). Put the mixture
into a small glass tube closed at one end, with all the precau-
tions as regards cleansing the aides of the tube, already men- 1

tioned, and apply the heat of a spirit-lamp flame ; you will
soon find that there is a very manifest difference between the
result and that which you noticed when sulphuret of arsenic
was the subject of operation. 1 question very much whether
you will succeed in obtaining any sublimate ; so comparatively
difficult is antimony of volatilization. Make yourself master of
the appearances, because the question whether the arsenical
crust as it is termed may possibly be mistaken for the anti-
monial crust, is still undetermined by writers on poisons. If by
chance, hereafter, you should be engaged in settling the
question of arsenical poisoning, the counsel for the prisoner
would in all probability try to prove, that the appearance
testified by you as resulting from arsenic resulted from anti-
mony developed from tartar-emetic given to the patient as a
remedy. Many disputes, which seem knotty enough in books,
resolve themselves into exceedingly plain matters of demon-
stration when treated practically. Make yourself master,
then, of the differences between the phenomena of antimony
and arsenic.

Antimoniuretted Hydrogen-— The fact has already been stated
that antimony is one of those metals which combine with
hydrogen gas, and is evolved in an invisible form. In other
words, antimony is a metal which, in this respect, strongly
resembles arsenic, and might possibly be confounded with it.
.Let us proceed, therefore, to perform some experiments with
antimoniuretted hydrogen. For this purpose we shall again
require the bottle with perforated cork and tobacco-pipe stem ;
by no means, however, employ the one already used in the
experiments with arsenic ; the delicacy of this kind of test is
such, that it is dangerous to rely on mere cleansing of the
apparatus ; far better is the plan of using a new bottle, new
cork, and new tobacco-pipe stem ; and here, as in many similar
Cases, you will not fail to recognise the advantage of working
with apparatus that is sufficiently cheap to admit of being
manufactured ad libitum. In addition to the previous appa-
ratus we shall require others. One is frequently employed
In the operation of testing for arsenic, and the reason of my
omitting to mention it under that head was, that 1 avoided
directing your attention to a multiplicitv of subjects all at
Once.

Fiff. No. l.

The other apparatus may be said to belong especially to
examinations connected with the metal antimony ; neverthe-
less, it will be found useful for many other purposes, there-
fore when once prepared, take care of it.

Taking a comparative glance at the two apparatus here

^presented, you will be struck with a certain similarity between
them ; that is to say, the generating bottles ▲ are precisely

like, though the other parts are different.
Apparatus No. 1, is intended for the purpose of generating

rsenruretted or antimoniuretted hydrogen gas, and presents
tome advantages over the tobacco-pipe apparatus. Assuming
the spirit-lamp to be removed, then, the only difference between

tie bottle with tobacco-pipe jet and this, is the difference
between a vertical and a norisontal delivery pipe ; the latter
jou will not fail to perceive must be just as efficient in deliver.

THti POPULAR EDUCATOR.

iug its gas and depositing a crust on anjr recipient (a plate is
here represented) as the former. The horizontal arrangement,
however, enables us to bring into operation another test, ».*.
that of heat, demonstrating a property of the gas not yet taken
cognizance of. If arseniuretted or antimoniuretted hydrogen
gas be transmitted through a horizontal tube of this kind, and
the heat of the spirit-lamp flame applied, the gas is decomposed
partially or entirely according to circumstance*, and the metal
(arsenic or antimony as the case may be) obtained.

Commence your experiments with the simpler apparatus,
Place the metals for the generation of hydrogen in the bottle,
add thereto a little tartar -emetic, replace the cork, and after
waiting a few instants until the atmospheric air existing in the
bottle shall have been expelled, ignite the gas, collecting the
result (1) on a piece of white porcelain—- a plate for instance {
(2) is an open tube, p, fig. No. 3, being a stiff piece of paper
serving as a handle, by means of which the tube is held, and
inconvenience to the fingers obviated.

Fig. No, 3,

<;•• • >

It may here be observed, in connexion with the develop -
ment of hydrogen gas, an operation of constant recurrence*
that although a mixture of zinc, oil of vitriol, and water is that
which yields the purest and most satisfactory result, yet if th
zinc cannot be procured in sufficient quantity iron may b
substituted.

Having by means of the preceding simple arrangement
satisfied yourself as to the general nature of antimoniuretted.
hydrogen gas, proceed to employ the more complex arrange*
ment which I will now explain in detail.

The bottle or generator part of No. 1 scarcely demands ft
word of explanation. It is so fitted up, as the student will
observe, that a fluid may be poured into it through the funnel
tube / without involving the necessity of removing the cork.
As regards the horizontal tube B, thin, as 1 have already
remarked, admits of the application of a spirit-lamp flam©
underneath, by which treatment the antimoniuretted hydrogei
as it passes invisibly along the tube, is decomposed partial]
or entirely, and a metallic crust results.

Mtdmttim if 6ulpfi wet qf Antimony to the MrtMe State.— To*
Will remember that we had not the slightest difficulty in effect-
ing the reduction of arsenic to the metallic state by heating it
in a tube along with charcoal and carbonated alkali ; you will
remember, moreover, that, practically speaking, we could not
succeed in obtaining by this means metallic antimony. I will
now show you a very elegant method of getting this result by
means of hydrogen gas under the influence of heat ; for this
purpose we shall avail ourselves of apparatus No. 2, which
differs from No. 1 in having a piece of glass tube about four
inches long secured at either end by means of two perforated
vks to the tubes / and ?.

Reverting to a former experiment, collect the orange sul-
huret of antimony already prepared either by filtration or
ecantation, remembering that it has been thoroughly washed
ad dried ; place it carefully in the tube b, dip the tube /' in a
ablution of tartar-emetic c, and generate hydrogen gas in the
Teasel a by pouring through the funnel tube a mixture of oil
f vitriol and water in due proportion on metallic iron or
inc. All this being done, it follows that the hydrogen gas,
to soon as developed, passes over the sulphuret in the tube b
without affecting it, and finally escapes in bubbles through the
irtar-emetic solution in c. In point of fact, no chemical
hange is perceptible, nor indeed does any take place. If,
however, a spirit-lamp flame be applied to the tube b, some
xtremely interesting results are developed. The most evident
phenomenon, though not the first in order of occurrence, is
he change of colour in the tartar- emetic solution ; from being
: totally colourless it becomes orange- red, owing to the genera-
tion of a powder which soon falls as a precipitate ; and now if
! you look at the tube b just where the spirit-lamp flame impinges
I upon it, in place of the original red substance (sulphuret of
I antimony) you will observe a black powder, which is metallic
[antimony in a finely divided state. The change which has
snsued is this: the sulphuret of antimony, being a compound
I of sulphur and antimony, vields up its sulphur to the passing
[hydrogen, and forms sulphuretted hydrogen gas, otherwise
I called, as I presume you recollect by this time, hydnmdphmie
I tcid. The reason why our solution of tartar -emetic becomes
coloured orange-red is now evident enough. Our old friend,
Sulphuretted hydrogen, has been making his appearance under
s new aspect. See how easily this decomposition and reeom-
position is represented by means of a diagram :

Hydrogen {^g^

Sulphuret \ Sulphur
of

Antimony ) Antimony
What can be more simple than these changes ? What more
easy than the process of determining them ? It is in vain for
elements to play at hide and seek with the chemist. They
may change their position, they may assume more different
forms than Proteus ever dreamed of, may; present themselves
under the aspect of solid, liquid, or gas — it is all in vain, they
cannot escape ; the chemist sets his trap for them, and they are
caught at last. By this time you will, I trust, have acquired a
more just idea of the nature of chemistry, especially that pert
of it termed analysis, than you originally entertained. Most
chemical beginners imagine analysis involves s sort of mecha-
nical picking out of the different elements of which a body it
composed ; a little progress in the way of the science soon
demonstrates how incorrect is this view. Suppose, for instance,
a piece of sulphuret of iron were given to you — that substance

which you employ in the manufacture of sulphuretted hydro-
gen—with the request that you would extract its sulphur
bodily ; perhaps you would have thought a delicate process of
sifting would have accomplished this result. Not so; the
best, the most direct, the shortest way to accomplish this, con-
sists in first collecting all the sulphuretted hydrogen gas out of
the substance, and then taking away the hydrogen from the
sulphuretted hydrogen ; for does it not follow, that if sulphu-
retted hydrogen be = Hydrogon-J-Sulphur, that Sulphur is =
(Hydrogen -f Sulphur)— Hydrogen ? or more shortly,

HS=H-(-8 .*. S^HS — H

Tliis separation of sulphur from sulphuretted hydrogen i*
readily effected by the action of chlorine, as wc shall discorer
hereafter.

SKETCHES FOR YOUNG THINKERS.

If*

SKETCHES FOR YOUNG THINKERS.

(Continued frotn page 143.)

Sriti6K biography next claims oar attention; and we rejoice;
to know that it contains ample illustrations of both the principles,
that mental and moral excellence are quite compatible, and thai
goodness is better than greatness. On turning up the pages of
history, we are at a loss where to begin. There are so many, and
such great men, that selection is difficult. We come, however,, to
Lord Bacon, who was born in 1561, and who became Lord High
Chancellor of England. Preferring to hear him spoken of in the
language of another, we make room for Addison, who, in one
passage, speaks as follows : —

" Sir Francis Baoon was a man who, for greatness of genius
and oompass of knowledge, did honour to his age and country ; I
could almost say, to human nature itself. He possessed, at once,
all those extraordinary talents which were divided amongst the
greatest authors of antiquity. He had the sound, distinct, com-
prehensive knowledge of Aristotle, with oil the beautiful lights,
graces, and embellishments of Cicero. One does not know which
to admire most in his writings, the strength of reason, force of
style, or brightness of imagination." Bacon has been called the
"Father of Experimental Philosophy, and the Prophet of the
Arts." He was a firm believer in the verities of Christianity.
He has one beautiful passage in opposition to the atheistic theory,
which wo cannot withhold : — " I had rather believe all the fables
in the Legend, and the Talmud, and the Alcoran, than that this |
universal frame is without a mind. While the mind of man look-
eth at second causes scattered, it may sometimes rest in them, and
go no further ; but when it beholdeth the chain of them confede-
rate and linked together, it must needs fly to Providence and
Deity." Here, again, is the combined force of goodness and great-
ness. While he was great in philosophy, he was ardent in his
attachment to God and truth ; and while his name is pronounced,
it will ever be with associations of a most pleasing nature. From
Bacon we naturally turn to Locke, who was born 71 years later.
He was one of the most celebrated of English philosophers. To
native talents of a lofty order he added a liberal education. His
m giant monuments of a profound judgment, critical
, tad noble execution. So far, he is merely an intellec-
ts history does not leave him here. He rises far above
all philosophy, and reposes his eternal interests in Christ's re-
demption. The manner in which he speaks of the Holy Scriptures
is truly excellent : " The New Testament has God for its author,
salvation lor its end, and truth, without any mixture of error, for
its matter." Lady Masham, in a beautiful letter which she wrote
concerning him, closes the communication in the following words :
-" Time, I think, can never produce a more eminent example of
reason and religion than he was, both living and dying." Such
were two of England's greatest sons ! Combining in themselves
all that learning could furnish, and all that religion could pro-
dnoe. Their memories are sacred and refreshing to many a weary
pflgrim ; they hang out, as* great beacon lights, over the ocean of
humanity, and will, doubtless, shed an undiminished lustre until
time itself shall die.

Robert Boyle, who ought, in the order of time, to have come
before Bacon and Locke, next appears as a further instance in
which are united mental excellence and profound piety. He was edu-
cated at Eton, and was not long in manifesting powers of a superior
order. So immense were his mental acquisitions, that Dr. Boer-
haave has paid him the following compliment : — " Boyle was the
ornament of his age and country. Which of his writings shall I
commend ? All of them. To him we owe the secrets of fire, air,
water, animals, fossils, so that from his works may be deduced
me whole system of natural knowledge." Another writer, to
whom we have been already indebted, gives the following testi-
mony : — ** The great object of his philosophical pursuits was to
promote the cause of religion, and to discountenance atheism and
infidelity." His intimate friend, Bishop Burnet, makes the follow-
ing observations on this point : — " It appeared to those who con-
versed with him, on his inquiries into nature, that his main
design (on which, as he had his own eye constantly fixed, so he
took care to put others often in mind of it) was to raise in him-
self and others more exalted sentiments of the greatness and glory,
the wisdom and goodness of God." This design was so deeply
impressed on his mind, that he concludes the article of his will,

which relates to the Royal Society, in these words : — " I wish them
a happy success in their attempts to discover the true nature of
the works of God ; and I pray that they, and all other searchers
into physical truths, may cordially refer their attainments to the
i glory of the great Author of nature, and to the comfort of man-
I kind." So could an eminent philosopher write. Let no one hence-
forward say that religion is only taken up by weak, fanatical,
enthusiastic minds. Had we no other examples to produce, the
point is established beyond successful denial. But there remains
a whole " cloud of witnesses," all bearing emphatic testimony.
The ages of the past, as well as the present generation, conour m
one confession — that the men who have conferred the most lasting
| obligations upon the world, and whose names will be held in
affectionate and reverential remembrance, have been eminent for
all the adornments of mental and moral greatness. Those men
have moulded opinion, attacked and confronted error in its thou-
sand chameleon hues and protean farms, and confirmed their
words by blameless and honourable lives. In them the truth has
been embodied; they regarded it as something more than theoreti-
cal and speculative; they looked upon it as demanding their
practical support, and as worthy of the loftiest homage they could
render. They loved learning with an almost idolatrous affection,
but were mindful that goodness had claims upon them of an infi-
nitely higher and holier nature. Herein their wisdom was dis-
played, for they oombined the greater with the less in harmonious
Unity.

Early in the eighteenth century we meet with the name of
Lord Lyttleton. fie, like Boyle and many other individuals of
eminence, was an Eton pupil. He won a proud position both at
school and college, and was looked upon by his fellow-students as
a superior scholar. As a writer, he was eloquent, logical, and
powerful. Here was intellectual excellence. So far, he has shown
the triumph of mind. The following anecdote of himself and
West will show that he became as distinguished for his Christi-
anity as he formerly was for his infidelity : — " The effect which
was wrought on the mind of the celebrated Gilbert West, by that
particular evidence of our Lord's resurrection which was afforded
to his apostles, was very remarkable. He and his friend Lord
Lyttleton, both men of acknowledged talents, had imbibed the
principles of infidelity from a superficial view of the Scriptures :
fully persuaded that the Bible was an imposture, they were deter-
mined to expose the cheat. Mr. West chose tne resurrection of
Christ, and Lord Lyttleton the conversion of St. Paul, for the
Subject of hostile criticism. Both sat down to their respective
tasks, full of prejudice and a contempt for Christianity. The
result of their separate attempts was truly extraordinary. They
were both converted by their endeavours to overthrow the truth
of Christianity. They came together, not as they expected, to
exult over an imposture exposed to ridicule, but to lament their
>wn folly, and to congratulate each other on their joint convic-
tion, that the Bible was the Word of God. Their able inquiries
have furnished two most valuable treatises in favour of revelation ;
one entitled * Observations on the Conversion of St. Paul ;' and
the other, * Observations on the Resurrection of Christ.' " This
is a remarkable evidence of the Divine authenticity of the sacred
canon, and shows the power of the truth in subduing the proudest
minds to its sovereign sway. The man was now complete. His
lordly birth and liberal education were not sufficient to complete
him. There was a void which nothing could fill but the truth of
God ; and a rebellion, which nothing could subside but the voice
pf 'Omnipotence. We need no further evidence of the majesty of
Divine truth ; such a case as this speaks in language which will
only admit of one interpretation. His death-bed experience is
truly refreshing, and breathes a spirit of penitence and lovi*
towards God. " At evening time it was light." His sun wn:
down, not in "a fearful and troubled glory," but with a ci.\u
brilliant, and softened splendour ; and now, from his tomb, th-r
Streams a glory of mingled moral and mental worth. Lord Ly%
tleton stands out as a tall, colossal figure, uniting all that* if
exalted in mind, and attractive in disposition. Hero he does no
dignify his moral excellence, but is the rather ennobled by it
yet, when such men exhibit such sterling virtue*, and defend thtf
truth with such overwhelming power, it becomes those witt
fewer acquisitions and less ability to pause and consider, boforfl
they deny and oppose the truth.

Joseph Addison is a name deserving the most honourable
mention in this series of illustrations. He was one of the
lights of the eighteenth century. He was not indeed a blasv

176

THE POPULAR EDUCATOR.

in* July ran, or a daiiling meteor, but a bright and cheer-
ful light. He was a refined scholar, and extremely urbane
to all who were favoured with his friendship. The most
superior and learned of his contemporaries, were anxious to
testify their high sense of his intrinsic menu. He was not " one
of the lower orders.' ' At the age of forty-fire he was appointed
to the office of State-secretary. As a writer he is well known
and justly celebrated. Dr. Johnson, who in many respects
was the Yery antipodes of Addison, speaks of hun in the
following complimentary terms : " He employed wit on the
aide of Tirtue and religion. He not only made the proper use
of wit himself, but taught it to others ; and from his time it
has been generally subserrient to the cause of reason and
truth. He has dissipated the prejudice that had long con-
nected cheerfulness with rice, and easiness of manners with
laxity of principles. He restored Tirtue to its dignity, and
taught innocence not to be ashamed. This is an elevation of
literary character beyond all Greek, above all Roman fame.
As a teacher of wisdom he may be confidently followed. His
religion has nothing in it enthusiastic or superstitious; he
appears neither weakly, credulous, nor wantonly sceptical :
his morality is neither dangerously lax, nor impracticably
rigid. All the enchantments of fancy, and all the cogency of
argument, are employed to recommend to the reader his real
interests, the care of pleasing the Author of his being/* Such
a testimony, from such a man, is not to be misunderstood.
Dr. Johnson was not the man to flatter any one, through fear
or favour. We cannot, however, dismiss Addicon without
subjecting him to the same death-bed scrutiny as those
already mentioned. After his busy pen had written what was
intensely admired and loudly applauded, he came, as other
men come, to the river of death ; before plunging into it, there
occured one most interesting and impressive circumstance,
which we will narrate in the language of a writer already
quoted : " The virtue of this excellent man shone brightest at
the point of death. After a long and manly, but vain struggle
with his distempers, he dismissed his physicians, and with
them all hopes of life ; but with his hopes of life he dismissed
not his concern for the living. He sent for Lord Warwick,
a youth nearly related to him and finely accomplished, but
irregular in conduct and principle, on whom his pious
instructions and example had not produced the desired effect.
Lord Warwick came : but life now glimmering in the socket,
the dying friend was silent. After a decent and proper pause,
the youth said, "Dear sir, you sent for me : I believe and hope
you have some commands; I shall hold them most dear."
Forcibly grasping the youth's hand, Addison softly said; 'See
in what peace a Christian can die.' He spoke with difficulty,
and soon expired." The reader will no longer doubt, that
moral excellence is compatible with mental refinement and
cultivation, and that this alone will bear a man in the misfor-
tunes of life, and support him in the agonies of death. What
further evidence need we require in support of Christianity ?
If men refuse these testimonies, conjoined with the Word of
God, " neither would they be persuaded though one rose from
the dead."

L'ouvrier sujet au vin ne deviendra jamais riche, et celui qui
neglige les petites cboses tombe peu a pea. — EccUsiastique.

La jalousie est le plus grand des rnanx, et celui qui fait le moms
de pitis* aux personnes qui le causent. — La Rochefoucauld.

La difference entre la jalousie et l'envie, e'est que par l'envie
nous desirous pour nous ce que arrive d'heureux aux autres ; par
la jalousie, nous craignona qu'ils ne participent a notre bonheur.

Charron.

Le jeu est le dissipateur da bien, la perte da temps, le gouffre
des riehesses, l'lcueil de l'innocence, la destruction des sciences,
1'ennemi des muses, le pare des querelles.— /.V. Rousseau. ,

Le joge est une loi parlante, et la loi un joge must.— -

Montesquieu.

Les hommes se croient supeneurs aux dlfsuts qoi'ils penvent
sentir ; e'est ce qui fait qu'on juge dans le monde si severement
des actions, des disco urs et des ecrits d'nutruL—yauvtnaraues.

On ne peut etre juste, si on n'est hum sin. — Idem.

Dans une societe* oa il y a des lois, la liberte* ne peut consister
■u*a pouvoir fairs ce que Ton doit vouloir, et a n'6tre pas contraint
• Mre ce qu'on ne doit pas vouloir .^Montesquieu,

LESSONS IN BOOKKEEPING.— No. X.

(Continued from page 153.)

COTTON BOOK.

lie the Day-Book, which was given in our last lesson, all the
transactions relating to the purchase and tale of the different
kinds of Cotton, have been entered as a primary record of these
transactions ; but if the Merchant be desirous of keeping a
distinct and separate account of his dealings in Cotton, in
order to be able to tell, at a glance, what is actually in his
Warehouse, or in Stock, as the phrase is, he will have a book
similar to the following, specially made for the purpose. In
this book, the transactions can be more clearly and distinctly
arranged ; for he can have a separate account of each kind of
Cotton, with columns for the number of the bags, the net
weight in pounds, the rate per pound, the prime east, and the
telling price ; and he can appropriate the one aide of the folio
for the purchases, and the other side of the folio for the sales ; so
that the difference between them can be found in a moment, if
necessary. If any particular kind of Cotton be all sold, then
this book will show at once what has been gained or lost by
the transactions in this kind; and as the same principle is
applicable to all kinds, it follows, that if all the Cotton of
every kind has been sold, this book will show, both indivi-
dually and collectively, the gain or loss on each, and the gain
or loss on the whole. This is a great advantage where a Mer-
chant deals chiefly or wholly in any particular kinds of goods ;
as he can form an idea of his gain or loss on the principal
part or the whole of his business accordingly, without con-
sulting his Ledger, or striking a general balance.

It is evident that in any trade, business, or mercantile pro-
fession, such a book as this for every separate species of goods
bought and sold would be of immense advantage, and would
certainly be preferable to one book, such as the Day-Book,
where all kinds of goods are indiscriminately classed together
according to the dates of the different transactions ; for the
order of dates, though highly important, is not so useful to a
Merchant as the classification of his transactions ; whilst even
in that classification this order can be preserved. Hence a
Merchant may have his Sugar-Book, his Indigo-Book, his
Tea-Book, his Coffee-Book, &c, according to the nature of
his business; and in keeping books by Single Entry, which
many persons yet mistakenly follow, such books as these are
indispensably necessary, inasmuch as the Ledger kept by
Single Entry gives them no information whatever, as to the
actual state of their Assets and Liabilities. If the book, such
as the preceding, be devoted to one or more classes of goods,
and each be kept separate and distinct, so that no confusion
be introduced into the different transactions, it may be called
legitimately the Stock or Warehouse Book, as the Merchant can
always tell his Stock of Goods by consulting it, without
actually going to the Warehouse and turning over the goods
in order to see what he has got in hand.

The following is the state of the Profit and Loss account, or
the account of clear gain made by the purchase and sale ot
Cotton of different kinds from January till June, as per
Cotton-Book :—

qu*apou
defakei

Gain on Berbice
„ Grenada
„ Maranham
„ West India
„ Madras
„ Demerara

Whole Gain

£60 6 8

33 4

85 14 8

123 16 8

355 4 10

111 16 5

£769 18 7

LESSONS IN BOOKKEEPING.

177

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THE POPULAR BDOOAfOA.

LESSONS PJ ITALIAN GRAMMAR.— No. X.

BY CHARLES TAU8ENAU, M.D.,

Of the University of Pa?ia. and Professor of the Italian and Germ
Language* at the Kensington Proprietary Grammar School.

n.«

Singular .

U-no ecu-do, a shield

D* it-no eeu-do, of a shield

Ad it-no scu-do, to a shield

U-no ecu-do, a shield

Da u-no tea-do, from a shield

In u-no ecu-do, in a shield

Cbn it-no ecu-do, with a shield

Per it-no tcit-do, for a shield

Plural.

Unfi6-re,f a flower
D* unjio-re, of a flower
Ad un Jit-re, to a flower
Unjio-re, a flower
Da unji6-re, from a flower
In unjio-re, in a flower
Con unjio-re, with a flower
Per unfi6-re, for a flower

ALcu-ni%ft&-ri % some flowers
D" al- cu-ni fio - ri, of some

flowers
,4rf al-cu-ni fi6-*i, to some

flowers
Al-cu-ni jio-ri, some flowers
2>a ff/-rii-ni fi6~ri, from some

flowers
Jn al-cu-ni Ji6-ri, in some

flowers
Cow al-cu-ni fib-ri, with some

flowers
P*r al-cu-ni Ji6-ri t for some

flowers

Al-cu-ni scu-di, some shields
D* al-cu-ni ecu- di, of som

shields
Ad al-cu-ni ecu-di, to some

shields
Al-cit-ni ecu-di, some shields
Da al-cu-ni ecu-di, from som

shields
7» al-cu-ni ecu-di, in som

shields
Can oS-ct-ni ecu-di, with somt

shields
ita- a^6-»f ecu-di, for somt

shields

Singular.

Una-mi- co, a friend

D' an a-mi-co, of a friend

^4J tin a-mi-co t to a friend

Efo a -mi- co, a friend

Da mm a-mi-co, from a friend

In Mt a-mi-co, in a friend

&» un a-ntl-co, with a friend

Per un a-mi-co, for a friend

JPZtiro/.

Al-cu-ni a-tni-ci, som^ friends
i)' al-cu-ni a-mi-ci, of some

friends
.dtf al-cu-ni a-mi-ci, to some

friends
Al-cu-ni a-mi-ci some friends
ZM al-cli-ni a-mi-ci j from some

friends
J» al-cu-ni a-mi-ci, in some

friends
Cbn al-cu-ni a-mi-ci, with some

friends
Per al-cu-ni a-mi-ci, for some

friends

Singular.

U-na gal-li-na, a hen

JD* u-na gal-li-na, of a hen

Ad 4i-na gal-li-na, to a hen

U-na gal-li-na, a hen

Da u-na gal-li-na, from a hen

In u-na gal-U-na, in a hen

Cb* u-na gal-li-na, with a hen

Per u-na gal-li-na, for a hen

Un* 6-ca, a goose

D" un* 6-ca, of a goose

Ad un* 6-ca, to a goose

Un 6-ca, a goose

Da un* 6-ca, from a goose

In un* 6-ca, in a goose

Con un* 6-ca, with a goose

Per un* 6-ca, for a goose

Plural.

* There are, besides the article, many other words (numerals,
pronouns, and adjectives) pointing out with more or less precision
the definite character of a noun, and generally connected with it
Some of these are of such primary importance for the very begin*
nings of reading and conversation, that I consider it useful U
present at once their various changes. The declension of thest
words likewise requires that only the three case-signs di, a, and da
should be placed before them. I shall also lay down here, as a
general rule in Italian, that any numeral, pronoun, or adjective,
which points out the definite character of a noun with a sufficient
or with a still greater precision than the article itself, renders the
latter superfluous, ana such words are on the other hand always
accompanied by the article when thev do not precisely determine
the noun before which they are placed.

f The word tt-no, for the masculine, and u-na, for the feminine,
is considered by many grammarians to be the indefinite article
corresponding to a or an in English. It, however, seems to me
illogical to call a word so which serves so many purposes, and has
so many meanings. It is a word expressing indefinite unity ; e. g.
unU-bro, a book, and 6-na cd-ta, a house, express the general J
idea of any book and any house. It is, moreover, a word expressing
definite unity, i.e. a numeral; e. g. vn'u6-mo e cfn-que den-nc, one
man and five women ; ii-na lib-bra e trtdnct, one pound and three
ounces. It is also frequently a pronoun, having the definite
articles lo and 2a before it signifying the one (masculine and femi-
nine) ; e. g. T li-no di-cc di si. T dUro di n6, the one says yes, the
other no ; V U-na i bclla, f dktra i brut-ta, the one (woman) is
pretty, the other is ugly. These examples, I think, will be suffi-
cient to show that it would only tend to mislead to call it an
article.

When a-no comes before a consonant, which is not the t impure,
we only say and write un ; e. g. un li-bro, a book ; tm oa-vdUo, a
horse ; un vec-chio, an old man. When it comes before the e im-
pure, u-no must be always employed; e.g. it -no epi-ri-to,
a spirit ; tt-no strt-gd-nc, a sorcerer. When it comes before a noun
of the masculine gender commencing with a vowel, the final o of
•i-no is not pronounced, and in writing an apostrophe is not
necessarily used instead ; e. g. tm ar-co, a bow, arch ; un eo-cee-eo,
an excess; tm in-g^gno, a genius; tm or-eo, a bear; un, u6-mo, a
man. The feminine, U-na, generally loses the a, and an apostrophe
most be substituted before nouns commencing with a vowel ; e.g.
un'd-ni-ma, a soul; tm'eV-to, an herb; tm'tf-ra, an hour; un'im-
prt-ea, an undertaking ; un* an-ghia, a nail, hoof. In all other
cases, U-na is written and pronounced in full.

t It is obvious that when a no and ii-na signify definite or in-
definite unity, they can have no plural. The words aUcU-ni, some.

pi. (for the masculine), and al-cu-ne, some, pi. (for the feminine),
mav be, however, considered as substitutions for the plural of u-no
ana u-na in such a case. Al-cu-ni and al-cu-ne are, strictly speaking,
the plurals of the pronouns alrcA-no (masc), and aUc+*a (fern.),
somebody.

Al-cu-ne gal-li-ne, some hens
J>* al-cu-ne gal-li-ne, of some

hens

dd al-cu-ne gal-li-ne, to some
hens
I Al-cu-ne gal-li-ne, some hens
I Da ai-cu-ne gal-li-ne, from'some

hens
|i» al-cu-ne gal-li-ne, in some

hens
I Cb» al-cu-ne gal-li-ne, with some

hens
Per al-cu-ne gal-li-ne, for some
hens

Singular.

| Tut-to il po\po-lo,f all the na-
tion

H tut-to il po-po-lo, of all the
nation

I tut-to il p6-po-lo, to all the
nation

ut-to il p6-po-lo, all the na-
tion
Da tut-to il p6-po-lo, from all

the nation
Jb tkt-to il po-po-lo, in all the
nation

m tkt-to il po-po-lo, with all
the nation
Per tut-to il po-po-lo t for all
the nation

Al-cu-ne 6-che*, some geese
D* al-cu- ne 6 - che, of some

geese
Ad al-cu-ne 6-che, to some

geese
Al-cu-ne 6-chc, some geese
Da al-cu-ne 6-che, from some

geese
In al-cu-ne 6-che, in some

geese
Con al-cu-ne 6-che, with some

geese
Per al-cu-ne 6-che, for 801110

geese

Plural.
Tut-ti i p6-po-li t all nations

Di tut-ti i po-po-li, of all na-
tions

A tut-ti i p6-po-liy to all na-
tions

Tut-ti i po-po-li, all nations

Da tut-ti i po-po-li, from all
nations

In tut-ti i po-po-li, in all na-
tions

Con tut-ti i po-po-li, with all
nations

Per tut-ti i p6-po-li, for all
nations

* The auxiliary letter, A, has been interposed between c and e to
eserve in the plural 6-che (6-kai) the sound of c in the singular
» (6-kahJ. Without the h, the plural of 6-ca would be c^a\ pro-
tunced o-tchai. This will be more fully explained hereafter,
f The words Ut-to (masc), tut-ta (fern.), all, entire, whole, and
i-bo-duc, both, have this peculiarity, that the article is placed after
I em whenever they come before a noun ; as, Ht4o U mttn-do, all the
world ; am-be-due i Jra-tU-U t both the brothers. Am-be-dae is used
fox the masculine as well as for the feminine, and it is obvious from
1 signification, that it can have no singular. The singular tat-to
■nd tat-ta signifies the whole of, all ran; the plural ttt-rsand
We merely signifies all. For example : t4t-to il cli-ro t the whole
clergy ; inpre-een-aa di tut-ti i cor-U-gid-ni y in the presence of atlV
urtieis ; tut-ta la dt-ta, the whole town ; tut-te It nat-ti, all night* *&
t-tigli irf-wu-m, all men : di Mt4a la ter-ra, of the whole eartka. ^.
mte to ddn-ne, of all ladies.

LESSONS IK ITALIAN.

170

Quel % giar-dt-no, that garden

Di quel giar-di-no, of that gar-
den

A quel giar-di-no, to that gar-
den

Quel giar-di-no, that garden

~ia quel g\
garden

Singular.

Da quel giar-di-no, from that

atjrard
>, from

In quel giar-di-no, in that gar-
den

Con quel giar-di-no, with that
garden

Per quel giar-di-no, for that
garden

Quest uc-dUlo, this bird

Di quest' uc-eil-lo, of this bird

A quest ue-cdl-lo, to this bird

Quest' ue-cdl-lo, this bird

Da quest' uc-ciUlo, from this

bird
In quest uc-cdUlo, in this bird

Con quest uc-oU-lo, with this

bird
Per quest ue-ckl-lo, for this

bird

Plural.

Quei§ giar-di-ni, those gar-
dens
Diquei giar-di-ni, of those gar-

A ami giar-di-ni, to those gar-
dens

Quei giar-di-ni, those gardens

Da quei giar-di-ni, from those
gardens

In quei giar-di-ni, in those gar-

Que-itt uc-ckUU, these birds

Di qud-sti uc-cdl-h, of these

birds
A qud-sti ue-oU-U, to these

birds
Qud-sti uc-cdl-U % these birds
Da qud-sti uc*se7-ft. from these

birds
In qud-sti ue-edl-li, in these

birds
Con qud-sti uc-cdl-li, with these

birds

Plural

Con quei giar-di-ni, with those

gardens
Per quei giar-di-ni, for those | Per qud-sti uodl-li, for these

gardens

Singular.

O-gni $ soUdd-to, each soldier

tr 6-gni scl-dd-to, of each sol-
dier

Ad 6-gni soUdd-to, to each sol-
dier

O-gni ssi-dd-to, each soldier

Da 6-md sol-dd-to, from each
soldier

is o-gni sol-dd-to, in each sol-
dier

Om 6-gni sol-dd-to, with each
soldier

Per 6-gni sol-dd-to, for each
soldier

Cin-que sol-dd-ti, five soldiers

Di dn-que sol-dd-ti, of five sol-
diers

A cin-que sol-dd-ti, to fire sol-
diers

Cin-que sol-dd-ti, five soldiers

Da cin-que sol-dd-ti, from five
soldiers

In cin-que sol-dd-ti, in five sol-
diers

Von cin-que sol-dd-ti, with five
soldiers

Per dn-que sol-dd-ti, for five
soldiers

Exercises. — Italian-English.

II pan-no. Del col-tel-lo. Al t6n-do. Dal sa-le. I ci-bi.
Dei cor-ti-li. Ai cud-chi. Dai s6-gni. In tea-tro. Nel

f A full explanation of the two important pronouns qudl-lo (masc),
queUa (fem.j, that, and qud-sto (masc), qud-sta (fern.), this, will be
given hereafter. It will be sufficient for the present to remark,
that whenever these two pronouns come before nouns, qui-sto points
out an object near to him who speaks (or writes), or an object just
\ mentioned, while qudl-lo points out an object at a smaller or greater
distance from him who speaks (or writes), as well as from him who
is spoken to ; e. g. dd te-nd quel li-bro, give me that (yonder) book ;
praL*dd-t6-vi qui-sto U-bro, take this book. Before words commenc-
ing with the s impure, qudl-lo is used. Before words commencing
with vowels, the final o's and a*s of qud-lo, qudUa, and qui-sto,
qud-sta, are generally not pronounced, and in writing an apos-
trophe is placed instead; e.g. qudl-lo sbir-ro, that bumbailiff;
quU-lo sceUe-rd-io, that wretch; quelV ttf-010, that man; quelt
ap-pa-ren-xa, that appearance ; ouesff aUl6-ro, this laurel ; quest
uLH-ma im-prdsa, this last enterprise. Before all other words of the
masculine gender, gtieimustbe used; e. g. quel U-bro, that book;
quel btl pod-ma, that fine poem ; quelpr6-de guer-rid-ro, that brave
warrior.

$ The masculine plural quei (also pronounced quH) or que\ is a
contraction of quil-li. Before vowels, or the s impure, qudhgU i«
used in the place of the plurals quil-li, quei, or que' ; e. g. qud-gli
4e-chi, those eyes; qui-gli spt-ri-H t those spirits. The feminine
plurals qudl-le and quests can not be marked with the apostrophe,
bet must always be pronounced and written in full.

H O-gni has no plural number, and can only be used before
moans

ru-scdl-lo. Nei pol-m6-nL Con da-na-ro. Col fas-so«16t-
to. Coi cap-pel-li. Per pia-cl-re. Pel man-tel-lo. Pei gio-
va-ni. Sui p6n-te. Sui qua-dri. Su que'-sta tdr-ra. Lo
staf-fid-re. Del-lospd-so. Al-lo stra-nie-re. Dal-lo stra-
max-zo. Gli spiS-di. De'-gli sme-rai-di. A-gli scrit-t6-ri.
Da-gli stam-pa-t6-ri. In i-sta-to. Nel-lo sp&c-chio. N£-gli
sti-va-li. Con i-stu-dio. C6I-I0 spi-ri-to. C6-gli scul-to-ri.
Per i-stru-me'n-ti. Per lo spac-ca-le'-gna. Per lo spa-da-jo.
Sul-lo sc6-glio. Su-gli scan-ni. L* dc-chio. DelT uc-c&Mo.
All' a-mi-co. Dall' ds-so. Gli er-r6-ri. Degl' in-ci-s6-ri.
Agl' in-gra-ti. Da-gli al-be-ri. In o-n6-re. Nell' an-no.
Ife-gli o-rec-chj. Con a-m6-re. Coll' a-bi-to. Cogl* i-ni-
aui. Per in-gan-no. Per V o-pe-ra-jo. Per gli a-du-la-to-ri.
SuU' e-di-fi-zio. Sugl' in-fe-lf-ci.

VOCABULABT.

Panno, cloth*

CoUeUo, knife.

Tondo, plate.

Sale, salt.

Cibo, article of food, aliment*

CortUe, court-yard.

Cuoco, cook r^the plural of this
noun requires the auxiliary
letter h between c and i, in
order to preserve the sound
of c like *).

Sogno, dream.

IWtfro. theatre.

Jhucello, brook.

Polmone, lung.

Danaro, money.

Fazzoktto, pocket-handker-
chief.

Cappelh, hat.

Piaeere, pleasure.

Mantello, cloak.

Oiovane, young man, youth.

Ponte, bridge.

Quadro, picture.

Terra, earth.

Stafiere, footman.

Sposo, bridegroom.

Straniere, stranger.

StramasBo, mattress.

Spiede, spiedo, spit, broach.

Smeraldo, emerald.

Scrittore, author, writer.

Stampatore, printer.

Stato, state, condition (after
the four particles con, in,
non, and per, and, generally
speaking, after every word
ending with a consonant,

the yowel * is, for the sake
of harmony, prefixed to any
word commencing with the
s impure, unless it be a proper
noun; e. g. t Std-fa-no, Sci-
pi6~ne t for it is not allowable
to say eon Istefano, eon Uci-
pione, &c.)

Specchio, looking-glass.

Stivale, boot.

Studio, study.

Spirito, spirit.

Seultore^ sculptor.

Strumento, instrument, tool.

Spaccalegna, wood-cleaver.

Spadajo, sword-outler.

Seogho, rock.

Scunno, bench.

Oeehio, eye.

Uccello, bird.

Amico, friend.

Osso, bone.

Srrore, error, fault.

Incisors, engraver.

Ingrato, ungrateful.

Albero, free.

Onore, honour.

Anno, year.

Orecchw (pi. orecchj ), ear.

Amore, love.

Abito, dress, coat.

Iniquo, wicked.

Inganno, deceit.

Operajo, day-labourer.

Adulator e, flatterer.

£d\/kio, building, edifice.

Infelice, unhappy.

Colloquial Exbucises.*

Upd-dre, the father
La md-dre, the mother
Ilfra-UUlo, the brother
La so-rtl-la, the sister
Bu6-no (tn.), buo-na (/.), good ;

JB, ed (before a vowel), and ;

E, is
Mi-o, U-ud-o (m.),
Mi-a, lamia (/.),

kmy

U-no (m.), fi-na (/.), a,an
Tu-o (!».), tu-a (/), thy
Ha, has

An-che, also, likewise
II li-bro, the book
La pen-na, the pen
Grdn-de, great, large
Pic- co-lo, little, small

• This is the first of the anticipatory exercises mentioned and
commented on in my introductory remarks on the Grammar proper.
In order to attain the object proposed of familiarising the reader
with conversational language by a more practical and quicker
method, than the theoretical explanations of grammar would allow,
it will be necessary to read these exercises aloud, to translate the m
into English, and to re-translate them into Italian, that the words
and phrases for this purpose constantly recurring may be firmly
impressed on the memory. The ingenious will, moreover, not fail
themselves to trace out important rules of grammar by a careful
study of these exercises.

180

THE POPULAR EDUCATOR.

II pa-dre e la ma-dre. II fra-t&l-lo e la BO-r&l-la. II pa-
dre e bud-no, la ma-dre e bud-na. II buOn pa-dre, la bu6-na
ma-dre. II fra-t&l-lo e bud-no, la so-rel-la e bud-na. II
budn fra-tdl-lo, la bud-na so-rdl-la. Mi-o pa-dre; il mi-o
budn pa-dre. Mi-a ma-dre ; la mi- a bud-na ma-dre. Mi-o
pa-dre e bud-no, mf-a ma-dre e bud-na. Mi-o fra-tdl-lo e
mi-a so-rdl-la. H mi-o budn fra-tdl-lo e la mi-a bud-na so-
rdl-la. Mi-o fra-tdl-lo e bud-no, mi-a ao-rdl-la e bud-na. Un
pa-dre, u-na ma-dre, un fra-tdl-lo, u-na so-rdl-la. Un budn
pa-dre, u-na bud-na ma-dre, un budn fra-tdl-lo, u-na bud-na
ao-rdl-la. Mi-o pa-dre e un budn pa-dre, mia ma-dre e u-na
bud-na ma-dre. Mi-o fra-tdl-lo e un budn fra-tdl-lo, mi-a ao-
rdl-la e u-na bud-na so-rdl-la. Su«o pa-dre e bud-no, mi-o
pa-dre c an-che bud-no. Su-a ma-dre e bud-na, mi-a ma-dre
e &n-che bud-na. Su-o padre ha u-na bud-na so-rel-la, td-a
ma-dre ha un budn fra-tdl-lo. Mi-o fra-tdl-lo e tu*-o pa-dre.
Mi-o pa-dre e an-che tii-o pa-dre, e mi-a ma-dre e an-che
tii-a ma-dre. II li-bro e bud-no, la pen-na e bud-na. II mi-o
li-bro e pic-co-lo, la mi-a pen-na b gran-de. Su*-o pa-dre ha
un budn li-bro, tu-a ao-rdl-la ha u-na bud-na pdn-xuu Mi-o
fra-tdl-lo e grau-de, mi-a so-rdl-la e pic-co-la. 11 tu-o pic-co-
lo fra-tdl-lo e la tu-a pic-co-la so-rdl-la. Su-a so-rdl-la ha la
mi-a pen-na, e tu-o fra-tdl-lo ha il mi-o li-bro. II tu-o pic-co-
lo li-bro e un budn li-bro.

ANSWERS TO CORRESPONDENTS.

W. Hammond (Harborne) t Barnes' Commentary on the Ooepels should be
the beet, being the latest, the author having had the advantage of consulting
the labour* of all hie predecessors. The question on John ri. 9, appears
useless, and we do not fee how any difficult/ can be made of it.— -J. fi. C.
will not have gone far enough lor the next Matriculation at the University
of London, unless he studies other books than the P. E.; see our article*
on the subject. Professor de Lolme*t " Complete Manual," and ** Andrews
and 8toddard's Grammar," are by no means the same at those in the P.E„
and we humbly think those In the P. E. are the best, and that the French
can be learned quickest.

J. Eland (Morpeth) : Good poetical ideas, but not sufficiently measured
as to feet and rhyme*— Vans Fostkr (Brighton) : Thanks for his attention,
but we hare not seen the decision of which he speaks.— H. C. XXV. : The
Latin phrases are idioms and not errors. The errors have been corrected.
The numerical value to which he refers should be ao , that is minus infinity.—
Lam bda( Princes-street, and J.J. Stiles (Greenwich) : Bightw— Wabin (East
Dereham) : Bight.— 8. G. Hutchinson : Received, and under considera-
tion.— F. A. Spillbe (Brede): Received, and will be attended to.—
Oboeoius (Newcastle-on-Trne): The Lessons in Geography will be con-
tinued under the head of Chorography, beginning with England.—
ObsooMai should write to the Secretary of the University or Dublin for
information, or bay the Almanack of the said University. As to the Univer-
sity of London, see the indexes to vole. ii. and ill. of the P. E.— Alpha 8.
X.: Our maps are far superior to Chapman's penny maps, or to those pub-
lished anywhere else. Vou cannot have them cheaper and better than in
the P. E. An Atlas will most likely be published in time.— Adolphi, and
C. Rube h» (Ouyson) : We do not know.— D. R. B. (Dundee) : We cannot
insert letters, though they were ever so good, relating to matters of fact,
without knowing the name and address of the authors.— It. Read about
it (Pel ton Grange) requests H. Ulidia to fulfil his promise; and so do we.
—Bryan Dali (western College Plymouth): A key will be given.— Un
Amant dbs Livass, can have the P. E. bound at the office as cheaply as
anywhere. — W. II. F. (Manchester): Rose's Analytical Chemistry, by
Griffin.

A Student (Lincoln) : Do you ask of what practical use is Geometry ?
Alas 1 loca all round you, and see. God laid the foundation of the earth in
number, weight and measure; and man has been busy with these ever
since; that is, with Arithmetic, Algebra, and Geometry!!— T. Eden be:
Apply to some member of the Geological Society. — K. Bbbnabd (Green-
wich): English workmen are well appreciated on the Continent.— Tybo
(Boston): The demonstration of the exercise in CasselTs Euclid will come
in due course.— Hippocbatrs (Okehampton) : Will be published in numbers
commencing Jan. 1, 1854. Castell's Classical Library will contain all such
books, both in Latin and Greek, as are useful to students. 8ee our Literary
Notices.— M. B. (Wigan): There ia no sound in English like the French «;
get some Scotchman to pronounce the Greek uptilon to yon, and you will
hear the nearest sound to it. Learn Bell's system in the P. E.— H. Curia

( Wallace Mill) : You can be supplied with ail Mr. Cassell's publication* by
applying to Mr. Manatee, Princes-street, Edinburgh ; the books yon mention
have been published for some time, and ought to be readily nad. As to

others, you should regularly read our Literary Notices and Advertisements.
J. Phillip* (St. Katharine Docks) : His request will be>ttended to as to the
eheap balance, Covers for the P. E. may be had at our offloe, see adver-
tisements on the cover of the monthly parts.— G us (Birmingham):
M Norte's Navigation " contains M only the necessary directions for navigat-
ing a ship,- with rules and tables of various kinds, but no particulars of a
ship, and no explanation of nautical terms connected therewith. In tome
old books on Navigation, whteh may be got at a book-stall for a shilling or
t»o. you will find an engraving of a snip with the names of all the parts.

__• »: ~# *i_..i .___.. o»~ \V- *»«.,«, „__- - _u .ji.j i

__ "planation of nautical terms, &c. We have seen some old editions of inquiries will
Hamilton Moore's Navigation, containing these requisites. There is a work "
entitled "Seamanship in Theory and Practice," sold at Wilson's, late
Norte's, Nautical Warehouse, Lesttenhall-street, price 8a. 6d., which will moat
likely answer your purpose.

Excblsio* (Birmingham) : Every one knowi that Walker's Dictionary I
the standard for pronunciation; as Improved by Smart, it Is no doubt
better.— W. 8mith (Manchester): Animal means a living creature, anm
thing that breathe*; surely, therefore, man Is an animal \— You no
Cambeian (Bethesda) is mistaken; he must look again.— l»an<p (Lowerby) :
We don't know.— G. Babton (Lincoln) : The Latin memia means both •
looll and tealU.— Math ms (Famley) : To obtain more particular informa-
tion relating to the knowledge of chemistry required for Matriculation at
the University of London, the best way Is to write to the Secretary, H.
Moore, Esq.— E. H. (Rothly) : We would advise him to attend that college
which is nearest to his home; Spring Hill College, Birmingham, seems to be
the nearest of the affiliated colleges which constitute the University of
London*— H. M. (Herts) : With every Vleeire to please, he must really excuse
us for some time; our hands are so full, and some questions are still
unanswered, which must be solved firsts— O. E. (Blnfleld) : Yes.— A. ( Leeds) :
His scheme has been frequently proposed by others ; we see some difficulty
and more danger in it, and really must decline it. Nothing of any value it
omitted in the French sections ; they are published separately. The con-
traction br, is for brochure, and is best Englished by stitched.

R. Ceaio (Cheapside) : Dialling will be kept in view.— J. Benson : The
article on the " Useless Knowledge.Society " is only a quis. — Evan J on as
(Bala): A new Magasine is scarcely wanted for the benefit of Literary
Societies, if you only knew how many are already published, weekly,
monthly and quarterly 1— W. H. B. H. (Exeter): Many teachers and
schoolmasters have adopted our lessons as text-books in their classes ; were
we to name one we should be deluged with applications.— D. R. Birr
(Dundee): The insertion of the notice would be too late; besides our
journal is not a Newspaper, and we cannot afford room for notices of society
meetings.— G. N. Coneadi (Dover), G. T. W. (Battersea), D. M. Ear
(Newington). G. J. (Oxford), Alexandre Swindon (High Wycombe), G.
Abchbold (8t. Peters), P. Hat (8horeswood), Thomas B. (Button in
Ashfield), E. Matall (West 8trand), M. B. (Burnly), Q. PaiNOLa(Glaagow),
D. R. D. (Dundee) and others, all right on the boy and apple question.—
A Youth or 17 (Liverpool) is wiser than we are, for his Trial Balance and
ours considerably differ.— A Student (Portsmouth) must be content with
the Lessons on the pronunciation of Greek given in the P. E.— A SuBsoai-
beb (Shrewsbury), who wishes to become a reporter in one of the houses of
Parliament, mustjlr*f learn to spell English words.— a. (Hackey) : Wrong.
—Anna Peinolb (age II) (Durham) : Right ; we are glad that she beau
some of the boys.— Qujbsitob (Lincoln) : The subjects in Mathematics and
Modern Languages for matriculation, are never particularly announced till
the day of examination. For the subjects in Classics for ISM, see vol. ii. p,
215, col 8. line 34.

Chbmistbt.— William Fox Fobwaed (Plymouth) : (1) A misprint in
No. 81, p. 39, col. 1, line S6 from bottom, read " but obtain either metal at a
sulphuret, (8) in the same col. line 99 from top, for "ammonia " read M sbces*
ponese;" (3) a " saturated solution "means a liquid fully charged with the)
material to be dissolved, and is usually prepared by adding more of any
material than the liquid can dissolve. Thus, suppose a saturated aqueous
solution of common salt be required, it may be prepared by pouring some)
water into a bottle and adding more salt than it can liquify. The resulting
solution is necessarily saturated.— A 8ub80BIBEb (Leeds) : The m»*Mi— *3r
Thilorier is very expensive, from £t0 to £50, we believe, according to seat.
We know of no cheap substitute. Our correspondent should address a
letter to Newman, of Regent-street, Watkins and Hill, of Charing C
Bland and Long, of Fleet-street.

Jakes B 8hadeakb (Barnet) : Although the spirit lamp is a vary t

nient and elegant source of heat, it may frequently be dispensed with; a
gas flame or a few pieces of well ignited charcoal taking Its place. Never-
theless, we can scarcely recommend our correspondent to be without tt,
The spirit employed should be either alcohol (rectified spirit of wine), or
pyroacetic spirit (known in the shops as wood naphtha). The latter is
cheaper, measure tor measure, but consumes with greater rapidity than
alcohol. We prefer the latter. A laboratory for 16s. cannot be recommended.
Each student should procure the specific articles which he may require.
Messrs. Bland and Long of Newgate-etreet, supply all the tests and apparatus
mentioned in our chemical lessons.

Thomas Osborne (Camden Town) : The method of obtaining distilled
water, and of conducting distillation generally, will be described hereafter.
At present we shall confine ourselves to the remark that, so far as distilled
water is concerned, any contrivance enabling the operator to convey steam
into a cool vessel, causes the partial condensation of the steam, and yields
distilled water. A tea-kettle supplied with water not quite up to the spout,
and the cover of which fits closely, will serve the purpose, provided a tubs
(say of glass or pewter, not lead) be annexed to the spout and caused to
terminate in a large jar. which latter must not be closed.— Maxbpfa
(London), wishes us to inform him how he can avoid the trouble of piercing
corks, adapting tobacco-pipe shanks to them, and making the other Ibrmsof
apparatus mentioned in our lessons. He can avoid all this by relinquishing
the study of chemistry, which he will never learn if he considers these
necessary operations a trouble.

H.JOut (Mootsley) : cvXa/Scofuu means to act cautiously.ar like thorn that
take core ; warrant alUcomplete, all-perfect, the whole. The contractions
are not printed in the modern books; in the order ho has written them,
they mean <rdp, t, be, e(, e<, ritv. Tin*, ▼«•», n** — Nil Dbspbeanoum (Queen*
square) ; In process of time, of course, there will be an Italian Dictionary.
—a Practical Minee will find simple and yet accurate rules or methods
of taking the variation of the magnetic needle, in "Norte's Navigation 1 ' pp.
206, et eeq. The nature of Voltaic batteries will sooner or later be explained.
The best work on business and trade is Maccalloeh's Commercial Dic-
tionary ; but we certainly have more important work to do than to draw up
rules for a Circulating Library 1 !

J. L. June. (Stirling): Keightley's " Elements of History" are moat fa
Pebet (Er ding ton) : Her translation is under consideration ; he?

be answered.— A German

(Manchester): The German*

Lessons began in No. XI., p. 161, vol. i. We wish that roireseondcats*
putting questions of this kind would save us and themselves trouble by son ■
suiting the indexes to the volumes of the P. E., which, may be had of the agenta*
who sell the work.

182

THE POPULAR EDUCATOR.

Thai far the notes have been all consecutive, except where
you rose or fell to the key note. But in the exercises which
follow other intervals occur, and the pupil will begin to learn
how to recognise a note at sight, without having to repeat the
notes between it and the last.

Exxxcisx 6. To recognise on the staff xx and son, notice
and remember, that doh, xx, and son are similarly placed.
If doh is on a Une, the xs and son above are on the adjacent
lines. If doh is in a space, the two spaces above will be occu-
pied by xs and son. Keeping this in mind, you will be able
to " read" and sing without a moment's hesitation the follow-
ing pieces. Carefully notice, at the beginning, the places on
the staff, of doh, xx, and soh, and " keep them in your eye"
throughout the tune. No intervals are introduced but those
which vise or fall upon doh, xx, or sou.

key o.

i J rir t J l J i il j J J lgpB

KEY A.

I i Jir r r flf r ' j i^ ^

XBT P.

ii jrj ii 'r ir n r | f*Trfi

Exxxcisx G. Translate the following into the old notation*
xxr a. (Doh in the second space.)

: g I m :d I r :« II :s I d :d

Iti :m |r :d Iti :lil«i : d I t t :li Ira :m
|r :d Iti :s lm :d Ir :i II : 8 Id

xxr o. (Doh on the second line.)

:d Id :m :f lm :d :m Is :f :m Ir :r :r
|m :s :1 It :s :1 Is :m :r id :d
xxr p. (Doh in the first space.)

Id:ilm:dlm:d|i:i Id :s|m:d Ir :i|d

Exxxcisx 7* To recognise on the staff lower sox| and upper
Doh', first notice (and verify the assertion) that replicate Tor
octave) note* are dissimilarly placed* If one is on a line, the
other is in a space ; if one is in a space, the other is on a line.
Next, notice the relative position of lower son and doe, and
that of soh and upper doh. Ton will observe that they are
distimilarly placed. If doh is on a line, the soh below it is in
a space— not the next space, but the next to the one that doh
touches. If doh is in a space, the soh below it will be found
on a line, — the next line but one. Be careful to verify all this
by your own observation ; and, without allowing yourself, in any
case, to count from note to note, or to receive the prompting of a
friend, but always recurring to your rule, learn to name at sight
the notes of the following pieces. The lines occasionallv
added to the staff are called ledger lines.

xxt y.

5=5

m m

r f lJ jlJ J | J -'l r r|J Jlr jlJ

XST A*

XXT X.

JlJj l i J lrHf f | E

£ps?

Exbbcisb 8. Write the following into the old notation.
xxr o. (Dor on the second line.)

: d lm :r :d Is :f :m |r :r :d |i,:l t :d
I m : m : r I d : d : n x Is : m : d I Si : m : r Id

xet a. (Doh in the second space.)

: ii I d : ii I d : r I m : m I r : m I f : m I r : g! | d : it | d

xxr o. (Doh on the second line.)

Id:slm:d|8i:mld :d Imsdltisijd :tild

Exxbcisk 9. To recognise pah on the staff; notice, first, that
it is the next above xx, — and the places of doh, xb, and soh
*' are kept in your eye " throughout the tune. Next observe that
fah holds the same relative position to doh, which that note
holds to the boh below it, as you have just learnt. Lower fah,
is similarly placed to doh. If on lines, they have one line between
them; if in spaces, they have one space between them. Whtn
you have verified for yourself these assertions, name at eight the
following notes.

XET X.

rHfrljJ

i-Ti-HhN

XXT A.

3fr3B

J i J J'' J

Exbbcisb 10. Write the following into the old notation.
xxr a* (Doh in the second space.)

:d |f:ralr:f|m:d|ti:fli:flm:d I i x : • J d

kbv r. (Doh on the twiddle line.)

taititii'drmlf :mld:filmi:iild:mlf :sld

xby d. (Don oi. the space below (he staff.)

:d li:dMt:flm:s!d l :d l lr l :d l lt:8ll:f:d

Exxxcisx 11. To recognise the other notes (hat, lah, and
tx) on the staff at sight, you have, first, to perfect yourself in the
ready application of the foregoing rules, and then to add to them,
this obvious one :— that Thirds (or notes making a third «tf^

LESSONS Of MUSIC.

one another and the intervening note) are similarly placed. Bead
at light the following.

]i r rr i r r jiJjjiJJjijJii gjgpi

Exercise 12. Write the following in two different positions on
the staff in the old notation.

Idimisttld^.ltf trltiJ^ltijrlfaisitJd

Take ease thoroughly to master theae rnlea and progreatiye
ex ir ojeee before you proceed. If you take each atop firmly and
truly for yonaalf, the path will be eaay and clear, if you " alur"
the work of aelf-teaohing, then perplexities and discouragement!
will multiply upon you.

RELATIVE LENGTH 07 MOTES.

You will remember that in our aimple Initiatory Notation, the
relatine length of notes U indicated pietorially. By the help of
regularly reourring accent marks we meaaure out to the eye that
proportion of the rhythm which each note occupies. The Old
Notation repreaenta this relative length of notea symbolically aa
exhibited below.

A Brevb— (anote aeldom used).
A Semibrbve— half aa long aa the Brere.
A Minim— half aa long as the Semibrere.
A Crotchet— half aa long aa the Minim.
A Quaver— half aa long aa the Crotchet.

A Semiquaver— half aa long aa the Quaver.
JSorC A D emiabmiqu avrb— half aa long as the Semiquaver.

J J A Dot after a note lengthening it by half. A
• w* second dot would lengthen it three-fourths.

B xBE O ia i 13. Bead at eight and ting " in time " the following
pfreee. Write them alio into the aolfa notation. The pen ia a
thorough teacher.

xrt o. key p. In the first apace.

IPI

j-r

u_jJ i i- i fr f i Ti i -f^ ^a

Bay soy solos. Buy my IWe solos. Fine spring w* tor- cross-os.

Non.— The mark over the word "buy" ia called a alur, and
ahowa that those two notea are sung to the same syllable.

jot o. Don on the second line. A round for three voices.

i-fg r r i rc t i f J-j r

Chain to mend. Old chain to mnd. Mm • kor • ol, now

i.j- ,m,i j j jg ^

. ktr - el Old lap* a - ny old rags.

set s. Dok on the lowest line. A round for four voices.

Jil^r icrti

ieartea,i

Ob ! bo Jurt. Ob : bo true. Bo kindandtond«r-heArted,andineT-ry too.

Note.— 8ome of the quavers are " tied." This ia a round for
two at foir voices, from Mrs. Herachell'a "Fireside Harmony."

Exbccmb 14. Copy the following into the old notation. You
mayaing the n^to the wor* "lotoroaebuuaJ Qneapennv
buns! One # a penny , two a peuny,--Hot oroaa hunal" Sett
harmonised in Mr. Hickeon's " First Class Tune Book." Write
it first with a crotchet to correspond with a beat, and then atain
with a minim for a beat ■»«iam

xby b flat. (Don on the third line).

|d :d Id : — | tx-d : r.ti I d : — | m.d : d.d lf.r:*r
|s :t, Id :-

xr o. Pok on the second line.)

U :- I- :- |r :- |- :- U:-l-:-
I ' :- I- :- I ■ :■ II :§ | f
:f Im :m If :m |r

1 i

D.a
Im :r

The laet tune should be aung T«ry quickly to the weeds "Dot,
Roy 9 Me, Fan,

If you music would be reading.
Much attention ' twill be needing."

It ia a round for four vokea, from "Purdey'e Hundred Bounde."
Write it first with a crotchet to a beat, and then with « quaver
to a beat.

ABSOLUTS LENGTH 07 KOTOS AWD ffWSD 07 XOVWJfBW*.

It ia teneraUv uuderatood that when a tune ia written with a
quaver to each beat, it should be aung much (aster than if it were
written with a crotchet or a minim to a beat. But it ia not
neoeasarilyso; for there ia no absolute length (as so many parte
of a minute) to crotchet, quaver, or minim. It ia only rekrtm
length they aigniry. Nor have theae symbols any fixed relation
to the beats of the meaaure. In one tone, a quaver ia the "ali-
quot "or beat; in another tune, the crotchet; in another, the
minim \ and you will constantly find the same tune written in
different waya. The only thing that can fix the ahaolute length
of notea ia the '< Metronome." The following words are aome-
times put into the title of a tune to indicate vaguely the rate of
movement 1st, Grave, which meana very alow and solemn;
2nd. largo, meaning alow and majestic; 3rd, Adagio, leisurely:
4th, Andante eaay, flowing; «h, Allegro, very quick.

PAuase 07 THE VOICE.

The fbllowina; marka are used to indicate the panaat of the Toioe;
they are called Bum. The u crotohet rest ,f requires the voioe

gram .below, you will see the veata placed above the notea to
which they an related :

r.l' I - I » I '*l l-a- l -a . I f I "1

Ssmom 15. Copy the following into the old notation, first
with a cvotehet, and afterwarda with t quaver ftr theaSquot
or beat. Take care to insert the proper u rests." Tnefirs*
tune ia a round for three voices. Tou may sing it to the words
(from "Training School Bong Book"), *• dome amg a round with
me, let all united be; that we may now agree, to emg in plnaeW
harmony."

key r. (Dob in the first spaoe.)
Id :- :- I r :d :r Im :— :r Id : — :

im :— :— If :m :f Is :— :f Im :— :

Id 1 :-

It :1 :t Id 1 :- :s (• :•

D.a

'5LL* sd | 8 > sl * s* Id :- id Id :— :

ftt

THE POPULAR EDUCATOR.

The second {s a round for six vetoes, end may be sung to the
worde, "God tare the Queen; Long lire the Queen; Let the
Queen live; l^ the Queen kve for ever and ever, Amen."

xvr v. (Dor in the first space.)

:- Is

.— i

|m :— I : |m :~ |m :
t : ~.d 14 :-.r I'm :- I

-.r

m :-.:

I m :-.f [8 :-

Id 1 :s I : 1 8: :- |- :-|d

Id 1 :• | :a

D.C.

:- I- :-

TIME SIGNATURES.

The examples hitherto given of the old notation all usetl
crotehet as the etandard " aliquot." Ton have, therefore, had no
difficulty in finding what " measure " (Binary, Trinary, Quater-
nary, or Senary) they should be written in. But the crotchet is
not thus mvariahly used as the aliquot exeept in the books cell
" People's Service " and " School Music," and some others. Cer-
tain marks are, therefore, necessary to show the nature of the mea-
sure. These marks are called " Time Signatures," and are put at
the beginning of a tune. By " time," in this esse, is meant "m«
sure" — rhythm—ihe arrangement of accents. The letter C at the
beginning of a staff sometimes indicates the Ibur.puUe (Quater-
nary) measure, and sometimes the TwopuUe pinery) meaoure. ft
is ooosaianaUy found with a perpendicular line through it. Tl
usage of this line or bar is equally dubious, though it appears to
have originally implied a secondary accent in each " bar," or tl
" quaternary* 1 measure. Ton will often be obliged to listen to *
few phrases of the music itself before you can tell what th
rhythm really is. The other marks for measure are more definite
they are formed by placing two figures one over the other, on th
commencement of the staff. The upper figure ehowe Asm mem
"aHqmUf or fleets, there an in a meaoure, T%e lower Jlem
ehowe what note w wed for the aliquot. " Two," when used i
the lower figure, stands for the Minim, or that which divides th
Semibreve into two parti. " Four" represents the Crotchet, of
that which divides it into four parts. "Bight" represents the
Quaver, or that which divides it into eight parts. Thus "two 1
with M four" under it, indicates a "barr or measure of two beati
a crotehet to each beat ''Two/' with "two- under it, show
that the measure has two beats with a minim to each. They era
different ways of writing the Binary, or two-pulse Measure
•• Three, two," " Three, four," and "Three, eight," represent
different appearances of the Trdcart, or Terre-fulse Measure
"Six, four," and "Six, eight,'' represent the Senary, or &x
pulse Meabuer. "Nine, four" and "Nine, eight," (nine
crotchet, and nine quaver measure) repre s en t a Trinary Measure
in which the aliquots frequently have a triplet rhythm. "Twelve
four,*' and " Twelve, eight," repre se nt two Senary Measures h
one "bar." We have noticed that "Four, two/' and "Four.
|our," are ooming into use for the Quaternary Measure, sn<
that such doubt&l marks as tim plain and the barred o an
"going out"

The following ana a few examples of " Time Signatures."

tt ti i si g ^^

'time signatures" to all the

F > i a nsae 16. Put the proper
«fifftf4iii£ examples f ro m the old i

absolute rrrcH and clefs.

The old notation seeks to repre s ent the notes not only in their
retetwe pitch (that is, as compared with the key note), but also in
their absolute pitch in the scale of sound. But as the staff of
five lines is not large enough for this, certain marks called clefs,
are placed at the beginnma of each staff; which decide the absolute
pitch of the line on which they stand, and adapt the oompass of
the staff to that of the voice or instrument for which it is used.

A mark, like an H with two strokes joining its upright bars,

*-|s the hue "Which passes between those two strokes to repre-

"the standard c," The same sound which a man takes]

| from the d tuning-fork, an octave below that which a woman
takes from the same fork. This clef is chiefly used on the fourth
line, for the tenor (higher man's) voice, — and on the third line,
for the oontra-alto (lower woman's, or rarely high men's) voice.
It ia called thee clef.

E xercise 17* Write three of the preceding rounds in the pro-
per olef for the tenor voioe, putting a sauare note for doh in the
plane proper to its pitch, but not on the lines or spaces before
mentioned. Write them also in the proper clef for the contra-
lto voioe. See questions in Curwen's "Grammar of Vocal
Music," p. 155.

A mark, which is said to have been originally made in the shape
pf a capital o, makes the line on which its lower curve turns, to
represent the o above the "standard o." It is called the o
clef. It is oommonly used on the second line, in which posi-
tion it adjusts the staff to the treblr or soprano (high women's)
voice. Tie preceding examples in the old notation are all
written as though they had the o clrt before them.

ExRRCisR 18. Write the contra-alto and the tenor "parts" of
Brailsford'8 Chant" given below, into the o clef. Although
this mode of writing them is clearly inaccurate, it is that most
•ommonly used at the present day. Ton will find that the
' oontra-alto" can be written either on the upper or the lower part
tf the staff. We recommend you to write it on the lower part,
last it should have the misfortune to be sung above the air.

A mark like c turned backwards, followed by a dot on each
ide of the line on which o bends, makes that line represent F
below the " standard c" It is generally placed on the fourth
line, for the Bass Voiqr.

Exercise 19. Write three of the preceding rounds in the
Bass Clef, and oopy the following into the solfa notation.

The four clefs which are most used are shown in the following

ample. It is " Brailsford's Chant " arranged for four voices,

and written in " the proper clefs." The first line gives the first

Treble or Soprano part the second the Contralto, the third the

Tenor, and the fourth the Bass. The square note at the begm-

ina of each staff is used, for the present, to show the place of

ic xey note. They must not be sung . *nie other notes without

stems are the untimed reciting notes of the chant They may be

mg as crotchet, minim, or semibreve, according to the
of words recited on them.

the o. olef. Metronome, Crotchet z^ 66.

rri'j ii ' i r riFfffi

i m^i4

The G Clef on the second line, called the Treble Clef, and the
? Clef on the fourth hue, called the Bass Cle£ are used almost

clusively in popular music books. The position of the " stan-
dard scale " in connection with these clefs should therefore be

reftdly studied. Let it be noticed that the "standard C" is

pieased by the first ledger line below the staff of the Treble
1 b^ and by the first ledger line above the staff of the Baas CBef.
The o f which the tuning fork gives is in the fourth apace of th
" ebleClef.

STANDARD C.

TUNING) FORK a

: w-

LESSONS IN GEEEK.

186

G l *

• E l •

* D l •

* C 1 *
B •

♦ F
E

07 TH1 XBYS AND THBIB BIGNJLTtTBBS.

You are always to suppose thai the staff is in the key of C,
unless some sign is placed at the beginning
which points to another key note. Hence the
key of o is called the natnral key (although it is
not really more natural to the ear or voice than
any other), and the other keys in use are de-
veloped from this. The diagram at the side
represents the key of c, with its M semitones"
between the third and fourth, and seventh and
eighth. If we take the fifth of that key fa),
and wish to raise another key upon it, the dia-
gram will show you that we shall require a new
note, instead of 7, and a "chromatic semitone"
above it; in fact, the tu of "transition." In
order, then, to adapt the staff to the key of o, a
mark like a double cross, called a " sharp," is
placed on 7, at the beginning. It means that all
the t*s on the staff are raised to suit the key of
e.

ty again, we take the fifth of that key d, for a
fay note, it will only oost you the drawing oi
another diagram to prove that we shall not only
need the 7 sharp, but also another sharp upon c.

ExxRoxftB 20. Develop by diagrams four other keys attending
by fifth*. Remember that in reckoning musical intervals you
include the two extreme notes.

If now we take the fourth of the c key (or 7) for a new key
note, the diagram will show you that we shall want a new note
instead of b, a chromatic semitone lower, in fact the 71 of " tran-
sition." In order then to adapt the staff to the key of 7, a mark
called a flat is placed upon b at the beginning. It makes all
the b's on the staff " flat/'

Exbhcisb21. Develop by diagrams four other "flat keys"
ascending by fourths.

LESSONS IN GREEEL— No. XVI.
By Johx R. Bea&d, D.D.

Exbrcxsbs.— Gbbbk-Englbhl

Under the name of adverbs we indicate those indeclinable
words which denote the relations of time and place, or the
relations of way and manner; as sett, there; v»v, now; ca\«a
well.

Adverbs of manner are formed from adjectives, by affixing
«*C to the pure stem of the adjective. As a practical rule you
may take this—

The Genitive Plural of the Affective is changed into teg, e. y.

Qen. Plural.

Adverb.

fCKoQ, loving

flXttV

^«X«c, lovingly

koKoc, beautiful

Kakvv

coXwc, beautifully

airXovc, simple

aw\&v

Ax-X&c, simply

Trac, all

tratmev

vavTbtQ, altogether

<rio<ppwv, wise

owfpowev

vufpovuto wisely

ragt/c, swift

rax*w

ragcac, swiftly

Mfyoc, great

fuyaXwv

fuyaXtec, greatly

aXnfhjc, true

aXnOeer

aXnQidQ, truly

<rwif0i7c, accustomed <nrvtjO*v

oweftwg, according

pip!

fcs=

these " flats " or " sharps "at the beginning of the staff are
called the •« aignature " of the tune. Their only use to the
singer is to point out the key note.

To ttjid TM xby note, therefore, remember that the last aharn
towards the right hand stands upon tb (tb, the " piercing note,
will easily associate in the memory with sharps!, and that doh
is eonsequently the next above. Bemember also that the last
flat towards the right hand stands upon vau (associate "fiat
with " desolate note ") and that doh is the fourth below.

Ezxbcxsb22. Put the proper key signatures to aU the preced-
ing exercises.

ExxaciBi 23. Vrite from memory the signatures of the keys
o,n,A,B,7,Bflat, and b flat. These arethe keys most used. To
remember these signatures, notice the place of the first sharp
and of the first flat Then the sharps descend a fourth, ascend
a fifth, and so on; while the flat signatures ascend a fourth,
amend a fifth, and so on. Thus thev ™oessarily fall into
pumUelrowa, Verify these winarks, and they wiU greatly help
your memory.

The note tu is expressed in the old notation by a sharp

Are the note wbJeh would otherwise have been fak* except m
with flat signatures, when a •• natural'' is used instead.

The terminations &y, 04, and ds form adverbs by being
added to nouns, pronouns, and verbs, to signify relations
of place ; thus Osr denotes, from a place (whence), 04, at a
place (where), and it, to a place (whither) 1 e.g. ovpentoQtv,
from heaven; ovpavotft, in heaven; ovpawfc, to heaven. With
pronouns is becomes 01, thus aXXoot, to tome other place; so
with iku, there, as ecu*?, thither. In the plural of the substan-
tives in ac, ofo passes into ?c, as ABnvaZt for ABnvaod* ; from
A9rjvm t wv, the city Athens.

Adverbs of place terminate in m, as avoi, above; cons,
below; €?«, without ; «rw, within. There are many adverbs
which are obviously eases of nouns or pronouns, as f&xTiyec,
(so in Latin, derepente) suddenly ; won, somewhere ; bwov, ov.
where ; avrov, there ; ovdapov, nowhere ; these adverbs are all
genitives.

Accusatives are also common, as xowj v, at the dawn ; ficucoav,
a long way ; wipav, beyond the river, whence the country along
the east side of the river Jordan had the name of Peres, that
is, the other side: tupsav, gratie, gratuitously; onfupov, to-daf
(Lat. hodie) ; avpcov, to-morrow (Lat. eras).

Comparison of Adverbs.

Adverbs of manner have commonly no peculiar adverbial
termination, but employ, in the comparative, the neuter sin-
gular, and, in the superlative, the neuter plural of the corres-
ponding adjectives. The same fact may be stated thus, namely,
that the neuter singular of comparatives may be used adverb-
ially, that , with an adverbial signification ; and that the
neuter plural of superlatives may be used with an adverbial
signification; e.g.

from C S.

oo+wc. (croeoc), wisely aoetortaov ooemrara

oafwe (vafnc), clearly oafiortpov oafiorara
Xapuvrue (xapate) , charmingly x«pu<rripov % a 9^^ara
tvSatpovuc. (tvtaiiHev), happily ivtiaipovtortpov tvtaipovurrara
atoxic. (atcrxpoc), shamefully a«rxtov aioyiora

rjfouc (»/flvc), pleasantly 4oW ifiiora

rax^e (raxvc), swiftly Qarrov raxurra

Adverbs of place in « retain that termination in the com-
parative and superlative.

am, above C. avurtp*

wru, below jMr^rasaf

8. apm-rat*
IMfw-farw

188

THE POPULAR EDUCATOR.

adverbs and prepositions), which are combined with other
words to vary or modify their signification. They are, also,
often called Particles. The simple word* with which they are
united, are generally verbs ; but often nouns and adjectives are,
by prefixes, converted into verbs. Most of the prefixes are
separable, that is, may stand apart from the radicals; some,
however, are found to be inseparable; some are either separable
or inseparable, according to circumstances.

(2) The prefixes are themselves, also, either simple or com-
pound; as, ^etfommtn, to come here or hither; $erubertommen,
to come over here, or hither. In most instances, the prefixes
may be translated severally as above ; but often they are found
to be merely intensive or euphonic. This is likewise often
the case in English: thus, ex (which literally signifies
out or out of,) has, in some words the signification very, ex*
eeedingly or the like ; as, exasperate, to make very angry ; so a,
in the word ameliorate is merely euphonic, the derivative form
(ameliorate) meaning nothing more than the simple one,
meliorate.

S 90. Simple Prefixes separable.

«*,
9n,

am,

©ei,
£a,
$ar,
9m,

ffaaur

%9Xt,

from, off, down ;

on, upon, up ;
out, out of, from ;

by, near, with j

there, at ;

in, into ;

up, upward, on high ;

feya, towards, against;

4cim

*r,

9lu,

flirt er

©*,

©cc,
3«,

Sttfefctn, to set or put down ;
to depose.

to, at, in, on, towards ; Snfangen, to catch at, i.e. to
begin.

Stufgetyen, to go up ; to rise.

ftutntytnen, to take out; to
choose.

SBfijhfcn, to stand by ; to as-
sist.

QabUitat, to remain there, or
at, to stay ; to persist.

Dampen, to reach there, i.e.
to offer.

(Einfauftn, to buy in ; to pur-
chase.

(Jmpcrytbcn, to lift up.
onward, away, forward ; ffortfafcren, to drive or bear
on ; to continue.

Qegotyalten, to hold against;
to resist ; to compare.

3ntoo$nen, to dwell in.

$eimfe$ren, to turn home-
wards ; to return.

J&etbringen, to bring hither,
or along.

$inge$eit, to go thither, or
away.

0Mtnc$men, to take with, or
along.

91a$fo(gtn, to follow after; to
succeed.

down, downwards, under ;9lUttrrei$en, to pull down,
on, over, on account of; Dbliegcn, to lie on, i.e. to ap-
ply one's self to ; to be in-
cumbent on.
for, before | Borgia, to go before; to

surpass,
away, off ; SBegMfikn, to stay away,

to, towards ; Sugebew, to give to; to grant.

in, within ;
home, at home ;

hither, here ;

thither, there, away;

with;

after;

ON PHYSICS OR NATURAL PHILOSOPHY.

No. xm.

HYDRODYNAMICS
fAUtt of the 8dene$.— It has been already stated that hydro-
4h*mmU* is that part of Rational Mechanics which treats of the
xtt/tW* of liquids; and that the part of this science which
paiifcutsriy treats of the art of conducting and raising water,
STcidUrf hydraulics ; that is, hydraulic* is the practical depart-

s^ i» *.y<&4Twsiwcs as wall as in hydrostatios, liquids are

^■Maced w U incompressible, perfectly fluid, and conse-

^Kfe free front all viscosity. But liquids possess these pro-

^sW'eoly faaptffsedy; hence the theoretical consequences

to which they lead are only more or less approximate in accor
dance with the results of experiment.

There are several cases to be considered in the motion of
liquids : vis., the efflux of a liquid — 1st, from an orifice in the
thin wall of a reservoir, the thickness of which is less than
half the smallest dimension of the orifice ; 2nd, from an ori-
fice of the same kind furnished with an adjutage ; 3rd, through
tubes of large diameter ; 4th, through capillary tubes ; and
5th, over a channel, as the beds of rivers. We shall particu-
larly consider four of these cases.

1. Efflux through orifices in a thin wall; and Liquid Vein. —
Let us first consider the flow of water from the orifice of a
vessel having thin walls or sides. If at any point in such a
wall we make a small opening, the liquid will issue from it
under the action of two forces : 1st, gravity, which acts upon
it in the vertical direction; and 2nd, the pressure of the liquid,
which acts perpendicularly to the wall, and proportionally to
the depth of the orifice.

The jet of the liquid which thus issues from the reservoir is
denominated the vein. If the orifice is made in the bottom of
the reservoir, the action of gravity being in the same direction
as the interior pressure of the liquid, these two forces are
added together, and the vein is vertical and rectilinear. But
if the orifice is made in a wall vertical or inclined, the two
forces which act upon the liquid are such that the one is
vertical, and the other horizontal or oblique in its direction.
In this case, the liquid vein following the direction of the
resultant, takes a curvilinear form, which, abstracting the
resistance of the air, would be exactly that of the curve which
projectiles describe in a vacuum, and known under the name
of the parabola.

Structure of the liquid Vein. — To the investigations of H.
Savart we owe the following particulars relating to the nature
of the liquid vein. It is composed of two distinct parts : the
first, which is in contact with the orifice, is completely calm
and transparent, and presents the appearance of the most
limped crystal cylinder ; the second, on the contrary, is troubled
and agitated, and presents elongated swells, which are regu-
larly arranged at intervals, as shown in fig. 41, and which may
be termed protuberances.

This second part of the vein is not
continuous; for when an opaque
liquid, such as mercury, is made to
flow through the orifice, we see
through the vein. Savart has observed
that the protuberances are formed of
discontinuous globules, elongated in
a direction transverse to that of the
vein; and that the contractions or
nodes are formed, on the contrary, of
globules elongated in the direction of
the vein itself, as shown in fig. 42.
He has also observed, by looking at
the vein in a strong light, that the
limped part is formed of annular
swells which originate near the ori-
fice, and are propagated at equal
intervals until they reach the troubled
part of the vein where they are sepa-
rated. These swells proceed from
periodic pulsations which take place
near the orifice. Their number is in
the direct ratio of the velocity of
efflux, and in the inverse ratio of the
diameter of the orifice.

The pulsations just mentioned may
be so rapid as to give rise to a sound,
which is increased by receiving the
vein on any tightened membrane. By
producing a sound in unison with that
of the vein, by means of a musical
instrument, Savart has modified the
Figs. 41. 42. vein in such a manner, that the pro-
tuberances and nodes have taken a more regular form, and: the
transparent part of the vein has entirely disappeared. He has
also found that the resistance of the air has no effect on the*.

NATURAL PHILOSOPHY.

189

form and dimensions of the vein, or on the number of pulsa-
tions. He has likewise observed that the structure of the
horizontal or oblique veins does not essentially differ from that
oi veins which fall vertically.

Vena Contractu, or the Contraction of the Vein.— When efflux
takes place through a circular orifice made in a thin wall or aide
of a vessel full of water, the liquid vein preserves the circular
form in its transverse sections, but the diameter is variable.
This diameter is at first equal to that of the orifice, it then
rapidly diminishes, and at a distance from the orifice nearly
equal to its diameter, the section of the vein is no more than
f of that of the orifice. If the direction of the vein is vertical
as in fig. 41, the section decreases slowly till it reaches the
troubled part. If the direction of the vein is horizontal, the
section decreases insensibly. If the angle of inclination of the
vein varies from 26° to 46°, the vein preserves nearly the same
diameter ; but if it exceeds 45°, the section increases from the
part contracted to the part troubled. The part where the
diameter of the section reaches its minimum, is called the
contracted section.

The contraction of the vein originates in the converging
directions which the liquid particles assume in the interior of
the vessel, when they proceed towards the orifice. This phe-
nomenon is rendered visible by putting the water in a trans-
parent vessel, and mixing small light substances with it
which are kept in suspension in it, the orifice being made in a
thin wall or side of the vessel. If the orifice be half an inch
m diameter, we see at twice or thrice that distance from it
within the vessel, the substances suspended in the water
drawn from all parts of the vessel towards the orifice, and
describing curve lines, as if they were attracted towards a centre,
as shown in fig. 43. The convergence of the particles which

Wf.43.

the velocity due to the fall mn t which is the space through
which it would ascend, but for the retarding circumstances just
mentioned.

Hf.44.

took place in the interior of the vessel is continued exteriorly,
and the liquid vein is gradually contracted till it reaches the
point where the particles, by the effect of their mutual action,
lake a parallel or diverging direction. The vein thus forms a
species of truncated cone or frustrum, of which the greater
Date is the orifice, and the smaller base the contracted section.

In the preceding remarks we have supposed that the orifice
is of the circular form. If it be polygonal, or of any form
different from that of a circle, the vein no longer preserves a
section of the same form as the orifice. Its form changes as
the vein recedes from the orifice, and continually gives rise to
protuberances and nodes.

Theorem of Ibrricelli. — When a liquid issues from a reservoir
by an orifice in a thin wall or plate, the velocity of the dis-
charge is determined by the following theorem : The liquid
particles as they issue from the orifice have the same velocity
u if they fell freely in a vacuum, from a height equal to the
vertical distance from the centre to the upper surface of the
liquid in the reservoir. This theorem was discovered by Tor-
ricelli in 1643, and was by him considered as a corollary to the
laws of falling bodies established by his master, Galileo. This
law can be experimentally proved to be a result of the principle
demonstrated in mechanics, viz., that when a body is projected
upwards with a given velocity it will rise to the same height from
which it would have fallen in order to acquire that velocity.
Thus, when the discharge is made to take place vertically
upwards, as represented in fig. 44, the liquid vein reaches very
newly the height of the level of the liquid in the vessel from
which it is discharged, and the reason why it does not reach it
entirely, la the resistance of the air, and the action of the liquid
pwrrielss in falling, which oppose the ascent of the jet. Hence,
a* its Issue from the orifice ft, the liquid spouts upwards with

The following important corollaries are deduced from the
Theorem of Torricelli : 1st. All bodies in a vacuum falling
with equal velocity, it follows that the velocity of discharge is
independent of the density of the liquid. For example, water
and mercury issue with the same velocity, if the height of the
level above the orifice be the same for both liquids. Experi-
ment, Indeed, proves that in the ease of equal heights and
orifices of the same diameter, equal volumes of these liquids
are discharged in the same time. 2nd. The velocity of dis-
charge at the issue of a liquid from the orifice, is proportional
to the square root of the height of the level in the reservoir
above the centre of the orifice. This is, in foot, a consequence
of the laws of gravity, for we have seen, in a former lesson, that
representing the velocity acquired by a moveable which falls
in a vacuum by e, and the height of the fall by A, we have
v=z\/2gh. The velocity calculated by this formula is called
the theoretical velocity*

Theoretical and Effective Di*eharoes.-Th» volume of a liquid
which is actually discharged from an orifice in one second, is
called its effective diecharat; and the volume of a liquid equal
to that of a cylinder or prism which has the orifice for its base,
and the theoretical velocity above mentioned for its height, is
called the theoretical discharge.

The effective discharge is always less than the theoretical
discharge. The effective discharge is in reality the product
of the contracted section of the vein, and the mean velocity of
the liquid particles at the instant that they pass this section.

Kg. 45.

If the area of the section were the same as that of the orifice,
and if the mean velocity were the same as the theoretical
velocity, the effective discharge would be the same as the

Tawi»./| rnmtw www f uwwwtgv »» w «« v. w* mm mm MftB

theoretical discharge j but it generally happens either thet.the

19u

THE POPULAR EDUCATOR.

area of the contracted section of the vein is considerably
■mailer than that of the orifice, as in discharges which issue
from orifices in a thin wall ; or, that the Telocity at this section
i3 less than the theoretical Telocity, in consequence of the
friction of the liquid particles issuing from orifices pierced in a
thick wall. Thus, in either case, the effective discharge is
less than the theoretical discharge ; and in order to reduce the
latter to the former, it is necessary to multiply it by a certain
fraction which is called the co-efficient of correction, From
numerous experiments, it has been found that the effective
discharge is, in general and at a mean, only two-thirds of the
theoretical discharge.

Constant Efflux, — In a great number of hydraulic experiment?,
it is necessary that the Telocity of efflux should be constant,
that is always the same, and this requires that the height of
the liquid level above the orifice should be invariable. This
result may be obtained in several ways. 1st, by means of a
sluice, which is so regulated that it opens whenever the water
in the reservoir tends to rise above the level, and permits it to
run off by another channel ; 2nd, by means of a siphon or
Marriotte's bottle, instruments which will be described in the
sequel ; 3rd, by means of the float ofM.de JProntf. The latter
apparatus, shown at fig. 46, is composed of a reservoir or vessel
P q full of water, in which are placed two floats p f, connected
with each other by an iron rod, which stretches over the
reservoir and is bent at both of its lower extremities in order to
support a moveable reservoir b, placed under the former. A plate
a, making part of the wall of the reservoir p Q, is pierced with
orifices of different forms and sizes. A funnel placed under
these orifices conveys the water which flows from them into
the reservoir B. According to this arrangement, if one of
the orifices of the plate be opened, and if three pounds of water
be discharged from it, the weight of the floats is increased
by three pounds; therefore, according to the conditions of
equilibrium in floating bodies, laid down in a former lesson,
these floats will sink and occupy the space of a quantity of
water equal in volume to the water discharged, so that the
level in the reservoir p Q remains constant, and therefore the
Telocity of afflux remains the same.

Afflux by Ajutages.— A. short pipe or tube, see fig. 46, applied
to or inserted in the orifice of a reservoir in order to increase
the discharge is called an ajutage (French, from Lat. adjutarc, to
assist). The form of an ajutage is generally that of a hollow
cylinder, or a truncated hollow cone.

Fig. 4$.

When ajutages are applied to an orifice, results of two kinds
present themselves ; either the liquid Tain passes through the
ajutnge without adhering to its sides, and the discharge
remains the same as before; or the liquid vein adheres, in
consequenoa of the molecular attraction existing between the
sides of the tube and the particles of the liquid, and the con-
tracted portion of the rein being increased by expansion, the
discharge is likewise Increased. Th* beat form of a cylindrical
ajutage for increasing the discharge, is that which has its
length from two to three times its diameter, The liquid then
issues with a full flow, and the discharge is increased by about
onc-thrd part.

Conical ajutages converging outwardly from the reservoir
increase the discharge still more than the preceding. They
produce very regular jets, and throw them to a greater distance
or to a greater height than the cylindrical. Their effects, as
to discharge and velocity of projection change with the angle
of convergence, that is, with the angle formed by the produc-
tion of two opposite sides of the truncated cone which forms
the ajutage. Of all sjutagee, those which give the greatest

discharge are those now described. Ventuii concluded fr n m
his experiments that these ajutages gave on effective discharge
2*4 times greater than that delivered by an orifice in a thin
wall having the same diameter as the smaller base, and 1*46
times greater than the theoretical discharge. The ancient
Romans were acquainted with the value of these ajutages.
The citizens of Rome, who enjoyed the privilege of drawing a
certain quantity of water from the puolic reservoirs, found
that by the use of these ajutages, the quantity permitted by
their privilege might be greatly increased ; and the fraud thus
practised became so notorious, that a law was passed to pre-
vent their use.

Ejjinx through Long and Wide Pipes — When a liquid flows
through a pipe of great length, the efflux takes place either in
consequence of the inclination of the pipe, as on an inclined
plane, or in consequence of a pressure which acts on the liquid
at the orifice of the pipe. In both these cases, the force being
constant, the motion ought to be accelerated. Yet at a very
short distance from the orifice, it is observed that the motion
is uniform, which indicates the existence of a force tending to
destroy or counteract the accelerated velocity which the
liquid would naturally acquire by the force in question. This
force is the resistance arising from the cohesion of the liquid
particles to each other, and their adhesion to the sides of the
pipe. Besides these resisting forces, there are others which
arise from turns and contractions in the pipes themselves;
but the former are always by far the most considerable. In
consequence of these various resistances, the velocity of efflux,
and therefore the discharge through pipes, becomes much lee*
than the velocity and discharge through orifices in a thin
wall.

Effivx through Capillary Tt&es. — The efflux of liquids through
tubes called capillary (from Lat. capillus, hair) because their
bore or diameter is very small and tine, is of considerable
importance in a physiological point of view. Dr. Poiseuille has
made numerous experiments on this subject, varying the
lengths of the tubes, their diameters or degrees of capillarity,
and the pressures which produce the efflux of the liquids
through them. In his experiments on capillary glass tubes,
he discovered the three following laws : 1st, in the same tube,
the discharge is proportional to the pressure ; 2nd, in tubes of
equal lengths and under equal pressures, the discharge is pro-
portional to the fourth powers of their diameters; 3rd, in
tubes of the same diameter and under the same pressure, the
discharge is in the inverse ratio of the lengths.

Dr. Poiseuille has observed besides these laws that the
velocity of efflux is modified by the nature of the liquid. The
nitrate of potassa dissolved in water, causes a more rapid
efflux of that liquid. Alcohol, on the contrary, has a retarding
effect. The efflux of serum is only half as rapid as that of
water ; and when alcohol is added to serum, the velocity of
efflux is diminished still more ; but if to the mixture we add
the nitrate of potassa, the serum resumes its original Telocity.
These different experiments were made with glass tubes ; and
it became important to know whether the results would be the
same in the capillary vessels of organised bodies. Now, in
experimenting on dead animals, which were cooled down to
the temperature of the surrounding atmosphere, it was found
by injecting serum into the principal artery of an organ, that
the nitrate of potassa increased the efflux in the capillary
organs of dead bodies, in the same manner as in glass tubes ;
and that alcohol, on the contrary, retarded it. These facta
tend, therefore, to prove that the circulation of the blood
in the arteries and the veins follows the same laws as the
efflux of liquids in capillary tubes.

Jets d^Eauj or Spouts of Water, — Streams of water which
spout up with force from an orifice in consequence of the
pressure of a liquid column more or less elevated above that
orifice, are called jets (Teau. If the orifice be made in the
upper surface of a horizontal wall or tube below the level in
the reservoir, the jet is vertical and upwards; if the wall or tube
be inclined to the horizon the jet is inclined, and describes a
curve, which, abstracting the resistance of the air, would be a
paralola.

According to a principle formerly mentioned, a jet of water
tends to rise to a height equal to that of the level of the watec
in the reservoir ; but this is never exactly the case, as it i ~

LESSONS IN CHBMI8TR?.

191

with three resistances : 1st, the friction of the water in the
tubes or pipes, which destroys a part of the velocity ; 2nd, the
resistance of the air ; 3rd, the resii tance which those liquid
particles, falling from the highest part of the jet, present to
those which are ascending.

In order to obtain the maximum height of a jet, the diameters
of the tubes must increase with their length; the tubes must
be free from all inequalities and all sudden windings; and, the
orifice of efflux must be made in a thin wall, and have a alight
inclination in order to avoid the third resistance just men-
tioned. Such orifices are those which raise the jet to the
greatest height, and impart to it the greatest regularity and
transparency. Conical ajutages also produce jets uniform and
transparent, but the height is only about eight or nine-tenths
of that produced by orifices in a thin wall. Lastly, cylindri-
cal ajutages produce confused jets, of which the height is only
about f of that which is produced by orifices in a thin wall.
In order that a jet may take the greatest range horizontally, it
is found by analysis, that when the resistance of the air is
abstracted from the calculation, the angle which it makes with
the horizon must be 45°, or half a right angle ; that is, mid-way
between the horizontal and the vertical directions.

LESSONS IN CHEMISTRY-— No. XII.

Rssumiwo the consideration of antimony, I now want the stu-
dent to take a little of the orange or black sulphuret of the
latter : powder it; and having thrown it into a Florence flask,
pour upon it some hydrochloric or muriatic acid, known in
commerce under the name of spirit of salt; applying now to the
flask either the naked flame of a spirit-lamp, or, what is pre-
ferable, the heat of a sand-bath, sulphuretted hydrogen gas

rig. No. U

f sulphuric acid. Now nine is the precise chemical equiva .

But of water, and forty the precise chemical equivalent of sul-

thuric acid* A few remarks concerning equivalents have al-
ready been offered ; I do not expect you, nowever, to under-
stand this rather abstruse subject perfectly just yet. I must,
nevertheless, have you to remember, even though you do not

understand it, the following fact : When I aay that our strong-
est English oil of vitriol is a compound of one equivalent of
water and one of real sulphuric acid, I do not mean equal
weights, but equal equivalents; the equivalent of the one being
tbrtv and the other nine, as we have seen. The same remark
applies to all similar expressions. Well, then, in order to indi-
cate the kind of hydrate which oil of vitriol is, chemists term
it the protohydraU of sulphuric acid, or protohydrated sul-
phuric acid. The Greek word irpwroc means first; that is to
aay, this is the first in the ascending scale of many hydrates.

From this digression (a necessary one, however) let us now
eturn to the materials in our flask—or rather let us investigate,
by means of a diagram, the changes which have ensued.

The case stands thus : —

Hyo^ocMoricaxidl^^"^ Hydroaulphurio acid

will be evolved, as you will readily discover by its disagreeable
odour ; and if a sufficient amount of hydrosulphuric acid have
been added, the whole of the sulphuret will be dissolved. The
result of this solution is termed the chloride of antimony, pro-
curable in commerce under the name of butter of antimony.
Let us see what decomposition must have ensued in order to
furnish us with these results. Sulphuret of antimony is, as its
name indicates, and as we demonstrated in our preceding les-
son, a compound of sulphur and antimony.

We have not vet demonstrated the composition of hydro*

chloric acid gas ; out its name, if analyzed, evidently points to

a compound of chlorine and hydrogen, just as the term hydro*

sulphuric points to something which is a compound of sulphur

and hydrogen. Remember, therefore, the following general

fret :— Whenever you see the syllabic prefix hydro (before a

vowel hydr*) t the prefix always means hyarozen — never water.

the presence of which is expressed, not by the syllabic prefix

hydro or hycY, but by the full word, hydrattd, or hydraU

Thus, for instance, Ayrfrv-sulphuric acid is synonymous with

sulphuretted hydrogen, indicating the compound of sulphur

ana hydrogen ; but hydraUd sulphuric acid, or hydrate of sul

phone acta, is a compound of sulphuric acid with water*

Practically we call oil of vitriol sulphuric acid ; really it is hy

orated sulphuric acid — or a compound of true sulphuric acid

(which is a solid) with water. But you will say— If I take oil

of vitriol and sad more water to it, I get a liquid which is no

eager oil of vitriol, but it is still hydrated sulphuric acid

Italy— the remark is just ; hence has arisen the necessity for

certain precise terms. The strongest oil of vitriol which we in

sVtsjUna obtain by our process of manufacture is composed of

i by weight of water united with forty parts by weight

Sulphuret of Anti- { Sulphur

inony \ Antjm<my N^ chloride of antimony

|f the resulting liquid be thrown into water, in certain propor-
tions, which may be ascertained on trial, a powder (oxide of
antimony) deposits. This powder is, however, readily dis-
solved by the addition of more hydrochloric, or a sufficient
quantity of tartaric acid.

The precipitate which occurs on throwing the chloride into
water is the type of an important feature in the demeanour of
antimony solutions, most of which are liable to become decom-
posed from the operation of very slight causes. Tartar emetic
is not so prone to be unstable as the others are; it may be mixed
'with mere water, in any proportions, without throwing down a
precipitate ; but tea — infusion of galls, or indeed almost any
vegetable or animal infusion, throws down, even with it, a
copious precipitate. Try these experiments ; the results will
be found to have an important bearing upon circumstances to
be mentioned hereafter. Assume, for example, that a person
has taken an injurious dose of tartar emetic, and that the eme-
tic action does not supervene; this is the case sometimes.
What would you do ? In the first place, propose to yourself
the object you would desire to accomplish. There is a general
rule to follow in all these cases — a rule which I have already
mentioned. It is this :— Convert the poisonous irritating fluid
into a solid. Give then— if tartar emetic be the poison under
consideration — give copious draughts of tea ; a fluid which, as
we have seen, renders tartar emetic insoluble— more insoluble,
at any rate, than it was originally.

Separation of Antimony from fine, Mangan$u y Cadmium, and
Arsenic— I trust that the student has sufficiently reflected upon
the properties of these four metals to recognise an indication of
a process by which this might be accomplished.

Firstly, It is evident that arsenio and antimony admit of
separation from the other metals by the operation of hydrogen,
which would remove them in the condition of arseniuretted
and antimoniuretted hydrogen gases ; and the latter, on oom-
bustion, would deposit the two metals in a mixed crust. Fi-
nally, these metals would be separable from each other by the
prolonged action of boiling nitric acid, which, as we have seen,
reduces the antimony to the condition of an insoluble white
powder, and changes the arsenio to soluble arsenic acid. The
latter proposition has not been demonstrated. Nitrate of pot-
ash produces this result, as I have explained (p. 42). Nitric
acid has the same effect ; indeed, nitre acta by virtue of its con-
tained nitric acid. Several other analytical processes suggest
themselves from combinations of agencies already discussed ; the
most evident process, however, is that which I have given ; and
my object not being to write a systematic course of analysis, I
need not detail the others.

Before concluding my remarks on this interesting metal, I
I will mention a curious fact. Two sulpnurets of antimony have
been spoken of: there exist others; one an orange-coloured
J sulphuret, generated artificially ; the other a black substance,
I usually sold as a ntim o ny by druggists. New, different theug

****** ;*y**l>. XEU tfeAwii imto tibaiB,
■dditfiCA^tti Ancs; feeresore dtttviidsu

In any site cobs, lets a c^w.
be a fesnagfe of which the md**cmjpmfit* fesntfeiides a;

tweea fee other two ado, bc sad b a.

Fromsc, the gntfer ode, cat off b b, a part aswal to the
lew aide b a, by Proa. HX

BeBssasfeetwossasBAsad Acm tagafear meter than
bc, WPBBB.XX* sad thst bb h\ by i n — f iei m i. eqwel to
ba; dee i e fae, ts hiag these eQ^m kswsT. fe e iianainn'ii ac je

*aB.D. **" •by a

It* slrwawhte/s
~ e/eByeBf«eitee*taf*e»le»

of a

•/***, *~l

thiidside^by tt&XI^therd

BBBMBBBOBABLBVe fetse BBSeS

be added to

twice fee

BBSthSB tie

one side of
by Prop. JJL,
be added to thcee bim^bbW, fee three
e mm fern twice the other two

MSB m. TO

aa i ii r w,»«V*e» mm mw ykl V I TeensT mmtmmmmt

m±md wdnm tmhm i i ■ s fl w ewal if ens tans let ems e/ftns
«*w*>nf Jew* eVwsm frtrn far mm pmmi»Umm *±*pmmi*4m

Ib io^ktABBdBbe

****** ha* exsen ib i

ynsftr.nnakmc the part Br cqnal tn the pert a b, by Prop.
iH. Jess rB,aad let It est cb sb fee points. Urn a a,
lBeBtB*ebnieM 1 > 1 » A «*^«>^nn™&tm^epoeBtBAs^

CBB«,B1

XV.;

B,SBB SBJJ^B^BS«BJBBltB BBeB>PB
L t% JBBllllB»eBBBlBBBBBBlBBBy.BVc«Bl

•.*/

Ifbb;

ABB
AO. In
mtPBlS

Aote

eae cmik we add the

ASSBJOBBl

BB M eCBBBOB Yi fee f

» beee c » ie eajsal to
it any be "
to 1m? straths* a bl
to the eUBJtg^n fiae c r. if to
_ fine ob, the two sttssejat liae* a s a»£ c s are equal to
the whole rn. Bat fee two esters sad KB, of the triangle
fbb, ere together greater then the eiders; aad anil
eoael to fb^ therefore ah sad aesre toj-echer pester than
* ** m B at it has been shown fesi a* sad BBmeawsl tors;
tbefore ah sad a s sre together paster thsa Acandos, that
k, ag safes are tacesher lees then the earn of a a and h a.
And the sasae anay be proTed af the two straigmi line* drawn
from the poms a Bads to Bay other pomt ia the straight line
c b. Theresbre, from two green pcesoa a and s on the same
aide of fee straight be* cb^ two straight Ebb* hart beea dries
to a point o is il, which taken toajecharars Ism than thafsm
of two afi 111,111 lines drawn from the eesse bojbbi to any other
posmtincii. aLP.

P«*wdj n ai ailii by XBecBeK Qrast Wadey, that feni
axiom* taken few grassed, rii -If one iBBBfiftade be meter
aa*her. sad af fee essse cveqasl saagsetsdm Wadded to each,
the esme BSBssmaty win resaam; that k, the asm of the
paster rasgrnTadft sad that whash ie added to it will be
gtastar fees fee asm of fee asm sasfssBsde sad that which is
added to it/* ft Bother axiom ia also taken far panted, ris.,
- If one magniiade be pester then sBafeaT. aad if the same
oreqaal am g a w ei l iB be taken from each, fee esme inequality
*ffl iwmam ; feat ia, fee difl e i g sMj e Uisuta fee greater mag-
Bitade sad feat which ia taken from it, will be greater than
fee dinwreaoe bstwaam fee leas sssgnipade Bad that which it
trios* from *."•

. L, n. and

r, Casnsfe; T.

, , «^-5 C L. HadieM

I. aai m. ay K. L. Josea, Penv
~ ^ssdLbyJ.JtasjtB),

ANSWERS TO CORRESPONDENTS.

rYarkV. ¥< wk> pilniw.asaal imttue of tban to
+mwLJm*k we earn n Imin I, — j tha eatj book of
>atW Brma-loant Haa»: T«-— T. a (Hj-atworth):
~ DBAs i«f ■ mill n J wat eaawwsi More. It UaQ
aMBwi;aMaheataeiieai amiai of a certain
a*rmfw«ar:Bj»sBns >M cm waaih asat awaaa^aa^tiiiha cab only
wat eat ay easavawam^-Tecas batcsaujv: W«4* a ik ao w.— Geasaiii-
' ,Vawl X. T. S. tDssoa): Tea.— T.

aib Plat .Wiiaifci i) awt Locat u pits xauxa: We oWt
. Moaaxs: Wria %» Mr. swJL--A Sraacaisn (Catoe) : Kif ht-
JliM|Bioi itm\ laaaat omen Bear? Moore. acq., Seartary to
Heaaa., Bra ■issii i af al sat fa art w Fortho
• Meawa, Bsawsr, Iwrnsattii no. O.F.Hct

LESSONS IN BOOKKEEPING.

LESSONS IN BOOKKEEPING.— No. XL

THE JOURNAL.

(Continued from page 177).

» f

Tib Journal, as we have before remarked, is no longer what
its name denotes, a Day Book ; but is now used, in Double
Entry, as a book for collecting all the transactions of business
for a given period into a focus, previous to their being entered
in the Ledger. In an ordinary business, where the transactions
are neither too numerous nor too complicated, the formation
of this book from the various subsidiary books of the concern,
may take place only once a month ; and then with reference to
time, as we formerly observed, it might be called the Month'
Book ; and in the same way, according to the regular intervals
when this collective book is made up, it might be called Week-
Book, or even Day-Book. The beet name, however, which
could be given to it, would be one indicative of its actual use,
without reference to time; we have already suggested the
name Sub-Ledger, and we may now propose a name which
would, perhaps, be more accurate and distinct, as regards the
method in which it is made up, and the connexion which it

has with the Ledger, we mean the Gsnbkal Postino Book.
Some of our students who are, no doubt, keen business-men,
and are on the alert to discover any improvements that can be
made in Bookkeeping, in order to shorten their labour, and
produce more accurate results, or, rather, to effect les3 frequent
liability to error, will, if they have gone with us thus far, pro-
pose some shorter or more pointed name than the preceding t
for once, therefore, we leave this subject in their hands. All
we shall say, is this : that gentlemen who have been in busi-
ness for twenty, thirty, aye, and forty years, have thanked us
personally many times for the lessons on this subject which
they have received from us, and particularly in reference to
our method of striking a General Balance, exemplified at the
end of this Journal, but which cannot be fully explained in this
lessen, as the Trial Balance and Ledger have not yet been sub-
mitted to the student. This will be done in our next lesson.

(i)

JOURNAL.

(1)

Bate.

Pol.

January, IS53*

D*.

Qa,

1
22

1
3

1
3
2
3

4
5

Cash Account Dr, ^ +<. £

To Sundries, as per C, B, fol. i

To Stock Account ... .,.

To London and Westminster Bank „■ ...

2205
I20O

288
403

751

£1200
1005

2205

Til
4.3

3
3

3
10
17
22

Sundries Dr.

To Cash, as per C, B. ibl. 1

London and Westminster B-ink „* ■♦.

Petty Cash Account „. ttt

Three Per Cents. Consols

Private Account

21
31

Sundries Dr.

To Bills Payable, as per B. P. B fbL 1

Osmond and Co. ... .„ „ #

Andrews and Co,

7
26

Cotton Account Dr. Mi .„

To Sundries

To Osmond and Co. , , ,„

To Andrews and Co, ttt W1 „.

' Afll'i

lf*wd m

JOURNAL.

(2)

«.

February.

Sundries Dr.

To Cash, as per C. B. fol. 1

London and Westminster Bank

Darling and Co.

Bast India Company

Petty Cash Account 9

TOt. IV.

Dr.

Cash Account Dr.

To London and Westminster Bank, as per C. B. fol. 1

£220 ]

100
50
60
10

Cn.

£220

220

THE POPULAR EDUCATOR.

(2)

JOURNAL.

(2)

Date.

Fd,

i
31

17
25

February.

Sundries Dr.
To Cotton Account
Brown And Smith
Williams and Co*

Cotton Account Br*

To fcundrie*

To White snd Co.

To Boat India Company

Charges Account Dr.
To James Manning

(3)

JOURNAL.

1
3
6
26
21
16
29

30
2

17
18

13
16
22

Mnrch.

Cash Account Dr.

To Sundries as per C* B, fol. 1

To Brown and Smith

To Three per Genu. Consols

To Dwling and Co.

To London and Westminster Bank

To W tilt a ma and Co*

Tu Thompson und Co* -■*

To Althozpe and Co*

Sundries Account Dr.
To Cash, ai per C* B. fol. 1
London and Westminster Hank

J am eft Manning
White and Co ,
Private Account

Baring Smith and Co* Dr

To Bills Payable, as per B. P. B. fol.

Sundries Dr.
To Cotton Account
Spencer and Co*
Thompson and Co.
Althorpe and Co*

£313
360

nil-

£r 2MJ

Ca*

£■■:.

?21

£t2ftl

Lfl

(3)

Cotton Account Dr

To Baring! Smith and Co.

(4)

JOURNAL.

13
25

April*

Cash Account Dr.

To Sundries, as per 0. B. fol, 2

To Spencer and Co,

To London and Westminster Bank

V-

Db,

21*20

21G0

425

288

1€0

I 257

141

283

Ca.

G9IH ' 13 I 1

£313

997

80C

36C

2*7

141

290£

28S

559

28*

£6904! 18 I I

(4)

Dn.

£1150

Cn.

£160
990

LESSONS IN BOOKKEEPING.

(4)

JOURNAL.

(4)

Date.

Fol.

April*

Da,

Cn.

Sundries Dr.

To Ca*h Account, as per C, B. fol. 2

£1161

EijiL India Company ... ,,. «*i

£061

Petty OdiU Account

Osmond and Co. ,.. ... .,. ■■•

183

Bills Payable ... , M ...

2SS

3 J

(

Private Account ... ,,. m hi

B ilia Receivable Dr. „, ,„

To Sundries, oi per B. It. B. fol. 1

To Allison and Co. .,, „t **•

COO

150

-y>

To Lloi d and Co, ... ... - ,,,,

243

10 •

To Thomas Jones „ mi *■•

ftt

Sundries Dr.

To Bill* Payable, as per B. P. B. fol, 1

43-1

4 .

Andrews and Co. ,,» .,, ,,, ■••

238

Ovington and Co, ,,. ... „«

667

Cotton Account Dr. ... ... ...

To Sundries

To Osmond and Co. ...

183

To Andrews and Co,

258

4 *

To Ovington and Co.

24o

Sundries Br.

To Cotton Account

Allison and Co. ... ... ...

150

Thomas Jones ... ... ...

770

Lloyd and Co.

223

r,_'ii

tvii-i

(«)

JOURNAL.

(•>

May.

Da.

c«.

Gash Account Dr, ,„

... £

1679

To Sundries, aa per C, B. fol. 2

To London and Westminster Bank ,„

...

£55U

To Bills Receivable

ii.

■ M

1031

To Brown and Smith .„ .,«

... **■

Sundries Dr.

To Cash Account, as per Ci B, fol. 2

lit

IGGl

Bills Payable

... *•*

327

Petty Cash Account

London and Westminster Bank

+..

.it »*■

£00

Perkins and Co,

...

823

4
2

Interest Account ,„

...

1
2132

3
10

Bills Receivable Dr.

..*

...

To Sundries, as per B, R. U. fol. 1

To Thomas Jones .„

791

To Lloyd and C j. .,. t „

, .1. «*■

21 1

To Powell and Co. ■

4 4

—

20b n

To Perkins and Co.

-*•• ■■•

■ &12

A D

*O0

THE POPULAB EDUCATOR.

(*)

JOURNAL.

Date.

Pol.

May.

S Da. |

3
8
7
8
8

8
6

Sundries Dr.
To Cotton Account
Lloyd and Co. ...
Thomas Jones
Powell and Co. ...
Brown and Smith

••• ...

= :

i 1

i £217 IS

I 241 j

299 1

97 1

2 J

Perkins and Co. Dr.
To Charges Account

• ...

...

i 21 i

10 (

1 0351 4

3 .1

Cc.

£85t> 9 I 2

(«)

JOURNAL.

(«)

2
3

1
2
2
3
1

2
8

June.

Dn,

Cn.

SO
3

Cash Account Dr.

To Sundries, as per C* B. fol. 2

To Bills Receivable

To London and Westminster Bank

«... ..♦ £

1800

■
135

1650

308
308

£l7flt

10(

1815

308

5
S
9

Sundries Dr.
j To Cash Account, as per C. B* fol. 2
Bill* Payable
Petty Cash Account
London and Westminster Bank
Private Account

■*! ...

Bilk Receivable Dr.

To Powell and Co. as per B, R. B. foL 1

*i* •»*

Powell and Co. Dr,
To Cotton Account

««* »*p

Charges Account Dr.

To Petty Cash Account ...

■ ** ...

A 1

iflwfl

£4?Of

(7)

JOURNAL.

fl)

1
1

1
2
2
3
3
8

9
2

■

9f
3

4
4

General Balance in June.

1>».

Ca,

Stock Account Dr.

To Private Account, for Personal Expenses...

, £d0
2G*4

772

1882

12
760

782

€
17

10
18

8
12

7
3

7
10

£59

2
2

308
7*>

2245
21

2664

782

394

Ml)

Balance Account Dr.

To Sundries, for my Assets, as per Ledger A

To Cosh Account ... ■«.

To Petty Cash Account ..* *.. -**

To Bill* Receivable

To Cotten Account

To London and Westminster Bank

To Perkins and Co. „, * ,,.

11
5
1

17
8

2
15

3
3

Sundries Dr.

To Balance Account, for my Liabilities, as per Ledger A

Bills Payable

Stock Account, for my Heal Worth ,., ..< ■! |

8undi.es Dr.

To Profit and Lots Account, for my Gains ... — |

Three per Cents. ... „ m ,».

Cotton Account

Profit and Loss Account Dr, ,„ .»<

To Sundries, for my Losses

To Internet Account

To Charges Account „, ,„

To Stock Account, for my Nit Gain m *♦•

1
3

0933

£6933'

12!

LESSONS IN CHEMISTRY.

201

LESSONS IN CHEMISIRY.-Xo. XIII.

Thx metal which I purpose making the subject of this day**
lesson is tin ; a very interesting, and at the same time a ver
useful metal. No student, however remote he may be from
towns, will experience any difficulty in obtaining a specimen
of tin for examination. He may employ, to this end, a littl
tin-foil, or one of the capsules wherewith bottles of spirit
pickles, &c. are now so frequently occluded. I need scarcely
remark that the metallic sheet known as tinplate, and used by
tinmen, will not serve our purpose. This material is not tin ,
but iron coated with tin ; however, supposing neither tin-foil
nor a tin capsule to be procurable, whicn is hardly likely, th
student may scrape off the superficial tin coating from a pie©
of tinplate.

The physical aspect of tin is very characteristic, so that, sup*
posing this metal to be presented to you in the metallic state
you could scarcely confound it with any other. In the first
place, it is a white metal ; not blue-white, like sine, but having
more the appearance of silver. With lead it could not be con*
founded, on account of the bright aspect which it always pre-
serves, whereas lead becomes tarnished. Tin melts with ex-
treme facility, much more readily than lead ; if held in the
flame of a candle, it does not burn, as zinc does ; neither does
it oxidize, as is the case with lead similarly treated. In short.
I repeat, tin in a metallic state can scarcely be confounded with
any other metal ; but you are aware that metals seldom exist
in nature in the pure metallic state, hence the only way of dis-
tinguishing them and separating them is by taking advantage
of their chemical properties. Under the head of antimony I
mentioned indirectly a leading characteristic of the chemical
demeanour of tin. I mentioned that this metal, like antimony,
is violently attacked by nitric acid (aquafortis), a white inso-
luble powder remaining.

Let us try the experiment. Having placed a little tin— tin-
foil by preference — in a watch-glass, saucer, or something of
that kind, pour upon it a little nitric acid. Chemical action of
a violent kind immediately ensues. The orange-coloured gas
previously observed is again evolved, and oxide of tin remains.
This result proves that the metal operated upon is either antimony
or tin (p. 156, col. ii), and characteristics by which the chemist
readily determines as between these two metals will soon be
made apparent.

It may here be remarked, that very strong nitric acid does
not readily act upon tin ; if therefore the result as described
does not immediately ensue, add to the nitric acid & few drops of
water ; you will then succeed.

From a consideration of the properties of tin just mentioned,
its conversion into peroxide of tin by the action of nitric acid, it
should follow theoretically that the peculiarity might be taken
advantage of in analysis. This is indeed the case ; the separa-
tion of tin from all metals, save antimony, by converting it into
this insoluble powder (peroxide of tin) is an operation of fre-
quent occurrence in analysis.

We will now take cognisance of the peroxide of tin under
another phase. We will begin by dissolving the tin in a suit-
able menstruum, and we will convert the tin, thus dissolved,
into an insoluble form. By this time you are aware, I assume,
that chemists usually begin their analytical operations by con-
verting into a solution the compound under analysis. There
are exceptions to this proceeding, but I give you the rule. If
a piece of glass were given you for analysis, "you would begin
by dissolving it; if a piece of compound metal, you would
again dissolve it ; if a flint stone, you would still proceed ac-
cording to the same rule, you would dissolve it. There is a
solvent for everything, even tiie hardest, the most intractable
bodies ; and a knowledge of" the proper solvent for any given
substance constitutes one of the most important parts of a
chemical education. I cannot refrain, whilst treating of solvents,
to direct your attention to one of the problems of the alche-
mists. These enthusiasts laboured hard to discover one uni-
versal solvent ; in other words, a fluid that should be capable
of dissolving everything wherewith it might come into con- 1
tact* //"such a liquid as this should be hereafter discovered, it

• They forgot, by the way, tlte important fact, that, supposing the
*qsM in question were generated, a vessel wou'd be required to hold it.

would be abhorred by chemists, and avoided by them to the
utmost of their power. The presence of such a liquid would
destroy all our means of analysis. We now effect the separation
of different bodies by taking advantage of their several powers of
solubility and insolubility, as you have seen in many cases and
will frequently see hereafter. If all the substances which have
come under our notice had been equally soluble in either of the
fluids employed, there would have been an end to our powers
of analysis.

To resume the special consideration of tin — hydrochloric or
muriatic acid (spirit of salt), termed by the French aeide
chlorhydrique, is a very good solvent for the metal ; still better
is a mixture of hydrochloric with nitric acid, sometimes called
nitro-muriatic or nitro- hydrochloric acid, also known as aqua-
regia, on account of its property of dissolving gold. As regards
our present purposes, however, the generally best solvent for
tin is not the best for us, the hydrochloric acid alone unmixed
with nitric is what we will employ.

There are certain reasons, I will not stop to explain them
just now, which involve the necessity of our performing this
solution in a vessel of such construction that the minimum of
atmospheric air may come into contact with the materials. It
follows, therefore, that we ought not to effect the process of
Solution in an open vessel. A flask, therefore, is the proper
apparatus to be employed ; and inasmuch as one product of
the solution will be a gas, the nature of which I should like
you to investigate, let us adapt a perforated cork and a bent
glass tube to the solution flask, causing the delivery-end of
the tube to terminate just under the mouth of a jar or bottle,
resting, as formerly described, on the shelf of a pneumatic
trough.

For the performance of this experiment, a Florence flask will
answer perfectly well, and a spirit-lamp flame may be employed
to aid the decomposition. Care also should be taken that
more tin is placed in the flask than there is acid to dissolve ;
otherwise we shall not get exactly the kind of solution we
require.

As concerns the gas developed and collected, it is a colla
eral product, the nature of which I shall not stop to explain,
fully anticipating that the student will accomplish this by his
Own unaided efforts. When the operation of solution has
eased, label the flask proto~chloride of tin, and set it aside.
Some chemists term it the proto- muriate or proto-hydrochloraU
of tin, by which name therefore the student will sometimes
find it denominated in books. Whether it be a proto-chloride
or a proto-muriate, depends on the solution of a problem, and
involves a very curious theory, concerning which chemists have
argued a great deal to very httle purpose.

What ! the student will perhaps exclaim, does the boasted
accuracy of chemistry come to this ? Can you not determine
the constituents of the solution of tin in spirit of salt ? Form
no hasty conclusion of the sort ; we can tell accurately enough
what constituents are there, but we cannot tell how these
constituents are united amongst each other. Take an illustra-
tive case : a certain number of gentlemen and ladies go into a

hurch arm-in-arm ; arm-in-arm they come out of church; but
it does not therefore follow as a consequence of the evidence
before you, that they sat arm-in-arm whilst in church, or that

ich couple had a separate pcw f

202

TH* POPULAR EDUCATOR.

Thus is it with many disputed chemical combinations, we

.put certain bodies together an4 they are lost to our view.
Afterwards we get them out again, but the manner in which

i they arranged themselves whilst there, is a mystery to us.

' The solution of common salt in water, affords a very prominent
example of one of these disputed facts. Common salt, if dried
and separated into its elements, yields chlorine and sodium \

' therefore it must be a chloride of sodium ; it cannot be hydro-
chlorate of soda, inasmuch as hydrochloric acid .contains
hydrogen, and soda contains oxygen, in common salt both
these elements are wanting. Dissolve this salt in water, and
the mystery begins. It may dissolve as thus :

Chloride 1

Sodium I Chloride of sodium with water.

Water J

or thus :

Chloride / Chlorine

of \

Sodium ( Sodium

r Hydrogen -V-

Water

I Oxyge

^ Hydrochloric "| Hydrochlo-
4 acid f rate of

^ Soda J Soda

Whenever you meet with an ambiguous case of this kind,
remember well the fact that the accuracy of chemistry is not
irapvyned thereby. Do not waste your time in mere ingenious
arguments pro and con. People who do this are not imbued
with the true philosophy of chemistry, which prompts to the
establishing of large physical generalisations rather than a
contemplation of these nicely balanced disputes. Some people
are such creatures of mere detail that they cannot take a com-
prehensive view of any thing. Give them a poem to read,
their first impulse is to hunt after stray commas, or determine
disputes of precedence between colons and semicolons. Give
them chemistry to study, they are delighted with no part of
it so much as the endless discussion about the aqueous decom-
position or non decomposition of haloid salts, for thus chlorides,
iodides, bromides and fluorides are termed.

All salts are termed haloid that result from the action of an
acid containing hydrogen on any body. Thus chloride of tin
is a haloid salt, inasmuch as it results from the action of
7/ytfrochloric acid on tin : in like manner, common salt (chlo-
ride of sodium) is a haloid salt, seeing that it results from the
action of hydrochloric acid on sodium, or what amounts to the
same thing, on soda. The term haloid is derived from the
combination of two Greek words, £Xc, salt, and c t£oc, likeness
or similarity.

Returning now to the consideration of our solution otproto-
chloride or protomuriate of tin (which you please), let us test
its properties. For the purpose of testing, the following re-
agents will be necessary —

(1.) A solution of carbonate of soda (washing soda).

(2.) Of potash (liquor potassse) .

(3.) Of ammonia (hartshorn).

(4.) Of carbonate of ammonia (smelling salts).

(5.) Of bichloride of mercury (corrosive sublimate).

(6.) Of chloride of gold.

(7.) Solution of hydrosulphuric acid in water.

(8.) Hydrosulphate of ammonia.

(9.) Some calomel.

Two of these solutions, of bichloride of mercury and chloride
of gold, require each special comment.

The former may be made of almost the strength of ten
- grains to two wine-glasses full of distilled water. The bichlo-
ride should be broken into fragments, projected into a Florence
flask and boiled with the water. When cold, pour the solu-
tion 'into a bottle (glass stoppered by preference*) and label
the bottle thus :

F0IS0H!
BICHLORIDE OF MERCURY,.

Hg. CI,
Antidote, white of egg.

The solution will frequently be required as a test, therefore
do not throw it away. Should you by some mishap iuwlkw
this amount of bichloride, you would dio after the lapse of
I about an hour. If some ignorant person should apply the
stomach-pump, the time would be less. If, however, imme-
I diately on discovering your mistake, you were to swallow the
whites of five or six eggs, you would live out the full number
of your days, none the worso for the dose. Probably you will
I consider this fact worth remembering. You may furthermore
| remember, as a collateral fact, that white of egg is also an
I antidote for verdigris and preparations of copper generally.
That moreover it is a material perfectly harmless in all cases ;
consequently, even though the kind of poison should not be
known, you may always give white of eggs.

Apparently we have not very far advanced with our consi-
I deration of the metal — tin. Two points, however, in connec-
I tion with it we have well determined. It is converted into an
insoluble white powder by the action of nitric acid, and it
i is dissolved by the operation of hydrochloric acid, yielding as a
I collateral result a gas, the name of which I have not mentioned,
I but which I expect you to determine. The problem related to
1 one of those truths already mentioned in the course of these
I lessons, and which will enable you, if you have been attentive,
to solve it. I shall conclude this lesson by informing you, that
chloride of gold is made by mixing together two parts ot nitric
acid with one of hydrochloric (by measure), and adding to this
fluid as much leaf gold as it will dissolve. Label the solution

CHLORIDE OF GOLD

Au. CI.

and preserve it as a test. Touch your skin with a little of this
solution and observe the colour of the stain — developed by
to-morrow, remember this result is indicative of gold.

And now one final word relative to the stain of chemical
symbols referred to in this lesson. Bichloride of mercury has
been represented in the symbol Hg. Cl 9 . Now Hg. is the con-
traction for hydrargyria (Lat. for mercury), and CI. for
Chlorine, the figure 9 expresses the fact that one equivalent of
mercury or (200 parts by weight) combined with two equiva-
lents of chlorine, or 36 parts by weight, gives rise to one equiva-
lent of the bichloride of mercury.

As concerns the chloride of gold, you will observe it is
simply termed chloride, without any numeral affix, because our
auriferous liquid is a mixture of two distinct chlorides of gold
(protochloride and bichloride) in variable proportions. It the
solution were carefully evaporated by means of a water or
steam bath, the result would be a chloride made up of thref
equivalents, 108 parts by weight, or of chlorium combined wit)
one equivalent, or 200 parts by weight, of gold. This com
pound is called in exact chemical language a terchloride, an
thus represented in chemical symtols :

Au. CI 3

Au., I need scarcely mention is the contraction for the La
word Aurum, gold.

And now for two final experiments : test the solution '
made (protochloride) with hydrosulphuric acid, or hydro*
phate of ammonia, and remark, the colour is black. J
boil the protochloride with nitric acid, and then test it.
colour will be a sort of yellow, because the act of boiling
nitric acid converts the protochloride into a perchloride.
the other tests mentioned in our list affect solutions o
Let the student observe their re-action, more especiall;
effect of mixing bichloride of mercury with protochlori

NATURAL PHILOSOPHY.

203

ON PHYSICS OR NATURAL PHILOSOPHY.

No. XIV.

CAPILLARY ATTRACTION.

CajnUary Phenomena.— In the contact of solids and liquids,
a. series of phenomena are produced, to which the name of
capillary phenomena is given, because that they are particularly
observed in tubes, whose diameter is so small that it is com-
parable to the thickness of a hair.

The effects of capillary attraction are very various ; but in
all cases, they are the result of the mutual attraction of the
liquid particles to each other, and to that attraction which
subsists between these particles and solid bodies. Take, for
example, the following phenomena : when we immerse a solid
rod in a liquid which will wet it, the liquid, in opposition to
the laws of hydrostatics, rises around the solid rod, as in the
case of glass and water ; and its surface, instead of being hori-
zontal, takes a concave form, as shown in fig. 47; but, if a solid
rod be immersed in a liquid which will not wet it, as in the
case of glass and mercury, the liquid, instead of rising, sinks
round the solid rod, and its surface takes a convex form, as
shown in fig. 48.

Fig. 18.

Fij. 47.

These phenomena become more evident, when, instead of a
solid rod, we immerse in the liquid glass tubes of small dia-
meter, as shown in the following figures a and d. According

Fig. A. Fig. B.

as theae tubes are wetted or not wetted by the liquid, so do
tfcey produce an ascent or a depression. This ascent or
depression increases as the diameter of the tube diminishes,
see figs. 49 and 50. When the tubes are wetted by the liquid,

Fig. 49,

the surface of the liquid takes the form of a concave mcnUcus
(Greek emcent- shaped), as in fig. 49, and when the tubes are
not wetted by the liquid, the surface takes that of a convex
meniscus, as in fig. 60. The surface of the liquid assumes the
same concavity and convexity on the sides of the vessel which
contains the liquid according as it wets or docs not wet ihe
sides of that vessel, as eliown in the following figures c end d,

where the one represents the effect of a tube immersed in
water, and the other that of a tube immersed in mercury.

Fig. c.

Fig. D.

I=J

==J)

L , ,— J

Whter.

Mercury.

When the liquid is contained in a vessel so large as that
capillary attraction has no longer an effect on its level surface,
still the liquid rises or sinks on the sides of the vessel, accord-
ing as it wets or does not wet these sides, see figures e and f.

rig. e.

Fig. F.

=:■ =^=~

£=

^. T~JJ

Laws of Ascent and Depression in Capillary Tubes. — M. Gay-
Lussac has proved by experiment that the ascent and depres-
sion of liquids in capillary tubes, are regulated according to
the three following laws : 1st. There is an ascent when the
liquid wets the tubes, and a depression when it does not wet
them : 2nd, this ascent and depression are in the inverse ratio
of the diameters of the tubes, so long as they do not exceed
the tenth part of an inch : 3rd, the ascent and depression vary
with the nature of the liquid and with the temperature ; but
they are independent of the substance of the tubes and of the
thickness of their sides, if the latter be previously wetted.
These laws hold good in a vacuum as well as in air.

The method employed bjr M. Gay-Lussac in the discovery
of these laws was the following : 1st, he measured the interior

Fi*. G.

/JffV

diameter of the tubes, not directly, which would have been
very difficult, but by selecting those which presented the same
sectional area throughout their whole length, and weighing the
quantity of mercury which corrrdetely filled them j the density

204

THE POPULAR EDUCATOR.

of the metal being known, it was then easy to deduce, from its,
weight and the height of the column, the required diameter,
as shown in a former lesson : 2nd, he then placed the liquid
under consideration in a vessel ab c d, figure o, and vertically
immersed in it, the capillary tubes which were successively
submitted to experiment ; close by each tube, he placed a rod
b p, tapering to a point, which, by the motion of a screw, was]
made to reach the exact level of the liquid ; then, by means of
a cathetometer, he measured the vertical distance between the'
upper extremity of the column of liquid in the tube, and the
lower extremity or point of the rod which came in contact
with the liquid. The heights which different liquids reach
are by no means the same, as may be seen in tho following
table ; for, in a tube whose interior diameter was about one
twenty-fifth part of an inch, the liquids rose to the different
heights here mentioned, above the level of the liquid in the
vessel :

Liquids. Heights.

Water M73 inch

Alcohol 0-479 „

Spirit of Turpentine 0*501 „

In the experiments of which these are the results, the liquids
were kept at the same temperature; for in proportion as
the temperature rises, the capillary phenomena are rapidly
diminished.

In the use of several apparatus, it is necessary to know the
amount of the depression of the mercury in glass tubes. The
following table gives these depressions to the nearest thou-
sandth of an inch, in tubes varying from 8 hundredths to 40
hundredths of an inch in diameter .

Diameters of Tubes.

Depressions of Mercury,

•08 inch

...

•178 inch

•10

...

•143,

•12

• ••

117

•14

...

•098

•16

...

•083

•18

...

•071

•20

...

•061

•22

...

•053

•24

«••

•047

•26

...

•041

•28

...

•036

•30

*•*

•032

•32

•>•

•028

•34

...

•025

•36

...

•022

...

•020

•40

...

•018

Laws of Ascent and Depression between two Plates Parallel or
Inclined.— Phenomena analogous to those presented by capillary
tubes, are produced between two bodies of any form immersed
in a liquid, when they are sufficiently near to one another.
For example, if we immerse in water two parallel plates of
glass so near each other that the two curvatures formed at
their contact with the liquid, are united, it is observed : 1st,
that the water rises regularly between the two plates, in the
inverse ratio of the interval which separates them ; and, 2nd,
that the height of ascent for a given interval, is the half of that
which would have taken pladB in a tube whose diameter is
equal to this interval. If parallel plates are immersed in mer-
cury, depression takes place, but according to the same laws.
Tig. 51.

If two plates of glas?, \ n and a c, fig. 51, be inclined to each

other so as to form an angle, and be immersed in a liquid
which wets them, so that their line of contact be placed verti-
cally, the liquid will rise towards the vertex of the angle
between the two plates, and its surface, from the highest to the
lowest point, will assume the form of the curve called an
equilateral hyperbola. The asymptotes of this cur re which is
double, being traced on each plate, are the vertical straight
line in which the edges of the plates meet, which is common
to both, and the horizontal straight lines which determine the
level of the liquid in which they are immersed, as shown by
the dotted lines in the following figure k.

Tig. H.

When the line of contact of the two plates is horizontal
instead of vertical, as shown in their sections represented in
figs. 52 and 53, and the plates are placed so as to form a very
small angle, a drop of water put between them is hollowed at
both its extremities into a concave meniscus, aa in fig. 52, and

Fig. 5J.

Fij. 53.

Mercury.

is attracted towards the vertex of the angle of the two
plates ; but if the liquid does not wet the plates as is the
case with mercury, the drop of the liquid is rounded
at both its extremities, into a convex meniscus, as in fig. 63,
and is repelled from the vertex of the angle. The directions of
attraction and repulsion in these figures are indicated by the
arrow heads.

The force of attraction of a liquid to the sides of a vessel
lies between two extreme cases ; it is equal to that of the liquid
to itself, or it is zero ; in the former case, the ascent of the
liquid in tubes is the consequence ; in the latter, depression is
the result. Between these two extremes, there must be the case
in which there is neither, ascent nor depression ; this occurs
when the force of the attraction of the liqrud to the solid is
exactly equal to half of the fo ce of the attraction of the liquid
to iiaelf. Water brought in contact with well polished steel
appears to realise this particular case ; for the liquid seems, on
the approach of the metal, to experience neither elevation nor
depression.

As already observed, every column of liquid elevated by
capillary action is teiminated by a concave surface; and every
column depressed, by a convex surface. In cylindric tubes of

LESSONS IN GERMAN.

•20 >

diffidently small diameter, these surfaces are hemispherical.
Between two parallel plates they are semicylindric. Since the
liquid columns in tubes rise in proportion to the small ness of
their diameter, it follows that the meniscus which appears at
the surface is proportionally increased in curvature, which fur-
nifhes us by its direction and force, or rather by the shortness
of its radius, an expression for the force which acts at tht
extremity of the column ; the concave meniscus indicating l
force which acts from the interior to the exterior or a traction $
and the convex meniscus, a force which acts from the exterior
to the interior, or a compression. This view is verified by th
following experiments. Take an inverted siphon, having two
unequal branches both in length and in diameter, as shown in
the following figures 1°, 2°, 3°, and such that the capillar
action is very marked in the narrow branch, and almost
nothing in the other branch, on account of its great diameter*
Pour water into it at three different times, so as to make it
assume the levels indicated by these figures.

F g l©.

rig. «©.

Fig. 3©.

In fig. 1°, the level being very low in the branch a, it ii
elevated in the branch b to a height corresponding to the
capillary action at that point, and the meniscus is concave
at b. In fig. 2°, on pouring an additional quantity of water
into the branch a, up to the exact level of the extremity b,
the two surfaces are then of the same height, and both
become plane ; in fig. 3°, on pouring an additional quantity of
water still into the branch a, up to the level which measures
the capillary action in the branch b at that point, the
water rises in the form of a convex meniscus, and exerts a
force of compression sufficient to prevent any flow ; but if the
level at a he increased in height above this point, the water
will then begin to issue by the narrow branch b.

Again, if in a conical tube, of which the following figures
marked w and m, are sections through their axes, we introduce

Fig. W.

-4*

Mercury.

a drop of liquid, it will take the former or the latter form,
according as it wets or docs not wet the sides of the tubes ;

and if left to itself, it will be attraoted in the direction of the
arrow heads.

Attractions and Repuhions of Capillary Action.— -The attrac-
tions and repulsions which we observe among bodies floating
at the surface of liquids, and which arise from capillary action,
are regulated by the following laws : 1st, When two floating
bodies are wetted by a liquid, as, for example, two balls of cork
in water, a powerful attraction takes place as soon as they are
put so near each other that a plane surface of water no longer
exists between them. 2nd, When two floating bodies are not
wetted by a liquid, as, for example, two balls of wax in water,
a strong attraction takes place as soon as they are put in the
same circumstances as the former. 3rd, When two floating
bodies are such that one is wetted by the liquid and the other .
not, as a ball of cork and a ball of wax in water, repulsion is
observed to take place as soon as they are so near each other,
that the two contrary curvatures of the liquid are found
in contact. The phenomena just described, depending on
the concave or convex curvature assumed by the surface of
the liquid in which the bodies are placed, we shall inquire into
the cause which determines the form of this curvature in our
next lesson.

LESSONS IN GERMAN.— No. LXXVIII.
$ 91. Compound Prefixes separable.
ton^etm (an+ty'im, to-home) ;

£a(tt

fcafjcr

taf)'m

Dagegen

Dameter

Daran

flnfcimftcUnt, to put home to,
i.e. to refer to.
(ta+ki, there-by) ; 3>abeijte$«n, to stand close by.

(fca-f-$cr, there-hither) ; S>a$trf<$lfuf?f n, to sneak along.
(ta-Hin, there- thither) ; £<n)ineiUn, to hasten away.
(ta-r-gcgcn,there-against); 2>agegcnfttn, to be against,
(fca-j-nicter, there-below) ; 2>amrterfc$lagcn, to beat down.

(fcor+an, there- to) ;

or lay
risk, to

JDarauf (tat+auf, there-on) ;
(tar+ein, there- in) ;
(ta+rcn, there-from) ;
(ta+*or, there-before) ;

Damn

Dawn

mtjhjct

£erab

Scran

J&erauf

tcrau*
erbci

herein

3)aranfefccn, to put
thereto, i.e. to
stake.
2>araufgeben, to give there-on,

i.e. to give an earnest
$arrinrefe<ii, to talk there-in,

i.e. to interrupt.
Dawnlaufrn, to run off, or

away.
Qawriiegen, to lie before.
(*a+witcr,there-against); $>annfctrtyab«n, to have (objec-
tions) against.
Qajutyun, to do (in addition)

thereto ; to add.
3)auuif4<nrften p to speak there

in the midst.
(Jinfyfrjif^cn, to draw along.
&ntgrgrngef>m, to go towards,

to go to meet,
(fritttvctfcrttftfn, to break or

burst asunder,
^erabfttfren, to put down; to

lower.
$rranfu$rrn, to bring on or

along.
<$erauffat?ren, to drive or urge

on.
$rraulfa$rcn, to drive out.
$erbf irufen, to call by or to-
wards.
$eretnf>i$rcn, to drive in or into.

tsawr
flDannrct

$aju (ta+ju, Ihere-to) ;

3)a$toif<$en(ta+jttriftyen, there-be-

tween) ;
I fin$«t (cin-J-^cr, into-hither) ;
rntgegen (ent+gegen, apart- to-
wards) ;
(ent+jtoet, apart-two) ;

(fct+afr, hither-down) ;

($er+an, hither- to) j

(fjer+auf, hither-on) ;

(fxr-f au«, hither-out) ;
fttr-f-bet, hither- along) ;

($tr+«tn, hither-into) ;
tmirter (^r-4-nirter, hither-down); $muefcerMi<fcn, to look under.
Qttubtc (btt- -fiber, hither-over) ; $trfibcrfommen, to come over,
trum ($<r-|-uni,hither-around); $trumgekn, to give or hand

around*.
■Otrunttr ($tr+untfr,hither-under); $enmterfa$ren, to drive down.
■Grreor ftec+wr, hither-for- ^ttwrtrcten, to step forward.

ward) ;
$crju (btr+ui, hither-to) ; $etjutrrten, to step towards,

inab foin+ab, thither-down) ; Sinabtrrten, to step down,
.inan ($in-j-an, thither-to) ; Sinaatrcten, to step up to

206

THE POPWJUfi EDUCATOR-

$htauf (ftn+auf, hithcr-on or

up);

$iaau* ($in4-au«, thithcr-out) ;

$iueia (bin-J-ein, thither-into) ;

$intan ($ijit(cn)4-aii, behind- to) ;

^intcr^r (^ifitap+^cr, after-hither) ;

$uiuber ($in-|-u&er, thither-over) ,

^tuiim ($in-{-ura,thither-around);

$tnuntet ($in-f-uutrr, thither-un-

der);

$intoeo, (bin-j-trcg, thithcr-away);

$inui (tin-|-J»i. thither- to wards);

Ucttrrin (u&er+ein, over -into) ;

limber (um+$er, around-hither);

tynauftiefea, to pull up.

Sinaultofrfen, to throw out.

<&ineingiefien, to pour into.

•Ointanfe fceit, to put behind ;
to undervalue.

£intcr$crfc$en, to see after-
wards.

^inubcrrragen, to carry over.

£inumffattern, to flutter there
about.

J&inunterfyringen, to leap down
there.

.fcintoegneftnen, to take away.

£in$utUen, to hasten away.

Uebereinfommen, to come over
into, i.e. to agree.

Itm^frftyweit, to gage around.

Unu)in (um+$in, around thith-
er);
JBoron (twr+a n ' beforc-to) ;
23orauf (wnr-f aitf, before-on or

up);

Starauf (©or+aus, before-out) ;

©ctfcei (wr+bei, before-by) ;

$or$cr (vor+^er, before-hilhcr) ;
StarJet (wr«4-«fcer, before- over) ;

©ottoea, (wr-ftoeg, before-away) ;

3u*or Gu+wr, before-to) ;

dnritd ^u+turf, back-to) ;
dufammen ($u-j-fammm, to-gether) ;

tmf intdnncn, to be able there
about; to forbear.

Soranfieflen, to place before.

aSeraufftrigen, to mount on be-
fore ; to ascend.

95orau«fe$rii, to see or spy out
beforehand; to anticipate.

Storbeireiten, to ride along be-
fore ; to ride past.

3?erbcrfc$en, to foresee.

Jl^ruterfatyren, to drive along
past in a coach.

Startoegnc^mtn, to take away
before ; to anticipate.

3uwri$un, to do before; to
excel.

3nrftcffe$ren, to return.

3ufammenfr|Kn # to put to-
gether.

S 92. PARADIGM OF A COMPO UND VERB SEPARABLE.

Slnfai^en, to begin. *

INDICATIVE.

SUBJUNCTIVE.

CONDITIONAL.

IMPERATIVE,

INriNITIVF.

PARTICIPLR.

Present Tense.

PresenlTense.

Present Tense.

Present.

• f 1

i$ fange an, I begin.

idb fange an, I may "

2. fange (tu) an,

anfangen, or

anfangent,

S 2

tu fdngft an, thou beginnest.

tu fAngft an, thou mayst

begin thou,

aiijufangrn, to

beginning.

S (3

er fAngt an, he begins.

er fAngt an, he may

3. fange (er) an,

begin.

* ( l

toir fangen an, we begin.

toir fangen an, we may

l.fangcn(n)ii)an

5 2

tyr fanget an, you begin.

iftr fanget an, you may

2. fanget (ibr) an,

£ (3

fie fangen an, they begin.

fle fangen tin they may

3. fangen (fie) an.

Imperfect Tense.

* I 1

i<$ ftng an, I began.

tc$ finge an, I might "^

$ 2

tu fingfl an, thou didst begin.

tu fingefl an, thoumightst

S (3

afingan, he began.

er finge an, he might

(* ( 1

roir fingen an, we began.

tvir fingen an, we might

2 2

if;r finget an, you began.

u)r finget an, you might

* (3

fie jtngen an, they began.

fte fingen an, they might

Perfect Tense.

Pei'fcct Tense.

Perfect.

i [2

3 (8

i($ Ijabe
tu baft
cr f}M

I have ]
£ thou hast
f he has I g

t<$ Jiafce
tu $at<cfi
er Im&e

I may have
g begun, &c.

angefangen ba-
ten, to have
begun.

angefangen,
began.

ci (1

nrir fyaUn \

*§we have f g>

ruir M<n

3 2

ibx $abet

§ you have | x

\f>x ffaUt

* (3

|tc fyaben

they have J

fie fea&en

Pluperfect Tense.

* ( l

to) pattc ~\

I had

ie^ Uttt ""]

I might have

% 2

tu battcfl

g~ thou hadst

tu I)Attcfl

g' begun, &c.

£ (3

cr tyattc 1

f he had

er $Atte

••1

B! (1

roir batten j

*g; we had

n?ir BAttcn

s 2

i$r fcattrt

g you had

i^r bAttet

en
g

* (3

fte Batten w

they had

fie$Atten

First 2\itvre Tense.

First Future Tense.

First Future.

First Future. *

il s

i$ toerte

I shall "

id} totr.be "

(if) I shall be-

ic^ tourte ""

angefangen n?er*

tu toirft

s thou wilt

tu toertefl

g gin, &c.

tu toflrtrfl

«2^

ten,

5 (3

n nrirfc
»ir tocrten

h |? he will
'•2. we shall

er toerte
toir toerten

«4

er tourte
toir toflrten

'is - • b£

to be about :
to begin. !

5 2

xffx toeitet

« you will

i^r toertet

i^r tourtet

* (3

fie toerben -)

they will^

fle toertcn ^

fie tourten -

Second Future Tense.

Second Future.

,(1

id) toerte

~ J I shall have
. & begun, &c.

i$ totrte

£ (if) I shall

i$ tourte "

Is? .

25?

tu toirfl

tu wertefl

£. have begun,

bu tofirtefl

*5JB

SC3

s f l

cr toirb
n>ir Kerten

ernxrte
toir toerten

.1 **•

er tofirbe
toir tourten

C fl S

S{2

tfyr njertet

t^r tverfcet

i^r tourtet

,« fcf..

* [z

fle toevten

fie toetten -

fte tourten

LONDON UNIVERSITY.

207

UNIVERSITY OF LONDON.— No. IV.

At the request of numerous students of the Popular Edu
gator, we insert the following papers; they will give valuable
information, not only to those who aspire to the honour of
becoming members of the University, but they will form a
body of useful exercises also to those' who have been our Stu-
dents since the commencement of our Lessons in the various
branches of learning in this work.

Matriculation Examination.— 1853.

[N.B. — Candidates are prohibited, tinder pain of instant
dismissal, from introducing any book or manuscript into the
Examination- Room, and from communicating with each other
during the Examination. Candidates are required to attend
In person on one of the last three days of the week immediately
preceding the Examination, to pay their Fees and write their
names in the Register. If the Candidate fail to pass, the Fee
will not be returned to him, but he will be admissible to any
future Matriculation Examination without the payment of any
additional Fee.]

PASS EXAMINATION.

Juit. 4. Monday. Afternoon, 2 to 4, French; 4 to 6, German.

5. Tuesday. Morning, 10 to 1. Mathematics. Afternoon, 3 to
6, English History.

G. Wednesday. Morning, 10 to 1, Greek Classic and History.
Afternoon, 3 to 6, Chemistry.

7. Thursday. Morning, 10 to 1, Mathematics. Afternoon,
3 to 6, Natural Philosophy.

8. Friday. Morning, 10 to 1, Roman Classic and nistory.
Afternoon, 2 to 5, The English Language.

Monday, July 4. — Afternoon, 2 to 4.
FRENCH.— (Examiner, M. Delillb.)
Translate into English :

I/homme appclc a commander aux autres sur les champs de
bataille a d'abord, coramc dans toutes les professions libcrales,
une instruction scientinque a acqudrir. 11 faut qu'il posscde
les sciences exactes, les arts graphiques, la theoric des fortifi-
cations. IngeY.ieur, artilleur, bon officier de troupes, il faut
qu'il devienne en outre gtfographe, et non gc'ographe vulgaire,
qui sait sous quel rochcr naissent le Rhin ou le Danube et dans

2ucl bassin ils tombent, mais geographe profond, qui est plein
e la carte, de son dessin, de ses ligncs, de leur rapport, de
leur valeur. II faut qu'il ait ensuite des connaissances exactes
sur la force, les intexdts et le caractcrc des peuples ; qu'il sache
leur histoire politique, et particulibrement leur histoire mili-
taire : il faut surtout qu'il connaisse les hommes, car les hom-
ines a la guerre ne sont pas des machines ; au contraire, ils y
deviennent plus sensible*, plus irritables qu'ailleurs, et Tart
de les manier d'une main delicate et ferine fut toujours une
partie importante de l'art des grands capitaines. A toutes ces
connaissances sup&ieures, il faut en fin que l'homme de guerre
ajoute les connaissances plus vulgaires, mais non moins nlces-
saires de l'administrateur. II lui faut 1' esprit d'ordre et de
detail d'un com mis ; car oe Vest pas tout que de, faire battre
les hommes, il faut les nourrir, let vfitir, les armer, lea gulrir.
Tout ce savoir si vaste, il faut le d£ployer a la fois et au milieu
des circonstances les plus extraordinaires. A chaque mouve-
ment il faut songer a la veille, au lendemain, a ses nanca, a ses
derricres ; mouvoir tout avec soi, munitions, vivres, hdpitaux ;
calculer a la fois sur 1' atmosphere et sur le moral des hommes ; et
tous ces elements si divers, si mobiles, qui changent,se compli-
quent sans cesse,les combiner au milieu du froid,du chaud, de la
faim et des boulets. Tandis que vous pensez h tant de choses,
le canon gronde, votre tfctc est menacee ; mais ce qui est.pire,
des milliers d 'hommes vous regardent, cherchent dans vos
traits l'espe'rance de leur saiut ; plus loin, derriere eux, est la
patrie avec des lauriera ou des cypres ; et toutes ces images, il
faut les chasser, il faut penser, penscr vite ; car une minute de
pros, et la combinaison la plus belle a perdu son a-propos, et
au lieu de la gloire, e'est la honte qui vous attend. — Thiers.

La Chenille.

Un jour, causant entre eux, difftrents animaux

Louaient beaucoup le ver a sole :
. "Quel talent," disaient-ils, "cet insecte diploic
£n composant ses ills si doux, si fins, si beaux,

Qui de l'homme font la richesse ! "
Tous vantaient son travail, exaltaient son adresse.
Une chenille seule y trouvait des deTauts,
Aux animaux surpris en faisait la critique,

Disait des matt, et puis des si.
Un renard s'ecria : " Messieurs, cela s'expliquc,

C'est que madame file aussi." — Florian.

Tuesday, July 5.— Morning, 10 to 1.

ARITHMETIC AND ALGEBRA.— (Examiner, Rev. Prof.
Heaviside.)

1. In dividing one whole number by another, what does the
quotient determine ? Divide 243584 by 346, and explain the
steps of the operation.

54180 into its prime factors.

3. Find the simple interest on £4572 15s. for 9 years at 4£
per cmt.

If the three per cent, stock be at 08, and the three and a
quarter per cent, stock be at 101, whieh stock is it most advan-
tageous to buy ? What income will £5000 invested in the
three per cent, stock produce ?

4. Explain the principle en which vulgar fractions arc added
together.

Add together L 3 , l l, " » »
15 20 21 25 30

What fraction of a guinea added to 4s. 6d. is equal to 15
shillings? Is a proper fraction increased or diminished by
adding the same number to its numerator and denominu'ur ?

7 11

5. Express as decimal fractions-!-, _ .

10 1000000

What is the

distinction between decimals and wholo numbers as respects
the prefixing and affixing ciphers to the right and left of the
significant digits?

Divide '305 by 20.

If in obtaining the quotient you cut off the cipher from the
divisor and actually divide by 2, what corresponding change
should be made in the dividend ?

G. Ferform the operations indicated below : —

(1.) 3601—2-987564.

(2.) 2-745 X45'674f

(3.) 233-8268-^-3 4f*

(4.) 6'25-f-000123.

(5.) \Z2U9-eSl6.
Verify the result of (4.) by vulgar fractions.

7. Why must the 4ecimal eqvivalent to - recur ? find that

decimal. Find the vulgar fractions equivalent to the recurring
decimals.

(1.) -7171717*1.

(2.) -80654654.

Find the value of '33333 of 2$ guineas.

8. State the rule of signs when one algebraical term is mul-
tiplied by another.

Add together 7* — iy f 3*-}-5y, 9jp— y.

From (2a+Zb) 2 take (a— 2b)\

Multiply o»—2fl 3 A+2a^— 30*3+2** by a*~2ab\&

Divide (3**— *— 10) by (3*+5).

Find (*— 2a)»

THR POPULAR EDUCATOR,

Solve the equations :

(1.) dx-4=8x+\2

(2.) ±+±=±+7
V J 2 3 4^

(3.)
(O

2*+3y=32 )
lly-9jr= 3/ •

x+y= 9
z+z=zlO

y+*=H

10. When arc magnitudes in arithmetical progression, and
'hen in geometrical ?

Sum the series 4-f 11+18-f-.... to 9 terms.
8um the series 3+0+12+.... to 6 terms.
Wh.it if the arithmetic mean between 2a — 3d and 2a+orf?
If a : b:: b : e, prove (I) b"-z=ae, (2) a : e : : a- : 6*

Tuesday, July 5.— Afternoon t 3 to 6.
ENGLISH HISTORY.— {Examiner, Db. Wil' iam Smith.)

1. Give a brief account, with dates, of the Roman conquests
in Britain. Name the Roman emperors who died in Britain.

2. In what part of England did the Danes chiefly settle ?
Give a list of the Danish kings of England.

3. Give a brief account of the Norman Conquest of England.
State the leading characteristics of the Normans and Saxons
at the time of the Conquest.

4. What is the date of the signing the Magna Charta?
What are its chief provisions ?

5. " During the hundred and sixty years which preceded
the uniou of the Roses, nine kings reigned in England. Six
of these nine kings were deposed. Five lost their lives as well
as their crowns. (Macaulay.) Give a list of these nine kings,
and mention briefly the circumstances which led to the deposi-
tion of the six.

6. In whose reign did Geoffrey Chaucer and John Wycliffe
live ? What services did they render to English literature ?

7. Give a list of the monarchs of the Tudor family. Des-
cribe briefly the character of each.

8. How did James VI. of Scotland succeed to the English
throne ? Give a brief account of his character.

9. What is the date of the Petition of Right ? Name its
chief provisions.

10. Who were the parties to the Triple Alliance in the
reign of Charles II. ? What was the object of the alliance.

11. State the provisions of the Treaty of Dover in the reign
of Charles II.

12. When was the Test Act passed ? What was its object ?

13. When was the Royal Society founded ? Name some of
the most eminent men who belonged to it down to the reign
ol Anne.

Monday, July A.— Afternoon, 4 to 6.
GERMAN.— {Examiner, Rev. A. Walbaum.)
Translate into English :

(Jin reiser 3ungling ju 9?om r>attte ihranf gelegen an eincm feyiocren
Ucbel ; entity genas cr unb toarb gefunb. $a ging et jum erftenntale
ftinauf in ken ©artcn, unb toar rote neugeboren unb »c(( ffrcube unb lebcte
®ott mit lautcr €>timmc. Unb cr toanbte fein Hnttifc gen $iinmc! unb
<pra<$ : O bu »f(genugfamer, f dnnte tin 2Wenfc$ bir e hvaf wrgelten, tote
gem toofltc ty aflc meine $abe geben !

@ot$r« $orte $ermae, genannt bar $irte, unb fpra<$ §u bent rcu$en
Singling : Son oben fommt bu gute (Babe ; bayin wrmagft bu nUyts gu
fenben. Jtomnt, folge mir !

$tr Singling folgte ban frommen Orctfc unb fie tamen in tine bunfle
J&utte, bafelbft n>ar citel 3ammer unb Glenb. $>enn bet ©ater lag franf
unb tie aflutter wetnete ; bic Sinker after nxtrcn nactenb unb feyrieen nacb
»rob.

2>a erfcyra* ber 3ung!ing. J&ermal abcr fr*acy : €>ie v e yier einen 9l(tar
(fit bein Dofec ' @te y c yiet bes $errn ©ruber unb ©tcCfoertrcteT.

2 a t^at Ux *ri<$e Singling feine Sanb fiber fte auf, unb gab i$ne»

retcylic} unb pflegete ber Aranfcn. Unb bte erauufteu 9rmcn fegnricn iyn.
unb n inn ten ibn einen Qrngel Gtottcft.

$crma* aber (acytlte unb frra$ : €to toenbe bu imnter bein baifbarrt
9Intli^ erft gen $immc( unb bann §ur drbe.

Krumxacbkr's Parubcln.

$cr englifcje ®efanbte ju $anno*er, Sorb (Slarenbon, tin Scneanbtcr ber
®tuart«, y atte fief) fo coen au9 einer HbenbgefeHfcyaft brt Jturfurflen na<y
£aufc begeben, aU ein 93ote brt @epctmcn.JKat v « »on Gnglant Urn ben
33efe v l uberbrac$te, ben Jturfurften oon bent Xotc flnna'f §u benac^nc^tigen
unb i y n a(« Jtdntg anjuerfennen. ftfcfaft eiltc Sorb Glarenbon naty £er»
ren v aufen jurucf , begab ftcy, o y itc auf tcr Xtcnrr (rintixntungen ju acytcn,
baf ber ^err fl<y bereitl jur Stuye gclegt babe, in baf @<b!afgemac$ te#
Jturfurflen, fnieetc oor beffen 33ette nieber unb (eiftete i^m auf ublute
SBetfe bic ^ulbtgung. S^txy in ber ndmlicyen 9lac^t bertef ber Jiurfurfl
feinen @taat«rat v unb ruflete ftcy gut tHbreife. iter 9ltfl fhrom:e nar^
^erren^aufen, urn ben Sanbei^errn n«y ein 3Ra( ju begrufen. 91 m 11.
Ge^tember verlief btefer mit bem Survrinjcn tai &$!<£ unb fiyt ntyt obue
Siuyrung burcy bas Cktrangc feiner llntertbanen, bte fUy urn iyn oerfam«
melt fatten. 9Wit mogltyfler 2<ynel(igfrit (cgte er bie JKcife nary bem $aag
jurucf, toofelbjl er ben ibn begru^enten (Beneralflaaten bte 9tarjuycrung
ertyeilte, ba« alte ©unknip Gng(anb4 mit ber 9{epuMif naty beflen itrdften
)u er v a(ten. (Sine gfotte von 22 ilrieg#fcyiffrn unter flbmiral Seecfley ge#
leitete if)n nacy &nglanb ; bei Qrecnroicy crfolgte bie Sanbung. %\» Gkorg
Subteig ben %uf auf ben englicyen :8oken fe^te, h>urte er ton bem primal
ber JTiteyC, bem (Srjbiftycfe von Canterbury beunUfommnet.

31m 1. October yielt C&ccrg I. feinen feierlicten ©injug in Senbon, unb
em^fing barauf in 9Bcfrmtntler<2lbtei bie Srone. 916 naty btefer 9eier(icy'
fcit, n?ie bie 3itte d etyeifcyt, ein gcvarnifcytcr fitter auftrat unb ieben
jum Sam^fe aufforbcrtc U)elcy?r ten fo eben gefrentcn Jtonig nic^t fur ben
recylmdfigcn (Sebteter oon (Mropbritannicn anfeye, toagte nur cine X^ane
ben bingen?orfenen ^ankf(yu v aufjune y men unb ju erflaren, baf 3acob III.
rc« Sanbe6 recytmdfiger ^err fei.

Havemann's Gcschichte da- Lande Braunschweig
und Liineburg.

Wednesday, Jufy 6.— Morning, 10 to 1.

HOMER, Odyssey, Book XL— (Examiner, Mr. Burciiam.)
Translate into English :

(A.) — 'H cV ig iriipaO' 'Uavt fiaOvfrpoov 'ilKtavoio.

tvOa li Kiputpitov dvdpujv ci'jfxSQ rt ir6At£ rt,
ijiptKai vt<pt\y KEKaXvuptvoi" ovSk iror ahrovg
'HeXtof QakButv Karat tpKtrai iiKTivtaaiv,
ov9' 6rr6r &v anixyai Trpic; ohoavbv acrripotvra,
ovff or Av aip Itti yalav air ovpavoOtv irporpdirnraC
aW Iti vi>£ 6Xo^ rtrarai ltiko~im fiporolaiv.
vrja flip, IvB' l\06vrtc, t UiXaafiiv' tc H rd fiijXa
i\X6pi9'' aitroi cV avn irapd poov 'QKiavolo
youtv, &dp' ic x^pov afiKOutW, ov typavt K/prr;.

Ev9' tepijia /if v UipiftrjCnQ EvpvXoxoc ti
iax ov ' h u & &°P ^W Ipvaaa^iivog napa pnpov,
/360pov opt/C> Sererov rt Trvyovaiov ivOa xai ivOa*
&p$ abrtf til yo^v x^t 1 ^ *"5<w»' vtKvtamv,
irpwra /i«Xtrp»;ry, fitrkirura tie ytii'i olvqt*
rd rpirov av9' %8ari* lic\ 8' &X<pira XtvK& irdXviw.
woXXd 8k yovvovpnv vikvwv aptvnvSt Kapnva,
iXOwv tig lOaKtjVj arupav fiovv, fjng apiarn,
pk%tiv iv utyapoiai, irvprjv r ifirrXrjaiftiv loQX&V
Teiptaiy o' airavtvOtv oiv Uptvaifttv oTw
irafipiXav, og firjXoi&i fitrarrpiirit 7//icr<poc(nv.
roue; 8* licti fi/Y<wXp<n Xirijai ri, 19 via vticpwv,
IXXitTapnv, rack pijXa Xafiwp aicitifiporSpnGa
Ig fio&pov, pit 8' alfia KtXaivtfig' at h" ayipovro
y^x ai v*i£ 'Epifitvg vtKvtov KarartOvnwrutv.

(B.)— "Qg l6dfinv' 6 8k p avriic Aptifioptvog irpoaittirt
Aioytvtg AatpnaSij, iroXvprixav '08vcatv,
ovrt /i£ y iv vrjetrat Uoati8atav Icapavctv,
hpaag apyaXkwv Aviuojv Auiyaprov avrpriv,
ovra ft AvApaioi aveptg IcnXriaavr tiri x*paov'
aX\d fiot AtyioOog rtvlag Oavarov rt fiopov rt,
tKra avv obXofuvy AXdxtyt olicovtit KaXlaaag,
8tnrviaoag &g rig rt KartKravt fioyv Irci 6arvy.
iig Bdvov oUrioTip Bavartp' rrtpl 8' AXXoiiraTpw
vtaXtpitog Krtivovro, avtg &g Apyt68ot'7tg t

LESSONS IN GREEK.

209

01 pa r iv dtfrvtiov dvdpbg piya cuvap'evoio
i) ydfiip fi lodvtf} i) eiXanivy rtBaXviy.
Ifin pkv icoXiwv 0oi>y dvcputv dvrefioXnoag,
povvdZ Kreivopevutv, Kai ivi Kpartpy vapivy
dXXd Kt xelva pdXiora iCujy bXo<pvpao Bvptf,
«C <W« W#P«» rpaire^ag re irXn9ov<rag t
KeipeB' ivi peydptp, bdirecov d' iiirav at pari Bvev»
ouerpordrnv d* ijKOvaa oira Hpidpoio Bvyarpog %
YLa<r<rav$ptiQ, r »}*' KTtivt KXvraipi'rio-rpn doXopnng
dptf ipoi avrdp iyw irori yaiy \i1pag deipiav
fldXXov d-rc o9 v j) cricwv rrepi (pacrydvy >/ H Kvvwirig
vo<r<piaar\ ovbk poi irXtj, ibvn irtp eig 'Atdao,
X*poi tear bfBaXpovg eXieiv, ovv re crop ipeloai.
tag ovk aivorepov Kai xvvrepov aXXo yvvaiKog,
ijrig drj roiavra perd fpeoiv epya fidXnrac
olov tirj Kai Kfivtj iprjvaro Ipyov deixeg,
Kovpidiy rev^ava ttogu Qovov* ijfroi fynv ye
aarcdciog iralSetroiv ifii dputecatv iuoXaiv
oiKafi' iXevoeoBac y d* t£oya Xvyp tic via
ol re Kar a\o%OQ e\ tv( ^aii^ffopivyaiv biriaaia
BnXvrkpyoi yvvat£i, Kai ty k evepybg iyaiv.

•1. Give the first futures, perfects, and second aorists
active and middle of the following verbs : — rpk$<a, Bdrrrut,
jpdfo, pdXXw, Xei-rcoj, Bvtiokio^ ^evyio, irrryvvpi, iornpi. Give
the full and the contracted forms of the nresent and imperfect
of $o it dot.

•2. Decline the following substantives : — dvqp, bpvig, ddpap,
Bvydrno, rpitipng, ifow, relxoct and the adjectives rdXag, fiapvg,
Tiprjv, ikuv, vag.

3. What sea is designated by 'Qriavoc in Extract (A..)?
Explain the construction in dvSp&v fiijp6g re ndXtg re-i)kpi Kai
vefkXy KiKaXvpptvoi. Quote from Virgil and Ovid descrip-
tions similar to those in the first extract.

4. Give the names of the extant Greek plays, and of
their respective authors, relating to the subject mentioned
in Extract B. What is the meaning of tyijv in the same
extract?

5. Describe the geographical position of the peninsula
known in ancient times by the name of the Thracian Cherso-
nese, and mention the names of the principal towns therein.

6. By whom was the Chalcidic peninsula colonized? Men-
tion the names of its chief towns, and the important events in
Grecian History with which they are associated.

LESSONS IN GREEK.— No. XVIL
By John R. Bbabd, D.D.

THE PRONOUNS.

Pronouns express the relation of an object to the speaker,
inasmuch as they present either the speaker himself as the
object (the first person), the person addressed (the second person),
or the person spoken of (the third person) ; as I ( first person),
the teacher, give you (second person) the book (third person).

Pronouns may be divided into five classes, namely, the
personal, the demonstrative, the relative, the indefinite, and
the interrogative.

1. Personal Pronouns.
A. The Substantive Personal Pronouns.

a. The simple, namely tvu (Lat. ego), I; av (hex* tu),thou\
ov, of himself.

N.
Q.
J).
A.

Jf.A.
Q.J>.

«y«, 1

fiov (epov) 9 of me
pot (c/ioc), to me
fit (ipe), me

vu t we two
t*»y,of (to) us two

Singular.

<tv, thou
oov t of thee
901, to thee
<rc, thee

Dual.

e$b), you two
9tyv % of (to)
you two

ob t of him
ol, to himself
1, himself

<r*4>cv,of(to)them
two

N.
G.
D.

»//mc, we

I'lfiiMtV, of US
>)/itV, tO U8

A. rjpag, US

Plural.

v/i€f£, you
vfoov, of you
v/uv, to you

vpag f you

v4>ug, n. o^ea,they
a<pwi>, of inem
rrtjHGi, to them-
selves
<r<f>ag, n. <r<psa t
themselves.

Avrog, n.o, is sometimes given as the third person, yet it
has the force of the English he, she, it onlv in the oblique cases ;
in the nominative it signifies not simply he, but he himself.
In truth, the Greeks had no pronoun which exactly cor-
responds with our personal pronoun of the third person.

Vocabulary.

rpappa, arog, rb, a letter, pi.

letters, that is, learning.
Aia<pepu>, (g.) I differ from.

Aia<pOtipu) t I corrupt, destroy.
Zt/yyatpw, (d.) I rejoice with
(some one).

EXBRCI8E8. — GrBBSL-EnGLXSU.

E)tu pev ypa$(i», <rv tie Trai&ig. Zefiopai ae, to peya Zev.
Q 7rai, aKove pov. *0 irarrjp pot QiXrarog eon. 'O Beog aei <rt
pXiiru. Ei fit fiXairreig, ovk e\Bpiav SiaQepttg. Eyw oov
Ipputfievearepog eipi. *HSewg iretGopai ffoi, ta varep. 'Hpetg
vptv ovyxaipopev. 'fl Xvpa vpag ev<ppaivei. 'O Beog ypiv
TroXXa ayaOa vapexti- '0 irarnp vpag orepyti. Avbpeuog
pa\eoBe, w o-rparnarai' hputv yap eon rnv rroXtv QvXarreiv
et yap vpeig Qevyere, iraaa i) rroXig 8ia$Beiperai. 'Hpojv
eonv, (a iraideg, ra ypappara (nrovdaiojg pavBapeiv. 'H ptjrnp
vut orepyti. Nyv nv jcajci; voaog. 2^w ex ire 0«^ov mororarov.
Y<pn>v b varnp x a P t & TCU ' °"^ w y a 9 vnovcauog ra ypappara
pavBavere. O tieoirora, axove pov.

The pergonal pronouns in the nominative are employed
only, then, when a certain emphasis falls on them, especially
in contrasts. In order to show in what instances they should
be used in the following Exercises, the words where they are
required are printed in italics.

Exbsci8B8. — English-Greek.

We write, but you play. We two write, but you two play.
I honour you, ye gods! O boy, hear us! God always
sees you. If thou injurest us, thou differest not from enemies.
You rejoice with us. I willingly hear you, O parents. Father
loves thee and me. Mother loves you both. It is my duty
(it is of me) to watch the house, for I am the guardian of the
house. It is thy duty, O boy, to learn earnestly. The lyre
affords pleasure to thee and me. You two have (core, with
dat.) a very faithful friend.

b. The reflective pronouns, epavrov, of myself; oeavrov, of
thyself \ iavrov, of himself

Singular.

aeavrov (ffavrov),ng
(navvy (ffavnft), y
oiavrov (oavrov), nv

Plural.

tavTutv or ainaVf or
<r0o>v avriov

lavroig, aig, or av-
roig, aig, or c^iaiy
avroig. aig

eavrovg, ag f a, or
avrovg, ag, a, or
o$ag avrcvg, ag,
a<f>ea avra.

c. The Reciprocal Pronouns.

While the reflective pronouns throw the act back on the
subject, the reciprocal denote the interchange of the act, or
the influence between two j«ii>ons or two set* of ptisons;
thus aXXnXuv means of one another-, aXXnXoig, to one another;
and aXXnXovg, cn+anotlter.

Q. epavrov, ng
D. epavrtp, y
A. epavrov, nv

eavrov (avrov), ng
iavrift (abrtp), y
eavrov (aurov),nv, o

tipiav avnav

rjpiv avreig,
aig

t)pag avrovg,
ag

vputv avruv
vu iv avroig, atg

vpag avrovg, ag

110

THE POPULAR EDUCATOR. '

Plural.

D. aXXifXoiCt a<f , oic
A. aWtjXovc, as, a

Dual.

aWnXoiv, aiv, oiv
aXXijXoiv, aiv, otv
aXXnXut, a, w

Vocabulary.

Oturia, ac, >/, essence; property.
Ovpavtdai, ol, the inhabitants

of ovpavoc, heaven ; that is,

the gods.
A+Qovoq, ov, free from envy.
BXa/Scpog, a, ov, injurious.

Kaieovpyoc, ov, (g.) evil doing;

as a noun, an evil doer,
£tyf\(/<oct ov, useful.
ftlovov, only.
Ilcpi^pb), I carry

hence our periphery,
JXXovrifa, I enrich. '

round;

Exercises. — Greek-English.
'O /3wc iroXXa Xvirnpa iv eavrw (or clvtw) ftpti. Tiyvwinct
otavrov (oavrov). BovXov aptvKiiv itaat, fin cavry fiovov. O
ao^oc «/ ^at/rw ictpvptpei rnv ovoiav. *iXwv c?raii/ov fiaXXov n
vavrov Xtyt. Apiri? kclB' iavrnv (per Be, m itself) tori caXij.
Oi irXeovecrat iavrov^ ptv irXovr&ovoiv, aXXovc tfc pXcucrovtriv.
6v% ol aKpartig rote ptv aXXoic /3Xa/3«poe, kavrotQ (or o<pioiv
avroig) 8e wifuXifioi umv, aXXa Kanovpyoi ptv rtav aXXtav,
tavroiV (or o<f>wv avrtav) St iroXv tcatcovpyorspoi, 'H/mc ptv
ypiv avroiQ ifdicrra xapt£o/u0a. AfBovoi Ovpavitai icai (even)
iv aXXrjXoic tioiv. Ol kokoi aXXnXovc pXanrovoiv.

English- Greek.

The wise carry their (the) property about in themselves.
The avaricious man enriches himself, but injures other*. Tou
gratify yourselves. The intemperate is not hurtful to others,
but useful to himself; but he is an evil-doer of others, and
a much greater evil-doer of himself. Good children love one
another.

B. Adjective Personal Pronouns, or Possessive
Pronouns.

Certain pronouns partake of the nature of an adjective as
well as a pronoun. For instance my, in " my book," qualifies the
noun book, and might, without serious error, be denominated
an adjective ; but since my also represents a noun, a noun of
the first person, or the pronoun I which holds its place, my
may also be termed a pronoun. My consequently is both an
adjective and a pronoun, or an adjective pronoun ; inasmuch,
too, as my, thy, his, &c, signify possession, they may be
also designated possessive pronouns . The possessive pronouns

tffurtpog, a, ov, our
vutrtpog, a, ov, your

Epoc, n>ov, my
ooq, n, ov, thy
<j<piTtpoQ, a, ov, theiis.

Instead of tpoQ, the Attics employed the genitive t/iavrov,
i|C» ov in a reflective meaning, and avrov, nc, ov, in the signi-
fication of the personal pronoun of the third person ; e. g.
tvttth rov iavrov viov, he strikes the son of himself, that is, he
strikes his son, or his own son ; you may also say rvirrn rov vlov
rov iavrov ; also tvttth avrov rov viov, or again rov vlov
avrov.

The possessive pronoun is used in Greek only for the sake
of emphasis. When no contrast or other marked force is
intended the pronoun is omitted, and its place is supplied by
the article, as ?/ pnrnp ortpyu rnv Ovyarepa, literally, the
mother loves the daughter, that is, the mother loves her daughter.
The person of the verb, and the import of the proposition
show what pronoun you should supply in English. Instead
of the adjective personal pronouns tpoq, ooq, fte., the Greeks
use with the same meaning the genitive of the substantive
personal pronoun, as epov, oov, also tuavrov, &c.

Vocabulary.

Mc&fpu)', or, neglectful.

IMEraxtiptZopat, I handle, con-
duct, govern.

Exercises.— Greek-English.
'0 tfiog irarnp ayaBoQ tonv or b irarnp jiov ayaBoc tativ* or

ayaQoQ tan fiov 6 irarnp* Uavrtc ortpyovai rove c^trtpovg
warepaQ or rove iavruv wanpag' or tovq irartpae tovq lavrwv.
Oi vfitrtpot icaitiic awovtiaiuyg ra ypappara jjiavOavovcriv. Oi
TraidtQ vfiwv KaXoi ihtiv. *Tpuv ol natSic trrrovdaioi timv. la
rjfiwv avrt/jv TtKva or ra rticva ra ly/xwv avruv if/tyo/icv. 'O
0iXo? oov mcroQ tcrnv. 'O <piXog fiov airiaroQ tariv. 'O ooq vovq
to 9ov ffiofia fitraxupiZiTai. 'O juv f/ioff iroiff ottov&uoc tanv,
6 de 90Q fuOtjiKov.

English- Greek.

Thy father is good. My father is good. Our father is
good. Their slaves are bad. Our children learn diligently,
but your children are neglectful. Thy friend admires his own
deeds, but not those of others.

2. Demonstrative Pronouns

Are so called because they demonstrate (LaL de and monttro,
I show) or point out persons and things, showing what par-
ticular person or thing is in any case intended. They are 6de t
that person J ovtoq, this person ; avroQ, he himself, him, them, $c.

J3 ►

-1 •<

*«

2 e

i 3

i 5.

a j 5

s. sc-a.

"si

i ^

-i

»l

i i

o# «*

fti

i»»

H 1

I 1

§
o

2
o

•s

S 3 h

'■ ts

1
ft

h 5 i

3 §-

«
-<

•3

a a ?-

" f.

•3

•o

i i

•1

o o

5 2j

-«

2 e

ft A

' 3

«
1

2 C

-s

o
o

n n

« S

a a

•5

•a

•O

«rj

•O

A
5

o e

•e

The pronoun bdt, qZe, rott, is mado cp of the article 6, $, to,
and the particle fc.

Like ouroc decline roGovrot, rooavrn, rooovro, so great ^
rotovroc, rotavrn, rotovro, sttch; rnXtKovroc, rnXueovrn, rsjAssw'-i
xovro, so old, so great ; remark, however, that the neuter I '
gular, besides the form in o, has a form in ov.

LESSONS IN ITALIAN.

ill

T090VTQQ

rovovrov

J).

ro<rovr<p
rovovrov

rocrovrot

roaovruv

TOffOVTOlQ

roaovrovg

N.A.
G.D.

TOffOVTW

roaovroiv

T090VT0 (p)

TOOOVTOV

TOffOVTif)

rotrovro (v)

rovavra
roaovrwv
tovovtoic
rocavra

rooovna T
roaovroiv

Singular*
roeavrn
roaavrtjQ
rovavry
rovavrnv
Plural,
rovavrai
rooovrwv
rovavraiQ
roeavrag
Dual,
roaavra
rotravraiv

The pronoun avroc, n, ©, signifies either he himself (ipse,
ipsa, ipsum), or performs the office of the oblique cases of the
personal pronoun, third person, singular and plural, as him,
h*r, it, them. In union with the article, thus forming o avroc,
ijavrrj, ro avro, it signifies the same, in Latin idem, eadem,
idem. The article by eras is mingles with the pronoun,
making one word, thus 6 avroc = avroc, and in the feminine
and neuter awrjf, ravro, commonly ravrov, but as the crasis
does not extend throughout, I give the pronoun in full.

o^avroQ contracted into avroc.
Singidar. Plural,

avroc abrn ravrov avroi avrai ravra

ravrov . rng avrnc ravrov r<*v avrwv, &c.
ravry rabry ravry roic avroiQ, &c.

rov avrov rnv avrtjv ravrov rove avrovg, &c.
Here you must pay attention to the difference of accent,
thus ravrf, to the tame (woman), is to be distinguished from
rabry, to this (woman) ; and ravra, the same things, is to be
distinguished from ravra, these things.

N.
O.
B.
A.

LESSONS IN ITALIAN GRAMMAR.— No. XIV.

BY CHARLES TAUSENATT, M.D.,

0/ the University of Paria, and Professor of the Italian and German
Languages at the Kensington Proprietary Grammar School.

CoLLOQtJIAL
J-oh&,l have
Tu hat, thou hast
E-gli ha, he has
Not ab-bid-mo, we hare
Vox a-ve-te, you have
E-gli-no han-no, they hare j
Jl giar-di-no, the garden

Exercises.

Com-prd-to, bought
Ve-du-to, seen
No-stro (m.) t our
Vo-stro (m.), your
II zi-o, the uncle
La zi-a, the aunt
i

Exercises. — Italian-English.

J-o ho un li-bro e u-na pen-na. Tu hai un budn li-bro e
u-na bud-na pen-na. HO un buOn fra-t£l-lo. Hai u-na bud-
na so-rel-la. HO un gran li-bro, mi -a so-rel-la ha an-che un
gran li-bro. Mi-o fra-tel-lo ha u-na pic-co-la pen-na. Hai tu
u-na so-r&l-la ? Hd u-na so-r$l-la ed un fra-tdl-lo. Hai tu
la mi-a p£n-na ? Hd il tu-o li-bro e la tu-a pen-na. Ab-bia-
mo un buon pa-dre ed u-na bud-na ma-dre. Ab-bia-mo an-
che un budn fra-tSl-lo ed u-na bud-na so-rel-la. II giar-di-no
e gran-de. Hd un pic-co-lo li-bro. Hai tu an-che un li-bro.?
Ab-bia-mo un gran giar-di-no. II mi-o pic-co-lo fra-t£l-lo ha
un budn li-bro. La mi-a pic-co-la so-rel-la ha an-che un buon
li-bro. Ab-bia-mo un gran li-bro ed tf-na pic-co-la pen-na.
A-?6-teun budn pa-drc ed u-na bud-na ma-dre. A-ve-te v6i
an-che un fra-t&l-lo ? Hd un li-bro. Hd com-pra-to un budn
li-bro. Ab-bia-mo ve-du-to un gran giar-di-no. Mi-o fra-
tfcl-lo ha an-cbe ve-du-to un gran giar-di-no. Hd com-pra-to
a-na pen-na. Hai tu com-pra-to u-na bud-na pen-na ? Hai
tu ve-du-to il mi-o li-bro? Hd ve-du-to il tu-o li-bro e la
ui-a pen-na. A-ve*-te v6i ve-du-to la mi-a pic-co- la so-rel-la ?
Mi-o pa-dre ha com-pra-to un giar-di-no. Tu-a so-rdl-la ha
com-bra-to un pic-co-lo li-bro. A-vc-te v6i ve-du-to mi-o
fra-tdl-lo. Ab-bia-mo ve-du-to tu-a so-rel-la e tu-o fra-tel-lo.
KuVstro pa-dre b un budn pa-dre e nd-stra ma-dre e u-na bud-
na ma-dre. Mi-o pa-dre e tu-o zi-o, e mi-a ma-dre e tu-a
*i-a. VO-atroTra-tel-lo ha ve-du-to il nds-tro giar-di-no. Hd

ve-du-to la vo-stro pen-na. A-vtf-te v6i ve-du-to il nd-stro
pic-co-lo fra-tel-lo ? II vd-stro li-bro e bud-no. Vd-stro fra-
tdl-lo ha u-na bud-na pen-na. Nd-stro pa-dre ha com-pra-to
un gran giar-di-no. Ab-bia-mo ve-du-to vd-stro zi-o. Hai
tu an-che ve-du-to nd-stro zUo ?

English-Italian.

Hypocrisy is a homage which vice renders to virtue. Nature
only requires that which is necessary. Reason demands the
useful, self-love looks for the agreeable, passion requires the
superfluous. The large trees give more shadow than fruits.
God is the father of men and the preserver of the creatures.
The stars of the heaven, the birds of the air, the fish of the sea,
the plants, the animals, are works of the Lord. The scope of
the creation is infinite, the intellect of man weak. The wis-
dom of God is like the light of heaven. The order, the beauty,
and the pleasantness of the world, are evident proofs of the
existence of a supreme being. The excess of the passions is
generally the cause of the misfortune of men. The outbursts
of anger, of envy, and of pride, powerfully disturb the equi-
librium of the humours, the system of the nerves, and
frequently at length injure the mechanism of the body. The
lust of intemperance and incontinence is the enemy which
brings to man the greatest damage ; it weakens his powers,
deprives him of riches, and injures his most precious good,
the health.

Vocabulary.

Hypocrisy, i-po-cri-si-a, f.

Homage, o-mdg-gio, m.

Which, che

Vice, vi-zio, m.

Renders, ren-de

Virtue, vir-tu, f.

Nature, no-tit ra, f.

Only requires, nan do-mdn-da
che (that which^s) .

Necessary (translate, the neces-
sary), ne-ces-sd-rio, m.

Reason, ra-gio-ne, f.

Demands, vuo-le

Useful, u-ti-U, m.

Self-love, a-mtr pro-prio, m.

Looks for, cer-ca

Agreeable, di-let-M-vo-lt, m.

Passion, pas-sio-ne, f.

Requires, cs*i~g$

Superfluous, su-ptr-fluo, m.

Large tree, grdn-de dl-be.ro,m.

Give more, ddn*nopiu

Shadow, 6m»bra, f.

Than, che

Fruit, fruUio,m.

God, Id-di-o, JDi-o

Father, pd-dre

Man, u'> -mo, m.

And, c

Preserver, con-ser-va-to-re, m.

Creature, <re~a-tu-ra, f.

Star, stel-la, f.

Heaven, cie-lo, m.

Bird, uc-cel-lo, m.

Air, d-ria, f.

Fish, jk-'-jm, m. (with the pi.)

Sea, md-re, m.

Plant, pidn-ta, f.

Animal, a-ni-md-Ie, m.

Are, so- no

Work, 6-pe-ra, f.

Lord, Si-gno-rc, m.

Scope, sco-po, m.

Creation, cre-a-zio-ne, f.

Is infinite, e in-fi-ni-to

Intellect, in~ge-gno, m.

Weak, de-bi-lc

Wisdom, sa-pieti'Za, f.

Like, c6'ine

Light, lu.ee, f.

Order, or-di-ne, m.

Beauty, bel-ltz-za (ts), f.

Pleasantness, g%o-con~d%-td y f.

World, Mon-do, m.

Are, so-no

Evident proof, pro-va ma-ni-
ft.sta, I

Existence, es-usten-za, f.

A being, un Be-se-r* (un fa-
te), m.

Supreme, su-prt-mo

Excess, ec-cts-so, m.

Ve&sion, pas- sid-ne, f.

Is generally, e or-di-na-ria-
mtri'te

Cause, ca-gio-ne, f.

Misfortune, in-ft-li-ci-td, f.

Outburst, a-guta-zti-ne, f.

Anger, i-ra, f.

Envy, in-vi-dia, f.

Pride, or-g6~glio, m.

Powerfully disturb, $con-ctr~
ta.no vio*Un~te-m£n-te

Equilibrium, e-qui*li-brio % m.

Humour, Jlu-i-do, m.

System, si-ste-ma, m.

Is erve, ncr-vo, m.

And frequently at length in-
jure, eperft-ne dan-nt'g-gia-
no dn-chc spes-so

Mechanism, tne-ca-nis-mo, m.

Body, c6r-po, m.

Lust, pia-c6-re, ra.

Intemperance, in-tem-pe-rdn*
za,f.

Incontinence, in-con-ti-n&n-
za, f.

Enemy, tut-mf-co, m.

Who, che

Brings, re-ca

The greatest damage, «7 piu
gran dan -no, m.

It weakens, is-so in-dt-bo-U-
sce

His power, la su-afir-za, f.

Deprives him, lo pri-va

Riches, ric-che*-za {ts), (f. with
the pi.)

And injures, e gurt-sta

His most precious good, il sUo
mi-glior be-ne, m.

Health, sa-lu-te, f.

212

THE POPULAR EDUCATOR.

Illustrative Exercises on the Use of D».
EXERCISES . — Italx ak-Enolish. *

U man-t6Mo del zi-o. L' a-bi-to di Gio-Yan-ni. La ca-sa
di mi-a so-rfil-la. II le-var, il tra-mon-tar del s6-le. II n6-me
di Gius-to, di Gran-de. La-na di pe-co-ra. Pan-to di vi-sta.
La ca-sa di cor-re-zi6-ne. Sdn-te-si un c6l-po di pis-to-la.
Ca-ve di pid-tra e di mar-mo. II su-o ca-po d' 6-pe-ra. II
cOr-po di guar-dia. Con un sol trat-to di pen-na. Un toc-co
di cam-pa-na. V6-tro di fi-nG-atra. Fi6r di lat-te. U'-na
ghir-lan-da di tl6-ri. Pez-zo d' i-gno-ran-te che s€i ! La pun-
ta di col-t61-lo. U'-na v6-na d* ar-gfcn-to. Do-ma-ni e gi6r-no
di p6-sta. Ma-6-stro di di-se'-gno, di scbir-ma. Tri-bu-na-le
d' Ap-p&-lo. Bi-glict-to di ldt-to, del m6n-te. La p6-sta de'
ca-val-li. Cer-ti-fi-ca-to d' uf-fi-cio. Im-pe-ro d'Au-atris.
Re^gno d' In-ghil-ter-ra, di Scd-zia, d' Ir-lan-da. La cit-ta di
Ldn-dra, d' E-din-bur-go, di Dub-li-no, di Man-ce-stria, di
Li-ver-pu-la, di Bir-min-ghg-inio, di Gla-sco-via. II me-se di
Gen-na-jo, di Mag-gio. II n6-me di Giu-sep-pe, di Fran-ce-sco.
1/ i-so-la di Si-ci-lia, di Sar-de'-gna. Un quar-to d* 6-ra. U'-
na raz-za di ca-ni. C6r-sa di ca-val-li. Le trfp-pe di pre-ai-
dio, di guar-ni-gi6-ne. La ra-da di TriS-ste. II di-rit-to di
ton-nel-lag-gio. Tas-sa di bol-lo. Un giuo-co di car-te. Pia-
me di struz-zo. L f ac-con-cia-tu-ra del ca-po. L' 6r-di-ne del
gi6r-no. Dig-ci brac-cia di te-la, di pan-no. Un ba-ri-le d' 6-
glio, di a-ce*-t6. U'-na lib-bra di car-ne, di for-m&g-gio. U'n
cen-ti-na-jo di zuc-che-ro, di caf-fe. Un mdg-gio di gra-no.
Un pez-zo di pa-ne, un tdc-co d' ar-r6-8to. U'n quar-to di
bu-tir-ro. Un bic-chiS-re di vl-no, di bir-ra. Ho com-pra-
to di&-ci bot-ti-glie di Bor-gd-gna e eei di Sciam-pa-gna. U'-na
cas-sa di pi-pe. U'n gran nu-me-ro di lu-pi. U'-na quan-ti-tk
di pe-co-re, di man-zi. U'-na in-fi-ni-ta di gcn-te. u'n pa-jo
di scar-pe vta-chie. Du-e pa-ja di sti-va-li, di cal-z6-ni, di

da. U'-na chic-che-ra di caf-fe. U'-na taz-za di te. U'-na
pre-sa di ta-bac-co. Pren-dl-te-mi la mi-sfera d' un cap-pot-
to e d' un pa-jo di cal-z6-ni. U'-na mu-ta di ca-val-li.

Vocabulary.

Mantello, cloak.

Zio, uncle.

Abito, dress

Giovanni, John.

Casa, house.

Levar (for le-vd-re, to rise),

rising.
Tramontar (for tra-mon-td-re,

to set, disappear), setting.
Sole, sun.
Nome, name.
Giusto, just.
Grande, great.
Lnna, wool.
Pecora, sheep.
Punto, point.
Vista, sight, view.
Corretione, correction.
Sentesi, one hears, is heard.
Colpo, blow, shot.
Pistola, pistol.
Cava, pit, mine, quarry.
Pietra, stone.
Marino, marble.
Suo, his.

Capo, head, chief.
Opera, work (capo a* opera,

master-work j.
Corpo, body.
Guardia, guard (corpo ai guar-

dia, main guard, or main

guard- house).

Sol (for ao-lo), sole, only,

single.
Tratto, throw, cast, stroke.
Penna, pen.

Tocco, touch, blow, stroke.
Campana, bell, clock (which

strikes).
Vctro, glass, pane.
Finest r a, window.
Fior (for Jio-re), flower.
Latte, milk (fior di laite,

cream).
Ghirlanda, garland.
Pezzo, piece.
Ignorante, ignorant.
Che, that.
Sei, thou art (pezzo oV ignorante,

blockhead, dunce).
Punto, point.
Coltello, knife.
Vena, vein.
Argento, silver.
Domani, to-morrow.
G tor no, day.
Posta, post.

Maestro, master, teacher.
Disegno, drawing.
Scherma, fencing.
Tribunate, tribunal, court.
AppeUo, appeal.
Biglietto, note, ticket.
Lotto, lottery.

Monte, mountain, pawn-house
(or Mont de Piete).

Cavallo, horse.

Certifieato, certificate.

UJJtcio, office.

Impero, empire.

Regno, kingdom.

InghUterra, England.

Scotia, Scotland.

Irlanda, Ireland.

Mese, month.

Gennajo, January.

Maggie, May.

Giuseppe, Joseph.

Francesco, Francis.

Isola, island.

Sicilia, Sicily.

Sardegna, Sardinia.

Quarto, fourth part, quarter.

Ora, hour.

Razza, race, species, kind.

Cane, dog.

Corsa, course, race.

Truppa, troop.

Presidio, gtiamigione, garrison.

Rada, road, roadstead.

Diritto, duty.

Tonncllagio, commodity pre-
served in casks (diritto di
tonncllagio, tonnage).

Tassa, tax.

Bollo, official seal, stamp.

Giuoco, game.

Carta, paper, card.

Piuma, feather.

Struzzo, ostrich.

Acconciatura, ornament.

Ovdine (military) order.

Died, ten.

Brace io, m. (pi. le brdc-cia, f.),
arm, ell, yard.

Tela, linen*

Panno, cloth.

Barile, cask, barrel.

Oglio, oil.

Acclo, vinegar.

Libbra, pound.

Came, meat.

Formaggio, cheese.

Oentinajo, hundred-weight.

Zuechero, sugar.

Caffi; coffee.

Moggh, bushel.

Grano, corn.

Pane, bread.

Tocco (pronounced t6e-co),
piece, bit.

Arrosto, roast meat.

Quarto, quarter (of a pound).

Butirro, butter.

Bieehiere, glass.

Vino, wine.

Birra, beer.

Ho comprato, I hare bought.

Bottiglia, bottle.

Borgogna, Burgundy.

Sei, six.

Sciampagna, champagne.

Cassa, box.

Pipa, (tobacco) pipe.

Gran (for gtdnde), great,
large.

Nutnero, number.

Zupo, wolf.

Quantitd, quantity.

Manzo, young ox.

Infinitd, innumerable multi-
tude.

Gente, people.

Pajo, m. (pi. lepd-ja, f.), pair

Scarpa, shoe.

Vecchio, old.

Stivale, boot.

Calzoni (ts), xn.pl., trousers.

Calza (ts), stocking.

Vcntbia, number of twenty,
score.

Zecchino, sequin (gold coin
current at Venice and in
Turkey, about 9s.).

Cinque, five.

Miglio, m. (pi. le mi-glia, {.),
(Italian) mile (of 3,000
paces), also an English, Ger-
man, or French mile.

Strada, road, way, route.

Chicchera, cup.

Tazza (ts), cup.

Te (pron. te), tea.

Presa, pinch.

Tabacco, tobacco, Bnuff.

Prendetetni, take.

Mixura, measure.

Cappotto, great coat or cloak.

Muta, team.

* That he may clearly understand the difference between the two
languages, the pupil will do best, wherever ic is allowable, to
translate these exercises by English compound nouns, or by corn*
bina'ion* of nou s, or by id jecivci preceding no n».

ANSWERS TO CORRESPONDENTS.

T. O. L.: Not the slightest precipitate results from the addition of
nitrate of surer to a solution of pure arsenlous add in pure water; neither
to a solution of arsenioas acid in alkali, e. g ., (liquor arseniealis) prorided
the alkali be neutralised by an acid (say acetic) previously to the addition of
nitrate of silver. If this treatment be not exactly followed, a precipitate in
solution of certain strength may occur ; nevertheless, it is different frost
the pure yellow precipitate resulUng from the ammonia— nitrate of silver.
T. G. L. is evidently a minute observer of phenomena. Previous neutralisa-
tion would have been taken for granted by a chemist.

A. C. H. : A common gas flame smokes all apparatus which it touches:
the spirit lamp flame yields no smoke ; hence the advantage in the latter.
Nevertheless, the mixed gas flame, as it Is called, yields no smoke. We
shall describe the method of employing this source of heat hereafter.

EDoaa Black.— The translation is this, (< Remarks upon various points
in the system of Latin instruction, Krunswick, 1844."— S.G.fLoughboro.):
Separate treatises are best ; buy Hymer's or Snowball's Trigonometry, or
H ami's, which may be had for a shilling.— J. Huasr( Wigan) .Ten thousand
thanks. Hebrew will take its place in the P. £. We shall make good use
of your letter.— W. 8. Follxtt (Bognor) : Many thanks for kind remarks.
— Kuogamma (Wolverhampton) : See Teubiter's list of Classics, which
nay be had of D. Nutt, Foreign Bookseller, Strand.— Pu i lomath (Aber-
deen): The Scotch colleges are the cheapest.— H. 3., UK FaANjois . We
think not.— J. C. Halliday (Newcastle') : You are wrong, and we ate right;
surely you do not mean to say that 5 times it 51!— Nine fiairisn
SCiiuLAHS (Wortest r) have sent its the correct solution of the boys aod
app'.er question ; we shall Insert their names, uhen they do greater tilings
than this!! and that of a Constant SuBscaiBsa v £ast H addon) tool— 3
Wills (Crewkcrne): No

NATUJKAL PHILOSOPHY.

213

ON PHYSICS OR NATURAL PHILOSOPHY.
No. XV.

CAPILLARY ATTRACTION.

(Continued from page 205 )

Quite of the Curvature of liquids in Contact with Solid*. — The
differences in the form of the surface of a liquid in contact
with a solid body, arise from the differences in the ratio which
exists between the attraction of the solid for the liquid , and of
die attraction of the liquid for itself. Suppose, for instance,
that a liquid particle m, fig. 54, is in contact with a solid body.
This particle is under the action of three forces ; "viz., 1st,
gravity, which attracts it in the vertical direction m p, 2nd,
the attraction of the liquid itself, which acts in the direction
nip, and 3rd, the attraction of the solid which acts in the direc-
tion mn. Now, according to the intensities of these forces,
their resultant will take the three following positions, figs. 64,
55, and 66 :

Fig. 51.

Fif . 55.

Fig . 5S.

1st, fig. 54. When p, the attraction of the liquid to itself, is
double of », the attraction of the solid to the liquid, the direc-
tion of the resultant m h, coincides with that of gravity tn p ;
and the surface of the liquid at m is horizontal ; for, according
to the condition of equilibrium in liquids, formerly explained,
their surface must be perpendicular to the direction of m r,
that force which acts upon their particles.

2nd, fig. 65. When f, the attraction of the liquid to itself, is
less than Ike double of w, the attraction of the solid to the
liquid, that is, when the force n increases, or the force p
diminishes, the direction of the resultant »»r is within the
angle nmr, and the surface takes a direction perpendicular to
that of the resultant ; whence it becomes concave.

3rd, fig. 56. When p the attraction of the liquid to itself is
greater than double of if, the attraction of the solid to the liquid,
that is, when the force p increases and the force n diminishes,
the direction of the resultant m r is within the angle pmp, and
the surface takes a direction perpendicular to that of the
.emltant ; whence it becomes convex.

Fig. 57.

Effect of Curvature on Capillary Phenomena. — On the concave
or convex form of the meniscus depend the ascent or depres-
sion of a liquid in a capillary tube. For example, since, by
the preceding statements, the liquid particles of a concave
meniscus abed, fi». 57, are kept in equilibrium by the forces
which act upon them, they exert no attraction on the lower
layers of the liquid ; but they act, in consequence of molecular
attraction, on the layers nearest to. them ; whence it follows
that upon any layer mn, situated in the interior of the tube,
the pressure is less than if there hod been no meniscus. Conse-
quently, according to the conditions of the equilibrium of a
liquid mentioned in a former lesson, the liquid must rise in the
tube until the interior pressure on the layer tn n be equal to
the pressure represented by op, which acts exteriorly on any
point,? of the same layer.

In the case of the liquid particles of a convex meniscus,
ghik, fig. 58, the equilibrium still exists, in consequence of

Fig. 58.

the molecular forces which act upon the liquid ; but the
capillary action of the particles which occupy this spaee being
counteracted, they no longer act upon the lower particles.
From this it follows, that the pressure on any layer m ti,
situated in the interior of the tube, is greater than if the space
ghikvfere full of liquid, for the molecular forces which act
within it are more intense than that of gravity. The liquid
must therefore sink in the tube until the interior pressure on
the layer m u, be the same as that at any point q of this layer,
exterior to the tube.

Cause of the Attraction and Repulsion of light Bodies floating in
a Liquid. — We have seen in a former lesson, that the light
bodies which float on the surface of water, and which are
wetted by that liquid, are drawn towards each other whenever
the distance between them is sufficient to admit of capillary
action. The same effect is produced between two light Dodiet
which are not wetted by the liquid. And if the liquid wets
the one body and not the other, they exhibit a repulsion,
which prevents their contact. The following is the explana-
tion of these three cases.

1st, fig. 59. When two plates of glass are immersed in water,
parallel and near to each other, they have a tendency to meet;

TOE. IT*

-M

for if the line of liquid level m n be drawn, every portion of
liquid situated above this level is raised in consequence of an
attraction which acts upon it.

Now it is evident that on the exterior face of the plate a,
the active portion of the attracted liquid rises only to the point
p t whilst on the interior face of the same plate this portion
rises to q. There is therefore a predominating force, which by
its surplus of intensity tends to draw the plate a on this side,
towards the plate u, and if it were free it would move in that
direction ; in like manner, the force indicated by the difference

214

THE POPULAR EDUCATOR.

of level between </ and p' t would cause the plate b to move
towards the plate a.

2nd. fig. GO. When the plates of glass are immersed in mer-
cury, this liquid assumes the foim shown in this figure, m

r\i. co.

formerly indicated. Now it is evident, according to the laws
of the equilibrium of liquids, thnt in the case of the plate a,
the mercury ribitiK on the one side to p and on the other side
to q, its exterior face is more powerfully urged or pushed
than its interior face, and that in consequence of this difference
of pressure the plate a must be pushed towards the plate b.
The phenomenon being symmetrical for the plate b, it is in
like manner pushed or urged towards the plate a.

3rd. fig. 61. When the plates of glass are such, that on
immersion, the one, a, is wetted by the water, and the other, b,

being rubbed over with grease, is not wetted, then, in conse- 1
quence of the latter cause, the plate B depresses the level I
between the plates, and the liquid rises only to q on. the
adjacent side of the plate a, whereas it rises to p on the other
side ; whence, the difference of these attracting forces,
measured by the difference of ievel between p and q, will
occasion a separation between the plates. Conversely, in con-
sequence of the attraction of the plate a, which raises' the level
between the plates, the liquid will only sink to q' on the adja-
cent side of the plate b, whereas it sinks to q' on the other
side ; whence, the difference of the pressure of these forces,
measured by the difference of level between p' and q\ will
occasion as before a separation between the plates ; and thus
the mutual repulsion of the plates, on account of both causes,
will be the result.

The theory of capillary action, one of the most difficult in
Natural Philosophy, can only be treated fully and completely
by the aid of mathematical analysis ; and thus has it actually
been investigated by the most eminent mathematicians of
modem times, especially by MM. Ciairault, Laplace, and
Poisson.

Curious Fact* relating to Capillary Action— When a capillary
tube is immersed in a liquid which wets it, we find that if we
withdraw the tube with care, the liquid column which remains
suspended in the tube is greater than that which rose in
it when the tube was immersed. The reason of this is
that the tube draws after it a drop of liquid which adheres to
its lower part, and there forms a convex meniscus whose
action unites with that of the concave meniscus at the top, and
thereby supports a greater column.

For a similar reason, when a capillary tube is immersed in a
liquid, no issue takes place, although the tube be shorter than
the liquid column which would rise in it were it longer. For

at the instant when the liquid has reached the top of the tube,
its upper surface changes from concave to convex, and conse-
quently the pressure becoming greater than if the surface were
plane, the ascensional motion is arrested.

Capillary action is the cause of oil rising in the wicks of
lamps, of the imbibition (drinking in) of liquids in wood, in
sponges, and generally in all bodies which are sensibly
porous.

LESSONS IN BOOKKEEPING.— No. XII.

THK LEDGER.

{Continual from page 200.)

We have already said so much on the Ledger, and the manner
of posting the Journal into it, in Lesson VI., p. 339, vol. III.,
that we have now only to refer our students to that Lesson
again for the proper explanations before commencing the
study of the Ledger. Wo shall here, however, repeat empha-
tically what was there taught in another form, in order to
impress their minds with the simplicity of the method of keep-
ing Books by Double Entry.

When an entry in the Journal contains only a single Dr. and
a Single Cr., thi? rule is to Titbit the Dr. and Credit the Cr.;
this has been explained at p. 341, vol. III. When an entry
in the Journal contains a single Dr.' and a number of Crs.,
included in the word Sundries, the rule is to Debit the Dr. and
Credit each of the Crs. When an entry in the Journal con-
tains a number of Drs., included under the word Sundries, and
and a single Cr., the rule is to Debit each of the Drs. and
Credit the Cr. Now, as nothing can be more simple than these
rules, we proceed to explain the method of striking a General
Balance, that is, of finding out a Merchant's Assets and Liabili-
ties, and consequently whether he has gained or lost by
trade.

In commencing the process of balancing the Ledger by
Double Entry, the first thing is to close up all accounts in it, of
which the two sides, Dr. and Cr. , when added up, are perfectly
equal, or balanced by the settlement of account. This will
generally be the case in a great number of the personal accounts
at the end of a given period, say the close of the year, or at
Midsummer. To close up such accounts is merely to add up
the suras on each side, to draw lines under the sums exactly
opposite each other, to put down the totals, and to draw lines
under them also. If there be any space left in the folio under
an account thus closed, it may be used for the entries of new
transactions under the same account, or with the same party.

' All the self- balancing accounts being closed up, the Trial
Balance is now to be made out ; this consists of a list of all
the unbalanced accounts in the Ledger, with the total sums of
all the entries on each side inserted in Dr. and Cr. columns,
for the purpose of easy reference in making out the General
: Balance, ar.d for the immediate object of ascertaining the accu-
i racy of all the entries in the Ledger. The latter object is at once
I obtained by adding up both sides of the Trial Balance, via.*
I the Dr. side and the Cr. side ; for if the sum of both sides be
I the same, the strong presumption is, that the Ledger is cor-
rect; and, of course, the Journal, and all the subsidiary Books,
equally so. We say the strong presumption only, because
i there sometimes occurs in a Ledger such a thing as a balance
of errors, that is, when a wrong entry on the Dr. side of the
Ledger is balanced by a wrong entry of the same amount on
the Cr. side.

In Balancing the Bools, as the phrase is, very great trouble is
I saved in making out the Balance Sheet and Check by Double
Entry, in consequence of the admission into the Ledger of all
the Property and Profit and Ldss Accounts, and indeed of every
J account in any manner affecting the business. In conducting
this process, as shown at the end of the Journal, in our last
I lesson, two new accounts arc opened in the Ledger, the one
I being called Balance Account, which is to be considered thecon-
I Terse of Stock Account as to its Dr. and Cr. sides ; for on the Dr.
| side are contained all the Assets, and on the Cr. side all the JMf-
bilities ; the other being called The Profit and Lost Account, which

ontains on the Dr. side the amount of all the Losses experienced
in business, and on the Cr. side the amount of all the Gains,
I By means of these two accounts, all the unclose/1 accounts in

LESSONS IN BOOKKEEPING.

the Ledger are balanced, and the Rail Worth of the Merchant,
as well as the Net Gain of the business, is ascertained, inde-
pendently of every book but the Ledger.

In order to effect this purpose, the Balance Account is now to
be debited to every Personal or Property Account on which there
is a balance in favour of the Merchant, such balances forming
what are called his Assets ; and Balance Account is next to be
credited by every Personal or Property Account on which
there is a balance against the Merchant, such balances forming
what are called his Liabilities. Consequently, on the principles
of Double Entry i a? soon as these entries are made, the
accounts of both kinds must be balanced, that is, the sums of
both the Dr. and the Cr. sides will be alike, and the accounts
themselves may be closed up in the same manner as those
accounts formerly mentioned which balanced of their own
accord, that is, from the nature of the transactions entered on
both sides. The two sides of Balance Account thus constitute
the Balance Sheet of the Merchant, and their difference consti-
tutes his Real Worth at the time when the Balance is made in
the manner we have described. For this difference, or Beat
Worth, Stock Account is made Dr. to Balance Account, and thus
the Balance Account is closed up as other accounts are in which
bolh Dr. and Cr. sides are alike. The amount for whioh Stock
Account is debited showing the Merchant's R.al Worth,

The Profit and lose Account, which may be called the Check
Account, because it constitutes the real check on the Balance
Sheet of the Merchant, is now to be debited ti> every Projjcrty
or Profit and Loss Account, on which there is a difference exhibit-
ing a Jams on the business ; and the samp Account I* to be cre-
dited by every Property or Profit and Loss Account on which
there if a difference exhibiting a Gain. Consequently, as soon as
these entries are made, all accounts of both kinds must be
balanced as before, and the accounts themselves may be closed up
as formerly directed. The difference between the amount of the
Lome* and the amount of the Gains on opposite sides of The
Profit and loss Account, will exhibit at once the Net Gain or the
Net Loss, according as the amount of the one or the amount of the
other preponderates. If the difference bo Net Gain, it is then
placed to the credit of the Stock Account, and the Profit and Loss
Account is then balanced by debiting it to Stock Account. If
the difference be Net .Loss, the Profit and Loss Account is then
balanced by crediting it by Stock Account. Of course the for-
mer process will show that the Merchant has gained by his
business, and that his Stock is increased ; the latter process
will show that he has lout by his business, and that his Stock
is diminished.

"The Net Stock, independent of Gains and Losses, is at once
ascertained by deducting from the amount placed to the credit
of Stock Account the amount abstracted from the business* for
Private Account, that is, for the Merchant's own private use, as
Household Expenses, &c. This is done systematically by
making Stock Account Dr. to Private Account, as we have done
• in the Journal, in the first entry under the head of General
Balance', this entry at once balances Private Account and
reduces Stock Account to its proper dimensions. When all the
entries above mentioned have been made in the Stock Account,
it will be found that the sums of both sides of this account are
the same, a demonstrative proof that the books are correctly
balanced, and that the Merchant's Real Worth has been cor-
rectly ascertained. Stock Account may now be closed up, and
the Books are completely balanced. If the Ledger will admit
of carrying on the business for another period, whether a whole
year, or half a year, all the accounts which are closed up by
'Balance Account must have the balances carried under the
closing up lines, to the opposite sides of these accounts, in
order to carry on the business as before ; but if a new Ledger
be required, the balances can be entered in the new Stock
Account, as New Assets and Liabilities, and Journalised and
posted as if they were original entries in the New Ledger.

In the old Italian system of Bookkeeping, the question was
usually put to the Bopkkccper, in order to test the clearness of
his views on the subject,. " What is the reason that the differ-
ence of the Stock Accflunl added to the difference of the Profit
and Loss Account, gives the exact difference of the Balance
Account V With thiagp/jestion we* leave our students at the
present, hoping that, frnm what we have said, they will be able
to answer it

Andrews and Company
Althorpe and Company
Allison and Company

Bills Receivable
Bills Payable
Brown and Smith
Baring, Smith and Co.
Balance Account

INDEX TO LEDGER
A

Cash Account
Cotton Account
Charges Account

East India Company

Interest Account
Jones, Thomas

I
J

London and Westminster Bank
Lloyd and Company

N
O

Manning, James

Oamond and Company
Ovington and Compauy

Private Account
Petty Cash Account ...
Powell and Company
Perkins and Compiny
Profit and Loss Account

Stock Account
Spencer and Company

Three per Cents
Thompson and Company

White and Company
Williams and Company

Q
R

X
Y

THB POPLLAB EDUCATOR.

(1)

LEDGEE A.

(1)

Db.

STOCK ACCOUNT

Cb.

June

To Private Account ...
To Balance Account

£59
1882

l! £1941

Jan.
June

By Caah Account

B y Profit and Lots Account

Db.

PRIVATE ACCOUNT.

Cb.

Jan.
Mar.

April
June

To Caah Account
To Caah Account
To Cash Account
To Caah Account

£10

£ 59

June

30 By Stock Account

7 £59

£59

Db.

CASH ACCOUNT.

Cb.

Jan.
Feb.
Mar.

April

June

To Sundries

To London and Westminster Bank?
To Sundries ...
To Sundries
To Sundries ...
To Sundries

£2206

Jap.

220

Feb.

2920

Mar.

1160

April

1679

May

1800

June

30
30

£9976

»>

By Sundries ...

By Sundries

By Sundries ...

By Sundries

By Sundries ...

By Sundries

By Balance Account

£2205
220
2908
1161
1661
1815:18
2\A

£9976|

ff>

LEDGEB.

(2)

Db.

PETTY CASH ACCOUNT.

Cb.

Jan.

Feb.
April
rfy
June

To Cash Account
To Cash Account
To Cash Account
To Cash Account
To Caah Account

£10

June

' >»

£60

By Charges Account
By Balance Account

6
7

£57
2

£60

8
11

Dju

BILLS RECEIVABLE.

Cb.

June

To Sundries ...

To Sundries

To Powell and Co.

£600

May

2132

June

6 1

308

£3040*15

By Cash Account
By Cash Account ...
By Balance Account

218

THE POPULAR EDUCATOR.

LESSONS IN CHEMISTRY.— No. XIV.

In our previous lessons we have not found it necessary to
specify the state in which any particular metal was dissolved
Whilst treating of zinc, for instance, we simply dissolved that
metal in dilute sulphuric acid, and called our result sulphite of\
tine. I certainly in general terms remarked, that the so-callcl
sulphate of sine was really a sulphate of oxide of zinc ; but I
did not intimate what denomination of oxide of zinc, whether
protoxide, binoxide, deutoxide,* peroxide, or any other oxide.

As regards the metal zinc, there was no necessity to have
been thus precise, inasmuch as only one oxide is capable of
forming solutions. As regards antimony there was no necessity!
inasmuch as, although that metal unites with oxygen in many
proportions, only one oxide combines readily with acids to
form solutions ; but had our labours been very far extended in
connexion with this metal, we should have been obliged tc
take cognisance of several oxygen compounds of antimony.
When we came to treat of arsenic, there was a necessity at
once for discriminating between the kind of solution yielded by
this metal. In one case we had nxsenious acid to deal with,
and its combinations ; in the other case arsenic acid and its com-
binations. The distinction between the action of certain tests,
especially nitrate of silver, 0:1 those two was very manifest,
showing the necessity of well discriminating between the two
kinds of existence in which arsenic might be found.

There exists the same necessity for discrimination as regards
tin. Thyi metal will come before us in the condition of com-
pounds of two different oxides : the protoxide, and the per-
oxide (from per, very much). Th» term- peroxide is applied
to the highest degree of oxidation short of acidity which any
body can assume.

The protoxide of tin is thrown down from the solution of the
protochloride, on the addition of potash (liquor potaasoe), car-
bonate of potash, or liquor ammonia). In an excess of the
former it is soluble.

The most prominent chemical characteristic of the protoxide
14 its strong affinity or tendency to combine with oxygen.
On the exercise of this property depend most of the chemical
operations in which protoxide of tin, or its compounds, take
part ; and it was in order to jiuard against the exercise of this
tendency tha', during the formation of our tin solution, we
prevented as much us possible the access of atmospheric nir,
lost the oxygen gas of the latter should combine with cur
solution of protoxide of tin, and convert it into a ptr wide.

If this precipitated protoxide be washed without exposure
to atmospheric air, with the same precaution, and carefully
bottled up, it may be preserved as protoxide. The conditions,
however, are almost impossible.

Lst us return to the examination of the protoxide as it
exists, or as it is generated in our solution. If we adopt the
ih'iory that the solution is a muriate of protoxide of tin, the
n -tide will be assumed to exist there ready-formed ; if we adopt
the other theory, the oxide will be formed by the agency of our
testing operations.

ExpcrinwiU 1. — Test a little of the solution with hydrosul-
phuric acid, either as an aqueous solution, or as a gas, and
remark the black precipitate.

How is this ? some person may say ; dAd you not tell us that
tin if one of those metals which afford a yellow precipitate
with the agent just employed ? Yes, it is quite true I did
state this as the result ; but I qualified my statement by the
remark that pers'ilte of tin only had this effect. We are at
present operating with a protosalt.

Experiment 2.— Repeat the testing operation with hydrosul-
phate of ammonia instead of hydrosulphuiic acid ; the result is
as before.

Here, then, we are at length introduced to that division of
the calcigenous metals which developc black precipitates with
hydrosulphurie acid and hydrosulphate of ammonia. Hence-

*' Binoxide. and Deutoxide are not convertible terms,
metal by m, and oxygen by o, the di (Terence is this :
Binoxide :=mo 2
Deutoxide =m 2

Representing a

forward we shall find that every metal capable of yielding
a precipitate with the*c reagents yields a black precipitate.
There can be no difficulty in remembering this fact.

Experiment 3. — Add to some of the protomuriate a little of
the solution of chloride of gold, and vou will produce what is
termed the purple powder of Cassi>(9. If the solution operated
upon bo very strong, the precipitate, instead of being purple, is
black. Dilution whh water brings out the purple colojr, but its
true beauty is only seen when fused with other compounds into
a glass. A little borax answers peifectly well for this purpose
and the platinum wire bent into a loop us formerly d'esscribed
serves as a very convenient support for the globule, while
undergoing the procrss of fusion. The chloride of gold is thus a
very delicate test f«.r tin in a certain btate of solution (proto-
salt) ; with no oilier metal does it produce a similar effect. It
follows, therefore, that if chloride of sold be a test for pro to -
salts of tin, the latter are also tests for gold in a certain stat$
of solution. Thus you learn two facts at once; indeed all facts
relating to the operation of testing are necessarily binary ; one
learns them in pairs.

Experiment 4. —The experiment about to be performed h
very curious and instructive. It will require some little
delicacy of management to insure complete success. Add
carefully, and by small quantities, a solution of bichloride of
mercury to a solution of protomuriate of tin. By due appor-
tionment of the two liquids, a white precipitate will fall. Add
now more, and this white precipitate changes to black.

Tig. No. 1

The operation snoiild be performed in a test tube as repre-
Sen ted in fig. No. 1, not only for the purpose of allowing the
action of heat, by which treatment a more perfect deposition
Of the powder is effected, but for other reasons which will
loon be made apparent.

Fhj. No. 2.

When all the precipitate has bec-v.ne black, thoroughly
deposited, and condensed into a small spa<:«\. pour off the liquid

LESSONS liN CHbMlSTHY.

219

which floats above, boil the precipitate with a mixture of
, water, containing a few drops of muriatic acid, decant the
liquid, finally wash with water and dry.

I will show you now Kow to dry a closed tube or a bottle or
flask, neither of which is so simple an operation as you may
think. For certain reason?, \*hich I need not explain in this

Slace, the amount of heat that you may employ without preju-
ice to your result is very trifling. "Without danger of any bad
consequences, however, the tube may be thoroughly warmed j
oefore a fire. Being warm, insert a tube thus, fig. No. % and |
exhaust the ait with the mouth, by which means all the mois-
ture will be gradually removed. Mere blowing will not d<\
inasmuch as the breath contains moisture. The exhnusti< cj
might in this case be performed, without prejudice to health, 1 i
the lungs; but in many other cases the vapour might 1
injurious; it is well therefore to be always on the guard against
contingencies, and get into the habit of performing exhaustion
by the mouth and cheeks, not bringing the lungs into play.

When the tube and its contents have become thoroughly
dry* proceed as follows, fig. No. 3.

lig. No 3.

Protochloridc / Chlorine \

i Tin i „,.

i l lin

, Bichloride f Chlorine ^

i of \

Mercury [Mercury .

— Pel chloride, of Tin

is deposited

One remark connected with this beautiful decomposition
still remains to be made. Our chart of decomposition only
shows the final result; the precipitation of metallic mercury.
Hut what was the nature of the white powder which fell before
the black precipitate? That white powder was the proto-
chloridc of mercury, ordinarily known as cuImuu-1. The fact
is, that bichloride of mercury admits of being considered as a
compound of protochloridc with chlorine, thus*

Bichloride / Chlorine

of
Mercury ( Protochloridc

Or as mercury united with a double dose of chloride, thus :

Bichloride / 2 Chlorine

of
Mercuiy ( I Mercury.

The first effect on a solution of bichloride which protochlo-
ridc of tin produces, is the removal of mi equivalent of chlorine,
as the result of which calomel (protochloridc) deposits; but the
protochloridc finding it has stolen with impunity one equiva-
lent of chlorine, it returns to the charge and steals the other
as well.

Holding the tube bv means of a paper handle in a spit it-
lamp flame, at about the angle of 15°, apply heat until
an incrustation takes p'lace in the tube somewhere about tht
position b. Now what, think you, this incrustation is ? Hub
it with the ( nd of a stick, and remark what follows. The crust
disappears and a number of liquid metallic globules become
evident ; somi times indeed they appear at a stage of the opera-
tion much anterior to this. These globules are of mercury,
they are metallic quicksilver. This fact is quite evident, then,
our protomuriate of tin has taken away, either directly or
indirectly, all the chloride from the bichloride of mercury.

* The reason of this change will be moat easily rendered;
apparent by means of a diagram, and in reference to this
diagram let me premiss that, just as we are allowed to call a
solution of protochloride of tin, protomuriate of oxide of tin,
so may we also call a solution of bichloride of mercury, bimu-
liate of oxide of mercury. AVe will frame our diagram in
accordance with this assumption.

Muriatic y -\ Permuiiate of

Ad I / | Peroxide of

rr0 f tO ^ e } Protoxide --/'---- p,roxidof' ^
oflm I ofTi|lf X . _,,..,_ !

Profomu
riate

Till- [

of J

of Tin j

Bimuriate r Muriatic /

of I Acid
Peroxide [

of Peroxide off Oxygen
Mercury I Mercury I Mercury.

*— is deposited

The preceding diagram demonstrates the changes which!
ensue on the assumption, that the two respective chlorides I
become muriates or hydrochlorates on solution ; the following 1
diagram demonstrates the changes on the assumption that the I
two respective chloridis dissolve as such. In this case the
.final result will be arrived at by the occurrence of the following |
Bit ion. •

LESSONS IN G K K M A N.— A'u. LX XIX.

J M. Obskrvations on thk Paradigm.

(1) An inspection of the preceding Paradigm will show, that
Hie separation of the prefix from the radical part of the verb takes
place in the Indicative, Subjunctive, Imperative, Infinitive,

when preceded by ju,) and the Perfect Participle. In the In-
dicative and Subjunctive, however, the separation is not made,
when, in dependent sentences, the ver j is placed at the end of
a clause or period : thus, at* tie Senile ticfen -Wprgcn aufging, fo

trjtywant tec 9t<M, when the sun rose (aufgiiui) this morning, the
fog disappeared.

2) In regard to the portion of the particle when separated,

It must be noted that, in the Indicative, Subjunctive, und Im-

erative, it stands after the radical ; often, also, after the several

words dependent upon it : thus, i$ fange ta6 &uc$ an, (where a n

belonging to fa ngr, comes after the object), I begin the book.

(8) In the Infinitive and the Perfect Participle, on the cou-
ttary, the particle comes be/ore the radical : being separated
ftom it, in the Infinitive, by $ it, (when that preposition is cm-
ployed), and, in the Participle, by the augment g c, which is
peculiar to that part of the verb: thus, anjufaiujcn, (au-f-ju+fnnaen)
to begin; to commence; vergcjtrUt, (w-J-»j<+iWlt) placed before
one; represented.

(4) It remains to be added, that particles, when separated
from the radicals, receive the full or principal accent; and
that the radicals (if verbs) have the same form of conjugation, •
old or new, regular or irregular, as when employed without
prefixes.

JjD4. Inseparable Pkkfixks.

The Prefixes of this class, as the name implies, are always
found in close union with their radicals. They allow not even
the augment syllable «e, in the Perfect Participle, to intervene,
rut reject it altogether : from this, however, must be excepted the
se of the Prefix mifr which, in a few instance?, allows the
gment %< to be prefixed; thus, (from mtpreuttn, to mis-
interpret) wc have, in the Perfect Participle, gr tiiijjmwt j as

2S0

THE POPULAR EDUCATOR.

toccft (not fceartedt) covered, from Uttdtn, to cover. Neither is
3U (when used) allowed to come between the prefix and the In-
finitive; but stands before the two combined into one word :
as, ju cmrfangrn, (not empuifanacn), to receive : except in case of
compound prefixes, wherein the first component is a separable
ardthc second an inseparable particle; ju being then inserted
between the two particles; as, anjuerfennen, (from ancrfrnncn).
The inseparable prefixes are always unaccented.

§05. Simple Prefixes inseparable.

Jlfter, after, behind afttrrrten, to talk behind

(one's back) ; to slander,
St, near, by, over, to make ; fPcfpnumn, to come by, i. e.

to get, to obtain.
Cmp, in, within; Grmpfmtcn, to find or feel

within, to perceive.
$nt, apart, away, to deprive of; (Sntyicn, to go away or off;

to escape.
£r, forth, for, on behalf of ; GrHAren, to make clear for

(one) ; to explain.
&c, (mainly, intensive or eupho- (Metcnfen, (same as ten fen)

nlc) ; to think of.

STOiji, wrdng. erroneously ; Qflifcteuten, to misinterpret,

©er, away, at a loss ; 8?crfa)(afen, to sleep away,

i.e. lose by sleeping.
flBiter against ; ffiiterfte&eii, to stand against;

to resist
3rr, apart, asunder ; Berfdjneiben, to cut apart, or

in pieces.

§ 96. Compound Prefixes inseparable.

Qkta to go.
Skbem, to draw.
©inten, to bind.
$aiu»t, the head.

Jlraft, power.

9(tte, dim-eyed, dull, bashful.

Srtnnnt, to burn
Bxrtdftn, to speak.

»nfc (an+fce, to —near) ;

Slner, (an+er, to — for) ;

Slufrr, (auf+er, up — for) ;

Huttt (aus+er, out — for);

Snfctreffcn, to hit or touch

near to; tfjeoncern.
flnerfennen, to acknowledge;

to own.
9luferbauen, to build up for;

to erect.
9lu*cro?a^en, to choose out
for ; to elect,
anvcr, (a;i+rct, to — away) j ?lnvertrauen, to give away in

trust ; to confide to.
93eauf, (be+auf, near — on or up) ; ifieauftragen, to bring (duty)

upon, i.e. to commission.
SMijiwr, (miji+m, wrong — away) ; SDHjjmjle^en, to understand

wrong, i.e. to mistake.
fBer&c (vor+te, before — near) ; 9?or*e$aften, to hold or keep

ahead, i.e. to put off; to
reserve.

§ 97. Observations.

(1) 33 e has in German the same power which it has in
English. It is, therefore, in most cases, better transferred than
translated. Its uses will be easily learned from examples.
Thus, from

JMogen, to mnan.
©treuen, to strew.
$o(gcn, to follow,
fcrfretten, to labour
8o$en, to laugh.
Bulge!, a wing.
(Slucf, happiness.
%tt\, free.

'.Beffagen, to 6«moan.

^ejlreuen, to bestrew.

Srfolgtn, to follow after, i.e. to obey.

JBforfcrttcn, to labour upon ; elaborate.

$etci$(n, to laugh at.

SBeffugeln, to furnish with wings.

©egludtn, to make happy.

a?efrcien, to set free.

(fratoefcn, to go away, to get oft

Gntjiefrn, to withdraw.
Cntbinten, to unbind.
ffnt$aia*ra, to deprive of head*

to behead.
(Sntfrdften, to deprive of power,

weaken.
ffntMctcn, to divest of shame,

be bold.
Gntcrennen, to take fire, to kindle.
©ntfpret^n, to answer, or cor*

respond to.

<J n t is sometimes, also, merely intensive or euphonic : as,
entUeren, (from leer, empty), to empty out.

(3) d x and v e r. (Br, a* a general rule, conveys the idea
of getting or gaining for some one, by means of that which is
expressed by the word connected with it; as, e r b i 1 1 e n, to get,
or try to get, by begging. It finds its exact opposite in * e r :
which marks what is against or away from some one's interest
or benefit; as, vettftten, to beg off, to decline. The force and
use of these particles are best illustrated by examples.
»atcn to bathe. Grfraten, to get or gain by bath-

giittcn, to find.

Steven, to stand.
&auen, to build
Bagen, to say or speak.

. In some instances, it is merely euphonic.

(2) firm* andent. (rm» is, probably, only another form
of cat: occurring, however, only in three verbs (onpfmben, to
feci; empfangen, to receive; emtftjfcn, to recommend) ; and bearing
a sense but remotely related to its original. The prime and
predominant power of en t, is that of indicating separation, de-
parture, privation.

In some instances it has the kindred sense of approach or
transition from one point or condition towards another. Ex-
amples.

ing.
(frpntm, to find out for one's

self, invent.
GfTfltfpn, to arise, originate.
(Frfautn, to erect, to produce.
3?erfagen, to speak against, to
deny.
aWautrn, to wall, or make a wall. 95ermaurrn, to wall against, stop

by wall,
©jrielen, to play. 95erfpieten, to play away, to lose

by gambling.
8u$ren, to carry, or lead. aScrfufrtn, to lead away, to se-

duce
©aljen, to salt SSerfaljen, to oversalt, spoil in

salting.

(4) Orr and.ber are, also, both employed in converting
nouns and adjectives into verbs expressive of transition from
one state or condition into another : thus,

Grfaltei!, (fait, cold) to take cold. a?erebdn, (rtel, noble) to enno-
ble.
Gr?u$nen. (f u$n, bold) to become 93crg5ttrrn f (®ott, God) to deify.

bold, dare.
<$rra$men, (la$m, lame) to be- SSeratten, (aft, old) to grow old

come lame. or obsolete.

CftHaren, (War, clear) to make ©creinen, (ein, one) to make one,

plain. unite.

In some instances, moreover, er and ttx are only euphonic
or intensive.

UNIVERSITY OF LONDON.— No. V.

(Continued from page 209.)

Wednesday, Jtdy 6.— Afternoon, 3 to 6.

CHEMISTRY.— (Examiner, Prof. Graham.)

1. Describe the chemical properties of the atmosphere,
referring particularly to the nature and proportion of its con-
stituent gases and the uses of each in the economy of nature.

2. What are the products of the combustion of metals, of
hydrogen, and of ordinary carbonaceous fuel, in atmospheric
air ? Explain the nomenclature of oxides.

3. GWe the chemical formulas and equivalents of the follow-
ing compounds :— water, nitric acid, ammonia, carbonic acid,
sulphuric acid, phosphoric acid, chloric and hydrochloric*
acids.

4. How is chlorine gas prepared ? Mention the remarkably
compounds into which that element enters as a constituent.

o What are the products of the action of diluted sulphtrsrtj
acid upon the metals zinc and iron? How is the solutiorx at

LONDON UmVERSlTY.

tel

«bo affected by bringing copper or platinum into contact with
that metal in the acid ?

6. Give an account of the composition and properties of the
alkali potass*.

7. What are the earthy salts which occasion the hardness of
water?

8. What takes place in the slaking of quicklime with water,
and in the setting of plaster of Paris ?

9. How is the metal iron prepared from the argillaceous car-
bonate of iron, the most common ore of that metal ?

10. What are the acid solvents of mercury, silver, gold, and
platinum?

11. What is the cause of the liquefaction of ice, and of the
conversion of water into steam ?

Ihuraday, July 7. — Morning, 10 to 1.
GEOMETRY.— (Examiner, Mr. Jihrard.)

1. Give Euclid's definitions of a point, a line, and a super-
ficies. Is it possible to define satisfactorily the elementary
abstractions of Geometry ? Distinguish between a postulate
and an axiom.

2. From a given point to draw a straight line equal to a
given straight line.

3. If two angles of a triangle be equal to each other, the
sides also which subtend the equal angles, shall be equal to
one another.

4. Show that if two triangles have two sides of the one equal
to two aides of the other, each to each, and have likewise their
bases equal ; the angle which is contained by the two sides of
the one shall be equal to the angle contained by the two sides
equal to them, of the other.

How may this proposition be proved, when the triangles are
on different sides of the common base ?

5. To draw a straight line perpendicular to a given straight
line of unlimited length, from a given point without it.

6. If a straight line fall upon two parallel straight lines,
show that it will make the alternate angles equal to one
another ; and the exterior angle equal to the interior and
opposite upon the same side ; and likewise the two interior
angles upon the same side together equal to two right angles.

Discuss Euclid's twelfth axiom. Is it necessary that some
positive property of parallel lines should be assumed as an
axiom, on which reasonings on such lines may be founded ?

7. Equal triangles upon the same base, and upon the same
tide of it, are between the same parallels.

Hence show that a triangle may be bisected by a line drawn
rom any point in one of its sides.

8. To describe a parallelogram equal to a given rectilineii
figure, and having an angle equal to a given rectilineal angle.

* 9. In any right-angled triangle, the square which is des-
cribed upon the side subtending the right angle, is equal to
the squares described upon the sides which contain the right
angle.

10. Find a point within a given triangle, from which lines
drawn to the several angular points will divide the triangle
into three equal parts.

librium of a lever. Is this condition independent of the weight
of the lever ?

A uniform lever is 12 inches long, find where the fulcrum
must be placed so that a weight of 70 ounces at one end shall
balance 50 ounces at the other (1) when the lever is without
weight, (2) when it weighs 30 ounces.

3. What is understood by obtaining a mechanical advantage ?
In a single fixed pulley, is any mechanical advantage obtained?
What is the greatest weight a man standing on the ground can
lift by means of a single fixed pulley ? In a single movable
pulley with the strings parallel, state' the condition of equili-
brium. If the strings be not parallel, will it require more or
less power to support the same weight ?

4. How is velocity estimated (1) when uniform, (2) when
variable ? How is • uniform force ' numerically measured ?
Is gravity a uniform force? If gravity be measured by 32*2
feet, find the space a body will fall through in one second from
rest : find the velocity it will acquire in 50 seconds ; find also
the space it falls through in four seconds and a half.

5. State the third law of motion ; mention any experiments
that support the truth of this law. What is understood by
the momentum of a body ? How is moving force estimated ?

If a weight of 100 lbs. fall freely, and a weight of 200 lbs.
slide down a smooth plane inclined at an angle of 30° to the
horizon, compare the moving forces.

6. Define a fluid ; distinguish between compressible and
incompressible fluids. Why is water considered generally in
hydrostatical problems as incompressible ?

How is it shown that by the transmission of fluid pressure,
any very small force may be in equilibrium with any very
great one ?

7. Define specific gravity ; in determining the specific
gravities of solid bodies, what advantages has a liquid (water)
as the medium of comparison? Show how to determine the
specific gravity of a lump of heavy metal.

8. Describe the construction and action of the common
barometer ; supposing the vacuum at the top of the tube per-
fect, would the mercur> be actually supported in the tube if
the open end were not inverted in a cup of mercury? In
ascending a mountain, does the mercury in the barometer rise
or fall?

9. How is a ray of light represented geometrically ? What
is understood by a pencil of rays ? Explain the reflexion of
light, and trace the position of the images of a point placed
between two plane mirrors parallel to each other.

Thursday, July 7.— Afternoon, 3 to 6.

NATURAL PHILOSOPHY.— (J£ramm«n, G. B. Jerrard, Esq.,
and Rev. Prof. Hxavisidb.)

1. Define force. Explain the advantage of representing
forces by geometrical lines, and show the propriety of doing
so. When two forces act upon a particle, what must be the
magnitude and direction of a third force acting upon the same
particle to keep it at rest ?

Will two forces acting in one plane always have a single
resultant}

Find the resultant of two equal forces acting on a point at
an angle of 120°.

2. Define a lever. Express generally the. ^audition of equi

Friday, July 8. — Morning, 10 to 1.
LATIN.— (Examiticr, Dr. William Smitii.)

Translate into English :

(A.)—" A." inquit " ille Virginius, quia in Capitolio non
fuit, minus supplicii (1) quam Ap. Herdonius meruit? Plus
hercule aliquanto, qui vere rem sestimare velit. Herdonius, si
nihil aliud (2), hostem ee fatendo (3) prope denuntiavit ut arma
caperetis (4) ; hie negando bella esse arma yobis (5) ademit,
nudoaque servis vestris et exsulibus objecit. Et vos (C.
Claudii pace et P. Valerii mortui loquar) prius in clivum
Capitolinum aigna intuliatis quam hos hostes de foro tolleretis?
Pudet deorum hominumque (6). Cum hostes in arce, in Capi-
tolio essent, exsulum et servorum dux profanatis omnibus in
cella Jovis optimi maximi habitaret. Tusculi (7) ante quam
Roma sumpta sunt arma. In dubio fuit utrum L. Msmilius
Tut culanus dux an P. Valerius et C. Claudius consulcs Koma-
nam arcem liberarent (8) : et qui ante Latinos ne pro se qui-
dem ipsis, cum in Ambus hostem haberent, attingere arma
passi sumus, nunc, nisi Latini sua sponte arma sumpsissent,
capti et deleti eramus (9). Hoc est, tribuni, auxilium plehi
ferre, inermem earn hosti trucidandam objicere ? Scilicet si
quis vobis (10) humillimus homo de vestra piebe, quam partem
velut abruptam a cetero populo vestram patriam peculiaremque
rem publicam fecistis, si quia ex his domum suam obsessam a
familia annate nuntiaret, ferendum auxilium putaretis (11 J.
Jupiter optimus maximus exsulum at que servorum septus
armis nulla humana ope dignus erat? et hi postulant ut sacro-
sanct i habeantur, quibus ipsi dii neque sacri neque sancti sunt r

3222

THE POPULAR KDUCATOD.

At enitn divinis humanisque obruli sceleribus legem vos hoc
anno perlaturos dictitatis. Turn hercule illo dip, quo ego con-
sul sum ere at us, male gcata res publica est. pejus multo qunm
cum P. Valerius consul periit, si tuleritis." — Livy. Book III.
chap, 19.

Explain fully the construction of all the words to which
numerals are attached in the preceding passage.

(B.) — Ad clad eg ab hostibus acccptas duo nefanda facinora
decemviri belli domique adjiciunt. L. Siccium in Sabinis,
per invidiam decemyiralem tribunorum creandorum secessio-
niirque mentiones ad vulgus militum sermonibus occultis seren-
tem t prosqeculatum ad locum castris capiendum mittunt.
Datur negotium militibus, quos miser ant expedition is ejus
comitcs, ut cum opportuno adorti loco interficerent. Haud
inultum interfecere : nam circa repugnantem aliquot insidia-
tores eecidere, cum ipse so praevalidus, pari viribus animo,
circumventus tutaretur. Nuntiant in castra ceteri pnecipita-
tum in insidius esse Siccium egrcgie pugnantem, militisque
quondam cum eo amissos. Primo fides nuntiantibus fuit.
Vrofecta deindc cohoro ad sepeliendos qui ceciderant, deccm-
virorum permissu, post qu am nullum spoliatum ibi corpus
Sicciumque in medio jacentem arrnatumque, omnibus in eura
versis corporibus, videre, hostium neque corpus ullum nee
yestigia abeuntium, profecto ab suis interfectum memorantes
rettulere corpus. Invidioeque plena castra erant, et Romam
ferri protinus Siccium placebat, ni decemviri funus militare ei
publica impensa facero maturassent. Sepultus ingentl mili-
tum msenitia, pessima decemvirorum in vulgus fama est. —
Livy. Book III. chap. 43.

1. Name the voice, tense, and mood of the following verbs,
and the present tense of each : — desideret, inehoastis, percuiit,
expulerat, assererct, faverit, arcessi, decrease, accendisset,
paterttur.

2. Name the principal parts (i.e. the present infinitive, pre-
terperfect indicative, and past participle) of the following
verbs :— abstraho, adorior, adimo, progredior, pergo, gpondeo,
prehendo, quiesco, queror, sino.

3. Decline the following nouns :— iter, bos, senex, vis, jus-
jurandum.

4 Name the distributive numerals from one to ten inclu-
sive.

5. Give the exact meaning of the pronominal adverbs : — hie,
hflc, hinc, hllc.

6. Give the etymology of the following words: — insidite,
mogister, integer, effircnatus, expeditus, iniquus.

7. Draw a map of Italy, showing its political divisions in
the last century of the republic.

8. Give the dates of the following events : — the battle of
>5ama, the capture of Corinth, the death of Tib. Gracchus, the
death of Julius Caesar.

!). Give a brief account of the internal history of Rome
from the expulsion of the kings to the legislation of the
decemvirs.

10. Translate into Latin : —

(« ) If I see him, I will tell him.

\b.) This prevented me from seeing my brother.

(e.) The e::emy sent ambassadors to say that they surrendered
everything to the consul.

(rf.) The chief knew that those things were true, and no one
received more pain/row his conduct (ex eo) than himself.

(e.) The chief said he knew that those things were true, and
no one received [he said] more pain from his conduct than
.himself.

(/.) You must consider what you are to do, whether jrou
HJU be at Rome, or along with mc in some secure place.

Friday, July S.— Afternoon, 2 to 5.
ENGLISII LANGUAGE.— {Examiner, Mr. Buroham.)

1. Who wore the Angles, and what wag their relation to
the Saxons?. Mention the chief Anglo-Norman elements of
the English Langing".
. 2. State the languages from which the following words

were introduced into the English i— flannel, jerked, hammock,
chapman, holme, holt, apparatus ) plaid, street, muslin.

3. Give a list of words in the English which seem to be
vernacular though they have a foreign origin. How do you
account for the introduction of such words ?

4. What is the grammatical distinction between gender and
text " We may consider such substantives to have been con-
sidered as masculine, which were conspicuous for the attri-
butes of imparting or communicating; or which were by
nature active, stiong, and efficacious, and that indiscriminately,
whether to good or to ill ; or which had claim to eminence
either laudable or otherwise." Give instances from languages
to which the above theory is applicable or otherwise.

6. Determine the meaning of compound words by the order
in which their components occur, and give examples.

6. «* In certain words of more than one syllable it is difficult
to say to which syllable an intervening consonant belongs."
How do you solve the question ?

7. In what different modes is the perfect tense of the English
formed ? What division has there been made of vtrbs and
tenses in consequence of this difference of formation r* tfow
do you account for the fact that a great number of verba in
one of these divisions has a double form of the perfect ?

8. What is the origin of the word own in the phrase to otcn
to a thing ? Explain and account for the phrast* — this trill do —
it did for him— mind and do this — he minded hu business.

9. What words may be called significant by themselves, and
what significant by relation ? Classify the words in the follow-
ing passage according to this distinction —

The man that hath no music in, himself,

And is not moved with concord of sweet sounds,

Is fit for treasons. •

10. " As words follow the nature and genius of things, such
substances admit of number as denote genera or species, while
those which denote individuals, in strictness, admit it not."
Explain the above passage, and enumerate the causes from
which individual or proper names have been made plural.

11. What is the reason that in the English and most lan-
guages the pronoun of the third person has its genders, while
the pronouns of the first and second have none at all ?

12. Give a rule for distinguishing between the genuine
pronoun and the genuine article. Why did the old gram-
marians call the relative pronoun— vieoraKriKbv &o9nov-the
9i4tyunctive article ?

LESSONS IN GREEK.— No. XVIII.
By John R. Beakj>, D.D.
3. The Relative Pronottn uc, t), o,- who.
Singular, Flwal. Dual.

A T . be, A 6, ni a\ a,

O. oh tjg ob, ■'"• -- J "

A. ov i)v o,

mv wv «in', oil' a\v o\v.

oi f ale oiq, o\v a\v oil'.

OVC, «£ a, w a w.

4. Indefinite and Interrogative Pronouns.

Declension of ric, some one ; and rig, who f
Indefinite rig, some one. Interrogative tic, «« 1*°?

m. &f. n.

R.N. rig, ri, somewhat, rfc, who, which ? W, what
G. nvoc,, or

rov rivoc, or rov
D. rtvi, or

ry rlvi, or rip

A. rivti ri riva ri

P.N. rivlc Tit'ti, or arret ttvtc. riva

G. nv&v rivwu

D. rial riot

A. rivac. tiv&, of arm rivag rivet

D.K.A. rivk rive

G;D. nvoXv. rivoiv

Lessons in greek.

The indefinite rig is an enclitic, *. e. it inclines or throws
back its accent on the foregoing word. In general the indefinite
pronouns are distinguished from the interrogative by being
enclitics, and by their coming after, while the interrogative
stand before* other words.

By uniting bg with rig, we obtain ooriCi t)ng, brt, who,
whoever ; which is declined thus :

Singular.
N. bang, tfrig, b n

O. ovrivog, or brov, i)orivog
D, utrtvt, or QTtp t yrci't
A. bvnva, qvrtva, 6 rt

Plural.

oirivtQ a'mvtg artva, or

arra
utvrivtov (rarely wrwv)
olarim (rarely broig), otartat
ovarivag, aartvag, ariva,
or arra

Dual, N.A. wnvt, artvt. G.D. oivnvoiv, aivnvaiv.

The interrogative pronouns, such as rrctog, of what kind }
irooog, how great ? irortpog, which {of two) t in becoming indefi-
nite and dependent, take 6 before them thus : biroiog, of whatever
kind; oinxroc, of whatever magnitude; birortpog, whichever.

The negative compounds of rig, namely ovrtg, ovri, /iijric,
ftnri, no one, nothing, follow the simple rig, thus : ovng,
ovrtvog, ovrtvt, ovnva, ovrt, ovrivtg, ovnva, &c.

VOCABI'LAITT.

EnoroXi}, tig, y, a letter.
Hfupa, ac, if, a day.
Erparqyog, ov, 6, a general.
Toowog, ov, o, a manner, mode

of life, character.
'Potiov, ov» ro, a rose.
'JSra?ro£, j|, ov, each, every

one.

Kptot, at, a, some.

Olof, a, ov, of what kind.

Mtjfoig, pnctfiia, /if/cer, pnett

vog, no one.
E£cra£w, I inquire into, prove,
♦povrt^w, I care for; with

ace, desire, pursue.

Exercises.— Greek-English.

'O avnp ovrog (or ovrog b avnp) ayaOog tanv. *H yvwpn
airy (or avry ») yviapn) tiiKaia tanv. *H yvvn, »/r*« (or tprit)
yvvn) icaXij eorcv. *0 avnp tKiivog (or crm'oc 6 avnp) fiaoiXtvg
iortv. '0 fiaoiXevg avrog (or ai;rof 6 ^afftXti'f) orparnyog
iortv. *«pe ai»r<p, w irat, rnv xXttv. Evioi ?r*pi rutv avrtov
rife avrqg i)ptpag ov r'avra ytyvtaaKovaiv. To Xiyuv Kai to
xparrtiv ov ravrov tanv. Tavra ra potia, a OaXXei tv rtp
Knmp, KaXa tanv. jEo^ov rt xpnpa 6 avQpiaicog tanv. ft
ftXiav rov (for rivoc) tiiwKug, rov rpoirov avrov t%tra%t. Tig
ypaftt ravnjv rijv imaroXnv ; Atyt pot bang ravrnv rnv
tviaroXrjv ypa<pti. 'Qv (by attraction for «) t\tig, rovrmv
aXXoig irapt\ov {communicate to others {tome) of those things which
you have). QXfitog torn* (p irailtg <pi\ot tiaiv. Exurog oX/^iw-
rnrog, ortp (for y rivi) pnttv kokov tarty. Ti $povn'£tig ; Ov Xtyu>
b ri jpovriZw. Oiov ro t9og Inaorov, roiovrog 6 fitog. Tig ttrriv
txttvn t) yvvn ; Atyt fiot, i/rtc tartv tKtivn r) yvrn.

There are some things in this exercise on which a few words
seem desirable. First advert to an exemplification of an
enclitic, as seen in the words oo<pov n :

re is here an instance of an enclitic ; first observe it comes
after aofov, and then observe that it is so connected with it
as that the two are pronounced together, almost or quite as if
they were one word, thus vofovri. In consequence of this, rt
receives the name of enclitic ; and for the same reason, losing
its own accent, it throws it back on the preceding word, thus,
oo+ov rt ; to in the Latin, sapiens?**.

You see, in these exercises, the free use made by the classic
Greeks of the article : thus they say b avnp ovrog, t) yvvn
fcitvi}, ovroc o iraig, rovro ro rrpaypa (or ro irpaypa rovro) 9
that is, the woman this, or this the woman, for this woman ; some-
times, as when emphasis is sought, we have such a construc-
tion at the following, 6 avnp b ovrog, the man, the thin.

The difference between the interrogative and indeterminate

pronouns is exemplified in two or three examples in the last
exercise, thus :

Interrogative, rig ypatyti ravrnv rnv tmoroXnv;
Indefinite, Xeye /iot bang ravrnv rnv tiriuroXnv ypafit,

The direct interrogative rip passes in the second sen-
tence into the indirect interrogative, or the dependent and
indefinite bang : take another instance —

Direct Interrogative, ri fpovrtZug, What are yon earing for >
Indirect Interrogative, ov Xtyut b rt fpovrtfa, I tell {thee) not

what lam caring for.

English-Greek.

These men ore good. Those opinions are just. Tho
children of this woman are beautiful. Thoso roses are beau-
tiful. The father himself writes the letter. His son (the son
of him) is wise. His daughter is beautiful. I admire those
beautiful roses, bring them to me. The children of the same
parents are often different. This rose which blooms hi
the garden is beautiful. Virtue is something beautiful. What
do they concern themselves about? fopovrcgw). They con-
sider (fpovriZ*) what friendship is. What is more beautiful
than virtue ?

Correlative Pronouns.

are such as express a mutual relation one to another, as is
exemplified in the words— how much ? so much ; this kind,
that kind, &c. Thev may be arranged under the heads of
interrogative, indefinite, demonstrative, relative and depend-
ent pronouns. Thus, *-6ooc, how much? (Latin, quanlue})
asks a question which is answered hv rooog, *e much (tantus) ;
itorrog may also signify of some size (aliquantus), and so become
indefinite ; and if we wish to say " I know not how much,"
v. r • mploy baog or bwoaog, and so call into use a relative and
it' i endent form.

Inter, ludef. Demon, Rel. $ Dtp.

irooog, n, ov, rroaog, n, ov, roaog {poetic.) baog, n. ov

how great? of tome size, roaog? t, or roo- birovog^,ov
how much ? ovrog, so great. how great.

ttoToCi a , ov, iroiog, a, ov, rotog, a, ov (poetic.) otog, a, cv
of what kind} of some kind} roiogf i,or roiovrog biroiog, a,ov,
qualis? of that kind, tnlis. of what kind.

irnXtKog,ri,ov,
of what age?

wanting. riiXucog,n,ov {poetic.) qXiKag, tj, ov
rqXtKog&i birnXiKog,

rnXiicovrog, IwwoM?

of that age.

The enclitic ye is appended to the personal pronouns of the
first and second person, so as to give force and prominence to
the word, as tyioyt, tfioiye, epovyt, tptyt, avyt, &c. It is almost
impossible to give an English equivalent for yt, for by this,
as well as by other particles, the Greeks expressed shades of
meaning to which we have no counterparts ; ye, however,
may be approximative^ rendered by at least, or but.

The particles tin, Snirort, and ovv are added to the inter-
rogative and Indefinite pronouns, as well as to oaog, in order
to generalise their application, that is, to make them apply to
everything included in the idea they convey, having a foice
similar to our ever, soever, &c-., as in whatsoever, whosoever,
hoto much soever, &c. ; e. g. barnin, borigtmirort, bangovv,
ringovv, briovv, whoever, whosoever, whosoever it mag be, &c.
(Latin, quicunque) ; genitive, ovnvoaovv or brovovv, r)oriv-
ogovv ', dative, tpriviovv or bnpovv, &c. ; so also, biroaogtn,
brroaogovv, birooogtnirort, how grrnter soever (Lat. quantue-
cunque) ; genitive, brroaovtn brroarigin, biroaovovv, biroangovv,
biroaovtintrort, bnoongtriicort.

The enclitic ictp is subjoined to relatives, in order to raise
the relative import into a demonstrative, as bgmp, ifirtp, birip,
who indeed) so boogtrtp, otofirep ; also, bOmtp and bOtvirtp.

The inseparable t demonstrativum, demonstrative iota, is
affixed to demonstratives as well as to some adverbs, to
augment the demonstrative force, being equivalent to our

THE POPULAR EDUCATOR.

1 which man do you mean ? thia man ?" j Anabasis, Book ifi M which are the subjects selected

vulgar there, aa'in"i .__ . - -„- _

* No, that man ther$r This use of * resemble* the Latin ce, **"***«"** BA - •»" *•.**£&"« **»™ iB *tt»». '
« in hit* and the French d. a. in celuW. : M yj£2iU^ ^ °°

JV. ' -- -

rovn, that thing

Jf.

#.iV. Oi'TOai, THAT MlOfl

tf. rot/rot/i
•D. rovTtfi
I' <tV. otrott

avrnt, that woman

ravrnct

ravryt

d by the University of
>, 185L

Tuesday, February

Fet to Master* of unendowed school* and Ushers, for a single Class, £1 ;
for aU the Classes, £l 10*.

At tendance upon these Lecture* and the examination, daring two yean,
will entitle the parties to be called Students of the Collrge, and so to be
■ Candidates for Degrees in Arts In the University of London, if they hare
- complied in other respects stfeli the Regulations of the University.
] Gentlemen, who are not Schoolmasters, on special application wOl be
. w A admitud to attend tl.ese Lectures at a fee or £3 for each C«nse, This attend-

So in oil, tf3t, roct, from oct ; ovrvtri from ot>re*£ ; tvBaCt, snee will count towards a Certificate of Studentship with a view to a decree,

for gentlemen who. on their adatisiiou to the Classes, shall show tkewuelree
to be Ucenty-Jiee gears of age, and trJto are wuUricuUtted Students of the
College, as follows -.—The Courses of M tthenuUcs and Natural Philosophy
as one short Coarse, and the Courses of Latin and Greek as one short
Coarse.

Hasten of unendowed schools and ushers may a!ao attend the Birkbeek
Erening Coarse of Instruction in Practical Chemistry, given by Professor
Williamson. The CiMirre* consist of Fifteen Lesions, of two hours each,
on Wednesdays and Fridays, in the months of May and June, from 7 to 9
P.M. Fee.XJ.

'I, itVOi.

CORRESPONDENCE.

UNIVERSITY OF LONDON.

Mb. Editor— I am one of your most obliged and grateful
admirer*, who, after the insight afforded in your most Taluable

K nodical of the possibility of matriculating at the University of
•ndon, took courage, worked steadily on by myself, and had the
good fortune of passing first class. Haying succeeded thus far, I
am desirous of going on for a B. A. degree, but find a cruel bar to
my progress in the certificate required, of having been two years
in one of the collegiate institutions connected with the University.
I therefore resort to your kindness, and crave of you your advice.

I am but a clerk in a mercantile firm, employed from 10 till 6
o'clock, therefore it is evident that I cannot attend any college
during the dag. Is there then no way of overcoming this obstacle ?
no means of obtaining a certificate without this attendance during
the day at one of the colleges ? Any suggestion you could kindly
favour me with I should receive with the deepest gratitude, and it
would cau«e me infinite relief, since from my elation at my first
success, I am now quite downcast at the appearance of this seem-
ingly insurmountable barrier,

I think the remarks you make in No. 41 concerning this certifi-
cate are most just ; for why should the not having been in a colle.
giate institution prove a barrier ? since there are self-taught students (
quite as worthy of being honoured as those reared in a college ;

We have formerly remarked that we should be glad if the Uni-
versity of London were open to all students who can show sufficient
evidence of proficiency in the Examinations for Degrees, whether
they have attended a College connected with the University or
. not. We think that the fees which must be paid previous to the
Examination will be a sufficient bar to any persons attempting to
pass who have not a reasonable hope that they are duly qualified,
especially as these fees are never returned, although very properly
the Candidates are allowed to try again. We would strongly advise
our correspondent, and others in the same circumstances and
having the same desire, of whom we have reason to believe there
are many among our subscribers and readers, to pet up a petition
to the Senate of the University of London, soliciting that body to
apply to Government for a new charter, which shall include a
regulation to this effect : that the Examinations for Degrees of
every kind shall be open to all persons who shall have paid the fees
required by the statutes, and who shall be able to show by Certi-
ficates of character from their employers, relations, or friends, that
they are known to be industrious and studious ; that they are of

, . w . good moral conduct; and that they have not, in any case, contra-

and, indeed, one would think they are more to be praired for perse- ' vened the laws of their country,
vering in their application to study, without the (almost invariably j As there will be a meeting of the Senate of the University of
necessary) spur of a preceptor ; moreover, do not self-taught I London about the middle of next month, we shell be most happy
students need some encouragement ? And if there is none (when ' to receive from the metropolis, and from all parts of the United
they have no defined object in view, no goal to reach), will not , Kingdom, the names of those of any of our students, and of others,
many linger behind, and perhaps finally give up the emulative , who are desirous of signing such a petition, with their reasons for
struggle in bitter disappointment ? Trusting that I may yet retain , the same, in order that we may draw up the document in proper
some hopes, with many thanks, I am in anticipation, yours, &c, form, submit it to their approval, and present it on their behalf to

Albert H. Ernest. that learned and influential body.]
London, 2, Mortimer Villas, King stand,
16 Dec., 1863.
[The subject on which our correspondent writes is a most import-
ant one, and his case is one which must enlist the sympathy of
every liberal-minded friend of education. Would that he could be
admitted to the degree under the circumstances he describes ! The
Regulations (or rather the Charter) of the University will not,

ANSWERS TO CORRESPONDENTS.

Hbxton (Halifax) : We think that the last lesson in French Indicates
'■ sufficiently that the 8xcond Pabt of the lessons in that language is
I finished.— A. Pupil: Neither India rubber nor Indian rubber is correct,
„ x . ! but Caoutchouc. In .French, read the works of Cuvier, Chateaubriand, 8t.

however, admit of it; for the Charter contains an express pro-, Pierre, Marmontel, Bufibn, Montesquieu, Pension, Pascal, &c
vision that every Candidate for the B.A. degree shall have studied | j. Maxtin (Btrood): HI* method of squaring the circle brings out the
at one of the affiliated Colleges ; and the Regulations fix the term • answer to every question more than twelve and a-half times greater than the
of such study at two academical years , and the Senate of the Uni- ' truth.

versity could not, if they would, dispense with this condition. j A Studbmt of Mensuration (Liverpool) will find a table of the areas

The only possible opening thst we are aware of (and we think it • of circles, commencing with a diameter of 1 Inch, and advancing sjadually
lUBwuij jrww> *v» w o m ^ 9mMm9MW%Am . . **:_;_ #h „ Q-kn^i , i ot an inch In every diameter, till it reaches 100 Inches, in •• Adcoek's
is really the only one) for our correspondent, is to join the School- | ^ neet . g Pocket .jlok"-^ book vhich contains many other useful
master's Class at University College, Gower-street. By the fol- . ub f cg ^_s. staetof (Swanscombe) : There is a Map of the World in the
lowing extract from the Prospectus of that college, it will be seen | p. e , vol. i., p. 305; but a larger one will be given,
that he might get the B.A. degree by so doing, but not before he is , j. c. A. (SomersMown) : Our subscribers would Justly laugh at us if we
26 j ears of age. This class is held in the evening two or three i answered hit queries. Let him consult the Indexes to the volumes of the
times a week ) **• E.— Cymxo Bach : We don't understand the passage, and perhaps it

LECTUBM TO SCHOOLMASTERS. ' £.*£ "" " m ~ ta '' '* ""» ""* " ** ** *"* " *"" ~

Then Leetureebate been eetablitlud out of fundi placed at the j *" (Stoafort) : The tern ,«<**<*. !• d.rired from itbe Omk «W>o»o^u.

FATXlOTi

Four Courses will be delivered, each of Fifteen Lectures, on Latin,
Mathematics, Natural Philosophy, and Greek, by the Professors in the
College of the respective •objects, on Tuesdays and Thursdays, from 7
to 9 P.M.

The Lectures on Latin will begin on Thursday, October *0th, and continue
till Thunday, February 2nd, iuclusive.

It is hoped that there wi.l be time to read all the books named by the
University for the Examinations this year, and also to give some half-hours
to detail* which be «r on Latin Composition. The Books are for the B.A.
degree, Cicero pro Archia. Pro Lege Manilia, Pro Marcello, Somnium
Bcipions; and for Matriculation, the first Oeorgtcof Virgil.

The Lectures on Mathematics will begin on Tuesday, October 18th, and

ntlnue till Tueiday, February 7th.

The Lectures on Greek will begin on Thursday, February 9th and con-
tinue till Thursday, June 1st, on the lphlgenia in Aulis, and Xenophon's

the study of Its general modes of aetion, of its relations with our faculty of
perception, and of the power of determining the characters of the beautiful
in its productions.

Jm. R. is right, but there are many before him. We have received
numerous answers to the boy and apple question. It was generally solved
by Double Position; otten by guess; and frequently by algebra. By the
last method, it Is solved as follows :— Let * be the number o apples; then
the 1st b3y received Jx+4, and there remained \*—\ \ the 2nd boy received
|x+t. and there remained i#— J ; the 3rd boy received |jr+ |( and there
remained \x—\, which by the question* is equal to nothing; therefore,
&*=!. or sr=7, the number required. We shall now propose a question our*
selves to all our students : If four equal balls, say of 10 inches diameter eaek>
be placed as close together as possible ;— that is, all touching each other j—
what must be the diameter of another ball which, placed in the middle of
the four, will touch all of them at once ?

LESSONS IN MUSIC.

225

LESSONS IN MUSI C— No. XXI.
(Continued from pay e 185, Vol IV.)

OP ACCIDENTAL FLATS AND SHARPS,

AND BULBS FOIl RRCOOSISIXG OS THR STAFF THB NOTES OF
TRANSITION, TUB DISTINGUISHING NOTES OF MINOR KRY5,
- AND CHJLOKATIC NOTES.

All notes which differ -from the ordinary notes of the key are
distinguished in the old notation by flats, sharps, or "naturals,"
placed immediately before thorn, and aro known by the common
name of " accidentals." They are not, however, truly accidental,
for each one has a distinct musical character and a special purpose,
as will sppear from the previous sections. It is important, then,
that tbe pupil, when he sees the dumb sum of flat or sharp, should
be able to decern its meaning, and to tell whether it indicates a
transition of the whole music into this or that related key, with
such or such a peculiar effect, or merely a chromatic variation
without changing the key.

The note tu being substituted for fah of the previous key, and
being about half a tone above it, is represented by a note in the
place of fah, with a sharp before it. It is often called the " eharp
fourth." Thus :

3=1

m
m 1

sd 1

tu sj
t d'

mm^*

¥=&

f
f

s till 1

»d ti r

s
d

In fanes which have flats in the signature, tu is represented by
a note in the place of fah, with a mark called a " natural" before
it, which neutralizes the previous flat (the last flat to the right is
always on fah), and so answers the purpose of a sharp. Thus :

^Sfe

d
d

f m tu, g
f "»li ti d

1 tu, s
r ti d

=j=j=a

m f r m

m f » mlt

till s f m
ti <U f m

The " natural " indicates tho removal of some previous flat or
sharp, and the restoration of the note before which it is placed to
its position in the (so-called) " natural " key. It thus sharpens a
note previously flat, snd flattens a note previously sharp.

The power of the " accidental " sharps, flats, or naturals, ex-
tends to any notes similarly placed in the after part of tho same
measure (or bar), even when the sign is not repeated, but no fur-
ther. Hence the necessity for putting a flat before the returning
fah. It would not have been required if there had been a bar
between it and the previous tu.

Accidentals are, however, frequently placed before notes where
tnt-y are not absolutely needed, especially in cases where the com-
poser fears that the singer or player might be in danger of mis-
take. However useful this practioe in helping bad players, it is
VOL. IT.

a frequent annoyance to the singer in his early attempts, alarming
him by the appearance of difficulty where there is none.

Tho note fi being substituted for tb of the previous key, and
being about half a tone below, is indicated by a note in the place
of tb, with a flat before it It is frequency called the " flat
seventh." Thus :

Key Rjtat.

"•

Kbt E.

d
d

d d 1
d «s

fi 1
f m

d d 1

d dg

fi 1 s

f m r

In tunes which have sharps in the signature, a " natural "
effects the same purpose as the flat in other cases. It removes the
sharp (the last sharp to the right is always on tb), and so changes
tb into FT.

Bah, being used instead of fah, and about half a tone above it,
is represented, like tu, by a note in the place of fah, with a sharp,
or, in flat keys, with a " natural," before it. Some treat it as the
same thing as tu. It is commonly called the "sharp sixth
(reckoning from lah) of the minor key."

Nb, being used instead of 6oh, and about half a tone above it,
is represented by a note in the place of soh, with a sharp, or in
keys with three or more flats in the signature, a " natural " before*
it. It is commonly called the " sharp seventh (reckoning from
lower lah) of the minor key." Thup,

=±=13*

fct

m bah ne 1

§&z

I 1 ne bah ne

Ni, being about half a tone above the son of its own key,
which corresponds with doh in the original key, is represented by
a note in the place of doh, with sharp or natural before it as the
case may require. It is the ** sharp seventh of the relative minor
of the cubdominant key.*' It is a note of frequent occurrence.

Nu, being about half a tone above the soh of its own key,
which corresponds with rat in the original key, is represented by
a note in the place of ray, with sharp or natural before it as the
case may require. It is seldom used.

3*E

E*E

fi, 1, r ni r

f, m { li ne li

±3=2

d l

tUi

d l

-li

nei

aas

THE POPULAB EDUCATOR.

Chromatic notes are expressed Vf the note from irhich they
spring, with a flat, sharp, or " natural " before it The true
chromatic notes (those which produce the chromatic effect) are
preceded by the notes from which they spring. Thus :

**=

IE5£

ti tOWi

»d

tUi

towi n

d doi r

m mow r

In oontequenee of the attempt of the old notation to easmbine
the expression of absolute with relative pitch, and to mingle, for
this purpose, the symbolic notation of flats, sharps, and " naturals,"
with the pictorial notation of the stafr, several difficulties arise in
connexion with this subject. For instance : —

How shall we express the note kb (the sharp seventh of the
minor mode) in the key of a ? The answer is— By putting a sharp
on b, which is the son of that key. But is not b sharp regarded
by the learner (and described by many teachers) as the same thing
as c natural, and will not this cause a puzzle ? Yes, it is the
misfortune of the notation to do so. But there are two reasons
why c natural would not be correct ; first, because it would not
point out the note (sou) instead o/whtch the ne was used ; and
secondly, because the real position of mi is only a chromatic part-
tone (three degrees) above b (soh), and not a lonule (five degrees),
as tho c natural would make it. Thus :

1 m ne 1 d l t 1 1 ne 1

ITow shall we express ns in the keys of b and r sharp, or tu
in the key of p sharp, for the note which we would sharpen is
already sharpened in the signature ? May we use the so-called
*' natural " note above ? No. Reasons corresponding to those
given in the la*t case compel us to invent a new symbol called a
double sharp. This placed before the note which would have been
son. indicates the origin of the ne, and shows more accurately its
position. Again : —

How shall we express a chromatic sharp when the note has
been sharpened before in the signature, or a chromatic flat when
the note has been flattened before in the signature ? For these
purposes we shall require, in addition to the double sharp already
mentioned, a double Jlat. These double sharps and flats are also
needed on other occasions.

ZXfil

li not li

roi m

$A* r '"r

s sow f m

When the pupil has carefully studied each " accidental," as
Riven above— seeking to appreciate its peculiar mental effect — to
know its exact position in relation to the notes of the oomBson
scale, and to mark the various forms in wt.i.-h it is clothed (if not
disguised) by the old notation — he should be able to answer for
himself the following qut &ii mi.

"Whin the no'-e that w'jix.i \ e ib \i iiWiiid, by flat or natural,

what does it indicate? Fi— the " returning pah " after a pre-
vious tu — or if tb immediately precede, the chromatic tow.

When the note that would be soh is raised, by sharp or natural,
what does it indicate ? Ne— or if soh immediately precede, the
chromatic soi.

When the note which would bs fah is raised, by sharp or na-
tural, what does it indicate? Tu— the ** returning tu" after a
previous pi— in minor tones bah — or with fah preceding, the
chromatic roi.

When the note which would be bat is raised, by sharp or
natural, what does it indicate ? Nc— -or with bat preceding, the
chromatic roi.

When the note that would be doi i is raised, by sharp or natural,
what does it indicate ? Ni— or if dok precede, the chromatic doi!

How do you distinguish the chromatic note ? By its being im-
mediately preceded by that from which it springs. 801 might be
called nb, but when preceded by boh it has a different effect on
the mind from nb, and therefore should be distinguished. So also
with poi and ru.

When these points have been once thoroughly understood, the
pupil will And little difficulty in recognising the ordinary " acci-
dentals'' as he comes upon them. Extraordinary accidentals may
still occur, which it is difficult to decipher from the signs of the
old notation, and perhaps difficult to explain on the principles of
music.

OTHER SYMBOLS Or FREQUENT OCCURRENCE.

For an explanation of all the terms and signs that are ever used
in music, we must refer to such works as " Hamilton's Shilling
Dictionary of Musical Term?," published by Cocks, London, and
Saroni's " Musical Vade Mecum," j ublished by Mason and Law,
New York. But a few signs of frequent use remain to be ex-
plained.

Thb Doublb Bar generally indicates the close of a line in the
poetry or a " pa; sage " in the music. A row of dots before it (or
sometimes two dot*) means that the preceding part of the music
should be repeated. A row of dots after it (or even apart from the
double bar) shows that the passage which follotcs will have to be
repeated. Try to sing the following.

Ket O.

f~nk Am "i fiu iur*

A curve with a figure three in the centre Is put over a triplet
of notes when they should be sung in the time of two. A small
curve with a dot in its centre, when placed over a note or rest,
allows to give to that note or rest any length of time which you
think good taste requires. A dot or strike above a note shows that
it should be sung " staccato," or shorter than the note would ordi-
narily be. Baroni says that the dot does not indicate so decided
a " staccato " as the stroke.

P^m

Je lis pour la premiere fois un bon livre, et j'y prends le me^ue
plairir que *i je faisais un nouvel *oi«. Je relis un livre que j'si hi,
e'est un aneien ami que je revois.— Vomaire.

La lecture est une partie du deroir ds l'honnlte homme.—
Christine.

On ne peut avoir l'ame grande, ou l'esprit un pen pene\rant
ssns quelque passion pour les \o\tr e*.-~ V c n *»enargw8 '

Aimer a lire, e'est faire un ^change des heures d 'ennui que Ton
doit avoir en sa vie contre des heures delicieuses. — Montesquieu.

Ce n'est pas dans les choses extraordinaire* et bizarre* que «•
trouve l'excellence de quelque genre ce soit. Les meilleurs line*
Rpnt ceux que chaque lecteur croi? qu'il aurait pu fslre; la nature*
qui »cuie est bonne, est toute faruihere et commune. • Je hsis les
nuts d'ei flurc. — f'ascul.

LESS0N8 IN BOOKKEEPING.

LESSONS IN BOOKKEEPING.— No. XIII.
(Continued from page 217.)

(4)

LEDGER.

(4)

Da.

DARLING AND COMPANY, LONDON.

Fob. 26 To Cash Account

£50

Mar.

£50

By Cash Account

£60

£50

Da.

OSMOND AND COMPANY, LONDON.

Ca.

Jan
April

To Bills Payable
To Cash Account

£288
183

4
3

Jan.
April

£471

By Cotton Account
By Cotton Account

£288
183

£471

LEDGER.

(5)

Da.

ANDREWS AND COMPANY, LONDON.

Cb.

Jan.
Fab.

To Bills Pavable
To Bills Payable

£463
238

3
17

JC702

Jan,
April

By Cotton Account
By Cotton Account..

£463
238

3
17

702

Da.

BROWN AND SMITH, LONDON.

Ca.

Feb.
May

To Cotton Account
To Cotton Account...

£313

Vfar.

May

£411

By Cash Account
By Cash Account

... ...

• ••

£313
97

14
8

£411

Da.

WHITE AND COMPANY, LONDON.

Cb.

Mar.

To Cash Account

£425

2 7

£425 I 2i 7j

I I I

Feb.

By Cash Account ••• •••

2 i £425
l £426

SS8

THE POPULAH EDUCATOR.

Dr.

WILLIAMS AND COMPANY, LONDON.

Cr.

Feb. 21

To Cotton Account

{£360

5
5

4
4

Mar.

£360

21 By Cash Account

£m

£360

5 4

LEDGER.

(«)

Dr.

EAST INDIA COMPANY.

Cr.

Feb.
April

To Cash Account
To Cash Account

: 2

' 4

£60

661 12

£721 12

Feb.

By Cotton Account

£721

£7 1

Dr.

JAMES MANNING, LONDON.

Cr.

Mar.

£3

Feb. 25

By Charges Account

2D £3

£3

12 2

Dr.

SPENCER AND COMPANY, LONDON

Cr.

Mar.

1
13i To Cotton Account

1 ' 1
£160 13J 7

April

1
13

By Cash Account

£160
£160

i
1

£160 |13! 7
! i '

Dr.

THOMPSON AND COMPANY, LONDON.

Cr.

Mar.

To Cotton Account

* ...

f
3

£257

12 1
12, ]

Mar. 16

By Cash Account

£257

I
12 1

12; 1
i
i

! 1

£267

£257

LEDGER.

i»

(7)

Dr.

ALtHORPB AND COMPANY, LONDON.

Cr.

Mar.

To Cotton Account

£141

BJ8

!
M»r. 24

1
I I

By Cash Account ... ••*

S | i m|_6

£141

£141 6

LESSONS IN BOOKKEEPING.

290

Dju

BARING, SMITH, AND COMPANY, LONDON

C&.

Mar.

To Bills Payable

£288

1
3

Mar.

j £288

By Cotton Account

j £288

£288

Da.

ALLISON AND COMPANY, LONDON.

Ca.

April 12 To Cotton Account

£150

Apri'

By Bills Receivable

£150

De.

THOMAS JONES, LIVERPOOL.

Ca.

Iff

To Cotton Account
To Cotton Account

£770
241

£1017

April
May

By Bills Receivable
Br Bills Receivable

£226

791

£1017

4
10

(•>

LEDGER.

(8)

Da.

LLOYD AND COMPANY, MANCHESTER.

Ca.

April 20
May -

To Cotton Account
To Cotton Account

£223

April

217

18
8

10
8

May

£441

By Bills Receivable
By Bills Receivable

£223

217

£141

Da.

OVINGTON AND COMPANY, LONDON.

Ca.

April

To Bills Tibbie

£245 8
£245 8

April

By Cotton Account

£245

£241

230

THE POPULAB EDUCATOR.

Da.

POWELL AND COMPANY, MANCHESTER.

Cr.

May
June

6 To Cotton Account

To Cotton Account

£299

Mar

306

June

£608

By Bills Receirable
By Bills Reuirabie

6
6

1 £299
308

£608

PERKINS AND COMPANY, LONDON.

C».

M*y

To Cash Account
T* Cri irgcs Account

£823

May

June

£844

By Bills Receivable
By Balance Account

£823
21

6
610

£844 jtlilO

LEDGER.

(«■)

Dm.

BALANCE ACCOUNT.

Cr.

Jan? 30 To Sundries

£2054

£2654

June

By Sundries

£2644

£2651

IT'10

Dr.

PROFIT AND LOSS ACCOUNT.

Cr.

June

To Sundries

£782 ! 8' 7 ! June 30

£782 8 7

By Balance Account

7 ! £782 H

1 £782

TRIAL BALANCE.

Dr.

Cr.

Stock Account

Priv.te Account

Cifth Account . «,

Petty Cash Account

Bills Rccei*?Me ,.*

Bills P/iynblc

Three P*r Cents.

Cotton Account

London And WettmkuEer Bink

Interest Account

Charges Account

Perkins and Co.

] £1200

£59

997*5

9973

3040

2732

751

1523

985

{.<-

2S«tt

3543

S!)10

3965

814

10 |

833

£24*42

£24542 J

LESSONS IX GKOLOGY.

aai

LESSONS IN GEOLQGY.— No. XLVIII.
Bt Thos. W. Jexxyn, D.D., F.R.G.S., F.G.S., &c.

CHAPTER V.
Otf THE CLASSIFICATION OF KOC^S.

SECTION II.

ON THB RELATIVE POSITION OF ROCKS IN THEIR VERTICAL
ORDER.

Every beginner in geology ought to make himself aa much matter
of too order of roeks io ilia crust of the earth as ha is of the let-
ters of the alphabet. Indeed the knowledge of this order el ver-
tieai position ia of more importance to him than accuracy in the
order of the alphabet ; f\«r if a took the place of *, or if v *tood in
the position of n, the axrsngfriuent would not in tho least embar-
rass the learner of a language.

The accurate and certain knowledge of the order of tho sedi-
mentary rocks, ia as essential to the geological etudent as a know-
ledge df the distribution of letters is to the compositor; or a know-
ledge of the fc helves of laces, ribbons; silks, and cloths to the
draper ; or the order of folios, quartos, octavos, and duodecimos
to the keeper of a library.

This order must be learnt. You may learn it in your own way;
but learn it you mu*»t. It will cost you no more trouble than did
your learning the multiplication table ; and this order, like that
table, when once completely mastered, will he useful to you
through life.

You had better learn this vertical order from some one approved
writer, and then make corrections according to the progress which
you make, either in geological reading or in scientific observation.
The order which waa presented to you in the last lesson, and
founded upon the enlarged science ot Sir Charles Ly ell, you may
depend upon as being one of the best. All geological writers
agree aa to the order in which the rocks lie on, or under, one an-
other. Tho subject on whieh they vary is the grouping of differ-
ent beds into what ia called a formation ; that is, whether such
bads ought to be grouped with the series above them or with the
series below them. It is true that there are many eases in whieh
certain beds art) found in anomalous and perplexing positions, for
which geologists find it difficult to account ; but such anomalies
are onlv exceptions, which do not disturb the regularity of the
order of position aa a whole.

To the well-sinker, the practical miner, the civil engineer, and the
field geologist, an accurate familiarity with the superposition, the
structure, the foesil contents, and the relative dates of the different
beds in a rock is an indispensable acquirement. Some rocks,
though formed in the same age, differ exceedingly, both in litho-
logical character and in fossil remains ; and other rocks, formed
under similar circumstances, but at epochs very remote from each
other, may very much resemble one another, and may therefore
be placed by the geologist in the wrong order of position. The
study of this order of strata, and the knowledge of tho mineral
peculiarities of each bed, form what is called descriptive geology.

The great mistake made by tho majority 0? beginners, in com-
mencing tho study of geology, is the supposition, that, were a
quarry or a section of immense depth to be exposed to their view,
or were they to dig a shaft from the surface of the earth down to
its centre, they would behold every one of these strata lying regu-
larly in the order presented in geological treatises. This is a great
mistake, and you must at once either avoid it or correct it ; for
the geological doctrine of the regular position of strata is far from
involving any auch idea. I will therefore try to explain the prin-
ciplea of this doctrine to you; and will take for granted that,
while reading my explanation, you will constantly refer to the
diagram presented to you in our last lesson. Observe particularly,
however, that under the Cambrian ought to be placed the Granite
BocJtt, and these being lowest, we denote them by w. The ideal
section will then be complete from a to w ; and the lowest stra-
tum can easily be filled up in the mind of the student.

1. It is barely possible that there may bo certain localities on
the earth's surface where, it a shaft were made to the centre, t£e
workings might pass through the whole series from a to w
aa represented in the diagram referred to. Such a oirwumatanco,
however, ia eearoely probable.

2. You are aware that, in very many districts, some one of the
different strata marked from a to w forms the turfaee rock of tho
country ; therefore it would be in vain for you, in digging your shaft,
to expect below that surface tho rocks which arc arranged above it.

3. The ecological doctrine about the superposition of rocks is,
that the different beds or formations lie .in order, according to
the later or earlier epochs in which they were formed, or accord-
ing to the more ancient rock on which they were deposited.

4. Suppose that you live in any part of England along a straight
Una from Devizes to Norwich or to Dover. There the surface
rock is the chalk formation, the a of your diagram. The mean-

it ing, then, of the geological doctrine is, that, if along either of
■ these lines you dig a shaft to the centre of the earth, you would
never meet any of the strata that are represented as lying between
e and a. If you live on the line from Bath to Lincoln, you
would dwell on k, the oolite formation ; and your shaft would
never meet with either of the strata that lie between k and a.
The same reasoning wouM be true if you lived on the coal
measures ; or on i, the old red sandstone, &o.

5. Still the order of superposition does not imply that, if you
digged your shaft downwards from o, for example, you would
meet all the strata that are represented between o and w,
for many of them might be missing. It is possible that o.
might be found to rest on x, and even on q, without any of
the intervening strata being present ; and r, the coal, might be
found to, rest, not on a, but immediately on the granite, w.

8. The moaning of the doctrine is, that x or l will never
be round above o, and that r will never be found below v.
This order may frequently be found imperfect or detective; but
it ia never, except in easily explained cases, inverted. As you
would dig your shaft downwards, you would often miss one or
more beds, or strata, and even formations, in the series ; ■ or
J might be missing, ss having never been deposited, or perhaps
| having been swept away by denudation ; and even several locks
| in succession, such as i, j, x, l, m, &c , might be altogether
I absent. Fix it therefore in your mind, that all that the doctrine
of superposition teaches is, that f will never be found taking the
place of o, or that in the vertical order r may coxae btfure x.
To sum it up in a sentence, I may say, that you will never find
the entire eeries in any one district ; but the members of any
series that are found to occur are always found to follow the ver-
tical order of sequence,

7. These statements about the regular order of superposition
are in harmony with processes of deposition which are now going
on around our own country. All the sediments, which our nume-
rous rivers are carrying in all directions to the ses, must be de-
posited somewhere, and must therefore form a sedimentary rock.

I Let us call this rock, wherever it is deposited, by the desig-
nation a, which represents a new sandstone or a shaly clay.
Between Kent and France, a, like the Goodwin Sands, rests on
g ; about Cornwall on w or t ; in the Bristol Channel upon t
or r ; in the Irish Sea on u or v ; around the north of Scotland
on t or v ; and along the east coast of England on c or r or o.

8. The exceptions which the practical miner and field geologist
find to this regularity of vertical sequence, and the anomalous
position in which some rocks are discovered, do not disturb the
stability of this geological doctrine. For instance, there may be
cases in which the rocks t, s, R, Q, and even x or o, formed
at one time the bottom of the ocean, at which epoch some piu-
tonta action from below w might impel upward a stream of
melted trap or porphyiitic granite, which would rise to the surface
and spread over the bed t or 8, or any other superior stratum.
If you commenced our supposed shaft in such a mass of granite,
you might infer, from the reasoning of our diagram, that, lower
down, you would not meet any sedimentary rocks; and yet the
(acta of the case would be otherwise. Agsin, there are cases, aa
in the Alps, and in the Apalachiane of North America, in which
certain beds have, by a tremendous power from below, been thrown
completely topsy-turvy ; so that, instead of the beds lying in the
regular sequence of a, r, c, d, they lie vertically in the order
of o, c, b, a, the upper beds being the lowest. This fact dis-
turbs the regular order of superposition no moro than when an
earthquake power would hurl up a tower, and cause it to fall with
its tuircts and pinnacles downward.

9. You are not to imagine that this geological arrangement of

282

THE POPULAR EDUCATOR.

rooks ii a fanciful one, made for the convenience of inquirers.
The order of vertical sequence is what has been found to he
strictly true in many localities, as they have been observed and
recorded by quarrymen, bv well-sinkers, by miners, and by civil
engineers, as well as by field geologists, who have marked the rela-
tion of rocks as they have found them exposed in ravines, in
cliff*, in mountain slopes, in quarries, in railway cuttings, and
in mines and collieries.

The geological beginner is often puzzled with the question —
that, since no man has ever seen a quarry half a mile deep, and as
no one has sunk a § haft to the depth of ten miles, how can it be
possible for geologists to know the order of sequence in the rocks
that constitute the earth's crust ?

The way in which they attain certainty in such knowledge is
thif . They collect together the results of the examinations which
have been independently made by separate geologists in different
districts, and then they apply such results to the appearances or
tections of rocks presented to them in any given countries. One
geologist may live in Norfolk or Suffolk, and he verifies all the
rocks in sequence from ▲ to d ; another lives about London, and
he ascertains the order of all the beds between d and o ; another
resides between London and Brighton, and he demonstrates the
order of rocks from o to x; another makes his inquiries in Glou-
cestershire or Northamptonshire, and he gives all the rocks
which he has observed between x and q. A practical miner in
South Wales, Staffordshire, or Northumberland, makes a sec-
tion of all the strata between o. and s. An able quarryman in
Scotland, in Breconshire, or in Devonshire, ascertains minutely all
the beds between s and u. A field geologist traverses North
Wales and Cumberland, and exhibits the regular system of forma-
tions that lie between t and w. By this division of labour, the
theoretical geologist finds that, for all the purposes of scientific
induction, he has a section of the earth's crust that is about ten
miles deep.

LESSONS IN ITALIAN GRAMMAR.— No. XV.

By CHARLE8 TAUSENAU, M.D.,

Of the University of Pavis, end Profeuor of the German end Italian
Language* at the Kensington Proprietary Grammar School.

Colloquial Exercises.

JS-gli, he

J57-&S, she, it (in reference to

a feminine noun)
E't-eo (m.), is-$a (/), he, «1 e,

it (of persons and things)
Ma, but
mol-lo, very

Che, 'who, whom, which, that
// cappel-lo, the hat

V o-roM-gio, the watch or

clock
// tem-pe-ri-no, the penknife
// ca-v. l-lo, the horse
T o-vi-to, found
Fer-duto, lost
Per, f >r
D6-te, where
11 fan-ciul-h, the child

Italian-En CL18H.

Mi-o pa-dre e bud-no ; 6-gli ha an-che un budn fra-tel-lo.
Mi-a ma-dre e bud-na ; el-la ha an-che u-na bud-na so-rel-la.
Ab-bia-mo ve-du-to vd-stro zi-o ; 6-gli ha com-pra-to un gran
li-bro. A-ve'-te v6i ve-du-to il nd-stro giar-df-no? es-so e
ra61-to gran-de. HO com-pra-to u-na pen-na ; 6s-sa e m61-to
bud-na. II tu-o li-bro e pic-co-lo, ma e"s-so c bud-no. Ab-
bia-mo un pa-dre che e bud-no. A-ve-te u-na ma-dre che e
bud-na. Hd un li-bro che e m61-to pic-co-lo. Mi-a so- r el-la
ha u-na pen-na che e m61-to gran-de. II li-bro che a-ve-te
com-pra-to e bud-no. II giar-di-no cbe ab-bia-mo ve-du-to e
m6l-to gran-de. Hai tu ve-du-to il li-bro che mi-o zi-o ha
com-pra-to ? 11 li-bro che vd-stro zi-o ha com-pra-to e m61-
to pic-co-lo, ma es-so e bud-no. Hd an-che com-pra-to un
li-bro, ma es-so e gran-de. Vd-stro fra-tel-lo ha il li-bro che
v6i a-v6-te ve-du-to. Hd un pic-co-lo cap-pdl-lo. II tu o
cap-pel-lo e gran-de. Mi-o fra-tel-lo ha un budn' o-ro-ld-gio.
Hai t • ' n-che un o-ro-16-sio ? II mi-o o-ro-ld-gio e pic-co-lo,
ei-so e m6l-to bud-no. Hd per-du-to il mi-o tem-pe-ri-no.
A-ve*-te v6i tro-va-lo un tem-pe-Ti-no ? Nd-stra ma-dre ha
com-pra-to un cap-pel-lo per mi-a so-iel-la. Hai tu ve-du-to

il cap-pel-lo che mi-a ma-dre ha com-pra-to? Ab-bia-mo
tro-va-to un lib-ro. A-v6-te vdi per-du-to un li-bro ? D6-ve
hai tu com-pra-to la tu-a pen-na r Vd-stro zi-o ha un budn
ca-val-lo. No-stro pa-dre ha an-che com-pra-to un ca-val-lo.
Ab-bia-mo ve-du-to il ca-val-lo che \6-stro pa-dre ha com-
pra-to. Mi-o fra-tdl-!o e un budn fan-ciul-lo ; e'-gli e mCUto
pic-co-lo.

Enqlish-Italian.

The tailor asks for nine yards of cloth, two dozen of buttons,
and half an ounce of silk. Send for a loaf of sugar and two
pounds of coffee. I shall return in a quarter of an hour.
Finish this glass of wine, and eat this small crust of bread.
Take the map and find me the city of Paris and the city of
London. I come by order of the master to tell you that
the preparations for to-morrow are to be made. The month of
April is changeable, the month of May, on the contrary, is
very pleasant. The months of December and January are the
roughest in the year. What dress will you put on for the ball
of to-morrow? Were you at the performance of yesterday ?
He had given him the lower rooms.

Vocabulary.

Tailor, tar-tb-re, m.

Asks for, do- mdn- da

Nine, no vc

Yard, brdc-cio, m. (pi. h brde-

cia,t.)
Cloth, part-no, m.
Two, dii-e

Dozen, doz-zi-na (rf*), f.
Button, bot-to-nc
Half an ounce, vuzza on-

cia, f.
Send for, man-da-te a prtn-

dv-re
Loaf. pd-nc, m.
Sugar, ziic-che>ro (te), m.
Pound, lib-bra, f.
Coffee, cuf-ft, m.
I shall return, ri-tor-ne-rb

(pron. ri-tor-ne-r6)
Quarter, qxuir-to
Hour, 6-ra % f.
Finish drinking, fi-ni-te di

bJ-re
Glass, bic-chic-re, m.
Wine, vi-no, m.
Eat, man-gid-U
Small crust, cro-sti-no, m.
B ezd,pd-ne, m.
Take, prcn-de-te
Map, cdr-ta geo-grd-Ji-ca t f.
ind m , nr-ed-te-mi
ity, «?■'' i*i
Pari", Pa-ri-gi
London, Lon-dra
' come, ven-go

By, per

Order, br-di-ne, m.

Master, pa~dr6-ne, m.

To tell you, a dir-vi

That are to be made, che rifdc-

cia-no
Preparation, pre-pa-ra-ii-ro,

m.
To-morrow (jgwr-tto, day, anl

do-md-m, to-morrow)
Month, me-se t m.
April, A-pri-le
Changeable, va-rid-bi4e
May, Mdg-gio
On the contrary, aW m-cwi-

tro
Very, tnbl-to
Pleasant, a-wc-no
December, De-cem-bre
January, Gen-nd-jo
Roughest, ilpiu ri-gi-do
Year, dn-no (with the genit.)
What, che
Dress, u-bi-lo

Will you put on, nut-ie-re-U
Ball, bdUlo

To-morrow, do-ntd-ni
Were you, tie-te eld- to
Performance {i.e., comedy),

ioni-me-dia, f.
Yesterday, ji-ri
He had given him, glifu-ro-

no ae-ee gnd-te
Room, cd-we-ra, f., $6t-lo, be-
low, underneath

Italian -English.

Ta-bac-bhie-ra d* d-ro. Un va-so d* ar-gen-to. Ve-sti-to
di vel-lu-to. Vi-no d* I-ta-lia. Un cudr di ma-ci-gno. II
fl-lo di fcr-ro. Guan-ti di pOl-le fi-na. Cap-pel-lo di pa-glia.
U'-na mi-nid-ra d' d-ro, d' ar-«6n-to. Ac-cia-jo d' In-ghil-ter-ra,
Fer-ro di Sti-ria. Fid-ra di Fran-co-fdr-te. La fe-sta di do-mi-
ni. II gi6r-no d'dg-ai. Lacom-md-diadijd-ri. II tea- tro d'dg-gi
gi6r-no. U'-na ma lat-ti-a di quat-tro set-ti-ma-ne. II vi-no di
dt-to, di v6n-ti £n-ni. Laguer-ra di sfit-te an-ni. Un bdl c61-po
d' dc-chio. Lo squil-lo del-la tr6m-ba. U'-na per-s6-na di
fe*-de. E'-gli e di td-sta du-ra. Ud-mo di c6r-te, di m6n-do.
U^-mo di ldt-te-re, di ddl-ce tem-pro. Ud-mo di grand' af-
fa-re, di ear-bo. Ud-mo di cat-ti-va con-ddt-ta. Ud-mo di
gran-de a-bi-li-ta, di gran rc-pu-ta-zi6-ne. Ud-mo di mez-za
ta-glia. Ud-mo di mal ta-16n-*o, di spa- da, di gucr-ra. Ud-
mo di b s-sa e-stra-zi6-ne. Ud-mo di po-ca ea-lu-te. La cd-

LESSONS IN ITALIAN.

283

sa e di gTi\n-de im-por-tan-zju Un me-di-co di gri-d >. L' Ar-
te del t6r-no, del tin-ge-re. La fon-de-ri-a de' ca-rdt-*e-ri.
Cam-po di pia-c6-re. Fi-la-t6-jo di co-t6-ne. P6n-te di bar-
cbe. In-spet-t6-re d6l-la fon-de-W-a do' can-n6-ni. % L' ab-bi-

Slia-me'n-to dci sol-dd-ti. Pro-gSt-to di 16g-ge. II de-crd-to
i nd-mi-na. Cer-ti-fi-ca-to d' o-ri-gi-ne. Sta-ti u-ni-ti d' A-
me-ri-ca. L* Im-pe-ra-t6-re de'l-le llus-sie. I con-fi-ni de*l-
la Sas-sd-nia. .E'n-tro il tcr-mi-ne di tre md-si. Un pro-di-
gio di ud-mo. Un uu-mo di tren-ta. II fi6r di ga-lant' u6-
mi-ni. Quel-lo sci6c-co di vd-stro sdr-vo. Quc-sto dii-vo-lo
di fem-mi-na. Quel drit-tac-cio di Gu-gli-el-mo. T6c-co di
bric-c6-no ! Quel po-ve-ri-no di mi-o ira-tcl-lo ! Tan-to di
vi-no ed al- tret-tan- to d' d-cqua. Fa un si bel chia-ro di lu-
na. U'-no di n6-me Gid-na. Giu-da di so-pran-n6-me (so-
pran-no-mi-na-to) Tad-dS-o. Per-mes-so (con- g 6- do) di tre
m£-si.

VoCABULABT.

Tabbaehiera, snuff-box.

Oro, gold.

Vaso, vessel, vase.

Argento, silver.

Veatito, dress.

Velluto, velvet.

Vino, wine.

Italia, Italy.

Cuore, heart.

Mocigno, sandstone, mill-stone,
stone.

Fih, thread, wire.

Ferro, iron.

GuatUo, glove.

Pel/e t f. t skin, hi'le, pelt, lea-
ther.

Fino, in., fina, f., line, thin,
delicate.

Oappello, hat.

Paglia, straw.

Miniera, mine.

Acewjo, steel.

InghUterra, England.

Stiria, Stiris.

Fiera, fair (for merohants).

Francoforte, Fiankfort.

Testa, fea*t, festival, festivity.

Doinar.it to-morrow.

Giorno, day .

Oggi, to-day.

Cbtntnedia, comedy.

Jeri, yesterday.

Teatro, theatre, j

Ogji giorno, now-a-day*. !

Malaitia, disease, iilueas, j

malady. j

Quattro, four. '

Settimana, week.

Otto, eight:

Venti, tweuty.

Anno, year.

Guerra, war.

JSet/e, seven.

Beilo, beautiful, tine.

Colpo, blow, stroke.

Ocehio, eye (colpo tC occhio,
sight, view, prospect, in-
stead of: vt-du-ia).

SquiUo, sound.

JVomba, trumpet.

Persona, person.

jfrfc, faith, fidelity.

E\ is.

Tetla, f., Uead.

Duro, m., dura, i , hard, ob-
stinate.

Uomo, man.

Corte, court (uomo di corte,
courtier, formerly the court's
fool).

Garbo, pleasing address, gen-
tility, politeness (uomo di
garbo, a polite man ; also an
honest man).

Cattivo, m., cattivo, f, bad,
wicked.

Condotla, f., conduct, beha-
viour.

Abilitd, ability.

Rcputazione, reputation, fame.

Mezzo, m., mezza, f. (ds),*
middle.

Taglia, size, stature, shape,
figure, waist.

Mala, ill, badly.

Talenlo, talent, inclination,
propensity, bent, bias, will
(mal talen'to, malignity, mali-
ciousneas, malice, malevo-
lence; uomo di mal ta lento,
ill-natured man).

Spada, sword.

Jiasso, in., bass a, f., low.

Estrazione, f., extraction, de-
scent.

Poco, m., poca, f., little, small,
few.

Salute, f., health

Medico , physician.

Grido, cry, report, reputation
(uomo, medico di grido, cele-
brated man, physician).

Arte, art.

Tortto, turner's lathe.

Tingere, to colour, dye, tinge.

Fouderia, foundry.

Caratlere, character ; hand-
writing, hand (earatteri, pi.,
types, letters).

Campo, camp.

Fiacerc, pleasure {campo di
piacere, military encamp-
ment for the diversion of
the prince).

Filaiojo, spinning-wheel, spin-
ning-mill or manufactory.

Mondo, world.

• Miod the difference of pronunciation and meaning between
these two words : mdz-zo (fc), dousth-like, over-ripe, shrivelled (of
fruit), and mezzo (<fr) mii^le, half, the ctntr" the middle, means,
media', ion.

Lettcra, letter (uomo di lettere,
learned man, scholar).

Dolce, sweet, gentle, soft.

Tempra, temper.

Grande, great.

Affare, affair, business ; station
of life, condition, rank (no-
mo di grand* affare, a man of
consequence or importance ;
a very able or clever man ;
a man of superior genius or
talents).

Cotone, cotton (Jilatojo di
cot one, cotton-mill or manu-
factory).

Ponte, bridge.

Barea, barge, boat (ponte di
bare he, pontoon).

Inspettore, inspector.

Cannone, cannon. f

Abbigliamento, ornament, dress,
fitting out, equipment.

Soldato, soldier.

Frogetto, project, plan.

Zegge, law. J

Deereto, decree.

Nomina, designation to office,
appointment, nomination
(deereto di nomina, diploma,
commission).

Certificato, certificate.

Origine, origin, descent, birth.

State, state.

Unito, united.

Jmperatorc, emperor.

Russia, Ruisia.

Covfoie, eottfnOf confines, fron-
tier.

Sassofiia, Saxony.

Entro, within.

Termine, space or point of
time, period, term.

Tre, three.

Mete, month.

Prodigio, prodigy, miracle.

Trenia, thirty.

Fiore, flower, bloom, prime;
the most excellent or valu-
able part of anything;
model, standard.

Galante, polite, civil ; obliging,
kind ; gentlemanlike ; love-
making, amorous, gallant
(gallant* uomo, an upright,
honest man; a man of ho-
nour, a perfect gentleman).

Quello, that.

Scioceo, fool, blockhead.

Vostro, your.

Servo, servant,.

Qucs to, this.

Diavoto, devil.

Femmina, female, woman.

Diittaccio (for dirittaccio), are
rant knave or sly fox.

Guglielmo, William.

Toceo, piece. §

Briceone, rogue, scoundrel.

Foverino, poor, unfortunate.

Tan to, so much.

Altreilanto, as much again.

Aa/ua, water.

Fa, it is, there is.

Si, SO.

Chiaro, light, brightness,
shining.

Luna, moon.

Uno, one.

Nome, name.

Giona, Jonas.

Giuda, Judas.

Soprannome, surname, family
name.

Sopranotninato, surnamed.

Taddeo, Thaddeus.

Permesso, congedo, permission,
leave (of absence), dis-
charge.

Colloquial Exercises.

La ttt-te-ra, the letter

La citf~fia, cap, coif, hood ( 4 ar-

ticularly for women)
Ri-ce-vu-to, received, got
Vm-du-to, sold.
Scrit-to, written
Gran-dU-si-mo, m., gran-die-

si-ma, f., very great
iSa-o,m., iit-a, f. f nis, her, its
II mau-Ul-lo, the cloak
V om-brel-la, umbrella

Qut-sio, m., que'sta, f., this

V o-tte-ri-a , inn, hotel, tavern,
public-hcuse

La car-roz-za (is), coach, car-
riage

V a-ntl-lo, ring
La ta-bae-chie-ra, snuff-box
Bel-lo, m., ttl-la, f., beautiful,

fine, handsome
Ilfi-glio, the son
LajUglia, the daughter
Ilre-gd-lo, the present, gift

Italian-English.

Que-sto ca-\Cil-lo c bel-lo. Quc-sta ta-bac-chie'-ra e m61-to
pic-co-la. Quest' o-ste-ri-a e grun-de. Quc-sto fan-ciul-lo e
mi-o fra-t6l-lo. Quc-sto li-bro c per mi-o pa-dre. Que*-
sto tem-pe-ri-no 6 per mi-o fra-tel-lo. H6^ tro-va-to
un* a-nel-lo. D6-ve a-ve-tc voi tro-va-to quest* a-nei-
lo? La vfi-stra pic-co-la so-iel-la ha un bel li-bro. Mi-a
ma-dre ha com-pra-to que-sto cap-pe".-lo. Tu-o fra-tel-lo ha
ve-du-to que'-sta bel-la car-r6z-za. Il vo-stro pic-co-lo fra-
t£l-lo e un buon fan-ciul-lo. D6-ve hai tu com-pra-to que-sta
ta-bac-chie-ra ? Qu&t' o-ro-16-gio e m61-to bud-no. Qu^-sto
bell' a-nel-lo e per que'-sto fan-ciul-lo. Mi-o zi-o ha un f i-
glio ed u-na fi-glia. H5 ve-du-to tu-o fra-tel-lo e tu-a so-rel-

f Can, ntf-iie, cannon, piece of orduance, and od-none, rule, pre-
cept \ canon (in ecclesiastical affairs and in music).

t iJg-gt, law, and l^Mfe, he reads.

f Sfrco, touch ; blow with a hammer, stroke of a clock ; and
tdc-co, toque a kind of bonnet ; piece, bit.

25*

THB POPULAR EDUCATOR.

la, Ab-bia-mo d-cc-rfc-to an re-gk-lo. A-v£- T .e vot sent- to
u-na le-te-ra * Mi-» K>-r?!-U hi ri-ce-vu-to fi-na bel-m cuf-
fi*. Ho ven-du-to la mi- a car-rur-xa. Hai tu an-che ven-
dfi *o la to.-a car-r&z-xi*? Que sto re-ga-!o e per v6-stra zi-a.
Yo-*tro f*-zlio e m-'l-tc t/k-co-!o, ma e'-gli e buo-no. Mi-a
fi-C.ia e gran-dis-ti-mi. Que-ft>pi dre hi u-ns bel-U ft-glia.
Q jc-4 o fan-ciul-lo e n.i-o fi-gl:o. II giar-di-no che ho ve-do-
t > c grac-dis-si-mo. Mi-o p*-dre ha per-du-to il s6-o cap-
pe'.-io e la su-a om-brel-li. N6-stro xi-o ha ven-da-:o la su-a
lei-la car-r&z-zt. Mi-a so-rci-la ha Uo-va to il au-o a-nel-lo.
Qoe-sto pa-dre hi per-du-to su-a fi-glia. Que*-tU ma-die ha
per-d6-to *u-o fi-glio. Mi-o zi-o ha com-pra-to u-na cuf-fia
p~r la su a pic-co-la fl-gli%. Que sto re-ga-lo e per mi-a so-
icl-ia. Que-sto f*n-ciu!-lo ha *crit-!o u-na gran-dis-si-ma let-
e-ra per s6-a ma-dre. No-stra zi a ha com- pr a- to un bel lis-
*imo mantel lo per su-o fi-glio. A-ve' te 161 tro-vi-to un' a-
net-io r Mi-o zi-o ha per-^ti-to il sti-o mari-!el-lo.

ExGLUH-lTAXJAir.

The present timet ate not the best. He had hidden himself
in the back room. Our town has a stone bridge ; yours has
orilj one of wood. Edward has received from London a gold
watch, a silver sword, and a pair of steel shoe-buckles. One-
they wore cloth dress ss and velvet waistcoats. The us* of
copper Teasels has been prohibited in Sweden. Beef, veal,
and mutton, are, for sale in the shamble*. What means this
ringing of bellrr What do you say of the cloth which I have
bought? It is good and fine. And of the colour? It is
beautiful. What do you think of the man whom you see, of
the boy whom he carries along with him, and of the beggar
who follows him ? Here are ten yards of the taffeta, some oi
which von wanted, and twelve yards of the cambric whieh you
have demanded. Send me a dozen of the lemons, and two
pounds of the figs which you have received from Smyrna.
Spare me a bottle of the eau de Cologne whieh has been sent
to you.

OX PHYSICS OR NATURAL PHILOSOPHY.
No. XVI.

{Oontinusi from page 214).
ENDOSMOSE. ABSORPTION AND IMBIBITION.

En-Josmose and Rzosmote.— These words, which are taken from
the Greek, signify respectively a forcing i meant* and a forcing
outwards, and are applied to the action of two liquids of differ-
ent kinds, which are separated from each other by a thin and
porous membrane, whether organic or inorganic. They were
first adopted by M. Datrochet, who, in 1816, gave a com-
plete explanation of the phenomenon of one liquid flowing
into a vessel or out of it, through a membraneous substance,
and mixing with another liquid of a nature different from
itself. This phenomenon was proved by means of the endos-
mometsr, an apparatus composed of a membraneous bag, fastened
to a long glass tube and made both air-tight and water-tight.

This bai* being filled with a mucilaginous or gummy solution
thick' r than water, as milk, albumen, syrup, is immersed in a
vessel full of waiter. In a little time the liquid in the tube
rises to the height of some psrts of an inch, and the liquid in
the vessel sensibly sinks ; from which it is concluded that a
part of the pure water has passed through the membraneous
bag and has mixed with the liquid within it. It is also found
that, after a cerum time, the water in which the endotmometet
is immersed contains some of the mucilaginous or gummy
solution ; a current is therefore produced in two opposite
directions ; and the process by which the mucilaginous liquid
is increased, u called endosmose ; while that by which the water
is diminished, is called exosmos*. If pure water be put in the
membraneous bjg, and it be immersed in a gummy solution,
endosmose take* place from the pure water to the solution,
that is, the level of the exterior liquid is elevated. The height
to which the liquid in the endosmometer rises varies in
different liquids. Of all vegetable substances, sugar in solu-
tion is that which, under equal density, possesses the greatest
power of endosmose ; of all animal substances, it is albumen.

Gelatine po ss e s s es but a very feeble power of endosmose. In
general, the current of endosmose is tow jrds the denser liquid.
Alcohol and ether, however, are exceptions ; for these liquids
act upon water like denser liquids. With regard to acids, it
is found that, according as they are more or less concentrated,
endosmose takes place from the water to the acid, or con-
versely.

If. Dutrochet has demonstrated by his experiments, that the
p heno mena of eadoemose can take place only when 1st, the
liquids are heterogeneous and miacible, as mater and alcohol ;
2nd, when the liquids are of different densities ; and 3rd, when
the membrane which separates them if permeable, at least, by
one of them.

All vegetable and animal substances are permeable ; as to
inorgani: auhlanec*, such as slates, stone, porcelain and pipe-
clay in certain states, they are less permeable in proportion as
they contain more silica. Pipe-clay, which is more aluminous
than porcelain, is more permeable; it is this property whkh
makes it catch the tongue. Through thin inorganic laminae
the current is feeble, but it may be indefinitely continued.
Organic membranes, on the contrary, are speedUy disorganised,
and endosmose ceases.

Several theories of endosmose have been proposed. Some
attribute it to an electric current which takes the same direc-
tion as the endosmose. Others suppose that the cause of the
phenomenon is a capillary action which is united to the affinity
of the two liquids. Others again suppose that endosmose is the
result of the unequal viscosity of the liquids. Lastly, this
phenomenon has been ascribed to the greater or less permea-
bility of the membranes by the different liquid*. Of all tht*e
hypotheses, not one explai:.s endosmose in a satisfactory
manner. Whatever the cause may be, the phenomenon
appears to be intimately connected with the causes which pro-
duce capillary action ; yet it is observed that an elevation of
temperature which increases endosmose, on the contrary
weakens capillary action.

Gaseous Endosmose. — The gases also present the phenomena
of endo>mo?e. It two gases of a different nature are separatee 1
by a dry membrane, there is a simple mixture of them, that is,
the currents are equal on both sides of it ; but il the membrane
be wet, endo*mo*e takes place, that is, the currents are unequal.
This is proved by the following experiment : a bladder tilled
with carbonic acid is inclosed in another bladder larger than
it, and containing oxygen. The latter bladder is soon filled
with the carbonic a<*id, which shows that the endosmose is
from the carbonic acid to the oxygen. In like manner, if a
soap-bubble be blown under a glass vessel fuU of carbonic
acid, il will become larger and larger.

Absorption and Imbibition. — The words absorption and imbibition
in physics are nearly synonymous ; both equally indicate the
penetration of a foreign substance into a porous body. Absorp-
tion, however, is used indiscriminately in speaking of liquids
and gases, nhile imbibition is restricted to liquids. In physio-
logy, absorption i« distinguished from inhibition. In the
former case, there is the penetration of a foreign substance
' into the tissues of a living being, while in the latter there is
only penetration into the ports of a body destitute of life,
whether organic or inorganic. In short, in absorption the
vital forces arc put in action ; in imbibition they are not.

Absorption of Gases. — The property of absorbing gases, in the
physical sense, belongs to all bodies possessed of sensible pores,
but in very variable degrees. This property is particularly
evident in oak charcoal ; extinguished under a vessel filled
with a given gas, this body absorbs, under the ordinary pres-
sure, 90 times its volume of ammonia, 36 times its volume of
carbonic acid, and 9 limes its volume of oxygen. In a humid
state, this charcoal absorbs only half as much, which proves
that its absorbing power is due to its porosity, and conse-
quently to capillary action. The absorbing power of fir-char-
coal is only half that of oak-charcoal. The charcoal of the
c.rk-tree has no absorbing power; neither has the- very com-
pact natural charcoal called graphite. Hence it is inferred
that, while porosity is a condition essential to tbe absorption of
gases, yet the pores of bodies which have this power are com-
prised within certain limits.

Absorption m Hants.— hi the vegetable kingdom, absorption
takes place in all parts of plants, hut especially la the spon-

LESSONS IN GREEK.

235

gioles or radicles in which the roots terminate, and in the
leaves. By these organs, vegetables absorb the carbonic acid,
the ammonia, the oxygen, the hydrogen, the carbon and the
nitrogen necessary for their nutrition.

The liquids and the salts which they hold in solution are
at first absorbed by the radicles, by the double action of endos-
mose and capillary attraction ; then the sap produced by the
vegetable, increasing in density in its superior parts, the phe-
nomenon of endosmose still takes place and gives it an ascend-
ing direction. Moreover, the ascent of the sap is favoured by
the vacuum which the exhalation of the leaves in the elevated
parts of the plant has a tendency to produce. As to the capil-
lary action, it can only raise the liquids in the lower cellules
and cannot produce a current. By this action alone the
ascent would only be about the eighth of an inch.

Dr. Boucherie, of Bordeaux, has made a fortunate applica-
tion of the absorbing property of vegetables, by introducing
into the structure of woods, salts of such a nature that one
kind 'gives them colours more or less bright, and another kind
increases their flexibility and tenacity, or renders them leas
combustible. For this purpose, at the lower part of the trunk,
a cavity ia'made which communicates with the solution pro-
posed to 'be absorbed. In a few days, this is transferred to
the top of the tree. In this manner,' a brown tint is obtained
by the pyrolignite of iron ; a black, by tannin ; and a blue, by
the prussiate of potash.

Absorption in Animals.— In the lowest class of animated
beings, which is possessed only of a cellular structure, the
process of nourishment is carried on, as in vegetables, by
imbibition and endosmose. In the higher classes of animals,
absorption takes place. For example, garancin or madder, when
taken interiorly by these animals, penetrates their bones and
givea them a red colour. In like manner, when a liquid is in
contact with a cutaneous surface from which the. epidermis haa
been removed, or with a mucous membrane, it ift found that, as
these substances are very vascular, the liquid pa»eea into the
vessels by the effect of endosmose, whioh constitutes tho
absorption.

The more that substances approach the state of a perfect
liquid, the more easily are they absorbed. In order, however,
that the absorption of liquids may take place, the membra-
neous substances must be wetted. Fatty substances, which are
not liquified, are not absorbed ; but M. Bernard has observed
that they are easily made absorbable by forming them mto an
emulsion with pancreatic juice. Dr. Lose has recently observed
that, by treating cod-liver oil in the same manner, it acquires
greater energy, because that by this means it is more fully
absorbed.

Absorption, as well as endosmose, is increased by heat.
After profuse perspiration or bleeding, absorption is likewise
Increased.

Solid substances are also absorbed by the aniru.%1 system.
This is frequently manifested hy, the, saturnine naiqlvais* which
tijirt, persons w-ho have feed their hand* far a, long time, in
contact with the a*l{» of lead or litharge. Aftex %* poisoning
has taken place, it is, found in many cases tha£ the deleterious
t distances were absorbed by different organs.

LE8SON8 IN ORE EK.-No. XIX.

By John B. Beard, D.D.

The NtTMBRALs; Recapitulatory Exbrcisbs.

Tm numerals express the relation of number. According to
their import they may be divided into five classes ; 1, the
cardinals ; 2, the ordinals ; 2, the multiplicative* ; 4, the pro-
portionals; and 5, the substantive numerals.

The foundation of the whole are the cardinals, or the
ales/ft *0 called because they are the Hinge (in L*Uo, eardo)
on which the others turn. The cardinals answer to the ques-
tion, how many? as "one," -two/' "five/' &c. Of the
cardinals, tho four that come first, and the round numbers
from two hundred (haKOotox) up to ten thousand (pufuot), as
well aa the compounds of uvmot, have the inflexions of adjec-
tirea ; all the rest are indeclinable. The thousands are
1 by the help of numeral adverbs, e.g, t rpic-xiXio*, 3000.

The ordinals denote the order in which the numbers follow,
or the place in the series held by a particular number ; as the
fourth,, rsraprec. They are all inflected like adjectives of
three terminations.

The multiplicative* denote how often a quality is repeated,
as two^fim, Jour-fold; they are compounds of ttXovq, and have
thr^ adjectival terminations, ovg, if, ocv, as dnrXovc;. Then
there are numeral adverbs in ajcic, which answer to the ques-
tion ft * no often} as Uarovraxic., a hundred times.

The proportionals are compounds of irXamoc, a, sv, and
denote so much the more than some other object, as dnrXaaiog,
ItPNV ps much.

The substantive numerals express the abstract idea of
number, as *} £vqf, g. aSog, duality.

The alphabet serves as signs for number, as well as supplies
the elements of words Hence, with the Greeks, the four
and twenty letters of the alphabet are so many cyphers. In
Ulc ries, however, three obsolete forms are introduced,
namely, after e the letter fiav or dioamma, r or 2ri, that is t,
as the sign for six ; also Koirira, that is 5 as the sign for 90 ;
and Sauwi, ^7\, as tfce sign for 900.

Tho first eight letters, from alpha to theta\ bau or $ti
included^ make the first aeries consisting of units ; the ensuing
eight, from iota to pi t including koppa, form the second series,
or the succession of tens ; and the remaining eight, from rho
to OMfyo, together with sampi, make up the hundreds.
Eleven "is ta', that is ten and one; twelve is i/3', ten and
two, &c.

Up to 999, the letters when used as figures have an accent
over them each, thus a, ty. When more than one sign s:and
thus together, the mark is over the last. With 1000 the
alphabet begins afresh. In order to indicate this the mark is
placed under the letter, thus a = i, but a = 1000 ; i =i 10
hut /:= 10,000. The present year in 6retk numerals is
written thus, t aiavtf t 1854.

I here subjoin lists of the cardinals and tho ordinals,
3ticr>mpanied by our numbers and the corresponding Greek
signs. The English words one, two, three, &c, need scarcely
be a -1 led, and of course first, second, third, tenth, &c., will
readily be supplied by the student.

Cardinals. . Ordinals.

1 «' «<C» MW> h irowrcc,, »/, ov

2 /3' $vo, or di/ti &vrtp<.£, a, ov

3 y rptig, rpue rpiroc,, rj, ov

4 $ x rerraptQ, a, or recragp rtraprog, q, ov

5 i newt rr^nrroc, rj, ov

6 t' i£ itroc,, tj, ov

7 V iirra ififiouoc,, m, ov

8 rf Otero* oySooc,, t), ov

9 9' iwia tvvarog, rj, ov
10 •' fowl focaroc, >;, ov
U Ml' Musa MtKaros, rj, ov

12 if? (We*a StotcKaroQ, if, ov

13 i/ TpiQKaiiUKa Tptc^aictKarog, rj, ov

14 i$' TtTrapcgKaifcipa or r "tv. rerrapaKaidiKarog, ij, ov

1£ *t* ig*ai£(Ka

17 iC iirraKaicUiea

18 ilf' OKTlOKCltClKa

9 & tvviacaietKa
10 k h*o*h(v)
%l *«' iiKomv «ic, fiia, tv
\0 X* rptaicovra

TriVTiCaiCiKClTOQ, |), ov

tjcjcaidejcaroc, tj, ov
£irrajcai#€iraro£, -,/, ov
ogruHcat&icaroc, t], ov
evvfaca^cicaroci n, ov
*l$QOTOQ, jy, ov
CiMxrroc, if t ov, irpwroc.if.ov
rpiaicocrroc, ij, ov

40 n' Ttrxapanovra or Ttoe. TtrrapaKQ.orac, t q % ov

M) y' 7StvTt)Kovra 7revrj|ico<rroc, tj, ov

60 I' ibjKovra UfjKoaroQ, y,ov

70 0' ificofirjicovra ifivofitiKoaroc, ij, ov

\0 it* oyCotiKovra aydotjKOGTOc,* rj, ov

HO V tvtvijicovra tvivrjKOcro^, tj, ov

1 r )0 p' iiea top i tear oar o$ t i\, ov

336

THE POPULAR EDUCATOR.

200 J luucoatot, at, a
300 r* rptamootott at, a
iOO v rtrpamoatot, at, a
£00 +' rtvraKOVtox, at, a
600 % Uaxoaun, ai, a
700 i/ ixroMovuH, ol, a
800 t* ocTuctrtUM, ai, a
900 7\' ivvaKOTUH, at, a
1000 a \i\iotv at, a
2003 fl lnx*"*» *". a
3000 t y rpcfxtAioc, ai, a
4000 / TtT^aKtcxtXtoi, ai, a
5000 jl rivractQxAio*, at, a
Uh'jQ jr iZaxicxkioi, at, a
70 >0 £ irraxiqx^ot, at, a

fcOOO ft OKT€UUQX*^ VOi t a *» a

0000 J3r iyuaKir^i\ioi t at, a
10,000 / uvptot, at, a
20,000 /t It^uvptot, at, a
100,000 jp iigajuffivpuHf at, a

rptaroeio+TQC, n, ov
rirpaKooweroz, n, ov
rtvraKOVtoaroz, n, ov
iZatoatooroz, n, ov
ivraxoaiooroQ, n, ov
ocraKooi&TTos, n. ov

tl'VaXOGUXTTOC, n, ov

XfAu>arcf , if, ov
< ~HX l * MKrro C» It ov
rptr^iXio^rof , n, ov
rcroacifxiXuMruc, rj, ov
7rtvrancx i ^ lo<rro Ct V. ov
cgartfxtXiOOTOf, 1* ov
t'jrrajrecxiXuKrroc, 1» ov

OKTUKlQX&iOGTOC, IJ, OV

tvvaKicxi\iooToCt n. ov

ftVOt04TTOQ % IJ, OV
ilCHVplOVTOC, ||, OV

CtKactcpvpUHTToc, r t , ov.

la forming compound numbers you may put the smaller
first an] the larger second, interposing koi and, as rtvrt cm
tucoctv, fire and twenty ; or you may reverse the order, still
however keeping the conjunction, as tucoat rai rtvrt, twenty
and five, 25. Thus, 345 will be either rtvrt cat rtrrapacovra
xai rpuucovioi, or rpuucootoi oat rtrrapagova koi rtvrt.

DccUmion of the four first Numeral*.
Namelr, «<c, ***\ ZvOt i**\ rot** ** rei * rtrraptg, four .

rtrrapa

rtrrapa.

Like tic decline its compounds otitic and uticttQ, no one,
thus, ovSttg. ovhuta % ov&iv ; g. ovctvoc, ov&tfuac, &c. Plural,
tvttvtQ, ovStutat, ovttva, ovStuutv, ov&tat, &c. ; the £ is
euphonic.

Avo is often used as an indeclinable word for all cases. The
numeral ap^w, both, has, like ivo in the genitive and dative
oi v, thus, aufotv ; the accusative is the same as the nomina-
tive; like ivo, aft}w is sometimes used aa an indeclinable.

Vocabulahy.

liia

Ivo

tVOQ

fitac

ivo$

tvotv

ivt

fiia

ivt

Ivotv

tva

fitav

Ivo

rotic

rota

nrrapte

TOl'JfV

rtrrapvv

TptOt

nrraoot

rp*«C

rpia

rtrrapae

KtXtKta, ac 6, Cilicia.

Qpvyta, ag, ij, Phrygia.

Eu^pariyc, ov, o, the river Eu-
phrates.

IIeArj7 17c, »'/, a small light
shield.

UiXraarrjc, ov, b, a shield-
bearer, targeteer.

'CffXirr/c, ov, 6, a heavy-armed
soldier.

Ilapaoayytjc, ov, 6, a parasang,
a Persian measure of length
= 30 stadia.

Aptluoc, ov, 6, a number.

Bappapoe, 6, a barbarian,
every one not a Greek,

Evutvroc, ov, 0, a year.

KvoVoc, ov, 6, the Cydnus.

UtXoirovvnffOQy ov, t), Pelopon-
nesus.

Ilfpffticoc, tji ov, Persian.

'Pif/taioni ov, 6, a Roman.

Zapoc, ov, 0, the Sarus.

Xra^fioQ, ov, 6, a station, a
day 6 march, stage == 5 pa-
rasangs or leagues,

101 feet English, or £ of a
stadium.

£raoW, ov, ro, a stadium =600
Greek or 606 J English feet.

Korvutpa, wv, ra, Coty6ra, a
town in Pontas.

Mvptac, ahoQ, »}, the number
10,000.

BafivXwv,^ arvoc, c, Babylon/

IIoi/c, TTocoi, 6, (hat. pet) afoot.

Avafiaotg, caic, 1}, a going up,
an expedition.

kara/3d(rct\ tw v» V, s going
down, retreat.

1 Apfia, apnaroQ,ro, a carriage.

Brjfxa, &toq, ro, a step, stride.

Xrpanvfia, utoq, ro, an army.

Evpoc, ovt, ro, breadth.

n\rj9oc, ovq, ro, a multitude,

IvvtroQ, n, ov, intelligent.

Apcn-avn^opoc* ov, scythe-bear-
ing.

Zv/i7rac, aaa, av, all, all toge-
ther, total.

2i/yyp«0u, I describe (ypa^w,
I engrave, write) .

nXiOpor, or, to, a plethr«.*3cs! IIapci/11, 1 am present

F.x racists. — ExousH-Gaxix.

EvfpartK *orapoc tan rotate rtrrapw oracimv. To it ara-
iiovtxt* -rapa roi£*P«#/MU0tc rtvrt max tucooat mat Uarov 3 q para,
fl rtvrt am tuDOOx oat iZamo«i<ovs roiaf. Kvpy rapnvav ai ta
Htkoro v vnooo vntr rpuueorra rtm. Tov Sopov, KtXunac
rorapov, ro tvpoq wv rota rXiOpa. To It rXtQpov t^tg
Uarov rocaf. ktrcro?, KiXinac rorauoc, ***** tOTt * TO »Xi©-
pwv. Tov Matavtpovt +pvyiag rorauov, ro tvpoc tortv uxovt
rtvrt roi—v. 'O rapaeayyiiz, TIimtixuv ptrpov, t\u Tpuuzoi'ra
or acta n rtvrnrorra gat irraxoatovc roi orracurxtJUotrc wat
fiupwvg rotas. Aptfyoc ovfiraoiiQ rife ocov rn* avaflaotwc
tat Kara&aatmc, *i pro *tvof*vroc ovyypaftrat, qeav or a Open
ttacovuH tuca rtvrt, rapuvayyat x&uh Uarov rtvrnxovra
rtvrt, or acta rptopvpta riTpaxnT\i\ia <gaco*ia wtvrujKovra,
Xpom ***&* rtig avafiavimc rac carajkurt*c tvtavroQ kci
T P"C M***- 'Eroc ^<>*a ovvtrov epttrruv toriv aowiru*
aravrw. Tov Kvpov orpanvf»aro£ nv aptO/toc rmv fit.
EWtjv+tv orXtrat fivpun eat rirpaxovtoi, rtXraorai it cW(tAcc<
koi rtvraKooioi, rmv ct ptra Kvpov Bapflapwv ttxa fivmattg
koi apfiara cptravqfopa a/191 ra itcooiv.

G&kbk-Emclish.

It is better to hare one intelligent friend than many unin-
telligent ones. Seventy years produce about (apfi and ace.)
25,655 days. The sum total of the way from the battle at (iv)
Babylon to (mc) Cotyora, of the retreat, which Xenophon
describes, is 122 stages, 620 parasang*, 18,600 stadia, the
length of the time eight months. The number of the army is
39,850. (There) are four generals of the army, each of the
four of (that is, commanding) 30,990 soldiers. In the battle
(there) were present 96,650 soldiers and 150 scythe-bearing
chariot?.

LESSONS IN CHEMISTKY.— No. XV.

I pukposb beginning this lesson with a consideration of the dis-
tinctive properties of peraalU of tin in solution. It was men-
tioned in the course of the preceding lesson, that our protochloride
of tin required to be well protected against the atmosphere, other-
wise it rapidly became converted into perchloride ; nevertheless,
it being now our object to prepare a perchloride of tin unmixed
with protochloride, we must adopt some more ready means of im-
parting oxygen than that of mere exposure to atmospheric air*

Nitric acid, or some of its compounds, are the bodies most com*
monly had recourse to by the chemist for imparting oxygen. You
have already seen that nitric acid, when added to solid antimony
and solid tin, is decomposed, with the evolution of orange-coloured
fumes, and a white powder in either case results : and here I may
offer a remark which is of universal application. Whenever you
add nitric acid to any body, no matter what, and observe that the
peculiar orange- coloured gas to which your attention has been
more than once directed escapes, rest assured that the portion ef
the nitric acid has delivered up its oxygen to the substance ope-
rated upon. The following diagram will render this change more
comprehensible than any mere words : —

Nitric acid
Tin

/ Nitrogen

>Binoxide of •Nitrogen

Peroxide of Tin

From an ex a min a tio n of this diagram, it appears that nitric acid
is composed of nitrogen and oxygen. The oxygen is represented
in our diagram as divided into two portions, such being the result
of decomposition. One of these portions goes to the tin, with
which it combines, giving rise to' oxide of tin ; the other unites
with the nitrogen, and forming the gas, binoxide of nitrogen,
escapes. As regards this gas, you have already been informed that
if collected without contact of atmospheric air, it is not orange
coloured, but altogether colourless. This circumstance, however,
does not in any degree affect the practical truth of my remark,

LESSONS IN CHEMISTRY.

that whenever you see an orange-ooloured gas escape after you
have brought nitric add in contact with any substance, the ap*
nearanoe is a proof that the nitric acid has been busy in giving
oxygen. In order to render the preceding diagram more simple
than it otherwise could have been, £ have avoided the appending
to it of proportional numbers. You miy, however, add them, if
you please, making the statemsn* as follows :—

237

2 equivalents of nitric acid

= 108
= 116
= 28
= 80
= 6)
= 148

2 „ of tin

2 „ of nitrogen

10 „ of oxygen

2 „ of binoxide of nitrogen

2 „ of poroxide of tin

m In order to effect the conversion of protochloride into perchlo-i
ride of tin, take about half a wineglasiful of the solution, add to
it about a teaspoonful (not measured in a teaspoon, however) of
strong nitric acid ; pour the mixture into an ovaporating-dish or
Florence flask, and boil ; continue the boiling operation until all
the liquid has been expelled by evaporation, and your protochlo-
ride will have become converted into the perohloride of tin.

Fig. No. 1.

In conducting this evaporation, as well as all others which result
in the liberation of corrosive vapours, care must be taken to make
tome provision for their escape. In laboratories special contri-
vances are adopted) but private operators cannot do better than
to conduct such evaporations under an open chimney. As regards
our present evaporation, it may be advantageously conducted by
placing the Florenoe flask in a bed of hot sand : for the purpose ot
holding the latter, an iron ladle or fryingpan, as depicted in fig
N ». 1, may be used.

U-mng evaporated all the liquid, and allowed the flask, ladle,
sind, and all to cool, add water to the result and dissolve it out.
Pour now a little into a test-glass, wine-glass, or any other con-
venient vessel, and try the effect of testing with hydrosulphuric
acid and hydrosulphate of ammonia. If the conversion of proto-
chloride into perchloride has been complete, you will obtain a
) allow precipitate; if incomplete, the precipitate will be more or
less black in direct proportion to the amount of protochloride still
remaining untouched.

In this case of incomplete conversion you will have to add a
mixture of nitric and muriatic acid, and repeat the evaporative
operation.

General Remark* concerning 4h$ Formation of Sulphur eU by My-
drondphurie Acid Oat and Hydrosulphate of Ammonia. — Remem-
bering the general rule, that whenever it is merely desired to test
the presence of a metal by the agency of hydrosulphuric acid, this
test may be employed in the state of aqueous solution— but that,
whenever it is desired to separate the w&jle of a metal contain* d
in a liquid by hydrosulphuric acid, then the test should b<* used
in the form of a gas— let me now direct your attention to a phe-
l noticeable in either case; as also when hydrosulphate of
is applied. Trie Phenomenon in question is the resolu-

tion of the precipitate sulphuret by excess of reagent. Your at-
tention was directed to this point whilst we were engaged on
arsenic; I now direct your attention to the same in respect of
tin, the sulnhurot of which does not fall completely, so long as tho
liquor which should deposit it contains an excess of hydrosulphuric
acid, easilv recognisable by the smell. Chemists, well aware of
this fact always submit a solution, through which hydrosulphuric
I acid as a precioitant has been passed, to a process of heating, in
order to get rid of the excess of hydrosulphuric acid. In some
cases this process of heating is carried on to the extent of ebulli-
tion ; in others, the liquid is merely put to stand in a warm place
far the space of a few hours. Practice and extended knowledge of
the nature of the bodies operated upon can alone determine which
process is the better of the two : in the case now under consider-
ation, the process of continuous gentle heating should be adopted.

Separation of Tin from Antimony.— We have already seen that
tin and antimony admit of being separated from all the metals
which hayo hitherto come under our notice by the agency of nitric
acid ; which converts tin and antimony into insoluble oxides, the
other metals being dissolved. I shall now describe one of several
methods which might be adopted for effecting the separation of
these two metals.

In the first place, the two insoluble oxides must be rendered
soluble, which is accomplished by fusing them with carbonate of
soda or potash. The process of rendering bodies soluble by fusion
with alkalis, or their carbonates, will come fully under our notice
when we arrive at the chemical examination of silica or JUnt.
On the present occasion I shall not detail the process, being con-
vinced that the descriptions involved would bo rather too difficult
for performance. Instead, therefore, of assuming that you are
endeavouring to separate tin and antimony from each other, both
existing in the condition of oxide, let us assume the problem to be
the separation of tin from antimony, both existing in the metallic
state.

The first step in this operation will consist in obtaining both me-
tals dissolved ; and hydrochloric or muriatic acid (spirit of salt) is
the best of all solvents that can be employed. Prepare, therefore, an
alloy of antimony and tin, by fusing tho two metals together in
an iron spoon or the bowl of a tobacco-pipe. When prepared,
break it into small fragments and throw the latter into a Florenoe
(lask. Pour hydrochloric acid into the flask, and apply heat,
by which treatment the two metals will be caused to dissolve. In-
asmuch as the treatment about to be adopted necessitates the exist-
ence of tin as a peroxide, it is well to add, towards the end of the
operation, a little nitric acid. Divide the liquid result into two
portions.

Separation of the Antimony. — If into one portion of the liquid
thus prepared and containing an excess of hydrochloric acid (that
is essential) a piece of pure tin be immersed, and the whole
warmed on a sand-bath, the antimony contained in the so-
lution is thrown down in the form of a black powder, tin being
dissolved from the bar to supply its place. By this simple method
we obtain all the antimony originally present ; and were our ana-
I lysis quantitative, we might learn the exact amount of the anti-
mony by collecting, drying, and finally weighing it.

Separation of the Tin. — If into the other portion of the liquid a
piece of zinc be immersed, with the same precautions before ob-
served as regards acidity and temperature, the whole of the con-
tained tin wQl be precipitated in the state of fine powder, but
perfectly metallic. Were we engaged in performing a quantita-
tive analysis, it is evident we could ascertain the exact amount of
tin by collecting, washing, drying, and weighing the result. We
must not discard tho metal tin without taking some cognisance of
its peculiar effect on glass, which it renders white and opaque.
For this purpose, powder a little flint glass ; mix it with a little
borax, in order to increase its fusibility, and dipping the looped
platinum wire, previously rendered adhesive by moisture, into it,
take up a portion and fuse it into a bead. This bead you will find
I to be beautifully transparent ; but if you now moibten the bead
I again, and attach to it a little oxide of tin (produced by the action
of nitric acid on tin), and fuse the whole together in the outer or
oxidizing portion of the blow-pipe flame, the bead becomes white,
enamel-like, and opaque; under certain circumstances, arsenic
produces a similar effect, but no other metal. All the milk-white
{lass, so frequently met with in commerce, owes its peculiar ap-
pearance either to the presence of arsenic or tin.

23*

THB POPULAft EDUCATOR.

Amttofw^UimmUt^am.Mtttfmmfomd of and* of tim,
and teetokaiiy kaowm a* fia-grsTe, it wry tube* if id in the his-
tory of pottery.

You m perhaps aware that the ndat Greek* ad Roans had
ao pottery stanler to our owa. Th* Sasriaa pottuy — ti at a
later perM the Etru«e*»— although beaatifal m aaaay naaacta,
aad a* to ita iassvovumaat within very Ban
itself was red, and the utsnost Bower of
was n^rietsd to the usMintfa^c/ alack. B

The ware

f ft. Vi

il) A variety of compouads is produced by the
verbs with boobs aad adjectives. These follow the same
laws which govern those produced by aseaas of prefixes,
of them, accordingly, are separable; as,

COVPOCVKS WITH BOCXS A» ABJKCTnTBB,

Soaae

the orwtmrntil eeramie art cf Greece aad Borne did aot go.

X ▼ it will at once fee reen that, era had the aacieat Greeks
sod Hasan* p. an and enamel colours, they eoold not hare given
euVct to them on a rtd ground- Before this chromatic nmaawnla-
tin eooH hsre been adopted, one of two tilings most have taken
piac* : either the oae of a potcry material so pare that the result-
ing wars would bs white throughout, or the employmeat af a
white en«2B»l, as su envelope to hid* the imperfection* of coloured
day. The first plan had been adopted by the Chinese from time
iniBMBMwial ; the second plan was introduced into Europe by the
Arabs of Spain. This iogenioas people eorered inferior pottery
with a ghxe of oxide of tin, and on this enamelled coloured
figures. The first European factorr ci this wsre was established
in Majorca; hence the msterial is known as Mqjotim mart. The
ornamental slabs still existing in the Alhambra — beaotifol as
when they were first made— are of afsjobea ware. The aaast
curious fact remains to be told : although the Greek* and Romans
were totally ignorant of the ass of tin enamel, the Assyrians and
Babylonians were so thoroughly conversant with this substance
and Um gissing properties, that they even employed it for the pur-
pose of enamelling ornamental bricks, as specimens lately brought
to light attest.

This discovery renders it doubtful whether the Saracens were
so much the inventors of tin-glaxe as the media for handing down

Xxxss which had been followed in Babylonia and Assyria, and
h perhaps had never tested to be followed in some obscure
locality.

gts ti s )l a* rB , to miscarry ; from fcei

$tcuvcvs)ca, to acquit ; v fret

0ta4raanunv to equal. *bia)

tcitabtu. to tear sway . . L*4

Gustjutcm. to take place , „ &zn

(2) Some are imstparabla ; as,

frstfofra. to exult : from frt$

Sristarfr*. to breakfast • , freft

^a^sa fas aya, to fawn; . ue*<

^sarasfea, to handle; feat

rcfiaarfa. to ogle : „ Hr»

gtrMrfra, to caress . » he*

Srstfmxfra, to su«pect ; m mats

Seflarsca, to perform ; . tcU

SSuVasrra. to gratify ; „ mU

S&rirugrn, to foretell ; noj

•ad &?**«.

mica,
pate*.

aad

LESSONS IN O E 11 M A N.— No. LXXX.
S 98. Pamirs separable and inseparable.

(1) The Prefixes of tin* class, when separable, are always
under the full accent ; when inseparable, the ascent falls upon
the radical.

(2) Their effect, when separable, is, in union with radicals, to
produce certain intransitive compounds, in which each of the
parts (prefix and radical) has its own peculiar and natural sig-
nification.

There are, however, some compounds of turd) and u m, in
which, though these particles are separable, the verbs are, ne-
vertheless, ttansitive. Still, it will be found, that in such cases
the signification of the compound is figurative; as, ununrixjett,
to bring about (one's death) ; i.e. to kill.

(3) Their effect, when inseparable, is, in connection with
the radicals, to form certain transitive compounds ; which, for
the most part, are used in a figuraive or metaphorical sense.

(4) We subjoin a list of the prefixes of this class ; illus-
trating each by a couple of examples ; the first being one in
which the prefix is separable ; the second one in which it is
inseparable.

btfre.

ftatfra.

ftwaavw.

Me*.

esaeta.

Basra.

fosrra.

(3) These verbs take the augment syllable $ r in the perfect
participle : except tcujufcra, which has rlu>$ra. In tome eases
however, verbs compounded with roll, a so, take the augment
as tcfljc^cifra. from rctt^uf «, to pour full.

S 100. THB ADVERBS.

(1; Adverbs in German, as in other languages, serve to mo-
dify the signification of verba, participles, adjectives and, often,
also thst of (toe smother : denoting, for the most part, certain
limitations of time, place, degree and manner. Hence are they
usually cluiittd according to their sseauaay.

(2) They are Indeclinable ; and formed, either by derivation
or composition, from almost every other part of speech : of some
however, the origin is wholly unknown. - '

Arranged according to derivation, adverbs are divisible into
the following classes :

$101. Adverbs formed from noons.

Adverbs are formed from nouns by affixing the letter I. This
termination I is nothing more than the sign of the genitive sin-
gular; which case, not only of nouns, but also of adjectives,
participles, Ac, is often made -to perform the office of an ad-
verb. Examples :

SRorgenl, in the morning ;
9lt*nW in the evening ;
Sags, in the day ;
3$tU0, in part, or partly ;
glug«, swiftly ;
3)urd)gcfctnt<, generally ;

from tar Sforsex, morning.
Uz 9tan), evening,
fcer $43, day.
from ter S^til, part.
,. *tr guig. flight
„ kurd>grfKat, passing
through.
„ Sufcytap^ looking at.

iDur^, through ;
J&inUr, behind;
Utbtr, overj
Urn, around ;

llntrr, under ;

CBiftrr, s;ain ;
back;

{fDar^'trittflen, to press or force through;
SDard^rin'gen, to p trie t rate ;
i Wtrroeycn, to go behind ;
I ^intfrgf>n, to deceive ;
( Ucberfe^n, to set or put over;
X Utbrfti'tn, to translate ;
( Um'^tfftn, to go around ;
( Umgr^'en, to evade ;
f Un / trrfn)ic6rn > to shove or push under ;
1 llnterfd)ie / feit, to defer; also, to substitute.
( SBir'trrffolcn, to fetch or bring back ;
t Wittrf)9Un ( to repeat ;

3u|'c6mM, visibly ;

S 102. Advbbbs formbo from AOJBCT1VBS.

(1) Adverbs are formed from adjectives by the addition of
the suffixes t i a), y af t and ( ing ; which, except the last, are also
regular adjective terminations. These endings are chiefly ex-
pressive of manner ; and may be translated sometimes by a cor-
responding suffix (as the English ly or wA/y), and sometimes by
some equivalent phrase. Examples :

SSUyrlid), truly ; verily;
JBof $oft, maliciously ;
SBcisltd), wisely ;
8rriUd> # sure ; to be sure ;
iBUntlingf. blindly;

•from toa^r, true.

„ bflfe, evil; wicked.
„ uKifr, wise.
„ frtt, free ; sure.
„ Mint, blind.

(2) The letter •, also, as above slated, added to adjectives,
gives rise to a class of adverbs : thus,

LKS60NS IN GERMAN.

23d

8fa$ta, on tbe right ;
8inf«, on the left ;
Slnbert, otherwise ;
JBereiM, already ;
IBefonber*, particularly ;
©t«M, continually,

from redjt, right.
„ iinf, lert.
„ anber, other.
„ bettit, ready.
„ fcefonter, particular.
„ fiet, continual.

The letter is, also, sometimes affixed to adverbs ending in
mat; as, *ormal«, formerly; bamats, at the time; vtclmatt, many
times. For numeral adverbs ending in mal, lei, &c , see the
Section on Numerals

(3) Here note, also, that almost all German adjectives, in the
absolute form, that is, in the simple form without the terminations
of declension, are employed as adverbs : thus, cr remit ftyneU, he
runs rapidly; cr $anbrtt tfftWa), he acts honestly.

S 103. Adverb formed from pronouns.

(1 ) These are, chiefly, b«, Mere / from b«r, blc, ba«, this or that ;
to*, where; from met, tea** who, what ; fftt, hither, and §in, thither ;
from some corresponding demonstrative pronoun no longer
found.

(2) The pronominal adverbs in combination with other words,
give rise to a number of compounds. Thus ba and wo, united
with prepositions, serve often instead of the dative and accusative
{neuter) of the pronouns bcr, tore and totldpt, respectively. It will
be noticed, that when the other word begins with a vowel or
with the letter it, b« and too are written bar and toot ; that is, that I
r is inserted for the sake of euphony. The following are com-
dounds of ba and too :

<ta&ti, thereby,

1. e. by this or that.
£afur, therefore,

i. e. for this or that.
&)amit, therewith,

I. e. with this or that.
$arin, therein,

i. e. in this or that.
£ftrttnter, thereunder or among,

i. e. under this or that.
J&octtin, there about or therefore,

I.e. for this or that: therefore.

$aran, thereon,

1. e. on this or that.
Jfowuf, thereupon,

1. e. upon this or that.
&ar«ul, therefrom,

i. e. from this or that
Staen, thereof,

i. e. of this or that.
&\m,u, thereto,

i. e. to this or that.
£abut$, there-through or

thereby, ?. e through or by

this or that

(&) In like manner ty« and l?in appear, also combined with
other words. Between these two particles a distinction exists,
wherever they are used, whether alone or in composition with
other words, which should be well understood and always refflora-
bered- They are, in signification, exact opposiies : tyx indicating
motion or direction towards the speaker ; bin implying motion
or direction away from the speaker. The following are ex-
amples:

SBrtit, whereby,

i. e. by which.
fiBofflt, wherefore,

i. e. for which.
SOtmlt wherewith,

1. e. with which.
SBotin, wherein,

i. e. in which.
SBorunter, whereunder, among,

i e. under this or that.
SB ovum, whereabout,

i. e. about or for whieh ;
wherefore; why.
SBeran, whereto,

i. e. to which.
SBocauf, whereupon,

i e. upon which.
gBotaus, wherefrom,

i e. from which.
SBown, whereof,

i. e. of which.
SBoui, whereto,

i. e. to which
SBeburd), whereby,

i. e. by or through which.

4crat, down hither (i. e. where

the speaker is).
$*rauf, up hither.
*}tvava, out hither.
$min, in hither ; into this place.
$irry*r, or tyetyer, hither here ;
this way.
gcrustr, over hither.
Vmntrr, under hither.

$inafc, down thither, (i. e. away

from the speaker),
£inciuf, up thither.
$tnauf, out thither,
-fcinrin, into that place.
J&icr^in, thither; this way for*
ward.
£tnub«r, over thither.
J&immtcr, under there.

I £a!)fr, from there hither, i. e. $iu)tn, from thither (to) there,

thence. i. e. thither,

SBolier, from which place hither, ffiotytit, from which place thither

i. e. whence. i. e. whither.

(4) We have no words in English, corresponding exactly in
use and force with bcr and fym ; and therefore, though every-
where in German their force may be felt, it cannot always be
expressed by single words in translation. Hence are they
often treated as expletives.

$ 101. Adverbs formed from verbs.

(1) Adverbs are formed from verbs by suffixing to the radical
part the termination lict>- All adverbs so formed, however, are
equally employed as adjectives: thus,

GMauMty (from glaufc+cn, to believe), credibly.
@tcrbuc$ (from ftcrb+cn, to die), mortally,
tfloglty (from flaj-f**"' to lament), lamentably.
SWerflty (from mtxt-l-eit, to note ; perceive), perceptibly.

$ 105. Adverbs formed by composition.

(1) Besides the classes given above, a numerous list of ad-
verbs in German is produced by the union of various parts of
speech. Thus, the word SB eife {mode, manner), combined with
nouns, form a class of adverbs employed chiefly in specifying
thiBgs individually or separately : thus, f$ritttof iff, step by step ;
ts/tittotift, part by part $ tropfennxife, drop by drop j nogennxifr,
wave by wave ; like waves. SBeifc is also added to adjectives ;
as, btebiftyrrweife, thievishly; g,lucfltc$erto*ife, fortunately.

(2) Sometimes an adverb and a preposition are united ; ex-
amples of which may be found above under the head of adverbs
formed from pronouns.

(3) Sometimes adverbs are formed by the union or the repe-
tition of prepositions : as, bureau!, througho u t ; thoroughly $
mrd) unb bu«$, through and through.

(4) Sometimes a noun and a pronoun joined together serve
is an adverb ; as, mcincrfeiti, on my side j bwflciM, on this side ;
ntterbingt, by all means.

(5) Sometimes one adverb is formed from another by I he
addition of a suffix j as, ructltngf , backwards : sometimes by the
Union of another adverb ; as, mmmerou$r, nevermore.

(6) Sometimes the several words composing a phrase are, by
being brought into union, made to perform the office of an ad-
verb: thus, fiirtoa&r (for furto<u)r), verily; fonft (for the o solete
to u« tjt, if it is not), otherwise ; else:

g 106. Comparison of adverbs.

(1) Many adverbs, chiefly, however, those expressive of
manner, are susceptible of the degrees of comparison. The
forms for these arc the same in adverbs as in adjectives.

(2) It must be observed, however, that, when a comparison,
I strictly speaking, is intended, the form of the superlative pro-
I duced by prefixing am (See Obs. $ 38.) should always be em-
I ployed ; as, n ftyrelbt am fcr/onftai, he writes the most beautiful
I (o/ all)

(8) If, on the other hand, we purpose, not to compare indi-

I viduals one with another, but merely to denote extreme excel-

I lence or eminence, there are three ways in which it may pro-

I perly be done : first, by using the si mule or absolute form of

the superlative ; as, et gnlfit |T«inMia;ft, he greets or salutes in a

manner very friendly, very cordially; secondly, by employing

auf« (auf4-*a«) with the accusative, or jum (ju+tcm) with the

dative, of the superlative ; as, aufs ftcunbltyfle, in a manner very

friendly ; jum faonften, in a manner very beautiful ; lastly, by

adding to the simple form of the superlative the termination

en«; teftcne, the best or in the best manner; fotyfUnf, at the

highest or at the most.

S 107. THE PREPOSITION.

(1) The prepositions in German, that is, the words employed
nicely to denote the relation* of things, are commonly classified

340

THE POPULAB EDUCATOR.

•eeordmf to the ease* will* which they are eonstroed. Sosae of ■
them are eowstmetj with the gesitive only; tone witk the
dative only ; some with the accusative onlr ; and tome either
with the dative or accusative, according to circumstances.

(2,» They nay also, «n a different priaefple, be divided into '
two general classes: the Primitive a&d the Derivative. The!
primitive preposition* always govern either the dative or the '
%rj itsalive : the derivative prepositions are found, for the moi: \
part, in connection with the genitive only. !

sorption, s : x penny stamp*, which we hive sen? to the Rev. Mr.
Carwcn, of Plairow. i -, Eamn, wbo wrote the appeal on the lady's
beha!', aad who alone ia ia eoaaxrunie*t:oa wi b he-, if a sufficient
proof that the letter and the tren'artion whieh i: so t imply, yet
beautifully, describes, are real and cot fictitious.;

COBUESPONDEXCE.
INDUSTRY AXD CHARITY.

•* TbU poor widow bath ea*t more in, than all they who bare cut iato the
treasury."- Msrfc, sJL 4J.

Sib, — This evening we received our weekly allowance of mental
food in the shape of the Popular Educator, with one or two
minor publications, which we uae as sauce for goose and gander ;
or, rather, to ubim us in the evenings, after the study of the
English, Latin, and oner lessens, that the P. E. provides for us.
Well, sir, I have said that we obtained your paper this evening,
and, as is generally the case, whilst my wife is busily engaged in
clearing the tea-things from the table, I take the Educator and
look down the outside columns of it, so as not to lose one morsel i
of the Knowledge which is often elicited from you hy some question-
ing correspondent who has been kind enough to ask for the very
thing I wanted. I have learnt some good precepts, some niefal
hints, in this manner, without (in my way of thinking) losing
time.

Yen most k- ok, air, tint my boys attend the day-school in our
rill ijje, where, amongst o'.'ser things, English grammar and com-
po i'ioo are tvifjht. These are favourite studies with my boys ; so
t'.ut Toi "»i;l kuppoie I (who never knew English grammar before
I studied the F. fe.) am obliged to make the most of my time to'
kf-cp pice with them ; for I like not the idea of my boys learning
that of which I (their father) know nothing. On scanning the
column of Correspondence, I saw your kind-hearted appeal to us,
in behalf of an unfortunate lady who is behind-hand with the
P E. I immediately proposed the following question :— " Who
will rote for the selling of the P. E. for the purpose of getting
*-;me plum-cake at Christmas ? " Not a voice ! u Which is the
better for us, to have plum-cake or the Populau Educator ? "
" Educator," cried three voices at once. Well, thru, said I, a
poor lady is in want of some help, so that she may be enabled to
purchase the remaining numbers which she has not in her pos-
sf anion. I then proposed this resolution : that we make a sub-
scription of one penny each, to send to the editor, for the benefit
of this poor lady.

The b>)S wrnt each one for his saving- box; I think, sir, you
would have smiled to see their alacrity ; the penny each was placed
on the table, my Denny with theirs. My wife gently hinted the
impracticability of sending pence, and proposed the making up of
the sum to sixpence, which could go in a note; for, said she,
though we hare enough to do to make bo'h ends meet, we are not
unwilling to gUe to a good cause. She i« willing, I assure you.
I hrard her say, not long since, she would make a half-pound of
sugar serve us (or a week, rather than that her husband should go
without the P. E.

We hope the unfortunate, hut well-deserving object of your ap-
peal will succeed in her praiseworthy exertions ; and by some
means be placed above the necessity of studying at such a dis-
advantage. She will surely thank you for your kind-hearted hint,
which we hope will be met by as kind a sympathy by very many or
our fallow-Christians. We would that ours was a larger sum ;
hot, air, we give a little and wait. If we bear from you again — as
my boys are saving their money for an Easter holiday— we will ruise
another subscription. I beg you to look down from your learned
eminence, and spare, or gently point out, the errors of your pupil, I
wbo is A Daily Labourer, i

P.8.— My ooys are longing; to see the letter which, say
they, father is writing to the editor of the Popular Educator.

December 7th, 1S53.

[We hope that our readers will be as much pleased with this I
letter as we have been. It docs much credit both to the head and
the heart of tho writer, as well as to those of his amiable family.]
We can as* lire the most critical of our readers that it is a genuine *
production, and not go 1 up for the sake of puffing the P. E. — a
thing of which wc bare been most unjustly accused. We have not
the most remote idea of the author or of his locality ; but the sub-

AX5WERS TO CORRESPONDENTS.

r* IscEsicno Civil : Try XeebiU's Lard Surveying or old Crofccsv—
ELTTf as stiruM apply to the minister or ccrala of kfa> pavrwh.

T.H. (Workington must ap?lr ax tbe HermW$ otsce ; we eac't assist
hia.— a Trro (DarLagtoa : Tet.— Klxmcsta-T SrweastJe} an*t loos,
nsore narrowly at our later natter*.

Or* Sense arssa 'Lteehvue; will find It necessary to boy blank books
fc*r bookkeeping, deaf. as be says, aad rule them himself.

C* LTCDIA5T FaA3C{Ai« 'Gwern*-*; : Thesectiiejs referred to ia the
Trent* were omitted as ose»esay— E. WncaaaT (Bristol) aad J. E- S. A.:
Tlwir kind s fjestioo* will be ke;.t la view,— ft. M. H.: Vol*, i.. u^aad
iiL of the P. E. are bound separately, and the cheapest saay be had for
lt.6d.earb.

II. Gcr (M orslej) : His M Remarks on tbe Study of Grammar"* are very
well written. Let aim persevere, and ae will greatly improve— J. P.
(Sbepwykc; : We ■ bould be sery g lad to oblige hiaa. bat the haws be wisbea
to be Inserted are an advertisement.— J. Hall f Hjd*} : See Errata, p. 164.
*' When two volumes of pore bydi o*en fas are mixed with one volume of
pare oxyren ga». and the mixture inflamed in a proper apparatns by tbe
eltetrie tparfc, tbe gates tota'ly di*ip r <ear, and tbe interior of tbe vees*-! a
covered wttb drops of pure water, equal in weight to that of the gases con-
sumed.*'— Branded Chemistry.

8. Clasb ' Asbtoo-ander-Ljnel . His remarks on tbe asymptotie paradox
arereryeaeilleo% and we would Insert them if we had room— W. Vfaao
(Stepney} and W. B. HuDSox (Lincoln; : The questions are twrv old, and
not well pot.— Nat i oo (Newton; will be anj«ered — D. Jaans (Glasgow) :
Beceired.— B. T. S. O. (Brcmley) »booid study EneUah before Book*
keeping.

Y. T. B. P. (Liverpool] : We hare made no errors in tie Map of France;
for we consider tbe Chief roams as those which bare the largest population,
and not those nbieh are appointed to by any government whatever ! !— Olo
Boa {Qoeenabead} is too technical far as.

Johw CrxaiaoHAM (Lirerpool} : In oer lesnm on tbe impressions of
rain-drops oo the surface of sandstone, we ascribed the discovery of these
phenomena to Dr. Buckland. Mr. Cnnningbam has >bown to o« that it was
ho who first observed these impressions, and that tt was he wbo first called
Dr. Bueklan<Ts attention to them, lie does us the justice to say that we
robbed him of this honour " unintentionally." We are, therefore, happy
in baring this opportunity of correcting our error, aad of giving to him
the palm which be baa so well deserved.

Kneici L. Fiixira (9tamford-street) : Study Italian and EngKsh
together, one hour an evening, and you will get on. — J. Roaias should study
our lessons in Penmanship and English Grammar, and his difficulties will
disappear.

L. FsawawDZX. (Oldham) wants to know our opinion of an exceedingly
had sentence in English, and whether there be any treatises on woollen
cloth and on ventriloquism!!— J. B. (Manchester): You are learning
tbe very system that tbe American minister recommends, vis., Ollen-
dorff.

Jambs Bcsskll (44, Meadowside, Dundee) very kindly offers to give
assistance gratis to the students of the Pofolab Eduoatob who reside
iu his neighbourhood, in Ousel?* Arithmetic, Algebra, and Euclid, between
the hours of 5 and 7 r.M , or 9 and 10 T M . We feel assured that many of
our readeis in Dundee will most gladly avail themselves of this generous
offer.

M as. Slipslop (Aberfeidyl : We thank her for the loan or her spectacles,
the j ar«: better than ours; uheti.er the printer's pair or ours were in fault,
it is i.ow too late to dctenum-; but we are glad to make the necessary
corrrc\ion. The error has arisen thus : there are two Xakor* In Genesis
zi , * !z., one in v. 22 and 23, and another in v. 26. 27, and 29 ; the one was
the f .tuer of Terah, and the other bis son ; the former has been, by some
unaccountable mistake, omitted in our table, p. 3, toI. i.

E. BraT (Sbepton Mallet) : Yes.— Rob est Humblb (Hartlepool) : The
laws of the resistance of the air to falling bodies will hereafter be con-
sidered. The tule for finding the height of a tower, as usually given, is, of
course, not strictly correct.

G. Asfinall (Liverpool): Apply to Mr. Bell, 13, South Charlotte-street,
Charlotte-square, Edinburgh.— Tub Pencil (Paddiogton): We are just
thinking ol the students of the pencil, and mean to do something soon.—
J. B. M. (Glasgow) : See col. 1. p. 376, vol. iii.— AmatorScibntlb (Dundee):
We prefer Bell's system to Pitman's.— II. Hales (8outhwark): We doubt
muen whether he would succeed in the business of making cheap apparatus
and rolling it himself, lie had better apply to our friend Mr. J. Griffin, of
Finsbury-square, and see what can be done there.

Isaac Newton (Sheffield) : Our friend with this glorious nom de guem
has not so sustained the credit of the name aa to admit of the insertion of
his solution of the boy and apple question 11— W. £. Williams (Centre-
bach) : The lessons in English are closed for the present; as soon as possible
Elocution will be taken up.— G. 8. (Cupar) : We know of no snch book as a
treatise on Greek pronunciation.— W. Wallis (St. Ninian's): air. Bell did
not say that his *' Vocabulary of 8yllabic Logogram*" was to be inserted in
the P. E. ; you have, therefore, no right to expect them in our pages.
Sereral correspondents have committed this error.

Erratum.

Vol. iv., p. 155, col 1, line 10 fiom bottcin, for insolubility read
solubility.

NATURAL PHILOSOPHY.

241

ON PHYSICS OR NATURAL PHILOSOPHY,

No. XVII.

{Continued from page 286.)

PNEUMATICS.

GASES AND THE ATMOSPHERE.

Physical Nature of Gases. — Gases or aeriform fluids are bodies:
whose particles possess perfect mobility, and which are in a
constant state of repulsion called expansibility, tension, or elastic
foroe\ in conformity with the latter of these appellations,
gases are frequently denominated elastic fluids.

The elastic fluids are divided into two classes, 1st, the per-
manent gome* or those which are properly called gases ; and
2nd, non-permanent gam, or vapours. The former are those
which maintain their aeriform state under any pressure or
diminution of temperature, aa oxygen, hydrogen, nitrogen,
binoxide of nitrogen or nitric oxide, and carbonic oxide. The
non-permanent gases, on the contrary, easily pass into the
liquid state, either by strong pressure or by lowering the
temperature. This distinction, however, is not rigorously
correct, for a great number of gases, which were considered
permanent, have been liquefied by Faraday and others, and it
must be admitted that those which have not hitherto been
liquefied, would be to if they were subjected to sufficient pros-
sure, or lowering of temperature. Gas, therefore, is the name {
applied to bodies which, under ordinary pressures and tern-
peratures, exist only in the aeriform state ; whilst vapour is
the term applied to the aeriform state which bodies take
under the application of heat, bodies which, like water, alco-
hol and ether,- exist in a liquid state under ordinary pressures
and temperatures.

In chemistry, the gases at present known are 14 in number,
of which 4 are simple, vis. oxygen, hydrogen, nitrogen, and
chlorine; 7 are found in natural productions, vis. oxygen,
nitrogen, carbonic acid, protocarburetted hydrogen ( marsh gas)
and bicarburetted hydrogen (oleflant gas), ammonia and sul-
phurous add. All the other gases are only obtained by
chemical processes.

Expansive Force of Gases.— The expansive force of gases, that
is, their tendency always to assume a greater volume, is proved
by the following experiment. Place under the receiver of an
sir-pump a moistened bladder furnished with a step-cock, and
containing a quantity of air. At first, there is an equilibrium
between the elastic force of the air in the receiver and that of
the air enclosed in the bladder ; but aa soon as the exhaustion
of the receiver commences, the pressure on the bladder is
diminished, and it swells or expands, as the process of
exhaustion advances, just as if it were inflated by the addition
of a greater quantity of air ; this expansion proves that the air
which it contains possesses an elastic force; see fig. 62.

Fig. 63.

When the exterior air is re-admitted into the receiver by means
of the proper stop-cock, the bladder is again compressed by it,
that is, reduced to its former dimensions, the equilibrium being
restored. In the same manner, we may easily prove the fact
of the expansive force of all the gases.

In consequence of its expansive force, it seems as if any gas
contained in an open vessel would make its instantaneous
escape. Such indeed is the case, if the vessel be placed in a
vacuum ; but, in ordinary circumstances, the pressure of the
exterior air is opposed to the issue of a gas from the vessel. It
can be proved indeed, by experiment, that an equilibrium can
be made with the expansive force of any gas, only by the
counteracting pressure of a gas of the same nature as itself.
Thus, the pressure of the sir cannot make an equilibrium with
the expansive force of hydrogen or carbonic acid. These gases,
however, do not escape into the air from the vessels containing
them, as they would in a vacuum; but the interior and
exterior fluids are rapidly mixed together, as we shall see in
the sequel* It will then be shown that the elastic force of
gases is always equal and contrary to the pressure which they
support, and that it increases with their temperature.

Process of collecting Gases. — A great many gases being colour-
less, inodorous and insipid, do not fall immediately under the
cognisance of the senses, like solids and liquids ; but they
become apparent by the processes employed in collecting them.
Suppose, for example, that it was required to get hydrogen, a
gas which forms one of the elements of water. * We take a double
mouthed bottle b, fig. 63, furnished with two tubes, and intro-

-'— v J

duce into it, a certain quantity of water and of granulated
sine ; one of the tubes, which is upright, is furnished with a
funnel by which the sulphuric acid is introduced, necessary to
the chemical reaction which produces the hydrogen. The
other tube, which is bent, conducts the gas as it is produced,
into a bell-shaped glass or inverted bottle a, filled with water
and placed in a vessel full of the same liquid.

Fig. W.

VM, XV.

Water Is composed of two gases, oxygen and hydrogen.

241

TBS. POPULAR EDUCATOR.

By the mutual action of the zinc sod the sa Jp e wri c acid
the water in the bottle it decomposed ; its oxygen it saute
with the xhic, sod the sulphate of zinc it prodaeed, whic
rem*ins in solution; its hydrogen it now art at liberty, a*
passes, in consequence o/ ttt elastic force, into the bell-i h s pc i
tl«M a, where it ii** to the top on tenant of ha lightness, or it
having lets specific gravity than water. The other gases si
collected in a similar manner, bat under die influence of ver
different chemical reactions.

Trmufirrm* *f Q*tm f*m mu tfass/ <• eaet**r.--Ia the aim
way at liquids are treated, so gases cam be poajtdfrem one vcsst

and arte with, equal farce m all dnectanaa. Astotke
sasaj from the accimi of giasity. b is irwalmad
exactly according to the laws of the [T— n it* tiqshli inaaiTi
explained; that ia, that it icereaaea pro p o r ti onally to the
density and to the depth: that it is eaeecant an the aaaae
horizontal stratam ; and that h is independent of the form
which the gaseous mats sesames. Moreover, for voiamee of
gas of small riranrwsinmr, thai preaaare is ao mule that the coat-
of its amount may be, in ordinary cases, entirely

into another. This experiment it easily made with carboni
acid, which ia mach denser than commam air. That, we ill
beD-shaped glaat with thk pa, by folleeting it ia the manne
above mentioned; them, taking a eeeond vessel of the aaaa
kind and size and fall of air, we poor the contents of the for*
mar into the latter, as shown in fig. 64, holding them lor soma
time ia a fixed position. In consequence of ita excess o
density, the carbonic acid de s cends slowly from the ▼easel s
tato the vessel a, from which it drives out the air, so that m
soon as the ▼easel • is fall of esrboaie acid, the vessel si ia fall
of sir. The proof of this rests on the property which carboni*
acid possesses of extinguishing lighted bodies. For, before thai
experiment, a lighted taper burns in the ▼easel a and is extin-
guished in the vessel m ; whilst after the experiment the con-
trary ia the case.

Weifhtof G—€m.— From their extreme fioidity, and espeeiilry
their expansibility, gases would teem not to be subject to thai
laws of gravity ; bat these subtle fluids obey this force ai I
well at solids and liquids, fn order' to prove this, suspend I
under the scale of a very sensible balance, a glass globe capable I
of holding about a gallon of air, and furnished with an air* |
tight stop-cock, see fig. 65. First weigh this globe full of air ;

Fif . 65.

then, after having created a vacuum in it by means of the air- I
pump, weigh it again, and it will be found that the weight of I
it the fteond time will be some grains * less than it was the first I
time, showing that this weight of air has been withdrawn from I
the glass globe.

By the preceding process, it has been found that 61 cubic I
inches of pure air at the temperature of 32° Fahrenheit, and I
under an atmospheric pressure of 30 inches in the barometer, I
weighs 20 grains, the same quantity of hydrogen weighs 1*39 |
grains, or about 14$ times less than air; and the same quantity I
of hydriodic gas, which is the densest of the gases, weighs 89 I
grains.

The Pressure of Oases — Gases produce two kinds of pressure, I
one on the particles of which they are composed, and another I
on the sides of the vessels which contain them ; the one pro- 1
ceeds from their elastic force, and the other from their weight.
The pressure which arises from their elastic force is trans-
mitted with the same intensity to all points of the mass of the
fluid and the sides of the containing vessel ; for the repulsive
force which exists between the particles is the same at all

• About se grains, if the tea s p s ra t a rs of the air bs taken at thai of
ths maximum dsajftty of water, ap4 the exhaustion be compistc.

THK ATMOSPHSU.

Ci s y ss iTww fftid < d /a majts re .---The i
I to that great ocean of air which surrounds oar globe* saai
I carried alonx with it, in its dairy and asmeal revolution*. The
air was considered by the ancients as one of the fear elements
I of which all things cnnsistfd, Modern eacasmtrv. has shown
I that it is a mixture of nitrogen sad oxyg e n , eosHarning in 100
cubic inches of the mixture, 79^0 cubic inches of n itro g en and
20-80 cubic inches of oxygen. Moreover, in 100 eances of air,
there are 76*99 ounces of nitrogen and £3-01 ounces of oxygen.
The atmosphere also co nta i ns a quantity of the vapoar of water
which varies with the te mperatur e of the sir, the seasons, the
■»1ti»»— t and the direction of die winds. Lastly, the air con*
taint of carbonic acid in a given volume, at a mean, oaly about a
two-thousandth part. The carbonic acid it produc ed bj the
respiration of animate, «»ri the combustion — d dw wwnaitian nf
organic substances. According to the estimate of M. Bous-
nngauh, there are nearly three millions of cubic metres (about
060 millions of Imperial gallons) of c arb o ni c add produced at
Paris, by these pioccases , in twenty-fear hoars ; the part pro-
duced by animal respiration being sboat one-ninth of the
whole.

Notwithstanding the continual production of carbonic acid
it the surface of the globe, the composition of the atmosphere
does not appear to be altered by it : the reason is, that in the
process of vegetation, the green parts of the vegetables decom-
pose the carbonic acid under the influence of the solar light,
MrWilatrrty the carbon and giving back to the atmosphere the
oxygen which is continually abstracted from it by the respira-
tion of ywiinal» and by combustion.

Air being heavy, if we conceive the atmosphere to be
divided into horisontal strata, it is plain that the superior
strata will press on those below them, by their weight, and the
result wUl be the compression and condensation of the inferior
strata. As the pressure on any stratum will evidently
diminish as the number of superincumbent strata diminishes,
the sir is evidently rarified in proportion to its distance from
he surface of the globe.

In consequence of the expansive force of the sir, it would
teem that the particles of ths atmospheric sir should extend
indefinitely into the planetary spaces. But by the very effect
of dilatation, the expansive force of the air decreases more and
more ; moreover, it is lessened by the low temperature of the
higher regions of the atmosphere, so that there is a point where
«n equilibrium is established between the expansive force of
the particles of the air, and the action of grarity which
attracts them to the centre of the earth ; hence it is concluded
that there is a limit to the extent of the atmosphere.

From the weight of the atmosphere, its decrease in density,
gnd the observation of crepuscular (twilight) phenomena, its
altitude is estimated at about 40 miles from the surface;
beyond this limit, the air ia extremely rarified ; and beyond
the altitude of about 50 miles, it is considered that there is an
absolute vacuum. Since we have already stated that the air
It a heavy body, and given the aotual weight of a certain
quantity near the surface, it St evident that the whole of the
atmosphere must act upon, the surface with a very considerable
pressure. The aotual exittcjfcfe of this pressure is proved by
the following experiments.

Tm Bladder GUtst.— Take • thort glass cvtinder about 4
inches in diameter, ground snaooth at one end, and furnished
aith a bottle-lip at the other ; aver dais and fasten a piece
f bladder, so as to be perfeodf air-tight ; well grease the
ground end of the cylinder, and place it firmly on the receiver
plate of an air-pump, so that no air may be admissible at the

N4TUEAL PHILOSOP??.

248

edges next the plate, fig. 66. Rapidly exhaust the i
the cylinder < end ee soon as 70a commence making a 1
the Madder at the top of the cylinder will first sin* ui

1 air from
i vacuum,
> top of the cylinder will first link under the
etmeepherie pressure, and then burst with a loud noise, which
is occasioned by the sudden re-admission of the air.

Fig. to.

li, Instead of the piece of bladder fattened to the top of the
eytiader, there he placed on it a square piece of thin glass
saade sir-tight, by having this end of the cylinder also ground
smooth and well greased, you will find that on the application
of the air-pump to exhaust the cylinder, the glass will first
bend under the pressure of the external atmosphere, and then
break into pieces with a loud crasb.

Magdeburg frmitpheres.— The blrdder»glass appears only to
prove the existence of tbe atmosphere pressure vertically
downwards. By means of the Magdeburg hemispheres so (named
from the town where they were first invented), it is proved
that this pressure acts in all directions. This apparatus is
composed of two hollow brass hemispheres, between 4 and 6
inches in diameter, fig. 67, furnished with broad edges ground

Fig. 67.

smooth and made to fit each other exactly, so that when well
greased they are completely air-tight. These hemispheres sre
each fitted with a strong ring or handle, and one of them is
furnished with a tube which may be screwed on the plate of
the air-pump* and a stop-cock to prevent the re-admission of
the sir. In making the experiment, first place the hemispheres
together with their edges well greased, and in close contact ;
fsrev tip apparatus to the plate of the air-pump, exhaust the
fjr from the sphere as completely as possible, turn the stop-
cockto exclude the air, and unscrew the apparatus from the

pump, screw on the handle at the end of it, and try to pull the
hemispheres asunder by the two handles, see fig. 68. This
attempt wjll fully convince you of the force with which the

Fig;. 88.

a t m os ph ere presses the hemispheres together ; for it will take
a force of about 500 lbs. toseparate them, supposing their diame-
ter to be 5 inches, and that the exhaustion of the air were com-
plete. This may be proved by. fastening the one handle to a
beam, suspending a scale to the other handle, and loading it
with weights until the hemispheres be separated. In the
original experiment performed by Otto Von Guericke at Made-
burg, in 1560, there were from 14 to 30 horses harnessed to
the hemispheres, which were two feet in diameter, without
effecting a separation ; when more horses were added, the
hemispheres parted with a loud report. If after the attempt
to separate the hemispheres by a force less than sufficient to
separate them, the stop-cock be turned so as to re-admit the
air into the apparatus, they can then be separated with the
greatest ease, because the equilibrium of pressure between tho
external and the internal air has been restored.

MEASURE OF ATMOSPHERIC PRESSURE.
' The Torricellian Experiment. — The preceding experiments
prove the existence of atmospheric pressure, but do not
acquaint us with its amount. The following experiment made
for the first time in 1643. by Torricelli, a disciple of Galileo,
gives the exact measure of the weight of the atmosphere, or
of its pressure on every square inch of surface at the bottom of a
column of this size, extending to to the top of the atmosphere.
Take a glass tube od, fig. 69, not less than 33 or 34 inches

Fig. 69.

long, closed at one end, open at the other, and of any conve-
nient diameter from ± of an inch to t an inch. Having placed

344

THE POPULAR EDUCATOR.

this tube in the vertical position with the doted end down-
wards, fill it completely with mercury ; then, doting the open
end o with the finger or thumb, invert the tube and immerse
this end in a cup nearly full of mercury. Withdrawing then
the finger from the tube at b, and supporting it with the other
hand at ▲, the column of mercury in the tube will sink two or
three inches, and then become stationary at a height a b of
about 30 inehes above the mercury in the cup, when the
experiment is performed at the levd of the sea, and during a
mean state of the atmosphere.

In order to explain the nature of this experiment, we observe,
that as the pressure of the atmosphere acts with great regu-
larity on the superficial stratum of liquids placed in an open
vessel, it does not in general disturb the horixontality of such
surfaces. But if by any means a limited portion of this stra-
tum be protected from the atmospheric pressure, the equili-
brium will be destroyed, and the liquid will rise up to fill the
vacuum produced above it, to a determinate height depending
on the nature of the liquid. This is indeed what takes place
when we immerse the one extremity of a tube in water, and
withdraw the air by suction at the other extremity. By this
process, we only diminish the pressure within the tube ; but
in the Torricellian experiment the pressure of the air is com-
pletely removed, and there is a complete vacuum at the top of it
when inverted. We have seen, that on the moment of the
inverted end becoming free, the mercury in the tube descends to
a level about 30 inches above that of the mercury in the open
cup ; this levd is always the same whatever be the length of
the tube, its shape, or its inclination.

In this experiment the elevated column in the interior of the
tube presses on the part of the cup on which it stands, with a
force which replaces that of the atmosphere; but the latter still
continues to press with the same force on the rest of the sur-
face of the mercury in the cup ; and the particles of the liquid,
yielding to this pressure, would have been forced up the tube
to the same height, supposing that it had been a perfect vacuum,
In fig. 70, where a section of the tube ang

Fiy. 70.

on its immersion.

It..

cup is shown, it will be observed, that when the mercurial
column acquires its stationary position, any horixontal stratum
x m, taken in the cup of mercury, supports at all points the
same pressure ; this pressure is composed of the weight of the
part k, to which must be added either the atmospheric pressure
without the tube, or the pressure of the elevated column within
the tube, these two pressures being equal, and capable of being
measured by each other. Hence it is that the vertical height
o p of a column of mercury is taken for the measure of the
pressure of the atmosphere.

If we perform the same experiment with any other liquid
instead of mercury, we must have recourse to much longer
tubes, in order to produce the vacuum at the top of the column.
The heights to which different liquids rise, in such experiments,

are inversely proportional to their densities. On the other
hand, if the weight of the atmosphere increases or diminishes
from any natural cause, in any given place, it is evident that
the length of the mercurial column will increase or decrease
accordingly.

Pascal' $ Experiments.— The celebrated Pascal, wishing soon
after, to prove for himself that the force which supported the
mercury in the tube of Torricelli was really the pressure of the
atmosphere, had recourse to the two following experiments,
which placed the fact beyond a doubt. First, foreseeing that
the column of mercury ought to descend in the tube in propor-
tion as it was raised in the atmosphere, because that then its
pressure would be diminished, he requested a relation living in
the province of Auvergne, in France, to repeat, on the moun-
tain called Puy-de-Dome (4,846 feet high) the experiment of
Torricelli. Here the column of mercury was diminished in
height by a quantity which was between three and four inches
in length ; this proved that it was really the weight of the at-
mosphere which sustained the mercury in the tube ; because,
as this weight decreased, so did the column of mercury.
Secondly, Pascal repeated the experiment of Torricelli, at
Rouen, in 1646, with another liquid instead of mercury. He
took a tube of about fifiy feet long, closed at one end and
open at the other ; he filled it with water, and inverting it,
placed it in a reservoir full of water; he then observed that the
water in the tube sunk to the level of about thirty-four feet
above the level of the reservoir. Now the altitude of the
column of water being about 13*6 times that of the column of
mercury, and the density of mercury being about 13'6 times
that of water, the weight of the column of water in this ex-
periment is equal to the weight of the column of mercury in
the Torricellian experiment ; hence it is justly inferred again,
that it is the pressure of the atmosphere which equally sup-
ports both of the liquid columns.

LESSONS IN GREEK.— No. XX.
By John R. Beard, D.D.

THE NUMERAL ADVERBS

Dbnote how many times a number is to be taken, as " six
times six make thirty-six;" here six timet is a numeral
adverb ; thus tic. signifies twice, t(*q three time*. The termi-
nation of the numeral adverbs is in general «c (weif, rone),
whioh is annexed to a cardinal, as rf<r<rapajrif, l&uuc,
Uarovraxic.

TUB MUMSBAL ADVERBS.

1 airaK

19 fweacacdeffactc

2 Sic

20 tucoaaicic.

3 rpic

30 rpta*ovrajrt£

4 TITpaKlQ .

40 rirrafMucovTaKic or

6 9r€vrajc<£

rtevap

6 Igactf

50 iriVTrjKovraKic

7 iirrawc

00 i£T)KovraKi£

8 OKTCUCIQ

70 tfiSofirjKevroKig

9 twiciKic., tvvatcis

80 oySorjKovraKic

10 dtxaicig

90 ivivrjKovraKig

11 IvSlKClKlC

100 tKaTOVTCLKlC

12 dutdtKOKlC.

200 ttaKoaiaictc.

13 rpt£jcat£fa*Ki£

800 rpcacoffuunc

14 rfrrap€gjcat££jrajci£orrfe'<raj

>. 1000 x^mucic

15 irtvrtKaidtKaKic

2000 *c£xi\tajec£

16 IKKOtiiKeUUQ

10,000 pvpttuue.

17 iirroKcu&iKcuue.

20,000 iicfivpiaxic

18 OKTUKCU&IKO.KIC.

Recapitulatory Exercises from the Classics.

1 . Avaxaptrig Kpttrrov fXcycv, iva fiXov t %*tv iroXXov a$tov,
$1 xoXAot/c fMfoVvef aliovQ. 2. Am»v, 6 wp&rpvrtpo£ % tic r*t
AifSvrjc tKtpatrt fuyaXffv dvvapiv tic ScieeXiav, *-e£«*v /ivputidg

LESSONS IN GREEK.

94*

•wrf , imrctc St IZaKtcx&iovc, tXtfavrac. St kZnicovra. 8. Tovc
Snpac laropovat fit\pt rputKoattov Znv truv, Kat rove. XaXSatovc
vwtp ra Uarov tTtj fttovv Xoyoc (eon). 4. Apyav0wto£,
6 Taprnvatwv fiaatXtvc, irtvrnKovra cat Uarov try fiuaaat
Xcyirac 5. 'O IlXaruv trtXtvrrjvt rtp Tcpvrtp rnc oySonc rat
Uaroarng OXvfiiria&oc, /3iot/g iroc iv xpoc toiq oySonKOvra. 6.
Anfinrptoc rtc. ccm ry Nepwi* <rv fitv aveiXtig tfiot rov Bavarov,
vol St "h +V91Q. 7. XxoXaorucoc arroputv, ra ptfSXta aurot;
Hrtirpaoxt, cm ypafwv wpoc. rov rartpa tXsyt, wyxaipt rffitv,
wartp, nStf yap rf/utg ra /3t/3Xta rptftt. 8. Avaxapot? 6
Smi^ifc <p*ff*i|0c<f viro rtyoc, ri ioti iroXtfitov avQpiairotc. ;
avroi, tf"jy, iavroig, 9. SxoXaoruroc ouctav 9rttfX*>v, X*0ov air'
avnic «C Sttyfia TTtpttjtpt. 10. Kpinpg «v, ait ravra wtpi rwv
avruv ytyvuoKt, ovStv rpoc. %apiv trouav. 11. ^vxnc twtfitXov
rife otavt\>v. 12. BovXov aptoxttv warn. 13. JTavrwv fiaXiara
aavrov atoyyvov. 14. 'Paarov diravrwv coriv avrov tKairarav.
16, Q ayaOt, fin ayvoti atavrov. 16. IfiKparnQ awrorofiov
fisv viae, tyv. wflofrraroc £f. Qvtoq ttwt irpoc. rtva rwv
f tryctutv* ro fit v tfiov ytvog air' tpov apxtrat, ro St aov tv aot
wavtrat. 17. OaXijc tpwrn9tic, n KOtvorarov; airtKptvaro
tkwi? icac yap o*c aX^o finStv, avroc iraptartv. 18. Olov ro
a0oc ijcao-rov *rotovroc b fitog. 19. topirai 6 N«Xoc awo rutv
Ai9iOTiK*tv bpwv /*iXP* ri 7C «C BaXaooav tK$oXnc araSta
fivpia cat AtoxiXta. 20. Ta flic frivrt StKa tortv. 21. Evriv-
9tv tUXawti araBfiovc. Svo, irapoaayyaQ wtvrt, eirt rov "Sapov
worapov, ov ip tvpog rpia w\t9pa.

Vocabulary.

1. agio?, a, ov, worth, worthy ; xoXX. a$. of grtat value.

2. Avvwv, woe, o, Hanno, the Carthaginian general, twt-
pafft (from ir<pac> beyond), transported, ' carried over; rciC^v
(from irf£of)t °/ foot-soldier* ; lirw«c (l7nr«vc) horsemen,
cavalry.

3. £t}pac (Sifp, off) ^ 5*r«, <i» /«o!ian p«op2« «?Ao produced
tUk ; £i|v (ii»ftn. of Caw- J live), to live ; XaXSaiovt, the Chal-
deans ; ra isarov try literally, above the hundred y ear t ; so with
either number the article is" used when a whole is contem-
plated in construing into English you must drop the article
m such cases : J3iovv (from /3io« t I live, /3u>c, life), to live.

4. fiutacu, to have, lived; Xtytrai, is said.

5. trtXtvrtpt (from r«Xoc, an end), came to an end, died;
OXvfiirtaQ, aioc, if, an Olympiad, a period of Jive years; the
Greeks reckoned time by Olympiads as we date from the
birth of Christ, a.d. ; fiiovq, having lived; irog lv, &c, one
year to eighty, that is 81 years.

6. ttTt, said ; Ncpftw, woq, o, the Roman emperor Nero ;
axuXtig (from air«Xf«, I threaten), threatenest.

7. JZaoXaartKoe, ov, 6, an idler, a witling ; airopiav, being in
straights ; twiwpaox 1 * 8oid '

8. tpmnfluQ (tpwraw, I ask), being asked; tfn, said, an-

9. ttiyua, aroc, ro, a specimen ; irtpu+tpt (irtpi and ftpw)
carried about,

10. yirvteaKt, pronounce the same judgment; rrpoq xapiv
wowv, doing nothing for favour.

12. opsmsv, to please, with (try) to please all.

13. atoyvvov (aioyyvopai), reverence.

14. tlawarav, to deceive, cheat.
16, ayvoti, be>thou ignorant.

16. oxvrorojioQ, ov, 6, a leather cutter, from oievroc, ovg, ro,
a hide, leather; tvytvns, well-born; apxtr. air. tpov, literally
begins from me, that is, with me ; iravtrai, comes to an end.

17. airtxptvaro (airo and icpcvui), answered; tXxic, hope;
maiyap,for.

19. ffptrai, is carried, flows ; acpoXn, ijc» V, a falling out of;
a*xpt, up to, down to, until.
21. tgfXovyft, marches.

Extracts from the Nbw Tsstaxbnt.

1. Kurt it o lijaovc, Uotnaart rovg avOptairovg aimrtativ.
Hv is X°P r °C iroXwc tv rtp roirtp. Avtmoov ovv ol aviptq rov
apiOfAov a»ae( -frtvraKi^xiXioi. (John vi. 10). 2. IloXXot St ruv
aieovaavrutv rov Xoyov tviortvoav' tcai tytvnOn 6 apiQjioQ ruiv
avipinv Cxrti x<Xta^<c irtvrt. (Acts iv. i). 3. Kat udov cat
nicovaa (putvnv ayytXtav iroXXuv KvicXtp rov Qpovov cat rwv
Z<xhdv xat rarv wptafivrtpwv jcac nv 6 apiOpoc avrutv uvpiaBtc.
uvpiafav Kai xiXiadec x*XtacW, Xtyovrtg ^wvy fityaXy, Agtov
tart ro apvtov ro tafayofttvov Xafitiv rnv Swapiv cat irXovrov
xat aofiav rat toxw icai rt/inv Kat dofav vat tvXoytav, (Rev.
Y. 11, 12). 4. *0 t\utv vow i//T/^t<rar<«> rov aptOftov rovQnptav*
aptOfioQ yap avOputirov tan, cat 6 aptdfio^ avrov (sc. etrrtv)
X^sr. (Rev. xiii. 18). 5. 'O oe Itaawnc tittKtaXvtv avrov,
Xtyutv, Eyw \pt\.av «x w vtto aov fiairriaBnvat, Kat ov tpxy ™oq
fit. (Matt, iii. 14). 6. AXXjjXwj/ ra fiapn fiaoraZtrt. mi
ovrutQ avawXiiptaaart rov vofiov rov Xptarov. (Gal. vi. 2). J.
H yap Kavxnvic rffiutv avrn tart, ro fiaprvptov rnc ovvttSnotwQ
ripuv, brt tv aTrXorrjri Kat ttXucpivaa Otov, ovk tv aoftq oaprtrp
aXX' iv X a f Hr * ©*ow, avtorpa^fifuv tv rtp Koaptp, irtptaooTtpuQ St
wpoc vpac. (2 Cor. i, 12). 8. Et rig ovv irapaKXnotg tv Xptanp,
et rt TrapafivQiov ayairng, it rig Kotvutvta wvtvfiarog, u rtva
awXayxya Kat oucrptpot, irXiipuaart fiov rnv \apav, tva ro
avro ipovnrt, rnv avrnv ayairnv t\ovrtQ, av^vxot, ro iv
tpovowrtc, fiifStv Kara tptOtiav n KtvoSoitav, aXXa ry rairtt-
vofpoowy aXXqXovf qyovfitvot virtptxovrag iavrwv, fin ra
lavrtav Uaarog oKOTCowrtc, aXXa Kat ra irtpvv UaaroQ. (Phi-
lippians ii. 1 — 4).

VOCABULARY.

1. Iqoovc, Jesus ; irotnoart (wouut, I make, do), make, cause to;
avairtativ (irtima, I fall), to sit down, x°P ro C» ov » °* 9 ra4S \
avtirtaov, they sat down ; rov aptB, as to number, that is, in
number, or to the number ; watt, about.

2. rutvoKovaav. (acoi/tu, I hear), of those who heard; trctartv
aav (none, faith), believed; tytvnOn (ytvofiat, I become), was,
rose to.

3. tiSov (tiSoc, appearance, shape), I saw ; nxovaa, J heard;
apvtov, ov, ro, lamb ; tofayoutvov (afaytov, a victim).

4. 'O t\u)v vow, let him who has mind; yj/nftaaria tynfoe,
a bean ; the Greeks reckoned with beans, as the Latins did
with pebbles, calculi, whence calculate), calculate.

5. SttKiaXvt (coiXvtii, J hinder), tried to hinder; pairTtoGnvai,
to be baptized; j&airrta, I dip ; fpx*?» comett thou ?

6. paoraZtrt (/3aora£o>, J carry), bear ; ovrug, thus; avairXn.
(ava, up, trXpobt, IfUl), fill up, fulfil.

7. KavxnatQ, tug, 17, boasting ; avvttSijatg, tut£, */, conscience ;
% avXornc, nroc, if, simplicity ; ttXtxptvtia, aQ, 1), sincerity ;
oapKiKog (aapK, fiesh), fleshly ; avtorpaf. we have behaved (con-
ducted*) ourselves, we have acted; Trtptaoortpvc (trtpt, denoting
abundance), more exceedingly.

8. *-apacXi?*t£, «a»c, if. exhortation, comfort; irapdfivQtov, ov,
ro, solace, soothing ; xotvwvta, ac, >), community ; irvtvfia, aroc.,
spirit; awXayxyov, ov, ro, bowels; oucrptfioc, ov, 0, pity;
TrXnpuaart (wXnpov, IfiU), fulfil; typtvnrt (^01 vie, the mind),
that ye desire, aim at, love ; ovfityvx 01 (^"Xl* *"* ^ouT), being of
the same soul, of one soul; tptOtta, ac., tf, strife; KtvoSoZta,
Octvoc, empty), vainglory 1 rairttve+poavvy, tjc, rj (ravrtivoc,
humble), lowliness of mind ; ifyovfitvot, thinking, considering ;
virtptxttv, to be superior ; oKoirowrtQ (acoirccv, to look, hence
tmoKoirttv, to overlook, whence our word bishop).

Remarks.

The pronouns are among the oldest words in every language.
Consequently, if in two languages the pronouns are found to
hare strong marks of resemblance, we may safely conclude
that those two languages are akin to each other. Such marks
of resemblance may be found by comparing the Greek and the

24*

THE POPULAR ftDUCAfOft.

English personal pronouns together. Thus the Greek ry»,
through the Latin sfo 9 is clearly the English / (also the Ger-
man ich and the French je). Look at the Greek accusative /u,
the Latin me, and the English me. Again compare the Greek
w, the Latin tu, and the English thou ; also tne accusative*,
namely <r«, U> the*. The i (the i aspirated and so made he) is
i/bviously our A*.

Similar remarks mar be made with regard to the numerals.
Obviously in structure, as well as in individual numbers, the
Greek numeral system is the same as our own.

The student, if he has well attended to these lessons, may
now rejoice in having made some considerable progress ; and
Uie progress he has made he may in a measure estimate by the
comparative ease with which he has just read passages from
the Greek New Testament

General View of what has been set forth.

Noun Substantive used to name objects, as, rrparumfc,
soldier (a soldier).

Artich used to determine nouns, as 6 vrparuerqc,* the soldier.

'of quality ayaOoc. aroarimrncy good soldier,

of number iuca orparwratf ten soldiers,

of order Sikcitov ray pa, tenth legion,

ovroc 6 avOowiro^, this man.

(Cftvoc 6 avvputroc, that man.

demonstrative 6 avroc. a?0pwwoc, the same man.

avroc 6 avOpwvoc the man hi ma elf.

avQpwxoi rtv«c some men.

interrogative rlc avGp*Tog, which man r

relative 6 apOovrroc. oc, the man who,

^possessive 6 ipoc. irarcp, my father.

Pronoun tyv, I ; <rv, thou ; ov, of himself*

LESSONS IN GERMAN.— No. LXXXL
I 108. Table of the Prepositions.

(1) Prepositions construed with (2) Prepositions construed with

THE GENITIVE.

THE

DATIVE.

Sitflatt, or

Dbcrtytfb,

»««,

Sto&ji,

ftatt,

%n%,

Safer,

ftufrtyilt,

Urn — nritten,

»«i

o*,

JDicffcit, or

Unfcrn,

£Binnen,

tifffcit*,

Ungcattytct,

Gntgegen,

$ammt,

$a\b, balktn, or

llnterljalb,

(Segenufcrr,

b]a{btr,

llnrocit,

©emftp,

eat,

Snuerfcatt*,

©ermittelfl, or

3cnfeir, or

mtttclft,

SKit,

®CH,

jenfcitl,

Serin i^e,

tfraft,

2Sa$ren*,

3ta($,

3a,

ydn^S,

ifficani,

fcaut

Sufolge.

92fc$ft,

3unrifeer.

(3) Prepositions construed with

(4) Prepositi

ons construed w

THE ACCUSATIVE.

THE DATIVE <

Da ACCUSATIVE.

£ur$,

tynt,

Sin,

llekr,

our,

Sontcr,

&uf,

Hitter,

tycytn, or

Urn,

Winter,

93or,

flcn,

Setter.

3n,

3»ifc$en,

S 100. Preposition* construed with the genitive.

Wc now jpve again the prepositions governing the several
rases respectively, with their proper definitions: subjoining,
also, some tew observations on such of them as seem to require
further explanation. And first, we mention those construed
with the genitive.

Safari, or ftatt
tEferfatt,

3>kff«t / or tfff»
fettf,

6*tben, or let-
ter,

3nner$alb,

Senfeit, or ien»

fen*,
Jtraft,

eaiff, (ate

gov. Dat)
Coat,

£wfc (also
gov. Dit)

without; oat-
aide,
on this aide.

* of.

within; inside,
on that side;

beyond,
by virtue of.
•iong.

according to.
above,
in spite of.

11m — Botes,
ttaecoipri,

UBtCtWUv,

Uaftra,

Uarottt,
JBernttfifl&or

ffetatige,

for the sake of!
notwtflrjtand
below; on
fewer
■ear; not Car

from,
near; not far

ftlMt.
by means of.

by dint Of.

£nfb(§e, (alto
gov. Da*)

on account of.
in

$ 111. PawoairiONs consteued with the dattvb.

after ; te>j «e~

«*ftr,

»ti,

JBtanca,

watfffaca,

fegexifer,
Centof,

SWit,

S 119.

out ; out of. 9ta$,
without; outside

of. 9*44*

by; near; with. Sbtfc

within. Do,

towards ; oppo- 6oswt,

site to. eat,

over against $on,

conformably 3a,

with,
with.

next; next to.
together with,
over; at
together with

jot

con*

trary.

P EXPOSITIONS OONSTKUEE WITH THE ACCUEATrVB.

through. eoattr, ****; without

fffir, for; the place of. list, about;

Qegen or gen towards. ffiker,
C$ne, without.

S 115. Prepositions conbt&oxd with
accusative.

THE DATIVE Oft

2ln,

on) at; neai

Ueber,

Otef; above.

*uf,

on ; upon.

Unter,

undet; among.

Winter,

behind.

»pr,

before.

3n,

in, or into.

3trifteit,

betwixt; be-

Slefcn,

beside.

fween.

% 116.

Observations.

These prepositions govern either the accusative or the dative;
but not without a difference of signification : for, when motion
towards, that is, motion from one point to another, is indicated,
the accusative is required : when, however, motion of rest «•
any given place or condition is signified, the dative is used;
thus, bet Stnabt tdnft in ken Qarten, the boy runs into (motion
towards) the garden ; btr Jtnabe Idsft in bent 9arteft> the boy runs
in (motion within) the garden. This is the general principle ;
which will be found, with more or less distinctness, everywhere
to prevail in the use of the prepositions of this class.

S 117. THE CONJUNCTIONS.

(1) Conjunctions are words used In eoflneeting sentences.
As, however, there are various kinds of connections existing
among sentences, it has been customary to classify the conjunc-
tions according to the nature of the connection which they are
employed to indicate. Hence wc have (among other classes)
the following :

Copulatives: as, unt, and; au<$, also,

Disjunctives: as, entnxber, either; oler, Or.

Adversatives : as, afar, but ; however ; aftcin, but ; *wf , yet.

Negatives: as, totttx, neither; nc$, nor.

Comparatives: as, roie, as ; fi>, so ; thus ; oil, than; gletytoit just as.

Conditionals: as, n*nn, if; faO*, in case that; nwfrro, provided

that

Causals: as, term, for; xotxi, since, because.

LESSORS IN CHEMISTRY.

C9*ce$*ives:

as, b«ram, therefore; *a$cr, hence; bt^ott, there-
fore,
as, ©frmofcl, obftyon, o&gtety, toenn ; although,
as, laf, that; auf ta$ ancUamlt, in order that; am

ju, in order to.

(2) We give below a list of the conjunctions that most eom-
lonry occur in German: premising only that some of the
w#rds here set down as conjunctions are also employed as ad-
verb* ; for it will of course be kept in mind, that the etfEet
performed bv a word determines its name and character. For
numerous examples illustrating their uses, see Sect. G.

Watts, but.
ftfft, estthant when.
Ufo so then ; consequently ; also.
SsS/f awOf *wr.
Sttfbof, in order that.
8U, until.
$>*, since.

Softer, therefore ; hence,
JDafern, in case that ; if.
JDaf , that ; in order that.
JDomit, in order that,
©arum, therefore; on tha
account
Stan, for ; because ; than
Sknnoc}, still; nevertheless.
JDefftott, therefore ; on that ac-
count.
$tfo the (Sect. 31. 6).
3>oo) yet; however; still,
vfo before that ; ere.
waractKt, either.
WU, in case that,
tfrtyty, consequently.
3^ — btfto, the— the (8. 31. 6).
Scsofc yet, nevertheless,
dates* while; because; since.
Wtotym, consequently.

$ 118. INTERJECTIONS.

(1) Interjections, as the name implies, ar*» commonly thrown
safe a sentence ; without, however, chanar.g either its structure
or its signification. They are mere!*' cne signs of strong or
sudden emotion ; and may be classified according to the
mmtmrt of the emotion which they indicate : some expressing
«ey, some torrow, some turpri*e y and so on. The list below
contains those only thai most commonly occur.

o $ ! o\ oh ! o !

9toe)t*in, after that.

Sfaxfc nor; nor yet.

fleas, therefore ; then.

ffhir, but ; only.

Ob, whether; if.

Cfcglety. though ; although.

Dbf^on, though ; although.

Dtoeftl, though ; although.

Dfeer, or.

JDftK, without ; except.

O$noea$tet, notwithstanding.

©o, thus ; therefore ; if.

Gontern, but

Unfe, and.

Unototyet, notwithstanding.

3Bd$renb, whilst.

SBdfyrtnb Urn, whilst.

flBtyrcnb *af, whilst, than.

SBeter, neither.

ISBenn, if; as.

Jffieil, because.

«Bcnn«lei<$, although.

SBcnff^on, although.

IBie, as ; when.

JBtasoftl, though.

2Bo, if.

SBofcrn, if; in case that

«$! alas!
affl ah!
rl eigh!
$a! ha!
*e! ho!

|cba! ho there!
frit! hold!
Mb! holla 1
We)! hush!
lo*tl alas!

tfiit ! fy !
Dft! hist!
fee$t, wo! alas!
fteifa ! hurrah !
jjm^wfa; huzza!
ttoftlan! well then!
ftut! hoa! quick!
fle$ ! lo !
$um! hem.

u It may be added thai other parts of speech, and even
m phrases, are often employed as conjunctions, and in par*
are treated as such.

Hero we close our Lessons in German in these pages. But
we bog to inform our readers that a continuation of them —
comprising a Syntax of the Language, at once popular and
complete— may be found in Casbbll'b Lkssons in German,
Part II. ; a publication which also contains all the lessons
upon Systematic Grammar which have appeared in the
PoruLAJi Educator; that is to say, those from No.XLIX.

LESSONS IN CHEMISTRY.-No. XVI.

Having finished our preliminary consideration of loe metals
which yield yellow or white precipitates with hydrosulphuric
acid, or hydrosulphate of ammonia, I purpose now leaving the
metals for a time, and discussing the chemical properties of
certain non-metallic elements. Oxygen shall be the subject
of discussion and experiment in the present lesson.

When I inform you that oxygen constitutes, at least, three-
fourths of the crust of the globe and its living inhabitants,
you will admit that it must be an important element. Oxygen*
by combination with other bodies, may assume the condition
of solid, liquid, or gss, but obtained separately, it is always
gaseous ; therefore we shall have to obtain it and examine it
under the form of oxygen gas. There are several methods of
generating oxygen gas, but only one capable of being followed
by a student who is unsupphed with special instruments.
This process I shall describe with a view to its adoption;
the others I shall afterwards mention, with the object of
making their theory understood.

First, let us begin by describing the instruments necessary.
You will require either a large test tube, about half or three-
quarters of an inch in diameter, made by preference of Ger-
man glass, as being more infusible than our own ; a bent glass
tube, and a pneumatic trough, or its substitute, and a receiver.
You will require, in point of fact, an arrangement like the fol-
lowing :

Fiy. No. 1.

or such a substitute for it as your ingenuity, stimulated by
your necessities, will easily supply. I need scarcely indicate
that your distillatory apparatus being small {i.e. the test tube),
your receiving bottle must be small also. In the present case,
ounce or ounce-arid- a-half phials will be of sufficient dimen-
sions. Scarcely more necessary is it to remark, that the distilla-
tory apparatus, as indicated above, will require some sort of sup-
port not represented in the diagram, and that the regular pneu-
matic trough may be dispensed with, by using a basin instead,
the receiving bottle being prevented slipping by means of some
heavy material, such as lead, brick, &c, placed in the basin,
and indicated by the letter u in our sketch. So much then fox
the apparatus.

Fig. No. S.

The substance we shall require as the oxygen-yielding ma-
tt rial, is a mixture of two parts by weight of the salt termed
chlorate of potash, and one part by weight of peroxide (black
oxide) ot manganese ; the substance procurable in commercial
circles, under the simple name " manganese." If the student
should by chance live in a remote place, where old chemical
terms still dominate, the druggist will inform him that he does
not keep such a material as chlorate of potash ; if the student

248

THE POPULAR EDUCATOR.

ask for it under the name of oxymuriate of potash, he will be
more successful.

The mixture of chlorate of potash and black oxide of man-
ganese should be effected, if possible, by rubbing the two to-
gether in a mortar ; mere incorporation, however, with the
blade of a knife will answer sufficiently well. You will not do
amiss by preparing at leant an ounce of this mixture, and pre-
serving it properly labelled in a bottle. The operation of gene-
rating oxygen will frequently be required in the course of
future experiments, and students who do not possess a gaso-
meter must prepare the gas little by little as it may be re-
quired.

Pour about a tea-spoonful of the mixture into the test tube,
replace the cork, arrange the apparatus, and apply heat. Oxy-
gen gas will come over rapidly, but the first portions being
necessarily contaminated with atmospheric air previously ex-
isting in the apparatus, must be thrown away ; all subsequently
collected is pure oxygen gas.

Collect six or seven bottles full of it, and before proceeding
to try any experiments, follow me in discussing the theory of
its production, and the nature of gases generally. What, then,
is a gas ? I know of no definition which is logically distinc-
tive. The definition long received was, " a permanently elastic
fluid" but it is incorrect. Nevertheless, the expression per-
manently elastic fluid, although not sufficiently general in its
significance to comprehend all gases, indicates the most salient
property of so many, and applies so perfectly to the gas under
consideration, that we may profitably discuss its meaning. I
have therefore to inform you that oxygen gas is permanently
elastic ; that is to say, neither cold nor pressure, nor both com-
bined, nor, in short, any other agency, has yet' succeeded in
condensing oxygen gas into a liquid or a solid condition.
Now many gases equally transparent and colourless as oxygen
have been condensed into liquids, and even solids. I dare say,
most people have observed the bubbles which escape from gin-
ger-beer, soda-water, champagne, &c. These bubbles are due
to the presence of a transparent, colourless gas, named, car-
bonic-acid ; it has not come under our notice yet, but it
speedily will. By the application of intense cold and pressure,
this gas may be converted into a solid, haying the aspect of
snow. A similar result has been accomplished in the instance
of many other gases ; therefore, it follows that the neatly
turned definition, formerly accepted as characteristic of gases,
is no longer admissible. Oxygen gas, however, has resisted
every attempt at liquefaction or solidification ; yet analogy
leads us to suppose that, if we could apply sufficient cold
and sufficient pressure, a similar result would ensue.

Abandoning all logical definition of a gas as hopeless, it is
still in our power to entertain a good, general appreciation of
the leading characteristic of gases, by remembering that persist-
ent elasticity, under common circumstances, is the special fea-
ture by which they are contradistinguished from vapours ; the
latter being readily condensed. For example, steam, or aque-
ous vapour, is the result of the application of heat to water.
We all know that steam is elastic, or else what would be the
use of expansion gear in a steam engine ? But it is not perma-
nently elastic under ordinary circumstances, for immediately
on coming into contact with the air, or any material sufficiently
cold, it condenses into water. When thus condensed, it
fills a position analogous with a liquefied gas ; and when, on
the further application of cold, ice results, we have a con-
dition analogous to that of a solidified gas.

Perhaps some such question as this occurs to you. How am
I to reconcile the apparently incongruous statements that oxy-
gen can only be procured as a gas, and that three-fourths of
the material elements of our globe are composed of it ? There
is no contradiction involved in these statements ; as a consti-
tuent of the solid and liquid matters of the globe, oxygen is
combined, and chemical combination, you are well aware, pro-
duces wonderful changes. Both clay and flint contain a vast
amount of oxygen, the latter nearly fifty per cent ; but the
oxygen existing in combination, its solidity is attributable to
that circumstance.

Experiments with Oxygen Gas.— Proceeding to examine syste-
matically the properties of oxygen gas, attend to the following
directions.

(1.) Having uncovered a bottle full of the gas, pour into it
a little transparent lime-water, and agitate; not the slightest
change results.

(2 ) Immerse in another bottle a slip of moistened litmus
paper, and another of moistened turmeric paper ; not the
slightest discoloration of either slip takes place, thus demon-
strating that oxygen gas is neither aeid nor alkaline.

(3.) Take a splinter of wood, such as a bit of lath, or a long
brimstone match, ignite the end, wait for a few seconds until
an incandescent coal has formed ; blow out the flame and
plunge the glowing though not flaming extremity into a bottle
of oxygen gas. Immediately the wood bursts into flame, thus
indicating the presence of a gas different from any already
noticed in these lessons. It is thus proved by this experiment
that oxygen gas is a supporter— a very powerful supporter— <A
combustion. It is moreover proved by the same experiment
that oxygen pas is not a combustible, because, although
causing the stick to burst into flame, itself does not. Remem-
ber how diametrically opposed these qualities are to those of
hydrogen. If the mouth of the receiving bottle be large
enough, the preceding arrangement may be varied as follows.

Flf . No. ».

Instead of a slip of wood use a piece of wax taper, attached,
as represented in the accompanying diagram, to a bent piece of
copper or brass wire. Proceed in other respects exactly as in
the experiment just detailed.

Fif . No. 4. '

(4.) Perform the following comparative ex-periment: take
two bottles full of oxygen, and open them. Place one to
stand during a few seconds open upon a table — mouth upwards
of course. Hold the other for a similar period open, and in-
verted, as represented in the diagram; finally, by means of an
ignited stick, test either bottle for the presence of oxygen.
The upright bottle will be found still to contain it ; from the
other it will have departed ; thus we prove that oxygen gas is
specifically heavier than the atmosphere. Nevertheless,
it is only heavier by a very slight amount; calling atmos-
pheric air one or unity, the specific gravity is one and one-
tenth and a little more — how much this " little more " may be,
chemists are not agreed upon.

The experiments just performed — indeed one of them, the
flame- ignition of the wood, or taper — are sufficient to distin-
guish oxygen gas from all other gases, save one, the protoxide
of nitrogen, or " laughing gas." By observing the character of
flame produced, we may, without further trials, distinguish
between these two. Oxygen gas yields a flame of exquisite

LESSONS IN ALGEBRA.

<H9

purity, without any halo surrounding it ; a reddish halo, how-
ever, envelopes the flame which is generated under similar
treatment in protoxide of nitrogen, or laughing gas. Moreover,
oiygen gas is devoid of taste, whereas, protoxide of nitrogen
is perceptibly sweet.

Although we hare succeeded in finding the characteristic*
which distinguish oxygen from all other gases, it is far too
important an element to be discussed in this one lesson. In my
next I shall describe another series of experiments, having for
its object the teaching of the various relations of oxygen to
other bodies. This lesson I shall terminate with an examina-
tion of the changes which ensue in the mixture of oxide of
manganese and chlorate of potash, as causes, concomitants, or
results of the evolution of oxygen gas.

First, then, let me remark, that although peroxide of man-
ganese contains, as its name indicates, a great deal of oxygen ;
although it is frequently employed alone as an oxygen-yielding
material ; yet, used as we have used it in combination with
chlorate of potash, it does not undergo the slightest change.
There are some instances of chemical decomposition determined
or aided by mere contact with a body that undergoes no
change in itself. Chemists designate this sort of action " ca-
talytic;" they might as well term it "incomprehensible" at
Once. However, not to weary you wit> mere names, remem-
ber that the oxide of manganese determines, we know not why
or how, an evolution of oxygen gas from chlorate of potash at
a much lower temperature than would otherwise be necessary.
Chlorate of potash, if heated alone, evolves all its oxygen, pro-
vided the temperature to which it is exposed be sufficiently
high t eut it is almost too high for glass to bear ; hence, the
advantage of mixing the chlorate with oxide of manganese.
In the following diagram I shall leave out the oxide of man-
ganese altogether.

1
Chlorate

potash

124

1 Chloric
acid
=76

1 Potash
—48

5 Oxygen

=40
1 Chlorine

=36
1 Oxygen

=8
Potassium

=40

6 Oxygen

(evolved)

=48

1 Chloride

potassium

=76

LES80NS IN ALGEBRA.— No. IX.

( Continued from p. 118.)

SUBTRACTION OF FRACTIONS.

137. Rule. — Chang* the sign of the subtrahend, that is, of
the fraction to be subtracted; and then proceed as in addition of
fraetums.

Examples.

1. From -r subtract — .
b m

Here, reducing the fractions to a common denominator, they

become 4-- -and-]-— . Now, changing the sign of the sub-
orn om

trahend, we have JH!L — bh ; then, proceeding as in ad-
orn bm

4. From

«+M

subtract

3»— 2d

Ans.

17«*-9«

*— d

5. From subtract — ~~.

m y

6. From — ~ subtract .

d m

7. From — subtract

Ans
Ans. -

by-dy+bm
my

am+m—d*+d

Ans.

So— 4a
~~aT~'

138. Fractions may also be subtracted, like integers, bv
setting them down, when the sign of the subtrahend is
changed, one after the other, without reducing them to a
common denominator.

8. From — subtract — — !— .
m y

h .h+d

Ans. *— .

m y

139. To subtract an integer from a fir action, or a fraction
from an integer.

Change the sign of the subtrahend, and write it after the
minuend; or, put the integer into the form of a fraction, and then
,proceed according to the general rule for subtraction of fractions.

10. From — subtract m.

. h K—my
Ans. m or .

y y

11. From 4o4- - subtract 3a -. Ana. aA - — .

' c d ' cd

e c if 2 b 2f

12. From 1-| — subtract -3—. Ans. 1-j - — .

» a a

d—b d-—b

13. From a+3A -— subtract 3«— A+ — -.

2 3

Ans. 4A— 2«+

56— 6<*

am bh am — bh

dition of fractions, we have -r— j^ = — jjj — -

Ans.

2. From —2-=- subtract —.

r d

a d—b
3. From — subtract .

Ans.

ad-\-dy—hr
dr

ay—dnv\bm
my

14. From ^ teke — •

b c

15. From 2±* take '-=±.

a c

16. From 7 — take -77— .

0— x d-\-y

17. From «— — take ^.

18. From x+y take .

19. From ^j~ take a ~~

Ans.

ac—cx—bd—by

be
ay-\-by-—cx^~dx

xy
ad-\-ay — bc-\-cx

'bd+by-—dx—xy
2s+3«fy

*+/

Ans.

Ans. a jr—

Ans. #+y—

?— y*— lOo+lOo

a —

20. From x ~~ toke *s 1 "'

1 2

21. From — subtract — .
x y

22. From — subtract — .

23. From — subtract — .

Ans.
Ans.
Ana.

lOx+lOy

Ans. c— a,
y—2s

2y—x

2*y

n iz—b**

xyz

itt

THE PC*UtAB toucAtok

1 s

24. Fnm -ttt- Subtract — Tr-.

25. From — subtract — .-r.
a? x+l

Ana.

s. — tt — «

26. From 7*— — subtract 3«— ^-. Ads. 4# ^

27. From ^*2 subtract :

*— y s+y

28. From 1 subtract

Ans.

*a_ya'

MULTIPLICATION OF FRACTIONS.

140. By the definition of multiplication, to multiply by a
fraction is to take a part of the multiplicand as many times as
then are hhe parte of an unit in the multiplier.

Thus : suppose * is to be multiplied by — . Here, a fourth

part of a is JL: and this taken three times is JL + — -4- —
4 4 4 4

= — , and so of other cases.
4^

141. To multiply one fraction by another.

Multiply their numerators together, and also their denominators ;
the products arc respectively the numerator and denominator of the

1. Multiply * by ■—.

2. Multiply f^by-^.

Ans.

Zbd
2cm*

3. Multiply

{a+m)Xh

Ans.

4ah+4dh
my— 2y

%£Um I "wWI

3«— 3n '

4. Multiply ^ by

3+^ J *+* '

Ans*

1 3

6. Multiply -jpp- by —. Ans.

4a | ik -am — hm
3

Q> C 0t

6. Multiply -T-, — and — together. i

7. Multiply — , , - and — -together.

m y c r — 1

Ans.

8o+24r*

acm
bdy

labK— labd
omry—cmy '

8. Multiply «* J •nd^fgrther. An.. "gjj.

9. MulUply ^ jp and _ together. Am. Wy+ ^ -

142. TA* multiplication may often be shortened, by rejecting the
same factors from the numerators and denominators of the given
fractions.

10. Multiply -1, - and — together.
, Here a, being in one of the numerators, and in one of the

denominators, may be omitted. The answer is then --. If *

be retained, the product will be -_. ; and this reduced to

ary

lower terms, will become ~, the same answer as before.
U. Multiply -j-, £ and 53 together. Ans. **

12. Multiply

a 1

Ans.

IS. MultW ^J^ ^ and ~ together.

8ft

Ans*

ttowr \ tdr
ham

143. To multiply a fraction and an integer together.

Rut*.— Jfttffcpfy the numerator of the fraction by M integer,
and the product tvith the snmedmominatorU the anekoer\ or divide
the Nominator by the integer, and the quotient with the same
numerator is the answer.

14. Multiply — by a.

„ m _ am
Here— X«= .

y y

For a=x-f ; and ~ X - == — .
1 1 y y

15. Multiply — by a.

Here, dividing the denominator by a, we hare H t which is

x
the answer. Or, by the former part of the rule, multiplying

the numerator by a, we have . But =: — , which is

ax ax x

the same result as before.

144. AfraetionumultipUrthyapumitty
tor, by cancelling the denominator.

16. Multiply - by b.

Here — x b=a. For | x &=y. But since the quantity

b is in both the numerator and denominator, it may be can-
celled, and we have a for the product as before.

17. Multiply — by (a—y). Ans. 3m.

18. Multiply ^±H by (8+m).

146. On the same principle, a fraction is multiplied into amy
factor in its denominator, by cancelling that factor.

19. Multiply £ by y.

20. Multiply A by <5.

Examples for Practice,

,,,.., a 4a . 10a

1. MulUply ~, -r- and -^- together.

2. Multiply - by g±g .

Ans,

4e>

usssojte In algebra.

•.Multiply T by-.

Ana.

4. Multiply

6. Multiply

by 8.

3 ix

by &e.

Ans.

6. Multiply ±,i? and -together.

8. Multiply ^byJ^.

9. Find the product y X £ X £ * 7-

10. Multiply •£ by •=*

11. Find the product aX r X^

12. Find the product ^ X ^L X {.

AnS. -7-.

Ant. 1.

An*. — .

An., p

12
Ans. 2afo

llMnitiply-^by^.

U.Mrf^^byg.

W. Multiply 1-^ by 2+

Ana.

IT l*«i^iw ***— 4 *'— 9 *+ * k 3*H-2* a +9#+6
17 - ***** 6*3+4^-9^6 * 6^'+3Hl2 '

18s«+19s«— 93** +36

Ans.

36*«— 6SLFH-96* 5 — 43* a +12 '

LESSONS IN READING AND ELOCUTION.— No. I.
PUNCTUATION.

PtmoTtTATfoir is peculiar to die modern languages of Europe. It
wii wholly unknown to the Greek* and Romans ; and the languages
of the East, although they have certain marks or signs to indicate
tones, hare no regular system of punctuation. The Romans and the
Greeks also, It Is true, had certain points, which, like those of the
languages of the East, Were confined to the delivery and prounciation
of words ; but the pauses Were indicated by breaking up the written
matter into lines ot paragraphs, not by marks resembling those in the
modern system of punctuation. Hence, in the responses of the
ancient oracles, which were generally written down by the priests
and delivered to the inquirers, the ambiguity — doubtless intentional
—which the want of punctuation caused, saved the credit of the
oracle, Whether the expected event was favourable or unfavourable.
As an instance of this kind, may be cited that remarkable response
which was |iven on a well-known occasion when the oracle was
consulted with regard to the success of a certain military expe-
dition. * IWi et redjhis nnnmuin. peribis in bello." Written, as

it was, without being pointed, it might be translated either " Thou
shalt go, and shalt never return, thou shalt perish in battle," or
" Thou shalt go and shalt return, thou shalt never perish in battle.*'
The correct translation depends on the placing of a comma after the
word nunquatn y or after reduMi.

The invention of the modern system of punctuation has been
attributed to the Alexandrian grammarian Aristophanes, after
whom it waa improved by succeeding grammarians ; but it waa so
entirely lost in the time of Charlemagne, that he found it necessary
to have it restored by Warnefried and Alcoin. It consisted at first
of only one point, used in three ways, and sometimes of a stroke,
formed in several ways. But as no particular rules Were followed
in the use of these signs, punctuation was exceedingly uncertain,
until the end of the fifteenth century, when the learned Venetian
printers, the Manutii, increased the number of the signs, and esta-
blished some fixed rules for their application. These* were so f&fg-
rally adopted, that we may consider them as the inventors of the'
present method of punctuation ; and although modern grammarians
have introduced some improvements, nothing but a few particular
rules have been added since their time. ,

The design of the system referred to was purely grammatical, and
had no further reference to enunciation, than to remove ambiguity
in the meaning and to give precision to the sentence. This, there-
fore, is the object of punctuation, and although the marks employed
in written language may sometimes denote the different pauses and
tones of voice which the sense and accurate pronunciation require,
yet they are more generally designed to mark the grammatical
divisions of a sentence, and to show the dependence and relation of
words and members which are separated by the intervening clauses.
The teacher, therefore, who directs bis pupils to " mind their pause*
m reading" gives but an unintelligible direction to those who are
unversed in the rules of analysis. A better direction would be to
disregard the pauses, and endeavour to read the sentence with just
such pauses and tones as they would employ if the sentence were
their own, and they were uttering it in common conversation. In-
deed it is often the case that correct and 'tasteful reading requires
pauses, and these too of a considerable length, to be made, where
such pauses are indicated in written * language by no mark what-
ever. It is not unfrequently the case that the sense will allow no
pause whatever to be made in cases where, if the marks alone were
observed, it would seem that a pause of considerable length is re-
quired. The pupil, therefore, who has been taught to mind his
pauses, must first be taught to unlearn this direction and endeavour
to understand the sentence which be is to read, before he attempts
to enunciate it.

The characters employed in written language are the following :

!
?

The Comma,
The Semicolon,
The Colon,
The Period,
The Dash,
The Exclamation,
The Interrogation,
The Quotation Marks
The Diaeresis,
The Crotchets,
The Brackets,
The Obelisk or Dagger,
The Double Obelisk or
Double Dagger

The Ellipsis, sometimes expressed by Periods, thus,
" sometimes by Hyphens, thus,
" sometimes by Asterisks or Stars, thus,
" sometimes by a Dash prolonged, thus, ■

These characters, when judiciously employed, fit the meaning
and give precision to the signification of sentences, which, in a
written form, would be ambiguous or indefinite without them.
Thus, " 1 said that he is dishonest it is true and I am sorry for it."
Now the meaning of this sentence can be ascertained only by a
correct punctuation. If it be punctuated as follows : *' I said that
he is dishonest, it is true, and I am sorry for it ;" the meaning
will be, that it is true that I said he was dishonest, and I am aorry
that I said so. But if it be punctuated thus, " 1 said that he was

The Hyphen,
The Breve,
The Apostrophe,

The Brace,

The Acute Accent,
The Grave Accent,
The Circumflex Accent,
The Caret,
The Cedilla,
The Asterisk,
The Section,
The Paragraph,
The Parallels,

•***•«

Written here, of course, Includes printed languag*.

2*2

THE POPULAR EDUCATOR.

dishonest ; it is tine ; and I am sorry for it ;" the meaning will
be, I said that he was dishonest ; it is true that he was dishonest,
and I am sorry that he was so.

Again, the following sentence, as here punctuated, is an innocent
remark: "BelieYing Richard Brothers to be a propbet sent by
God, I have painted bis portrait/' But the sentence, as it was
originally written by its author, with the comma after ami, instead
of after God, is a piece of horrid profanity.

A farther instance of the importance of correct punctuation was
afforded by a late advertisement, in which the commissioner for
lighting one of the most commercial cities of Europe, by the mis-
placing of a comma in his advertisement, would have contracted for
the supply of but half the required light. The advertisement repre-
sented the lamps as " 4,050 in number, having two spouts each,
composed of not less than twenty threads of cotton.' This ex-
pression implied that the lamps had each two spouts, and that the
two spouts had twenty threads, that is, each spout had ten threads.
But the meaning that the commissioner intended to convey was,
that each spout had twenty threads ; and his advertisement should
have had the comma after *• spouts,'* instead of after " each," thus:
The lamps have two speuts, each compoaed of twenty threads, ficc.

These instances might suffice to illustrate the nature and the
propriety of correct punctuation ; but the following instance,
known to many, will show the importance of the subject. The
clerk of a congregation, in Scotland, hsd a paper handed to him,
as the custom is, to read just before the minister stood up to pray
with and for the congregation, containing the following words, un-
pointed : " A msn going to sea his wife desires the prayers of the
congregation." The clerk read it as if a comma had been pat at the
end of the word wife, and unfortunately excited, in no small de-
gree, the risible faculties of the people assembled : — thus, " A
man going to sea {see) his wife, desires the prayers of the congre-
gation."

Bat although the meaning of a sentence is thus materially af-
fected by the punctuation, it will be seen in the following lessous
that the punctuation alone is an unsafe guide to follow in the enun-
ciation of any collection of words. For, in many cases, these
marks indicate no pause, emphasis, or other remarkable circum-
stance requiring notice in the enunciation of the sentence.

The nature of the marks used in written language may also be
understood by a reference to the origin of their names.

The word Comma is derived from the Greek language, and pro-
perly designates a section, or part struck off from a complete sen-
tence. In its usual acceptation, it signifies the point which marks
the smaller portions of a period. It therefore represents the short-
est pause, and consequently marks the least constructive, or most
dependent parts of a sentence.

The word Colon is from the Greek, and signifies a member of a
sentence, and the Latin prefix semi means half. Hence, a Semi-
colon is used for the purpose of pointing out those parts of a com-
pound sentence, which although they each constitute a distinct
proposition, have yet a dependence upon each other, or on some
common clause. The Colon is used to divide a sentence into two
or more parts, which, although the sense be complete in each, are
not independent.

The word Period is derived from the Greek, and means a circuit,
or well-rounded sentence. Hence, when the circuit of the sense is
completed, with all its relations, the mark bearing this name is
used to denote this completion.

The word Interrogation is derived from the Latin, and means a
question. Hence, the mark so called is put at the end of a
question.

The word Exclamation is from the same language, and means
a passionate utterance. Hence, the mark so called is put at the
end of such utterances.

The word Parenthesis is derived from the Greek language, and
means an insertion. A sentence, clause, or phrase, inserted between
die parts of another sentence for the purpose of explanation, or of
calling particular attention, is properly called a parenthesis.

It is to be remarked, however, that the name parenthesis belongs
only to the sentence inserted between bracket* or crotchets, and not to
those marks themselves.

The word Hyphen is derived from the Greek language, and sig-
nifies under one, that is, together ; and is used to imply that the
letters or syllables between which it is placed are to be taken
together as one word.

The hyphen, when placed over a vowel, to indicate the long

sound of the vowel, is called the Macron, from the Greek, signify-
ing toy .

The mark called a Breve, indicating the short sound of the
vowel, is from the Latin, signifying short.

The word Ellipsis, also from the Greek, means an omission, and
properly refers to the words, the members, or the sentences
which are omitted, and not to the marks which indicate the omis-
sion.

The word Apostrophe, also from the Greek, signifies the turning
away, or the omission of one letter or more. The word apostrophe,
as here used, must not be confounded with the same word as the
name of a rhetorical figure.

The word Dueresis is also from the Greek, and signifies the
taking apart, or the separation of the vowels, which would other-
wise be pronounced as one syllable.

The term Accent is derived from the Latin language, and im-
plies the tone of the voice with which a word or syllable is to be
pronounced.

The word Section, derived also from the Latin, signifies a cut-
ting, or a division. The character which denotes a section teems
to be composed of ss, and to be an abbreviation of the words
signum sectionis, or the sign of a section. This character, which
was formerly used as the sign of the division of a discourse, is
now rarely used except as a reference to a note at the bottom
of the page.

The word Paragraph is derived from the Cheek language, and
signifies a writing in the margin. This mark, like that of the sec-
tion, was formerly used to designate those divisions of a section
which are now indicated by unfinished lines or blank spaces.
This mark, as well as the section, is now rarely used except as
a reference.

It may further be remarked, that notes at the bottom of the
page, on the margin, or at the end of the book, are often indi-
cated by figures, or by letters, instead of the marks which have
already been enumerated.

The word Caret is from the Latin, and signifies it is wanting.
This mark is used only in manuscripts.

The Cedilla is a mark placed under the letters c and g to indicate
the soft sound of those letters.

The Asterisk, Obelisk, Double Obelisk, and Parallels, with the
section and paragraph, are merely arbitrary marks to call attention
to the notes at the bottom of the page.

As these marks which have now been enumerated all have a
meaning, and are employed for some special purpose, it is recom-
mended to the student never to pass by them without being assured
that he understands what that purpose is. Correct and tasteful
reading can never be attained without a full appreciation of the
meaning which the author intended to convey ; and that meaning
is often to be ascertained by the arbitrary marks employed by him
for the purpose of giving definiteness to an expression. At the
same time the student should consider these marks as his guide to
the meaning only, not to the enunciation of a sentence. Correct
delivery must be left to the guidance of taste and judgment other-
wise acquired.

In many excellent selections for lessons in reading, the pieces
hsve been arranged in regular order, according to the nature of
their respective subjects, under the heads of Narrative, Descriptive,
Didactic, Argumentative, and Pathetic pieces, Public Speeches,
Promiscuous pieces, the Eloquence of the Bar, of the Pulpit and
of the Forum.

By Narrative pieces is meant those pieces only which contain a
simple narration or story. Descriptive pieces are those in which
something is described, chiefly from nature. Didactic pieces an
those designed to convey some particular kind of inatruetfcm,
whether moral, religious or scientific. Argumentative pieces are
those in which some truth is designed to be proved in an agree-
able manner. Pathetic pieces are those by which the feelings of
pity, love, admiration and other passions, are excited. Prossis-
cuous pieces are those which do not fall exclusively under any of
the classes which have been enumerated, or which consist oft
mixture of those classes. The Eloquence of the Bar consists of
speeches (or pleas as they are technically called) made by distin-
guished lawyers in the courts of justice in favour of or against t
supposed criminal. The eloquence of the Pulpit consists of ser-
mons or discourses delivered on religious occasions. The Hs»
quence of the Forum consists in the speeches, addresses, oration)
&c, addressed to political or promiscuous nssembliri.

LESSONS IN ITALIAN.

253

To many, this information may teem superfluous or puerile. But
est hese lessons are designed for the young and the unlearned, it must
not be forgotten that their sources of information are few and that
they will not always take the pains to inform themselves of the
meaning of words, even when they are familiar to their eyes in
capital letters, and in the running titles of the books before them
every day. It is often the case that the teacher also, taking for
granted that his pupils are familiar with the meaning of words so
often presented to their eyes, neglects to question them on the
■object ; and in riper years it becomes a matter of surprise to the
pupil himself that, in early life, words which he had heard sounded
almost every day at school presented no idea to his mind beyond
that of an unmeaning, or ratber an unintelligible sound.

The object of all education is not so much to fill the mind with
knowledge as to strengthen its powers, and enlarge its capacity.
Those exercises, therefore, are always most beneficial in education,
which tend most effectually to produce this result. There is, perhaps,
no branch of study connected with popular education, which, when
properly pursued, is more highly subservient to this end than the
study of correct and tasteful reading, as an art. It necessarily
involves a complete knowledge of the subject to be read, the rela-
tion and dependencies of the phrases, clauses and members of the
sentences, the proper meaning of the words employed, and the
connexion between the sentences themselves. This cannot be
acquired without a vigorous employment of the perceptive powers,
aided by those of comparison, of analysis, of reasoning, of judg-
ment, of taste, and of discrimination. Subordinate and auxiliary
to the acquisition of this important art, the student is leoommended
to exercise also the power of classification, while studying a read-
ing lesson (which should always be studied previous to practising
it), to ascertain under which of the above mentioned classes,
whether narrative, descriptive, didactic, &c, the piece he is about
to read belongs. The student who thus employs his faculties ssnnot
fail to feel a vigorous growth of intellect springing up in his own
mind, and will be amply compensated for his labour, by a com-
mand over the stores of literature not to be gained by any other
method.

LESSONS IN ITALIAN GRAMMAR.— No. XVI.

BY CHARLES TAU8BNAU, M.D.,

Of the University of Pavim, and Professor of the Italian and German
Languages at the Kensington Proprietary Grammar School.

Vocabulary.

Time, Um-po, m.

Present, a-dh-so (adv. now)

Beet, wiyUo-re

He had hidden himself, d-gli

»i i-r+ na-sc6-*to
Boom, etdn-ui (or cd-me-ra)
Beck, dti-tro (adv. behind)
Oar, no-stro, m., no-ttra, f.
Bm,ha

Bridge, pon-te,m.
8feme, jsil-lre, a. f .
Your*, wA-etro, m., v6-stra, f.
Hee only, ha so-la-men-te
Ota, tJ-s», m., u-na, f.
Wood, te ffso, m.
Bdwardf .BafM or -do
He* reeehred, ha ri-ce-vu-to
From,*

Wfjfeeh, o-ro-16-gio (o-ri-uo-lo)
Gold, 4-rv, a. m.
8 word, •***-*•,£
Silver, mr-gen-to, s. m.
Fair, •*->*. m.
ttioe4raekle,/&-W«, f.
Steel, ae-eid-jo, s. m.
Onoe, u-nm *A*.to
They irore, si por-td-va-no
These, d-bi-to, m.

Cloth, jNfft-fto, m.

Waistcoat, gi4i t m. (pi. un-
altered)

Velvet, •**-&<», m.

Use, «-*>, m.

Vessel, vd-so, m.

Copper, rd-me, m,

Has been prohibited, e std-to

pro-i-bi-to
Sweden, Sve-xia
Shambles, bec-ehe-ri-a, f.

(slaughter-house)
Are for sale, si tro-va da

ven-de-re
Meat, cdr-ne, f.
Young ox, mdn-to, m.
Calf, vi-tel-lo, m.
Wether, ea-stro-ne, m. (meat

of ox, of calf, of wether)
What means, ehe si-gni-Ji-ea
Ringing, sud-no, m.
Bell, cam-pd-na, f.
What do you say, che di-te

(with the case-sign di)
Which I have bought, ehe ho

cotn-prd-to
It is, ee-to i

Good, bud-no, m., buo»na, f.
Fine, fi-no, m.,f!-na, f.
Colour, eo-16-re, m.
Beautiful, btl-lo, m., UUla, f.
What do you think, ehe pen-

sd-te (with the case-sign dt)
Man, uA-mo, m.
Whom you see, ehe pe-di-U
Boy, ra-gds-tto, m.

Whom he carries along with

him, eh f e-gli mi-na ti-eo
Beggar, men-di-eo, m.
Who follows him, ehe gli va

diS-tro
Here are, ic-co
Ten, dii-ei
Yard, brde-eh, m. (pi. le brde-

cia, f.)
Taffeta, taf-fe-td, :n.
Some of which you wanted,

del qud-le vo-le-vd-te a-ve-re
Twelve, do-di-ei
Cambric, tt'-la ba-ti-sta, f .
Which you have demanded,

ehe a-vS-te do-man-dd-ta

Send me, man-dd-te-mi
Dozen, dot-zi-na ids), f.
Lemon, li-mo-ne, m.
Two, du-e
Pound, lib-bra, f.
Fig./I-co, ra. (pl./?-«Ai)
Which you have received, che

a-vi-te ri-ee-vu-ti
From, da
Smyrna, Smir-na
Spare me, ee-dd-U-mi
Bottle, Jia-schdt-ta, f.
Eau, d-cqua, f. (water)
Cologne, Co-16-nia
Which has been sent to you,

ehe vi d ttd-ta man-dd-ta

The use of this particle frequently coincides with the use of
the preposition to in English grammar. Generally speaking,
any kind of direction, expressed by a verb, to or towards a per-
son or tiling, is denoted by this word. The ideaa of similarity
or resemblance, of approaching or approximation, of a direction or
mere reference to any thing, end, aim, or point of time, form,
as it were, only parts or branches of this fundamental significa-
tion of the particle a, and whenever the action of the subject of
a sentence (t. e. of the nominative) expresses such direction or
approach to or towards persons or things, a must be placed
before them ; e. g. ac-c6-sta-ti dl-la td-vo-la, approach thyself
to the table ; al-cd-ne dd-te gli 6s- si, give the bones to the dog ;
il fi-glio ras-so-mi-ylia alpd-dre, the son is like the father ; ne
par-le-ro al cu-gi-no, I shall speak of it to the cousin ; al cdn-
to si H- co -no- see V ue-ekUlo, by the song one knows the bird ;
C a-vd-ro nan pin-sa che al da-nd-ro, the avaricious man only
thinks of money; i-o lo dis-si al a-mi-co v6-stro, I told it your
friend; 4-gli lo dU-de el pS-ve-ri, he gave it to the poor; i-o
vd-do a £6-ma, I go to Rome ; tton ere-di-te a 16-ro, do not be-
lieve them ; dis-si a lui, an dd-te a cd-sa, I told him, go home
(i. e. to the house) ; pic-chid-re dl-la por-ta, to knock at the
door; scri-ve-re a qual-che-du-no, to write to somebody; ag-
giu-gne-re u-na cd-sa ad un* dl-tra, to add one thing to another ;
ce- de-re su-o di-rit-to a qual-che*dU-no, to transmit or cede one's
right to any one ; eo-sirin-ge-re u-no ad u-na a-zio-ne, to compel
or force any one to some action ; ver-ro a tnex-zo gior-no, a miz-
za n6t-te, dl-le du-e, al tkm-pofis-sd-to,alpri-mo del tnd-se, I shall
come at noon, at midnight, at two o'clock, at the appointed
time, on the first of the month.

Phrases, not literally or strictly expressing an abode, resi-
dence, stay, continuance, or being in a place, but merely
nearness or presence, require the particle a and not in, which
always denotes a real and not merely imaginary continuance
or being in (i. e. in the interior of) a place or thing, or some
action taking place in it ; e. g. i-gli * al bdl-lo, he is at the ball ;
alfe-sti-no, at the (dancing and gaming) evening party ; a td-
vo-la, at table ; al con-eer-to, in the concert ; a gim-ed-re, at
play or game ; a stu-did-re, (engaged) in study.

From what has been explained, it is obvious that in those
phrases which merely denote the moving, approaching, or
tendency to or towards a place or thing, and not strictly the
entering or penetrating into it, a and not in must be used ; for
m means the actual motion or penetration into the interior of
any locality ; e. g. i-o vd-do al bdl-lo, I go to the ball ; a td-
nola, to table; a ed-na, to supper ; a im-pa-rd-rc, to learn, t. e.
to (the pursuit of) learning ; a gim-ed-re, to play, t. e. Co (the
diversion of) playing.

The proper nouns of towns, cities, boroughs, or similar loca-
lities, are an exception to the last-mentioned rule, for it is
quite allowable indiscriminately to place a or in before them
whenever the abode, residence, stay, arrival, continuance, or
being mi or within them (». e. in their interior) is to be
designated ; e. g. e-gli i a or in Nd-po-li, he is at or in Naples ;
tro-pdn-do-si t-gU U-na v6l-ia a Pa-ri-gi, being once in Paris ;
dl-la e ar-ri-vd-ta a or in Var-sd-via, she is arrived in Warsaw.

Ihe verbs par Ax-re, to depart, set out or off, and con-ti-nu-
d-re, to continue, proceed on (one's journey;, are another ex-
ception, for they require the preposition per before the name
of that locality or eyen country, towards which a Journey Of

{

THE POPULAR EDUCATOR.

any motion is directed ; e. g. k-gli i par-ti-toper Co-stanH-nt-
po-li, per Pie-tro-burgo, per la Soiz-te-ra, he has started for
Constantinople, for St. Petersburgh, for Switzerland; con-ti-l
nu-d-re U su-o vidg-gio per la Fo-B-nia, per Mo-sea, to proceed on
one's journey to Poland, to Moscow.

Next to di, the particle a is of the most extensive use, and
though the relations in which this word stands to others are
not quite so loose and vague as those of di, they are various
enough to admit of modes of application which, even in
Italian, might sometimes be more suitably dispensed with by
the use of prepositions of .a more logical distinctness, and conse-
quently a greater clearness in special instances ; e. g. mon-td-
re a ca-vdUlo (for *6-pra un ea-vdl-lo), to get or mount on horse-
back ; i-vi apo-ehi gi6r-ni ri-tor-nd (for ac-po p6-ehi gior-ni), he
returned a few days after ; fd-re a vo-lon-td di cia-scu-no (for
se-eon-do la vo-lon-td), to act according to, or to conform to the
will of everybody ; bat-U-an-si a pdUme (for c6l-le pdl-me), they
fought with the palms of their hands ; le rot-tu-re fu-ro-7+0 mu-
rd-te a pie-tra e a eal-ei-na (for con pii-tra e eon eal-ei-na), the
breaches were walled up with stone and lime ; ncn ei eon-ver-
rd com-bdt-te-re a ei p6-ca gtn-U (for o6n-tra ei p6-ca gin-te), it
will not become us to fight against so few ; mdl-ti fdn-no bi-ne
a spe-rdn-sa digua-dd-gno (for per i-spe-rdn-ta), many are honest
through the hope of profit, arc.

It if obvious that this variety of the significations of a will,
for the purpose of translating it into English, require the use
of many prepositions or otber words, and sometimes even of
adverbial expressions or phrases, which only practice and a
patient method of reading good writers, by accurately compar-
ing the idioms and genius of the two languages, fully can
teach. In a course of merely elementary lessons, I must
naturally restrict myself to some, I think, useful hints in the
following illustrations : — The particle a may be translated by
the objective case (without any preposition) ; e. g. fd-re
ve-dtfre ad al-cu-no u-tta ed-sa, to let any one see some-
ihi:ij;; do-man-dd-re ad al-cu-no, to ask one; toe-ed-re ad
al-cu-no, to concern one ; so-prav-vi-ve-re ad al-cu-no, to
survive one ; sup-pli-re a qudl-che c6-sa, to complete or make
Up something: by the preposition to; e.g. ap-pli-cdr-si ad
t*-«* c6-sa, to apply one's self to something ; vol-ger-si ad al-cu- 1
mo, to turn to somebody ; a si-ni-stra, a tndn-ca, to the left ; |
a di-sira, to the right ; an-dd-re, ve-ni-re a un lud-go, to go, I
come to a place ; do-lkn-te a mdr-te, grieved to death ; pas- 1
sd-re afil di spd-da, to be put to the sword (». e. to the edge of 1
the sword) : by the preposition at ; e. g. al le-vdr del s6-le, at
sun-rise ; alpri-mo cen-no, at the first hint or sign ; a mi-o skn*
no, to my mind, liking, taste, fancy, will ; se-de'-re a td-vo-la, to
sit at table ; is-se-re (std-re, tro-idr-st) a un luo-go, to be at a
place : by the preposition on or upon ; e. g. a pi-na di tnSr-te,
upon (or under) pain of death ; af-Ji-ddr-siadat-cu-no, to reckon
or build upon one ; ap-po-gidr-si a qudl-che cd-sa, to lean, rest,
or to rely on something ; in-si-ste-re a qudl-che cS-sa, to insist
on something ; a ptt-ai, a ca-vdllo, on foot, on horseback ; a
con-di-sid-ne, on condition ; ad im-pri-sti-to, on trust or credit j J
by the preposition in ; e.g. a du-e mi-si, in two months ; dl-la
sfug-gl-ta, in passing by or in flight; di-pin-ge-re a 6-glio t to'
paint in oil ; vt-eti-to a bidn-co, dressed in white; dt-lafran-ci*
se t alT in gld-se, in the French, English manner or fashion ; di-
re aW o-rdc-chio, to say or whisper in any one's ear ; a Um-po
in time, in the nick of time ; ve-ni-re a grdn-di sehU-re, to come
in great crowds or masses : by the preposition according to (or
after) ; e. g. a ma-nii-ra, after the manner or fashion ; a de-chio
according to a measure taken merely by the eye ; a vo-lon-td d
eia-sehe-du-no, according to the will or liking of everybody ; by
the prepositions against or towards ; e. g. ri-M-ldr-xi ad al-cu
no, to rebel or mutiny against somebody ; alV o-rien-lc, alC oc
ei-den-te, towards the east, west: by the preposition with; e g
a trec6l-pi V ucd-se, he killed him with three blows ; an-dd-r
a grdndi pas- si, to walk with long or great steps ; std-re a toe
caa-pfrta, a 6c-chi a-ptr-ti, a brdc-eia a pSr-te, a cd-po chi-no, a
chid -me sciol-te, to stand with an open or gaping mouth, with
open arms, with the head inclined, with dishevelled hair j a bri
glii sciol-ta, with slackened reins, at full speed or gallop ; cor*
ri-spon de-re ad al-cu no, t » agree with somebody ; u-ni-toadaL
cii-no, united with somebody ; pa-ra-go-nd-re ii-na co-sa a gudt
che ot-st, to compare one thing with another : by the prepos
tion for ; e. g. con-fan-nd-to a vi-ta dl-le ga-U-re, condemne

>r life to tfce galleys ; i$-**-re sen-si-bi-le a avdUch$ob , -ta t t» fee 1

impassion for (or to be susceptible of) something: toy tne
preposition by; e. g. h fa-rdi afor-xa, thou wUt do Itby con-
itraint: by the preposition of; e. g. chU-de-re ad al-ci-no, to
desire or require of somebody : by the word as ; e. g. mlt-Ur-

asfr-90 con al-cu-no, to engage one's self to somebody as a
aervant : a-vi-re a si-gn^re, to have as a master: by at a wm;
*, g. a du-eadh-e, two at a time, two and two: bv w**™* 1

spressions or phrases ; e. g. a bucn mer-cd-to, at a ™^}V™*!

tieap ; dl-lasca-pe-strd-ta, licentiously, dissolutely ; dMs J^f-

10, as bad as possible; dl-la rin-fk-sa^ confusedly, promttcH-
Susly ; a nUn-ti, a tne-tno-ria, bv heart (to learn or know) ; a
Hc-ca, by word of mouth ; ve-n(-re dl-le md-nt, to come to Wows
Or to engage in close fight; an-dd-re a spds-so, a di-p6r-to, to,
take a walk ; a gudt-tro oe-ehi, a tk-sUs a ti-sta, m pnvate^alone
together (I. e. between four eyes, UU-^tHe); a ba-em-f*
•nough; a md-no, at hand, near at hand, in readiness ; with
ttrbytheband; artificially; by election; underhand, by fraud
• ir deceit.

I have already stated that to avoid hiatus by a wcession of
towels, generally ad, in the plaee of a, is used before a jowel,

nd I shall conclude this explanation of the uses of a by the
remark that, in Italian classics, not a few passages, wh«fi at
irst sight the particle a appears to be a somewhat arbitrary
substitute for other prepositions or words, without any change

f construction, will admit of a perfect elueiasUon by ellipsis.
Other uses, and some omissions of the particle •, will be

ommented on hereafter.

XXV.

LESSONS IN GEOMETRY.— NO.
LECTURES ON EUCLID.
(Continued from p. 196.)
BOOK I. -PROPOSITION XXI.— THEOREM.

If from the ends of one side of a triangle, tJiere be dratcn two

straight lines to a point within the triangle, these together shall

be less than the other two sides of the triangle, but shall contain

a greater angle.

In fig. 21, let jl bo be a triangle, and from the points b and

c, the ends of the side b c, let the two straight lines bd and

c d be drawn to the point d within the triangle. Then b d and

t> c together shall be less than the other two sides B a and 4 c

of the triangle abc, but shall contain an angje bbc greater

than the angle b a c.
ProduceBD to b. Then, the two sides BAft*4 AB,pf tfce

triangle a b k are greater than the third F%. al.

lide bb (I. 20). To each of these un*

equals add x c, and the two sides b a and

ac are greater (As. 4) than bb and xc

Again, the two sides c sand EDof the

triangle c b d are greater (I. 20) than the

third side c d. To each of these unequals,

add d b, and the two sides c b and b b are

greater (Ax. 4) than o d and db. But it

has been shown that b a and a c are greater than b » a»4 •£

Much more then are b a and a 0, greater than B D anil J) p.
Again, the exterior angle BDCof the triangle o • ■ ia greater

than its interior and opposite angle cid (I. \A>)- And (fee

exterior angle cbro( the triangle abb is greater than its
interior and opposite angle ba c Ct. 16). Bnt the angle i»cm
greater than die angle ceb. Much more, theesisre, **■*

I angle bdo greater than the angle bac. WhereeoBa* *•* *■■
the ends of, &c. Q. E. D.

Scholium. Jl.— -Respecting this proposition. Dr. 8unson
makes the following observation: " Mon*. ClaUmult, in tip
preface to his Elements of Geometry, publis^e4 l n *rencn 4*
Paris, anno 1741, says *t|iat Euclid has beep at the P"JS fc>
prove that tl^etwo sides of a triangle which is included ^^JJ
another, are together less than the two sides ^[.^fj^jjj 8
which inc"
vis. that
unless f

LESSONS IN GEOMETRY.

greater dim the sides of the triangle which includes it, in any
ratio which u less than that of two to one, as Pappus Alexandri-
nus has demonstrated in Prop. III. Book III. of his Mathemati-
cal Collections.'* To prove this without consulting Papp
will be a very good exercise for the students of the P. B., and
th e ref ore we leave it in their hands.

thhetium 2. — Respeoting this proposition also, Dr. Thorns
very properly remarks, that it ,f is never referred to by Buo
fin Ms after writings], except in the eighth proposition of the
third took ; and that proposition may be proved without it."
The P*op. VIII. Book Hi. is, in fact, proved without it, in
fJassell'e j£nelid. Tbjis, it would appear that one of the links
of the great Euclidean chain of reasoning is unnecessary. All
attempts to shorten that chain are no doubt praiseworthy ; for
art is long, and Hfe is short, Nevertheless, the propositioti
contains a geometrical truth, useful in many cases of which
Bnelid never dreamed ; and, therefore, we ought to retain this
extra link.

EXERCISE TO PROPOSITION XXI.

Jf from any point within a triangle, straight lines be drawn to the
porticos of the three angles, these three straight tines taken
together shall be less than ths sum of the three sides, but greater
than half that sum.

Let a.b b, fig;, y, be a triangle, and o any point in it ; also,
let straight lines o a, c b, and o b be drawn from c to its thi
angular points a, b, and b. Then, the sum of the three straight

Fig.Y.

Fig. 22,

V*** A, ob and q,B is less than the sum of the three sides ab,
BBandAB; but greater than half their sum.

By the preceding proposition, a c and o b together are less
tun a Band n together; bc and b o together are leas than
AB and* ab together : and ao and ob together are less than a n
4*4 9 > together. Therefore, by axiom IV. twice ac, twice
b o, and twice c b together, are less than twice a b, twice bbsi ■ ;
twice ab together ; wherefore, a o, b o and c b together are leaf
than a b, b b and a b together.

Again, by Prep. XX., a o and ob together are greater thi H
ab ; b o and o b together are greater than b B ; and a c ang c i
together are greater than ab. Theeefore, by Axiom IV„
twice a c, twice bo, and twice c s together, are greater than a t>,
* ■ •**<* ± b together. Wherefore, ac, bc, and ob togethc
•«• greater than the half of ab, of b b and of a b together.

Therefore if from any point within a triangle, &c. Q. E. D.

k this demonstration, a very obvious axiom is>
taken for granted, vis. that the halves of unequal* are unequal ;
•r, as it may be more explicitly expressed, if the double of m
series of ' magnitudes taken together, be equal to the double of
another series of magnitudes taken together, the sum of tl
former aeries is equal to the sum of the latter series, ftc.

PROPOSITION XXH.— PKOBLSM.

To make a triangle of which the sides shall be equal to three giv
straight lines, but any two whatever of them must be greai
than the third (I. 20).

In fig. 22, let a, b, and c be the given straight lines, of
which any two whatever are greater than the third, via., jj
end b greater than p. j 4 and B greater tfcan 8 ; and b and
mate AfA A* ft ?« mm?** «0 m& » triangle of which
the sides shall be equal to a, b, and o, each to each.

Take a straight line p b termi-
nated at the point d, but un-
limited towards b. Make (I. 3)
n b equal to a, vo equal to b, ana
o 9 equal to 0. From the centre
v, at the distance pd, describe
{Best 3) the circle dxl. From
the oentre o, at the distance o h,
describe (Fist 3) another circle
hlx. And join it and xe.
The triangle kpo has its sides
equal to the three straight lines
a, b, and 0.

Because the point p is the centre of the circle dxl, the
straight line pd is equal (Def. 15) to, the straight line v x. But
FD is equal (Const) to the straight line A. Therefore fk is
equal (Ax. 1) to a. Again, because o is the centre of the
circle lkh, the straight line oh is equal (Def. 15) to the
straight line o x. But o h is equal to 0. Therefore also o k
is equal to o. And fo is equal (Const.) to B. Therefore the
three straight lines x p, f o, and o x are equal to the three
straight lines a, b, and c. Wherefore the triangle x f o has
been made, having its three sides xf, fo, and ox, equal to
the three given straight lines a, b, and c. Q. £. F.

Scholium 1. — This is the general proposition of which Prop.
I. is but a particular case. It is evident that upon the other
side of the base f o, another triangle might be constructed,
having its three sides equal to the three given straight lines.
In the demonstration, it is assumed that the two circles will
intersect each other. To prove this, it is sufficient to observe
that the sum of the radii of the two circles is, by hypothesis,
greater than the distance between their centres.

Scholium 2. — Dr. Simson remarks on this proposition, that
<( some authors blame Euclid, because he does not demonstrate
that the two circles made use of in the construction of this
problem, must cut one another : but this is very plain from
the determination he has given, viz. that any two of tne straight
lines df, fo, o h, must be greater than tne third. For who
Ib so dull, though only beginning to learn the elements, as not
to perceive that the circle described from the centre f, fig. 22,
at the distance fd, must meet f h betwixt f and h, because pd
is less than fh ; and that for the like reason, the circle de-
sribed from the centre e, at the distance o h, must meet d q
betwixt n and o; and that these circles must meet one another,
because f d and o h are together greater than 10?" Forsee-
ing, however, notwithstanding his predecessor's remarks just
cited, that some learners mignt be so dull as not to perceive
what seems so clear to a geometer, Dr. Thomson has very
properly inserted the following paragraph in his construction,
after the words "another circle hlk;" and to this insertion all
beginners would do well to take heed :

. " Now, because (hyp-) f b is greater than f d, the circum-
ference of the circle dxl will cut f k between f and h ; and
therefore, the circle krl cannot be wholly within the circle
p x l. In like manner, because (hyp.) d o is greater than o h,
the circle dxl cannot lie wholly within tne circle x h j„
Neither can the circles lie wholly without each other, since
[hyp.) v f and o h are together greater than pp. The circles
must, therefore, intersect each other ; let them intersect in
the point l ."

EXERC18E I. TO PRO*. XXII.
To make a triangle equal to a given triangle.
Consider the three sides of the given triangle, as three given
Straight lines of which any two are greater than the third,
Prop. XX., and by the preceding proposition, construct a
triangle of which the three sides sbiU be equal to these three
given straight lines. By Prop. VII I. U is plain that the angle
Contained by any two sides of the one triangle is equal to the
angle contained by the two sides equal to them of the other ;
md by Prop. IV. that the two triangles are equal to each
other in all respects. Wherefore, a triangle haa been con-
structed equal to the given triangle. Q. & F. *

* This oxerc'iM was solved to q. L. Hadtold, $pHon-le-Moocs ;
%. Pbwolb, Glasgow ; T. fcococx, Greet warier ; J. H. I^bbwo^b.
ftllddleton ; and B. J. BmBMKVii, Carl We.

266

THE POPULAK EDUCATOR.

Fig. S3.

EXERCISE II. TO PBOP. XXII.
7b make a rectilineal Hgure equal to a given rectilineal figure.

Divide the given rectilineal figure into triangles, by draw-
ing straight lines from one of its angular points to every other
angular point in the figure, except the two angular points
adjacent to the assumed one. Then, the given rectilinear
figure will be divided into as many triangles as the figure has
sides, wanting two. Now, by the preceding exercise construct,
at any assumed point, a series of triangles contiguous to each
other, and such that each of them shall be equal in succession
to the triangles into which the given rectilineal figure has been
divided. Then, it is plain, by Axiom II. that the figure con-
structed of this series of triangles, shall be equal to the given
rectilineal figure in all respects, viz. in sides, angles, and area.
Wherefore, a rectilineal figure has been constructed equal to
the given rectilineal figure. Q. E. F. #

PROPOSITION XXIII.— PROBLEM.

At a given point in a given straight line, to make a rectilineal

angle equal to a given rectilineal angle.

In fig. 23, let a b be the given straight line, a the given point in
it, and dob the given rectilineal
angle. It is required to make
an angle at the given point a in
the given straight line a b, that
shall be equal to the given recti-
lineal angle dci.

In cd and c b, take any points
n and b, and join d e. Upon the
straight line a b make (I. 22) the
triangle afo, the sides of which
shall be equal to the three straight
lines c d, d b, and b c, that is, a v
equal to c d, a o to c e, and fo to d b,
equal to the angle dob.

Because the two sides pa and a o are equal to the two sides
wc and cb, each to each, and the base fo to the base db.
Therefore the angle fag is equal (I. 8) to the angle dcb.
Wherefore at the given point a, in the given straight line a b,
the angle fao is made equal to the given rectilineal angle
d c b. Q. E. F.

Scholium.— It is evident that upon the other side of the
straight line a b, another angle might be made equal to the
given angle dob; and that thus an angle might be doubled.

EXERC18E TO PROPOSITION XXIII.
At a given point in a given straight line, to make an angle equal to

the supplement of a given angle ; also, to make an angle equal

to the complement of a given angle.
First : Produce one of the legs of the given angle, and by
the preceding proposition, make an angle equal to the angle
contained by the other leg and the part of the line produced ;
but this angle is the supplement of the given angle. Where-
fore, an angle has been made equal to the supplement of the
given angle.

^Secondly ; From the vertex of the given angle, by Prop.
XII., draw a perpendicular to one of its legs, and by the pre-
ceding proposition, make an angle equal to the angle contained
by this perpendicular and the other leg ; but this angle is the
complement of the given angle ; wherefore,, an angle has been
made equal to the complement of the given angle. Q. E. F.f

The angle fao is

La liberalite* consiste moins a donner beauooup qu' a donner a
propos.— LaBruyere.

Pour juger de la beauie d'un ouvrage, il suffltde le considerer en
lul-meme ; mais pour juger du mettte de l'auteur, il faut le com*
parer * son Steele.— FonteneUe.

Un bon livre est le inetileur des amis. Vous vous entretenei
agreablement avec lui lorsque vous n'aves pas un ami a qui vous
ptiissies vous fi-r. II ne revHe pas vos secrets, et il vous enseignc
la .*«. esse.— Maxmves dm Onentsmx.

• This exercise was solved by E. J. Brsmmbb, Carlisle ; J. H.
Eastwood, Mtddleton ; C L. Hadfield, Bolton-le-Moors ; T. Bo*
©ocx, Great Warley ; and Q. Pkihole, Glasgow.

t This exercise was solved by Q. Pbinole, Glasgow; E. J. Bbbm
kbb, Carlisle; and others.

ANSWERS TO CORRESPONDENTS.

J. T. E. (Nottingham): We thank the correspondent for his suggestions.
There is much want of a good Italian dictionary, and the subject will
receive due consideration. With respect to the use of the Italian definite
article, our intelligent correspondent will have the goodness to consider
that it is impossible to prepare illustrative exercises where some points of
the grammar, however few, should not be anUcipated in order to relieve
them from dulness. To explain all these points as they occur would over-
load the grammar with notes. 8ome general hints have been thrown oat
In the course of the lessons, but it is impossible to lay down a short rule on
the subject, which will answer our correspondent's question as to the use of
the article, there being too many points, delicacies and exceptions. all of which
will be fully (practically as well as philosophically), explained in special
lessons. A careful pupil, like our correspondent, will not fail to recur to
previous exercises, and test and correct them by the progressive rules as they
are stated. With regard to the special sentence mentioned, it may be briefly
stated that the article la ought to be placed before temperansa, though aq
abstract noun ; because temperance is here expressly stated to be an indivi-
dual possession— il tesoro del savio.

8. T. (Chester): Personal pronouns are indispensable before English verba,
- - - • - fad

for want of inflections, e. g. have is the Identical word in the first .
singular, and in the first, second, and third persons plural. Our correspon-
dent must have remarked that thi« is not the case in the Italian auxiliary
avert, to have, and on lb is account personal pronouns before Italian verbs
are, generally speaking, not Indispensable, though used where stress, con-
trast, distinctness, &e. demand. With respect to the use of the article
before possessive pronouns, it is a peculiarity of Italian that it Is more fre-
quently used than omitted in such cases, and the possessive pronouns often
are not considered (as in English) sufficient to determine the noun. The
use and the omission of the article before possessive pronouns will be
explained hereafter. It was stated In a note that the colloquial exercises
alluded to by our correspondent are anticipatory ones, and it is a useful
exercise to the student to apply his understanding to find out grammatical
rules for himself.

J. 8. 8. We are glad that he is about to purchase all the back numbers
of the P. E., and we wish that thousands would do the same ; we are cer-
tain that they would find their advantage in it. They may be had through
any bookseller at the regular published price; not otherwise.— A Masts*
key (Stoke-Newington) has made some very good poetical lines, but we wish
that he could sprll and write better.

J. W. Moxlby (Hoxne), must learn to spell and write English, before he
can give advice about "disease and essences."— A Cornish Bcbsgbibbb;
Brande's Chemistry.— Adiamtum (Basingstoke) : The Ferns are principally
distinguished by the shape and sise of their fronds, and the position of the
fructification in them. A strong magnifying glass Is necessary to distinguish
many varieties. The specimen sent is one of the Asplenia or Spleen-wort.
—A Lbarnbr (Hackney) : No general rule for aspirating the fetter* can
be given.— J. Smith ( Theobald's Road): See P. E. vol. i. p. 281, col. 1.
The Lessons in English are finished.

Un Com m is (Manchester) : We can't give you the information you require,
as we have not been in France since the reign of Louis XVIII.— T. BaiM
(Perthshire): Snowball's Trigonometry.— J. C. Fieldbn (Blackburn)
wishes to know something about Zerah Colburn, the American Calculating
Boy, who could in a few minutes multiply mentally a row of 6 or 7 figures
by a row of the same number of figures: as he sajs he can do the same in 1
minute and 15 seconds correctly, the sum to be set by any person.

W. A. O. (N. Folgate) : The remaining sections are omitted in the P. E-
but will be found in Cassell's «« Lessons in French,** Part II., so far reprinted
from the P. E.— Aw Esquimaux (London) should drink cod-liver oil ; he wfll
then grow much less than twelve inches, the next Jour years ; his latitude will
exceed his longitude.— Colombus( Manchester) : The Map of England and
Wales Is contained in No. 66 of the P. E. The cheapest drawing instruments
are to be had at the*' Society of Arts," Adelphi, London.

LITERARY NOTICES.

JOHN CA89ELL'S LATIN WORK8.

The Latin Dictionary, in Numbers at 3d. and Parts Is. each, by Dr.
Beard, is now in course of publicati n, 3 numbers are ready, andnhe 1st Part
will be ready with the Magaslnes for February.

" A Grammar of the Latin Language, by Professors E. A. Andrews and
8. Stoddard." This Grammar has been put to the test of experience, and
pronounced by competent judges, who have brought it into use, to be a
production of superior merit.

"CasseWs First Lessons in Latin:* This consists of a short and easy
introduction to the Latin language, with Grammar, Exercise, and Vocabu-
lary. It deserves the special notice of conductors of schools, masters under
Government inspection, pupil teachers, self-instructing students, and all to
whom cheapness, as well as excellence, is an object.

*' Lessons in Latin, by Dr. J. R. Beard.'' This volume contains an
Elementary Grammar of the Latin language, in a series of easy and progres-
sive lessons ; also, numerous Exercises for Translation from English into
Latin, and Latin into English. For the benefit of those who are desirous of
learning this language without a master, John Cassell has also published •
Key to the above-mentioned Exercises, which, as well as the Mesons and
Exercises, is by Dr. Beard.

CasseWs Classical Library, Vols. 1 and 3, containing Latin Exercises and
a Latin Reader, are both now ready.

EaaATA.

Vol. iii., p. 877. English-Greek, line 4, for plays read edu c ate* ', voL iv„p.
16l,Greek-English,line7 formatter read are %dle; English-Greek, lines,
for OfMKOve-i vend ommcoitcu, for BXaarvovsri read BAoasvoawisv

Hbnxy G.' D. is partly right and partly wrong; the above will oorreet
what is really incorrect

NATURAL PHILOSOPHY.

257

ON PHYSICS OR NATURAL PHILOSOPHY.

No. xvni.

(Qmtinued from page 244).
THE ATMOSPHERE.

Amount of Atmospheric Pressure. — From the height at which
the mercury becomes stationary in the Torricellian tube, at a
mean state of the atmosphere, we can determine the amount of
its pressure, in pounds avoirdupois, on a given surface. As
the height is usually measured in inches, we shall fiwt find the
pressure of the atmosphere on a square inch. Now, supposing
the area of the internal section of the tube to be a square inch,
it is plain, by the rule for measuring the solid content of a
cylinder, that the area of the base, one square inch, multiplied
by the altitude, 30 inches, gives the solid content 30 cubic
inches. Again, to find the weight of 30 cubic inches of mer-
cury, we have this proportion, by the method explained at the
end of Lesson XI., p. 158, viz., 1,728 cubic inches : 30 cubic
inches : : 13,600 ounces : 236 ounces ; so that 236 ounces, or
14f lbs. avoirdupois, is the weight which represents the pres-
sure of the atmosphere on every square inch of surface. In
this calculation, we have taken the specific gravity of mercury
at 13 6; consequently, by multiplying this number by 1,000,
we have, according to the rule above cited, 13,600 ounces for
the weight of a cubic foot of mercury.

The problem to find the atmospheric pressure on any given
area at the surface of the earth, is now solved; for we have
only to find the number of square inches which that area con-
tains, and multiply it by 14} lbs., the measure of its pressure
on a square inch ; the product will be the number of pounds
representing the pressure of the atmosphere on the whole area.
According to some writers, the surface of the human body,
taken of an ordinary stature and condition, contains 2,325
square inches ; hence the mean pressure of the atmosphere
supported by every man, on an average, is 34,294 lbs., or up-
wards of 15 tons weight ! It would seem that, under such a
Sressure as this, we should be crushed to atoms ; but our
odies resist its action by the reaction of the elastic fluids
which it contains. Our limbs, also, suffer no pain in moving
under this pressure, because, acting as it does in all directions,
it supports us in every position, by pressures equal and con-
trary, and which, therefore, balance each other. Indeed, on
those days when the atmospherio pressure is the lightest, we
suffer a species of uneasiness which makes us say the " weather
is heavy, ' an expression exactly the contrary of what should
be said.

THE BAR^klETER.

Cistern- Barometer, — Instruments which are employed to mea-
sure the weight or pressure of the atmosphere are called
barometers (from the Greek baros, weight, and raetron, mea-
sure). Barometers are of two kinds ; those with mercury, and
those without mercury. Mercurial barometers are of three
kinds: cup-barometers, siphon-barometers, and dial-baro-
meters.

The cup or cistern barometer is composed of a straight glass
tube, of about thirty-four inches long, filled with mercury and
immersed in a cup or cistern containing the same liquid. Such,
in fact, is the apparatus already described under the name of
the Torricellian tube (fig. 69). With the view of rendering
the barometer more portable, and the variations of level in
the cup leas apparent, when the mercury rises or falls in the
tube, the form of the cup has been considerably varied. In
fig. 71, a barometer of this kind is shown, which can easily
be carried from place to place. The cup or cistern has two
divisions, of which the largest is cemented to the tube,
and communicates with the atmosphere only by a small
opening, having a lid made of leather, which is shown on
the top of the cistern near the tube. Below the first com-
partment of the cistern, there is a smaller one, completely
full of mercury, the former being only partially filled.
These two compartments are connected by a neck, or con-
tracted part, in which the lower end of the barometrie tube
la inserted. This end does not completely fill up the passage
between the two compartments ; but it is constructed so as

TOL. IT.

to admit of a space between the sides of the cistern and those
of the tube, so narrow, that its capillary action prevents the
escape of the mercury from the small compari-
ng, 71 ment, when the barometer is inclined or in-
verted; consequently, in all positions, the
tapering point of the tube is immersed in the
mercury, and thus the air is completely ex-
cluded from it.

This instrument, like all others of the same
construction, is incapable of marking the varia-
tions in the barometric column with precision,
because that the zero of the scale does not in-
variably correspond to the level of the mer-
cury in the cistern. In fact, the pressure of the
atmosphere being variable, this level varies
whenever the pressure increases or diminishes ;
for then a certain quantity of the mercury
passes either from the cistern into the tube, or
from the tube into the cistern.: so that, in
most cases, the graduation of the scale does not
indicate the true height of the barometer. The
manner in which this cause of error may be
avoided in the construction of a barometer will
soon be explained.

The height of the barometer is the difference
between the level of the mercury in the tube
and the level of the mercury in the cistern.
As the pressure with which the mercury acts
at the bottom of the tube is, according to the
laws of fluids, independent of the form and
the diameter of the tube, provided there be no ■
capillary action, the height of the barometer is
also independent of the same circumstances ;
but the height of barometers made of different
liquids is in the inverse ratio of the density of
the liquid. In the mercurial barometer, the
mean height at the level of the sea, is 30
inches; in the water barometer, the mean
height is 34 feet.

Construction of the Barometer.— In the con-
struction of barometers, mercury has been
specially selected as the most convenient
liquid, because of its having the greatest
density, and consequently the least height in
the tube ; besides this, it has the property of
being the least volatile of liquids, and it does
not wet the glass of which the instrument is made. It is of
great importance that the mercury should be pure and free
from oxidation ; otherwise, it adheres to the glass and soils
it. Moreover, if it be impure, its density is diminished, and
the height of the barometer is too great.

In every barometer, the vacuum at the top of the tube (figs.
70 and 71), which is called the barometrie chamber, or vaeuumof
Torrieelli, must be completely freed from air and watery
vapour; otherwise these fluids would, by their clastic force,
lower the mercurial column. This object is attained by
first pouring into the tube a part of the mercury with
which it is to be filled, and heating it to ebullition ; this
being allowed to cool, the rest of the mercury is then poured
in and heated in the same manner, until the tube is full. Thus
the air and humidity which adhere to the sides of the tube
are expelled by the vapour of the mercury. In order to ascer-
tain whether a barometer has been freed from air and humidity,
give it a gentle inclination, and if it produces a dry and metal-
lic sound, by the mercury striking against the top of the tube,
it has been properly constructed ; but if there be any air or
humidity in the tube, the sound will be deadened, and the
instrument inaccurate in its indications.

The Portable Barometer. — Another form of the cistern baro-
meter has been constructed by M. Fortin, but it differs
considerably from the preceding one. The bottom of the
cistern is made of deer-skiu, and it can be raised or lowered by
means oi a screw placed below it ; thus yielding the double
advantage of obtaining a constant level in the cistern, and of
rendering the instrument more portable. For the purpose of
travelling, it is sufficient to screw up the bag of deer-skin con-
taining the mercury, until the cistern and the tube are com-
i pletely filled with it ; the barometer may then be placed in any

2*8

THE POPULAR EDUCATOR.

position, even an inverted one, without the danger of breaking
the tube by the shaking of the mercury.
This instrument is shown at fig. 72, where the tube is en-

Flf. 72.

Fijr. 73.

cH-ed in a brass case for safety. In this case, there are two
loipitudinal slits exactly opposite to each other, through which
thi level of the mercury in the tube may be seen. On the
case, there is placed a graduated scale, with divisions to the
25 th part of an inch. A slide a, moved by the hand, and
furnished with a vernier, gives the height of the barometer to
the 250th part of an inch. In fig. 73, the parts of the cistern
are shown upon a larger scale ; it is constructed in the form of
a glass cylinder, in order to show the level of the mercury in
it. The bottom of this cylinder is closed by a piece of deer-
skin b d, which is raised or lowered by the screw c.

This screw works in the bottom of a brass cylinder, to which
the glass one containing the mercury is internally fixed so as
to be completely protected from injury. In the top of the
cistern there is fixed a small ivory rod a, the point of which
corresponds exactly to the zero of a graduated scale, with
divisions to the 25th part of an inch, marked on the case. In
using this instrument, care must be taken, at every observation,
to bring the level of the mercury in the cistern to this point,
by turning the screw o either way, as occasion may require.
In this manner, the distance a o, fig. 72, represents exactly the
height of the barometer. '

The Siphon Barometer.— The siphon barometer is composed
of a glass tube bent into two unequal branches. Of these, the
greater, which is closed at the top, is filled with mercury,
like the cistern barometer; and the smaller, which is open,
takes the place of the cistern. The difference between the
level of the mercury in these two branches is the height of the
barometer. Jn fig. 74 ia shown the siphon barometer, as
modified by M Gay-Lussac, who, in order to render it portable,
and prevent the admmsion of air into the tube, united the two
branches by a capillary tube. When this instrument is
inverted, the tube, in consequence of the capillary joint,
remains always full, and the air cannot find its way into the

Fig. 74.

greater branch. Still, if it be subjected to too sudden a

shock, the column of mercury in the tube may be divided,

and the air allowed to gain admission. To obviate this incon-
venience, M. Bunten has adopted the modification shown

in fig. 75. The capillary tube, instead of being

fastened to the greater branch, is fixed to a

tube x, of larger diameter, into which that

branch enters in the form of a tapering point.

By this arrangement, if air-bubbles pass into

the capillary tube, they cannot enter into the

tapering point of the tube, but must lodge in x,

the highest part of the tube of larger diameter,

as shown in figure; there they cannot affect

the operation of the instrument, as the vacuum

always exists at the top of this part.

In the barometer of Oay-Lussac, the short

branch is closed at its upper extremity, and

there is only a small lateral opening at c, which

communicates with the atmosphere, and allows

its pressure to take place. As to the measure

of tne height, this is effected by means of two

scales, having their common zero at o, near

the middle of the greater branch, and graduated

in contrary directions, the one from o towards

x, and the other from o towards d, on two

brass rules parallel to the barometric tube.

Two verniers are made to slide on the scales in

such a manner as to indicate the number of

25ths of an inch, and tenth parts of the same,

contained between o and a, and o and b. The

sum of the two numbers thus obtained will be

the whole height a b of the barometer. In fig.

74, the barometer of Gay-Lussac is represented

as fixed on a mahogany board for the pur-
poses of demonstration ; but for travelling pur-
poses, it is enclosed in a brass case, exactly

like that of the portable barometer, only

wanting the cistern.

Correction of the Height. — In cistern baro-
meters, there is always a certain depression

in the height, arising from capillary action.

In order to correct this error, we must know

the interior diameter of the barometric tube,

and then, by means of the table given in

Lesson XIV., p. 204, we find the correction

which must always be added to the observed

height. In the barometer of Oay-Lussac, this

correction is avoided by making the two branches a and b

of the same diameter ; for tjyn the depressions at a and b
being equal, the column a b preserves its
true length.

In all- observations made with the barometer,
whether of the cistern or siphon construction,
the temperature must be taken into considera-
tion. For, since mercury expands or contracts
by variations in the temperature, its density
changes, and consequently its height ; because
this height, as before remarked, is in the in-
verse ratio of the density of the liquid con-
tained in the tube ; hence, for different atmos-
pheric pressures, we might have the same
height in the barometer. It is important,
therefore, at every observation, always to
compare the height with that which it would
be at a fixed ana invariable temperature. This
being entirely arbitrary, we may adopt the
temperature of freezing, or 32° Fahrenheit.

The method of making this correction will be explained when

we treat of the subject of heat. For the purpose of ascertaining

the temperature of the mercury, a thermometer is placed near

the tube, as shown in figs. 71 and 74. By a very simple

calculation, the height of the barometer can be referred to

zero ; for it is only necessary to employ tables of correction

which have been constructed for this purpose.

Variation in the Height of the Barometer. — When observa-
tions are made on the barometer during several successive'
days, it is found that its height varies in every place, not only
day after day, but even during one and the same day. The

Fig. 7r>.

NATURAL PHILOSOPHY.

mnp Htuie of the variation* that is, the mean difference between
the greatest and the least height, is not always the same. It
increases from the equator to the poles. The greatest varia-
tions, except in extraordinary oases, are about a quarter of an
inch at the equator; 1$ inch at the tropic of Cancer; If
inches in latitude 46°, or about the mean latitude of France ;
and 2} inches at 25° from the pole, or in latitude 66° N.
Moreover, the greatest variations occur in winter.

The mom diurnal height of the barometer is found by taking
the height every hour for 24 hours, and dividing the sum of these
heights by 24. M. Ramond has observed that, in France, the
height of the barometer at noon is almost exactly the same as the
mean diurnal height.

The moan monthly height is found by adding the mean diurnal
heights taken during a month, or rather during 30 ■ucoesiive days,
and dividing their sum by 30.

Tho moan annual height is found by adding the mean diurnal
heights taken during a whole year of 865 days, and dividing by

At the equator the mean annual height, at the level of the sea,
is 20-84 inches. It increases between the equator and a certain
limit, and reaches, between the latitudes of 30° and 40°, a maxi-
mum of 30 04 inches. It decreases in hither latitudes, and at
Pari* it is only 29*80 inches. The general mean height, at the
level of the sea, appears to be 29*96 inches. The mean monthly
height is greater in winter than in summer ; and this arises from
the coldness of the atmosphere.

In the height of the barometer, two kinds of variations are
observable : 1st, the accidental variations, which present no regu-
larity in their occurrence, and which depend on the seasons, the
direction of the winds, and the geographical position of the place ;
these are specially observed between the latitudes of 40° and 50°.
2nd, the diurnal variations, ' which are periodically produced at
certain hours of the day.

At the equator and in the inter-tropical regions, no accidental
variations are observed; but the diurnal variation take place
with such regularity that a barometer might be used as a sort of
dock. After midday the barometer falls till about 4 p. m. when
it reaches a minimum ; then it rises and reaches a maximum
about 10 p. m. Again it falls, reaches a second minimum about
4 a. m. and a second maximum about 10 a. m.

In the temperate sones, there are also diurnal variations ; but
they are more difficult to determine than at the equator, because
they are mingled with accidental variations. The hours of the
maxima and the minima of the diurnal variations appear to
be the same in all climates, and in any latitude ; but they vary a
little with the seasons.

Cause of the Variations of the Barometer, — In general it is
observed that the motions of the barometer take place in a contrary
direction to those of the thermometer ; that is, when the tempera-
ture rises the barometer falls, and vice versa. This fact indicates that
the variations of the barometer, in a given place, arise from the
expansions or contractions of the air in that place, and consequently
from changes in its density. If the temperature of the air were
constant and uniform, throughout the whole extent of the atmo-
sphere, no current would be produced in its interior ; and the
atmospherio pressure, at the same hoight, would be invariable in
every place. But when a certain [region of the atmosphere is
heated more than those in its vicinity, the expanded air rises in
consequence of its specific lightness, and flows through the higher
regions of the atmosphere ; whence it follows that the pressure
de cr eas es and the barometer falls. The same effect would be pro-
duced, if any region of the atmosphere preserved a given tempera-
ture, and those in its vicinity were cooled down from that tem-
perature ; for then the air of the former would still rise in conse-
quence of its less density. It also generally happens that an
e xtr a ord inary fall of the barometer at any place on the globe, is
compensated by a corresponding elevation at another place. As
to the diurnal variations, they seem to arise from the expansions
and contractions periodically produced in the atmosphere, by the
calorino action of the sun's rays during the revolution of the
earth on its axis.

Relation between the Barometer and the Weather— It is observed
that, in our climate, the barometer commonly stands at the height of
30 inches', that it falls below this point when there is rain, snow,
wind, or storm ; and that, when for a certain number of daya
the barometer has stood at 30 inches, there are, at a mean, as
many days of fine weather as there were days of rain. Accord-

ing to this coincidenee between the height of the barometer and
the state of the weather, the following indications have bee©
marked on the scale of the barometer, above and below the
standard point.

Height. State of the Weather.

28*0 inches stormy.

28'5 „ very rainy, or snowy.

29*0 „ rainy or windy.

29*5 „ changeable.

300 „ folr, or frosty.

30*6 „ settled fair, or frosty.

310 „ very dry, or hard frost.

In consulting the barometer in reference to the changes of the
weather, it must not be forgotten that this instrument is only
intended to measure the weight of the air, and that it only rises
and falls as this weight increases or diminishes. Now although
the changes of the weather most frequently take place at the
same time-with the variations in the pressure of the stmosphero,
it does not follow that they are invariably connected. The winds
which come to Europe from the south-west, being always the
warmest, and consequently the lightest, cause the barometer to
fall; but as they are at the same time charged with watery
vapour by traversing the ocean, they also bring rain. The winds
which come to it from the north and the north-west, being on
the contrary, the coldest, and consequently the densest, cause the
barometer to rise ; but as they come across vast continents to «>•• ■
climates, they are dry or freed from watery vapour, and ?•
generally accompanied with a clear and serene aky.

The warm winds of the south-west tend to increase the pressure
of the atmosphere by the weight and tension of the vapour which
they contain ; but at the same time they tend to diminish it by
their expansion. The latter cause being the most powerful, the
ultimate result is, that owing to the elevation of the temperature,
the winds ia oar climate cause the barometer to fall. At the

Fig. 76.

mouth of the river De La Plata, the barometer rises higher in
consequence of the winds blowing from the Atlantic on the east,
than it does from those blowing from the land on the west, because
the temperature of the latter is more elevated.

When the barometer slowly rises or falls, that is during two Of
three days, towards the point denoting fine weather or that denft*-

260

THE POPULAR EDUCATOR.

ing rain, it follows, from a great number of observation*, that the
indications of this instrument are then extremely probable. As
to the sudden variations, either in' the one direction or in the other,
they indicate bad or stormy weather. If to these considerations
be added the observations on the direction of the winds and the
temperature of the air, indications may be drawn from the baro-
meter, which are very useful for agricultural purposes. But it
must be remarked that the table showing the relation between
the height of the column and the state of the weather is the result
of old and numerous observations in some particular locality ; and
that it is not adapted for every country in the world, or even for
every place in the same country. In every country, the indica-
tions of the barometer are greatly modified by the geographical
position of the place, and this must always be taken into account
in the accurate construction of such instruments.

The Wheel Barometer, or Weather Glass.— As an elegant piece
.of household furniture, and not as a philosophical instrument, the
wheel barometer is specially intended to indicate good or bad
weather ! It is sometimes called the dial barometer, because it is
furnished with a dial and index like a clock, see fig. 76. This
instrument is merely a siphon barometer furnished with a
mechanism which is put in motion by the rising and falling of the
mercury, see fig. 76.

on two circular springs d. These springs, pressing upwards, act
upon the lever p, and oppose the pressure on the part m. Now,
suppose that the atmospheric pressure increases, the ton m is
pressed down, the lever p is lowered and transmits its motion by
the piece k to the lever b, and to the plate a which presses on the
springs d. But this plate carries an arm which rests on a rod s ;
and this rod by means of a bent lever h, communicates the motion
to a chain o wound on the axis of an index c; and thus the chain
conveys its motion to the index. Under the index is fixed a dial,
fig. 78, which is experimentally graduated so that its in d i c atio n s
may agree with the barometers of MM. Fontin and Gay-Lussac'
The aneroid barometer is very sensible and veryportable ; but
the number of pieces in it is very considerable. When we come
to treat of the manometer, a barometer of new construction, and
without mercury, will fall under our notice.

As the barometers we have described are chiefly of French con-
struction, the scales in our engravings have been marked with the
initials of the words used by the makers of these instruments, and
with their graduations in millimetres, a millimetre being '039371
of an inch, or very nearly one-twenty-fifth part of an inch.
Accordingly, we give below a table of the initials engraven on
these instruments, the French words for which they stand, and
the corresponding English words; the number of millimetres

Kg.

Fig. 78.

In this mechanism a pulley o is fastened to the axis of the
index, and over this pulley a cord passes, carrying a weight p at
one extremity and at the other extremity an iron float, a little
heavier than the weight; this float rests on the mercury in the
smaller branch of the barometric tube. If tho atmospheric pres-
sure increases, the level of the mercery falls in this branch, and
the float descends and moves the pulley and the index from left to
right-. The contrary motion takes place when the pressure
diminishes, because then the mercury rises in the smaller branch
of the tube, and causes the float to rise with it. If the instru-
ment has been carefully constructed, the index will point to the
words changeable t rainy y fair weather, &c. when the barometer
takes the heights corresponding to these indications ; but this is
so seldom the case in the instruments brought to the market,
that they can only be looked upon as pretty philosophical
t»ys.

The Aneroid Barometer. — A new kind of barometer, in which
no mercury is employed, has attracted notice for some years past,
known under the name of the aneroid barometer (from the Greek,
signifying a Liquidless Barometer) . This instrument is constructed
by M. Vidi of Paris, and was originally suggested by M. Conte\
a learned member of the French expedition into Egypt. The
parts of this instrument are shown in fig. 77, and in fig. 78 ; the
whole is represented.as enclosed in a case with a dial, its diameter
being only about 3* inches. The principal part of this barometer
is a cylindricreservoir m, made of brass, and having the top very
thin and flexible. A* vacuum is made in this reservoir, so that
the atmospheric pressure tends always to push in the top part m.
But upon this top are fixed two uprights s, which, by means of a
connecting bar, press on a lever p t intended to balance the pressure
upon m. For this purpose, this lever is fixed to a bar x, which
oscillates freely on two pivots placed at its extremities. By means
of a lever b, this bar x is connected with a plate a, which

on their scales, and the corresponding number of English
inches.

Initials. French Names. English Names. Millimetres.

Tempete,

O.P.

Grande pluie,

Pluie, ou vent,

Variable,

B. T.

Beau temps,

B.F.

Beau fixe,

T. 8.

Tree sec,

English in,

28-78
2914
29-49
29-84
30*20
30 55
30-91

8tormy; 731

Very rainy ; 740
Rainy, or windy; 749

Changeable ; 758

Fair Weather; 767

Settled fair; 776

Very dry; 785

Measurement of Heights by the Barometer.— The pressure of the
atmosphere decreasing in proportion to the elevation of the place
to which the barometer is taken, the height of the barometer
follows the same law, and thus it becomes an instrument for
determining the altitudes of mountains. It was, in mot, soon
observed that when the altitudes of the places of observation
increased in arithmetical progression, the densities or
of the atmosphere decreased in a geometrical
following approximate table of the d en si t ies of
heights above the surface of the earth, will give
principle.

Heights.
1

3* miles *

10* I

14
17*
21
&c.
It has been remarked that, according to this approximatfea

LESSONS IN CHEMISTRY.

261

to the law of progression in the density, or rather in the rarity of
the atmosphere, exhibited in this table, it might be shown that a
cubic inch of the air we breathe at the surface of the earth, would,
at the height of 500 mile* above it, fill a sphere equal in diameter
to the orbit of Saturn ; that is, on the supposition that the power I
of expansion in the sir were not counteracted by intense refrige-
ration, or by the action of gravity on its attenuated particles.

For measuring the heights of mountains by the barometer,
Laplace has given a formula, which was modified by M. Biot into
the following :

d = 60346 (I +.002837 cos *) \ l + 1000 J^H'

in which d denotes the vertical distance, in English feet, between
the two places whose difference of level is required; H,*he height
of the barometer at the lower station, and h the height at the
upper station ; t and t denote the corresponding temperatures of
the sir on the centigrade thermometer, at the stations respectively ;
and 0, denotes the latitude of the place.

M. Oltmans has constructed tables by means of which this
formula can be easily calculated in metre* ; the only difference
being in the factor 60346 feet, which in the original formula is
18393 metres. These tables, with the manner of using them, are
to be found in the "Annuaires des Bureau des Longitudes."
The student will find a similar formula with an example worked,
in «* Miller's; Hydrostatics." If the altitude te be determined by
the barometer be not very great, one observer alone can perform
the experiment ; but if the altitude be very considerable, and
requires a long time between the observations in order to complete
the ascent, the pressure of the atmosphere may vary, and it will
then be necessary to have two good barometers. One of the
observers with one barometer then remains at the foot of the
mountain, while the other observer ascends to the top with the
other. At a given hour, each observes his own barometer, and
thus the true height of the column at each place, the true differ-
ence of the columns, and consequently the true difference of level
between the places are accurately obtained.

LESSONS IN CHEMISTRY.— No. XVII.

esJring, however, this acid seldom comes before the notice of the
chemist ; moreover its compounds are characterised by their dif-
ficult solubility, hence it may be considered as " hors de combat."

Applying the facts just deduced, remembering that the grand
combustion-supporting function is strongly developed in chlorate
of potash — remembering that nitrate of potash (nitre) is a con-
gener of the former, and that it is an essential component of gun-
powder — you will now know, if you did not know before, the reason
why gunpowder burns when rammed into a gun from which all the
atmospheric air is excluded. Gunpowder carries within itself
i imbustibles — charcoal and sulphur, and a supporter of combustion,
oxygen (in the nitre) — hence it is totally independent of the aid
of atmospheric sir. Many gunsmiths are so ignorant of chemistry,
that they are not aware of the true conditions under which gun-
powder burns. Tou may sometimes see a little hole drilled in the
tide of a gun breech, the use of which, gunmakers will tell you,

to let in the air and promote the burning of the powder. This
U simply ridiculous.

In tne first place, the powder does not want air ; in the second
place, through this hole no air could enter, seeing that the expan-
sive force of the inflamed gunpowder is outwards. This little

lie facilitates the loading of guns — rifles especially, — and facili-
tates also the escape of foul air or vapours : beyond this it is of no
service whatever.

Seeing that nitre is a congener of ohlorate of potash, you may
perhaps ask whether it might be used instead of the chlorate for
- le purpose of yielding oxygen gas. Yes ; it sometimes (unmixed
With oxide of manganese) is used for this purpose ; but yielding
. p its gas with greater difficulty, it is less efficient. You perhaps
also ask, whether the chlorate might not be used instead of nitre

i a constituent of gunpowder ? Theoretically I might answer

es ; but practically, No. Gunpowder made with chlorate of potash
fax too explosive for safety. Not only would there be danger
Of explosion from the act of ramming, but the danger attendant on
the manufacture of such gunpowder on a large scale would be
frightful. The French tried the manufscture during the wars of
the great revolution, and are even said to have used chlorate gun-
powder in one of their campaigns ; but the frequent explosions
Which occurred at the powder-mills led to the final abandonment
of the process.

A very simple, though indirect, method of demonstrating the
I icility with which ohlorate of potash evolves its oxygen is as
follows. Powder two or three grains of the substance separately,

Resuming our consideration of oxygen, I shall require you to , , . ,. ., . , - . , . -,,

«jjnge ibip^w^A jndtwJbein/don., ?*™T?™?* ?^?%2^ r ^X^?^Z
to fill several eight ounce, or ounce and a half, bottles full of the
gas. We will proceed to use this gas very speedily. I wish,

however, before doing so, to direct your attention to certain
properties of chlorate of potash dependent upon the oxygen it
contains.

The most prominent characteristic of oxygen, as you are now
aware, is its property of supporting combustion ; the idea would
seem likely enough, then, that a substance containing so muoh
oxygen as does chlorate of potash, and delivering up this oxygen
so readily, should also be a powerful supporter of combustion
We shall see.

Dissolve some chlorate of potash in water ; dip into the solution
a piece of paper (blotting-paper is best) ; dry the paper, and bring
it into contact with flame or a red-hot coal. I do not wish th<
paper itself to burst into flame, but the contrary ; if therefore this
should occur, blow out the flame, leaving a mere ignited paper
edge. Remark now how curiously the ignition traverses tha
paper, which no longer burns as common paper. I dare say you
will recognise something like this phenomenon. You will say i
burns like touch-paper. Touch-paper indeed it is, of the best qua
Hty ; far better than you could have made with the ordinary agent
— saltpetre ; and now you may remember the following important
.fact: that " any substance capable of making touch-paper must con*
tain an acid which holds Jive atoms of oxygen. 1 * Therefore, know
ing this rule, it follows that chlorate of potash, if placed befor
you as an unknown substance for examination, would at once hav
been determined as containing one out of four acids.

Nitric \

Iodic J

Straining a point, we might admit a fifth acid, the li perchloric f*
containing no less than seven equivalents of oxygen ; practical

si piece of paper, by means of a feather or other soft body ; wrap
the mixture in a piece of paper, place the envelop on an anvil or
Other hard surface, and strike it smartly with a hammer. The
whole explodes with a violent report. Occasionally the experi-
ment is varied by rubbing a few grains of chlorate of potash and
an equal Quantity of sulphur sharply together in a mortar, by a
eries of sharp short strokes, or rather downward pushes, half
Stroke, half blow, when a series of explosions results. When per-
cussion guns first came into use, this mixture of sulphur and chlo-
rate of potash was employed as the material for charging caps;
but the result of its combustion was found to be so destructive to
the lock, that its employment was soon abandoned in favour of
the so-called anti-corrosive caps, in which fulminating mercury
takes the place of chlorate of potash and sulphur. We will now .
teturn to the consideration of gaseous oxygen.

If oxygen gas be so powerful a supporter of wood and other ordi-
nary combustibles, the supposition would appear likely, from d
priori reasoning, that bodies incombustible in atmospheric air, or
imperfectly combustible, should readily burn in this gas. I do
not know whether you will bo surprised to be informed that iron,
and indeed all metals without exception, are combustible. As
regards iron, you have often, I doubt not, witnessed its oombus-
tion when heated to whiteness in a smith's forge and rapidly
withdrawn, though probably you failed to reason on the bearings
of the phenomenon. We will now show how exceedingly com-
bustible is iron in oxygen gss. There is an old-established — a
conventional — a " lecturing " method of performing the combus-
tion of iron in oxygen gas, which I will describe further on. It
is well adapted for display in lecture-rooms and generally on the
large scale ; but it is not the best adapted to the requirements of
our little Dottles.

I shall modify the experiment as follows. Take a circular disc
of tin plate, fig. 1, large enough to cover the mouth of your oxygen
battle, and perforate this pipe centrally with a little hole, just

THE POPULAR KDUCATOE.

Urge enough to admit a needle tightly ; finally, stick the eye end
of the needle in a cork, so that an arrangement may result as fol-
lows ; finally, dip the extreme point of the needle in melted brim-
stone, and this part of our arrangement is complete.

Fif. l.

rig. s.

«H>

Now proceed as follows. Ignite tho brimstone at the point of
the needle, and plunge the latter into a bottle containing oxygen
gas, fig. 2. Theneedle will burn vividly, throwing off sparks in
all directions,. some of which, in all probability, will stick in the
glass, partially fusing it.

I repeat that the mode of operation here described is not the
most elegant, but it in the best adapted to the necessities of our
present apparatus. The usual method of performing the experi-
ment is by employing, as tho gas receiver, a jar of this kind,
placed to stand in a plate containing water, and covered with a
glass pane, fig. 3 ; using a helical or corkscrew-formed wire of this
kind, fig. 4. If you can procure some of these gas jars, well and

Fif. 3.

Fif. 4.

good, you may employ them in performing the experiments about
to be detailed ; if not, you must be content to use large-mouthed
bottles.

Experiment. — Bore a hole through a piece of charcoal;
nass through the hole a wire ; bend the wire into a sort of knot
underneath, and attach it above to a tin-plate disc and cork, as
represented in fig. 5. Ignite the charcoal ; plunge it into tho jar or
bottle, fig. 6 ; wait until the combustion has ceased ; then secure the
mouth of the jar or bottle with a glass pane. The charcoal will

Fig. 5.

Fi*. 6.

burn with extraordinary splendour, and the sole result of com-
bustion will hereafter be found to be a gas, invisible like oxygen,
bat totally dissimilar to it in every other characteristic.

Sxpsaiionrr. — For the performance of the sue...
perimentwe shall require^cn addition to the glass jar orl
cork, and metallic djsc, already described, tho following little instru-
ment, fig. 7, being a small copper ladle, secured by rivetting— not

Fig. 7.

soldering — at the point markod /. These instruments arc termed
by chemists deflagrating ladles, and serve the purpose of exposing
to the action of gases, liquids or fusible solids. We shall require
two of these ladles ; one for the purposo of igniting sulphur, tho
other for tho purposo of igniting phosphorus, in oxygen gap.

Ignition of Sulphur. -II aving put a little sulphur into one
ofi-thesc deflagrating ladle*, attached to a cork and disc in the
manner already described, ignite the sulphur by heating it in the
flame of a spirit-lamp, mien thoroughly ignited, dip it into a
jar or bottle containing oxygen. Remark the character of com-
bustion — the pale blue lambent flame, the small amount of light,
the gaseous nature of the result of combustion. When the sul-
phur has ceased to burn, cover the receiver or bottle with a glass
pane, and put it aside.

Experiment.— Combustion of Phosphorus in Oxygen Gas. —
I am about to mention certain details connected with the perform-
ance of this experiment, and you must attend to them implicitly,
otherwise your experiment will fail, and yourself, most likely,
will be severely burned. Pour a lump of phosphorus from the
water in which you will purchase it, into a plate of water ; cut off
a very little lump (not bigger than a pepper-corn) under water ;
remove the piece thus cut off, not with the finger and thumb, but
a pair of tweezers, scissors, or something of that sort ; dry it by
contact with blotting paper; put it into a deflagrating ladle;
ignite it by contact of a hot wire applied to its surface, not by a
flame applied underneath the ladle ; plunge it into a bottle or ajar
containing oxygen, and remark every peculiarity of the combus-
tion which ensues. Preserve tho results of this combustion, as
you have preserved the others. The examination of all these pro-
ducts shall be the subject of our next lesson.

LESSONS IN GEOLOGY.— No. XLIX.

By Thos. W. Jenkyn, D.D., F.R.G.S., F.G.S., &c.

CHAPTER V.

ON THE CLASSIFICATION OF ROCKS.

SECTION III.

ROCKS OP RECENT FORMATION.

The rocks which contain fossils, and which on that account are
distinguished by the name of foesiliferous rocks, hare been
divided bv geologists, generally, into three series. The lowest
contain the most ancient forms of animal existence! and
are therefore called palaeozoic (from vaXcuac, palaios, old,
and fan, zoe', life), that is, old-life rocks. The aeries rest-
ing upon the palaeozoic are called secondary rocks, or
mesozoic (from Micro?, mesos, middle, and £wi|, soe", life),
that is, middle-life rocks. The series resting on the mesozoic
arc called the tertiaries, so called because their beds contain a
third form of organic life. In the lowest and in the middle series,
all the imbedded fossils are remains of animals altogether extinct,
tn the third series, or the tertiaries, the lowest group of rocks
contains some extinct species and a few of existing species; a
higher group contains less extinct species and more of the present
race ; and in the highest group, there are extremely raw of the
ancient species, and a vast majority of the species which now lifiw

LESSONS IN GEQLOGY.

209

On these accounts, the tertiary aeries, according to the comparative 1. Peat Boos. Peat mosses are well known in all tho moun-
amounts of extinct and existing fossils which they contain, hare tainous districts of the north of Europe and America. They are
been called Eocene, Meiooene, and Pleiocene ; terms which, will divided into two distinct classes : first, immersed formations pro-
be explained in oar next lesson. All the tertiary beds contain duced by the accumulation of aquatic plants, such as reeds, sedges,
fossils of the present race of animals; but the group called the &c.; and secondly, the emerged formations, caused principally by
Newer Pleiocene by some, and Pleistocene by others, contains so the growth and decay of the plant called sphagnum, dome
much as 96 per cent of the present species, and is therefore called peat mosses lie frequently in highly inclined planes. Near Kiel, in
a rock of modbrn formation. Northern Germany, vast beds of peat show the two formations

But, in the order of superposition, there are series of rocks much superimposed, where the peat has first grown in a basin or hollow

higher and newer in geological sequence than the Pleistocene several feet deep, and when it has reached the surface of the

beds ; rocks which are characterised by having all their fossil water, the emerged formation has commenced. A third mode of

shells identical with the species that are now living. It is this peat growth has been observed in the Vosges, and in Denmark,

fact that distinguishes the lowest of these beds from the newer where, in deep, but small basins, the peat-forming plants have

pleiocene, or rather the pleistocene, whose deposits always contain begun to grow at the surface of the water, and the bajpn has

some proportion of an extinct species. It has hitherto been found become gradually filled by the immersion of the floating turf, and

difficult to coin a term or a phrase that shall properly and fully this continually thickened by the growth of new plants,

express the geological characteristics of these later groups of You may easily think that such abysses, concealed by verdure,

rocks. Some have called them Post Tertiary, others Post Pleiocene, have often proved dangerous to travellers and to cattle. Thee?

and some continental geologists have tried to introduce the name basins are filled with numerous bones and instruments of various

Quaternary, or the fourth series, a term which seems as admis- kinds, both anoient and modern, which give a clue to the different

sible as the word tertiary for the underlying rocks ; and in some epochs in their formation,

works they are called recent formations. 2. Deltas of Rivers. The streams and brooks which issue

It will answer all the purposes of this lesson, if we agree to from mountain sides are all charged with earthy particles, which

designate all the beds which contain the fossil remains of the they deposit in the beds of rivers as mud, gravel, and pebbles, and

existing races of plants and animals, by the term post pleisto- thus gradually form alluvial plains. If the force of streams be

cbnb rocks. This class of modern rocks comprehend not only strong, the current transports an immense quantity of detritus to

those strata which can be proved to have originated since the the mouths of rivers, where they form the accumulations of silt

creation of man, but also sedimentary beds of much greater and sand, called deltas. In these deltas are imbedded the leaves

extent and thickness, which contain no signs of man or his works, of plants, branches of trees, remains of animals, shells of fish,

but enclose remains of species of animals identical with races human bones, and works of art. Specimens of such formations

now living. It is true that in some of the lower beds of even ftre supplied by some of our rivers in England, especially the

these modern rocks we find the bones of anoient quadrupeds, such Mersey, the Dee, the Severn, and the Thames ; but they are pre-

as the mammoth, the mastodon, the megatherium, &c, species tented on a large scale by such rivers as the Nile of Egypt, the

that probably never co-existed with the human race ; nevertheless Ganges in India, and the Mississipi in North America,

the shells that are found fossil in these beds are the same as those To constitute a series of deposits a post pleistocene group,

of testacea now living.

POST PLEISTOCENE SERIES.

. The present period

or
Rocks now forming.

Submarine Deposits.
Deltas of Rivers.
Coral Reefs.
^ Deposits in Lakes.— Salt.
Peat Mosses.

Beds of Lava, and Volcanic Cones.
Sand Dunes.

it is not necessary that they should always be found superim-
posed upon the Tertiaries, for sometimes they may be found
resting on the most anoient rocks. In the annexed diagram,
a a represents rocks of the greatest antiquity, and d the ante-
historical deposits ; c, the rocks formed since the creation of
man, and b rocks that are now in the process of formation.

2. The historical

(Raised Beaches.
Shell Marl.
Submerged Forests.
Deposits ,m Caverns.
Beds of human remains

Fig. 1. Recent Deposits Resting upoti Ancient Rocks.

3 ' ^neriod*"^ 101 ^ 1 fLoess of the Rhine.

Rocks formed since J Jjf^ bott0m 8oil of India -

3. Submarine Deposits. You have already seen in the lessons

on the agency of running water, that rivers which deposit their

gravel and sand in deltas, carry their finest particles far into the

- x IIC x 1U bosom of the sea, where, after having been transported by currents

nresenfra^sof ] The Newer part of the Boulder forma- •** agitated by ;the waves, they 'finally settle down as a sediment

nlants andanimalfl li<m witn Erratics. on the deep and quiet floor of the ocean. Colonel Sabine, in his

p ' ^ calculations on the sediments carried down by the river Amazon

N. B. In the rocks of this ante-historical 'period, all the fossil * n South America, has shown that strata arc now formingin

shells are of the species now living ; they are destitute of regular deposits over great spaces of tho bed of the ocean. The

human remains ; and the bones of quadrupeds imbedded in system of dredging carried on by scientific men, uniformly shows

them are partly of extinct species. that the strata which are now deposited in the bed of the sea, are

It is right to I
post pleistocene rocks, biui« «» umhv w uy amuiiRJiiMnifc. in any w .. • , • A

work on Geology; and that it is made solely to iadSSe your ^comparatively quiet.

• -« ™ ' . * * - * J - * €M "^'* ,W zy™ Besides these rocks deposited mechanically in the sea by rivers,

it is well known that there are many beds now in the course of

•v that rmi will tiAt ft n j ♦»,;- ^.^sk.,*^.. ~* *u pebbly where the waters are much agitated, sandy where the

progress in the knowledge of this particular formation,
series is divided into three groups of rocks, via. rocks 1
now in the process of formation ; rocks that have been
since the existence of man ; and rocks that have been d^
since the creation of the present race of plants and animals'

I. ROCKS NOW IN THE COURSE OP FORMATION

This

At
beds
are now forming in the Mediterranean. On the shores of the Red
Sea a rock formation is now in progress, composed of sand, gravel,
corallines, fragments of older rocks, weed, pottery, and bits of
Tour attention has been already directed to the rocks that are wood washed up by the sea and cemented together by carbonate
now in the process of formation, in the lessons which have been of lime slightly coloured by oxide of iron.

given on the reproductive agency of fire, water, and wind, as 4. The Growth of Coral Rocks. Tho best modern instance
agents of change in tho crust of the earth. You are therefore of the formation of coral rocks is found in the Bermudas, and the
prepared for the statement that rocks are being formed in our own Bahamas. The coral reef in these districts consists of masses
day. of numerous species of madrepores, astrsea, and several others,

264

THE POPULAR EDUCATOR.

growing confusedly together, without any other apparent
order than that of accidental succession and aggregation both
upwards and sidewards. In the cavities of the mass are found
fragments of corals, shells and other organic remains, perfect or
broken, sand and chalky mud, and the whole becomes solidified
into a compact rock by the aid of calcareous cement, while the
upward growth of the living coral, and the accumulation of loose
material on the surface proved at the same time together. The
coral work is ever in progress until it reach* s the surface of the
water. The loose materials are either dispersed through the
crevices and inside of the reef, which thus pack and cement it
together, or else they are carried landward or seaward to form the
compact bases of other formations.

6. Salt Formations. Very little is known of the origin of
rock salt, and geologists have not been able to decide whether the
precipitation of salt is owing to evaporation, or not. It seems
clear that, in the basins of lagoons, lakes, or inland seas, pure
salt can be formed only in the central parts of such basins, parts
where no earthy sediment could be Drought by currents, and
where no sand could be drifted by winds. We cannot say what
chemical processes are now going on in the quiet depths' of the
Mediterranean, the Red Sea, and the Dead Sea ; but the Runn of
Cutch in the delta of the Indus, and some of the lakes in the
districts of Mount Ararat, explain to us how beds of salt are
formed in the present day. Professor Abich, in his notice of
" the Natron Lakes in the plain of the Araxee," says that in one
lake, at the north-west foot of the Greater Ararat, the water, in
the warmest season, retires three or four feet from its usual banks,
on which a crust of salt a few feet broad and about half an inch
thick is found deposited, of generally a pale rose-red colour.
Other lakes lying to the south-east of Little Ararat, are of the
same description. One of them is remarkable for having a broad
zone of white clayey soil covered with luxuriant reeds and
grasses. This soil forms the margin of the lake all round, and is
so soft that the feet sink in it. It is covered with an accumula-
tion of irregular lump-like incrustations of a very compact salt, of
a white colour and inclining to red, and with a foliated structure.
These saline crusts lie all around the white shore, chiefly floating
in the water of the lake ; and some fragments that were broken
off floated about, like shoals of ice, on the deep-red surface of the
water, which had all the appearance of water just on the point of
freezing. On examining the floor of the lake, as far as could be
done by tying several Cossack spears together, it was found
covered with a similar saline crust in unbroken continuity, and
appeared to increase in depth, from the shore, in such a manner as
to leave no doubt that a layer of salt, several inches thick, extends
over the whole bed of the lake.

Our space will not allow us to consider other rocks that are now
forming as sheets of lava, as volcanic cones, and a* sand dunes.

II.

U0CX8 FORMED 8INCE THE CHEAT I ON OP MAN.

Every honest geologist acknowledges that he is not able to
mark the point of union between historical and geological time,
and that he cannot define where geological epochs terminate, and
the historical era begins ; that is, that he cannot tell, from the
contents of rocks, at what time man appeared on the earth. If
we might be allowed to argue in the old Aristotelian method, we
might infer that, where we find in existence a large number of
animals that seem to contribute to the use of man, we have also
some evidence of the existence of man : for, if the bones of the
ox, the horse, the dog, the deer, &c, the bones of animals
vrhich are chsracteristic of the present creation, are found in the
sediments of ancient lakes or the alluvium of ancient floods, there
is nothing to prevent the indirect inference that the race of man
had commenced when such beds were deposited.

When the attention of mm was first directed to organic
remains found in rocks, many fossil bones were mistaken for the
bones of man. In 1577, Professor Plater, ef Basle, found near
Lucerne, the bones of a man, which he made out to be a giant nine-
teen feet high. Theso turned out to be the bones of an elephant.
Scueuchzer published an account of a fossil skeleton, under the
title of •« Homo Diluvii Testis" or man a witness of the deluge.
Cuvier afterwards proved that this was the skeleton of a gigantic
salamander or proteus. Spallanzani gave an account of a hill
in the Island of Cerigo, that consisted of fossil human bones ; but
B lumen bach showed satisfactorily that all of them belonged to
quadrupeds. Sir Alexander Cochrane brought and placed in the

British Museum an indisputable specimen of a human skeleton,
found imbedded in a rock of solid limestone formed on the shore*
of Guadeloupe. This rock can be proved not to belong to the
class of ancient limestones, but to be a very recent alluvial forma-
tion; for it contains, besides shells of the present sea, fossil
arrows, stone hatchets, and pieces of rude pottery. A battle
between the Oaribs and the Gallibis took place on that spot in
1710, and there is every probability that this is a skeleton of one
of the slain, either buried there, or sunken and imbedded when
the coralline mass was soft.

The circumstance that has occasioned the greatest perplexity to
geologists is, that some signs of human contrivances, and even
human bones, have been found in caverns, mingled with the bones
of animals that are certainly extinct as to those districts, if not
absolutely extinct as to the globe at large. As far, therefore, as
mere geological evidence is concerned, it would be unsafe to aay
that man has not been ax inhabitant of the earth for a much
longer time than modern chronologista assert. As to the human
bones which have been found mixed with those of extinct ■wim«1«
in certain caverns of Belgium and France, all of which seem to
have been deposited at the same time during the formation of the
most recent tertiary strata, Dr. Buckland has shown that the
human remains must have been introduced subsequently.

That some rocks have been formed since the creation of man, is
evident from the fact that they contain the remains of human
beings, implements of human art, and several vestiges and traces
of the operations of man. In basins or hollows covered with peat
mosses, and in districts known as submerged forests, human bones
and works of art are imbedded in company with the remains of
recent animals. On the west shore of the Red Sea a rock has
been formed composed of sands, gravel, corallines, pottery, and
weeds, cemented by carbonate of lime, being in thickness from
an inch to three or four feet, and sometimes alternating with
thin and loose layers of shingle. This rock stands at five or six
feet above the high-water level, overlying the raised coral beach,
and inclosing bones of camels and fish which to this day contain
animal matter. On the shores of Sicily, Greece, Asia Minor and
Aden, similar marine calcareous rocks have been formed. At
Rhodes, at the height of six feet above high- water mark, a cal-
careous conglomerate is observed that contains fragments of
ancient pottery, recent shells, and pebbles of limestone, gneiss,
basalt, serpentine and porphyry. In several places on the cal-
careous cliffs that skirt the Mediterranean between Alexandria
and Aboukir, there is a bed, about a foot thick, consisting of
bleached human bones, derived from the ancient Roman and Greek
cemeteries, intermingled with those of the slain in battle in the
neighbourhood. These bones are covered with a layer of sand
and gravel, varying in thickness from a few inches to three or four
feet. They appear to have been washed into their present posi-
tion by the drainage water running from the higher grounds to
the sea. What is remarkable in these bones is, that though they
are in an excellent state of preservation, they are not fossilised.

Fig. 2. The present Com of Vesuvius, with Somina to the left,
and Naples in the foreground.

Geologists can satisfactorily prove that a vast portion of the
lavas, the tufas, and the trap dykes of Etna, of Vesuvius, and of

LESSONS IN ITALIAN*

266

the Island of Ischia in the Bay of Naples, has been produced
since the historical period. The Post Pleistocene formations about
Naples show that very great changes have taken place through-
out the whole of the volcanic district of Campania during the last
two thousand years. One of the most remarkable is the formation
of the modern cone of Vesuvius since a d. 79, which is represented
in fig. 2. Before the year just mentioned, Mount Vesuvius
might have been regarded as an extinct volcano, but at that
period the rocks of the mountain were blown to pieces and fell
into the gulf beneath, and its clifls form the circular ridge, called
Somma, which is several miles in diameter, the highest point of
which appears to the left of the engraving. The enormous cone in
the centre has been formed since the year a.d. 79.

In the Bay of Baise, not far from Naples, there is an entire
mountain, consisting of pumice and ashes, a mile and a h»M in
circumference, and 460 feet high, which was formed by an earth-
quake on Sept. 29, 1538. During this catastrophe the north coast
of this bay was permanently elevated twenty feet, exhibiting
tn&ceous strata filled with articles fabricated by man, such as
fragments of sculpture and pieces of pottery, which are every-
where mingled with marine shells.

Examples of raised beaches, of shell marl, and of submerged
forests, are found in almost every part of the world ; and they, in
the majority of instances, afford proofs that they have been
occasioned by physical changes of very modern date.

These Post Pleistocene groups of rocks claim the particular atten-
tion of young geologists, as they furnish us with the clearest
instances of the harmony between Geology and Revelation ; for
these rocks establish the fact stated by Revelation, that man is
among the latest of the «niimn1 t created to inhabit this earth.
They show also that the epoch when the existing races of plants
and a nimal s were placed on the earth, must have been recent.
Suppose that human remains, say bones or implements, had been
found in ancient rocks which can be proved to have been formed
at the bottom of deep oceans, or that they were found mingled
with the earliest organic fossils in the Silurian rocks, it would
have been impossible, for geologists, at least, to reconcile the
two records of the Almighty Creator. Instead of this, geology
proves, in harmony with Scripture, that the introduction of man
among the creations of earth has not been of very remote anti-
quity.

III. &OCJL8 FORMED SINCE THE CHE ATI ON OF THE FEB8ENT
BAG! OP PLANTS AND ANIMAL8.

It has been intimated already that it is next to impossible to
mark the limits between chronological time and geological
epochs. Tou have seen that some beds in this Post
Pleistocene group give indubitable proof that they were
formed after the creation of man. Still, there are other beds, lying
lower in this group, that present satisfactory evidence that they
were deposited before man came upon the earth. First, no fossils
of human bones, and no relics of human art, have ever been found
in them. Secondly, in none of these rocks, formed as alluvial
beds in the waters of the ocean, have any human remains of any
kind been discovered. Thirdly, nevertheless the remains of
animals and of plants, identical or very similar to the existing races,
are found in the lower formations of the group. Fourthly, a
comparison of these beds with the physical conditions of the globe
at the beginning of the Pleiocene period, shows that the state and
aspect of the earth were very similar to the present, and that this
similarity continued to increase till we approach the historical
era.

The districts of Italy, to which your attention has been already
directed, abound in proofs and illustrations of this statement.
In the Bay of Baite there are, besides the beds of tufa just men-
tioned, other tufaceous beds of a date evidently anterior to the
origin of man. These rocks are so thick as to form hills of from
500 to 2,000 feet high. These beds contain all the marine shells
now abounding in the neighbouring sea, and yet they are inter-
stratified with different- sheets of lava. In the same manner,
similar beds, consisting of clay and volcanic tufa, rise, in the
neighbourhood of Naples, to the height of 1,500 feet above the sea;
but these differ much from the kindred strata at Puzzuoli, for they
contain no relic or trace whatever of the existence of man.

In this lower division of the Post Pleistocene group are classed
the Loess of the Rhine, the Cotton soil of India, the Till of Eng-
land and Scotland, and the newer part of the Northern Drift.

1. Thb Loxas op the Rhine. This Loess is sometimes called
Lehm, and consists of a deposit of yellowish marl, often not less .
than fifty feet thick, abounding with calcareous concretions and
sandy nodules. -It is this kind of rook that forms groups of low
hills at the foot of each mountain chain that enters the river valley.
It is sometimes as high as 1,500 feet above the level of the sea,
showing that the bed of the Rhine was once at that elevation.
It forms also the subsoil of the plains on which Coblentz and
Bonn are situated, and extends up as far as the falls of Schaffhau-
sen, where it is seen to repose on beds of rolled flints and other
pebbles of the drift period. It contains land shells and fresh-
water shells of many existing species ; but the only mammalian
remains found in it, are a few bones of the hone and the mam-
moth.

2. Thb Rbouh op India. The Regur is the cotton soil which
covers one-third of all southern India, ranges northward to a
great distance, and extends into the Burman empire. Its colour
is bluish black, greenish or dark gray. Its thickness varies from
three to twenty feet.

3. Thb Till. In almost every district of the globe there is
found under the vegetable mould that covers the surface of the
earth, a deposit of sand, mud and loose gravel, which has been
called alluvium, from aUuo to wash, and aUuvio, an inundation. It
is called by this name, because the bed of gravel has every appear-
ance of having been spread by a flood, and the grains of sand and
pebble appear as if they had been rolled by water, and had formed
the bed of a mighty river.

It is found in the higher latitudes of North America and of
Europe, where it extends from Finland and the Scandinavian
mountains to the North of Russia, and the low countries bordering
on the Baltic, and on the eastern coast of Scotland and England.
This deposit consists, of sand, mud and clay, sometimes in a strati-
fled stato, but very often wholly unatratitied, having a depth of
more than a hundred feet. It is the unstratified part of this
formation that is called by geologists " the Till." It contains
numerous fragments of rocks, some angular, some rounded,
derived from formations of all ages. Some of the blocks are of
immense size. This rock is almost everywhere destitute of
organic remains, except where they have been washed into it
from older formations.

4. The Bouldbk Formation. When this formation contains
large blocks of ancient rocks it is called " the drift," and '• the
boulder formation, " whose probable connexion with floating ice
has already been considered. Wherever it has been examined
in Russia, it has been found throughout to be superimposed upon
strata that contain recent shells, and that, consequently, the
accumulation is post pleistocene. The same is the case about
Upsala in Sweden. Everywhere it shows that the transport of
erratic boulders continued to take place after the North of Europe
had assumed its present physical features.

LESSONS IN ITALIAN GRAMMAR.— No. XVII.

By CHARLES TAUSENAU, M.D.,

Of the University of Pavia, and Professor of the German and Italian
Languages at the Kensington Proprietary Grammar School.

Exs&oiaBs. — Italian-English.

Ha man-da- to la ldt-te-ra a Gio-van-ni. Ti-ra-re ad un uc-
cel-lo. II mer-can-te pen-sa al gua-da-gno. Toc-ca un fio-
ri-no ad u-no. O-gnu-no ti-ra 1' a-cqua al su-o mo-li-no.
Dal-le pa-rd-le si ven-ne al-le ba-sto-na-te. A chi 1' a-vc-te
mo-stra-to? a Pie-tro o al-la cu-gi-na? A che pen-sa-te?
pdn-so all' av-ve-ni-re. Ar-ri-ve-re*-ino prd-sto al-la prda-si-
inapd-sta? E'-gli 6 c6r-so su-bi-to al-la por-ta. Par-la- va
ad u-no stra-nig-ro. Lo in-ci-to al-la col-le-ra. Pre-fe-ri-sce
il b€-ne al ma-le. La su-a con-ver-sa-zi6-ne mi vid-ne a nd-ja.
E'-gli se lo rfi-ca a dis-o-n6-re. La li-be-ra-li-ta gli vien im-
pu-ta-ta a di-fet-to. E's-si 6-ra-no al-la cac-cia, al-le noz-ze,
a pran-zo, a ce-na, al fe-sti-no. An-dr6-te do-ma-ni al ri-d6t-
to ? al con-cdr-to > l'-o an-drd do-m£-ni a un bal-lo. An-da-
te a im-pe-ra-re, a scri-ve-re, a dor-mi-re, a man-gia-re. E's-
si van-no a spas-so, a pas-seg-gia-re. An-dia-mo al cai-fe.
Per d6-ve si va al-la pd-sta ? al-la do-ga-na ? E'-gli e a Ber-
li-no. Sog-gi6r-na in Fi-ren-ze. E'-gli mo-ri in Not-tin-ga-
mo. . E'-gli lo con-dur-ra a Ce-stria. JBl-la giun-se a Li6-ne.
E'-gli e ar-ri-vti-to in Bri-stdl. E'-gli e na-u> in Pli-mut-te,

966

THE POPULAR EDUCATOR.

L' I-sti-tn-to po-li-tA-cni-co in Pa-ri-gi. La p6-tta p4r-te 6-gui
dl per 1' I-ta-lia, per Ve-ntVsia, per Ro-ma. B'-gli de-ye re-
car-si a Mi-la-no. ET re-etl-to tot-to il gi6r-no a em-ss. E / -gli
non va a pa-las-so, a cor-te. Di qui a Neo-ca-stel-lo,
Jork.

VoCABULABY.

Ha ma ndal o, he has sent.

Lettera, letter.

Giovanni, John.

Tirart, to draw, trail, drag;

to shoot or fire, fcc.
TJceeUo* bird.
MercanU, merchant.
Pensa, thinks.
Guadagno, profit.
Tocca, falls to the lot or share

(toc-cd-re* al-ck-na co-sa ad

n-no, to fall to the lot or

share of one).
Fiorina, florin.
Ognuno, every bod)'.
Tira, draws, conveys.
Aegm, water.
Molino, mill (tirar V aegua

al suo molino, to convey water

to one's mill ; to look to the

main chance or to number

one).
Da, from.
Parola, word.
Si venne, one (they) came.
Bastonata, blow (with a stick).
Chi (only of persons), who ?
V avtU mottrato, have you

shown it?
Pietro, Peter.
0, or.

Ougina (f.), cousin.
Che, what ?

Pensate, do you think.
Pento, I think.
Awenire, the future.
Arriveremo, shall we arrive.
Presto, soon, quickly.
Prossimo (m.), protsima (f.),

next.
Pasta (f.), post.
Egli, he.
K cor so, Tin.
Subito, immediately.
Porta, door.
Par lava, he spoke.
Straniero, stranger.
Lo incitd, he provoked him.
Collera, anger.
Preferisee, he prefers.
Bene, good.
Jfa/#, evil.

Suo (m.), «ua (f.), his.
Conversation*, intercourse,

company, conversation.
A/*°, to me, me.
I'ttne, comes, becomes.
Noj'a, ennui, disgust, tedium,

annoyance (mi visne a noja,

annoys or sickens me).
Egli to lo rtca, he regards or

reckons it.
Ditonore, dishonour.
F.iberaUtd, liberality.
Glivitn imputata, is imputed

to him.
Difetto. fault.
Bsni, thev.

Erano, were.

Caocia, chase.

Notu (is), f.pl., wedding, mar-
riage feast.

Pronto, dinner.

Oma, supper.

Festino (dancing, gaming, ftc),
evening party.

Andrete, will you go.

Domani, to-morrow.

Ridotto (in some towns of
Italy), public masquerade.*

Concerto, concert.

Io andro domani, I shall go to-
morrow.

BaUo,biXl.

Andate, go.

Imparare, to learn.

Scrhere, to write.

Dormire, to sleep.

Mangiare, to eat.

Etti vanno, they go.

Spatto, pastime, diversion,
pleasure {etti van no a spemo,
they take a walk).

Passepgiare, to take a walk.

And%amo, let us go.

Cafe, coffee, coffee-house.

Per dove si to, which is the
way.

Dogana, custom-house.

Soggiorna, he lives or resides.

Firenze, Florence.

Egli mori, he died.

Nottingamo, Nottingham.

Egli lo condurrd, he will bring
or conduct him.

Cestria, Chester.

Ella giunst, she arrived.

Lions, Lyons.

Egli e arrivato, he has ar-
rived.

Bristol (also Bri-st6l-U or Bri-
ttd-lio), Bristol.

Egli 4 nato, he was born.

Plimutte, Plymouth.

IstUuto, school or institute.

Poliiocnieo, polytechnic.

Parigi, Paris.

Parte, starts.

Ogni, every.

IA, day.

Egli dere recarsi, he must de-
part.

Mxlano, Milan.

K restato, he has remained.

Tulto, all, whole.

Egli non va, he does not go.

Palazzo(ts), palace; court; guild-
hall, townhall, council-
house (andare a palatzo, to
go to the townhall ; to go
to the sitting of the court).
I Gorte, court (of a sovereign);
court of justice (andare a
corte, to go to court ; to go
to law).

Di qui, from here.

EwOUSH-ItAUAIT. *

Thy mother has lost her umbrella. My sister has found &
pen. Where have you bought this penknife? Hast thou
seen our horse? We have seen a large inn. Tour little
brother has a good watch. Our brother is taU,t but our sister
is little. I have a hat which is very fine. The watch which
you have bought is good. Our uncle has received a letter.
This son has lost his mother. This daughter hat lost her
father. This present is for this child.

Bkglisk-Italiax.

Mr. Thomson has gone to the exchange. Let us rp into the
concert. The sisters have gone to-day to the evening enter-
tainment. He is at the ball, and the brother in the concert.
We have paid a visit to the neighbour ; he lives on the second
floor, and the son on the ground floor. We are now sitting
at table. Think of more serious things. The misers are Ilk*
the horses that carry wine and drink water, and like the astee
that bear gold and eat thistles. He lives at the Black Eagle,
and not at the Golden Lion. I have spoken to him at the
coffee-house. Shall we play a game at cards or at chess ?

Vocabulary.

Mr. Thomson, il Si-gn6r J

Thomson
Has gone, e an-dd-tc
Exchange, bor-sa, f.
Let us go, an-did-mo
Concert, con-obr-to, m.
Have gone, s6-no an-dd-U
To-day, 6g-gi
Evening entertainment, con-

ver-sa-zio-ne, f.
He is, i-gli e
Ball, baUlo, m.

We have paid, ab-bid-mo fdt-to
Visit, vi-si-ta, f.
Neighbour, vi-ei-no, m.
He lives, i-gli d-bi-ta (also al-

l&g-gia or sta, with a)
Second floor, se-con-do tpid-no,

m.
Ground floor, pidn ter-re*-no,m.
We are now sitting, noi se-did-

tno 6-ra^
Table, td-vo-la, f.
Think, pen-sd-te (»'. e. direct

your thoughts to)
More serious, piu st-rio, m.,

piu si-ria, f.
Thing, c6-sa, f.
Miser, d-vd-ro, m.

Are like, ras-to-mi-glia-no

Horse, ca*vdl~lo,m.

That, ehs

Carry, mi-na-no

Wine, vi-no, m.

Drink, btrvo-no

Water, d-cqua, f.

Ass, d-ti-no, -m.

Bear, por-ta-no

Gold, v-ro, m.

Eat, mdn-gio-no

Thistle, car-do, m.

Black Eagle, d-cqui-la ni-ra, f.
(with the preposition a)

And not, $ non

Golden Lion, loon oV 6-ro % m.
(with the preposition a)

I have spoken to him, f-ogli
hd par-ld-to

Coffee-house, caf-fi, m

Shall we play, tw-^ttd-mo /*-
re\

Game, par-it-ta, f.

Cards, cdr-te, f. pi.

Or,o

Chess, sedc-chi, m. pi. (sing
sedc-co, m., one of the sixty-
four houses or squares on a
chess-board)

Da.

I have already stated that the particle di denotes a mere
mental separation of ideas or notions, while the particle da

• In some of i's mranings, this word denotes discreditable places
of resort, and, to avoid ambiguity, it should only be used with
precaution in the above-stated signification.

• After a careful study of the previous colloquial exercises, even
ordinary pupils will be quite able to translate the following sen-
tences without the aid of a vocabulary.

f In Italian, tall and great frequently are expressed by the same
word.

% When the word Si-gno-re is followed by a noun, the final e is
dropped, except when the noun that follows begins with the s ee-
pure; e.g. U 9t-gn0r An-U*do,VLt. Anthony; il Signer Fran-ob-tot,
Mr. Francis; U 8Lgn&r odn-U, count; il 9i-gtutr ba-r6-ne, baron; U
Si-gndr dot-Uf-rt, doctor ; U Si-gndr con~si-gti&re, counsellor ; U M-
gnd-re SU-JU-no, Mr. Stephen.

{ O -ra, now, at present ; hour, time, and 6+a (for a**t»), light
wind, breath of wind, gentle air, breese.

|| The verbs gwo-od-re, to play (at cards or at any other gasse),
and/d-rc iMtapor-M-te, to plav a game or make up a match (at cards
or any other game ), invariably require the preposition a ; e. g.
giuo-cd-re a un giuo-co. ai dd-di (or a dd-di), 61-le cdr-te, 4gU s ee h e M
(or a scdc-clu), a tre-set-ie, alt dm-brt, dUapdlrla, apic-ch&-to, fcc., to
play at a game, at dice, at cards, at chess, at tre-sept (an Italian
game at cards), at omber, at tennis, at piquet, &c. ; Jao cid mo asm
partita al bi glidr-do, al whist, al cribbage, &c., let us have a game
or make up a match at billiards, at whist, at cribbage, fcc.

UB880N8 IN ITALIAN.

207

expresses a real separation of objects. This is the fundamental
signification of da, and, on this account, it must be pronounced
to be the very opposite or logical antagonist of the particle a.
This latter word indicates any kind of tangible or mental and
imaginary approach or direction to or toward* a person or thing,
while da expresses any kind of tangible or mental and ima-
ginary, but clear and real separation, removal, distance, or
direction from a person or thing, and the ideas of direction to or
toward*, and of a direction/rom a person or thing, are, to some
extent, the very poles or extremities of all relations in which
words and things stand to each other ; e. g. in this sentence,
pdr-lo dilui, I speak of him, it is evident thst there is no direc-
tion whatever to or towards, but rather a direction from a
person. This direction is, nevertheless, not sufficiently clear
and real enough to justify the use of da ; while, in the sentence
vin-go da lui, I come from him, a real removal, distance, or
separation from the person, from which I come, is understood,
which can only be expressed by the particle da. As a further
illustration, in the phrase un mer-cdn-tedi Ve-r6-na, a merchant
of Verona, the particle di is a mere sign or intimation to
distinguish the merchant from the town in which he lives,
and not of his absence from it; while in the sentence i-gli
vii-ne da Ve-rb-na, the particle da denotes an actual re-
moval from that place. This fundamental explanation of the
particle da, however, is not sufficient to convey a complete notion
of all its uses ; every language, generally speaking, being far
too complex a vehicle of human thought anywhere to admit
of such a summary discussion of its more important branches.
Now, and hereafter, I shall be therefore obliged to explain
the various modifications and exceptions of this general
rule.

The ideas of removal, distance, separation, dependence, deduction, I
or derivation, and origin or descent, are, as it were, only collateral
or subordinate branches of the fundamental notion of a direction
from a person, or thing, and that word (person or thing), the!
removal, distance, deduction or derivation, origin or descent!
from which, and the dependence on which, is expressed, re- J
quires the particle da before it ; e. g. se6-sta-ii da qui-sto lm-
go, begone from this place ; al-lon-ta-nd-re it-no da un lut-go, to
remove one from a place ; ca-vd-re d-cqua dal p&x-so, to draw
water from the well; ve-ni-re da lon-td-no, to come from
afar; i-o 9kn-go dal giar-di-no, da cd-sa, I come from the!
garden, from home ; V uc-eU-h i u-sci-to ddl-la gdb-bia, the bird
has flown out of the cage; ac-cat-td re pd-ne da u-no, to beg
one's bread of one ; do (pron. ci6) di-pin-de ddl-la forAk-na, da
voi, that depends on good luck, on you ; de-dur-re u*-na ra-g io-
ns da un prin-ci-pio fdl-so, to deduce an argument, proof, or
evidence from a false principle ; ddl-la qual cA-sa nd-cquc-ro di- 1
vir-se pa-u-re, from which arose various fears ; de-ri\
vd-re r o-ri-gi-ne di u-na c6-sa da un* dl-tra, to deduce the origin
of one thing from another ; di-vl-de-re u-na e6-sa da un' dl-tra, j
to separate one thing from another.

It is obvious that the idea of origin, expressed by da, neces- 1
sarily includes any action proceeding from a person or place. For \
this reason, on the one hand, the English preposition by, when-
ever in connexion with passive verbs it denotes cause, author-
ship, instrumentality, &c, must be translated by da ; and, on
the other hand, all verbs expressing a going away, or depar-
ture, generally demand this particle; e. g. Car-td-gi-ne fu fab-
bri-cd-ta da Di-d6-ne, Carthage was built by Dido ; fu 4-gli da \
al-eu-ni tuo-i se-gre'-ti ne-mi-ei ac-cu-sd-to, he was accused by
some of his secret enemies ; a qui-sto giar-di-no I' d-cqua t ab-
bon-de-vol-men-te som-mi-ni-strd-ta da u-na fre-schis- si-tna fon-
td-na, the water for this garden * is abundantly supplied by a
very cool fountain ; e'-gli d par-ti-to da Lon-dra, he has de-
parted* from London; eo-min-cid a an-dd-re da Na-za-rU-te
a Ge-ru-sa-Um-me, be began to go from Nazareth to
Jerusalem.

Whenever the verbs u-sci-re or sor-ti-re, to go or come out
or from ; par-ti-re, to set off, depart ; ve-ni-re, to come ; fug-

• Da, as well as the English Ay, is in these oases the preposition,
which must be placed before the nominative case of the original
sentence of the active voice whenever the latter is to be changed
Into the passive ; e. g. u-na fre-schis- si-ma fontd-na scm-minl-stra
em bom-de-vol-men-te V d-cqua a qui-sto giar-di-no, a very cool fountain
abundantly supplies the water for this garden.

gi-re, to fly, escape, &c., admit of the preposition di before that
place from which the going away or departure takes place,
this apparent deviation from the general rule, without diffi-
culty, will be explained by ellipsis ; t . c. by the omission of the
preposition da, with some other general noun ; e. g. ve-ni-re,
par*ti-re di R6-ma (t. e. ddl-la dt-ld di R6-ma), to arrive, to
depart from (the city of) Rome; 4-gli e di A-ber-dd-nia (*'. #.
d>tt-iii eit^td di A-ber-do-nia), he is a native of (the town of)
Aberdeen ; u-sci-re, sor-ti-re di cd-sa, di cor-te, di pa-ldz-zo, di
fat-tov di chie-sa, to go or come from home, from court, from
guild-hall, from theatre, from church.

The particle da, also, is used, in order, by naming the birth-
place, to distinguish one person from others of the same appella-
tion. The birth-place thus becomes, as it were, the surname of
the individual. This employment of da certainly is quite
conformable to its fundamental notion, for the birth-place
is a part of the general idea of origin, descent, or extrac-
tion; e. g. Gio-vdn-nida Fie-so-le, Pii-tro daOor-tv-na, Leo-ndr-
do da Vin-ci, Gut-do da 8it-na, Po-li-dd-ro da Ca-ra-vdg-gio,
Bn-faH-Io da Ur-bi-no,* &e.

Dit, aiao, may denote any origin or commencement referring
to time, and then it means since ; e. g. da che vi vi-di la pri-ma
vnUta t since (that day when) I saw you the first time ; ddl-la
tm'-a gia-va-ne%-za in si-no quc-sto tfm-po, since my youth till
this day ; dalV an- no passd-to in qua, 6ince last year ; da du-e
mi-si in qud, two months since; ddl-la m&r-te di mi-o pd-dre in
qud % since the death of my father, f

The phrases da mat- U-na, da se-ra t da n6t-U, mean : in the
morning* in the evening, in the night (by night, at night) ; e. g.
6*pe~ra da far da mtut-tt-na, work to be done in the morning ;
noti c-scc da cd-sa che da se'-ra, he only goes from home in the
evening j td-li cd-se non si fdn-no da n6t-te, such things are not
done by night.

£t i also signifies about, nearly, dose upon, not far of from,
&c, e. g, hd gua-da-gnd-to da ein-que U-re sterli-ne, I have
gained or won about five pounds sterling ; ho per-dd-to da s4i
a U-to idUle-ri, I have lost from about six to eight dollars ; da
RA-ma a Nd-po-li sa-rdn-no da dn-to ses-sdn-ta mi-glia, it is
about a hundred and sixty miles from Rome to Naples ; e'-gli
vi rs ste-rd da ein-que a sei gtdr-ni, he will stsy there from about
five to six days ; sli-md-va-si a-vi-re in Fi-ten-u da no-van-ta-
mi-la b&e-ehe tra u6-mi-ni efem-mi-ne e fan-ciid-li, about ninety
thoiuandpersons, men, women, and children, were estimated
to be in Florence.

A logical contradiction and anomaly, though introduced and
sanctioned by a universal usage, for the most part in the
place of the preposition a, the constant employment of
da in connexion with those verbs which, with some
luHjsr, mansion, apartments, lodging, or any other place
of continuance, denote any kind of motion to or towards,
any kind of living or residing with, and any kind of visit
paid to, a person ; e. g. an-dd-re dal nU-di-co, dal cal-u>~ld-jo t
to go to the physician, to the shoemaker; do-md-ni ver~ro
da t->n t I shall come to you to-morrow; i-o vi me-ne-rd da
lui, I ah all conduct you to him; ve-m-te da me, dal tner-
ctiii-tt;, come to me, to the merchant ; s6-no std-to da lui, dal
fra-UUh, I have been at his, at the brother's house (with
him, with the brother) ; d-bi-ta, al-ldg-gia da sU-o zi-o, he lives
or resides with his uncle.

Da k sometimes a substitute for di; e. g. Is pta-si-md-va du-
ra.meht-tt, 6-ra da fol-U-a, 6-ra da co-dar-di-a (instead of di
foiiia t di eo dard i a ), he severely blamed them, now for their
folly, now for their cowardice; it-si nun-no mM-ti ma-di da al-
teg-yid-r* o da pas-sd-re quSl-lo (instead of di alley giare, di
pasture) t they have many means to make it easier or to pass
over t.

The particle da can never be really omitted, and the cases
of ellipsis that I mentioned only serve the purpose of
grammatical explanation.

■ The English learner will, perhaps, best understand this use
oi dabj Translating it with sprung from.

t 4iJra (denoting time, and not in the scuse of as or beoaum) is
translated by fm da, da. ...is qua, or d6-po, when it preceoes a

noun.

THE POPULAR EDUCATOR.

LESSONS IN OEOMETRY.-No. XXVI.
LECTURES ON EUCLID.

(Continued from page 256.)
BOOK I.— PROPOSITION XXIV.— THEOREM.

If two triangles have two tides of the one equal to two sides of
the other, each to each, but the angle contained by the two sides
of one of them ijreater than the angle contained by the two sides
equal to them, of the other ; the base of that which has the greater
angle is greater than the base of the other.

In fig. 24, let ab c and d k f be two triangles, which hate the
two sides A b and ac equal to the two sides db and dp, each
to each ; viz., a b equal to db, and a c to d f. But the
angle bac greater than the angle edf. The base b c is- greater
than the base b f.

Of the two sides db and dp,
let db be the aide which is not
greater than the other. At the point
D, in the straight line de, make
(I. 23) the angle iuo equal to the
angle bac. Make do equal (I. 3)
to A c or dp. And join e o and

OP.

Because db is equal (Hyp.) to
ab, and do (Const'.) to AC, the
two sides, zd and do, are equal to the two ba and ac, each
to each ; and the angle b d o is equal (Const.) to the angle bao;
therefore the base e o is equal (I. 4) to the base b c. Again,
because do is equal to dp, the angle dfo is equal (I. 5) to the
angle dop; bat the angle dof is greater (Ax. 9) than the
angle bop; therefore the angle dfo is also greater than bop;
much more then is the angle zfo greater than the angle bop.
Now, because the angle ifo of the triangle b p o is greater than
its angle bop, and the greater (I. 19) angle is subtended by the
greater side ; therefore the Bide e o is greater than the side b p.
But b o was proved to be equal to b c. Therefore b o is greater
than B p. Therefore if two triangles, Sec. Q. E. D.

Scholium 1. — Dr. Simson, in the construction of this proposi-
tion, introduced these words : " of the two sides d b, d f, let d b be
the side which is not greater than the other," in order to avoid
three distinct cases of construction, which would arise by taking
that side which is greater than the other.

Scholium II. — It has been remarked that Euclid's demonstration
of this proposition appears to be defective, because of the omission
of the words introduced by Dr. Simson, as stated in the preceding
Scholium. But upon consideration of the three cases referred to
in the following exercise, it would appear that Euclid had originally
contemplated their Insertion, inasmuch as the second case of it, as
demonstrated below, requires only a simple and direct reference to
Prop. XXI. Now Euclid is not guilty, in general, of bringing in
propositions, in any book, which do not bear upon those that fol-
low ; but it has been universally admitted that Prop. XXI. was
of this description ; now if he considered the three cases of
Prop. XXIV., this objection is at once removed. Why they are
not found in the common Greek text, we cannot tell at present.

EXERCISE I. TO PROPOSITION XXIV.

Demonstrate this proposition, by making the construction on the
greater of the two sides of the triangle dip, and exhibit the three
distinct cases above mentioned.

Let abc, fig. 1, and dbp, figs. 2, 3, and 4, be two triangles
which have two sides of the one equal to two sides of the other,
each to each, viz., the side a b to the side d b, and the side a c to
the side d f, but the angle bac greater than the angle edf. The
base b c is greater than the base e p.

Of the two sides i> b and dp, let d b be that which is greater
than the other. At the point d in the straight line d b make the
angle bug equal to the angle bag (I. 23). Make do equal to
a c or u v (I. 3) and join b o.

Because db is equal to a b (Hyp.) and do to a c (Const.), and
the angle b d o to the angle bag (Const.) ; therefore the base b o
is equal to the base b o (I. 4). Now, if the point f falls upon bo,

u hi tig. 2, bo is greater than ef (Axiom IX.) ; bat bo
shown to be equal to b c, therefore b c is greater than b f.

Fl*. 1

\<*

Fig.s.

Next, if the point f falls within the triangle d b o, as in fig. 3.,
i> r and f e, taken together, are leu than d o and o s taken to-
gether (I. 24); but do is equal to dp (Const.). Therefore bo is
greater than b p (Axiom 5) ; but BO was shown to be equal to b c,
therefore bc is greater than if.

The case in which the point f falls without the triangle d b o, as
in tig. 4, is demonstrated in the same manner as above, in the pro-
position itself, and therefore it need not be repeated here. Where-
fore the exercise is demonstrated. Q. £. F.*

EXERCISE II. TO PROPOSITION XXIV.

Demonstrate tliat, in Dr. Simeon's construction, the straight line
i: Q tut* the straight line dp in some point between d and f.

In fig. z. let dp meet bo in the
point ii ; it is required to demonstrate
that the point h lies between the p .
points D and p. >'

Because d b is less than d o (Hyp.),
the angle dob is less (I. 18) than the
angle deo. But the angle d h a in
greater (I. 16) than the angle deo;
much more, then, is the angle dho
greater than the angle dob. There-
■fore the side do is greater than the
fide dh(I. 19). But DOis equal
to d f (Const.). Therefore d f is
also greater than d h. Therefore
b o cuts d f in the point h, between
the points d and f. Q. £. D.+

PROPOSITION XXV. — THEOREM.

If two triangles have two sides of the one equal to two sides of the
of?t*r y ach to each, but the base of the one greater them the km ef
m other-, the angle contained by the two sides of that which has the
greater base, is greater than the angle contained by the two sides
equal to them of the other.

In fig. 25, let a b c and d b f be two triangles which have the two
sides a b and a c equal to the two sides d b and i> f, each to each ;
vtx,, a b equal to d b, and a c to d w ; but the base b o i

* These exercises were solved by J. H. Eastwood, MiddJetoa;
C< L. Hadfield, Bolton-le-Moors; and Q. Pringle, Glasgow.

LESSONS IX GEOMETRY.

269

The angle b A c is greater than the

Fl*. 85.

than the base b f.
angle bdp.

For, if the angle bag be not
greater than the angle b d f, it must
either be equal to, or leas than the
angle bdp. The angle bac is not
equal to the angle bdp, because
then the base b o would he equal
(I. 4) to the base e p : but it is
(Hyp.) not equal. Therefore the
angle b a c is not equal to the angle

bdp. Again, the angle bac is b o b p

not less than the angle bdp, be-
cause then the base b c would be less (T. 24) than the base b p : but
it is (Hyp.) not less. Therefore the angle b a o is not less than the
angle bdp. And it was shown that the angle b a c is not equal to
the angle bd p. Therefore the angle b a c is greater than the angle
bdp. Wherefore, if two triangles, &c. Q. E. D.

Corollary. — If two triangles have two sides of the one respec-
tively equal to two sides of the other, the base of the one is greater
than, equal to, or less than the base of the other, according as the
angle opposite to the base of the one is greater than, equal to, or
less than the angle opposite to the base of the other.

PROPOSITION XXVI.— THEOREM.

If two triangles have two angles of the one equal to two angles of
the other, each to each ; and one side equal to one side, — viz., either
the tides adjacent to the equal angles, or the sides opposite to equal
angles in each ; then their other sides are equal, each to each, and
alio the third angle of the one to the third angle of the other.

In tig. 26, let a b c and dbf be two triangles which have the two
angles a b c and b c a of the one, equal to the two angles dbf and
b p d of the other, each to each ; rix., a b c to d b f, and b c a to
bpd. Also, let a side of the one triangle be equal to a side
of the other.

No. 1 . First, let those sides be equal which are adjacent to the angles
that are equal in the two triangles ;
▼is., b o equal to if. Then their
other sides are equal, each to
each ; viz., a b to d b, and A o to
dp; and the third angle bag of
the one is equal to the third angle
b d f of the other.

For, if a b be not equal to d e,
one of them must be greater than
the other. Let a b be the greater
of the two. Make b o equal (I. 3)
to D b and join o c.

Because, in the two triangles obc and dbf, the side b o is equal
(Const.) to the side d b, and the side b o (Hyp.) to the side b p, the
two sides o b and b c are equal to the two sides d b and b f, each
to each. But the angle o b c is equal (Hyp.) to the angle dbf.
Therefore the base o c is equal (I. 4) to the base D f, and the tri-
angle o b o to the triangle di f ; and the remaining angles of the
one are equal to the remaining angles of the other, each to each ;
▼is., those to which the equal sides are opposite. Therefore the
angle Qob is equal to the angle dps. But the angle d f e is
(Hyp.) equal to the angle bca. Wherefore also the angle b c o is
equal (Ax. 1) to the angle b o a, the less to the greater, which is
impossible. Therefore the side a b is not unequal to the side db ;
that is, a b is equal to d b; also b c is equal (Hyp.) to bf. There-
fore the two sides a b and b c are equal to the two sides D b and
b p, each to each ; and the angle a b o is equal (Hyp.) to the angle
dbf.. Therefore the base a o is equal (1. 4) to the base d f, and

Fig. 26.

No.1

the third angle b a o to the third angle bdp.

No. 2. Next, let those sides which are Flff* 2**
opposite to equal angles in each triangle
be equal to one another ; viz., a b equal to
d b. Then their other sides are equal ;
▼is., a c to dp, and b c to if; And
the third angle b a c of the one is equal
to the third angle b d f of the other.

For, if b o be not equal to bf, one b

No. 8.

of them

must be greater than
be the greater of she

than the other.

is equal (Const.) to the side bf, and the aide ab to (Hyp.)
the side db; the two sides a Band bh are equal to the two
sides d b and b f, each to each. But the angle a b h is
equal (Hyp.) to the angle D b f. Therefore the base a h is equal
to the base d f, and the' triangle abh to the triangle dbf;
and the remaining angles of the one are equal to the remaining
angles of the other, each to each ; via., those to which the equal sides
are opposite. Therefore the angle b h a is equal to the angle bpd.
But the angle b f d is equal (Hyp.) to the angle bca. Therefore
also the angle b h a is equal (Ax. 1) to the angle bca; that is, the
exterior angle b h a of the triangle a h c is equal to ita interior
and opposite angle bca; which is impossible (I. 16). Therefore
b c is not unequal to b f ; that is, b c is equal to bf ; also ab is
equal (Hyp.) to db. Therefore the two sides ab and bc are equal
to the two sides d b and s f, each to each ; and the angle a b c is
equal (Hyp.) to the angle d B f. Therefore the base a c is equal
(I. 4) to the base d f, and the third angle b a c to the third angle
e d k. Therefore, if two triangles, &c. Q. E. D.

Scholium. The enunciation of this proposition may be thus
simplified : If two triangles have two angles of the one, equal to
two angles of the other, each to each, and a side of the one equal to
a side of the other similarly situated as to the equal angles, the two
triangles are equal in every respect. The demonstration might also
be conducted on the principle of supraposition, employed in the
4th and 8th propositions of this Book. This will form a good
exercise for our students, and we leave it for them accordingly.
EXERCISE I. TO PROPOSITION XXVI.

In an isosceles triangle, if a straight line be drawn from the angle
opposite the base, bisecting the angle, it bisects the base; or, if it bisect
the base, it bisects the angle ; and in either case, it cuts the base at
right angles.

In fig. a, let a b c be an isosceles triangle,
of which the sides a c and cb are equal; and
first, let the straight line c d bisect the angle
a cb. Then the base a b is bisected at d.

Because, in the two triangles a c d and
b c d, the two sides a c and c d are equal (Hyp.)
to the two sides b c and c d, and the angle
acd is equal (Hyp.) to the angle bcd; d

therefore the base a d (I. 4) is equal to the base d b. Wherefore
a b is bisected Jn d. Also, by I. 4, the remaining angles of the
triangle a c d are equal to the remaining angles of the triangle
bcd, each to each, viz., those to which the equal sides arc
opposite ; therefore, the angle a d c is equal to the angle bdo;
but these are adjacent angles ; therefore (Deft X.) they are right
angles.

Secondly, let the straight line C b bisect the base a b. Then the
angle a c b is bisected by c d.

Because, in the two triangles acd and bod, the two sides AC
and c D are equal (Hyp.) to the two sides b c and c d, and the base
a d is equal (Hyp ) to the base d b ; therefore the angle a c d is
equal (1. 8) to the angle bcd. Wherefore the angle a c b is
bisected by cd. In the same manner, it may be shown that the
angle a d c is equal to the angle bdcj but these are adjacent
angles ; therefore, by Def. X. they are right angles.
Q. E. D.«

EXERCISE II. TO PROPOSITION XXVI.

Through a given point to draw a straight line which shall make
equal angles with two straight lines given in position.

In fig. b, let o be the given point and a b and cd the two
straight lines given in position. It is required to draw through o,
a straight line which shall make equal angles with a b and o d.

Produce a b and cd till they meet in s ; bisect the angle ab c
(I. 9) by the straight line b f. From the point o (I. 12) draw o p
at right angles to b f, and produce it to % so as to meet a b and
c D in the points R and s. Then o Q is the straight line required.

Because in the two triangles rip and 8 b p, the angle rbpu
equal (Const.) to the angle a B p, and the angle * P b to the angle
s p B, each of them being a right angle, for r p b is equal (I. 15) to
8 P f ; and the side b p is common to both ; therefore (I. 26) their
other angles are equal, viz. the angle p r b to the angle p a e.
Wherefore a straight line o o. has been drawn through the point o,

and join a h.

Because in the two triangles

abh and dbf, the ride b h

* This exercise should have been been appended to Prop. VIII. ; It
was solved by K. L. Jokes (Pembroke Dock); Q. Prinole (Qlssgow);
D. H. Drxpfibld ; £. Jobbs ; £. J. Bbembbr (Carlisle) ; and others.

370

THB POPULAR EDUCATOR.

wpkmg eqiMlaMleswfckthe two
fi position. Q. E. F.«

lama* a » Aid d, give*

**.*•

&fo#MM. If the linM are parallel, this construction fails. For
■nob a case, it is only necessary to apply Prop. XII. to the con-
struction, and Prop. XXVIII. to the demonstration.

LES30NS IN ALGEBRA.— No. X.

(Continued from p. 251.)
DIVISION OF FRACTIONS.
146. To divide a fraction by a fraction.
Invert the divisor, and then proceed as in multiplication of
fractions.

To invert a fraction, is to turn it upside down, or to make
the numerator the denominator, and the denominator the
numerator.

Examples.

1. Divide \ by 4-
o a

a d ad

Here, we have — X — = tt. Ana.
• o c oc

To understand the reason of the rule, let it be premised,
that the product of any fraction by the same fraction inverted,
is always a unit.

= 1.

»*. « o ab , . _

Thus -r- X — = -t = 1. And -r-r- x

b a ab h+y «*

Bat a quantity is not altered by multiplying it by a unit.
Therefore, if the product of the dividend by the divisor in-
verted be multiplied by the divisor itself, the last product
will be equal to the dividend. Now, by the definition,
" division is finding a quotient, which, multiplied into the
divisor, will produce the dividend.' 1 And as the dividend
multiplied by the divisor inverted is such a quantity, the
quotient is truly fonnd by the rule.

2. Divide £ by £.

Hexawehmve^x^ = ^-. Am.

Froot sl x 7 = i? the ft*****-

3. Divide -**— by — .

r 7 y

Ans,

4. Bivide — ^- by •

x 'a

*y\dy

Mr '
ad

Ans,

30</ 18A

5. Divide — =— by — -.

5 lOy

6. Divide — ^ — by

Ans.

dhr—amy +h my

~* 12 *

7 . Div ide *=** by -i-.

4 * a+\

147. To divide a fraction by an integer.

Divide the numerator by the given integer, when it can be done
without a remainder ; but when this cannot be done, multiply the
denominator by the integer.

8. Thus the quotient of — — divided by m, is ~.

9. Divide — -j by*.

10. Divide — by 6.

* ah—bh'

Ans. — .
8*

148. To divide an integer by a fraction.

Reduce the integer to the form of a fraction, and proceed as be-
fore. Or t multiply the integer by the denominator, and divide the
product by the numerator.

11. Divide a by—.
d

Here, a =-— ; and — divided by - is - X — = — . Ans.
l 1 a \ c c

, c aXd ad

Or, a — -r = = — • Ans. as before.

d c c

12. Divide xy by

a+b

Ans.

Ixy

13. Divide ab+exhy—-r.

14. Divide Zac—x by — .

Ans.

a+b

iab+4ex
am

9ac—Zx

149. By a former definition <; the reciprocal of a quantity is
the quotient arising from dividing a unit by that quantity.'

Thus the reciprocal of— isl-7- — =lX — = - .
b b a a

Hence, the reciprocal of a fraction is the fraction inverted. For

is ;/ ', the reciprocal of

instance, the reciprocal of
1 , **.

**+?

— is ~ or 3y ; the reciprocal of i is 4. Hence the reciprocal
3y 1

of a fraction whose numerator is 1, is the denominator of the

fraction. Thus, the reciprocal of — is a ; of — — , is a+b, &c.

a a+b

Examples for Practice.

Zabc
1. Divide by Zab.

* This eawdae was solved by E. J. Bmmkhb (Carlisle); and J.
WATKiMV (Pembroke Dock).

2. Divide **"*/" by box.

10— y '

3x-4-ll

3. Divide — -*— by 3a.

x J

4. Divide aJr }~ X by d.

led

5. Divide — E- by ~.

x b

Ans.
Ans.

e
x^y

2x+V>

10— f

Ans.^1
k 3«

Ans.

a+1-

Ana.

2cd>
ab+b*

LESSONS IN ALGEBRA.

6. Divide -£r by A * .

Zab ' 4+2«

7. Divide fil by -i-r.

8 a — 6

Am.

is+2mx
3a6y

a*— 6*

8., Divide ^-^ by

7a6
10. Divide 21a*eby- — .

12 *

*+y
6 '

11. Divide Ssy by

lab

Ans. 3«s.
4&gy

12. Divide ISax by *^jf *\

18. Di ^deB±tf) bjr Hf(^L) <
3 '2m

14. Divide 2* + ittl by x + i±?. Ans.

Ans,
Ans.

Ans.

ab '

27gi»

*— y'

6«m+6ms
fl i — ay

4ax+6o+2d

ab*c*
xh,

15. Divide — ^- by ■ :: -^.

*-3

, 2s— 1

16. Divide — — - by , , , .

*+2 ' 3#+l

17. Divide-^- by-^-.

y— 2 J y-+2

18. Divide ^ by — ^.

«+« a — o

19. Divide — by

Ans.
Ans.

2x*+xy+bz.
Ans. — /-.

6s»— #— 1
«*— *— 6

y 3 +2y

y a — 3y+2 '

Ans,
Ans.

20. Divide by -— -.

y* y*»

21. Divide 1 + — by 1 — -\.

22. Divide^ b y f!=i*.

* ' x*y

ax*+ab*
x* — ax

a*x+a»
x*—b*x '

Ans. (*y)»*- n .

Ans.

Ans.
Ans.

a— 1

£ — 6 #

oar 45 — a

24. Divide 1 5-— by 1 + -5 a . Ans. 4 , , , .

a? 3 +« ' ' x 9 — or z*-\-a*x*

15a*

3* a

25. Divide *«+4«»+ -,—5. by*+2a+^-^

Ans

* a +a 2

26. Divide 9* 3 —28 + - ¥ by 3*— 4 . Ans.

' x* * x

SIMPLE EQUATIONS.

x+2a'
3gg+4g— 2

160. Most of the investigations in algebra are carried on by
means of equations. In the solution of problems, for example, we
represent the unknown quantity, or number sought, by a certain
letter ; and then, in order to ascertain the value of this unknown
quantity or letter, we form an algebraic expression from the con-
* *ona of the question, which is equal to some given quantity
Taber.

lb. — A drover bought an equal number of sheep and
cows for 840 crowns. He paid 2 crowns a-head for the sheep,

and 12 crowns a-head for the cows. How many did he buy
of etch?

Here, let * = the number bought of each.

then 2m = the cost of the sheep.

and \2x = the cost of the cows.

Hence, 2*4-12* =840 by the conditions of the question.

Therefore, 14* = 840 by addition ;

and x = 60, the number bought of each.

Here, the last expression is obtained from the preceding one
by dividing each member by 14, the co-efficient of 14*.

It will be perceived, in this example, that the unknown
quantity or number sought, is represented by the letter x ; and
from the conditions of the problem, we obtain the quantity
14s, which is equal to the given quantity 840 crowns. This
whole algebraic expression, 14* = 840 crowns, is called an
equation.

151. An equation, therefore, is a proposition expressing in alge-
braic characters the equality between one quantity or set of quantities
and another, or between different expressions for the same
quantity.

This equality is denoted by the sign =7, which is read "is
equal to." Thus, x+a=zb-\-c ; and 5+8=17—4, are equations,
in one of which the sum of x and a is equal to the sum of 6
and c ; and in the other, the sum of 5 and 8 is equal .to the
difference of 17 and 4.

The quantities on the two sides of the sign= are called mem-
bers of the equation ; the several terms on the left constituting
the Jtrst member, and those on the right the second member.

When the unknown quantity is of the first power, the
proposition is called a simple equation ; or an equation of the
first degree.

1 52. The reduction of an equation consists in bringing the unknown
quantity by itself to one side of the sign of equality, and all the
known quantities to the other side, without destroying the equality of
the members.

To effect this, it is evident that one of the members must
be as much increased or diminished as the other. If a quan-
tity be added to one, and not to the other, the equality will
be destroyed. But the members will remain equal,

1. If the same or equal quantities be added to each. Ax. 1.

2. If the same or equal quantities be subtracted from each.
Ax. 2.

3. If each be multiplied by the same or equal quantities.
Ax. 3.

4. If each be divided by the same or equal quantities.
Ax. 4.

The principal reductions in simple equations are those which
are effected by transposition, multiplication, and division.

Reduction of Equations by Transposition.

In the equation x —7=9, the number 7 being connected with
the unknown quantity x by the sign — , the one is subtracted
from the other. To reduce the equation, let 7 be added to both
sides. It then becomes x— 7+7=9+7.

The equality of the members here is preserved, because one
is increased as much as the other. But on one side, we have
— 7 and +7. As these are equal, and have contrary signs,
they balance each other, and may be cancelled. The equation
will then be =9+7.

Here the value of * is found. It is shown to be equal to
9+7, that is, to 16. The equation is therefore reduced. The
unknown quantify is on one side by itself, and all the known
quantities on the other side.

In the same manner if x — b=a ;

Adding b to both sides, we have x — £4-6=0+6 ;

And cancelling as before, we have x=ia-\-b. Ans.

153. When known quantities, therefore, are connected with the un~
known quantity by the sign + or — , the equation is reduced by
transposing the known quantities to the otner side, and prefixing
the contrary sign.

This is called reducing an equation by addition or subtrac-
tion, because it is, in effect, adding or subtracting certain quan-
tities, to or from each of the members.

Example 1.— Reduce the equation #+36— m=zK—d.

Here, transposing +36, we have *— -m=A— rf— 36 ;

And transposing — m, a=A — a— 36+ni. Ans.

272

THE POPULAR EDUCATOR.

164. When leTeral term* on the tame aide of an equation are
alike, they must be united in one, by the roles for reduction in
addition.

Example 2.— Reduce the equation *-f6*— 4A=76.

II« re, transposing bb — 4 A, we have z=z7b — 56-|-4A ;

And uniting 7b— bb in one term, we hare zz=2b+ih. Ana.

1 55. The unknown quantity must also be transposed, whenever
it is on both sides of the equation. It is not material on whieh
side it is finally placed, though it is generally brought to the
left-hand side.

Example 3.— Reduce the equation 2x+2h=h+d+Sx.

Here, by transposition, we have 2h—h — d=zZz— 2x;

And by incorporation,* h — <k=x. Ans.

156. When the tame term, with the same sign, is on opposite
tide* of the equation, instead of transposing, we may e xpu xge it
from each. For this is only subtracting the same quantity
from equal quantities.

Example 4.— Reduce the equation x-\-W*>\-d=b+3h-\-7d.
Here, expunging 3A, we have x+d^b+Td ;

And by transposition and incorporation s=h-\-bd. Ans.

157. A* aii the terms of an equation may be transposed, or sup-
posed to be transposed, and it is immaterial which member is
written first, it is evident that the tign* of all the term* may be
changed, on both sides, without affecting the equality.

Thus, if we have x-b=d—a

Then by transposition, we have — rf4-a=— x-\-b

Or, by changing the places of the members, — x+b=— rf-fa.

158. If all the terms on one side of an equation be transposed,
each member will be equal to 0.

Thus, if x\b=d\ then it is evident that x+b-d=0.

Examples.

a+2x — 8=* — t+x+a. Ans. xz=b+4.

y + ab— hmz=a+2y — ab+hm. Ans. y = 2ab

— 2hm — a.

A+30+7*=8— 6A+6V — d+b. Ans. *=*— 7 A

— d-22.

bh + 21 — 4x+d=\2 — Zx+d— 7bh. Ans. x=

Sbh+9.

bx+\Q+a=!25+ix+a. Ans. j"=15.

5c+2*+l2— 3=a:+20+6>. Ans. *=ll.

a+b— 3x=20+a— ix+b. Ans. s=20.

£+3—2*— 4=34-4-3*— 4— bx. Ans. a=31.

5. Reduce

6. Reduce

7. Reduce

8. Reduce

9. Reduce

10. Reduce

11. ^Reduce

12. Reduce

ANSWERS TO CORRESPONDENTS.

K. 8. (Greenock) : For Dr. Beard's " Latin Made Easy," you mast apply
to the publishers of that work, vis. Messrs. Bimpkin and Marshall, Lon-
don.— T. II. E. : Beta's Latin Testament.— 8— l (bunderland) : We don't
know.— Voluntary Education (Sheffield): "Cassell's Lessons In Ger-
man" are expre*»ly stated to be a reprint from the P. E. The " Historical
Educator" is intended as a substitute for the promised Lessons in History
in the P. E. You will not get on well with the German, or, indeed, any
language, without a dictionary; "Cassell's German Dictionary" is now
publishing in numbers at 9d. each.— Juvbnis (Springfield) would have
written better had he heard a good sermon ; the grammar appears to be
well enough.— Dkutciik: Yet.— Plodding Genius (Louth;: His paper
on" Perseverance in lieu of Genius," is very good; but it Is capable of im-
provement. Let him try again, but take this new teat : " Perseverance is
Genius "

C. 8. (Kinross) : The magic lantern will be explained by-and-by under
Optics. Lenses of every kind may be had in town. — Sacra Bott (Atholl) :
The most common unit for measuring the earth- work of ditches is the
eubic yard. The best rule is *o consider the ditch, if uniform, as a prism,
lying on one side, and cast up the earth-work accordingly.

G. Haipih (W. Hall): We have not seen a Geographical Pronouncing
Dictionary.— A. K. B. (Edinburgh): Yes.— J. Mathbson (Glasgow): You
are doing very well ; go on as -you have begun; finish the lessons in the P. E.
first.— Tymo (Manchester) : Not decided.— Johannes (Bradford) : The rule
to inaccurate ; it should be, every syllable in Greek is pronounced as in
English : example, ttonvnt* **-re*-w«w.— A. Alison (Liverpool) had better
learn good manners before music— J. B. (Edinburgh): Bome was not
built in a day. We can't put everything into the P. E. at once. We can't
recommend you books on Logic and Moral Philosophy unless we were
intimate with your previous otudies .

This term is used to include both additions and subtractions.

A Wiu-Wumi (Arsett); ** Although offensive, sulphuretted hydrogen
may be Inhaled, when largely mixed with air, without apparent injury ; and
I hare known it to be inhaled in large quantity, when fresh, without oro-
dacing further harm than faintness. I have breathed a strong admixture of
it with air repeatedly, and never experienced the slightest evil result.
Thenard says that birds are killed by a mixture of T ^ of it In air; dogs
by ibo of it; and a horse by ^ of it." J. C. B.— A. Scholar: Nitric
acid is composed of U parts of nitrugen and 40 parts of oxygen, or 1 propor-
tional of nitrogen ami G proportionals of ox > gen. *' It is used extensively
in chemistry and the arts ; foi etching on copper, and as a solvent of tin to
fbrm » mordant for some of the finest dyes ; in metallurgy assaying to bring
the met.iU to their maximum oxidation ; in medicine as a tonic. The nitric
acid of commerce Is half water, and is called double aquafortis ; another
kind, containing three-fourths water, is called simply aquafortis.**— Gray.

All of our Correspondents up to this date 16tit Jan. 1854, are in error
about the Four-ball Question. In the solutions we have received, the four
ball* do not touch each other.— B. Crimshaw (Lambeth) should take the
adviee of his friends.— T. Cave (Oee Cross) : The " verted sine of a piece of
cheese " Is an expression that cannot be admitted into the P.E.— B. O.
Bbay (Bodmin) : The rule about committing all exercises Xp memory, must
be taken cum grano tali* ; an author sometimes jocosely, like a doctor,
prescribes more than he knows will be Ukeo, in order that some may be
taken.— T. H. Mbtiivbn (Hoxton): Man) thanks for his kind hints.— J.
Young (Huddersfleld) : The Krench Lessons are finished. ** Le Giviliaateur "
may be had of 1>. Nutt, Foreign Bookseller to the Queen, 270 Strand.

II. Hartbbo (Dover) : Study I^tin, Greek and Hebrew in order, and in
the P. E. until jou can read the Scriptures in their original tongue*. J.
Bentok : Mathematics, Natural Philosophy, and Chemistry are the most
useful sciences; all arts are founded on these.— B. Nuxsi (Maehen),: The
Lessons in English are finished.— Wai N : Received.— L. Murthy (Queen-
borough) : He has hinted what we intend. A rav of white light is divided
in the following proportions, according to Newton and Fraunhofcr
respectively.

Red. Orange. Tellotc. Green, Slue. Violet
Newton 45 27 40 60 1U8 c*

Fraunhnfer 56 27 27 46 95 109

J. W. W. (Portsea) : The honours attainable at Matriculation and Gra-
duation In the University of London are substantial, see the P. L. vol. ii. p.
138, col. 2 ; and p. 215, col. 2.— A. P. T. (Cranbrook) : Your trisection of
an angle won't do.— Constant Bbadbr (Wishlel): "The population of
China has been variously computed at from 150 millions to so high a number
as 360 millions — the latter of which is the native statement, issued under the
imperial authoiity. This is considerably more than one-third of the estimated
population of the globt-, aud would amount to an average of upwards of 280
inhabitants to the square mile." Hughe* Manual of Geography.— &. Man :
See vol. ii. p. 137.— Passaio (Glasgow): Cassell's Arithmetic, Algebra, and
Geometry, abb not rl prints from the P. E. but works which were
demanded by the readers of that work, before the lessona on these subiect*
could be completed ; they may be read before the P. E., after the P. E., or
along with the P. E. the last method being the beet. Some French books arc
on the tapis. The Latin Lessons in the P. E. are the best; they may be
followed by Zumpt's Latin Grammar by the higher students. As to
the French Dictionary it will soon be completed ; don't grumble ; editors are
as liable to be taken ill as other people. As to the use of the word Fin**, you
are right, my bo> ; but it is never used in books note; we only follow the
multitude ; but if a fellow does not know when a story is done, he has not
surel> attended to it while in progress; and in that case, he would be none
the wiser, if we said our story i* ended.

LITERARY NOTICES.

JOHN CAS8ELL»8 FBENCH WOBK8.

Now ready, price 4s. in stiff Wrapper, or 5s. strongly bound in cloth,
the First Part complete, consisting of the French and English, of Casibll's
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Price 9s. fid. bound in cloth, or the Two Divisions may be had separate.

A Comtletb Manual or tub French Lanuuaob, by Professor Ds
Lolme, just published, price 3s. neatly bound. This forms one of the
most simple, practical, and complete Guides to a thorough knowledge of the
French Language which has hitherto been published. The plan upon which
it is conducted is admirably calculated to accomplish the proposed object.
In the first place, the Grammatical Principles of the Language are clearly
laid down, and, secondly, these Principles are copiously illustrated by suitable
Exercises of English to be turned ioW French.

Cassbll's Lbssons in Fbbnoh, Parts I. and II., in a neat volume, price
each 2s. in stiff covers, or 2«. 6d. neatly bound in cloth ; or bound together,
4s. 6d.

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LESSONS IN MUSIC.

273

LESSONS IN MUSI C— No. XXII.
{Continued from p. 226, Vol IV.)

In explaining, in our two preceding lessons, the nature of the old
and established notation, we have slightly anticipated the subject
of the present lesson. We shall now conclude our lessons on
Music for the present by elucidating the subject of " Minor
Tunes." Why they are so denominated we shall explain presently.
But, first, let us ask our readers to recall all that we hare said

in former lessons on the " mental effect " of the note lah (the
sixth above the key-note or the minor third below), or, better
still, let them recall all they have themselves observed and felt
in connexion with it. Was it not always, when sung slowly,
the iorrovrful note t Then let us suppose ourselves trying to
compose a very sorrowful tune, — should we not naturally
employ this note in the most effective positions? Without
composing, however, let us just recall one of the oldest tunes of
this kind in existence.

Key F.

*=*=}

X=K

e - viL

A-

m :m

gainst Thee,

m : m .m

Thee on-ly,

f :m
have I

r :d

sin* ned,

.r r :r

And done this

d :■

ti :li

thy sight.

You notice what a sorrowful effect is produced by simply I sadness. Take the example with which Mr. Hickson Ulus-
cloaing on lah instead of the key-note. Yet more stnk- trates this subject : —
ing is this effect, if the tune also opens with this note of I

Key C.

1 :t

Far from

d 1 :r*

home and

m 1

all

:f l

its

m l :r'

kin - died,

far,

far

: .1

1 :-

way.

Two other examples, in the well-known tunes St Bride** I mind the effect of lah when thus placed in effective
and Wirhsworth, will bring more clearly before the | positions : —

Kbt C. Lah Mods.

. :d'

joys and

t 1 I » :f

griefs are jpawed a -

m :m l

way, Their

1 :r*

wealth and

d l :t

hon - 0111

1 :

gone.

Kbt 8 jUt. Lah Modi.

££

And

m .r:d:ti

must this bo-dy

L:— :m

die, This

8 .f : m : r

mor-tal frame de-

m:— :d

cav ! And

tj.L :m :d

must these active

r .d:tx :t.

limbs uf mine Lie) mould'

m .r:d :ti

'ring in the

clay?

Our pupils will now be prepared for the following exposition
of the subject before us.

0. In some tunes— chiefly those which are intended to ex-
press a mournful sentiment — the note lah is found to predo-
minate. It is necessarily heard both at the beginning and at
the end of such tunes ; and assumes almost the importance of
a governing or key-note, but without changing (as soh and

VOL. IT.

fah do when they become key-notes by " transition") its own
musical effect. It still leaves on the mind the impression of
" sorrowful suspense."

b. Modern musicians, in order to give to lah a closer resem-
blance to the ordinary key-note, and to direct the ear to it
mere decisively as the note on which the tune closes, as well
as to increase the general effect of such tunes, occasionally

274

THE POPULAR EDUCATOR.

introduce a new note, which we shall call btb, a tonule below
lab. This note bean the same relation to lah which tb bears
to doh. Musicians also think it necessary sometimes to intro-
duce another new note, which they then use instead of fah.
It is a tone below ws, or a chromatic part-tone above fah.
We call it bah. It bears the same relation to kb which lax

bears to tb. Bah, kb, lah, heard in succession, resemble, in
mental effect, lah, tb, doh. The learner may sr metimes strike
bah more easily by thinking of it as TV. The note kb is in
frequent use, but bah is very seldom used in f rdiaary music.
Tr the following Scottish tune :—

Key G. La Mode.

e. Tunes of this kind are commonly called minor tunes,
from their haying the interval called a minor (smaller) third
immediately above their predominating note lah — (lah, doh),
and in distinction from other tunes which have a major (larger}
third above their predominating note doh. They may be said
to be in the lah mode. It is advisable to take their pitch by
means of doh, ts in other tune*. The signature may be written
in this form, " Lah mobb, key A."

Those who studied with us the modifications in the mental
effect of the note lah, will be quite prepared to understand
how this kind of tune may be used in the serio-comic style,
and how by quickening the speed thsy may even express a

Key D. La Modb.

lively careless abandonment. Of this we have several examples
in the old English music. It will be a good vocal exercise for
our pupils to learn to solfa them. What a pity that such fine
music should have been set to the words of a foolish sentiment
or a savage drinking-song I For the first, better words are
given in ChappelTs collection of " National Bnglish Airs. 9 * It
is entitled the Widow's Song. To such words the tune must
be sung more slowly. There is nothing comic in this tad wail.
To the second we have adapted words from a poem of tragic
truth, by James Russell Lowell. The third wo have left at
it is.

td^t
Oh!

Ls :m.d I r:m

leave me to dream and

weep, Or

1:-I—.M d'rd^dMt^id^t

lift ye the church-yard

l:-|-:Lt
stone, And

d l idS.d 1 Itj'id.t
send me my dead thro* the

5fe

w=m

-h

*SE?

1 :1 |m :d l .,l

twi- light deep; For I
Key F. La Modb.

1 .g :m .d I r :m

sit by my hearth a •

1 : - I d' : -.1

lone, I

1 .s :m

sit by

.d ir :m

my hearth a •

d l :l

=8*

1 : ne 1 1 : m

Sis - ten two, all

f:r|m:-

pmbo to you,

f :m It :d

with your fa - ces

8 :Si Id: —

pinched and blue;

1 : ne 1 1 : m

To the poor man

f :r |m: —

you've been true

* f : m I r :d

From of old ;

8 .,8 :% x Id:-

Hun-ger and Cold !

l:-.ne II -.t

You can speak the

d' :t Id 1 :-

keen • est word,

dLrtrnJ Is :n

You are sure of

:S=5

=£

f, w Jf

r.m ; f.s fl :

be - ing heard,

l:-.l |i:-.g

From the point you're

f:-.f I mi-
ner - er stirred,

d 1 .t : Lne I l_j_r

Hun-ger and Cold !

m .m : m 1 1» : —

Hun*ger end Cold !

LESSONS IN MUSIC.

275

Kbt B Jtat. Lah Mode.

There
He

li : — : li |n$i:-:mi

wai a jol - ly
worked and sang from

d : — : d I U : - : r

mil - ler once, LivM
morn till night, No

d:— :li Hi.:— :nei

on the nv - er
lark more blithe than

Dee, • •
he, • •

r: — :r I r : — : ti

of his song For

d:— : — It,:

be,. .

-:mi
i

lii-

ili I Mi rlMhiMBi
for no - bo - ay,

4:-:dlt.:

no, not I,

d :-.ti:li ! 1m 2=— :

no - bo - dy cares

Mi
for

1, :-:---:

me. . .

The musical facta which are here ascribed simply to the eotn-
mm seal* used in a peculiar manner, and admitting occasional
variations— rare usually supposed to be founded on an entirely
new scale, and that of a very remarkable structure. This new
scale is described as having its "semitones" between its
second and third, and fifth and sixth notes. (If you reckon
from'LAH t to lah, in the common mode, you will find the
tonules thus placed.) But the scale, it is said, only retains
this form in descending, *° r in trending the sixth and seventh
are sharpened (making our occasional bah and nb) so as to place
the "semitones" between the second and third, and seventh
and eighth. This is, in fact, two scales ; and some teachers of
the pianoforte have gone so far, Dr. Mainser tells us, with this
" illogical system," as to make their pupils play with the right
hand ascending the seals— bah and nb, at the same time that
the left hand descending produced the sounds par and soh !
He justly remarks that " the simultaneous unison of notes so
opposite, producing an effect so discordant, is more calculated
to destroy than awaken the musical sentiments of the pupil."
Let us examine facts and authorities on this subject.

First, then, it appears that the common scale, even without any
now not* (nb or bah), but simply allowing lah to predominate
and to be heard at the opening and at the close of a tune, it
quit* snJMent to pr o d uc e a true "minor" tune~ and that many
fine melodic*, manifestly minor, are firmed on thie model, using the
ordinary notes of the common scale (from lah a to lah) both
ascending and descending, and not requiring the aid of any
accidental note. No one can doubt that the first, second,
third, fourth, and sixth of the examples given above are minor
tones, nor hesitate to allow that they are formed on the com-
mon scale, and are simply distinguished by their making lah,
the proper mournful note, predominate. Accordingly we find
Dr. Crotch describing his " ancient diatonic minor key "
(which corresponds with our common scale when you reckon
from lah to lah 1 ) as "the scale of the ancient Greek music,
and found in the oldest national tunes, in psalms and oathedral
music,'' — Dr. Bryce speaking af this as the " proper " formula
of minor tunes, in which are written " multitudes of exquisite
melodies, especially among the ancient national music of differ-
ent ooantria» f , '-*and Dr. Mainser maintaining that this is the
only true end the only agreeable arrangement of notes for such
tunes. By Usee, then, and by competent authority, the com-
mon soalb with lah predominating is declared sufficient to
produce e true minor tune. But still, it may be argued, are
not bam and MB the "sharp s'crth and seventh " (reckoning
from lah, ae though it were the key-note) always used in tunes
of this kind (instead of pah and soh) when the music attend* ?
Are they not, therefore, essential at least to every minor passage
in which the music atoendt from its sixth or seventh note?
Must we not necessarily suppose a distinct scale in which these
essential notes easy find a place ? We deny the proposition,
and the conclusion falls, for —

Secondly, it appears that the new note* bah and nb (" the
sharp sixth and seventh ") ewe not eeeential even m -"—J*"

passages, and that the use of them ie entirely arbitrary. Nothing
can prove this more clearly than the great discrepancy and
disagreement among the best authorities on this subject. If
there had been any fixed usage, long established by the require-
ment of good ears and the example of the best composers, such
opposite statements of fact could not have existed. In refer-
ence to bah (the " sharp sixth ") we find Dr. Callcott describ-
ing this note as " accidental," but rendered necessary for the
sake of avoiding what he calls " the harsh chromatic interval,"
pah nb, "from p natural to o sharp "—while M. Galin and M.
Jeu de Berneval refer to this very interval as " a constitutive
interval of the minor mode," full of " melancholy," "replete
with anguish and tears," and speak indignantly of those who
would "cancel" the very interval which is most " character-
istic " of the " minor mode." Is it not evident from this, that
the use of bah is arbitrary — by some approved, by others dis-
approved ? In reference to nb. Dr. Callcott declares that it is
an " essential " part of the " minor scale " in ascending, but not
to be used in descending. M. Galin and M. Jeu speak of nb ae
" invariable " and essential both in ascending and in descending,
and M. Jeu gives examples of its use in descending. Schneider,
in his " Elements of Harmony," maintains the same opinion.
Marpure y " one of the most influential theorists, who flourished
-during the latter half of the last century" (Mainser, 77), declaree
that "this custom" (of using bah and nb) by no means
changes the essential nature of the tonnlity (key or mode
reckoning from lah to lah 1 ), and the two sharp* which are
prefixed to the sixth and seventh degree are purely accidental.' *
Dr. Crotch says distinctly of both bah and nb, " thete altera*
tione are only occasional. 11 Dr. Goss says, "The sixth and
seventh (pah and soh) are generally made accidentally major in
ascending." Dr. Bryce ascribes the introduction of these
notes to modern musicians, who prefer harmony to melody.
Dr. Mainser says that there are a very large number of com-
positions " in which the leading note (nb) does not appear at all
in the minor keys, and this is the case with many composer*
of the fifteenth, sixteenth, and seventeenth centuries. He
then adduces examples from Gabrielis, from Falestrina, and
from Morale, and also shows how, in the eighteenth century,
along with professedly improved harmonic*, nb was intro-
duced as an occasional note, but not essential— MareeUo, for
example, introducing the following passage immediately after
one in which nb haa occurred.

li :Si,fi lS i :«i

ptd - tos

Dr. Mainzer, who is a high authority on subjects of musical

276

THE POPULAR EDUCATOR.

taste, and none the less so because he laboured generously to
make music the property of the people, thus concludes:—
"Let any one sing the shore scales one after the other (four
varieties of the so-called "minor scale "), and- assuredly he will
not be long in discovering which of the four is the most
agreeable and natural, and most in the character of the minor
tonality (key). It is evident that the scales with leading notes
(me), instead of being pleasing, are disagreeable to the ear, and
impracticable to the voice. The absence of the leading note
(nb) on the contrary often gives to the melody something mqjestu
and solemn. The Gregorian chant, so remarkable for melodious
beauties, affords many proofs of this, and also the popular
melodies of different countries, especially those of Ireland and
Scotland, so much admired by the greatest musicians." Surely
here is example and testimony enough to prove these notes—
whether good or bad — at least non-essential and arbitrary.

One question yet remains. Should not the scale on which
minor tunes are framed be still treated as a distinct one, and
something mere than the common scale used in a peculiar
manner } To which we answer— Yes, if it is distinct ; but, if
otherwise, why multiply difficulties and conceal the truth i
But it dearly is not, in any particular, distinct. First, in refer-
ence to the "character " or musical effect of the notes — the most
important particular of all — the notes of the so-called minor
scale correspond precisely with those of the common one (rec-
koning from lah to lah 1 .) Not a single note of the common
scale changes its character when used in a minor tune. "Lab. it
still the sorrowful, t* the piercing, fah the awe-inspiring note,
&c, as before. Next, in reference to the exact intervals be-
tween the notes — they are precisely the same at those of the
common scale (from lah to las. 1 ) with only this peculiarity,
that the graver (flatter) position of the " variable note " bat is
ordinarily used in tunes of this character, whereas it is only
occasionally used in other tunes. Premising that from doh to
doh 1 is commonly called by musicians a major key (beginning
with a major, or greater, third, doh mb), and that a minor key
beginning on a note in the position of our lah would be called
its relative minor, let us quote the following testimonies to the
last point. Colonel Thompson says—" The change to the rela-
tive (or, as it would more properly be called, the synonymous)
minor reduces itself to avoiding the acute second of the old
key (r*) and using only the grave (r % )." (See " Westminster
Review," April, 1832). Dr. Crotch aavs— " Some authors
make it " (the first note of the principal minor key)- " the same
as the note lah of the relative major kev, viz., a in the key of
c, a minor tone " (smaller tone — of eight degrees) " above o
<soh). In that case all the natural notes excepting n (bat)
correspond with those of the major key of c." (See Crotch's
" Elements "—Tuning, &c") Turning to his illustrative plates,
we find the scale of minor tunes requiring the smaller tone
(eight degrees) between doh bat, and the larger tone (nine
degrees) Let ween rat me, while other tunes usually require
a hrger tone between doh bat and a smaller one between
rat me. In fact the variable note assumes its grave position.
But it sometimes does the same in the common scale. Is this,
then, a peculiarity sufficient to establish a new scale ? More-
over, is it not natural to suppose that the common scale, which I
is found to be essentially the musical scale of all nations, must
hold a peculiar accordance with the ear and the sympathies of
the human race } and is it not proper, therefore, to consider
this as the one scale, and everything else that cannot establish a
distinct and independent character as but a modification or a
peculiar use of it ? It is certain that great detriment must be
done to the mind of our pupils, and great hindrance given to
their progress, if we first cause them to study and practise our
theory, of a new and self-contradictory minor scale, and then
leave them to discover that, in music itself, instead of the arti-
ficial difficulties they have so laboriously mastered, there is only
to be found the common scale, so used as to produce a peculiar effect
and the merely occasional, non-essential, introduction of a new note I

[We were present, in October last, at « several choral performances
of pupils who were taught to ting on the method developed in these
letsooB. some of which were attended by more than 8,000 people. We
saw a choir of cfiUdren who sang magic sAftrst sight, a thing quite new
to us. The " Tonlo Solfa Association - numbered 2,000 pupils in Lon-
don alone last year, and the meetings referred to were the means of
originating at once three new classes of about 200 pupils each. We !
may claim, for the Popular Educator, the credit of giving a cosmo*
politan influence to these vsluable effort*.]— Ed.

Sometimes in the course of a tune
the music takes the " minor " charac-
ter, introducing the new note xb, and
returns again to the ordinary use of
the common scale. Occasionally, too,

I the mufric passes into the minor of the

1 soh ut, making a new note, a tonule

[below mb, which (to distinguish it

I from xb of the original key) we call

1 mu ; and, not unfrequently, it enters

I the " minor" of the pah kbt, origi-

I nating another note, a tonule below bat
(r*), which we call in. The modula-
tor at the aide will illustrate these
changes.

Another " transition " into what is called the " minor of the
same tonic " (doh becoming lah), is more proper to " tern-
I pared " musical instruments than to music itself or the unaided
voice. You may treat it as transition into the key of m flat,
or, retaining the syllables of the original key, the new notes
may be treated as chromatic. Thus you will have the oddly-
sounding notes mow, low, and tow, as any one may perceive
by drawing the two keys side by side, and bearing in mind the
difference between the tonule and the chromatic part-tone.

Our pupils will now be able to ransack the stores of classical
music, and to take their '< part " in fireside glees, at their plea-
sure. They will be very largely, and, we hope, very long, re-
warded for all the patience and painstaking which we have
demanded of them.

d»

ft-f

1
ne

d
ti— tu x

n !—«•*,

•i

n\x — n x

•i

Flf. TO.

ON PHYSICS OR NATURAL PHILOSOPHY.
No. XIX.
{Continued from page 261.)
THE ELASTIC FORCE OF GASES.
Experiments of Boyle. — The principle that the elastic force of
air increases in proportion to its density, was first proved by
Boyle in 1660, in the following manner : — He took a uniform
tube abc, fig. 79, closed at c and open at a.
and bent upwards so that the part ox was
parallel to the part a m. Mercury was poured
in at the open branch a until the level in both
branchea of the tube stood at m and h respec-
tively, and the air in the closed branch on was 1
of the same density as the external air in the
branch a m. The distance o x was then mea-
sured and found to be 12 inches ; the pressure
in both branches was equal to 30 inches of
mercury, being that of the atmospheric air;
and the height of the mercury in the longer
branch a m above the level of that in the shorter
branch was 0. More mercury was poured in
at a, until the distance c w waa diminished to 10
inches, and the mercury stood in the longer
branch 6 inches above that level ; the pressure
in both branches was now eoual to the atmo-
ipheric pressure, 80 inches of mercury, and 6
inches of mercury additional, or 86 inches in
all ; more mercury was again poured in at a,
until the distance on was diminished to 8
inches, and the mercury stood in the longer
branch 15 inches above that level ; the pressure
in both branches being now equal to the a t mosnh
end 15 inches additional, or 45 inches in alL Tne
was repeated again and again, end the results tabulated as
follows : —

sb both
of the

Distsness from c

to h In the shorter

branch.

Heights of Men

in ax above

level In c h .

12 inches
10 „

8 „

6 „

4 „

inches

6 „
1* ,.
30 „
60 „

30 inches
86 „

80 M
90

The distances from c to n in the shorter branch diminishing

NATURAL PHILOSOPHY.

277

at the heights of the mercury inrfhe longer branch, and conse-
quently the pressures in both branches, increase, proves that
the densities of the air in the shorter branch increase as the
spaces diminish ; and that the elastic force of the air, mea-
sured by the pressures, is proportional to its density ; for we
have, by comparing the distances in \h* first column with the
pressures in the third column, the following inverse pro-
portions:—

10
8

36
45
60
90

30
36
45
60

These proportions clearly show that the pressures, and conse-
quently the densities, are inversely as the spaces occupied by
the same quantity of air ; whence it follows that the elastic
foree of air is proportional to its density.

Mariotte' t Law. -Mariotte, a French philosopher, was the
next experimenter who established the same principle in 1668,
by the announcement of the following law, which has ever
since borne his name, vis. :— " That the volume of any quantity
of gas. at a given temperature, will diminish in the inverse ratio
of the pressure to which it is subjected." This law is verified
in the case* of air by means of the following apparatus :--Un
a wooden board placed vertically, is fixed a glass tube bent

Fig. 80.

upwards in the form of dn inverted siphon ; that is, having
two unequal branches, see fig. 80. Alongside of the shorter
branch, which is closed at the top, there is placed a scale
indicating equal capacities or volumes in the parts of the tube
corresponding to the parts of the scale ; and alongside of the
longer branch there is also placed a scale indicating equal
altitudes In centimetres. The zeros, of the two scales are on
the same horizontal line.

In order to make the experiment, mercury is poured into the
tube at the top of the longer branch, so that the level of this
liquid may correspond to the zero of the scales of the two
branches, a result which may be obtained by several trials.
The air contained in the shorter branch is then subjected to the
atmospheric pressure, which acts in the greater branch, when-

ever the level in both branches is not the eame. Mercury is
again poured into the larger branch until the pressure which
arises from it reduces the air contained in the smaller branch
to one-half its volume ; that is, this volume, which was at first
measured by 10 on the scale, is now reduced to 5, as shown in
fig. 801 Now, measuring the difference of level c a between
the mercury in the two branches, wo find that it is exactly
equal to the height of the barometer at the moment when the
experiment is made. The pressure of the column c a is there-
fore equivalent to that of one atmosphere ; by adding to it
the atmospheric pressure which acts at c, at the top of the
column, we'see plainly that at the instant when the volume of
air is reduced to one-half, the pressure is double of that which
it was at first ; which proves the truth of the law in this case.

If the greater branch of the tube were long enough to admit
of mercury being poured in till the volume of air in the smaller
branch was reduced to a third of what it was at first, we should
find that the difference of level in the two branches is equal to
twice the height of the barometer ; that is, it is equivalent to
the pressure of two atmospheres, to which adding that which
acts directly on the surface of the mercury in the greater
branch, gives a pressure of three atmospheres. It is therefore
under a triple pressure that the volume of air is reduced to
one-third of Us volume. The law of Mariotte has been experi-
mentally verified in the case of air by MM. Dulong and
Arago, as far as 27 atmospheres, by means of an apparatus
similar to that now described. In order to demonstrate the
truth of the law for any gas, the apparatus must be modified
to admit of the introduction of the particular gas in question.

The law of Mariotte has been verified also in the case of
pressures less than that of the atmosphere. Thus, a baro-
metric tube being filled only to about two- thirds of its length,
the other third containing air, it is inverted and immersed in
a deep jar or vessel full of mercury, fig. 81 ; the tube is then
sunk in the vessel until the level of the mercury be the same
within and without the tube ; the volume of the air contained
in the tube is determined by a scale fixed to the vessel, this
air being now under a pressure exactly the same as that of the

Fig. 81.

atmosphere. The tube is now raised, as shown in the figure,
until, oy the diminution, of the pressure, the volume of air is
doubled, as shown by the scale ; it will then be found that the
height of the mercury in the tube at a is the half of the true
height of the barometer. The air of which the volume is thus
doubled, is therefore submitted to a pressure of only half an
atmosphere, for it is the elastic force of this air which, united

278

THE POPULAR EDUCATOR.

to the weight of the raised column, balances the pressure of the
exterior atmosphere. The volume of the air is therefore still
in the inrerse ratio of the pressure to which it is subjected.

In the experiments just detailed, the mass of air in the tube
remaining the same, its density becomes mater in proportion
as its volume Is reduced ; whence we deduce the following as
a consequence of the law of Mariotte, that, " at a given tem-
perature, the density of a gas is proportional to the pressure
which it sustains." Consequently, under the ordinary pres-
sure of the atmosphere, the density of air being a 770th part
of that of water, it follows that, under a pressure of 770 atmo-
spheres, air would have the same density as water, if at such a
pressure it would be still a gas.

Till recently, it has been considered that the law of Mariotte
was true for all gases and under all pressures. M. Despretx was
the first who showed that this law ceases to be striotly true when
the gases are subjected to a pressure nearly equal to that which
produces their liquefaction. Lastly, M. Regnault has proved that
this law does not apply equally to all gases. Thus, air and nitro-

£n are compressed a little more, and hydrogen a little less, than
at whioh it indicates. In the case of carbonic acid, it does not
even furnish an approximation to the truth when the pressure Is
considerable.

Applications of Mariotte* s Zatc. — The following examples of
the application of this law may be useful to students of Chemistry
and Phytic*.

1. A vessel in which air can be compressed contains 4 3 gal-
lons of air, the pressure measure bv the barometer being 29*6
inches; what will be the volume of air at the pressure of 30- 4
inches ? If * denote the volume required, we have,

* : 4*8 : : 29*6 : 30*4 ; whence,

30-4 8

S. Haying 20 gallons of gas under the pressure of one atmo-
sphere ; to what pressure must it be subjected, in order to reduce it
to 8 gallons ?

If p denote the pressure required, we have,

: 20 : 8 ; whence,
.20X1 —

pi\

: 8$ atmospheres.

3. A gallon of air weighs 80 grains at 32° Fahrenheit, the
barometric pressure being 30 inches ; what will be its weight at
the same temperature, when the pressure is 28 inches ?

If w denote the weight required, we have,

w : 20 : : 28 : 30 ; whence,

p== 20X28.

30 "

:18£ grains.

The Manometer. — The name manometer (from the Greek, rarity'
measure) is generally applied to instruments employed in measu-
ring the tension of gases or vapours when it is greater than the
pressure of the atmosphere. There are various kinds, as the free-
air manometer, the oompressed-air manometer, and the metallic
manometer. In these different kinds, the unit of measure which
is employed is .the atmospheric pressure, when the barometer
stands at 30 inches. Now, we hate seen that this pressure on a
square- inch is 14} lbs.; consequently, if we say that a gas has
a tension of two or three atmosp betas* we mean, that it acts on the
sides of the vessel which contains it with a pressure of twice or
thrice the weight of 14} lbs. per squire inch.

Free-air Manometer.— This manometer is composed of a strong
glass tube b d, fig. 82, about H yards long, and a cistern
d, made of iron, containing the mercury in which the tube is
immersed. This tube is cemented to the cistern and fixed on a
board, along side of which If placed another tube a c, made of
iron, and about 5 yards long | by means of this tube the pressure
of the gas or of the vapour is transmitted to the mercury in the
cistern. As manometers of this kind are most frequently
used in cases where vapour of high temperature, or steam,
would soften the cement which is employed to fix the glass
tube to the cistern, the tube a o is filled with water ; and it
is by this means that the pressure of the vapour is transmitted
to the mercury.

In order to graduate the manometer, the orifice a is allowed
to communicate with the atmosphere, and at the leyel where

the mercury becomes stationary in the glass tube, the figure

1 is marked, signifying one atmosphere ; then, proceeding

from this point by 30 inches at a time, the

figures 2, 3, 4, 5, and 6, which indicate the

number of atmospheres, are marked, because

a column of mercury of the height of 80

inches represents the pressure of the atmo-
sphere. Then the intervals from 1 to 2, 2 to

3, &e., are divided into ten equal parts,

which give the tenth parts of an atmosphere.
If the tube a be now put in communication,

for example, with a steam boiler, the mercury

will rise in the tube b d to a height which

measures the tension of the steam. In the

figure, the manometer is shown as marking 4

atmospheres, which are represented by 3

times the height of 80 inches, besides the

atmospheric pressure at the top of the

column. This kind of manometer is only

used for pressures which do not exceed 6 or 6

atmospheres. Beyond this point it would be

necessary to make the tube so long that it

would be easily broken. In this case, recourse

must be had to such a construction as that

explained in the next paragraph.

Compressed-air Manometer. — This manome-
ter, founded on the principle of Marietta's

law, is composed of a strong glass tube closed

at its upper extremity and filled with dry air.

This tube is immersed in a cistern partly filled

with mercury, to which it is cemented. The

cistern, by means of a side tube a, fig. 83, is

put in communication with a close vessel,

which contains the gas or vapour whose

elastic force is to be ascertained. As to the

graduation of this manometer, the quantity

of air contained in the tube is such, that

when the orifice a communicates with the
atmosphere, the level of the mercury is the
same in the tube and in the cistern. At this
level, therefore, 1 is marked on the board to
which the tube is attached. In continuing
the graduation, it is nec essary to observe
that the pressure which is transmitted through
the tube increasing, the mercury rises in the
tube until its weight, added to the tension
of the compressed air, balances the exterior
pressure. If, therefore, We mark 2 atmo-
spheres in the middle of the tube, we shall
commit an error; for, when the yolume of
air in the tube is reduced to one-half, its
tension, by the law of Mariotte, is that of two
atmospheres ; and, therefore, when increased
by the weight of the column of mercury which
is elevated in the tube, it represents a pressure greater than
two atmospheres. The number 2 must not therefore be
marked in the middle of the tube, but a little lower and
at such a height that the elastic force of the compressed
air, added to the weight of tfce column of mercury in the
tube, shall be equal to two atmospheres. By such a calcu-
lation as this, the tUtt position of the figures 2, 3, 4, fcc.,
on the scale of tut lliahomettf if determined. This in-
strument is not very accurate when the pressures are great*
for the volume of air becoming less and less, the divisions of
the scale approach too near to each other.

The inconvenience of both the preceding Instruments hat
been attempted to be remedied by employing an apparatus of
the following description, fig. 84, Nos. 1 and 2. Tfia mano-
meter, invented by M. Richard, and of which Ho. 1 is the
front view, and Ko. 2 the side view, is of the free-air descrip-
tion, indicates very high pressures, and is of a very moderate
height. It consists of a tube doubled several times on itself
so as to present a series of vertical branches connected with
one another by bent knees ; that is, the instrument presents a
continued series of siphons in the same vertical plane, alter-
nating up and down and having the same vertical branches. The
columns of mercury are separated by columns of water, whioh
occupy the upper bent knees and the upper half of £ho height

NATURAL PHILOSOPHY.

279

of the branches. The apparatus being oompletely filled with
columns of mercury and water, if one of the extremities of the
tube be put in communication with the vessel of gas or vapour
whose tension is to be ascertained, the other extremity remaining
open to the free-air, the excess of the pressure in the vessel over

Fig. 88.

that of the atmosphere will produce the elevation of the level
of the mercury in all the branches; these elevations will be of
equal height if the tube be of the same bore throughout ; and
in this case, the effective pressure of the gas in the vessel will

Figr. 84.— Noi. 1 and 2.
No. 1. - No. 2.

I the columns of mercury. This correction will be made by
' multiplying the preceding product by the fraction ft, which
represents the ratio of the excess of the density of mercury
above that of water, to the density of mercury. The doubled
tube is made of iron; the second vertical branch open to the
air is mounted with a glass tube to show the extremity of the
column of mercury ; and the scale, which is made of brass, is
graduated to atmospheres.

Metallic Manometer. — H. Bourdon, a mechanician of Paris, has
recently invented a new manometer, represented in fig. 86,

be given by the height to which the mercury is raised above
the point of departure in the open branch of the tube, multiplied
by the number of vertical branches, minus the correction due to
the influence of the weight of the intermediate water between

This instrument, which is wholly metallic and without merourT,
is constructed on the following principle, discovered by the
inventor ; when a tube having flexible sides and a slightly flat*
tened or oval shape is wound up in the form of a spiral, in the
direction of the less diameter, every interior pressure on the sides
has a tendency to unwind the tube ; and, on the contrary, exterior
pressure has a tendency to wind it up.

According to this principle, the manometer of M. Bourdon is
composed 6f a brass tube, about 2} feet long, having its sides thin
and flexible. A section across the tube, represented at s on the
left in the figure, is an ellipse whose greater axis is about A of
an inch, and smaller axis about A of an inch. The extremity «,
which is open, is fixed to a tube with a stop-cock d> for the pur-
nose of putting the apparatus in communication with a steam-
boiler.

The extremity b is closed, and moveable like the rest of the
tube. Now, when the stop -cock d is open, the pressure which
is produced by the tension of the vapour on the interior sides of
the tube causes it to unwind. The extremity b is then drawn
from left to right, and with it an index #, attached to it, which
indicates on a dial-plate the tension of the vapour in atmospheres.
This dial-plate is previously graduated by means of a free-sir
manometer, by putting the apparatus in motion with compressed
air. This manometer has the great advantage above the preced-
ing manometers, of being extremely portable and not easily
broken. It is now in operation in the locomotives upon several
railroads in France.

Metallic Barometer. — M. Bourdon is also the inventor of a
metallic barometer founded on the same principle as his mano-
meter. This apparatus, represented in fig. 86, is composed of a
tube similar to that of the manometer, but shorter, hermetically
, closed, and fixed at its middle point ; so that the vacuum having
been made in it beforehand, whenever the atmospheric pressure
diminishes, this tube unwinds itself in consequence of the principle
above mentioned. The motion is thus communicated to an index
which indicates the pressure of a dial-plate. As to the trans-
mission of the motion, it is effected by means of two small wires
b and e, which connect the extremities of the tubes with a lever
fixed on the axis of the index. If the pressure increases instead
of diminishing, the tube will close in upon itself, and there is a
small spiral spring at e, which then brings back the index from
[right to left, under the dial-plats. This biremeter is of i — M

280

THE POPULAR EDUCATOR.

size, very sensible, and remarkable for its very great simplicity of
construction.

Laws of the Mixture of Gases. — When two or more gases are
inclosed in the same Teasel, their mixture, when not effected by
flhemirert combination, is regulated by the following laws :

Fi*. 86.

1st. The mixture, which always takes place rapidly, is con
tuiuous and homogeneous, so that all the parts of the whole mass
contain the same proportions of each gas.

2nd. The sides of the vessel where the mixture takes place
beinc inextensible, and the temperature constant, the elastic force
of the mixture is equal to the sum of the elastic forces
of the gases contained in the mixture, when each is referred to
the whole mass, according to the law of Mariotte.

The first law is a consequence of the extreme porosity and
expansive force of gases. It was first proved by the French
chemist Berthollet, by means of the apparatus shown in fig. 87,

Fi* . 87.

All gases which do not act chemically upon each other, when
subjected to the same experiment, give the same result; and it is
remarked that the mixture acts more rapidly in proportion to the
greater difference of densities between the gases. The second
law is proved experimentally by the help of the manometer. It

Fig.SS.

is found also that if the gases are mixed at the same pressure,
before and after the mixture, the volume of the mixture is equal
to the sum of the volume mixed, it being! of course understood
that the mixture takes place in a vessel whose sides are inexten-
sible. Lastly, gaseous mixtures are subject to the law of
Mariotte, in the same manner as simple gases; that is a fact
which has been already proved in the case of air, which is a
mixturo of oxygen and nitrogen.

which is composed of two glass globes, each furnished with a neck
and stop-cock, and screwed to each other. The upper globe was
filled with hydrogen, of which the density is '0692, and the other
globe with carbonio acid, of which the density is 1*529 or 22
times greater than the former. The apparatus was placed in the
cellars of the Observatory at Paris, in order to keep them from
being shaken, and from every variation of temperature. The
stop-cocks being then opened, as in fig. 88, the carbonic acid
in the lower globe b, notwithstanding its greater weight, passed
partly into the upper globe a, and, at the end of a little time, it
was observed that the two globes contained equal proportions of
hydrogen and carbonic acid.

LESSONS IN CHEMISTRY.-No. XVm.

Consideration of the Results of Combustion in Oxygen (?«*.— The
experiments performed in our last lesson require that we
should now investigate the theory of combustion.

We have seen every instance of combustion which has
hitnerto come under our notice to have been the result, or at .
all events the concomitant, of the union of the combustible with
oxygen as the supporter. In point of fact, almoat all instances
of combustion are the result of the powerful action of oxygen
upon combustibles : not all, however, as was formerly sup-
posed ; hence the definition of combustion, formerly accepted,
namely, " rapid union of a combustible with oxygen," is not strictly
true. Chlorine, iodine, bromine, sulphur, and perhaps certain
other elements, may in some cases take the place of oxygen as
supporters of combustion. The only definition of combustion
justified by known facts is, " rapid chemical action attended by the
evolution of light and heat."

The result of the combustion of substances in oxygen gas
may be an oxide, an acid, or an alkali, according to the nature
of the combustible. The first and second we have generated
in the course of our preceding experiments; the third we shall
form hereafter.

, Returning now to a consideration of the contents of the'jars
or bottles in which our various substances were deflagrated,
let us begin with that vessel in which the iron was burned.
You will observe, scattered all over its sides and base, various
little globules of a material not unlike iron to look at. If you
remove these globules from the vessel, you will find them to
be heavy and hard ; not unlike the original iron in appearance,
but more dull. In reality, they are a compound of oxygen
with iron, or, in other words, the oxide ofciron, " the black
oxide," as we may call it, by way of contradistinction to iron
rust, or "red oxide" of that metal.

LESSONS IN CHEMISTRY.

281

If you now take one of these little globules, break it on
an anvil or stone with a hammer, and strew the particles on
litmus paper moistened with a little distilled water, not the
slightest effect of redness will be developed on the blue litmus
paper. We will therefore take the fact for granted, that the
powdered material in question is not an acid — I say, we will take
the fact for granted, because, although the reddening of blue
litmus paper is a general— it is not a universal test of acidity.
There exist certain acids, neither soluble (in ordinary language)
nor sour, nor capable of reddening litmus paper ; but these are
exceptions to a rule. The result of the combustion of iron,
then, in oxygen gas is not an acid, neither is it an alkali, as
you may demonstrate by comminuting another portion, and
strewing it on moistened yellow turmeric paper, or moistened
litmus paper previously reddened t>y contact with an acid. Had
the substance operated with been alkaline, the turmeric paper
would have been affected with a brown stain, and the reddened
litmus paper would have been restored to its original blue tint.

Meaning of the term Oxide. — Inasmuch as the result of burn-
ing iron in oxygen gas is neither acid nor alkaline, but is never*
theless a compound of oxygen with the iron burned, we call it
an oxide of iron. And here you may remember, as a rule of
chemical nomenclature, that the term oxide is given to such
compounds of bodies with oxygen as are neither acid nor alka-
line. Occasionally the result is of such ambiguous character
that one hardly knows what to call it. For example, the sub-
stance white arsenic, which has already come under our con-
sideration, was formerly termed oxide of arsenic ; it is now
termed arsenious acid, because its acid characteristics, akhough
slight, are nevertheless evident. More ambiguous is the so-
called oxide of tin, or stannic acid, according to the view wc
choose to take of it. I allude to the white powder resulting
from the action of nitric acid upon tin. Again, in the oxides of
alkaline earths we have certain ambiguous resuka. Lime is the
product of the oxidation of a metal termed calcium. Lime is,
therefore, treated of as the oxide of calcium ; but the oxide is so
distinctly alkaline, that chemists also denominate lime " an
alkaline earth." You may readily demonstrate this alkalinity of
lime by touching a slip of turmeric paper, or reddened litmus pa-
per, with a portion of lime water. The distinctive change of
colour due to alkaline re-action will be immediately recognisable.

Having examined the solid result of the combustion of

iron in oxygen, let us next see whether the gaseous contents of

the jar manifest any peculiarity. For this purpose, portions of

the gas may be transferred by means of the pneumatic trough,

Fiy. l.

as represented in fig. 1, into small test tubes, which may be
allowed to remain standing mouth downwards in a late or
saucer containing a little water until wanted, fig. 2 ; and when

removed for use, they require no stopper, the thumb being all
that is required, fig. 3.

Fig. s.

I scarcely knowwhetheritbe necessary toobserve that suppos-
ing a test tube containing gas to be standing in a little water upon
a plate as represented in fig. 2 (the depth of water being
necessarily inconsiderable, otherwise the tube would fall), it is
under these circumstances impossible to remove the tube
directiyfrom the saucer or plate, without spilling some of the
gas. The proper course to be adopted is this : steadying the
rig. 4.

tube with the right hand, support the plate by means of the
left ; immerse' 'plate and tube in the pneumatic trough, allow
the plate to sink, secure the mouth of the tube with the thumb,
and withdraw it, fig. 4.

On testing successive tubes filled with the air remaining in
the vessel used for the combustion of iron, you will find that
it contains no new principle; it has neither taste nor smell,
does not whiten lime-water, or but faintly whitens it, does not
turn blue litmus paper red, red litmus paper blue, nor yellow
turmeric paper brown. An ignited taper burns in it without
any peculiarity. The gas demeans itself like atmospheric air.
Atmospheric air indeed it is ; consequently we arrive at the final
deduction, that the sole result of the combustion of iron in oxygen
gas is a solid, nothing but a solid— the black oxide of iron.

Examination of the Results of Charcoal burned in Oxygen.— The
first point deserving your attention as regards this result is the
total absence of solid products. Iron generated heavy,
hard-metallic-looking globules ; charcoal generated none of
these. The products of its combustion are totally invisible, so
that if one piece of charcoal had been sufficiently small in com-
parison with the amount of oxygen employed, and sufficiently
tree from all impure contaminations, it would have entirely
disappeared. Do not think, however, that the charcoal has
been destroyed — lost by this combustive energy. No element
is ever lost. All the fires which have burned since the crea-
tion of our globe, all the waters that have ever flowed, all the
manifold agencies of death and decay, have not altered by the
smallest fraction of a grain the original weight of the world's
material elements. Under the three forms of solid, liquid, and
gas, they still exist, and must continue to exist to the end of time.

The sole result of the combustion of charcoal in oxygen is,
then, a gas. Now, consider well the consequences of its gaseous
nature. Carbon, you are aware, is especially the combustible
of man ; either as wood or eoal, or charcoal, or oil, or coal gas,

*tt

THE POPULAB EDUCATOR.

carbon, alone or in combination with hydrogen, I repeat,
it our chief combustible. Only contemplate what the result
would have been, if the product of the combustion of charcoal
had been a solid ! Just picture to yourself if you can, the
appearance of our world at this late epoch in its history. Every
part of it where fire had been frequently lighted would have
been covered with a vast heap of stone-like cinders.

The product oi 'the combustion of charcoal in oxygen being
a gas, we must collect a little of this gas in tubas or bottles,
and test it methodically.

The gas is colourless.

Possesses a taste.

Possesses a smell.

Does not support combustion (try by means of an ignited
taper or chip.)

Does not burn.

Is heavier than the atmosphere. (Demonstrate by two
comparative experiments. Fill one bottle and allow it to
stand mouth upward unstopped ; fill another bottle and
allow it to stand mouth downward unstopped ; examine both
for the presence of carbonic acid gas). Fig. 6.
Wf.d.

It reddens blue litmus, and is therefor* an acid.

It whitens lime-water.

Now any colourless invisible gas which reddens blue litmus
paper, whitens lime-water, and dam not smell like hunting sulphur,
must be carbonic acid.

Tou will by this time begin to see the reason of our previous
employment of certain negative tests. We tested hydrogen
gas with lime water, with litmus and with turmeric ; we in
neither case developed any effect. But we proceeded on the
assumption that the gaaea operated upon were unknown, and
we were therefore bound to sallow one systematic undeviating
course of testing. •

Under the head of carbon, we shall have to take up carbonic
. aoid systematically \ at this time I merely treat of it collaterally.

Examination of the Results of the Combustion of Sulphur in
Omygen. — Here again we do not observe any solid result. If
the combustion had been conducted in a perfectly dry Teasel,
or even in a vessel containing water, provided the results of com-
bustion were examined speedily after the occurrence of that
phenomenon, we should have demonstrated the existence of a
peculiar gas. In the present instance the gas may be absent
inasmuch as it is readily soluble in water. If present you will
smell it, if absent the water will be found to contain it ; at any
rate some will be found absorbed by the water, to which there-
fore we may first apply our tests.

It is sour to the taste.

Smells like burning brimstone.

Reddens litmus paper, then bleaches the paper.

It may or may not whiten lime water : dependent on the
mutual quantities of the two.

Tou will now do well to prepare another portion of this gas,
and transfer it into a bottle over the pneumatic trough ; although
the gas be absorbable by water, nevertheless by avoiding
unnecessary agitation a sufficient amount may be collected.
You will find that it neither burns nor supports combustion.
It is called sulphurous acid, and under the head of sulphur will
come before us in further detail.

Examination of the Results of the Combustion of Phosphorus in
Oxygen Gfa*.— After agitating well the contents of the jar in
question, with a little water, you will find that the liquid thus
produced is sour, and reddens litmus paper ; hence it is an
acid. Tou will also find that the air contained in the bottle is
atmospheric air. neither more nor less. Hence the sole result of the
combustion of phosphorus is a white solid, exceedingly soluble in
water. The solid to question is deaomii*te^^

LESSONS IN GREEK.— No. XXL
By John R. Bba&d, D.D.

The Verb.

General Explanations,
ttfu, I am.

ThsBubotontm Verb

Lst us examine the proposition 6 erpartatntc sort ayaOog , the
soldier is good. Soldier is what is termed the subject of the
proposition ; that is, it is that of which something is asserted
or declared. Good is the attribute, or that quality which is
ascribed to the subject soldier. And is bears the name of verb ;
the essential function of which is, you see, to declare or affirm
something. The verb if, in union with the attribute, forma
the predicate, and makes a declaration respecting the subject.
The sentence or proposition thus composed may be desig-
nated in this manner : —

3ubi$ct

o orparuerne
the soldier

Predicate.

f " ■*- ' *\

verb. attribute.

sort ayaOof.

is good.

Instead of a noun, the subject may be a pronoun, vit. cvt* , /,
ij/uiQ, toe, &c. As the personal pronoun is not used in Greek,
except for emphasis, since the person intended ia marked by
the termination of the verb, the subject may be involved in
and expressed by the verb itself, as Xsw, X fosse. The verb
may also form the predicate of a proposition, and so contain
the verb and the attribute ; that is, the verb may of itself make
the affirmation. Such is the office performed by Xv«, /
boss. Accordingly, in Greek as in Latin, a verb may contain
in itself the subject, the verb, and the attribute ; in other
words, it may comprise both predicate and subject, as ypa+» f
I writ*.

Toiobs.

Again, let us compare together these propositions —
1. Xvfct, I loose, active.

j Xvofuu,
3. Xvofiaif

I loose my self t
lam loosed,

middle,
passive.

Here we have a verb in three forms ; the first form is called
the active voice, the second form is called the middle voice,
the third form is called the passive voice. Those verbs ate
active which simply express action. Those verbs are middle
of which the action comes back on the subject. Those verbs
are passive in which the subject is acted upon. These varieties,
it will be noticed, are varieties in both form and meaning.
Thus XtMi», the active, differs in form from Xvopuu the middle.
It differs also in signification ; for while Xwu signifies I loose,
Xvopai signifies I loose myself. This active voice may be
transitive or intransitive in import ; thus, we may aay Xsw, I
loose, using the verb generally without any specific object;
here the verb is intransitive; the intransitive form is seen
better in OaXXte, I blossom. We may also say Xm» rev avQpwwov,
I loose the man, when Xvet has a definite object, and is
transitive.

Observe in relation to numbers two and three, as given
above, that the English I loose myself % and Iamloosmi, are very
nearly related in meaning. If I loose myself, clearly I am
loosed. The chief difference between the two is, that in the
former the action is restricted to one person, namely, the

subject ; while, in the latter, it extends to a second person,—
the person, that is, by whom the subject is wrougnt upon.
The difference, in consequence, is rather in the person than the
act Accordingly, tou see that the form remains the. same,
being in both cases Xve/uu. In other words, Xvofuu may have
a reflex for middle) import, as / loose tnysojf, or a passive im-
port, as / am loosed. Strictly speaking, there ia but one form
m the present tense. Grammarians diner as to the name which
they give to that form, some calling it a middle, others a
passive voice. Very few, if any verbs, are known to possess
all the tenses of the three voices, as they might be formed
analogically. What forms really exist will appear as we
proceed.

Twass.

Again, study taw following teas) which, for the sake of

LESSONS IN GRBBK.

288

brevity, I at onoe present arranged, and to which I append
the meanings : —

A, P r ir m p a l tentes, that is—

1. Present Xvsj, I loot.

2. Future Xv<r«, IsAotf foots.

3. Perfect XcXvca, I have looted,

B. Historical ttntet, that is—

1. Imperfect fXvov, I wot looting, I loosed.

2. Aorist cXvoa, J foosfti.

3. Pluperfect tXsXvssiy, I had looted.

Baoh of the historical tenses is formed from its corresponding
principal, thus—

T as J Principal Xv« Xtww XsXvca.

• \ Historical cXvov e\v<ra eXeXvatiy.

The exact manner of their formation will be explained by
and by. At present observe that an action may be considered
as now proceeding, hence the present tense ; as proceeding in
past time; hence tne imperfect tense ; as proceeding in time to
come, hence the future tense ; as actually done in past time, i
hence the aorist tense; as having proceeded in past time,
hence the perfect tense ; and as having proceeded previously
to some other past act, hence the pluperfect tense. Accord-
ingly the present tense properly signifies, as in Xv*», I em
lootening ; and the passive, Xvopac, I am being loosened. Mark,
also, that the imperfect denotes both an act going on in the I
past, and a continual and repeated act. The aorist, as the word
signifies, denotes an action as simply past, without any exact
limitation ; and so is called the indefinite (such is the meaning
of the term) tense, or the tense of historical narrative. The
perfect denotes a past act which, in itself or in its conse-
quences, comes down to or near the present time. The
pluperfect denotes an act done and past, when another past
met was proceeding, or was completed. There are some

HI f

■a ? 2

I I I I

«,
?

s s

Iri

Moons.

Hood is a grammatical term employed to point out the
manner of an action. If I describe an act as simply taking
place, Z use

*• tint •JiWSPSW^PVj W nW| A HfOmWf

so called because it merely indicates or declares the act ; this
is the mood of independence and reality.

If I describe an act as dependent on some other act, as
dependent on a conjunction or a verb, I employ

2. Tk$ Bnojunctipe, as Xvy, he may boom.

This is the* mood of dependence, or of conception ; so called
because it implies dependence on another act expressed or
understood ; that is, an act really performed or conceived of
in the mind.

The Bubjunotive of the historical tenses is, in Greek
Grammar, called

3. The Optative, as \v<u/u, / *n?A< (or would) fro*.
If I express an act in the way of command, I use

$» The Imperative, as Xvs, Iqoh thou.

These four moods are called finite, that is, definite or
limited, because they all express the act under certain limita-
tions or modifications.

But if I express an act indefinitely, or in its abstract form,
dlsoonn cted, that is, with person or number, I then employ
the mood termed

6 m The Infinitive, as Xwnv, to loot*.

Another modification of the verb is found in

The Verbal Aajeotive,

Xvrioc, he mutt be looted,

which resembles the Latin participle passive in due, as aman~
due, ht mutt be loved; and accordingly has a passive force.

Thh Participle.

Participles are so called because they partake of the qualities
of the verb and the adjective ; as expressive of the quality of
the verb they denote action, as expressive of the quality of the
adjective they denote modification, e,g. /SovXfvsiv avqp, a
counselling man, that is, a Counsellor.

Persons.

In Greek, as in English, there are three persons ; 1st, the
speaker, I; 2nd, the person spoken to, thou; 3rd, the person
spoken of, he. The persons in Greek are in general indicated
by personal- endings, that is, changes in the termination of the
verb j as, 1st, person Xv**j ; 2nd, Xv-ttg ; 3rd, \v~u.
I loose, thou loos**, he loosss .

tn the English termination e, est, ee, you have an example
of these person-endings.

Numbxxjb.

With characteristic superabundance, the Greek has three
numbers, the singular, the plural, and the dual. The singular
number denotes one single object; the plural denotes more
objects than one; and the dual denotes precisely two objects.
The dual, however, is comparatively little used. For the first
person of the dual there is in the active and passive aoiists no
special form ; their place is supplied by the form of the first
person plural.

Conjugations.

The term conjugation denotes peculiarities of formation in
number, person, tense, mood, and voice. These peculiarities
in Greek have been brought under two heads, and so two con-
jugations have arisen: these are, the first conjugation, con-
sisting of verbs of which the first person singular ends in ut —
this class comprehends the great bulk of the Greek verbs ; and
the second conjugation, comprising the verbs of which the
first person singular ends in fu ; e.g.: —

First conjugation Xv-ai I loom.

Second conjugation tent-/** I plate.

Some grammarians admit only one conjugation, that of the
verba in ai. These regard the verbs in ui, whose peculiarities
extend to only three tenses, as exceptional forms. The dif-
ference Is merely a matter of arrangement. In either view the
facia remain the same.

._ r

284

THE POPULAR EDUCATOR.

Prbfixes, Suffixes, and Stbms.

In order to represent the two ideas, namely, existence (or
affirmation) and attribute, which enter into the signification of
the verb, three essential elements are employed; first, the
stem ; second, the suffix or inflexions ; and, third, the prefix
or augment, e.g. :—

Augment. Stem. Inflexion.

f \v <ra

1 have looted.

The stem is variable. Thus we have the stem or root of the
verb ; the stem of the verb may in most verbs be found by
cutting off io, the personal-ending ; thus, Xvw, Xv.

Besides the stem of the verb, there is the tense stem, thus,
i\voa; the first aorist, by dropping the personal-ending a,
gives i\v<T y the tense stem of the first aorist active ; of this
form, fXt/9, the c is the augment or prefix, the force of which is
to denote past time.

Of the form cXvou, the oa is the inflexion or suffix of the
first aorist ; and of the oa, the a is the ending of the first
person singular. Full particulars will be given in our next
lesson.

LESSONS IN ITALIAN GRAMMAR.— No. XVIII.

BY CHARLE3 TAUSENAU, M.D.,
0/ the University or Pavia, and Profeuor of the Italian and German
Language* at the Kensington Proprietary Grammar School.

Exercises. — Italian-English.

E'-gli e ri-tor-na-to dal bd-sco. V&n-go da Ldn-dra, da
ca-sa mi- a. E' gia par-ti-to da Na.po-li. I'-o s6-no tra-di-
to da voi, da tut-ti. Di-scen-de da u-na schirft-ta nd-bi-le.
Lon-ta-no dai mid-iee-ni-t6-ri. Lun-gi da Fi-rim-ze. Da chi
di-pen-de*-te voi? Non si di-stin-gue V u-no dall* al-tro. Ri-
tor-na-re dal-la Ger-mi-nia, Jdall I-ta-lia, dal -la Rus-sia, da
To-ri-no. Non e an-c6-ra u-sci-to dal-la cit-ta. Por-ta-i
qu&ste car-te dal ghi-di-ce al no-ta-jo. Scen-de, ca-de dal
teVto. L' a-cqua sc6r-re giu m6n-te. Da per ttft-to. Da
un can-to, da un la-to. Non vo-16-va-no u-sci-re di qua. E %
ri-tor-na-ta pdc' an-zi di Prus-sia. E'-gli e di Gla-scd-via,
I? u-sci-to di ca-sa, di tea-tro, di c6r-te, di pa-laz-zo, di cit-
ta, di chie*-sa. S6-no sta-to da mi-a so-rdl-la. Og-gi pran-
ze-rd dal mer-can-te. D6-po pran-zo an-drd da lui. E* ve-
nu-to sta-mat-ti-na da me. E -gli a-bi-ta, al-ldg-gia, sta da
su-o pa-dre (or in ca-sa di su-o pa-dre ; or pres-so si-o pa-
dre*).

Vooabulabt.

Glascovia, Glasgow.

B y useito, he has gone.

Sono stato, I have been.

Oggi, to-day.

Pranuro, I shall dine.

Mer canity merchant.

Dopo, after.

Pranxo, dinner (dopo pranzo,
after dinner ; in the after-
noon).

Andrd, I shall go.

Lui, him.

E x venuto, he came.

Stamattina (for que-sta mat-tt-

na), this morning.
Me, me.
Egliabita, aUoggia, tta % he lives

or resides.
Presso, near, close to, with,

about.

Colloquial Exercises.

In, in

Nel, in the (m.)

JVW-&,inthe(t.)

Cor., with

Col, with the (m.)

CW-fc, with the (f.)

Su, on, upon

Sul, on or upon the (m )

Sul-la, on or upon the (i.)

La chie-sa, the church

La scud -la, the school

11 cor-H-U, yard, court-yard

La stdn-za, room, chamber,

apartment
La td-vo-la, the table
II Ut-to, the bed
Da, from, by

Di que-sto giar-di-no, of this

garden
LH mi-opd-dre, of mv father
Da mi-o pd-dre, from my

father
A, to*
A que'-sto giar-di-no, to this

garden
A mi-opd-dre, to my father
T'O d-mo, I love
K-gli d-ma, he loves
I'-o pen-so, I think, direct my

thoughts to
E'-gli pin- sa, he thinks, directs

his thoughts to
Dd-to, given
Prs-std-to, lent

Bgli t ritornaio, he has re-
turned.

Bosco, forest, wood.

£ % gia partito, he has already
departed.

Napoli, Naples.

Io sono tradito, I am betrayed.

Diseends, he is descended.

Sshiatta, race, family.

NobiU, noble.

Lontano, distant, far.

Miei, my (pi. m.J.

Genitore, father, i genitori, pi.,
parents.

Zungi, distant, far.

Chit who?

Dipendete voi, do you depend.

Non si distingue, one does not
distinguish,

Uno, one.

Altro, other.

Ritornare, to return.

Germania, Germany.

Torino, Turin.

Non e ancora useito, he has not
yet gone.

Portai, I carried.

Carta, {., paper.

Giudice, judge.

Notajo, notary.

Scende, he descends.

Cade, he falls.

Tetto, roof,

Seorre gib, flows down.

Monte, mountain.

Per tutto, da per tutto, every-
where, in all places, all over.

Canto, lato, side.

Non voUoano useire, they did
not want to go.

Qud, here, di qud, from here
(also, on this side ; through
this place, through here;
in this world or life).

JT rUornata, she has returned.

Poc* anzi (for pd-co dn-zi), a
little while or time before ;
lately, the other day.

•To live or reside with one, may also be translated by a-bi-td-ft
Wrlog-gia'-re, std-re), in cd-ta di quaUil-no (to live or reside in the
house of one), or pr U-so qua! cu-tto (near or about one).

Colloquial Exsrcisis.— Italian-English.

D6-ve a-ve"-te voi per-du-to il vd-stro li-bro } In qu£-sto
giar-di-no. A-ve~-te voi ve-du-to vd-stra zi-a in u-na car-iOz-
za ? D6v* e vO-stra ma-dre ? E'l-la e nel su-o giar-di-no con
mi-o pa-dre. Col li-bro e c61-la pe'n-na. La ta-bac-chi^-ra e
sul-la ta-vo-la, e 1' a-ndl-lo e sul 16t-to. II mi-o pic-co-lo fra-
tdl-lo e n61-la stan-za e mi-a so-r61-la d nel cor-tf-le. Col
mi-o cap-pdl-lo e c61-la mi-a om-brel-la. D6v* e to-o pA-dre ?
E'-gli e nel nO-stro giar-di-no. Ab-biiUmo tro-va-to un li-bro
in qu^-sta chie'-sa. II mi-o pic-co-lo fra-tel-lo e ncl-la scud-
la. D6v' e la mi-a om-brSl-la ? EVsa e n^l-la car-rdz-za. TI
tem-pe-ri-no di mi-o fra-tel-lo e bud-no. La p^n-na di mi-a
so-rdl-la e an-che buo-na. A-v6-te voi ve-du-to 1' om-brdl-la
di mi-o pa-dre ? La scuo-la di mi-o zi-o e gran-dis-si-ma. Hu
ve-du-to la ta-bac-chid-ra di v6-atro pa-dre. A-ve^te voi per-
du-to il tem-pe-ri-no di mi-a so-rel-la ? Qu6-sto fan-ciul-lo e
il fl-giio di mi-a zi-a. Hai tu ve-du-to il pa-dre di que'-sto
fan-ciul-lo ? Que'-sto fan-ciul-lo ha per-du-to la ta-bac-chie-
ra di su-o pa-dre. HO ri-ce-vu-to un man-ieU-lo da nd-stro
fra-tdl-lo. Ab-bia-mo ri-ce-vu-to un ca-val-lo da vd-stro zi-o.
Mi-o pa-dre ha ri-ce-vu-to u-na ISt-te-ra da nd-stra zi-a Hai
tu ri-ce-vu-to que'-sto re-ga-lo da tu-a so-rdl-la ? Mi-a ma-dre
ha com-pra-to que'-sta cuf-fia da vO-stra so-rdl-la. II tem-pe-
ri-no che ab-bia-mo ri-oe-vu-to da nd-stro zi-o e bud-no e bel-
lo. A'-mo mi-a so-rei-la. Qu6-sta ma-dre a-ma su-o fi-glio.
Pen -so a mi-o fra-i^l-lo. Mi-a zi-a pen-sa a su-o fi-glio ed a
su-a fl-glia. Que'-sto fan-ciul-lo ha scrit-to u-na l§t-te»ra a
su-a ma-dre. Mi-o zi-o ha ven-du-to il su-o b&l ca-val-lo a
mi-o pa-dre. Hd dd-to il mi-o tem-pe-ri-no a mi-a so-rel-la.
A-ve'-te voi pre-sta-to la vd-stra om-brdl-la a mi-o fra-tdl-lo ?
II fi-glio di nd-stra zi-a e gran-dis-si-mo. Ab-bia-mo scrit-to
u-na gran-de let-te-ra a nd-stro pa-dre. Mi-a zi-a ha ri-ce-
vu-to que^sta cuf-fia da su-a fl-glia. A-ve'-te voi ven-du-to la
vd-stra ta-bac-chie-ra a mi-o pa-dre ? Hd pre-sta-to a trf-o
fra-tdl-lo il tem-pe-ri-no che io hd ri-ce-vu-to da mi-o zi-o.
Ab-bii-mo da-to un man-tel-lo a que'-sto fan-ciul-lo. Hai tu
pre-sta-to il tu-o li-bro a que-sto budn fan-ciul-lo ? A-ve%te
voi tro-va-to que^-sta pe'n-na nel-la scud-la ? Fen-ao a que-sto
fi-glio ed a que^sta fi-glia.

Enolisu-Italian.

He comes from the riding-school and not from the garden.
He has received the goods from the merchants of Hamburgh.
Has Mr. Baring returned from the fair ? The letters which I
have received from France speak much of a great theft. Does
the brother-in-law import the goods from England or from

LESSONS IN READING AND ELOCUTIOiN.

086

Holland ? From Hamburgh to Paris is a hundred and ninety
French miles. Oxford is not far from London. Does he come
from the shop ? No, sir, he comes from the counting-house.
Do you come from the play ? No, we come from the ball.
The furniture of Mr. Hall has been sold by his heirs. Do you
come from the garden ? No, I come from the coffee-house.
Where do those gentlemen come from? Some return from
the chase, others from walking, and these latter from fishing.
Here is the money which has been sent to me by the father.
This depends on the mother and not on the brother. The
transition from virtue to vice is far shorter than from vice to
virtue. On the goodness of the laws, (on) the integrity of the
magistrates, (on) the obedience of the subjects, (on) the bravery
of the soldiers, (on) the spirit of enterprise of the merchants,
and (on) the nard work of the labourers, depend the
maintenance and the welfare of the states. Fidelity, glory,
and bravery must guide the soldier if he wants to deserve the
name of a defender of the (native) country. I expect an answer
from John ; he has been already for three months in London.
William has returned to-day. from Paris, and his brother is
expected from Cambridge. I go every day to Mr. Smith, be-
cause I see, hear, and learn many things at his house. Count
Alfieri has been with the prince to-day. Go to James and tell
him to come to us this evening. George lives at the merchant's
house. The servant is gone to the shoemaker and to the
secretary, and, on his return, I shall send him to the physician
and to the aunt.

Vocabulary.

He comes, i-gli vik-ne

Not, non

Riding - school, ca-val-le-riz-

ta (to), f.
He has received, 4-gli ha ri-ce-

vu-to
Goods, mer-can-si-a (/«), f.
Merchant, mer-cdn-te, m.
Hamburgh, Am-bkr-go
Has returned* 4 ri-tor-nd-to.
Fair,^M-ra, f.
Letter, Ut-U-ra, t
Which I have received, che M

ri-ee-vu-te
France, la Frdn-cia
Speak much of, pdr-la-no mtt-

todi
A great theft, un gran la-tro-

ci-nio, m.
Does import, fa vt-ni-re
Brother-in-law, co-gnd-to, m.
England, V In-ghil-tir-ra
Or, o

Holland, V O-ldn-da
Paris, Pa-ri-gi
Is a hundred and ninety miles,

ci s6-no dn-to no-vdn-ta mt-

glia, pi.
French, Jrem-ed-se ~
Oxford, Os-fcr-dia
Is not far, non k lon-td-no
Does he come, vien d-gli
Shop, bot-U-ga, f .
No, sir, non, 8i-gn6-re
Counting-house, scrit-t6-jo, m.
Do you come, ve-ni-ie voi
Play (comedy), com-me-dia, f.
No, we come, no (pron. n6) t ve»

nid-mo
Ball, fctf-fc, xn.
Furniture, t m6-bi-li, pi. m.
Has been sold, s6-no std-ti ven-

du-ti
His heir, U su-o (pi. su6-i) e-ri-

de, m.

Do you come, vUn El-la

I come, i'O vin-go

Coffee-house, caf-ft t m.

Where do come from,

don-de ven-go-no

Gentleman, Si-gno-re, m.

Keturn, ri-tor-na-no

Chase, cdc-cia, f.

Other, dl-tro

Walking, pas-seg-gio, m.

Latter, td-ti-mo, m.

Fishing, pe"-sea t * f.

Here is, ic-eo

Money, da-nd-ro, m.

Which has been sent to me,
che mi & std-to spe-di-to

This depends, que'-sto di-pen-de

And not, e non

Transition, pas-sdg-gio, m.

Virtue, vir-tu, f.

Vice, vi-xio, m.

18 far shorter than (the transi-
tion), & as-sd-i piu c6r-to che
non e* il pas-sdg-gio

Goodness, bon-td, f.

Law, Ug-ge, f.

Integrity, pro-bi-td, f.

Magistrate, ma-gi-strd-to, m.

Obedience, ub-U-dUn-xa t f.

Subject, siid-di-to, m.

Bravery, va-16-re, m.

Soldier, soUdd-io, m.

Spirit of enterprise, spi-ri-to
spe-co-la-ti-vo, m.

Hard work, la-bo-rio-si-td, f.

Labourer, la-vo-ra-t6-re, ra.

Depend, di-phx-do-no

Maintenance, vi-g6-re

Welfare, pro-spe-ri-td, f .

State, std-to, m.

Fidelity, >-#W-*d,f.

Glory, gio-ria, t

Must guide, di-vo-no gui-dd-rs

If he wants to deserve, se vuM
tnc-ri-td-re

Name, n6-me y m.

Defender, di-fen-so-re,m.

Native country, pd-tria, f.

I expect, f-o a-spit-to

Answer, ri-spd-sta, f.

John, Qio-vdn-ni

Has been already, I gid

Three, tre

Month, me'-se, m.

William, Gu-gli-tt-tno

Has returned, & ri-tor-nd-to

To-day, 6g-gi

His, su-o

Is expected, vic-ne a spet-td-to

Cambridge, Cam-brig-ge

I go, i-o vd-do

Every day, 6-gni gtir-no

Because, per-che

Him, lui (at this house, t. e.

with him)
I see, hear, and learn many

things, ve-do, sin-to ed im-
pd-ro 6- gni s&r-ta di cose

Count, con-te

Has been, e std-to

Prince, prin-ci-pe, m.

Go, va

James, Jd-co-po

Tell him, di-gti

To come (i. e. that he may

come), che ven-ga
This evening, sta-s4-ra (for

qui-sta se'-ra)
Us, not

George, Oibr-gio
Lives, d-bi-ta
Servant, ser-vi-to-r$, m.
Is gone, e an-dd-to
Shoemaker, cal-zo-ld-jo, m.
Secretary, se-gre-td-rio, m.
On his return, al sii-o ri-

tor-no
I shall send him, lo man-de-ro
Physician, mt-di-eo, m.
Aunt, zt-a, f.

LESSONS IN READING AND ELOCUTION.— No. IL
PUNCTUATION.

I. TBS FSBXOD.

• Mind this important difference : pi-sca, fishing, fishing-place,
fishery ; and pi-sea, peach ; lividity, black and blue spot (from a
blow) ; blew, thump, cuff.

1. T/te Period is a round dot or mark which is always put at the
end of a sentence.

2. In reading, when you come to a period, you must stop as if
you had nothing more to read.

3. You must stop only as long as you can count one, two, three,
four,

4. You must pronounce the word which is immediately before
a period, with the falling inflection of the voice*

5. The falling inflection (or bending) of the voice is commonly
marked by the grave accent, thus \

Examples,
Charles has bought a new hat.
I have lost my gldves.

Exercise and temperance strengthen the constitution.
A wise son makes a glad father.
The fear of the Lord is the beginning of wisdom.

II. THB NOTB 07 IHTBRBOOATION.

6. The note or mark of Interrogation is a round dot with a hook
above it, which is always put at the end of a question.

7. la reading, when you come to a note of interrogation, you
must stop as if you waited for an answer.

8. You muststop only as long as you do at the period.

9. You must in most cases pronounce the word which is placed
immediately before a note of interrogation, with the rising inflection
of the voice.

10. The rising inflection of the voice is commonly marked by
the acute accent thus, '.

Examples.

Has Charles bought a new hat ?

Have you lost your gl6ves?

Hast thou an arm like God ?

Canst thou thunder with a voice like mm ?

If his son ask bread, will he give him a stone ?

If he aska fish, will he give him a serpent r

11. In general, read declaratory sentences or statements with
the falling inflection, and interrogative sentences or questions with
the rising inflection of the voice. *

Examples.

Interrogative. Has John arrived ?

Declaratory. John has arrived.

Interrogative. Is your father well ?

Declaratory., My father is well.

Interrogative. Hast thou appealed unto Caesar *

Declaratory. Unto Cesar shalt thou g*.

88*

THE POPULAR EDUCATOR.

12. Sometimes the sentence which end* with a note of interro-
gation should be read with the falling inflection of the yoke.

Bsramplee.
What o'clock ii It?
How do yon do to-day ?
How much did he give for his bcdk ?
Where is Abel, thy brother ?
How long, ye simple ones, will ye love simplicity ?
Where watt thon, when I laid the foundations of the earth r

Sometimes the first part of an interrogative sentence should be
read with the ruing inflection of the voice, and the last part with
the falling inflection. These parts are generally separated by a
Comma thus ,

14. At the comma, the ruing inflection is used, and at the note
of interrogate tha falling inflection.

EzampUt.

Shall I give you a peach, or an apple ?
Are you going home, or to school f

Last Sabbath, did you go to church, or did you stsy at home ?
Whether is it easier to say, Thy sins are forgiven, or to say, Arise
and walk?

Why did the heathen rage, and the people imagine vain things ?
Is your father well, the old man of whom ye spake ?

15. Sometimes the first part of an interrogative sentence must
be read with the falling inflection of the voice, and the last part
with the ruing inflection.

Example*.

Where have you been to-day? At home?
Who told you to return ? Your father ?
What is that en the top of the house? A bird ?
What did you pay for that book ? Three shillings ?
Is sot the list' more than meat? and the body than raiment ?
What went ye out to see ? A man elothed in soft raiment ?
What went ye out to see ? A pi6pbet r

How often shall my brother sin against me and I forgive him ?
Until seven times ?

16. In the following examples some of the s ent e n ces are Ques-
tions requiring the ruing, and some the falling inflection of the
voice. A few sentences also ending with a period are inserted.
No directions are given to the papil with regard to the manner of
reading them, it being desirable that his own understanding, under
the guidance of nature alone, should direct him. But it may be
observed that questions which can be answered by pes or no,
generally require the rising inflection of the voice ; and that ques-
tions which cannot be answered by yes or no, generally require the
falling inflection.

Examples.

John, where have you been this morning ?

Have you seen my father to-day ?

What excuse have you for coming lets this morning ? Did you
not know that it is past the school hour ?

If you are so inattentive to your lessons, do you think that you
shall make much improvement ?

Will you go, or stay ? Will you ride, or walk ?

Will you go to-day, or to-morrow ?

Did he resemble his father, or bis mother ?

Is this book yours, or mine ? His, or hers ?

Do you hold the watch to-night ? We do, sir.

Did you say that he was armed ? He was armed.

Did you not speak to him ? I did.

Art thou he that should come, or do we look for another ?

Why an yon to silent ? Have you nothing so say ?

Who hath believed our report? To whom hath the arm of the
Lordfaen revealed ?

III. THE NO** OF aXOLAMATION.

17. The note or mark of Exclamation is a round dot with an upright
dash or stroke above it, which is always put at the end of a sentence
expressing surprise, astonishment, wonder, or admiration, and other

18. In reading, when you come to a note of i
must stop in the same manner as if it were a note of mterrofatioo.

19. You must stop only as long as you do at a period.

20. You must generally pronounce the word which comes
Immediately before a note of exclamation with the falling inflec-
tion of the voice.

How cold it is to-day!
What a beautiful house that is 1
How brightly the sun shines 1
How mysterious are the ways of God I
How are the mighty fallen in the midst of the batOe t
How are the mighty fallen, and the weapons of war plrisheri 1
Would God I had died for thee, O Absalom, my son, my sou 1
Oh, what a fall was there, my countr y m en I
It is a dread and awful thing to die 1
Oh ! deep enchanting prelude to repose I
The dawn of bliss the twilight of our woes I
Lovely art thou, O Peace ! and lovely are thy children I and
lovely are thy footsteps in the green valleys I

21. The student was taught in No. 2, that when he comes to a
period, he must stop, as if he bad nothing more to read. At the
end of a paragraph, whether the period or any other mark be used,
a longer pause should be made than at the end of an ordinary sen-
tence. The notes of interrogation and exclamation generally
require pauses of the same length with the period.

It may here be remarked, that good readers always make their
pauses long ; but whatever be the length of the pause, the pupil
must be careful that every pause which he makes shall be a total
eeeemtion of the voice,

Eaamples.
To he read a§ if marked.

George is a good boy. He gets his lesson well. He is satemtrve
to the instructions of his teacher. He is orderly and quiet at
home.

A good scholar is known by his obedience to the rules of the
school. He obeys the directions of his teacher. Hb attend-
ance at the proper time of school is always punctual. He is
remarkable for his diligence and attention. He reads no other
book than thst which he is desired to read bv his master. Hie
studies no lessons but those which are appointed for the day. He
takes no toys from his pocket to amuse himself or others. He
pays no regard to those who attempt to divert his attention firem
his book.

Do you know who is a good scholar ? Can you point out many
in this room? How negligent some of our fellow-pupils are!
Ah I I am afraid that many will regret that they have not improved
their time !

Why, here comes Charles 1 Did you think that he would return
so soon ? I suspect that he has not been pleased with his visit
Have you, Charles ? And were your friends glad to ate you ?
When is cousin Jane to be married ? Will she make us a visit
before she is married ? Or will she wait until i
her name ?

My dear Edward, how happy I am to see you ! I heard of your
approaching happiness with the highest pleasure. How does most

do ? And how 'is our old whimsical friend the Baron r Ton must
be patient and answer all my questions. I hare many faa quhl s s to
make.

The first dawn of morning found Waverly on the esplanade in
front of the old Gothic gate of the castle. But he paced it long
before the draw-bridge was lowered. He produced his order to
the sergeant of the guard, and was admitted. The place of nil
friend's confinement was a gloomy apartment in the central part of
the oastle.

Do you expect to be as high in your class ss your brother r Did
you recite your lessons as well as he did ? No. Lasy boy 1 Care-
less child ! You have been playing these two hours, You have
Sid no attention to your lessons. You cannot say a word of them.
ow foolish you have been ! What a waste of time and talents
you have made !

FRENCH READINGS.

287

FRENCH READING 8.— No. I.

LE SAPEUR DE DIX ANS.

Sbctiok X.

Il y avait* en mil huit cent denize an neuvieme regiment
de lipne, 1 un petit tambour qui n'avait 5 que dix ans. 2
CTetait un enfant de troupe c qui s'appelait d Frolnt de son
veritable nom, 3 mais que lee soldats avaient surnomme
Bilboquet. 1 En effet, il avait un corps si long, si maigre
et si fluet, surmonte d'une si groase t£te, 6 qu'il reasemblait
assez a l'object dont on* lui avait donn6 le nom; 8 Frolat
6u Bilboquet, comme vous voudrex, f n'etait pas au reste*
un £arcon autrement remarquable. Le tambour-ma! tre lui
ay ait si souvent battu la mesure sur les epaules 7 avec sa
grande canne de jonc, que rharmonie du ra et du fia avait
fini par lui entrer dans la t£te et dans les mains. Voila
tout. Mais il ne portait h pas le bonnet de police suspendu
sur i'oreille droite, 8 comme les moindres fifres le faisaxent ; *
il ne savait' pas marcher en se dandinant, a l'exemple de
see supeiieurs,' et un jour de paie qu'il avait voulu laisser
pendre son sabre par devant, comme les elegants du re-
giment, il s'etait embarrasse les pied* en oourant et etait
tomb£ but son nez, 10 qu'il s'etait norriblement ecorche, 11 a
la grande joie de ses camarades. On riait k beaucoup de
lui, 13 qui ne 1 riait de personne. 13 Aussi avait-il dans ses
habitudes un fond de sauvagerie et d'£ioignement u bien
rare a son age. 1 '

Colloquial Exebcise.

1. Quel Itait le regiment du
petit tambour?

2. Quel age avait-il ?

8. Comment s'appelait-il?

4. Les soldats 1 avawnt-ili sur-
Damme* P

6. Pourquoi l'eveient-ib sur-
nomme' Bilboquet ?

6. A quoi ressemblait-il ?

7. Quel trsitement le tambour-
maftre lui misait-il eprouver?

8. Imitait-il ses camarades dans
la maniere de se ooiffer P m

9. Marchait-il comme ses su-
perieurs?

10. Que hii etatt-il arrive' un
jour de paie P

11. Quelle avait ete la conse-
quence de sa chute P

12. Se moquait-on de lui ?
18. Riait-il des autre* P

14. Qu'arait-il dans ses habi-
tudes?

15. Ob oaraosere est-il eommun
aux enfimts de Page petit
tambour?

Nona avd Rbfmwitces.*— «*, II y avait, there woe; L. part
il, § 61-2 1 8. "82, R. 3, 4.-5. L. S. 10, R 6.— c. en&nt de
troupe, *oldier>* okild.-d. L. p. 94, last sentenoe of Res. of Ex.
— #. 8. 84, R. L--f. from v<mloir t L. p. 110, part ii— g. au
reste, betide*.— k. S. 22, R. 10.— i. from fair*, L. p. 98, part ii.
—j. from ftssotV, L. p. 104. part ii— *. from rir*> L. p. 104
part ii— J. 8. 5, R. 7. — m. se coifler, to pat on hie cap.

LB SAPEUR DE DHL ANS.

0BCTIOH TX

Un jowr, e'Maitle vingt^ept juillet 1 mil* huit cent douse,
le genera} revolt b de l'Empereur l'ordre de s'emperer c d'une
position a qui etait de l'autre oote d'un enorme ravin. 9 Ce
ravin etait deibndu par una batterie de six pieces de canon, 4
qui enlevait des files enttfres de soldats, etjpour arriver a
Pemdroit qu'avnit design*} l'Empereur/ il faUait s'emparer
de cette batterie. 5 A pe moment, lc regiment de Bilboquet

* The references m these Readings are te Oassell's M Lessons in
French," parts i. and ii In all cases where the part is not spe-
cified part i. is understood. L. means "OatseU's Lessons in
French" ; &, Section j R, Rule.

etait sur le bord de la Dwina; 6 car l'histoire que je vous
rapporte sfestpassea* dans la fameuse f campagne de Russie. 7
Tout-4-coup, on voit arriver au grand galops un aide-de-
camp du general, qui apportait rordre a deux compagnies
de voltigeurs de s'emparer de cette batterie. 8 Cetait une
operation bardie 9 ou il y avait a parier h que periraient
plus des trois quarts de ceux que Ton y l envoy ait; aussi les
voltigeurs, maigre leur intrepidity, se regard&entrils* entre
eux lu en sccouant la t£te et en haussant les epaules : on en
entendit meine quelques-uns et des plus anciens, qui dirent
tout bas en grognant et en montrant les canons :

— Est-ce qull croit, k le general, quo oas eadeta-la 1
crachent m des pommes cuites? 11 Ou bien eet-ce qu'il a
envie* de nous servir en hachis aux Cosaques, qu'il nous
envoie ° deux cents contre cette redoute ? l2 %

—Soldats ! s'ecria l'aide-de-camp, e'eet l'ordre de l'Empe-
reur ; et il repartit au galop. 18

— U fallaitP dono le dire tout de smite, 14 dit alors un
vieux sergent en assujettissant sa baionnette an bout de
son fusil : aUons, allons, il ne fauti pas faire attendre le
Petit Caporal ; r quand il vous a dit de vous faire tuer il
n'aimo pas qu'on nesite. 1 *

Colloquial Exbrcibe.

1. Quel etait le jour du mois ?

2. Quel ordre le general avait-
il recti?

3. Oh etait la position?

4. Comment Is ravin 6tait-il
dafendu ?

5. Que ndlait-ilnurepour arriver
a rendroit designe ?

6. Ou etait alors le regiment de
Bilboquet ?

7- A quelle epoque cette histoire
s'est-elle passee ?

8. Quel ordre apportait l'aide-
de-camp?

9. I/operation e'tait^Ue dan-
gereuse?

10. Que firent d'abord les volti-
geurs?

11. Que dirent-ils en montrant
les canons?

12. Quel nombre envoyait-on
contre la redoute ?

13. Que leur repondit Taide-de-
camp?

14. Queditlevieuxsergentapres
lo depart de 1'aide-de-camp?

15. Qu'aiouta-t-il en parlant da
Petit Caporal?

Notes Aim Rs**bbyoes.-~0. L. part il S. S3, R (5)— h.
from receeoir, L. part ii. p. 60.— e. L. S. 93, R 3.— d. L. S.
66, R. 1.— *. L. S. 44, R. 1.—/. L. S. 11, JL 5.-^. au grand
galop, at fuU epeed.—h. il j avait a parier, one might entity
think : lit. one might bet.~i. L. S. 28, R. 11.—?. the Os is here
expletive.— *. Est-ce qu'il eroit, doe* he believe ; L. 8. 24, R. 3.
— t. ces cadets-la, thote fellows, i. e. the eannon*. — si. orachent,
tend forth. — n. L. S. 20, R. 4. — o. from envoy er; L. part ii. §.
49, R. 2.— p. from faUoir ; L. p. 92, part il— q. from falloir.—
r. a name given by the soldiers to the Emperor.

II y a du plaisir a rencontrer les yeux de celui a qui on vient de
donner.— La Bruyer*.

11 vaut mieux lire deux fois un bon ouvrage qu'une fois un
mauvais.— J.-B. Sep.

Les hommes naissent nus et vivent habile^, eomme ils nsssent
independanls et vivent sous des loia. Les habits genent un pen Us
mouvemeuts du corps, mais ils le protlgent contre les accidents ou
dehors ; les loia gtnent les passions, mais elles d^fendent Thonneur,
la vie et les fortunea. —Bwarol.

La loi doit etre comme la mort, qui n'epargne personne.—
Montesquieu.

C'est une plaisante chose a consid^rer de ce qu'il y a des gens
dans le monde qui, ay ant rcnonc^ a toutes les loU de Dieu et de la
nature, s'en sent fait eux-mliBes auxquelles ils obiissent exacte-
ment ; comme, par example, les voleurs, etc.—PesceL

Sans la liberty de blimer, U n'est point d'eloge flatteur. —
Beaumarchalt.

11 y aurait une espece de feToeittf a rejeter indifferemment toutes
sortes de louances : Ton doit ttre sensible a eelles qui nous vien-
neut des gens de bien, qui louent sinoerement en nous les choses
louables.— La D rmjii i .

Loaer les priaoes des vertus quHls n*ont pas, e'est leur dire
impunlment des injures,-*!* JJmsjsjTiimsmMi

C'est un grand slgne de meVlioeriU, de loner toujouis medstsV

THE POPULAR EDUCATOR.

UNIVERSITY OF LONDON.

Having had frequent inquiries made by our correspoodenU a* to the agea at which they may Matriculate end take Degree
in the Unrrersity of London, we give the following statistical Table on this subject from the documents bekmgmg to th
UnsTersity, under date February Mod, 18S3. Those who wish more exact information than this Table affords, should immc
diately apply to the Secretary, Henry Moore, Esq., University of London, Somerset House.

Xwmhtr ewe* Attraf* Ap of QmdidaUt

for Matriculation and Ou teoerai Dtartn, end tka Number that kao$ pasotd mek

tion, in oach *tmr.

•- *

P»

-1.-1

Baenslur of Mrdirine.

Doctor of

Matriculation,

JHCUCIVI VI

Arts.

Master of Area

Law*,

Lew*,

First

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CORRESPONDENCE.
THE BLOWPIPE,

81E, — As many of my fellow-rtadenU in Chemistry are prevented
from prosecuting their experiment* for want of a blowpipe, I trust
ytu will give publicity to the following simple plan of making one.

A blowpipe fit for all ordinary purposes may be constructed in
the following msnner.

Procure one of Bmrns* Outtp Pipt* (it being the lightest), fit a
cork to the bowl, air-tight ; bore a hole through the cork, into
which introduce about If inohes of the shank end of a common clay
pipe, and the instrument is completed. It generally happens that
the hole in the common pipe shank is too large; if so, apply a little
pipe-clay, or plaster of Paris, to the point of it, and punoture it,
while damp, with a needle of the proper dimensions. Tours, &c,

John Paton.
Cardiff, January, 1864.

A Is the Bowl; B.ths Cork; C, ths Pipe-stem; and O. the damped
Pipe-day.

AN8WER8 TO CORRESPONDENTS.

Several eorrecpondrate having exsreeisd an earnest desire that the
Lessooe In German should be carried on to the conclusion of the Syntax in
the PorcLAa BnuoAToa, we shall take an etrly opportunity of continuing
the serf ?t .

R. R. 8. (Glasgow) :'A very inUlUfeot eorrespondont, under this signature,
wiahee to know if there be any cUib {we should have said cl*u) formed in
the great western metropolis of 80 jtland, for the etady of cheraietry ; as he
and four or five rente, of his acquaintance wish to become members of the
same; or if there be no each thinf in our ** Auld Reekie.'' to form one, to meet
once or twice a week, at may be grand conrenlent, with the view of making and
studying the experiments detailed in our Leesons In Chemistry. As we are
Glatruensians ourselves, we should have been happy to loin them, for the
amusement of the thing ; for we well remember what pleasure we had in
hearing the lectnresof Da. U as, when be was professor of Chemistry in
the Andereootan University (the raairr of all the Mechanics' Institutions tn
Great Britain) : and this was before we became, in our early days, professor
of Matbom4tics in the same Institution, and lectured to Mechanise on the
Geometry of the Greeks, as we are now doing to the students of the P. B^
but our vocation here le frest and onerous, and therefore we can ooly
recommend our townsmen to avail themsclvee of every opportunity of sett-
improvement; and to remember that tmkm u tirtmgtk in science, as in
ever> thin* «Ue; and that the world is lu rapid progress, and will wait for
nobody. We recommend to our correspondent, as classical French, the
works of Pascal, La Rochefoucauld, Massillon, fioileau, Racine. La Brujers,
La Kontaine, Boasuet, Beurdaloue, Malebrancbe, FonteneUe, sfontesquieu,
Rousieau, 8u Pierre, Chateaubriand, ftc. lie informs G. g. (Cupar), that
there was a treatise on Greek pronuncUUon published in Edinburgh by
Professor Blackie.

We have received letters from a considerable number of correspondents,
requesting tnat their names may be appended to any petition which we msv

?;et up addressed to the Senate of the University of London on their behalf.
or the purpose of requesting that application may be made to Government
for the extension of the Charter of the University, so that all $elf sdncel ed
and tetf-«tuo atin g ttutUntt in the realm may be admitted to the honours
and degrees hitherto attainable only by the students of the affiliated colleges
and institutions of the said University. A movement is in progrees on their
behalf, which we shall be happy to submit to them when it le matured: la
the meantime, we append the initials of those who have favoured as with
their names and their viewe on the subject; via* R. 8. P. (Westminster) ;
W. F. (Bishopsgatc) ; T. W. G. (Morpeth) ; W. M. (New Swindon) ; W. L
M. W. (Pentium); J. g. B. (Leeds); J. M. W. (IPortsea); J. M. (Den-
holm) 1 A. M. B. (Thornton); and others t» ehists.

J. C. (Salisbury) : Learn mathematics, and try to solv% problems ; mil
will improve both your memory and your Judgment ~J. B. H. (Lnndoa):
Grammar should not be a mere set of rales with en d l ess aaaepaoas, the
only way to overcome many difficulties is to read much and ta read the best
writers — A. (Leeds): Very well; dans fairs battre means as renhng er
vanquishing men. 7or the remaining sections of the French Lessons, see
•• CasselTs French Lessons. Part IL W — H. Rossill ( Weymouth) : Try agala ;
se compliquent means they oscome complicated.— »A Total AnerAUisa
(Norwich): We must not take the physician's place ; it has rarely happened
in onr experience that a prescription which answered on one occasion was
ever food for a nyt h in g again; patients are so variable, that what answered
st one time will not answer at another. The valuable sugveetioas he hat
made about the P. B. will be kept in view.

LESSONS IN PHYSICS.

289

ON PHYSICS, OR NATURAL PHILOSOPHY.
No. XX.

(Continued from page 280).

Laws ofihe Mixture of Gases and Liquids.— -Water and several
other liquids possess the property of absorbing gases ; but
under the same conditions of temperature and pressure, the
same liquid does not absorb equal quantities of different
gases. For instance : at an ordinary temperature and pressure,
-water absorbs '025 or one-fortieth of its volume of nitrogen,
•046 or about one- twenty-second part of its volume of oxygen,
a volume equal to its own of carbonic acid, and 430 times its
volume of ammonia. Mercury appears incapable of absorbing
gases. It has been proved experimentally that the mixture
of ases and liquids takes place according to the three follow
ing laws : —

1st, The weight ot a gas absorbed by a liquid at a given
temperature is proportional to the pressure ; or, the density
of the gas absorbed is in a constant ratio to that of the same
gas not absorbed.

2nd. The quantity of a gas absorbed increases as the tem-
perature diminishes ; that is, as the elastic force of the gas
diminishes.

3rd. The quantity of a gas absorbed by a liquid, is inde-
pendent of the nature and quantity of other gases which the
liquid may hold in solution.

Thus, if in place of a single elastic fluid, the atmosphere
above a liquid contains several elastic fluids, it is ascertained
that each of these gases, whatever may be their number, is
absorbed in the same proportion as if it were single, the pres-
sure which is proper to it being taken into considera-
tion. For example : oxygen forming only about £ part of the

an elevation of temperature, for then the elasticity the gas
held in solution increases.

Equilibrium at different Temperatures .—Equilibrium can only
exist in the same fluid, whether liquid or gaseous, so long as

Fir. 89.

the pressure is constant on all the points of each horisontal
stratum ; neither can it exist unless the density be the same
everywhere in the stratum ; otherwise, the lighter particles
would rise in the fluid mass, like floating bodies, and the more

Fig. 90

air, water in an ordinary state absorbs precisely the same
quantity of oxygen as if the atmosphere were entirely com-
posed of this gas, under a pressure equal to £ part of that of
the atmosphere. According to the first law, when the pres-
sure diminishes, the quantity of gas absorbed must decrease.
This fact is verified by placing a gaseous solution under the
receiver of an air-pump, and forming a vacuum ; the gas is
observed to act by its expensive force, and to disengage itself
from the liquid in bubbles. T^e same effect is produced by

TOi. IT.

dense particles would sink in the same. Now, gates and
liquids being very liable to expansion under the action of heat,
the density diminishes when the temperature increases.
Consequently, in order that a fluid mass may remain in equi-
librium, it is necessary that the temperature should be the
same at all the points of every horisontal stratum of the

Moreover, in order that the equilibrium may be stable, the
fluid strata must be arranged in the order of their density.

290

THE POPULAR EDUCATOR.

Still this condition does not require that the upper strata shall
be more heated than the lower strata ; for the latter being
more compressed by the superincumbent mass, tend to become
more dense ; it is sufficient, therefore, if the density increases
more by the effect of pressure, in the lower strata, than by
that of the diminution of the temperature ; and this is gene-
rally the case in the atmosphere. The currents which arise in
a fluid mass, in consequence of the differences of temperature
in the same horizontal stratum, are shown in the draught of
chimneys and in the apparatus for warming by means of hot
water. These applications will be considered in the sequel.

AEROSTATION

Quaquavtrsal Pnssure of Oases.— The pressures produced by
gases, in consequence of their elastic force, are equally trans-
mitted in all directions ; this has been proved in the case of
air by means of the- Magdeburg hemispheres. From this it is
evident that what has been formerly stated regarding bodies
immersed in liquids, is equally applicable to air and gases, and
that bodies immersed in elastic fluids lose a part of their weight
equal to the weight of the quantity of air or gas which they
displace. This lost of weight in air is proved by means of the
baroscope (front the Greek, a wight-mark), an apparatus which
consists of a beam, having at one end a hollow brass sphere
four inches in diameter, and at the other a small leaden
weight as a count erp oise , flg. 89. In air, the two bodies, the
sphere and the weight, balance each other ; but if we place
the apparatus wilder the receiver of an air-pump, and exhaust
it of thenar, the beam will lean to the side of the sphere, as
shown inThe figure, which indicates that in reality the sphere
is heavier than the leaden weight, since they do not experience
any pressure from the air, but are only acted on by gravity.
It therefore fellows, that in the air the sphere loses a certain
part of its weight. If we wish to prove, by means of the
same apparatus, that this loss is nearly equal to the weight of
the air displaced, we measure the volume of the sphere, which
is about 33£ cubic inches ; and as this volume of air weighs
about 1 1 grains, we attach this weight to the leaden weight at
the end ox the beam. The equilibrium which previously ex-
isted between the leaden weight and the sphere, when placed
in the air, is now destroyed ; but as soon as the apparatus
is placed in the exhausted receiver, we find that it is re-
stored.

The principle which Archimedes discovered, as belonging
to liquids, being thus found true for bodies immersed in air,
we can now apply to them all that has been formerly said re-
garding bodies immersed in liquids. Hence, when a body is
heavier than the air, it falls in consequence of the excess of
its weight above the upward pressure or buoyancy of the fluid.
If it be of the same density as the air, its weight and the up-
ward pressure are balanced, and the body floats in the atmo-
sphere. But, if the body be lighter than the air, the buoyancy
carries it upwards, and the body rises in the atmosphere until
it reaches air of the same density as itself. The force of
ascension is then equal to the excess of the buoyancy above
the weight of the body. This is the cause of the ascent of
smoke, vapours, clouds, and balloons in the atmosphere.

BALLOONS.
Discovery of Balloons — Balloons, as their name denotes, are
round or globe-shaped bodies/made of a light material imper-
meable to air, and filled with heated air or hydrogen gas, which
rise in the atmosphere in consequence of their relative light-
ness. Their invention is due to two brothers, Stephen and
Joseph Montgolfier, paper-makers in the atnill town of
Annonay, in the department of Ardeche, m France, where
their first attempt was made on the 5th of Juno, 1788. Their
first balloon was a globe made of linen, and lined with paper,
about forty yards in circumference, and weighing about five
cwt. Being open below, it was inflated with heated air, by
burning under it paper, wool, and wet straw. The academician
Lalande wrote thus on the occasion :— " At this news, we all
said : Such must be the case ; how was it never thought of
before?" It had been thought of; but there is a difference
between the conception of an idea, and its realisation. Dr.
Black, Professor of Chemistry in the University of Edinburgh,
had stated, in his course of lectures in 1767, that a bladder filled
with hydrogen would naturally rise in the atmosphere ; but

he never made the experiment, considering it only aa an
amusing remark. Cavallo, in 1782, had communicated to the
Royal Society of London some experiments which he had
made, and which consisted in filling soap-bubbles with hydro-
gen, which spontaneously rose in the atmosphere, the gas with
which they were filled being lighter than the air. But the
brothers Montgolfier knew nothing of the experiments ox
Cavallo, nor of the lectures of Dr. Black, when they made their
discovery. As they employed heated air only to fill their
balloons, the name of Montgolfier* was given to such balloons,
in order to distinguish them from those filled with hydrogen,
which are the only kind employed in the present day.

H. Charles, Professor of Natural Philosophy at Paris, who
died in 1823, was the first who substituted hydrogen for
heated air in the construction of balloons. On the 27th of
August, 1783, a balloon inflated with this gas was launched
into the airy element from the Champ-de-Mars at Paris. In
reference to its appearance, Mercier thus writes : " Never was
a lesson in Natural Philosophy given before a more numerous
and attentive audience." On the 21st of November, 1783,
Pilatre de Rosier undertook, in company with the Chevaliei
d'Arlandes, the first atrial voyage in a balloon made to ascend
bv heated air. The ascent took place from the garden " de la
Muette," near the wood of Boulogne. The aeronauts kept up,
under the balloon, a fire of damp straw, in order to preserve
the expansion of the air in its interior; thus the fire was in
danger of being communicated at every instant to the balloon.
Ten days after, MM. Charles and Robert ascended from the
garden of the Tuilleries at Paris, in a balloon filled with hy-
drogen. On the 7th of January, 1785, M. Blanchard, in
company with Dr. Jeffries, made the first passage from Dover
to Calais. The two aeronauts reached the coast of France with
very great difficulty, and only after having thrown their clothes
into the sea, in order to lighten the balloon. Since that period,
a very considerable number of ascents in balloons have been
performed. The ascent which was made by M. Gay-Lussac
in 1804, was the most remarkable for the facts which it added
to science, and for the altitude which this celebrated philo-
sopher reached, being 23,019 feet above the level of the sea,
Lastly, Mr. Green has risen to a greater height. At that"
height, the barometer fell to about 13 inches, and the centi-
grade thermometer, which stood at 31° (that is, 87° '8
Fahrenheit) on the ground, was then at— 9° (that is, 15°-8
Fahrenheit), being 5 degrees below aero or the freezing point.
On the occasion of a recent ascent, a much lower temperature
was observed at the same height. In these elevated regions
of the atmosphere, the dryness was such, on the day of Gay-
Lussac's ascent, which was in July, that hygrometric sub-
stances, such as paper, parchment, &c, were dried and twisted
as if they had been put before a fire. Respiration and the
circulation of the blood was accelerated in consequence of the
great rarefaction of the air. M. Gay-Lussac found that his
pulse beat 120 times in a minute, instead of 66 times, the
usual number when on the ground. At this great height, the
sky was of a very deep-blue colour, approaching the aspect of
night ; while an absolute and solemn silence surrounded the
sBTonaut. Having ascended from the court of the " Conserva-
toire dee Arts et Metiers" at Paris, Gay-Lussac descended
near Rouen, after an aerial voyage of six hours, having travelled
about 90 miles.

Construction of BeMeons.— The globe of balloons is pear-
shaped, and made of long stripes of silk sewn together and
covered with varnish or a solution of caoutchouc, to render the
silk impermeable to the air. At the top of a balloon is placed
a valve which is kept shut by a spring, and which the aeronaut
can otjen at pleasure by means of a cord. A light wicker car,
in which several persons may be seated, is suspended from the
balloon by the net- work which surrounds the pear-shaped
globe, see figs. 90 and 91. A balloon of ordinary ^mftnsiona!
which can easily lift three persons, is about fifty feet in
height, and thirty-six feet in diameter ; and its volume, when
completely inflated, is upwards of 24,000 cubic feet. The
globe weighs about two cwt, and the appendages about one
cwt. Balloons are inflated either with pure hydrogen, or with
carburetted hydrogen, such as is used for the purpose of light-
ing shops and streets. Although the latter gas is mora dense
than the former, it is now generally employed, because it k
cheaper and more easily procured than pure hydrogen. It k

LESSONS IN PHYSICS.

2*1

only necessary to place the balloon near a gasometer, and fill
it by means of a connecting-pipe.

In fig. 90 is represented the mode of filling a balloon with
pure hydrogen. On the right of the figure is shown a series

Fig. 91.

of casks, which contain iron filings, water, and sulphuric acid,
substances necessary for the preparation of the hydrogen.
From each cask, the gas is conveyed to a central cask, open at
bottom, and immersed in a butt full of water. The gas, after

f>assing through this water, is conveyed into the balloon by a
ong canvas pipe, fixed at one end to the central cask, ana at
the other to tne bottom.

In order to facilitate the filling of the balloon, two masts
are erected, having at their top pulleys traversed by a rope,
which passes through a ring fixed at the top of the valve. By
this means, the balloon being at first raised about a yard above
the ground, the gas is admitted ; then, in proportion as the
balloon is filled, it is raised a little higher, and it is allowed to
expand more and more, until it frees itself from this apparatus.
It is now necessary to oppose the force with which it begins to
ascend. For this purpose, a number of men are employed to
hold it down by means of cords fixed to the netting. When
the balloon is completely filled, it is then necessary to remove
the pipe which conveyed the gas, and to attach the car to the
net-work. These different preparatory operations require At
least two hours. The aeronaut is then seated in the car, and
at a given signal, the cords are loosed, and the balloon ascends
with a velocity in proportion to its lightness as compared with
the air which it displaces.

It is important to observe that a balloon should not be com-
pletely inflated ; for the atmospheric pressure diminishing in
proportion to the height of the ascent, the interior gas expands
in consequence of its elastic force, and tends to make the bal-
loon burst. It is sufficient that the force of ascent ; that is,

the excess of the weight of the air displaced above the whele
weight of the apparatus, be about ten pounds. It is to be
observed that this force remains constant so long as the
balloon is not completely inflated by the expansion of the
interior gas. For, if the atmospheric pressure be reduced to
one-half, the gas in the balloon, according to Mariotte's law,
is increased to double its volume. Whence it follows, that the
volume of air displaced is itself doubled, and its density is re-
duced to one-half; therefore its weight, and consequently its
upward pressure or buoyancy are still the same. But as soon
as the balloon ii completely inflated, if it continue to rise, the
force of ascent diminishes ; for the volume of air displaced
remaining the same, the density diminishes. Accordingly, the
balloon will ere long reach a point where the upward pressure
is zero. Consequently, the balloon can only take then a
horizontal direction, being carried by the currents of air which
exist in the atmosphere.

The indications of the barometer are the most certain means
by which the aeronaut knows when he is ascending and when
he is descending. In tbe former case, the column of mercury
falls ; in the latter, it rises. By the assistance of the same
instrument, he is enabled to ascertain the height which he has
reached. A long streamer fixed to the car, fig. 91, also indi-
cates, by the position which it takes above or below the car,
whether he is ascending or descending. When the tBron.iut
wishes to descend, he draws the cord which opens the valve
placed at the upper part of the balloon ; the hydrogen mixes
with the exterior air, and the balloon descends. On the con-
trary, in order to slacken his descent when it is too rapid, or
to re-ascend if placed in a perilous situation, the aeronaut
empties bags full of sand, a sufficient quantity of which had
been placed in the car for this purpose. Thus lightened, the
balloon rises again, in order to descend in a more suitable place.
The descent is facilitated by suspending an anchor to the car
by means of a long cord. When this anchor has taken hold
of a proper obstacle on the ground, the car and balloon are
lowered by gently drawing the cord.

Balloons have not as yet received any important applications.
At the battle of Fleurus, in 1794, a balloon, retained by a cord,
was employed to discover the movements of the enemy, which
were made known to the army by signals made by an observer
seated in the car. Several ascents have also been undertaken
with the view of making meteorological observations in the'
higher regions of the atmosphere. But balloons will only be-
come of real utility when the power of directing them has
been attained. The trials hitherto made for this purpose have
completely failed. At present, we can only rise in the atmo-
sphere until we meet a current of air which will carry us in
the direction answerable to the end we have in view.

The Parachute, — The object of the parachute (from the French,
a guard from falling) is to enable the tcronaut to leave his bal-
loon, by giving him the means of slackening the velocity of his
descent. This apparatus is composed of a large circular sail,
fig. 92, of about five or six yards in diameter, which, by the
effect of the resistance of the air, expands and forms a huge
umbrella which slowly descends to the ground. On its edges
are fastened cords, which support a car, in which the aeronaut
is seated. In the centre of the parachute, there is an opening
for the escape of the air which is compressed by the effect at
the descent ; without this, the air would produce oscillations
on the parachute, which would be communicated to. the car
and render the position of the asronaut perilous. In fig. 91 is
shown, on the side of the balloon, a parachute folded and
attached to the netting, by means of a cord passing over a
pulley and fixed to the car. By loosening this cord, the
parachute is placed in the power of the aeronaut. M. J.
Garneri t a-&s the first who descended in a parachute; but
M. Blaui-dard appears to ha?e been the inventor.

Weight required to raise a Balloon.— In order to calculate the
weight required to raise a balloon of given dimensions, when
it is supposed to be perfectly spherical, the following formula
is employed: vzziJitd 3 , which represents geometrically the
volume of a sphere, whose diameter is d, tt being the ratio ot
the circumference to the diameter, or 3* 141$ nearly. Thus,
if a balloon of thirty-six feet in diameter were completely
filled with hydrogen, its volume would be about 24,430 cubic
feet. But in genera], the balloon, when it begins to ascend, is
only about half filled, whence its volume may be assumed at

292

THE POPULAR EDUCATOR

12,216 cubic feet ; and such U the volume of displaced air at
the Ant moment of its ascent. According to calculations
formerly shown, this quantity of air weighs about 99 1 ^ lbs. or
nearly nine cwt., and this is the upward pressure which tends

Fif. 92.

to raise the balloon. But in order to calculate the real force
of the ascent, we must subtract from this pressure the weight
of the hydrogen in the balloon, and of the globe of which it is
made, with its apptndages. Now, the weight of hydrogen is
about i*t part of the weight of air ; whence, the weight of the
gas in the balloon is about 991J-H4=71 lbs., nearly. Adding
to this weight that of the globe and its appendages, formerly
reckoned at about three cwt., we hare upwards of 3$ cwt.,
say four cwt., for the weight to be subtracted from the nine
cwt. just mentioned ; this leaves a remainder of about fire
cwt. tor the force of the ascent. But we have seen that it is
sufficient for the force of ascent to be about 10 lbs. ; whence,
there is a little let's than the weight of five cwt. remaining
for the additional weight which a balloon may safely carry
into the atmosphere.

LESSONS IN CHEMISTRY.— No. XIX.

The subject of our present lesson shall be the metal silver;
not only so interesting for its commercial value, but as regards
its striking chemical qualities.

There are not many metals which admit of being traced through
a long list of combinations, and again obtained in the metallic
form, so easily as silver. Its chemical physiognomy is, in point of
fact, exceedingly well marked, as we shall presently see. It is
always well to begin the chemical examination of a substance, by
choosing the same in a pure condition, unmixed with any acces-
sory that might veil its properties or obscure the result. I
therefore recommend, as the source for obtaining a silver specimen,
a few grains, say eighteen or twenty, of the salt called, nitrate of
silver. This substance occurs in commerce under two forms:
either as sticks something like slate-pencil, only whiter, or as
crystals. The latter will be somewhat the purer of the two ; but
the former, known popularly as •• lunar caustic," will answer very
well.

Let the student then take about eighteen or twenty grains
of lunar caustic, or rather more of crystallised nitrate of silver,
and effeot a solution of the substance in about half a pint of dis-
tilled water. The solution takes place with great facility, and

may be readily accomplished in a Florence flask, — all the mors
rapidly under the influence of a gentle heat The solution will
be perfectly colourless and transparent ; not the slightest amount oj
mUkimess will be perceptible. I can fancy many a reader poring
over his solution at this moment, and imagining the writer of these
lessons to have erred. Some, in looking at a milky opalescent
solution, will be ready to think that the assurance of " perfect
clearness " is altogether untrue. Jf the water be quite pure, the
solution will be absolutely transparent ; but inasmuch as nitrate
of silver is a most delicate test for certain classes of impurities, it
is more than probable that many students may get a turbid solu-
tion.

Should this be the case in the present instance, heed it not.
The occurrence will serve to mark a fact, without interfering with
the current of our experiments. You have only to wait awhile,
and the turbidity will settle, leaving a clear solution above, well
adapted for our purposes. Having followed out the preceding
directions, it is evideni that a solution of nitrate of silver in water
will hare been obtained. We will proceed to investigate its
chemical characters presently ; meantime, let it be well impressed
upon the mind that the solution is colourless : hence it follows
that any solution which is not colourless, must contain some
other substance besides nitrate of silver. We may generalise
still more, and say that all silver solutions are oolourless.
Strictly true this assertion is not, I am aware ; but it is, never-
theless, so nearly true, as to warrant its being considered by tho
student as a universal fact Accepting the proposition as absolute,
we may then make the further assertion, that, though a metallic
coloured solution may contain silver, it start contain some metal
in addition to silver.

The appreciation of these broad qualities — these general cha-
racteristics, are of the highest importance in chemistry : several
metals being recognisable at once, by noticing the colour of their
solution. That the reader may at once see the force of this re-
mark, let him dissolve a small silver coin in some pure aquafortis,
diluted with about an equal volume of water, for the purpose of
moderating the violence of the action which ensues. The experi-
ment is best conducted in a Florence flask, which may be placed
in hot sand on a grate hob, in order that the injurious fumes
which escape may be carried up the chimney.

When the operation of solution has been effected, remark well
the tint of the resulting fluid. The experimenter has employed
a silver coin, I have assumed, dissolved it in an acid, t. e. aqueous
nitric acid or aquafortis. Having regard to the substances used,
therefore, it would seem that a solution of nitrate of silver should
result. Nevertheless the solution is no longer colourless but blue,
and if the student evaporates it, blue' crystals will appear. It
follows, therefore, that if there be any truth in what I have
stated, the silver coin must have contained something in addition
to silver. Now supposing the colouring agent to be metallic, and
it must be so— by " construction,' ' as geometers say — in other words,
it must be so, because we have only used a metallic coin, then it
follows, firstly, that the coin was not of pure silver, but an alloy.
Secondly, that the alloying substance was a metal yielding a blue
nitric acid solution. Now I am only aware of two metals which
are capable of yielding such a blue solution. These metals are
copper and nickel ; and most people know, I presume, that copper
is the metal used for alloying our silver coins. Pure silver
would be altogether too soft for the purpose, as the reader will
not fail to see when he shall have developed a little of that metal
from its liquid combination.

Put away this cupreous silver solution, duly labelled. To
expatiate on it here would be so far out of order, that we are
discussing the properties of silver, not copper. It will, neverthe-
less, come under our notice when we treat of the latter metal ;
indeed even before, for I shall pnt the student in possession of an
easy means by which all the silver may be separated, and the
copper left behind.

Returning now to our solution of nitrate of silver, let the
student question it thus :
(1) What is its nature ?

To arrive at an answer to this question, drop a little of tout
strong solution, say twenty or thirty drops, into a wine-glass;
fill up the wine-glass with distilled water, and test with hydro-
sulphuric acid solution. We get a well- pronounced black preci-
pitate, on observing which we immediately deduce the following
truths. . (1) The solution contains as its base, a metal. (2) A cal-
cigenous metal (vide Lesson p. 39). (3) Neither sine, arsenic,

FRENCH READINGS.

298

antimony, cadmium, nor tin, in the state of persalt ; because the
precipitate would either have been white or yellow. (4) Nor
iron, manganese, nickel, cobalt, or uranium, because hydrosul-
phurio acid without ammonia does not precipitate them. Con-
sider, then, the nature of these deductions, and see into what a
corner we are driving metal, even by the evidence of one single
witness.

Let us now try another witness, namely .ferrocyanide of potassium;
and once for all let the student remember that hydrosulphuric

FRENCH READING S.— No. II.

LE SAPEUR DE DIX ANS.
Section III.

Cependant il entrait* encore quclque h
>mpagnie, 1 ct deja deux fois le capitaine

hesitation dans la
qui commandait

acid, hydrosulphate of ammonia, and ferrocyanide of potassium, j avait donne l'ordre au tambour-maitre de prendre deux
are the three witnesses always first cited in a court of chemical tambours, de se mettre en avant, et dc battre la charge. 2
inquiry, supposing the substance ondcr question to bo in . Celui-ci restait appuye sur sa grande canne, 3 hochant la
the stite of liquidity and totally unknown. Whatever evidence teto et peu dispose a obeir. Pendant ce temps Bilboquet, a
is to follow, theirs comes first; all three, if we want them, or ^hevalb 8Ur son tambour* et les veux leves sur son chef,

now under
hydrosulphate
given already i
chemical examinations,

tive. It is so in the present instance. Let us now proceed to
use the third test, ferrocyanide of potassium ( yellow prussiate of
potash), in solution of course. For this purpose, add a few drops
of the strong nitric acid solution to a little distilled water, and
test with prussiate of potash. We now get a whitish sort of
precipitate.

Omitting to repeat such of the evidence yielded by this test as
we happen to know already, what novelty does it communicate ?
What has it to ray of its own specific knowledge ? Why it tells
us that, in addition to all the metals amongst which ours is not, it
furthermore is not

Copper
Uranium
Molybdenum
Titanium ;

because either of these, similarly treated, would have yielded a
mahogany brown colour. This fact I have not brought before the
student hitherto ; let it therefore be committed to memory at once,
and never forgotten. It follows, then, that our unknown metal is
at length hunted into an exceedingly narrow corner. If the student
will only refer to a listof metals, and see the names of those of which
the present is not, he will arrive at the conclusion that it must be
one of a very few. At this point I will assume the operator to
appeal to the evidence of another test, either hydrochloric acid
(spirit of salt), or else common salt dissolved in water; practi-
cally, so far as relates to the present investigation, these tests are
the same, and the student may use whichsoever he pleases.

Treated with either of these substances, our solution (assumed to
be unknown) will throw down a dense white precipitate ; henee
we know at once that the metal we are hunting for is either silver
or mercury ; no other metals being oapable of producing a similar
effect.

Finally, the addition of a little hartshorn (liquor ammonia?)
causes the precipitate to dissolve and the whiteness totally to
disappear ; which characteristic result demonstrates the metal to
he silver, nothing but silver.

CURIOSITY.

Its aim oft idle, lovely in its end,

We turn to look, then linger to befriend ;

The maid of Egypt thus was made to save

A nation's future leader from the wave ;

New things to hear, when erst the Gentiles ran,

Truth closed what Curiosity began.

How many a nob!e art, now widely known,

Owes its young impulse to this power alone ;

E'en in its slightest working, we may trace

A deed that changed the fortunes of a race :

Bruce, banned and hun'ed on his native soil,

With curious eye surveyed a spider's toil;

8ix times the little spider strove and failrd ;

Six times the chief before his foes had quailed ;

" Once more," he cried, •« in thine, my doom I read,

Once more I dare the fight, if thou succeed ; "

Twas done : the insect's fate he made his own •

Once more the battle waged, and gained a throne.

sous le nez f du tambour-maitre, il le toise avec orgueil, lui
rend d'un seul mot toutes les injures qu'il avait sur le
eoeur, et luit dit : — Viens f done, grand poltron !*

Le tambour-maitre veuts lever sa canne, 9 mais deja Bil-
boquet etait a la tete des deux compognies, 10 battant la
charge comme un enrage. h Les soldats, a cet aspect,
s'avancent apres lui et courent vers la terrible batterie. 11
Elle decharge d'un seul coup ses six pieces de canon, et des 1
rungs de nos braves voltigeurs s'abattent et ne se relevent
plus. 12 La funiee, poussee* par le vent, les enveloppe, le
fracas du canon les etourdit ; mais la fumee passe, le bruit
cvsse un instant, et ils voient k debout, a vingt pas devant
eux, l'intrepide Bilboquet battant la charge, 13 et Lis en-
tendent son tambour, 14 dont le bruit, tout foible qu'il soit, 1
scinble narguer tous ces gros canons qui viennent m de tirer.
I41 voltigeurs courent toujours, et toujours, 15 devant eux le
tambour et son terrible rlan rlan les appellej* enfin una
aetond decharge de la batterie eclate et perce d'une
grele de mitraille les debris acharnes des deux belles com-
pagnies. 10 A ce moment, Bilboquet se rctourne etvoit qu'il
rcste a peine cinquante hommes des deux cents qui etaient
partis, 17 et aussitot, comme transports d'une fureur de ven-
gOKucc, il redouble de fracas : 18 on cut dit vingt tambours
battant a la fois ; jamais le tambour-inaitrc n'avait si hardl-
ine i it frappe une caisse. Les soldats s'elanccnt de nouveau
et tntrcnt dans la batterie, 19 Bilboquet le premier, criant a
tue-teteP aux Kusses :

— Les morceaux en sont bons, les voici; 20 attendez,
attendez !

Colloquial Exercise.

1. Que remarquait-on nean-
uioins dans la compagnie?

2 . Quel ordre le capitaine a vait-
il donne' au tambour-maitre?

3 Que fit celui-ci apres avoir

rccu cct ordro ?
4. Ou 6tait Bilboquet pendant

00 temps la ?

n. Quo faisait-il ?

6. Ifi tambour-maitre parais-
ptiit-il dispose' a obeir au troi-

emo ordre ?

7. Que fit alors le petit tam-
bour.

B. Comment apostropha-t-il lo

1 umbour-maitre ?

!i Que voulut faire le tambour-
maitre?
10. Ou e'tait alors notre he"ros ?

11. Quo firent les soldats en
voyant son intrepiditl ?

12. Quel effect produisit la d4-
charge des six pieces dc canon?

13. Que virent les soldats quand
la fumee fut dissipee ?

14. Qu'entendaient-ils malgre'
le bruit du canon ?

15. Que firent alors nos volti-
geurs ?

16. Quel fut l'effet d'une sc-
conde decharge ?

17. Combien d'hommes restait -
il?

18. Que fit Bilboquet a la vUe
du carnage ?

19. Que firent alors les soldats?

20. Que cria alors le petit tam-
bour?

II entrait, there teas ; the verb

Notes and Reverences. — a,
w lipersonal in French
seated across. — c. venait d'

d. from paraitre ; L. part ii., p. 98. — e. sous le nez, close to the
fare ; literally, under the no**.—f. from venir ; L. part ii., p.

; L. part ii., § 43, R. (7).— b a cheval,
d'etre, hod Just been ; L. S. 25, R. 2.—

THE POPULAR EDUCATOR.

10&— $. horn tomtoir; L. part. iL, p. 110.—*. enrage, madm m m .
— *. 3. 4, B. 1.-?. s. &«*, R 1. — ir. from toir ; L, part iL, p. lia
— /. ratymeriv? of flr*. — «k from wir ; L. 8. 25, R 2- — a. L.
part iL, $ 4&. B. (I,i.— *. en «at dit, a*e ro«/<* Aa** tkomght
that; literal!/, —id.-^p. a toe-fete, «A» a// to n^a/.

Sacnos IT.

Pendant ce tempi, Napoleon monte snr on tertre, regar-
dait execute!" cette prise hcToioue. 1 A chaque decharge,
fl trratfiilliit cor son coeval iaabelle ; puis, quand lea aoldats
ettrerent dans la hatterie, il baiiaa aa lorgnette en disant*
Uni baa : Bravee gena ! *

Et dix mille hommee de la garde, qui etaient derriere lui,
ae mirent • a battre dea mains et a applandir' en criant :

— Bravo, lea voltigeun!! Et ils s*jr amnaisaaient, 4 je
Tons aarare.

Anaaitot, *or Tordre de Napoleon, nn aide-de-camp con-
rut* iuaqn'a la batterie' et revint f an galop.

— Combien sont-ils arrives ? s dit rEmpereur.

— Qnarante, repondit laide-de-camp.

— Qnarante croix demain,* dit rEmpereur en se retonr-
nant vers son major-generaL

VeritabLement, le lendcmain, toot le regiment forma nn
grand oercle antonr dea rcste* dea deux compagniea de vol-
tigenrs,' et on appela succeaeivement le nom dea qnarante
bravee qui avaient pris* la batterie,* et Ton remit h a chacnn
d'eux la croix de la Legion-d'Honneur.' La ceremonie
etait finie, et toot le monde allait se retirer, lorsqu'une

ar etaat qu'un enfaas ?

14. Qneludoima-t-il?

15. Bilboqnet pra-il la pieee?

16. Begardait-on le petit tarn-
boor?

17. Qneiaisait-flaion?

Kora ajcd Bxtxrxscb. — a
L. part ii, p. 68. — c. se mirent,
ils s'y eotmT
66.R6-*
L part iL, p. 104. — $. from prendre

l&Leai

flademir~
Id. Qu aOak-on ]

«g«arf-

20. Que dit-fl
raL

21. Que fit-il apeaa avoir mat
1' argent dans aa poche?

L S. 20, R 2.-*. fomdtrv;
ommenced ; L. 8. 68, R Z.—d.
X,tk*y were good jndgn of mckthimg*; L. 8.
from comrir; L. part iL, p. 84.-£ from rexemr ;
; L part iL, p. 100.— A. re-
mit, presented ; from remettre ; L part iL, p. 102. — t. fit en-
tendre, ntUred; from/oar*; L. part iL, p. 92.-^. accent, ton*.—
Jr. L p. iL, $ 33, R i$).— /. plant*, Handing; literally, pUmUa\
potted— m. feu etais, I was ome of them, of tk§ — btr.— a. L
part iL, § 33, B (9).— o. fiqpm battre ; L. part iL, p. 80.— -p. L
S. 80, R 2. — q. que veox-tu, how earn I kelp ii ; UteraDj, aalat do
pom wish.— r. L. S. 61, R 5.— «. en attendant, mmwmiU.—t. from
dire ; L. part ii., p. 88— a. il s'etait nut, Oar* aw.—*, fiom
parmtre; L. part ii, p. 98.— «?. L & 2$, R *-*. toojonrs,
notwithstanding ; literaUr, alecap*.

Seciiox V.

A partir de ce jour, on ne ae
petit Bilboqnet, 1 mais il n'en b devint*

pma antant da
pas ponx oela plna

commnnicatif ; an contraire, il «»mM*^ ronler dana aa tete
. _ ^ , f qaelque famenx projet, et, an lien de* depenaer aon anrent

voix sortit dn rang et fit entendre' ces mote, 1 * prononcea avec ^ camarade*, comme cenx-ci aV attendaienV 3 le
avec on singnber accent < de surprise : : germ soigneusemcnt. 2

— Et moi ! moi!* je nai done rien? | Q ne i que temps apres, lea troupes francaifiea f entreient

Vardeor ; Bilboqnet en
t alia ae promener* dana

^Mais, mon general, j*en etais a dit Bilboqnet preaqne
en colere ;" e'eat moi° qui battais la charge en avant, c^st
raoi aui suis^ entre le premier.

— Que venx-tu,'* mon garcon ? on t'a oublie, repondit le
g&neral ; d'ailleurs, ajouta-t-il en considerant que e'etait nn
enfant, tu ea encore bien jeune, on te la donnera quand tn
anras' de la barbe au men ton; 13 en attendant,* voila de
quoi te consoler.

En dutant* ces paroles, le general tendit nne piece de
vingt francs 14 au pauvre Bilboquet, qui la regarda sans
penser a la pendre. 15 II s*etait fait* un grand silence
autour de lui, et chacun le considerait attentivement ; li lui,
derncurait immobile devant le general et de grosses larmes
roulaient dan.-* scs yeux. 17 Ceux qui s'etaicnt le plus
moques de lui poraissaient * attendris, 1 " et peut-etre allait-
on elever unc reclamation l ' J en sa faveur, lorsqu'il releva
vivement la tete, comme nil venait v de prendre une grande
resolution, et il dit au general :

— Cest bon, donnez toujours, 1 ce sera jwnr une autre
fois. 20

Et sans plus de facons, il mit la piece dans sa poche et
s'en retourna dans son rang en sifnant d'un air deHbere et
satiHfait. 21

Colioqxtul ExiRCIflS.

1. Que faisait Napoleon pen-
'dant ce temps-la ?.

2. Que fit-il quand lea soldats
entrercnt dans la battcrie ?

3. Quo flrcnt les soldats dc sa
garde?

4. Quel ordrc XapoMon donna-
t-il a un aide-de-camp ?

5. Que dit-il a l'aide-de-camp
a son retour ?

6. Quel ordre donna-t-il au
general?

7. Que fit le regiment le len-
demain?

8. Qu'appela-t-on BUOcessiTe-
ment?

9. Que donna-t-on a ces braves
gens?

10. Qu'arriTa-t-il lorsque la <&•
r^monie fut finie ?

11. Que vit alors le g^n^ral ?

12. Que repondit le petit tam-
bour a la question du genl-
ralP

preaqne tons lea vi-
v cxmsiderait d'un air riant 9

et semblait lea examiner comme un amateur qui choiait
des marchandises. II fant 1 vous dire cependant, qull ne
regardait ainsi que les pa jaans qui portaient* dea grandes
barbea. 7 Elles etaient sans doute trea longues et trea
fonrnies, k mais d'un roux si laid, qn'apres nn moment
d'examen Bilboquet tournait la tite et allait plna loin.
Enfin, en allant ainsi, notre tambour arriva an quartier dea
Juifs. s Les Juifs 4 Smolensk, comme dana toute la Pologne
et la Ruasie, vendent toutea sortee d'objeta* et ont nn
quartier particulier. 10 Des que Bilboqnet y l fat entre, ee
rat pour lui un veritable ravisaement: 11 imaginea-vona lea
plus belles barbes dn monde, noirea comme de l*ebene; l>
car la nation juivc toute dispersee qu'elle eat, parmi les
autres nations, a garde la teinte brune de sa pean et le
noir eclat de sea cneveux. 13 Voila done™ notre Bilboqnet
enchante. Enfin il se decide, et entre dans nne petite
boutique u ou se trouvait un marchand magnifiquement
barbu. 15 Le marchand s'approche de notre ami et lni de
mande humblement en mauvais francais :
— Que voulez-vous mon petit Monsieur? 18
— Je veux n ta barbe repondit cavalierement Bilboqnet 17
— Ma barbe! dit le marchand stupefait; vous Youlea
rire? 18

— Je te dis, vaincu, que ie veux ta barbe, reprend le vain-
quenr superbe en posant la main gnr eon faore \ mais ne
crois paa que je veuilleP te la volar ; u tiena, 4 ! tow nn na-
poleon, ta me rendraa mon reete. T

OOLLOQTTULL EXBBOin.

1. A partir de ce jour, comment
traita-t-on notre heros ?

2. Que fit-il de son argent ?

3. Que firent les troupes fran-
caises quelque temps apres ?

4. Que fit le petit tambour lo
jour de son arrivee ?

5. De quoi paraaaaanVil con-
tent?

6. De auelle maniere conai-
derait-il le visage des habi-
tants?

7. Quallasperaoni]
Upartwauafaniaaif

LESSONS IN GEOMETRY.

295

8. Ouamva-t-uenfin?

9. Que font les Juif* en Ecu-
tie P

10. Oudemeurent-ils?

11. Quel sentiment eprouva
Bilboquet, quand il fufc entrl
dans ce quartier ?

12. Pourquoi etait-il si content?
18. Quelle remarque l'auteur

fait-il a propos de la nation
juive?

14. On Bilboquet entra-t-il en-
fin?

15. Qui trouva-t-il dans la bou-
tique?

16. Que dit le marchand au
petit tambour?

17. Que lui demanda celui-oi ?

18. Quelle fut la reponse du
marchand?

19. Qu'ajouta Bilboquet en met-
tant la main sur son sabre?

Noras and References. — a. From se moquer; to laugh at.
— b. en, on that account. — e, from devenir; L. part iL, p. 88. —
d. L. S. 34, E. 4. — e. ils sJV attendaient, they expected.— f. L.
part ii., § 145. — g. L. S. 35. a. 5. — h. from paraitre ; L. part ii.,
p. 98. — i. il faut, I must; ttomfalloir ; L. S. 47; also L. part iL,
p. 92.-2*. portaient, wore. — k. fournies, thick.~-4. L.part ii., §
39, E (18). — m. roua done, behold then. — ». from vouloir ; L.
part iL, p. 110. — o. rous voulez rirt, yon are joking, you are not
t» earnest. — p. from vouloir, — q. tiens, here ; literally, hold;
from tenir, L. part ii., p. 108. — r. rcste, change.

SKELETON MAPS.— No. V.

MAP OF SOUTH AMERICA.

Our Map of Russia in Europe (the approximate seat of war)
not being ready, as intended, for this month, we insert in this
Number a Skeleton or Outline Map of the Continent of South
America, including the continental part of the West Indies
called Guiana, and the small islands adjacent to the con-
tinent all around it. This. Map will be useful to emigrants,
settlers, or colonists, who wish to transplant themselres to
South America, where there is abundance of room for specu-
lations of all kinds. If such persons have sufficient time and
skill to fill up this Map for themselves, the process of doing
so will make them better acquainted with the country in
which they intend to settle, than many Lessons in Geography,
which consist of the mere descriptions of places, but give no
idea of their relative position in regard to one another.

An extensive list of the latitudes and longitudes of the chief
or capital towns in the various countries and sub-divisions of

the continent, and of the islands of South America, will be
found in Vol. iii., at page 250; and, as the continental part |
of the West Indies is included in this Map, the latitudes and
longitudes for the chief towns of this part will be found at
page 118. On the marginal space of the Map, we have given
the latitudes and longitudes of the principal islands, capes,
bays, rivers, and ports along the eastern and western coasts of
the continent, from Cape Horn to the Isthmus of Panama, in
regular order, proceeding from south to north, and along the
coast of America situated on the Caribbean Sea. These we
have added to the latitudes and longitudes of the places in the
interior of the continent above-mentioned, so as to enable
our students to make their Map as complete as possible.

LESSONS IN GEOMETRY.— No. XXVI.
LECTURES ON EUCLID.

{Continued from page 256.)

. PROPOSITION XXVII.— THEOREM.

If a straight line falling upon two other straight lines, make the
alternate [angles equal to one another ; these two straight lines
are parallel.

In fig. 27, let the straight line Fi* . 87.

s p which falls upon the two
straight lines a b and cd, make
the alternate angles aef and bfd
equal to one another : then a b is
parallel to c D.

For if a b be not parallel to o n.
these two straight lines wiU
meet, if produced either towards A and o, or towards B[and d.

Let them be produced and meet towards b and d, in the point o ;
then o b f is a triangle.

Now,' in the triangle oip the exterior angle a if is greater
(1. 16) than its interior and opposite angle kfo; bat the angle
a b f is equal (Hyp.) to the angle b f g ; therefore the angle aif
is both mater than, and equal to, the angle efo; which is impos-
sible. Wherefore the straight lines a b and o b, if produced, do
not meet towards b and n. In the same manner it may be proved,
that they do not meet if produced towards a and o. But those
straight lines in the same plane, which do not meet when
produced ever so far either way, are parallel (Def. 33) • There-
fore A b is parallel to o d. Wherefore, if a straight line Calling
upon two other straight lines, &c. Q. E. D.

Scholium I. TheanglesABF and bfd are called alternate angles,
or more properly interior alternate angles, because they are on oppo-
site sides of the straight line b f, and the one has its vertex at b
the one extremity of the portion between the parallels, while the
other has its vertex at f the other extremity of the same.

Scholium 2. In the diagram the crooked lines b b o and fdo
must be considered straight lines, and the figure efbgbi triangle,
for the sake of the argument. Otherwise, the figure might have
been constructed so that the straight lines ab and CD should
actually converge and meet in a point.

EXERCISE I. TO PROPOSITION XXVII.

If a straight line falling upon two other straight lines, make the
exterior alternate angles equal to each other, then two straight
lines are parallel.

In fig. 28, let the straight line e f, which falls upon the two
straight lines a b and o d, make the two exterior alternate angles
a a e and f h d equal to one another ; then a b is parallel to o D.

Because (I. 13) the two angles age and A o h are equal to two
right angles, and the two angles fhd and o h d are equal to two
right angles; therefore (Ax. 1) the two angles AOBand a ok
are equal to the two angles fhd and ohd, But (Hyp.) the angle
A g b is equal to the angle fhd; therefore (Ax. 3) the angle A o H
is equal to the angle g h d ; and they are alternate angles ; where-
fore (I. 27) the straight lines ab and c n are parallel. Q. E. D.*

EXERCISE II. TO PROPOSITION XXVII.

If a straight line falling upon two other straight lines, make the two
exterior angles on the same side of it equal to two right angles,
these two straight lines are parallel.^

In fig. 28, let the straight line B f, which falls upon the straight
lines ab and od, make the two exterior angles on the same side of
it, bob and fhd, equal to two right angles ; then a b is parallel
to o D.

Because (I. 13) the two angles bob and b g a are equal to two
right angles, and (Hyp.) the two angles bob and fhd equal to
two right ^angles ; therefore (Ax. 1.) the two angles bob and boa
are equal to the two angles igb and fhd; from these equals
take away the common angle bob, and (Ax. 3) the angle b o a is
equal to the angle fhd; but these are the two exterior alternate
angles ; wherefore, by the preceding exercise, the straight lines a b
and o d are parallel. Q. fe. D.

PROPOSITION XXVIII.*-THEOREM.

If a straight line falling upon two other straight lines, make the
exterior angle equal to the interior and opposite angle upon the
same side of the straight line ; or make the two interior analee
upon the same tide of it, together equal to two right angles ; these
two straight lines are parallel to one another.

Let the straight line e f, falling upon the two straight lines a b
and o d, make the exterior angle bob equal to the interior sad
opposite angle ohd upon the same side of
if; or make the two interior angles
bqu and ohd on the same side of it,
together equal to two right angles ; then
ab is parallel to od.

Because the angle b g b is equal (Hyp.)
to the angle ohd, and the angle eob ii
equal (I. 15) to the angle aoh; therefore
the angle aoh is equal (Ax. 1) to the

Fig. 98.

• Solved by Q. Pringle, Glasgow ; J. R. Eastwood, Middtetoo;
E. J. Bremner, Carlisle,
f See new edition of Cassell's Euclid, 1854.

296

THE POPULAR EDUCATOR.

angle ohd; and they are alternate angles ; wherefore a b which parallel [straight] lines, though indefinitely produced, emu
parallel (I. 27) to c d. never intersect. This is, perhaps, the most ordinary idea of

Again, because the two angles boh and ohd are together! parallelism. Almost every other property of parallels requires
equal (Hyp.) to two right angles ; and the two angles ao h an J j *° me consideration before an nninstructed mind assents to it ; bvt
b o h are also together equal (I. 13) to two right angles ; theru- the possibility of two such [straight] lines intersecting is repuff.
forsthctwo angles a oh and boh are equal (Ax. 1) to the two nan^ every notion of parallelism ..__.. .
angle. BOH^fd oh n Take away fro^ theie equaU the con> J f ^^

mon angle b oh, and the remaining angle aohu equal (Ax. Sj liroved Wm ' Thi J is the cage with Euclid > 8 definit J on of * ii e £
to the remaining angle ohd ; but they are alternate angles ; there- fa 0Wj it may be asked, does it appear that two right (straight]
fore a b is parallel (I. 27) to o D. Wherefore, if a straight line, lines can be drawn upon the same plane so as never to intersect
&c. Q. E. D. though infinitely produced ? Euclid meets this objection in his

Scholium 1. The twelfth axiom will now be admitted by tl , 27th proposition, where he shows that if two [straight] lines be
.j-..* ii — *~ *u: :*: i.n u— fa — inclined at equal alternate angles to a third, the supposed possi-
bility of their intersection would lead to a manifest contradic-
tion. Thus it appears, that through a given point one right
[straight] line at Uatt may always be drawn parallel to a given

student as a corollary to this proposition ; especially when Proj
XV II. and the note added to the twelfth axiom are taken into
account.

Scholium. 2; We think it right to introduce our students at th
point, to a discussion on the " Theory of parallel straight lines,
which will be of immense advantage to them in their future studies.
Our first extract shall be from the Gower-street edition of Euclid.

% "The theory of parallel [straight] lines has always been coi
sidered as the reproach of" Geometry. The beautiful chain of
reasoning by which the truths of this science are connected her
wants a link, and we are reluctantly compelled to assume as an
axiom what ought to be matter of demonstration. The most eminent
geometers, ancient and modern, have attempted without success
to remove this defect; and after the labours of the learned fo
2,000 years have failed to improve or supersede it, Euclid's theor
of parallels maintains its superiority. We shall here endeavour
to explain the nature of the difficulty which attends this invest!

Ktion, and shall |rive some account of the theories which hav ,
en proposed as improvements on. or substitutes for, that o
Euclid.

" Of the properties by which two right [straight] lines describe*
upon the same plane are related, there are several which charac-
terise two parallel [straight] lines and distinguish them from
[straight] lines which intersect. If any one of such properties bt
assumed as the definition of parallel [straight] lines, all the others
should flow demonstratively from it. As far, therefore, as theatric
principles of logic are concerned, it is a matter of indifference
which of the properties be taken as the definition. In the ohoict
of a definition, however, we should be directed also by other cir
cumstances. That property is obviously to be preferred from which
all the others follow with the greatest ease and clearness. It is also
manifest that, caterit paribus, that property should be selected
which is most conformable to the commonly received notion of
the thing defined. These circumstances should be attended to
in every definition, and the exertion of considerable skill is
necessary almost in every case. But in the selection of a defini
tion for parallel [straight] lines there is a difficulty of another
kind. It has been fouud. that whatever property of parallels be
selected as the basis of tneir definition, the deduction of all the
other properties from it is impracticable. Under these (circum-
stances, the only expedient which presents itself, is to assume,
besides the property selected for the definition, another property
as an axiom. This is what every mathematician who has
attempted to institute a theory of parallel [straight] lines has
done. Some, it is true, have professed to dispense with an axiom,
and to derive all the properties directly from their definition.
But these, with a single exception, which we shall mention here*
after, have falleu into an.illogicism inexcusable in geometers.
We find invariably a pctitio principii, either incorporated in
their definition, or lurking in some complicated demonstration.
A rigorous dissection of the reasoning never fails to lay bare the
sophism.

"Of the pretensions of those who avowedly assume an axiom it
is easy to judge. When Euclid's axiom is removed from the
disadvantageous position which it has hitherto maintained,
put in its natural place, and the terras in which it is expressed:
somewhat changed, I think it will be acknowledged that no
proposition whioh has ever yet been offered as a substitute
for it, is so nearly self-evident. But it is not alone in the degree
of self-evidence of his axiom, if we be permitted the phrase, that
Euclid's theory of parallels is superior to those theories Which
are founded on other axioms. The superior simplicity of the
structure which he has raised upon it is still more conspicuous.
When you have once admitted Euclid's axiom, all his theorems
flow from that and his definition, as the most simple and obvious
inferences. In other theories, after conceding an axiom much
further removed from self-evidence than Euclid's, a labyrinth of
complicated and indirect demonstration remains to be threaded,
requiring much subtlety and attention to be assured that error
and fallacy do not lurk in its mazes.
* Euclid selects for his definition that property in virtue of

right [straight] line. But it still remains to be shown, that no more
than one parallel can be drawn through the same point to the same
I right [straight] line. And here the chain of proof is broken. Euclid
l was unable to demonstrate, that every other [straight] line except
that which makes the alternate angles equal will necessarily
intersect the given right [straight] line if both be sufficiently

Sroduced. He accordingly found himself compelled to place the
eficient link among his axioms."

We now add to this extract, notices of thirty different methods,
proposed at various epochs in the history of Geometry, for getting
over the difficulty of the Ttcelfth Axiom of Euclid's First Book.
This collection is taken from Col, P. Thompson's '* Geometry
without Axioms," pp. 157 — 156.

" The uses of such a Collection are to throw light on the particu-
lars which experience has shown are not to be left unguarded in
any attempt at solution, and to prevent explorers from consuming
their time in exhausted tracts. To which may be added, that out
of so many efforts, some, either by improvement or by a fortunate
conjunction with others, may finally be found operative towards
the solution desired.

1. The objection to Euclid's Axiom (independently of the objec-
tions common to all Axioms), is that there is no more reason why
it should be taken for granted without proof, than numerous other
propositions which are the subjects of formal demonstration, and
the taking any one of which for granted would equally lead to the
establishment of the matter in dispute.

2. Ptolemy the astronomer, who wrote a treatise on Parallel
Lines, of which extracts are preserved by Proclus, proposed to prove
that if a straight line cuts two parallel straight hues, the two
interior angles on each side are together equal to two right angles,
by saying that if the interior angles on the one side are greater
than two right angles, then because the lines on one side are* no
more parallel than those on the other, the two interior angles on the

»ther side must likewise be together greater than two right angles,
and the whole greater than four, which is impossible ; and in the
same way if they were supposed less. In which the palpable
weakness is, that there is no proof, evidence, or cause of probability
assigned, why parallelism should be connected with the angles on
one side being together equal to those on the other; the very ques-
tion in debate being, whether they may not be a little more than
two right angles on one side and a little less on the other, and still

he straight lines not meet.

3. Proclus himself proposes " to take an Axiom of this sort, being
Che same that Aristotle employed to establish that the world is
finite. If from the same point, two straight lines are drawn
making an angle, the distance between them when they are pro-
longed to infinity will exceed any finite distance that may be

ssigned. He then showed that if the straight lines prolonged
from this centre towards the circumference are of infinite length,
what is between them is also infinite; for if it was finite, to increase
the distance would be impossible, and consequently the straight
lines would not be infinite. The straight lines therefore on being
prolonged to infinity, will separate from each other by more th«n

ny finite quantity assigned. But if this be previously admitted,
I affirm that if any straight line cuts one of two parallel straight
lines, it will cut the other also. For let A b and c d be parallel,

nd let e f cut a b in o ; I say that it will cut c D also. For since

* ouiivyap nuWovai a{ 711 wapa\\f|Xoi fj al fd nfi. — ProcU Comment, i*
rimum Eucltdis Librum. Lib. 4.

Jt it but right to notice, that Proclus calls this napaXo^iofiin and £c(fe«r
rBivtia ; and Barocius the Venetian Translator in 15b0, notes it in the

largin as FlagUiosa Ptolenuri ratiocinatio.

Professor PlayJair says it is curious to observe in rrocius's account aa
argument founded on the principle known to the moderns by the name of

\t sufficient reason (Elem. of Geom. p. 405). If the allusion la to this part,
the " sufficient reason " of the moderns most be something very feeble.

LESSONS IN GEOMETRY.

29T

from the point o are drawn two straight lines o b, q f, and pro-
longed to an infinite length, the distance between them will become
greater than any assigned magnitude, and consequently than that
which may be the distance between the parallels ; when, therefore,
they are distant from each other by more than this, o f will cut
CD."* Without disputing that the distance between the straight
lines which make the angle will become greater than any assigned
magnitude — (though the reason given appears to be founded on
ignorance of the fact that a magnitude may perpetually increase
and still be always less than an assigned magnitude),— the defect
is in begging the question, that the distance between the paral-
lels is constant or at all events finite. For the very point in dispute
is, whether the parallels (as for instance two perpendiculars to a
common straight line, both of them prolonged both ways) may not
open out or grow more distant as they are prolonged, and to do
this so rapidly, that a straight line making some very small angle
with one of them, shall never overtake the other, but chase it
unsuccessfully through infinite space, after the manner of a line
and its asymptote.

4. Clavius announces that "a line every point in which is equally
distant from a straight line in the same plane, is a straight line ;"
upon taking which for granted, he finds himself able to infer the
properties of Parallel Lines. And he supports it on the ground
that because the acknowledged straight line is one which lies
evenly [ex aquo] between its extreme points, the other line must do
the same, or it would be impossible that it should be everywhere
equidistant from the first.f Which is only settling one unknown
by a reference to another unknown.

5 and 6. In a tract printed in 1604 by Dr. Thomas Oliver, of Bury,
entitled, De rectarum linearum parallelismo et concursu doctrma
Oeometrica (Mus. Brit. ), two demonstrations are proposed ; both
of them depending on taking for granted, that if a perpendicular
of fixed length moves along a straight line, its extremity
describes a straight line. Which is Clavius's axiom a little
altered.

7. Wolfius, Boscovich, Thomas Simpson in the first edition of
his " Elements," and Bonnycastle, alter the definitions of parallels,
and substitute in substance, "that straight lines are parallel which
preserve always the same distance from one another ;" by distance
being understood the length of the perpendicular drawn from a
point in one of the straight lines to the other. Attempts to get
rid of a difficulty by throwing it into the definition, are always to
be suspected of introducing a theorem in disguise ; and in the
present instances; it is only the introduction of the proposition of
Clavius. No proof is adduced that straight lines in any assignable
position, will always preserve the same distance from one another ;
or that if a perpendicular of fixed length travels along a straight
line keeping always at right angles to it, what mathematicians call
the locus of the distant extremity is necessarily a straight line at

8. D'Alembert proposed to define parallels as being straight
lines "one of which has two of its points equally distant from the
other line ;" but acknowledged the difficulty of proving, that all the
otherpoints would be equally distant in consequence J .

9. Thomas Simpson, in the second edition of his " Elements/'

Eroposed that the Axiom should be, that " If two points in a straight
ne are posited at unequal distances from another straight line in
the same plane, those two lines being indefinitely produced on the
•ide of the least distance will meet one another."

10. Robert Simpson proposes that the Axiom should be, " that a
straight line cannot first come nearer to another straight line, and
then go further from it, before it cuts it." Q By coming nearer or

• We omit the Greek.

t " Nam si omnia puncta linens a B,ssqualiter distant a recta n o, ex aqno
sua interjacebit puncto, hoc est, nullum in ea punctum intermedium ab ex-
tremis sursom, aut deorsum, vel hue, atque illuo deflectendo subsultabit,
nihilque In ea flexuoium reperietur, sed ssqaabiliter semper inter sua puncU
extendetur, quemadraoduni recia o o. Alioquin non omnia ejus puncta
ssqualem a recta d d, distantiain haberent, quod est contra hypotheeln.
Neque verd cogiutione apprchendl potest allam lineam prater rectam, posse
habere omnia sua puncta a recta llnea,qus9 in eodem cum ilia piano existat,
ssqaaliter distantia.*— Clavii Opera. In EuclidU Lib. I. p. 50.

% *' la vraie definition, cc me semble, et la plus nette qu'on puisse

donner d'uire paral!£lc, est de dire que c'est une ligne qui a deux de ses
points egalement eloigner d'une autre ligne.— il faut ensuite dlmontrer (et
c'est-la le plus difficile) , que tous les autres points de eette seconde, seront
egalement eloigners de la ligne droite donnee."— Kkclyclopedie. Art.
Parallile.

|| This and most ef what has preceded, is in the Arabic. In a manuscript
eopv of Euclid in Arabic but in a Persian hand, bought at Abmedabad in
181"?, the editor on the introduction of Euclid's Axiom commenta as
follows.

" And this is what is said in the text. I maintain that the last proposi-
tion's not of the universally-acknowledged truths, nor of anything that is de-
monstrated in any other part of the science of geometry. The best way there-
fore would be, that if it should be put among the questions Instead of the
principles ; and I shall demonstrate it In a suitable place. And I lay down
fur this purpose another proposition, which is, that straight lines in the same

going from it, being understood the diminution or increase of the
perpendicular from one to the other.

The objection to all these is, that no information has been given
on the subject of the things termed straight lines, which points to
any reason why the distance's growing smaller should be neces-
sarily followed by the meeting of the lines. It may be true; but
the reason why, is not upon the record. On the contrary, it is
well known that there exist lines (as for instance the neighbouring
sides of two conjugate hyperbolas) where the distance perpetually
decreases and yet the lines never meet. It is open therefore to
ask, what property of the lines called straight has been promul-
gated, which proves they mav not do the like.

11. Varignon, Bezout, and others propose to define parallels to
be " straight lines which are equally inclined to a third straight
line," or in other words, make the exterior angle equal to the
interior and opposite on the same side of the line. By which thev
either intend to take for granted the principal fact at issue, which
is whether no straight lines but those that make such angles can
fail to meet ; or if their project is to admit none to be parallel
lines of which it shall not be predicated that they make equal angles
as above with tome one straight line either expressed or under-
stood, then they intend to take for granted that because they make
equal angles with one straight line, they shall also do it with any
other that shall in any way be drawn across them, — a thing utterly
unestablished by any previous proof.

12. Professor Piayfair proposes to employ as an Axiom, that
" two straight lines, which cut one another, cannot be both parallel
to the same straight line ;" in which he had been preceded by
Ludlam and others, and which he says " is a proposition readily
enough admitted as self-evident." The misfortune of which is,
that instead of being self-evident, a man cannot see it if he tries.
What he sees is, that he does not see it. He sees that a straight
line's making certain angles with one of the parallels, causes it to
meet the other ; and he sees that by increasing the distance of the
point of meeting, he can cause the angle with the first parallel to
grow less and less. But if he feels a curiosity to know whether he
can go on thus reducing the angle till he makes it less than any
magnitude that shall have been assigned (or in other words*
whether there may not possibly be some angle so small that a
straight line drawn to any point however remote in the other parallel
shall fail to make so small a one), he discovers that this is the very
thing nature has denied to his sight; an odd thing, certainly, to
call self-evident.

13. The same objections appear to lie against Professor Leslie's
proposed demonstration in p. 44 of his "Rudiments of Plane
Geometry;" which consists in supposing a straight line of unlimited
length both ways, to turn about a point situate in one of the
parallels, which straight line, it is argued, will attain a certain
position in which it does not meet the other straight line either way,
while the slightest deviation from that precise direction would
occasion a meeting.

14. Professor Piayfair, in the Notes to his " Elements of Geo-
metry," p. 409, has proposed another demonstration, founded on a
remarkable non causa pro causa. It purports to collect the fact*
that (on the sides being prolonged consecutively) the intercepted
or exterior angles of a rectilinear triangle are together equal to four
right angles, from the circumstance that a straight line carried
round the perimeter of a triangle by being applied to all the sides
in succession, is brought into its old situation again ; the argu-
ment being, that because this line has made the sort of somerset it
would do by being turned through four right angles about a fixed
point, the exterior angles of the triangle have necessarily been
equal to four right angles. The answer to which is, that there is
no connexion between the things at all, and that the result will
just as much take place where the exterior angles are avowedly not
equal to four right angles, Take, for example, the plane triangle
formed by three small arcs of the same or equal circles, as in the
figure ; and it is manifest that an arc of ihis circle may be carried
round in the way described and return to its old situation, and yet
there be no pretence for inferring that the exterior angles were
equal to four right angles. And if it is urped that these are curved
lines and the statement made was of straight; then the answer is
by demanding to know, what property of straight lines has been
laid down or established, which determines that what is not true in
the case of other lines is true in theirs. It has been shown that, as

plane, if they ate subject to an increase of distance on one side, will not be
subject to a diminution of distance on that same side, and the contrary ; but
will cut one another. And in the demonstration of this I shall employ
another proposition, which Euclid ha* employed in the Tenth Book and
elsewhere, which is. that of any two Suite magnitudes of the same kind, the
smallest by being doubled over and over will become greater than the
greatest. And it will further require to be laid down, that one straight line
cannot be in the same straight hue with straight lines more than one that do
not coincide with one another ; and that the angle which is equal to a rif ht
angle, is a right angle." We omit the Aiabic.
• I. 32. Cor. ».

THE POPULAR EDUCATOR.

a general propotition, the connexion between a line returning; to
its place and the exterior angles haying been equal t j four right
angles, is a no-, a. -uHmr ; that it is a thing that m»y be or may not
be; that the notion that it rttarni to its place became the exterior

angles hare been equal to four right angles, it a mistake. ( From
which it is a legitimate conclusion, that if nature had contrived to
make the exterior angles of a rectilinear triangle greater or leas
than four right angles, this would not hare created the smallest
impediment to the line's returning tojte old situation after being
carried round the sides ; and consequently the line's returning
Is no proof of the angles not being greater or less than four right
angles.

15. Franceschini, Professor of Mathematics in the University
of Bologna, in an Esaay entitled La Teoria delle parallel* rigorosa-
monte aimostrata, printed in his Opuscoli Malcmatichi at Basssno
in 1787, offers * a proof which may be reduced to the statement,
that if two straight lines make with a third tae interior angles on
the same side one a right angle and the other an acute, perpen-
diculars drawn to the third line from points in the line which makes
the acute angle, will cut off successively greater and greater por-
tions of the line they fall on. From which it is inferred, that
because the portions so cut off go on increasing, they must increase
till they reach the other of the two first straight lines, which implies
that these two straight lines will meet. Being a conclusion founded
on neglect of the very early mathematical truth, that continually
increasing is no evidence of ever arriving at a magnitude assigned.
The remainder in ow next.

LESSONS IN ITALIAN GRAMMAR.— No. XIX.

By CHABLE8 TAU8ENAU, M.D.,

Of the University of Pavia, and Professor of the German and Italian
Languages at the Kensington Proprietary Grammar School.

In.

The preposition in denotes being, continuance, or motion
in the interior of a thing. It also denotes any kind
of motion or penetration into it. The idea of existence
til a time or in a certain condition, particularly in a certain
state or disposition of the mind, likewise requires the use of
in. The preposition a, on the contrary, merely expresses
presence near or about a thing or motion*,' approacn, and
tendency to it ; e. g. e'-gli e nel giar-di-no, in quel -la cd-me-ra, i
in eit-td, in pidz-za, he is in the garden, in that room, in the
towrij in the square ; e'-gli an-drd in In-ghil-ter-ra, in 1-spd-gna,
he will go to England, to Spain ; n€lC dn-no tnll-le set-te cen-to,
in the year 1700; sog-gior-nd al-qudn-to in Jin-ma, he staid a
while in Rome; Ge-su Cristo nd-cque in Be-te-Um-me, Jesus
Christ was born in Bethlehem ; e'-gli mo-ri nel mil-le ire cen-tc,

• See the Notes to Plajfair's Elements of Geometry, p. 406; where there
Is a figure.

he died in 1300 ; isn- m er ge -re it-no neW d-cqua, to plunge oae
in the water ; i-gli e-ra qui tit quest* i-etdn-te, he was here fin)
this moment; e'-gli e in a-ge-ni-a, he lies in the agonies of
death ; is-se-re in e&l-le-ra, in gi&-ja, in af-JK-zt'6-ne (i. e. nel-lo
std-to di col-h rj, di gio-ja, di af-Jtt-zio-ne), to be angry, cheer-
ful, sad (i. e. in a state of anger, joy, affliction) ; a-rerqudl-ehecA-
sa in boc-ca, in md-no, to have something in one's mouth, in
one's hand ; is-st-re, std-re in cam-pd-gna, to be, reside in the
country ; an-dd-re, en-ird-re in u-na chii-ea, to go into, enter a
church ; ca-*cd-re in u-nafus-sa^ to fall into a pit or hole ; mH-
te-rt 7 e ind-ni in tu-sca, to stick or thrust one's hands into one's
pocket; me-nn-re il ca-tdUlo in i-stdl-la, to lead a horse into
the stable; sa-U-re in cd-me-ra, to go up into the room; e i -v i -
va in un $4-colo di bir-bd-rie, he lived in an age of barbarity.

I hare already remarked that the proper names of towns and
similar localities are exceptions to the above-stated rule, for
they have the preposition a as well as tit placed before them,
whenever a stay or arrival tn them is expressed ; e. g. e'-gli
stet-teptr trt dn-ni in (or a) B6-ma, he lived for three years in
Rome ; la std-te pas-sd-ta i-o stit-ti dk-e me-ei a (or m) JFS-rejs-sv,
last summer I lived two months in Florence. There is, how-
ever, a shade of difference between the employment of a end
in in such cases, which will be at once understood by the fol-
lowing examples ; e in Lvn-dra, in the strictest sense of the
word, means a person being or en occ ur re n ce taking place
within the precincts properly called London ; while i a Z6n-dra,
in the more enlarged or general meaning of the word, means a
person not necessarily being in, or an occurrence not necessarily
taking place within, those precincts, but perhaps in the neigh-
bourhood of London ; e. g. at Kensington.

The motion to or towards a town or village, conformably to
the nature of the preposition, is always expressed by <u
Motion to or towards (and, naturally, being or staying tit)
parte of the world, countries, provinces, and tsiands, requires
the preposition in. The reason of this appears to be, that
in the Utter instance, the idea of a penetration into the
interior of these more extended localities prevails, though,
strictly and logically speaking, the idea of going to or into
a town amounts to the same thing ; e. g. sm-did-mo con Im a
Fie-iro-bkr-go, let us go with him to 8t. Petersburgh ; e'-gli
par-t} da Mo-na-co per re-cdr-si a Vi-rn-na, he departed from
Munich to go to Vienna ; e'-gli si por-td a Cel-s4-a, he repaired
to Chelsea ; e'-gli i an-dd-to a Pa-rt-gi e poi an-drd a Oel-te-nam,
he is gone to Paris, and after that he will go to Cheltenham ;
qwn-do nn-drt'-te in Frdn-ciat when will you go to France?
fa-re- mo un vidg-gio in Mo-sco-tia, a Afo-sco-ria^ we shall go on
a journey to Russia, to Moscow ; i-o vd-do in I-ecd-eia, in 1-oet-
tiii f I go to Scotland, to Sweden ; il Ba-scid fu e-si-li-d-to netf
i-to-la di C(-pri, the pasha was exiled to (the island of) Cyprus;
e-gli * in Frdn-cia, nel-la Chi-na, he is in France, in China ;
nd-cque nclf i-so-la di IA-sbo, he was born in the island d
Lesbos.

Usage allows the omission of the article after in before many
nouns familiarly known and constantly recurring in conversa-
tion ; e* g, t-gli va ne'l-la cd-me-ra, nel-la cit-td, nil-la ehU-em,
nil -la con-ti-na, &c. ; or, e-gli va in cd-me-ra, in cit-td, in chie-sa,
in tan-ti-na, &c, he goes to the room, to town, to church, to
the cellar, &c.

Before the words day, week, month, year, morning, earni ng ,
when time is the^ subject, it is customary to omit the
preposition in; e. g. V dn-no che mo-ri il Ga-U-U-o, nd-cque U
Jfetcian* in the year in which Galileo died, Newton was born ;
i7 Kte'-n vm-tu-ro, (in the) next month ; la sei-H-md-na eoar-sa,
(in the) last week ; la not-te che vil-ne, (in the) next night, sVe. ;
instead of: nelf dn-no, nelmi-ee, &c.

The words cd-sa, c6r-te, pa-lde-so, ted-tro, Ui-tOj and sem i fa,
hare a proper or original and a figurative signification. In the
former case, they demand the preposition tit ; in the latter, the
preposition a (without an article) before them ; e. g.

E , *gli 2 nel-la cor.te, nel pa-
ids-si, in ted-tro, in let-to, in
i-acu6~?a t in cd-sa.

E'-gli i a cor-te 9 a pa-ldz-zo,
a ttd-tro, a Ut-to, a ecu6-la t a
cd-sa t

He is in the court-yard, in
the palace, in the play-house,
in the bed, in the school, u «.
(building), in the house.

He is at court, at Guildhall,
at the play, sink in bed at
school, at home.

LK8S0NS IN ITALIAN.

299

r-o mUoh m%4a c6r-U, ml
pa-lda-ao, ml teH-tro, nslUUo,
nil-la seuA-la, nil-la cd-sa.

T-o vd-do a c6r-ts, a pa-lds-
zo, a tcd-tro, a let-to, a scut-la, a
cd-sa.

I go into the court-yar .'..
Uo the

into the palace, into the play-
house, into the bed, into the
school, i. e. (building), in
the house.

I go to court, to Gulldha I .
to the play, to bed, i.[e. (
sleep), to school, home.

In addition to these uses, in has some indefinite meaning
which will admit of several prepositions or adverbial expre
sions for the purpose of translating them into English ; e. g. n
no-mi-nd-re, di-re qudl-che c6-sa in la-ti-no, to name, say some-
thing in Latin ; spe*rd-r$ in Di-o, to hope in God ; in ma-m
ra td-le, in such a manner ; — on or upon : por-td-re qudl-c*
eS-sa in d&i-so, in tS-sta, in edr-po, to carry something on one's
back or shoulders, or about one's self, on the head, on tl
body; por-td-re scdr-pe in piS-di, to wear shoes on one's feel
lapd-squa e sem-pre in u-na Do-mi-ni-ca, Easter is always on 4
Sunday ; 4-gli mi-se un' a-nkUlo in di-to, he put or placed a rin
on his finger ; ab-bdt-ter*si in it-no, to light on one, meet him
by chance; di-stin-de-re qudl-che c6-sa incdr.ta, to pen or not
something on paper ; — round: gli git-id U brdo-cioin cU-lo (far
in-Ur-m il cM-lo), he clasped him with the arm round his neck J
mioso-li u-na ca-te-na ing6-la (for in-tor-no la g&-la), after havin
put a chain round his neck ; — to : le cac-ctd di eU-le in c&t-l '
he chased them from hill to hill; di ttm-po in tkm-po, froi
time to time; con-ftc-ed-re in u-na cr6-ce, to fasten or nail
something to a cross; — towards: in mo mo-pen-do do* U-gi
6c-chj i rd-i, turning towards me the rays of her beautiful eyes ;
— of against : vt-de in so ri-v6l-to Up6-po-lo, he saw the peopl
rebelling against him ; — at : guar-dd-re in it-no, to look at
cne ; in place of: a-dot-td-re u-no in Jl-gliu6-lo, to take one in
place of a son, to adopt one ; — as : dd-re qudl-che c6-sa in do
no ad 6-fio, to give one something as a present ; di-re qwU-cK
c6-§n in su-a seu-ea, to plead something as one's apology or
noose ; o Di-o, non m' un-pm-tdr-to inpec-cd-to, O Lord, do not
impute it to me as a sin ; e-Us-se-ro m Pd-pa il Car*
di-ndl Ma-std-i-Ftr-rit-ti nei mil-Is 6t-to-c4nto qua-rdn-ta-sl-i
They elected Cardinal Mastai-Ferretti as pope in 1846;—
adverbial expressions : in av-ve-ni-re, in future, for the future,
henceforth ; in fdt-ti, indeed, in fact, in reality ; in frit- ta, in
a hurry, hastily ; in 6-gni e6n-to, at any rate, at all events j
m fdc-cia, to one's face.

Exancisas.— Itauan-Emolisk.

El-la e nel-la stan-za vi-ci-na. S6-no qua-si in pdr-to.
E'-gli e in A'u-stria, in I-ta-lia, in cam-pa-gna, in vil-leg-gia-
tu-ra. E'-gli va nel giar-di-no; in quel-la ca-me-ra; in]
Fran-cia; in cam-pa-gna; in I-scd-zia; in Tur-chl-a. Mo-
rl-ro-no a-men-du-e in un gi6r-no e in un' 6-ra. Tu 6-ri in
chit-sa. C e nis-su-no in ca-sa? E'-gli d nel cor-ti-le, nel-la
cu-ci*na, nel*la oan-ti-na. E' an-da-to in ohi6-sa, in cit-ta, in
piaa-ze, in o-ste-rl-a, in tea-tro. A-bi»ta-va in quel-la ca-sa.
Lo tro-va-i in ldt-to. An-t6-nio & in c61-le-ra eon me. Se ne
par-la in tut-ta la cit-ta. E par-ti-to in fire*t-ta. Vi e an-da-
to in car-r6a-aa. Do-ma-ni po-tre'-mo an-dar in i-slit-ta. E's-
si*so-no sor-ti-ti in qu6-sto pun-to. A-dee-so sie-te nel-le
mi-e ma-ni Lo pre-ven-ni in pun-ta di pid-di e qui 1' a-spdt-
to. I'-o mi ri-p6*so nel-la ca-pa-ci-th di mi-o fra-tdl-lo. Al-
quan-te cd-pie se ne stam-pe-ran-no in oar-ta ve-li-na. Voi
sid-te nel nor de'-gli an-ni. A-ve'-te a-vu-to Mi tem-po nel
v6-stro viag-gio. In i-sorit-to ; in i-sta-to. In pri-mo lud-go ;
in fon-do. In pa-ra-go-ne di noi e^-gli e an-co-ra fe-Ii-ce. In
mex-xo del (or at) pae-se. In me'-no d' un' 6-ra. In se-gui-
to (do-po fit-to ; pdi). In ca-so di bi-s6-gno : in 6-gni ca-so.
In prin-ci-pio. In av-ve-ni-re. Nell' 6-ra stes-sa. In f5r-ra
(or in tir-ti) d' un trat-tsVto. Nel t6m-po stes-so. In nis-su-
na ma-nU-ra, Nel cu6r d61-la Rus-sia. Nel cu6r dell' in-
Ter-no. Nel cuor del-la stu-te. In ve-ri-ta; in fkt-ti (or di
fdt-ti). Te lo di-ce in fac-cia. In su-a v6-ce, in su-o lud-go.
In qu^-ato -md-4o r in tal mo-do. Tutt' in un trat-to, ad un
trat-to. Ih tA-11 cir-con-st&n-2e. In vi-sta di cid. In 6r-di-
ne a ci6, che vi h6 det-to. In fa-v6-re dell' ac-eu-s4-to. In-
ci-s6-re in ra-me. Pe-iS-to in ax-te. Ca-st^l-li in a-ria. Dot-
t6-re in am-be le lCg-gi. In tdm-po di guer-ra. Nel t&m-po
dell' ul-ti-ma gudr-ra. Vi sta-va c61Je brac-cia in cro-ce.
T6r-to in ar-«o. In o*no-re d414a y/ixAA. C6-me si di-ee
qu6-sto in in-gl6-se ? in i-ta-lia-no ? Vuo-t6 il bic-chid-re in

tre v61-te. H su-o a-ve-re eon*ai-ste par-te in da-na-ro, e par-
te in b£-ni sta-bi-li. E* ve-nti-to in per-s6-na. Do-vi-va
ata-re in pie-dL E'-gli si mi-se in gi-no-chi6-ni. Ee-se-re in
bu6-na sa-ld-te. An-da-re in bar-ca. In n6-me di Di-o.

VooABtnAKY.

Stanza, f., room, chamber.
Vkino t m., vieina, f., neigh-
bouring, contiguous, adjoin-
ing.
Sono t I am.
Quasi, almost, nearly, well

nigh.
Borto, port, harbour.
Vampagna, country.
Villegiatura, summer season,
for pleasure or recreation
spent in the country; country
amusement, rural diversion
or sport (essere in viflegia-
tura, to spend the summer
season in the country, to
enjoy the pleasures of (he
country).
Egli va, he goes.
Camera, chamber, room.
Scotia, Scotland.
Turchia, Turkey.
Mfbrirono amenaue, both died.
Ora, hour.
Tu eri, thou wast.
■T i nissuno, is nobody.
Tortile, court-yard.
Tucina, kitchen.
Cantina, cellar.
T andato, he is gone.
fHazza, market-place, square.
Qsteria, public-house, tavern,

inn.
Teatro, play-house, theatre.
Ibitava, he lived.
lo trovai, I found him.
Letto, bed.
Antonio, Anthony,
Collera, anger.
Me, me.

Be nepatla, they talk of it.
/ *partito, he has departed.
retta, haste, hurry, precipi-
tation.
/ 'i i andato, he is gone there.
Carroxta, coach, carriage.
9tremo andar, we shall be
able to go.
Slitta, sledge.
Uisono sortiti, they have gone
out

mUo, point, point of time,
moment.

desso, now.

lets, you are.

ano, t, hand.
lo prevenni, I came before

him.
Funta, point (of anything).
Piede, foot, leg (punta del piode t

end or point of the foot, t. e.

toe).
E qui T aspetto, and here I

wait till he comes.
lo mi riposo, I repose myself,

sit down ; I rely.
i ipacitd, ability, talent, skill.
A Iquanto, m . , alqnanta, f . , some,

several.

nrid, t, abundance, plenty;

occasion; copy.

Se m stamperanno, will be

printed.
Carta, t, paper (carta velina,

vellum-paper).
Voi siete, you are.
Fiorc, flower, bloom, prime.
Anno, year (UJior digli anm or
dtU etd, the bloom of youth,
flower of life, prime of one's
age).
Aveie ewuto, you have had*
Tempo, time, weather.
Viaggio, journey.
Seritto, writing (misoritU, in
writing, written, under one's
own hand).
Stato, state, condition (in Un-
to, having it in one's power,
able).
Prhno, first.

Luogo, space, spot, place (m
primo luogo, for the first, in
the first place, firstly).
Fondo, bottom, ground (in fen-
do, at the bottom, in the
main, after ali).
Paragone, eompa*>en, paral-
lel (inparagone di, in com*
parison with, when com-
pared to).
Noi, we, us.

Anoora, again, still, even, yet.
Felice, happy.

Mezzo, middle, midst (in metso,
in the middle or midst of).
Paese, land, region, country.
Meno, less. •

Di, than.

Seguito, suite, train, attend-
ance, retinue ; sequel, conse-
quence, issue, result, effect.
Dope, after.

Fatto, deed, fact, action.
Poi, afterwards, after that (in
seguito*, dope fatto: poi)
thereupon, afterwards, after
that, thereafter, hereafter,
in time to come).
Oaso, case.

Bisogno, need, want, the neces-
sary (in easo di bisogno or
al bttogno, in case of need or
necessity, at the worst).
Principio, beginning.
Awenire, future.
Stcsso, m., stessa, I, myself
thyself, &c. ; the same, self-
same.
Forxa, force, power, strength.
Virtu, virtue (in forxa di, in
virtu di, by or in virtue of,
by, in conformity with, ac-
cording to, in consequence

° £ >-
Trattato, treaty.

Nissuno, m., nissuno, f., not
any, none.

Mantera, manner (in nissuna
maniora or in neesun mode, in
no manner, by no means,
upon no account, not at all)*

302

THE POPULAR EDUCATOR.

left to right, and from right to left, by meant of a winch or
icver m x ; to that when one of the pistons is raised the other
j lowered, and rice ttria.

The t»o barrels are cemented at the bottom to a brass sup-
port, which is furnished with a plate d, fig. 94 ; upon this plate
stand* a ttror.g bell-shaped glass, with a ground edge, the
former being sometimes called the plate*, and the latter the
receiver. It is in the receiver that the vacuum is to be made,
or that the air is to be rarefied ; in the centre c of the platen,
there is an opening which forms a communication between the
interior of the receiver and the barrels of the pump, by means
of a tube represented in plan, in fig. 95, and dividing itself
into two branches, K the, and Kcdo. In fig. 96, there is a
representation of a vertical and anterior section of the barrels.
It show* how the pinion h, worked by the lerer m i», conveys
the motion to the two racks, and consequently to the pistons
p and a. These pistons are not solid ; in their interior is a
cylindrical cavity closed at bottom by a small valve which has
a weak spring. The cavity in which the valves are placed
communicates with the upper part of the barrel by an aperture
above the valve which is always op« n to the atmosphere for the
egress of the air. Betides the valves placed in the interior of
the pistons, two o'her valves o and * are placed at the bottom
of the barrels. These valves are conical, and are each fixed to
an iron rod, which easily slides up and down through the
pistons. These barrels open and shut alternately the com-
munication between the barrels and the receiver. If the piston
p, for example, descends, it draws with it the iron rod and
shuts the valve * ; if it rises, the rod and the valve are raised,
but only a small height, because that this rod is of such a

air which is below is gradually compressed until its elastic
force exceeding the pressure of the atmosphere, raises the valve
in the interior of the piston. The compressed air then passes
above the piston, and, by the aperture in the top of the piston,
escapes into the atmosphere. \f hen the piston reaches the
bottom of its course, all the air which had been withdrawn
from the receiver is expelled. At the second stroke of the
piston, the same series of operations takes place in succession
in both barrels, until a limit has been reached, when the air
which comes from the receiver is so rarefied that it can no
longer raise the interior valve of the piston, even when the
pt*ton is at the bottom of the barrel.

The Siphon- Gauge.— When the operation of pumping the air
has been continued for a certain time, the elastic force of the
air which remains in the receiver is measured by the difference
of level which the mercury shows in the two branches of a
tube bent in the form of an inverted siphon, the one branch
being open and the other shut, as in the siphon-barometer.
This appendage to the air-pump, when properly filled with
mercury, is fixed on a vertical scale and placed under B, flir.
91, a small glass receiver of its own, which communicates with,
the platen receiver e by means of the tube which connects tne
aperture c in the platen with the barrels of the pump. Now,
before any air has been withdrawn from the receiver, its elastic
force balances the column of mercury in the sipoon -gauge, and
it is then full ; but in proportion as the air is rarefied by the
action of the pistons, the elastic force diminishes, and then it
can no longer balance the column of mercury. This column,
sinks, and the mercury approaches the same level in both
branches. If an absolute vacuum were obtained, the mexcuqf

f^. te.

Fir. 97.

length that it soon strikes the top of the barrel, and then it
only slides in the piston which afterwards rises by
itself.

In order to understand the working of the machine, it will
be sufficient to consider what takes place in one of the barrels,
since they are both alike. When the piston Q, for instance, is
first at the bottom of the cylinder, it is raised by the action
of the winch, and it then draws with it the rod and the valve
o. As to the valve which is in the interior of the piston, it
remains closed while the latter is raised in consequence of its
own weight end that of the atmosphere ; for the tops of the
barrels are pierced with small apertures tn and ft, by which (he
exterior pressure is conveyed. According to this arrangement
of the valves, there is a tendency to the production of a vacuum
below the piston as it moves upwards ; but the air in the re-
ceiver, yielding to the law of its elasticity, passes partly into
the barrel through the orifice o. If, for example, the volume of
the barrel is ^ of that of the receiver, then *V of the quantity
of air in the latter passes into the barrel. When the piston
moves downwards, the rod of the valve o is drawn down, this
valve shuts, and the air in the barrel does not return into the
xeceiver. The piston continuing its motion downwards, the

would reach exactly the same level ; for there would be no
pressure on it in either branch of the gauge. But with the
best constructed machines, the level in the shut branch is
always higher than that in the open branch, by about A put
of an inch, which shows that the vacuum is not perfect, and
that there still remains a quantity of air, whose tension
balances a column of mercury of about one-twenty-fifth part
of an inch in height.

It is evident that practically the air-pump cannot produce
an absolute Yacuum, because, as has been already observed,
there is a limit where the air which remains in the receiver
becomes so rarefied, that even when the pistons are at the
bottom of the barrels, its elastic force cannot overcome the
atmospheric pressure on the valves in the interior of the "pis-
tons, and consequently they can no longer be opened for the
expulsion of the air from the receiver. Even theoretically, an
absolute vacuum is impossible, because if, for example, the
volume of each barrel is jfo of that ot the receiver, there it
withdrawn, at every stroke of the piston, only; J$ of the'
quantity of air which remains in the receiver ; consequently,
the air which it contains can never completely be withdrawn.'
It can be shown, indeed, by an easy calculation, that it would

£E§8QNS JN PHYSICS.

308

require an infinite number of strokes of the piston to make
a perfect vacuum in the receiver.

Im p n md Stop-Cock. — M. Bobinet has applied to the air-
pump a stop-cock which admits of the rarefaction of the air
being carried to a very great eater t, This stop-oock is placed
at the point where the connecting tube between the receiver
and the two barrels separates into two branches, and it is per-
forated by several passages, which are successively used in
working, by turning it in two different directions. Fig. 9a
represents a horizontal section of this stop-cock a, in such a
position, that by its central aperture, and its two lateral aper-
tures, it establishes a communication between the orifice x in
the platen, and the valves o and s. The machine then works
as already described. In fig. 98, the stop-cock has been moved
round by a quarter of a turn, and the transverse passage d b t
which was horizontal in fig. 96, is now vertical, ana its orifices
are shut by the sides of the tube. But a second passage, which
waa not u>ed at first, and which has taken the place of the
former, now puts the barrel on the right alone in communica-
tion with the receiver by the passage eb «, fi*. 93 ; and it also
puts the barrel on the right in communication with that on
the left by a passage a to fig. 98, or aieo fig 97. This passage
proceeds from a central aperture a placed at the bottom of the
barrel on the right, and terminates at the valve o of the other
barrel, passing through the stop-cock, as represented in figs.
89 and 90; but the same passage is shut by the stop-cock, when
the latter is in its former position, as shown in figs. 95 and 96.

This arrangement being understood, when the piston on the
right is raised, the air is
withdrawn from the re-
ceiver; but when it is
lowered, the air which is
withdrawn is now forced
into the barrel on the left,
through the orifice a, the
passage e t, and the valve
o. fig. 97. which is then
open. When after this,
the piston on the right is
raised, that on the left is
lowered, but the air which
is below does not return
into the barrel on the
right, because the valve
o is now shut. The piston
on the right continuing
thus to draw air from
the receiver and to throw
it into the barrel on the
left, the air is accumulated
in the latter, and reaches
a tension sufficient to raise
the valve of the piston q,
a thing which was impos-

Fig. 100.

sible before the application of the stop-cock with the double
passage. Now, each time that we can thus open the valve Q,
some air is expelleO.

Use of the Air-pump, — A considerable number of experiments
with the air-pump have been already explained in former
lessons ; such as the shower of mercury, the fall of bodies in a
vacuum, the expansion of a flaccid bladder in a vacuum, the
bladder-glass, the Magdeburg hemispheres, and the baroscope.
The air-pump serves also to prove that the air, in consequence
of the oxygen which it contains, is necessary to the support ot
combustion and of animal life. For example, if we place
under the receiver, any lighted body, such as a candle, we see
the flame diminishing as the exhaustion advances, and very
soon becoming extinguished. In like manner, an animal

S laced under the receiver, first becomes motionless, and then
ies, as the air within it becomes more and more rarefied.
Mammifers and birds die at once in a vacuum. Fishes and
reptiles can bear the want of air for a considerable time ; and
I insects have been allowed to remain in a vacuum several days
without losing their vitality.

Substances liable to fermentation have been kept for a very
I long time in a vacuum, without the slightest alteration in 1 heu
[state, because they were not exposed to contact with oxygen,
[which is necessary to this process. Alimentary substsices
have been preserved for a long time in bottles hermetically
'sealed, in which a vacuum has been previously made ; and
; they have been found as fresh at the end of several years aft
they were the first day they were sealed.

The fountain in a vacuum, represented in fig. 99, is also an
experiment which is performed with the air-pump, and which
is employed to prove the expansive force of air. This is simply
I a bottle containing water and air. The mouth of the bottle is
[shut by a cork, and a tube immersed in the liquid, passes
through it. The whole being now put under a receiver, aa
soon as the air in the receiver becomes sufficiently rarefied,
the water issues from the upper extremity of the tube like a
fountain — an effect which is produced by the pressure or elastio
force of the air contained within the bottle.

Another experiment is represented in fig. 100, which show*
the pressure of the atmosphere on the human hand. This
consists of a glass cylinder bottle-shaped at one extremity, and
open at both ends. The larger end, ground and well greased,
being put on the platen, and the palm of the hand placed on
the upper end, a vacuum is made in the cylinder, 'lhe atmo-
spheric pressure being no longer balanced in reference to the
upper and lower surfaces of the hand, the upper surface
is powerfully pressed on the top of the cylinder, and;
it can scarcely be withdrawn from its position except,
by a very strong effort. Besides the elasticity of the fluids
in the organ being ho longer counterbalanced by the
weight of the atmosphere, the palm of the hand becomes
swelled, and the blood has a tendency to issue from the pores
of the skin.

Fig. 101.

Fig. 103.

364

THE POPULAR EDUCATOR.

j'wmpJuwic Railway, — An important - application of the
vac ■ um principle wa* made some years ago in the construc-
tion of atmospheric railways. Vallance, an Englishman,
ap*- ars to have been the original inventor, in 1824 ; but it was
on! - in 1831, that the first atmospheric railway was construc-
ted in Ireland, by the engineers Messrs. Clegg and Samuda.
The principal details of this principle of railways is represented
in t.^. 101. A cast iron pipe m sr, is placed between the rails,
the -rhole length of the road. In the interior, there is a piston
a, w-th a rod of about ten feet long terminated by a counter-
weight b. The first carriage is connected with the piston-rod
by an iron plate c. To allow of the play of this plate as the
piston advances, a longitudinal slit is made along the whole
length of the pipe ; this is covered by a continuous band of
leather, so that when the train is in motion, it is gradually
raised as it proceeds. In fig. 102, a transverse section of the
pipe, and of the parts now mentioned, is represented ; where x
u the piston rod ; c the plate which connects it with the train ;
b the covering valve, at the instant when it is opened to admit
of the passage of the plate c. The prime mover of the train is
the atmospheric pressure. For this purpose, the extremity x
of the pipe remains open, while the other extremity m is shut,
and is put in communication with a powerful exhausting
machine, or air-pump, driven by a steam engine. In the front
of the piston, therefore, the air is rarefied, and the pressure is
thus reduced to one- third or one-fourth of that of the atmo-
sphere, whilst in the rear of the piston, the whole of the atmo-
spheric pressure is permitted to act. The piston, therefore,
advances in the direction of x m, drawing after it the whole
of the train. It is necessary that the valve which closes the
longitudinal aperture or slit in the pipe should only be raised
to admit of the passage of the plate o, when the piston is pass-
ing ; if this precaution were not taken, the air would find its
way into that part of the pipe which is in advance of the
piston. This object is attained by means of a disc fixed on the
piston-rod and projecting into the longitudinal slit of the pipe,
so as to raise the valve s. x is a piece or part of the first
carriage in the train, which shuts this valve as the train pro-
ceeds on its journey. In the figure, the parts of the piston are
exhibited on a scale twice the size of that of the carriages.

LESSONS IN CHEMISTRY.— No. XX.

Befork resuming our active consideration of the metal silver,
I feel it desirable to draw the reader's attention to a fact, which
I trust, however, he will have already recognised and given it
due consideration. He can scarcely fail to have seen that the
preceding lesson, although totally devoid of showy experi-
ments, contained several aggregative groups of facts of the
highest importance. The learner should master them one by
one, and every one. It is aot for me to tell him how this
mastery is to be effected. Different people have different
methods. Some persons depend on frequent reading ; some
on frequent writing ; some rely on frequent experiments.
Any plan that accomplishes the end is good ; but I would
recommend the following as an accessory at least. Write
each little aggregation of facts in large characters on a large
piece of paper, and stick or pin those pieces of paper in your
ted- room, or some other part of the house where you must see
them every day. It is astonishing how, in this way, deduc-
tions become impressed on the mind, absorbed, as it were,
unconsciously by the recipient. Nor is the result to be
marvelled at, when we reflect on the mind's susceptibility to
external images and impressions. Who is there amongst us
who can recall a house, which we have often seen, except
with all the accessories of trees and flowers, and other local
objects in relation to it at the period of our last view ? Who
is there, who, after having seen a certain room, with its acces-
sories of furniture, does not feel the mental impression to be
violated by any alteration? Thus it is. The mind un-
consciously takes a sort of daguerreotype image of things
around us : houses, furniture, faces, and chemical deductions
printed or written on a sheet of paper. Once for all, the facts
must be learned. The plan which we have followed in the
preceding lesson furnishes an epitome of the chief tests for

silver in solution. The learner most not imagine them, how-
ever, to be the only tests. There exist others, of which the
following are important : —

Solution of iodide of potassium — known in certain country
shops under the name of nydriodat* of potatk — throw* down
from salts of silver a palish-yellow precipitate. Metallic cop-
per, immersed in a solution of silver — or, at any rate, in a
solution of nitrate of silver, throws down the metal in a finely-
divided metallic form.

There are other tests ; but we may simply pas* them over ;
the best have already been indi c at e d more would be "— ^if«
at present.

Method of obtaining Silver in m Metallic Form /rem « SOmr
Solution, — Not every metal, as I have already stated in the pre-
ceding lesson, readily admits of being recovered from its
solution in a metallic state. Silver is embarrassed with fewer
difficulties than any other in this respect, many efficient
processes existing by which it may be obtained in a pore
metallic condition.

Reduction by Copper. — First of all, we have seen that
it admits of being thrown down from a solution in nitric
acid by immersion of a piece of copper. The metal may
be precipitated in such a condition of fine powder, that
the metallic character is scarcely r ec o v e rable. However, if a
little quicksilver be thrown into the vessel in which the
powder is deposited, and agitated, the quicksilver and the
silver will combine, forming a sort of metallic paste, to which
the term silver amalgam is applied, amalgam being the gene-
ral expression indicating the composition of any metal with
quicksilver. If this amalgam be strongly heated in a crucible,
or even the bowl of a tobacco-pipe, all the quicksilver will
escape in vapour, and all the silver will remain as a sort of
button. The reader will easily see, that instead of simply
evaporating away the quicksilver, and allowing it to go to waste,
as in our experiment, the process of distillation might have
been had recourse to ; in which case the quicksilver would
have been recovered. Supposing this to have been ac-
complished, we should have exactly copied the procedure of
the gold and silver metallurgist, who extracts gold almost
universally, and silver from certain ores by the process of
amalgamation, as it is called : that is to say, he first brings
the gold or silver particles in contact with mercury or quick-
silver under favourable conditions ; accomplishes their union,
and finally, distilling away the quicksilver, leaves the noble
metal pure.

Of all the machines devised for the purpose of conducting
amalgamation on the large scale, Berdan's, of which a diagram,
fig. 6, is appended, is the best. It consists of cast-iron basins
(their number variable), in each of which rotate two cast-iron
bolts — the rotation being effected by motion imparted to the!
basins. Into each basin is placed a portion of the ore to be
crushed and amalgamated along with water and quicksilver.
The machine being now set in motion, the ore is speedily re-
duced to powder ; and, coming into contact with the quicksilver,
amalgamation is effected. But the chief peculiarity of the
machine consists in this. Under each basin is a fire, which,
heating the contents, the mercury comes in contact with the
metal, hot and expanded — conditions under which its combin-
ing agency is greatly exalted.

Although metallic silver may be readily obtained from a
solution of its nitrate by precipitation with copper, neverthe-
less this plan is not frequently had recourse to in practice. Far
more usual is it to throw it down as a chloride, by the addition
of hydrochloric acid, or solution of common salt, and subse-
quently extract from this chloride its contained silver.

Two processes may be adopted for accomplishing this : the
first is reduction by fusion with a carbonated alkali; the
second is reduction by contact with metallic tine.

Before trying this process, let us examine, a little more at-
tentively than we have done, the substance chloride of ailver. To
this end, let the student prepare some, by the addition of a solu-
tion of common salt to a solution of nitrate of silver. The opera-
tion will be most conveniently performed in a Florence flask;
and the solution of common salt should be added, little by
little, until no further precipitate results. The precipitate being
white, assimilates, so far as relates to colour, with thousands,
nay, tens of thousands of other substances ; but certain physical
appearances presented by it are so peculiar, that it might be

LESSONS IN CHEMISTRY.

305

almost individualised without invoking the aid of any
test.

As the student adds the solution of common salt, he will
remark the peculiar flaky dense white precipitate. This flaki-
ness is characteristic of chloride of silver — rodide and bromide
of silver are also flaky — but their colour is not quite the same,
and their flakiness is not so great. Next, let the student
remark, that on adding one solution to the other in certain

precipitates of those which usually come before chemists—
that have the property of effervescing when acids are poured
upon them — are sulphite of silver (produced by adding sul-

Shurous acia or a sulphite), and carbonate of silver (pro-
uced by adding carbonic acid or a carbonate). In either
case, effervescence is the result of the escape of gas ; car-
bonic acid in the one instance, sulphurous acid in the
other; the latter, melting like a burning brimstone match,

Fig. 5.

Berdaris Crushing and Amalgamating Machine.

proportions, the result is rendered turbid, from the refusa as
it were, of the genera^d chloride to deposit itself.

Fig. «.

Let the student now take the flask in which the mixture has
been effected, and agitate it circularly, fig. 6. Thus treated, he
will find the diffused particles of the precipitate soon aggregate
into one curdy mass, and, depositing, will leave the superna-
tant liquid clear. Thus we not only have a good characteristic
of chloride of silver, but we have a means of practically
separating it in the course of analysis ; but the test of ultimate
appeal for chloride of silver is hartshorn — liquor ammonia —
in which it readily dissolves, although totally insoluble in
nitric acid.

Other White Precipitates occurring in Silver Solutions, and how
they may be distinguished from the Chloride. — Solutions of oxalic,
tartaric, sulphuric, sulphurous, carbonic, and many other
acids, as well as their combinations, yield white precipitates
when projected into silver solutions ; but these may be readily
determined not to be the chloride, by means of nitric acid and
ammonia. The reader may try experiments with some or all
of these tests, if he pleases ; but their fuller description more
properly belongs to another part of our subject. Meantime,
It may be as well to point out that the only two white silver

is easily recognised ; and therefore, by negative evidence ih*
former.

Having procured some chloride of silver, let the student ex-
pose a portion of it to sun-light ; and, remarking the blackening
which ensues, let him associate this appearance with the sub-
stance chloride of silver — and, indeed, with silver salts — all of
which, if exposed to the direct agency of light, in contact with
organic matter, assume a dark tint.

Resuming now the process of extracting silver from its
chloride, proceed thus. Collect a portion of chloride ; squeeze
it between blotting-paper until nearly dry ; mix it with twice
its weight of carbonate of soda (wasning soda), and fuse it in a
crucible or tobacco-pipe bowl. Chloride of sodium and metal-
lic silver will result, as rendered evident by the appended
diagram :—

Carbonate of Soda
Chloride of Silver

Carbonic Acid

- escape;

Sodaf° x /* en — "
I Sodium \^

Chlorine Chloride of)

Sodium /"remain.

Silver J

The chloride of sodium, being soluble, may be removed by
washing, then leaving the silver pure.

Process of Reduction by Zinc. —A far more generally applicable
and elegant method of obtaining metallic silver from its
chloride consists in agitating it with a sheet of metallic zinc
immersed in water, slightly acidulated with hydrochloric acid.
Treated thus, chloride of silver is rapidly decomposed, with the
formation of chloride of zinc and the liberation of metallic silver.
If the materials, t. e. zinc, acid, and water, be all quite pure,
then the resulting precipitated silver will be chemically pure
also, and may be freed from any adherent chloride of zinc by
copious ablution. This plan of obtaining silver from chloride
of silver is of frequent occurrence in the laboratory, where the
valuable precipitate continually accumulates as the result ot
testing ; and, in this way, the student may obtain all the silver
contained in what remains of the nitrate of silver which he has
dissolved for the purpose of experiment.

•06

THE POPULAR EDUCATOR.

LESSONS IN ITALIAN GRAMMAR.— No. XX.

BY CHARLES TAU8ENAU, M.D.,

Of the University of- Pavia, and Professor of the Italian and Garaian
Language* at the Kensington Proprietary Grammar School.

Om.

When the preposition with denotes company, society, union,
community, connexion, or when it denotes the instrument or
means by which something is effected, it coincides with the
use of con in Italian. In the former case, the words together
with, beside*, to, or similar ones, and in the latter, the words by
means of, by agency of, by dint of, by, through, are frequently
equivalents of with, and are translated by eon ; e. g. an-dd-r*
col fra-til-lo, to go with the brother ; si at-so-cid eon un mer-
cdn-te, he entered into partnership with a merchant ; k-se-re,
ttd-re con u-no, to be with one, to belong to one, t. e. to one's
family, company, &c. ; con chi std-te rot / with whom are you ?
(«'. e. in whose service are you ? or with whom are you on a
visit ? or with whom do you stay and take dinner ? Ac.) ; *&•*
go con vox, I come with you ; eom-bdt-te-re col ne-mi-co, to fight
with the enemy; congiU-gne-rcuntog-gH to col sb.o pre-di-ed-to,
to join a subject to ita predicate ; con-cer-td-re u-na cd-sa cm
u-no, to concert a thing with one ; pa-ra-go-nd-rw Una cd-sa con
un* dl-tra, to compare one thing with another; eon que'-ste md-
ni, with these hands; con gran fa~tl-ca, with great pains; eon
frd-de ed in-gdn-no, with fraud and deceit ; con un col-Ul-lo, with
" a knife ; con un ecu-do gua-da-gndr-ne tre t with one crown or
doilar to gain three ; la~vo~rd~re cvl-la li-ma, col pen-ntl-lo, col
tcar-ptUlo, to work with the file, with the pencil, with the
chisel ; fd-re u-na c6-ta con pia-ct-re, con do- Id-re, confa-ci-li-td,
con dif-fi-coUtd, eon de-sir e^-xa, eon bu&n gdr-bo, to do a thing
with pleasure, with grief, with ease, with difficulty, with skill,
with good grace.

The adverb in-sti-me, together, very frequently has the pre-
position con after it, and exactly coincides with the English
together with ; e. g. in-sie-me con lui, together with him ; in-
sU-me con un dl-tro, together with another ; i-o in-siS-me con
ml-opd-dre, I together with my father.*

It is obvious that it is not allowed to translate with by con
whenever this preposition does not represent any of the above-
stated meanings ; e. g. I am satisfied with him, sd-no con-tin- to
difui; I am delighted or greatly pleased with you, mi ral-U-gro
di rot. In these cases, to translate with by con would com-
pletely alter the sense. 86-no con-thx-to con lui, and mi ral-U-
gro con lui (di qudUche ed-sa) would mean : I am satisfied along
with him (i. e. as well as he), and 1 am delighted or greatly
pleased along with yon (•'. e. as well as you=J congratulate you
on somethin >

Con, with a noun following, frequently supplies the place
of adverbial expressions; p. «.;. con pru-din-za, with prudence;
Mft ci-vil-td, with politeness ; cm so-brie-td, with sobriety ;
eon su-ptor-bia, with haughtiness, &c, for pru-dentc-men-te,
prudently; ci-vil-me'n te, politely ; so - brio-men- te, soberly ; su-
per-ba-m^n-te, haughtily, &c.

Con, before an infinitive, which in this case occupies the place
of a real noun, is quite an idiom, and will be best translated by
the prepositions by, through, by the conjunctions while, when, as,
and particularly and, or by the present participle of the English
verb ; e. g. coif an-dd-re a spds-so non si pud ar-ric-chi-re, by
taking walks («. e. by idling) one cannot get rich ; 4-gli ti scu-

td eon di-re he excused himself by saying, saying, and said,

while he said; i-glifi-ce tc-sta-mdn-to confdr-mi e-ri-de di dit-
to il iu~o, he made his will, and constituted (or constituting)
me heir of all his property.

Pu uc-ci-so con un c61-po di pi-etMa. Con sem-bifcn-te tter-
ba-to mi dis-se. Con i-stu-dio. Con i-stu-p6-re. Qut-eti
bot-t6-ni non s' ac-cdr-da-no col co-16-re. Vi-a di qua con
que*-sta cO-sa. Con bdl gar-bo (or con bil-la grd-tia). Con p6-
co gar-bo. Con su-a bud-na gra-zia. Con 6-gni ma-gni-fl-
cen-ia. Con 6-gni fOr-za. Con ri-sp6t-to par-lan-do (or mO-
va vfi-nia).

VoCABULAKT.

Exntcisis. — Italian-English.

Si ne*t-ta col faz-*o-1e*t-to. Guar-dar c61-la (con la) co-da

dell' dc-chio. Tem-pe-rar il vl-no coll* (i-cqua. Fa-vo-rl-te

di Ve "£ 1r con me (° r m€ ' co )- P&r-ta tC-co (con te) la lan-teY-

na. E'-gli lo pre*-se se'-co (con Be). Coll* an-dar del tem-po.

* 1* *■ *too allowable to separate in-sii-me from con, and to place
It after the ease governed by eon ; e. g. con hd in-sie-me, together
with him ; ml-co (i. e. con me) in-sieme, together with me. The
adverb tn*ie-me-m4n-te also means together with, but It is not so
much in use as tn-sihm* con.

Si netta, he wipes himself
clean.

Fazzoletto, handkerchief,

pocket-handkerchief.

Ouardar, to look.

CM*, tail.

Oeehio, eye (eedm del? occhio,
the lesser or external can thus
or angle of the eye ; guardar
uno colla coda del? occhio, to
look at one from the corner
of one's eyes, generally from
contempt, also "from suspi-
cion or envy, to look askance
or cast a suspicious glance
at one, to look at one
with an evil eye, not to like
one).

Tcmperare, to mix, dilute.

Vino, wine.

Favorite, please.

Venir, to come.

Me, me.

Meco, with me.*

Porta, carry.

Te, thee.

Lantema, lantern.

Egli lo prese, he took it.

Se, himself, him.

Andar, to go, going, pace,
walk, course.

Tempo, time (coif andar del
tempo or col tempo, in time,
in time to come, hereafter).

Fu ttccuo, he was killed.

Colpo % blow, knock, shot.

Pi*tola, pistol.

Sembiantc, visage, face, coun-
tenance, appearance, air,
aspect.

Turbato, disturbed, alarmed,

troubled.
Mi disse x he told me.
Studio, study, diligence, care
{con istudio or a studio, on

purpose, of purpose, de-
signedly, intentionally).
Stupore, astonishment, sur-
prise, amazement.
BoHone, button.
Non t* aocordano, do not match.
Colore, colour.
Vim di fed, away with.
Garbo, good grace, pleasing
manners (ft*/ garbo, address,
skill, cleverness ; good grace,
pleasing manners).
Grama, greet, charm, favour,
kindness, permission (bell*
or hmm frazia, good grace,
pleasing address).
JVst, little {poco garbo, want of
good grace, unskilfulness,
awkwardness).
Om tuabuona gratia, with your

kind permission.
Oam, etch, every, alL
Mafntytcema, magnificence (eon
ogni mmgniflctnea, most mag-
nificently or superbly).
Forta, power, strength, force
(con ogni forza, or con tutta la
forza, a tutta forta, di tutta
forta, a mareiaf forta, a
vita J forta, par vita forta,
with all one's might, with
might and main, by main
force).
Rispetto, respect, regard, defer-
ence.
Farlando, speaking (con rispetto
parlando, with respect, or
saving your reverence or
honour).
Salvo, m., salva, f., safe, secure,

saved, unhurt.
Tenia, f., remission, forgive-
ness, indulgence (salva venia,
with your permission, under

your favour).
Colloquial Exercises.— Italian-English.

V a-mf-co, m., the friend,
T a-mi-ea, f., the female
friend.

V dUbero, m., the tree.

V ud-mo, m., the human being,
man.

Rie-eo, rich.
Pd-ve-ro, poor.
CH6-r**m, young.
// gid-va-ne, the young man,
youth.

Am -ma -Id -to, distempered,
diseased, out of health,
sick, ill.

An-cb-ra, yet, still, also, even,
again.

II vi~ci.no, m. v la •vcshbs, f,
the neighbour*

B cu-gi-noy m,, la o u at no, £,,
the cousin.

II eisr-e V mi r e, m., the gar-
dener.

• In the place of am me, with me; em it, with thee; and*****,
with hiawelf, herself, itself, themselves, tnsoo, tteo, and soot, are
frequently used ; and in elegant style am as a mere expletive, osa
meco, con toco, con seeo.

f The adjective mdr-cio, m., and mdr-cia, f., rotten, putrefied, vile,
despicable, is sometimes nothing more than an augmentative, giving
greater force to the word to which it is joined, and, in this ease,
somewhat similar to the English arch, chty, principal, eery* e. g. a
mdr-cia for-m, with all one's might j fritLco i *
a tA-o mdr-ch dt+p&to, in defiance of thee.

% Vi-vo, m., and ef-rc, f , living, lively, brisk.

LESSbNS IN GREEK.

807

i,* piar-di-nijl'ra, f* a ihc female

gardener, the gardener's

wife,
V iwS-ma, m., the male person,

man, husband.
La dnn+mi, f., the woman, wife,

lady, mistress.
fl §ci dd-toi m., the soldier*
If i#r*w, m., the servant*
£o Ac0.£i-re t m., the pdpil,

learner, scholar*
fb aeitl-t6*re f m*, the Sculptor,

statuary,
lAipic-chfo, m., trie ldbfttng-

glass, mirror,
la tcrUgtiQ. m. t the coffer,

casket , safe, iron safe, strong -

box, small taonev * tiox,

draper, pnrtable desi,
-Xo jedN-fio, m., the long stool,

form, bench*

g*crit4o t m., the writing,
r-Jb, thatte*.
JS Cdr^to t of tin fries*
vf CdV-&, to Charles.
JDfc €dr-fo t from, or by Charles.
j£k~rt'<&> Henry.
D' £n-rt-m f of Henry,

Ad Ex-rl-eo, to Henry,

Da £n-ri-co t from Of by

Henry,
Mi id na, Milan*
Di Mi^tdno, of Milan.
A .}fi-fu-nu. to, in ot at Milan.
Da Mi-tu-n&t from Milan*
Gia-tnin-Hif John.
Zu-f-tji, Lewi-*.
lban-c4-*eo f Francis.
Gv-gli-$l-me t William*
A-d&l-fQ t A do! ph. us,
Iti-dol-fa, Rodolph; lUlph, «
An- tf>-mo t Anthony*
Pte-fa-no, Stephen 1 ,
Pk'r-di»ndn-do t Ferdinand,
Ci$r*K-na t Caroline.
Lr*~i-gia> Louisa,
Ft-fo-na, Vienna,
Fe-ni^xia, Venice.
iVc-rf-^i, paris,
tAii-drOf London.
Ar-ri-nd-tOf. arrived.
Far-tLto per— departed for—
Si ehtd-ma t is called {L e. one

calls or names, we, they,

people call or name).
K di— belongs lo — (i.*, is of—)

Exercises. — Italian-English.

Hd ve-du-to T om-brdl-la di vd-stro pa-dre. L' a-mi-co di

?' il-o 2I-0 e ric-cb. Quest' ud-mo e 1' a-mi-co ui mi-o pa-dre.
I fan-ciuT-lo di quest' u6-mo e am- ma-la- to. Que*-sto fan-
ciul-lb e an-cd-ra gi6-va-he. A-ve-te voi ve-du-to V al-be-ro
che mi-o pa-dre ha com-pra-to? L* ud-mo, che a-v6-te ve-du-
to, e m6l-to pd-ve-ro. Su-o fi-glio e am-ma-la-to. Hd da-tb
la hen-na a que*- s to pd-ve-rb fan-ciul-lq. A-v6-te vol ve-du-
tb 1' d-rb-ld-gio cne mi-o zi-o ha ri-ce-vu-to ? E'-gli ha ven-
du-to que -s to o-ro-ld-gio a mi-o pa-dre. La zi-a di que*-sto
gid-va-ne ean-cd-ra am-ma-14-ta,, Que-sto pd-ve-ro fiin-
citit-lo Ka pcr-dfi-tb stt-a mi-dfe. it 1 il-b a-mi-co e un ii6-mo
m61-to ric co. Quest' u§-mo e il nd-stro giar-di-nie-re. Que*-
sta don-na e la nd-stra giar-di-nie-ra. II nd-stro vi-ci-no e
ric- ch is -si- mo. La yd-stra vi-ci-na e u-na bud-na ddn-na.
JL-ve%te vol ve-du-to mi-o cu-gl-no. Hd ve-du-to vd-stro cu-
gl-tto e vd-stra cu-fci-ha. Vd-stro cu-gi-no e l'a-mi-cd di
mi-o fra-tel-lo. Mi-a so-rel-la e 1' a-mi-ca di vd-stra cu-gl-na.
La bud-na glar-di-hle-ra ha pef-du-to su-o fi-glio ; su-a nglia
e an-cd-ra am-ma-la»ta. La vi-ci-na di mi-o zl-o ha un gran-
dis-si-mo fi-glio. II nd-stro giai-di-nid-re e il pa-dre di que*-
sto fan-ciul-lo. La fi-glia di qu&sta pd-ve-ra ddn-na e am-ma-
U-ta. Hd ri-ce-vu-tb uh re-ga^lo da tu-0 cu-gi-no. Mi-a so-
rdl-la ha scrit-to rf-na ldt-te-ra a vd-stro cu-gl^no. Il sol-da-tb
che a-ve*-te ve-du-to e mi-o cu-gi-no. Lo sco-la-re di mi-o
zl-o ha pet-du-to lo spdc-chio di su-a ma-dre. D6v* e lo scrit-
to di mi-a so-rel-la ? E's-so e nel-lo scri-gno. Lo spec-chio e
sul-lo scftn-no. II sdr-vo ha ri-ce-vu-to que'-sta ta-bac-chifi-ra
da u-no scul-t6-re. Mi-o cu-gi-no e un bud-no sco-la're, A-
v6-te ri-ce-vu-to u-no spdc-chid da mi-a ma-dre. Ca-nO-va e
un gr&n-de scul-td-re. II fi-glio di mi-o zi-o si chia-ma Car-lo
e s6-a fi-glia si chia-ma Lu-i-gia. II fan-ciul-lo di que*-sto
scul-t6-re si chia-ma Gu-gli-el-mo. La zi-a di Fer-di-n&n-do
e ar-ri-va-ta ; ma* su-o }>a%dre e par-ti-to per Ldn-dra. La so-
rel-ltt di Lu-l-gi e gran-dis-si-ma. Pen-so ad En-rl-co ed a
St A-ra-n'H. La zi-a di Lu-i-gia ha scrit-to u-na gran-de let-te-
ra ad A-ddl-fo. Fran-ce-sco ha ri-ee-vd-to que-sta p^n-na da
un gi6-va-ne, che si cbia-ma Ri-d61-fo. II cu-gi-nq di Gio-
van-ni e par-ti-to per Pa-ri-gi. V om-bTdl-la di Car-li-na e
pic-co-lis-ai-ma. Ab-bia-mo da-to la nd- stra ta-bac-chid-rk a
Gu-gli-el-mo. Que-sto cap-pel- lo e di Gio-van-ni, e que-sto
man-tel-lo e 6? A-ddl-fo. Nd-stra zi-a e a Mi-lfr-no. Lo scul-
td-re e a Vi-en-na. Que^sta ddn-na e di Ve-ne-zia. II nd-
stro rf-ml-co k 01 Pa-ti-gi. II nd-stro sdr-vo e ar-ri-va-to da
Ldn-dra. Mi-a so-rel-la pen-sa a Car-li-na. Std-fa-no ha

Est*ftA-to 11 tem-pe-ri-no eh' 6-gli ha ri-ce-vu-to da A-ddl-fo;
u-i-gia e la 60-r4t-l* di Cat-rt-na, ed An-td-nio e 11 frm-tdl-lo
di Gio-van-ni.

Enqljwh-ItaualW.

Our gardener is a good man. Your gardener's wife is a good
wonian. My friend h the unule nf this youn^ man, I have
bnu^ht thili irei? r>om yoiir gardener. Our (f**mHleJ Tipighh»ur
hits a Vtry good non and a very gr»od dnug1it»-r Hast thou
s^en this pdbr ifaan*H ehilLi ? My (mule) coUMn's lbipkliig-gla»fl
is very large. Thy (male) neighbour i* the pupil of my
father* My book in on ihe form. I have given my l.at to this

rbr child. The boolt which 1 have received from a l>iend
lost, Loiilsli h&a lost her bonnet* tiave ybu (*iW.) fdiind
Charles's ring? Henry *a father {i. f, the father of Henry) is
very rich, John's garden is very small* AYilHam's friend has
departed. My cousin has (i ft, is} arrived. We have received
a lt?rt^r from Louis \ be is at Milan. Have you seen Francis
and Ferdinand ? Hodolph has departed for Venice* Wfe have
written a letter to Stephen in Paris. Have yon («'«(£ ) seen
th~ -^ichof Louis? Hus (i. e, is) yoijr (stn^,) uncle departed
for Paris P Carolirje's aura is in London, Our (male] neigh-
bour has a son, who is called Adoiphus, and a daughter who is
called Louisa,

E N I"! L TS T I - I T A 1. 1 A N .

The nephew has gone with the general's son and daughter
into ihe park to dine there* Next vuetk they will go together
into the country, A courier has arrived with the news of the
conclusion of pence. The cousin came here with the express
order to buy a horse and a coach. I have never offended him
with one single word. In time, and with patience, one learns
everything. Man ought to spend the first part of his life with
the dead,- the second, with the living, and the third with him-
self. The world is rilled with ungrateful persons : we live with
;the ungrateful, we work for the ungrateful, and we always
have to do with the Ungrateful.

Vocabulary.
INephew, ni-p6-U, m.
Has gone to dice there, e on-

dd-to a prdn'td-re
Park, bo-sehii-to, in.
General, jfe-tie-rd-it, in.
Week, 9et'ti-md-na t f.
Next, veb-tt-ro, m., ven-tu-

TO) f.
They will go, v6-glio-ho an-dd-

Together, tut-ti in-ate-me
Country, cam-pd-gna % i,
(There) has arrived, e giun-to
Courier, eor-rii-re, m.
News, nu6-va, f.
Peace, pd-ce; f. (i. e,

the peace)
Cousin, cu-gi-no } m;
Came here, ar-ri-vd qui
Express order, 6r~di-ne es-pres-

80, m.
To buy, dicoin-prd-re
Horse, ca-pdl-lo, m.
Coach, Mf-rus-«a, f.
I have never offended him, i-o

non V qf-f^si tnd-i

One single word, u-na*6-topa-

r6-la t f.
Time, tempo, m.
Patience, pa-ti-6n-2& Ifs— ft),f.
One learns everything, s' tw-

pd-ra titt-to ,

Ought to spend, <&-be pas-ad-

re
First part, pri-ma pdr-te, f.
His life, la 8u»a vi-ta
Dead, m6r~to, m.
Second, se-c6n-do t nt;, se~c6n-

da,{.
Living, vi-vo, m.
Last, {U-ti-mo, m., id-ti-ma^ f.
news of Himself, *e stSs-so
World, m6n-do t m.
Is filled with, € pit-no di
Ungrateful (person), in-grd

to, m.
We live, si vi-ve
We work, si la-vo-ra
Tor, per
And we always have fo do, e si

ha da far sSm-pre.

LESSONS IN GREEK.— Nd. XXlf.
By John R. Bbard, D.D.
AccoRDiifO tc these general statements and explanations, the
verb may be regarded as a total comprising a number of ideas,
lor representing a number of facts. This may be exemplified
in XctTTitf, I leave; and XiifBttrriv, they two are left; thus —
Xftwca.

Person. Number. Tense. Mood. Voice.

First. Singular. Present. Indicative. Active.

XttfQeinjv.

Person.
Third.

Number.
Dual.

Tense.
Aorist, 1st

Mood.
Optative.

Vote*.
Passive.

308

THE POPULAR EDUCATOR.

From this instance you learn that the Greek verb varies, or
is modified in person, in number, in tense, in mood, and in
Toice. Accordingly, it is the business of the learner to be-
come familiar with the verb in all these its modifications, so
as to at once recognise every form he may meet with in
reading, and be ready at first sight to assign its meaning.
The task is not an easy one, but will yield to persevering ap-
plication. The task, being difficult, must be undertaken in
detail.

Before we proceed to the general conjugation of the Greek
verbs, we must present a peculiar form, namely, that of the
substantive verb, or verb of existence, mhu, to be.

Future.

«o

2 2
II

is:

f
{

Imperfect.

[J?5 B

Present.

2' *

13-3 s

§ 1 3

e -

9 i

5 3^

* 1

a i n jr

55-3

311"

Ck I* ">

5 e e «

ei
O

111

IS?

!ijp

Before I make any remarks on this verb, I will explain the
contractions, the rawer because they will recur again and
again.

List of Contractions, with Explanations.

1. 2. 3.— That is, the first person, the second person, the
third

8. D. P.— That is, the singular number, the dual, the

plural.
N. denotes the nominative case.
G. denotes the genitive case.
M. denotes the masculine gender.
F. denotes the feminine gender.
N. denotes the neuter gender.

The English is only given in part, it being presumed that
the learner can easily supply the rest ; thus, when he knows
that ttfu means I am 9 he can hardly fail to know that the
plural runs we are, you are, they are.

Let it be premised that the significations given in the
paradigms, or examples of conjugation, are sometimes only
approximately correct ; for the exact meaning the student
must wait until he is familiar with the details of Syntax and
other details, which will follow.

The verb whose forms are given above, belong, it will be
seen, to the class of the verbs in pi. .There is another form,
distinguished in part by accents, namely, tlfu, I go, (tlpi, lam) ;
the conjugation of which will be given in its place under the
verbs in jit.

The second person of the present, c &, is more used than c eg .
In the imperfect, the second person, 17c, often becomes noQa, by
the addition of a euphonic suffix ; the third person is qv, more
frequently than ij.

Instances are found, particularly in the first person singular
and the third person plural, of another imperfect, which re-
sembles the imperfect of the middle voice.

S. ij/iijv t]<jo tiro. P. tjpuOa naQi nvro.

A middle imperative form is also found in the second person
singular, namely, iao, be thou.

The entire present subjunctive, namely, m yc 9, &c., sup-
plies terminations to all the verbs in «*. The second and
third person singular have the iota subscript, as seen above.

The optative forms, eirjv ttrjg ccsy, lend their terminations
iav, &c, to the optative of the verbs in pi. For the form
wjfitv, iifitv is used ; and for uijaav, ecev is much more com-
mon ; iuv is also found in the sense of well t very well ! be
it so!

The future, in all its moods, is a middle form ; its termina-
tion, ooudi, is that of all the middle verbs in the future. The
original forms were —

taofiai tataai tatrcu.

In laurai the second <r was elided, and the word became
(.aiai. The ta was contracted into n, the 4 was written under,
and thus toy arose.

This observation extends to all the second persons in 7, of
the middle and passive verbs. Also, in the optative, texxo
stands for tcrouro i<rrai t a contracted form of tctrai, is more
common than etrirai.

The participle looptvoQ (the Latin Juturus) is declined like
ayaQoQ, ayaOrj, ayaQov.

The substantive verb lacks the perfect, the pluperfect, and
the aorist; these tenses are supplied from yiyvo/uu, I
become.

The stem of the verb is cc, as found in ta/itv, taopat, &c.

The present participle is declined thus —
Singular. Plural.

M. F. N. M. F.

iv". uv ovaa ov ovrtQ ovaai

O. ovtoq ovarjc ovtoq ovtwv owner

D. ovri ovtrg ovrt ovai ewatc

A. ovra ovaav ov ovtoq ovaaQ

So decline the participles in «*v, of all the verbs.

By the aid of prepositions various compounds of tifu an
formed, and these compounds are conjugated like their primi-
tive ; as icap-tifu (adsum), I am present ; aw-iifu (absum), /
am absent; ptr-ufii (intersum), I am among; vw-tifu (una
sum), / am with; irpoc-tifu (insum, accedo), / am near y I ap-
proach ; iript-tifju (supersum, superior sum), J turner I am
superior; and others. The preposition remains invariable;
only the verb undergoes the conjugations! changes.

LESSONS IN GERMAN.

300

The verb uui is instructive in regard to the original personal
endings. These personal endings in ei/u I will mark off by a
hyphen, thus — u-uu

Singular, Dual. % Plural.

1. u- fit w-ptv

2. €(7-Ot(ll) lO-TOV tff-TC

3. €<r-rt(v) %9-tqw «i-<ri(v).

The terminations of the three persons of the singular are
properly appended pronouns ; thus pi is found in us, n (con-
tracted into a) is found in n, and rt in the stem of the
article to. Accordingly, in their original form, these

The Personal Terminations.

Active.

Middle.

rinci

pal Tenses. Historical T.

Prineipal Tenses.

Historical T.

fUU

unv

ecu

—

rat

U€V

usOov

TOV

vBov

TOV

T1\V

<t9ov

aBnv.

fUV

fuSa

00C

English- Grrbx.

This is in my power. The laws are in your power. It is in
your power (that is, it depends on you) to purchase com. It
was in the power of the enemies to be present. It is in the
power of good boys to excel. It will be in my power to ap-
proach the city. Punishments belong (wpocMvai) to sinners.
Thy care of thy friends is an example to all. The ships hare
come to the king.

v{yr)

nvrai

By studying these terminations now, and by reverting to
them afterwards, the student will be materially assisted.

One thing let me enforce on the student, he must make
himself thoroughly master of all the paradigms before he
attempts to set a step in advance. The remarks made
thereon are, in the commencement, of less consequence.

VOCABTJLAJLY.

EirtXft7rw,I leave,lack, circXtwt,
second aorist active, failed.

Hpiauat, I purchase, TcptaoQat,
infinitive present middle,
to purchase, ovk nv irpiaa-
Oai, literally, was not to pur-
chase, that is, could not be
purchased.

*OpaM, I see, behold; &p&v,
infinitive present active, to
behold ; «<m bp&v, literally, it
is to see, that is, you may see.

SvyjcaXe**, I call together, con-
voke; 6 avyicaX&Vt con-
vener.

Nuea«*, I conquer.

'Apuorruv, to fit, befit, suit,
agree with ; the infinitive is
in the text used as a noun,
and may be rendered, in
harmony.

OcXw, I desire, I will.

top*, I bear.

Av«>, I go down, enter; rpo
dwrog, rjXtov, before sunset. !

Exercises. — Greek-English.

' H raZtc nv iicarov aviptc. Hv rnc utpac fwcpov irpo Svvroc.
tjXiov. Ol vofiot Znutai c«Ti rutv auaprniktav. Tovroig Oavaroc
mttiv r) Znfua. 'O <rtroc €irt\iirt t kcu irptavQat ovk nv. Eon
bpav to opoc. "H AynfftXaov aptrrj irapadnyua nv. 'Huiv
apurrov ovk tariv. Eyto tffofiat 6 <rvyiea\£jv. Ovtoq tan 6
vveStv. Eyw pxa rovrutv etui. Ba<rt\cvc voaiZ,u vuac avrou
tivat. Eotiv ovv rnc yaapyiKnq Tt\vnc V rutv ^^vdpittv <pvrua.
Eortv avroiQ ayopa. Ev rote atropoig nutv. 'O Kvpoc ev
rovroiQ nv. Em ooi ttrrat rovro. 'Ov utxpov ayaOov rtp
apporrttv irpoqtortv. Ty flia icpocuaiv ex^pai Kai Kivdvvot.
Ty ifTtfifXtuf. irtpuivai rtov ^cXwv 0iXa». Uaprjv AytaiXaoc
impa Qipvv. Kvp<p wapnoav tK TltXoirown<Tov vntg.

Ta£«c, ewe, r), a rank, or file of
soldiers.

*Qpa, ac, r), an hour (Latin,
hora), time.

Apurrov, ov, to, breakfast;
r)fuv apurrov tart, we havj
breakfast ; ccvw,with adat\ \ .
of the person, has the force o\ .
to have ; the pronoun must
be put in the dative, the
person being preserved, thus
tori pot is I nave ; wn aoi,
thou hast, &c.

Qvrtia, ac., ifr, planting, care.

TtutpyiKOC, ii, ov, agricultural,
hence the name Oeoryics,

fiven to Virgil's Didactic
oem on agriculture.
Ayopa, af, rf, a market.
Airopogt a, ov, impassable ; ra
airopa, straits, extremities;
observe that etvcu, with the
preposition ttri, signifies u to
be in the power of."

LESSONS IN GERMA N.— No. LXXXII.
§ 119. SYNTAX.

Syntax is that part of Grammar which unfolds the relations
and offices of words as arranged and combined in leniences.

The essential parts of every sentence are the subject, which is
that of which something is affirmed ; and the predicate, which
is that which contains the affirmation.

The subject is either a noun or that which is the represen-
tative or equivalent of a noun ; the predicate is either a verb
alone, or a verb in conjunction with some other part or parts of
speech. All other words entering into a sentence are to be
regarded as mere adjuncts. The following sentences exhibit
the subject and the predicate under several varieties of form :

Predicate.

exists.

is mortal.

contents his natural desire.

was his crime.

Subject.

God

Man

To be,

Throwing the stone

In the sentence, God exists, the verb exists is the predicate :
affirming, as it does, existence of the Almighty. But in the
sentence, man is mortal, mortality is what is affirmed of man ;
and the verb (is) is the mere link that connects the subject and
the predicate together. It is thence called the copula. § 158.

Sentences are either simple, that is, contain a single assertion
or proposition ; or compound, that is, contain two or more as-
sertions or propositions. Of the various parts of a sentence,
whether principal or adjunct, we come now to speak more in
detail ; so as to show the relation, agreement, government, and
>. rangement of words in construction.

§ 120. THE ARTICLES.
Rule.
The article in German, whether definite or indefinite, is gene-
rally employed wherever the corresponding article would be
used in English. *

Observation.

This rule is of course founded upon the presumption that the
student is familiar with the usage of the English in respect to
the article. In the specification that follows, therefore, he is to
look only for the points in which the German differs from the
usage of our own language.

(1) The Germans insert the definite article :

(a) Before words of abstract or universal signification ; as,
to e r 2Renf<$ tft ftarbli$, man (i. e. every man) is mortal ; b a « ©olb
if! fce$n*ar, gold is ductible ; b a 8 Scbcit ifl furj, life is short ; b i t
Sugtnb fu&rt gum ®Iurfc, virtue leads to happiness :

(b) before the names of certain divisions or periods of time :
as, bcr @onntag, Sunday; btr SRontag, Monday; ter Dcjemfcr, De-
cember ; bet 2lugufi, August ; b«c ©ommet, Summer :

(c) before certain names (Jeminines) of countries; as, bte
Jturfet, Turkey ; bte @<ytt>eij, Switzerland ; bte Sombarbet, Lombardy:

(d) before the names of authors, when used to denote their
works; an, i$ tefe ben Sffiing, I am reading Leasing:

(e) before the proper names or titles of persons, when used
in a way denoting familiarity or inferiority ; as, flrujie b t e (Wane,
greet (or remember to me) Mary ; fage b e m Sutter, taf \a) ibn ju
feben nmntye, tell Luther that I wish to see him: also, when
connected with attributive adjectives : as, b i e Heine ©opfcie, little
Sophia:

(f ) before words (especially proper names of persons) whose
cases are not made known either by a change of termination,
or by the presence of a paeposition ; as, bar 8eben bet 8u*fl«a,the

310

the Popular educator.

life of princei; tie ffrau te« Sefrate*, the wife of Socrates; ter
Xai ter Maty, the clay of (the) vengeance :

(g) before the mimes of ranks, bodies, or systems of doc-
trine: as, ta« Spotlamcnt, Parliament; tic 3legicrun$, government
tie 'JMonardjie, monarchy ; tafl (tyriftcntljum, Christianity: also in
such phrases as, in ter £tatt, in town; in tec £in$e, at
church ; t i e meiffcn flKenfc^en. most men :

(h) before the words (signifying) half &nd both: as, tie $al&e
(not fall* tie) Bofrl. Aa/f the number ; tie bciten (not beitea tie)
©ruter. both the brothers :

(i) before words denoting the limit within which certain
specified numbers or amounts are confined, wherein in English,
the indefinite article would be Used! as, jweimal tie 2Bo$e, twice
a week:

(2) Note, further, that the German differs from the English
in omitting the definite article, ~

(a) before certain law appellatives : as, ©eflagter, (the) defen-
dant; JHaott, (the) plaintiff; BpriHant, (the) appellant; ©applicant,
(the) petitioner :

(b) before certain common expressions ; such as, in tefler Drt#
ming, in (the) best order ; Uefrerbvinger ttefe«, (the) bearer ot this ;
and certain adjectives and participles treated as nouns; as,
erfkrrr, (the) former; leiteur, (the) latter; befagter, (the) before-
said (person) :

(c) before certain proper names and places : as, Oftintien, (the)
East Indies; HBefHntten, (the) West Indies; and before the
names of the cardinal points: as, Often, (the) East; 2Beft<n,
(the) West ; ®uten, (the) South ; Shorten, (the) North :

(d) before a past participle joined with a noun, which, in
English, precedes the participle : as, ta* serlorene $aratte*, (lite-
rally, the lost Paradise) Paradise Lost.

(3) Note, again, that the Germans, in using certain collective
terms preceded by adjectives, employ the indefinite article where
the English would use the definite : as, ein ftocfyveifct JRatb, the
(lit. a) most learned Senate; cine 16Mi$e llniwfttar, the (a)
honourable University.

(4) In German, also, the indefinite article stands before (not
after, as in English) the words, such, half: thus, ein folder SDlann,
(not fohftet ein SMann), such a man ; ein halbes 3afcr. (not balta ein
3*br), half a year. In questions, direct or indirect, like the f
following : Gincn rote langen Srajierritt bat er aematyt, how long *» |
ride has he taken ; it must be noticed that the article stan<:«
before roie: thus, elnen rote langen (a how long) and not, as in
English, how long a.

(5) The German differs again from the English in not using
an article at all in the phrases answering to the English ; d few ;
a thousand ; a hundred.

§ 121. THE NOUN.
Rule.
A noun or pronoun which is the subject of a sentence mast
be in the nominative case : as,

£er 2Revi$ tenfr, (Mott lenft, man devises, God disposes.
£ie iBcrge tonnern, the mountains thunder.
Observations.
(1) The subject or nominative in German is seldom omitted,
except in the case of the pronouns agreeing with verbs in the
second person (singular and plural) of the imperative : as,
*efe (tn), read ! C&eM unt faoet (3br) ibm, go and tell him.
See, however, § 136. 2.

§ 122. Rule.
A noun or pronoun which is the predicate of a sentence, must
be in the nominative case : as,

<Jr roar ein gwfer flonig, he was a great king.

jDiffcr itnabe tft jtaufmann geftcrten, this boy is become a merchant

flleranter bief ter (Mrofo Alexander was called the Great.

Observations.

(1) This rule applies, where the subject and the predicate are
connected, as above, by such verbs as fctn, to be; rocrtcn, to be-
come ; btipe n, to be coiled ; bleibcn, to remain, &c.
• (2) So, also, the rule becomes applicable when any of those
verbs which in the active govern two accusatives (§ 132. 2.), are
employed passively: as, (Jicero rourte ter 3?ater te« Qtaterfantet genonnt, ,

Cicero wis called tne father of his country ; (ft i# arexantrr §e«
tauft roorten, he has Been christened Alexarider. From this re-
mark, however, must be excepted the verb tetyren, since It has
no passive.

§ 128. Rule.

A noun used to limit the application of andther noon signi-
fying a different thing, is put in the genitive ; as,
£er £auf ter Sonne, the course of the sun.
Iter ®obn meinrt ffreuntet, the son of my friend.
T\t (Jrjiebung ter Jttnter, the education of the children.
T\t JffiaM eince greuntd, the choice of a friend.

How this limitation is made, is easily seen : thus, ter $<ntf tft
Sonne, the course of the sun. Here we speak not of any course
indefinitely, but of the suns course definitely: the word ter
Sonne, is the genitive, limiting ter Sauf, which is the governing
word.

Observations.

(1) If, however, the limiting noun (unless restricted itself by
an adjective or some other qualifying word) signify measure,
number, weight, or quantity, it is then put in the same case with
that which it limits ; as, jwei <S»la« ffieia, (not Seine*), two glasses
(of) wine; fe$l $funb Xfeee (not Sytef), six pound (of) tea: but
(with a restrictive term), fed* $fftttb ttefel 2$eef ; jam ®ta« tiefe*
2Bcine3.

(2) It should be observed that the two nouns under this rule
must be of different signification ; for two nouns standing for
the same thing would be in the same case, forming an instance
of apposition. See § 133. (1).

(3) The noun in the genitive, that is, the U miting noun, is
commonly said to be governed by the other one. This genitive
is either subjective or objective ; subjective, when it denotes
that which does something or has something : objective, when
it denotes that which suffers something, or which is the
object of what is expressed by the governing word. To il-
lustrate this, we have only to take the examples given
above : ter Sauf tet Sonne, the course of the sun ; tie ffrjitfintfs ter
fttnter, the education of the children ; where, in the first ex-

[ ample, the sun is represented as performing or hating a course,
' and is consequently subjective', and, ill the second example, the
r'::Idren are represented as being the objects of education, and
the word is consequently objective. This objective genitive* 1ft
should be added, occurs only after verbal noon's, arid chiefly
those ending in the suffixes er, which marks the doer, rind ana,
which marks' the doing of an action.

(4) It seems hardly necessary to observe that under this role
come all words which perform the office Of nouns ; as, pro-
nouns, adjectives used substantively, &c. ; thus, tie equate tec
(Mroflenjfche favour of the great.

(o) We say often in English, He is a friend to, or tttt ctietaf
to, or a nephew to any one : where, were these phrases pot into
German, we might expect the dative to be used. Bat, in such
cases, the Germans always employ the genitive : thils, er tft fin
fteinb fetnet SSaterlante*, he is an enemy of his native cottntrt.
. (6) We say in English, the month of August, the citt «/ Lon-
don, and the like : where the common and the proper name oi
the same thing are connected by the preposition of. Tne
Germans put the two nouns in apposition. See § 133. (£).

(7) So, too, in English we say, the fifth of August ; but in
German, the numeral is put in direct agreement with the name
of the month : as, tet fttnfte flitgufl, the fifth (V) August, or
August fifth.

(8) In place of the genitive, the preposition sen, followed
by the dative, is, in the following instances, generally used :

a. When succeeded by nouns signifying quality, rank, mea-
sure, weight, age, distance, and the like; as, ririSfanrf wa fefeat
€ttante, a man of high standing ; ein Gtyiff rtft jnrtt fuittert Zdtetn.
a ship of two hundred tons ; ein (Stamtyt von faaf $funt, a weight
of five pounds; ein SRann von a^tjtg 3ayten, a man of eighty
years ; eine Strife sen tret 3Retlen, a journey ot three miles ; eis
Gngldnter vontSfebutt, an Englishman by birth, &c

b. When followed by nouns denoting the material or sub-
stance of which any thing is made : as, ein 9ed)rr wn ©tfter, S
cup of silver, i. e. a silver cup ; eine W$t wit Qotte, a gold watch

LESSONS IN GEOMETRY.

311

c. When followed by nouns whose cases are not indicated by
the terminations of declension nor by the presence of the
article : as* ter €tyein von StebCtyfeit, the appearance of honesty ;
rill Soter von fed)* ^intern, a father of six children ; bit Jt&nlglrt von
ffttglanb, the queen of England ; tie Gwnjen von Sranhrty, the
boundaries of France; vet ffiiftyof von Jkonftani the bishop of
Constance.

d. When followed by a word indicating the tribe**, of which
the word preceding expresses but a part : as, tin* von tntttten
©dmraten, one of my acquaintances j todtycr von Mbcnf which of
the two?

LESSON8 IN GEOMETRY.— No. XXVII.

LECTURES ON EUCLID.

PBOPOSITION XXVTtl. — THEOREM*

{Oniinmdfrom page 298.)

16. A fallacy somewhat more subtle than Franoesehini'a,
though akin to it, may be framed on the consideration of the
angle of intersection, bet ^ b. c d be two straight lines in the
same plane making with a third straight line ao the angles cab,
k D, of which a c D is a right angle and cab less than a right
Ingle. And to improve the appearance v though this is not
indispensable) draw a straight line a b on the other side of a o
ahd in the same plane, making an angle oab equal too a b. And

it* Jf,--

from A let a straight line of unlimited length as w x travel along
the straight lines a b and a b, cutting a c always at right angles
in some point G between a and c. This line will represent
Franceschini's succession of perpendiculars. But instead of
arguing from its continually cutting off greater and greater por-
tions a g» let it be argued that becau.se it at any time makes with
A b an angle a h o orB h x, it may always be removed to a posi-
tion further from a without ceasing to cut a b and a b. From
whioh it at first sight might appear to bo a reasonable conclusion,
that the straight line w x may be carried forward without the
possibility of failing to cut a b and a e, till it arrives at c. And
the fallacy will perhaps be still more taking, if a b and a e are
made to begin by being placed ate. and so are moved from c
towards a, as represented by a & and a e ; under whioh circum-
stances the allegation that there must always be an angle of
somo kind at A, has a very inviting appearance as a reason why
a b and C d, being continually prolonged, cannot quit one another
or fall to meet and make an angle or some magnitude or other,
the consequence of which would be that a 6 and a e might be
moved till 41 coincides with a and a 6 with A B, Without the
possibility of parting company with c d by the way.
. The answer to this is by inquiring, whether there are no lines
in whioh the same facts may be determinable on the subject of
the angle, but where it is certain that a straight line as w x can-
not be carried on to an unlimited extent as proposed. And here
it is easy to show that there may. Take, for example, any
hyperbola} and from the vertex draw a perpendicular to each of
the asymptotes; ana let the two halves of the linear hyperbola,

Se t siha w with the porpeudioulari mi the portions of Ae asymp-
totes eat off by them on the side remote from the intersection of

the asymptotes, be placed so that the perpendiculars shall coin-
cide and the asymptotes in consequence be in one straight line,
as s t in the figure below. Upon which it is clear, that how-
ever it may be pleaded that there may always be an angle
smaller than a h o or b h x between w x and ar.wx cannot
be carried beyond the line of the uymptotes s t without ceasing
to meet a B ; and consequently cinnot be carried till it meets c d,
If c i> lies on the other side of s t as represented in the figure.

It follows therefore, that to say there will always be the possi-
bility of a further diminution of the angle, is not enough. It may
be (as it is in the case of the hyperbolic angle above) the sophism
bf Aohilles and the tortoise ; which argues, that because after
running a mile, half a mile, a quarter of a mile, Ac, Achilles
Would always be behind by the last-mentioned fraction of a mile,
he would never overtake or pass the tortoise. The solution
resolving itself into the fact, that these quantities, though endless
In number, are limited and surpassable in amount.

To establish the, union of the lines to any particular extent that
may be desired, it is consequently necessary to prove, not only
that the angle at the intersection is capable of diminution, but
that the* angle on each side of the travelling line (that is to say,
both the angle ahs and the an^le on") will never be reduced
to to* than tome given, angle. W hich is v-Ki r has been attended to
accordingly, in the oase of the intersection : with a travelling line
in Proposition XXV111. C of the " Geometry without Axioms."

17* Another course taken has been to define a straight line to
be one "of which every successive portion has the same direc-
tion," and parallel straight lines to be " straight lines having the
Same direction with each other." From '"hich it is purported to
be collected, that a straight line cutting two parallel straight
lines makes the interior angle equal to the exterior and opposite
on the same side of the line. % For, it is argued, the direction of
the cutting line is at the two points cf intersection the same ;
and the directions of the two parallel straight lines cut, are at
those points the same with each other's ; whence the differences
of direction, which are the angles, will be equal. To which rfeply
may be made by asking, what definite idea is attached to two
lines having the name direction. It does not mean that they tend
to the same point, for they do not. It means, then, that they
never run against each other; or are parallel. And a line every
successive portion of which has the same direction, means •» »»!»n
of whioh the parts all lie in the straight line leading to a p *«.■•"*
lar point or object. The argument therefore resolves itscn into
the proposition, that if a straight line falls upon two parallel
straight lines, it makes the exterior angle equal to the interior and
opposite on tne same side of the line ; propounded in other terms,
without the intervention of any new or explanatory idea.

18. In a tract entitled " The Theory of Parallel Lines per-
fected: or the 'twelfth Axiom of Euclid's Elements demon-
strated. By Thomas Exley, A. M.— London. Hatchard 1818 "
— the proof rests on taking for granted (in the Second Proposi-
tion) that if /our equal straight lines in the same plane, making
right angles with one another successively towards the same
hand, do not meet and enclose a space, & fifth if prolonged both
ways must inevitably accomplish it. A conclusion which may
be resolved into taking for granted that the three angles of a
rectilinear triangle are greater than a right angle and a naif; for
if they were equal to this, the angles ot an equilateral and equi-
angular octagon Would be right angles, and the fifth straight line
in the series proposed would never meet the first ; still more if
they were less. And in the same manner, if it was urged that a
sixth, Hventh, Ac. perpendicular must meet the fii>t straight line,
it would only resolve itself into a demand for admitting, without
proof, that the three angles of a triangle are greater than somo
other amount capable of being specified. There is no obscurity
about the fact that four such straight lines, and still more five,
are found on experiment to meet; but the object was to discover
wtnt they necessarily meet. And between the observed fact
and the explained fact there is a difference of the same kind as
between Kepler's observation of the proportion between the
periodic times and distances of the planets, and Newton's expla-
nation of the cause.

19. in "A Treatise on Geometry, by D. Cresswell, M.A.
Cambridge, 1819," the principle proposed to be taken for granted
is, that through any point withm an angle less than the sum of
two right angles, " a straight line may be supposed to pass, which
shall cut the two straight lines that contaiu the angle.' The
grounds for such admission being stated to be, that "if it be
granted that among the infinite number of points outside the
angle, there are two, on contrary sides of the angle, which are
in the same straight line with the point within: or if it be
granted, that, inasmuoh as the sides that make the angle are
unlimited in length in the directions removed from the angular
pointy two points in those sides may be taken; one in each, so that
every point in the straight line whioh joins them shall be farther

812

THE POPULAR EDUCATOR.

distant from the angular point than the point assigned within
the angle : in either of these oases the assumption made above
will have been allowed " (p. 28). To which the answer seems to
be, that to know by what necessity attendant on the constitution
of the straight line, the soveral results here taken for granted
Will take place, is precisely the object which it was in question
to attain. The apparent application of the proposed principle in
the 20th Proposition of Euclid's Eleventh Book, is a mere error
of Euclid's, and corrected by the Arabs, and subsequently by
Legendre and probably others, through a very simple alteration
in the construction. Euclid's straight lines will fail to meet,
whenever his greatest angle exceeds naif the angle cut oft by not
less than a right angle, Th-is if the angles composing the solid
angle were 7<)°» W , and l.'i0°, neither by cutting off one of the
smaller angles nor the other, could Euclid's intended construc-
tion take place.

20. Professor Thomson, 'of Glasgow, proposes to take as an
Axiom, that " if a triangle be moved along a plane, so that its
base may always be on the same straight line, its vertex describes
a straight line equal to that which is described by either extre-
mity of the base. * In which there are two things demanded,
where either would be enough. For if it could bo established:
that the locus of the vertex is a straight line, every thing else
might be demonstrated without premising that the lines described
are equal ; us has been done m kindred cases by Clavius and
others. Or if it could be established that the distances between
the first and last situations of the travelling points respectively
are equal, this would suffice for the author's own demonstration,
without asking whether the vertex had been always in the join-
ing straight line. But how the equality of these distances is to
be established, does not appear. One way of trying to proceed,
would be to show, that it the line on which the base of the
triangle travels (and of part of which the base is composed),
instead of a straight line were a circular arc, the vertex would
travel farther than the point in which the straight line from the
vertex to the centre cuts the base, if on the convex side, and lets
far if on the concave ; which is easily done, by proving that if
not, the straight lines that ought to be the radii of the circle
would not meet And this would throw the responsibility on
establishing, that the radius of a circle may be increased till a
portion of the circumference approaches within any assignable
difference to a straight line of given length ; in other words, that
there cannot be three points not in a straight lino, through which
a circle may not be described. Whioh involves Euclid's
Axiom.

21. The demonstration presented by M. Legendre in the
earlier editions of his "Elements de QeomStrk," consisted in first
establishing that the three angles of a rectilinear triangle cannot
be greater than two right angles (which may be passed over as
irrefragable and liable to no remark), and afterwards proceeding
to show cause why they should not be less. But the evidenco
offered on this latter point, depended on taking for granted that
two straight lines (d e and b e in fig. 35 a in the Fourth Edition,
and probably in tho subsequent editions as far as the Eighth
inclusive) meet when tfccv make with a third straight line (d b)
angles of which one (as ED B) is, or may be made to be, less than
a riqht angle, and the other looks less than a right angle, but
without further proof.

22. In the Seventh Edition another attempt was made to show
that the lines must meet ; but what is advanced as the proof
involves the same fallacy as that of the Bolognese Professor.f

23. This was withdrawn in the 'Ninth Edition, and a new
demonstration offered in the Twelfth. The new one depended
upon taking in any triangle an angle that is not less % than any
other in the triangle, and a second that is not greater (See Heme
«***;<*»/>• 20, and plate); bisecting the side opposite to the second
angle, and drawing a straight line from the angular point to
the point of bisection; cutting off in this straight line audits pro-
longation a part from the angular point equal to the side opposite
to the firstrmentioned angle (vis. that angle which is not less than
any other in the triangle ), and in this side and its prolongation
towards the same hand a part equal to double the straight line
between the angular point and the point of bisection formerly
mentioned, and joining the extremities of the two parts thus cut
off. It is not difficult to show, that in the new triangle thus last

• «* The first Six and the Eleventh and Twelfth Book* of Euclid's Ele-
ments; with Notes and Illustration*. IJy James Thoinsom, LL.D. Pro-
fessor of Mathematics in the University, Glasgow, 1834. Aotes, p. 308."
t Elem. de Geom. Par A. M. Legendre, 7eine 6 Jit. p. *80. Note II.
J A"°f te *f w and J nct fireaterue substituted for the greatest and least of the
original. The demuustraUon is plainly Intended to be applicable to any
triangle j but the terms in the original would not apply to an equilateral
triangle, nor to any kind of isosceles. «4u*»wrw

I constructed, the sum'of the three angles is the same as in the
original triangle ; and moreover that of the angles of these two
I triangles which are at a common point, that belonging to the
new triangle is not greater than half that of the old, while another
of the angles of the new triangle is equal to their difference.
And if these operations be applied in like manner to the last con-
structed triangle, a third triangle will be constructed having the
same relations to the second ; and so on. Whence it follows,
that the described process may be continued, till two of the angles
of the last-resulting triangle are together less than any magni-
tude that shall have been assigned ; and consequently the third
or remaining angle may be made to approach, within any mag-
nitude however small it may be chosen to assign, to the sum
of the three angles of the original or any of the intervening
triangles.

All this is irrefragable ; but not so the inference next taken
for established, which is that the third angle last mentioned
approaches within any magnitude however small it may be
chosen to assign, to the sum of two right angles. That it
approaches it (that is, that the angle continually grows larger) is
certain ; but that it approaches to it within any magnitude how-
ever small, is the point which, as in so many parallel instances, is
taken for granted without sufficing proof. The weakness in the
actual case, is in the fact that the base or side opposite to the
continually increasing angle, becomes itself of unlimited length.
If the resulting triangles had been all on the same base, the
inference might perhaps have been conceded to be good. But it
is precisely because by the extension of the base to an unlimited
magnitude the progress of the operation is removed from human
eyes, that the force of the inference is diluted and done away.
J ust as fast as the diminution of the two acute angles appears to
induce a necessity for the obtuse angle's approximating to the
sum of two right angles, does the increase of the length of the
sides hold forth an augmented probability that the angle may
after all evade increasmg by the quantity required to make it
attain to two right angles in the end. To argue that when the
acute 'angles are nothing, or the lines coincide, the third angle
will make a straight line,— Is substituting for .what really happens,
what by the construction is not to happen. The demonstration
is therefore finally of tho same strength as Franceschini's and
others that have been mentioned. There is evidence of a per-
petual approach towards a given magnitude ; but there is not
evidence ot the degree and rapidity of approach whioh are
necessary to insure arriving at it.

24. Another demonstration, or step towards a demonstration,
presented by the same author (See Note 11. p. 279, 12&H4 idition\
consists in representing, that if any angle less than two right
angles is bisected, all perpendiculars to the bisecting straight
line must meet the sides, because otherwise there would be a
straight line shut up between the lines that make an angle,
which is repugnant to the nature of the straight line*" On which
it is sufficient to observe, that tho existence, cause, and origin of
this repugnance, are precisely what it was demanded to demon-
strate. ,

25. The next paragraph in the same page is directed to estab-
lishing the sort ot postulate assumed in the last, viz. that a straight
line cannot be shut up within an angle. The argument appears to
be, that either of the straight lines which make an angle, being
prolonged both ways, will divide, the infinite plane in which it
exists into equal parts, and any other straight line must do the
same; but a straight line that should be shut up [renfermee]
within the angle, without being able to escape from it by cutting
the sides in any direction however prolonged, would out off more
on one side and less on the other ; therefore a straight line can-
not be shut up within an angle. Whoever examines this clo5ely,'
will see that it would equally prove that two straight lines can-
not be parallel to one another ; for in that c.ise it might equally
he urged, that if the one divides the infinite plane into two equal
parts, the other must cut off more on one side and leas on the
other. The whole is consequently a mal-reasoning, arising from
overlooking Plato's observation (See Note to Prop. IV. ol -Book
J), that tonality of magnitude can only be predicated or things'
[finite.

2G. The next, in order is the so-called anafy&HLproof, which
professes to demonstrate that if two angles in One rectilinear
triangle are respectively equal to two in another, the remaining
angles are necessarily equal. If two angles of a triangle and the
side between them are g*ven. the rest of the sides and angles of
that individual triangle are determined ; that is to say, they cam
severally be onl** of one certain magnitude and no other. Hence,
said the advauuv/s of this demonstration, the angle opposite to
the given side is a. function of the two angles and the given side;
—their meaning by this term being, that a quantity is a function
of other quantities, when on those other quantities being fixed :
and determined in magnitude, the first quantity is necessarily

Lessons in geology.

813

fixed and determined in magnitude,* or is what Euclid in I
Book of Data would call given. *' Let the right angle be repre-
sented by unity or 1, and then the angles will all be numbe
somewhere between and 2 ; and since the third angle is a fun
tion of the two other angles and the side . between them, it will
follow that the side cannot enter as an element into the detenu
nation> of the magnitude of the angle." And this, they sai<
because the side is heterogeneous with the other quantities whk .
are numbers, and no equality can be compounded or made to
exist between them.f

LESSONS IN GEOLOGY.— No. L.

By Thos. W. Jbnxyn, D.D., F.R.G.S., F.G.S., &c.

CHAPTEB V.

ON THE CLASSIFICATION OF ROCKS.

SECTION IV.

ON TH* TBBTJJLRTBS.

Ths term " Textiaries,'* as applied to certain beds, has a reference
to the three grand divisions into which the foesiliferous rock
have been distributed by geologists. If you will consult thi
tabular view given in the commencement of this chapter, you
will find that, taken in an upward direction, all the rocks from
the Silurian to the Permian are called primary; that all the
rocks from the Trias to the Chalk are called secondary; and thai
all the beds between the Chalk and the Recent, or what I have
called Post Pleistocene are called tertiary.

The tertiary rocks are generally divided into three, or rather four
distinct groups, called, as viewed downward, the Pleistocene, the
Pleiocene, the Meiocene, and the Eocene. These terms were
introduced and invented by Sir Charles Lyell. The reasons of
this distribution are founded on the proportion which the fossil
shells of each group bear to the species now living. All the
recent rocks, called in our last lesson Post Pleistocene, might
have been called Anthroposoio, that is, human-life rocks, but for
the fact that their lower division contains fossils of all the existing
species of shells, without any remains or traces of the human race.
Sir Charles Lyell takes the fossils of this division of recent rocks
as his standard in grouping the other beds downward to the
chalk. All the different- beds downward to the chalk, contain
different proportions of the shells called present, modern, or
recent. The Greek word for recent or new is *cuvog, kainos, and
the feminine Kcuvn kainee. It has been the arbitrary custom of
English scholars to write the Greek at as a diphthong, thus ae, and
the cue Hence the uncouth word etene, now generally written
eene and pronounced teen. Hence, the .above names are pro-
nounced as if written Ply'-sto-seen, Ply'-o-seen, My'-o-seen,
E'-o-seen.

The beds which contain the greatest abundance of living or
recent shells., i.e. from 90 to 95 per cent., are called Pleistocene,
from wXaoToc, pleistos, most. The beds which contained some
smaller proportion than this, but more than the inferior beds, are
called Pl&ocene, from xXuwv, pUtin, more. The next underlying
beds, as they contain only from 35 to 60 per cent, are called
Mliocene, from funav, mewn, fewer or less. The lowest of these

•_ « toute quantity formes d'une manidre quelconque d'une autre
quantity."— Lagrange, TMorie dee Fonctions Analytiques.

f " II faut done que Tangle o soil sniiertment determine, lorsqu'on eon-
niit lea angle* a et b, avec le cdt* p ; ear, ii plusieurs angles o pouraient
eorretpoodre tux trois donnees a, b, p, 11 y aurait autant de triangles diffe-
rent* qui auraient un cOte" 6gal adjacent a deux angles 6gaux, ce qui est im-
possible : done Tangle c doit etre une fonetion determines des trois quantites
A, B, p ; oo que j'ex prime sintl, = ^: (a, b, p). H

•»8oit Tanfle droit Cgal k Tunite. alors les angles a, b, o, seront des nom-
bres compris autre et 2 ; et puisqae o = <f> : (a, b, j»), je dis que la ligne p
ne doit point entrer dsns la function A. En effet, on a vu que c doit etre
entierement determine* par If s seules donnee* a, b, p, sans autre angle ni
lign.- quelconque* main la llgnep est h6te>ogeue avec les nombres a, B, o;
at s- on arait une equation quelconque entre a, b, o, p, on en pourrait tirer
la vuleur dtp en a, b, o ; d'oil 11 retulteralt que p eat 6gal a un nombre, ce
qui est absurde : d#»ne p ne pent entrer dans la fonetion <p, et on a simple-
mento = *: (a, h). n —Legendre t JSUm. de Gloss. IStste Sdit, AoIm. p.
281.

The entire passage is inserted at the end of these notes in English, that
our stuaents way be able to judge for themselves of the merits of this con- 1
troYewy.

beds in which are only about 8 A per cent, of species identical with
the present, are called E'ocene, from ijwc, eeoe, dawn, as if in this
group we find the first indication or dawn of the existing species,
since no recent or present species have been discovered in any of
the secondary or the primary formations.

As the geological designations of these rocks are founded on
their respective proportions of fossils identical with the recent
fauna, you will perhaps find that the following summary
explanation of them will ai — - . .

learn the science.

answer every purpose in your efforts to

1. The Pleistocene [ tn08t reoent > or containing most of recent
I shells.

2. The Pleiocene i very fTft or hayin8 a ^S number of
^^ ( recent shells.

3. The Meiocene 1 ****** T^, k*™* a "^ P ro P or -

I tion of recent shells.

4 ThAT7'nPfin« / eomewhat recent, having some few indica-

4. ineJSocene t tions of the present race of shells.

These groups are ascertained partly by their lithological charac-
ter, and partly by their palaeontology, or their fossil contents.

\ 1. THE LITHOLOGICAL CHARACTER OF THE TERTIAR1E8.

The lithological character of a bed means the kind of material,
sandy, clayey, flinty, or limy ingredients of which the rook is
composed.

The upper group of the Tertiaries are called Pleistocene, and
ire thus divided into minor formations.

I. THE PLEISTOCENE.

1. The Boulder Formation, or Drift.

2. The Norwich Crag.

3. Cavern Deposits and Osseous Breccia.

4. Sicilian Limestone.

I. THE BOULDER FORMATION, OR DRIFT.

The drift, or boulder formation, Las been described in a preced-
ag lesson as being found associated with freshwater strata and
marine beds, and as having been formed about the close of the
pleistocene period. The mineral ingredients of this formation
exhibit every where a confused mixture of the ruins of adjacent
lands, and an immense number of stones, some angular and rugged,
Others rounded and smoothed, and brought to their present posi-
tion from very remote districts, by the agency of icebergs. In
tie Eastern counties of England, this formation supplies speci-
mens of almost every known rock. It extends from Scotland as
Jar south as to Muswell Hill, near London, and no trace of it is
fbund farther south. The best place to study it in England, is in
tie cliffs of the Norfolk coast, where it presents a section from 50
to 70 feet high, and about 20 miles in length. In that section
ft consists of clay, loam, and sand, partly stratified and partly un-
ratified., It contains pebbles and boulders) of porphyry, green-
stone, lias and chalk. These are found everywhere interspersed,
but especially in the Till.
Your attention has already been directed to the vast extent of
lis formation in North* America, and in the northern parts of
Bussia and Germany, and also to the Alps as another centre from
Which these erratic blocks have been carried by icebergs. Tou
And the same to be the case in your own oountry, as instanced in
the mountains of Galloway, Cumberland and North Wales.

Though the drift is, comparatively, a most recent formation,
you are not to expect to find it always resting on some other
tertiary strata. In many places, and especially in Scotland, it is
>und to rest immediately on some of the older rocks, and is
covered by stratified beds of sand and clay which are usually
without any fossils. Such a position is represented by the
diagram, fig. 1, page 263, where a represents the ancient rock, and
d t c, by various beds of the tertiaries.

II. THE NORWICH CRAG.
On each side of the river Tare, within five miles of the city of
orwich, are seen beds of sand, loam and gravel, which are call*
by the country people crag, or gravel. These beds abound wu •
the shells of animals, marine, freshwater, and land. The strr
have every appearance of having accumulated at the botto *■
lie sea near the mouth of a large river. This formation is ( • ,
in patches of different thickness, and covered with a deneu + r

«4

THE POPULAR EDUCATOR.

of stratified flinty grave), and retting on the chalk. In the sea
olifla, near Thorpe and Southwold, Suffolk, this aaa and riTer
formation is exposed in good and clear sections, where H c ons i s t s
of sand, shingle, loam, and laminated clay. Some of the strata
appear to have been deposited in tranquil waters.

*»«• ^«, ^^

III.

CAVERN DEPOSITS AXD O8SEOU8 OB BONY
CONCRETIONS.

When rounded pebbles and gravel are cemented together into a
hard atone, the man ia called a conglomerate, and aometimes,
plum-pudding stone; but when such a cemented mass is oompoeed
of angular and unworn fragments of rock and other materials, it
is called, from the Italian, Breccia,

In mountainous districts, many fissures are found, into which
animals seem to haye fallen from time to time, or into which they
have been washed by floods. These animal remains are frequently
found covered with alluvial matter and with fragments of rocks
which have been detached by frost. The whole mass is then
formed, by stalactite infiltration, into what is called a bony or
osseous breccia.

Limestone hills often abound with a aeries of caverns with low
and narrow parages from one suite to another, which hold a
tortuous coune through the interior of the mountain. These
caverns and passages seem to have served, at some early period,
•s the subterranean channels of springs and rivers. In the ter-

tiary period, these channels had become and remained open fox
ths tamos and shelters of animals which perished and Ian their,

bones there. The preservation of such bones ia due to the i
but constant supply of stalactite nutter brought into Uss eavessjs
by water infiltrating from the roof.

Cavern breccias are found in every part of the world, but at
San Giro, in 8icUy, there ia one of great interest It is about 20
feet high, 10 wide, and 180 above' the sea. Within it there is an
ancient se a-b ea ch formed of pebbles of different rocks brought
thither faun very distant plaoes. $rojj«n corals end sheila mingle
with the pebbles. Under a mass of bxeocia w^re found an
immense quantity of bones of the mammoth, ftc, in a dark
brown calcareous marl, and many of the bones were worn as if
rounded by the action of the waves. This bed of breccia is about
20 feet thick, and under it is a bed of sand filled with sea sheik of *
recent species.

IY. SICILIAN LIMESTONE.

In 8icily the Pleistocene, tertiariea enter largely into the struc-
ture of rocks, covering- nearly one half of the island, and in the
centre forming hills which rise 2,000 feet ahoy* the level of the
sea. The structure and arrangement of these beds are best
developed at Oirgenti, Syracuse, and Oastrogiovanni.

The Sicilian beds consist of two divisions.

The upper division is calcareous or limy, and conaiata of a
yellowish white stone in some places, ana in others of a rook'
nearly as compact aa marble. The beds are usually regular and
horixontal, and their thickness are from 700 to 800 feet.

The lower division is clayey, or argillaoeoua, and pass down-
wards into a sandstone, and conglomerates ^ below whieh there
are again clay and bine marls, abounding in perfect shells and
corals.

In the south plains of Catania these pleistocene beds are inter-
mixed with volcanic matter, which must have been thrown up
while the rock was forming at the bottom of the sea, and while
the day, sand, and yellow limestone were in the course of 1
deposited. All these Sicilian rocks belong probably to the i
period aa the Norwich crag.

II. THE PLIOCENE.

1. The Suffolk Crag.

2. Tne Subapennine Bods.

I. THE SUFFOLK OKAG.

The Pleiocene roclpi are confined chiefly to the eastern parti
of the county of Suffolk, where these beds like those of a later
class in Norfolk, are called crag. This rock Js a mass of shelly
sand, which ia much used in agriculture. The shells imbeooel
in it, indicate that the bed was formed in a sea of moderate depth,
in most places from 15 to 25 fathoms, but in some narte deeper,
and at the distance of about 40 or 50 miles from any land.

The natural group of the Suffolk Crag 'series la divided by
Mr. Charlesworth into three subdivisions, which, in the down-
ward order, are thus designated.

1. Tun Makmalifkrocs Ckag ; which ia a sandy loam and
clay formed by sea and river water, and charged with, shelly
detritus. It occurs about South wojd in Suffolk, and Cromer in
Norfolk. It contains the t^etb. apd bones of several aKtinct
mammalia, or animals that suckle their young.

2. Tus Bed Csao ; which is so. called from its deep ferrugk
nous or irony colour. It consists principally of quartsose sua
and comminuted shells and oorak, and ia about 40 feet thick.

3. Tub Coralline Cbag ; which ia a aeries of caujawons %
marly strata of loose white sands, layers of shells and confcv I
ooncretionaxy bands of stone. It is of very Kmfted extent, aboujb
20 miles in length, and three ox four in, breadth, covering t
district in Suffolk between the rivers Aids and Skonr. A\ 9&fc
bourn, near Orford, in this county, there is s large quarry m thai
ipr mat^p fu rnishin g a spffc bui ld i n g stone. Cdl some pwoesu tka
softer mass is divided into thin flags of hard limestone, fiyyuvi
fossil corals in the upright position which they essnnted in that*
growth*

Where the red end the coralline crags are mat together in tips
same district, the red always lies uppermost, and both lis on the
IiOndon clay. In, some, sections, tjhe coralline bed seems to have
Buffered denudation before the red crag bad been deposited on it
The red crag is distinguished by its deep ochqaong, ox yellow
e/)V)ur ths rrralline by its ^hto-wbrcred sands.

ipSBOHS IN GBQLO0Y.

•W

II. THE SUBAPENNINE BED8.

^he A'pejinines, composed chiefly of secondary limestone,, are a
chain of hills which commence at the base of thp Liffurian Alps and
extend through the whole length of Italy. At the foot of these
mountains and on each aide ox them, is found a series of tertiary
strata which forms a line of low hills between the central ridge of
mountains and the Adriatic on the east aide, ana the Mediterra-
nean on the west.

The strata of these low subapennine hills consist generally of
light-brown or blue marl, covered by a yellow calcareous sand
and gravel, imbedding fossil shells. The marl is very aluminous,
containing much calcareous matter and scales of mica. Near
Parma it attains a height of about 2,000 feet, abounding in marine
shells. Near Sienna, the yellow sand conglomerate rests imme-
diately on the Apennine limestone, and at St. Vignone (pro-
nounced Vinion) it passes into a calcareous sandstone. As this
yellow sand formation is superimposed upon the marl, it repre-
sents the deltas of rivers and torrents which gained upon the bed
of the sea where the blue marl had been previously deposited.

Geologists now acknowledge that all the subapennine tertiariee
do not belong to the same period. The beds indicate three dis-
tinct geological eras.

1. The beds of Piedmont, e.g. at Superga, are lieiocene.

2. The beds of North Italy, Tuscany, and the Seven Hills of
2}ome, are Pleiocene.

3. The Tufaceous formations about Naples, Iacnia, &c., axe
Pleistocene, and Post Pleistocene.

III. THE MEIOCBNE.

1. The Faluns of Touraine.

2. Part of Bourdeaux.

3. Part of the Molasse of Switzerland.

I. THE FALUNS OF TOURAINE.

In French Brittany, near Dinan and Rennes, and also in the
provinces bordering on the river Loire, there is a tertiary forma-
tion called by the peasantry Faluns (faloons). It consists of shelly
sand and marl, and is used for agricultural purposes. Some of the
shells and corals are entire, some are' rolled, and others are in
comminuted fragments. In some places, as at Dou6, near Saumur,
these sands and marls form a soft building stone, which is com-
posed of broken shells united by a calcareous cement, and which
looks much like a mass of the coralline crag in Suffolk.

This formation exists in scattered patches of slight thickness,
and very rarely exceeding 60 feet in depth. They are frequently
found to rest on a grea> variety of older rocks, such as gneiss and
clay slate. In other districts, as between the Seine and the Loire,
they repose upon the upper freshwater limestone of the Parisian
tertiaries. At some points south of Tours, the shells are stained
a ferruginous colour, like those of the red crag in Suffolk.

The fossil shells indicate that these Faluns were formed partly
on the shore itself at the level of low water, and partly at very
moderate depths, not exceeding ten fathoms below that level.

II. FART OF THE BOURDEAUX BED3.

Immense deposits of tertiary rocks are found in the country
which lies between the Pyrenees and the Gironde river. Seven
hundred species of shells have been found in these beds, and they
all indicate that this division of the Meiocene strata is older than
the Faluns of Touraine.

III. THE MOLA8SE OF SWITZERLAND.

In Savoy we find, at the northern base of the great chain of
the Alps, and throughout the lower country of Switzerland, a
soft green sandstone, which is probably one of the oldest lieiocene
groups hitherto discovered. It is associated with marls and con-
glomerates and is called " molasse/' derived from "mol," *°fi> as
the stone is easily cut in the quarry. It is of very great thickness,
and might perhaps be divided into several formations.

No rocks of the Meiocene period are found in England.

IV. THE EOCENE.

The Eocene group of rocks is divided by Sir Charles Lyell intc
three subdivisions, which he calls the Upper, the Middle, and the
Lower Eocene.

I. THE UPPER EOCENE*

1. Upper freshwater limestone, marls and siliceous mill-
stone.

2. Upper marine sands or Fontaincbleau sandstone.

II. THE MIDDLE EOCENE.

1. Lower freshwater limestone and marl, or the gypseous
series.

2. Sandstones and sand with marine shells.

3. Limestone with marine shells, or Calcaire grossier.

4. Hard, flinty, fresh water limestone, or Calcaire siliceaux.

III. THE LOWER EOCENE.

1 . Lower sands with marine shelly beds.

2. Do. with lignite and plastic clay.

i. The Upper Eocene is represented in the upper marine
>eds of Paris, the Fontainebleau sandstone and millstone, the
fUeyn Spawen beds, the Berlin tile clay, the tertiary strata about
Mayence, and the freshwater formations in Auvergne.

1. The freshwater marls and limestones of Paris seem to have
>een formed in marshes and shallow lakes. Some of the siliceous
roefcs of this formation are used for millstones.

i. The upper marine sands consist of marls, micaceous and
martzose sand, with beds of sandstone abounding in marine
ihells.

The Upper Eocene is not found in England.

li. Tub Middle Eocene is represented by the Paris gypsum,
the beds of Headon Hill in the Isle of Wight, the Barton beds,
ind the Bag&hot and Bracklesham sands.

' Near Paris we find, below the upper marine sands, a series of
■white and green marls, with beds <:f gypsum lying under them,
which are best developed at Montmartre, where its fossils were
first discovered by Cuvieb. The gypsum is quarried for the
manufacture of the plaster of Paris.

• In England, the Middle Eocene is developed in various
instances.

* 1. In Headon Hill, in the Isle of Wight, we find beds of marl,
play, sand, and a friable limestone containing freshwater shells.
These beds are seen in the sea cliffs, where some of the strata con*
tain a few marine and estuary shells.

2. In the cliffs of Barton, the pure white sand without fossils,
on which the freshwater series of Headon Hill rested, is found to
repose on a marine deposit, in which 209 species of shells have
Veen found. This is the newest purely marine bed of the Eocone
series known in England.

3. The Bagshot sands consist chiefly of siliceo'ts sand found
about Bagshot and in the New Forest. They may bs divided into
three beds, the upper and lower being of light yellc w sands, and
the middle of dark green sands and brown clays, al 1 reposing on
the London clay.

4. At Bracklesham near Chichester, there is a bay, bounded by
a low cliff of blue clay and green sand, full of fossil shells ana
teeth.

The lower Bagshot sands have supplied the boulders of sand-
stones which are frequently found in some of the chalk valleys*
and which are called Sarsden stones, and Druid sandstone, as may
be seen at Stonehenge in Wiltshire, and Kitt Kotty near Maid-
stone in Kent.

in. The Lower Eocene consists of the London clay, the
Sables (sab-16) of the Paris basin, the mottled and plastic clays
| of Hampshire and London, and the nummulites of the Alps.

In the Paris basin, just below the Calcaire grossier, are exten-
sive deposits of sand, having in the upper portion some marine
beds called 44 lits coquilliers," in which 200 species of shells have
been found. At the very base of the tertiary system in France,
are beds of sands and plastic clay abounding with fossil oysters.
Xa the lower clays and sands layers of lignite are found.

1. The London Clay consists of a tenacious brown and bluish-
gray clay, with layers of concretions called Septaria, which are
employed in manufacturing Roman cement. The best places to
study this bed are flighgate near London, the Isle of Sheppey
in Kent, and Bognor m Sussex.

2. Mottled or Plastio Clays are accumulations of sand, pebbles,
and mottled days. They are well developed in some of the rail-
way cuttings about Beading, in Berkshire ; in different parts of
Hampshire ; and especially about BLackheath and Woolwich. In

1 many places it appears to be a mixture accumulated by the oom-
i bined action of river and sea-water. At Poole, in Dorsetshire,
I {hit day is used far pottery % and hence the tem « nltrtw elaT, 1 *

316

THE POPULAR EDUCATOR.

3. The Nummulite of the Alps and Pyrenees. This ia a cal-
careous rock, consisting often of a compact crystalline limestone,
full of nummulites or shells of the class Foraminifera, or ex-
tremely diminutive forms of shelly animals. As these fossils are
. very much like pieces of coin, and as nummus is th« Latin for
coin, and nummulae, is little coin, this rock is called Nummulite.
In the Alps this rock is of great thickness. In many parts of
Euiope, Asia, and Africa, this group forms a very large part of
the Tertiary formations. It ia found in Algeria and Morocco ; in
the Carpathian Mountains ; in the districts between Egypt and
Asia Minor ; and between Persia and India.

FRENCH READING S.— No. III.
LE SAPEUR DE DIX ANS.
Section VI.
Le pauvre march and voulut fairo entendre 11 raison 1 a**
petit Bilboquet, mais il etait entete comme un cheval aveu-
ifle,'- et il s'engagea b une dispute qui attira bientot quelques
soldats. lis entrerent pour s'informer du motif do la que-
rclle, et ils trouverent l'ideo du tambour si drole, 3 qu'ils
obligercnt le pauvre Juif a lui ceder sa barbe,* et Tun
(Vcux, Gascon et perruquicr du regiment, tira des rasoirs de
sa poche, so mit c a rascr le malheureux marehand 5 et
remit d solennellement la toute a Bilboquet qui remporta"
en triomphe. 6 En arrivant au regiment, il la fit f coudro
par le taQleur sur un morceau dc peau d'un tambour creve, 7
et sans rien dire dc son dessein, il la mit au fond de son
sac. 8 On en causa* pendant quelques jours, 9 mais il fallut h
bientot penser a autre chose. On se remit en l marche, et on ne
pensait plus au petit Bilboquet, quand on arriva a Moseou.

Alois il arriva J d'aflreux malheurs, le froid et la devas-
tation privercnt Tannee francaise de toutes ses ressources, 10
la famiiiu ratteignit, k et bientot il fallut se retirer a travers
nn pavs desert et des nciges sans fin. 11 Je no veux pas
vuus faire un tableau dc eet horrible desastre ; e'est une
chose trop vasto et trop epouvantablc l - a la fois, pour que
je vous en parlc dans eette liistoire : qu'il l vous suffi.se m de
navoir que chaeun s'en retournait comme il pouvait, 13 et
que e'est a peine s'il n rcstait quelques regiments reunis en
corps d'armee et obeissant ° aux geueraux. Celui de Bil-
boquet etait de ce nombre. II etait de Farriere-garde, 14 qui
einpeehait des milliers dc Cosaques, qui suivaient la retraite
de l'arm6e, 13 dc massacrer les malUeureux soldats isoles.

Un jour, ils veuaient de p franchir une petite riviere, et,
pour retarder la poursuite des ennemis, on avait cssaye de
faire sauter * deux arches d'uu pont de bois qu'on venait do
traverser ; 16 mais les tonneaux de poudre avaient ete poses
si precipitamment, 17 que l'explosion ne produisit r que peu
d'eflet : les arches furent cependant demantibuldes, mais
toute la charpente appuyait encore sur une grossc poutre
qui la" retcnait, 1 * et qui, si les ennemis fussent arrives, cut
bientot permis de recoiistruire le pout. 19

Colloquial Exercise.

Notes and References. — of. Fairo entendre raison an petit
B., induce little B. to listen to reason; L. S. 96, R. 4. — *. il
s'engagea une dispute, an altercation commenced; the verb is uni-
personal. — c. from se tnettre ; L. 8. 68, R. 3, also part iL, p. 96.
—d. remit, delivered; from remettre ; L. part ii., p. 102.— e. L.
S. 43, R. 6.—/. fit coudre, had it sewed; L. S. 31, R. 3.—^.
causa, talked, spoke. — h from falloir ; L. part ii., p. 92. — i. on

so remit en marche, the march was resumed; L. 8. 34, R. 1, 2.

j. the verb is unipersonaL— k. from atteindre; L. part ii. f p. 78.
— /. qu'il, let it.—m, from suffire ; L. part ii., p. 106. — n. sMl
restait, if there remained ; the verb is unipersonal ; L. S. 84, R»
4.—o. L. 8. 77, R. 2.— p. L. 8. 25, R 2.—q. fairo sauter, Horn
up. — r. from produire; L. part iL, p. 100. — «. la retenait, sup-
ported it.

1. Le marehand chcrcha-t-il a
lo dissuader ?

2. Pourquoi ne put-il lui fairo
entendre raison ?

3. Comment les soldats trou-
verent-ils l'idec du tambour ?

4. Que firent-ils ?

5. Que fit lo perruquier du re-
giment?

. 6. Le tambour parut-il content
de sa prise V

7. Que fit-il dc cette barbo en
arrivant ?

8. Ou la pla^a-t-il ensuito P

9. Parla-t-on longtemps de
oetto oventurc ?

10. Qu'arriva-t-il a l'armeo fran-
caise apres son entree a
MosoouP

11. Quo fut-ellc bientot obligee
dc faire ?

12. Pourquoi l'auteur ne veut-il
point faire le tableau de eet
horrible desastre ?

13. Qua 8ufHt-il de savoir ?

14. Ou bc trouvait le regiment
de Bilboquet P

15. Que faisaient les Cosaques?

16. Qu'avait-on essayo de faire
apres avoir passe" la riviere P

17. Pourquoi l'explosion n'a-
vait-elle pas eu beaucoup
d'etiect?

18. Pourquoi la charpente du
pont no toinbait-elie pas ?

19. Qu'est-oo que les ennemis
auraient pu faire, s'ils etaient
arrives?

ANSWERS TO CORRESPONDENTS.

Oioroi Isaac E. (Nottingham) : The Italian language has no natal
•oanris, and each rowel keeps iti alphabetical sound irrespective of any
consonant that may follow; e. g. in the words tempo, Une; sento, I feel;
mento, chin, the consonants m and n hare no influence whatever on the
pronunciation of the rowel e, such as they hare in French on the pronuncia-
tion of each vowel preceding them. The combination gn, pronounced as in
Pre- ch, is the only exception, and approaches a nasal sound. This consti-
tute* an important difference between the two languages, French being to
a great extent a nasal language, and Italian a language spoken from the
chest. A great many examples in the first ten lessons, exclusively devoted
to the explanation of the principles and mechanism of Italian pronunciation,
have clearly illustrated this. The best Italian translation of the Bible, for
Protestant readers, is bv Giovanni Diodati. The M Society for Promoting
Christian Knowledge," 67,Lincoln's>inn-rlelds,and the'* British and Foreign
Bible Society,** Karl-street, New Bridge-street, Blaekfrlars, have both pub-
lished this translation. The price varies from 3a. 8d.,4*. 8d. t &c., according to
the binding, and it may be had at the above-stated premises in Lincoln's-inn-
Field«, or at Bag*ter's, Paternoster-row. With regard to the Italian
Dictionary, we roust refer you to former remarks, and only beg to repeat
that the anbject will be duly considered.

Anna Prinqlb (Ferry Hill): She must try and beat the boys in the Four
Hall question ; neither they nor she have mastered it yet. 8he is very
right about fractional questions and solutions ; we are proud of her corres-
pondence.— K. Phillips (Mac hen): We are sorry that we can't give our
correspondent the information he requires.

T. O. L : The result will be most conveniently illustrated by regarding
the solution a* hydrochlorate of protoxide of tin : to which solution nitric
acid being added, the latter becomes decomposed, — yields oxygen to the
protoxide of tin, and converts it into peroxide. One portion of this peroxide
is precipitated, leaving an excess of hydrochloric acid to combine with the
rest. Thus the h>drochlorate of peroxide of tin results.

A. C. Hillary: Probably the metal was not In the state of fine powder,
or the acid employed was not sufficiently strong.

E. Williams: The result of such distillation would not be simply one
chemical product, but many very complex products, whose lnvestlgaUon
would belong to the higher departments of organic chemistry.

D. B. C. (Hartlepool) : We do not answer some questions for fearof giving
offence to some readers, especially when they refer to religions worship.
—J. D. (Newcastle): High Dutch is German.— O. W. B. (Walnut-tree
Walk) : The ch in archbishop is pronounced like ch in church.— Mathetu
The Greek uptilon is generally replaced by m in English ; as in ev*. with;
and in <rKi/0nt. scythes, a Scythian.— H. Watkins (Wolverhampton): The
astronomical day begins at the noon of one day, and terminates at the noon
of the next day. The civil day varies in different nations; with ourselves
it begins at midnight of one day, and terminates at midnight of the next day.
— G. H. H. (Hasllngden): Bee our answer to R. 8. 8. (Glasgow).— A Poor
Studknt will get solutions of his questions in any treatise on Trigonometry.
—Don Quijotb (Grahamston): We don't know any Spanish Dictionary
about 8s. or 10s. that we can recommend.— B. H. (Bristol): See page 79,
vol. iii. P. E., where the rule is that things without life are neuter. Now
heart said hand apart from the body are without life, and therefore strictly
neuter. But by poetic gender, as it is called, sex may be attributed to these
nouns : in that case, toe should call the heart feminine, and the hand oaaseu-
line, that Is, if we were writing poetry.— Hopeful: Very well, go on.—
Socius (Liverpool) should have had an answer if his address had been
given.

Youno Whitebrbad wishes to know the proportion in which liquor
potasse must be added to sugar of lead in order to produce the potash eola-
tion of oxide of lead so useful as a test for sulphur.

A slight amount of consideration will prove to our correspondent that the
proportion will altogether depend on the strength of the liquor i
of the lead solution. The best plan of procedure consists in <

weighed or measured proportions, and adding liquor potaesss to
solution until the desired result is accomplished. Thus, having taken

solution of acetate of lead (sugar of lead), or still better,solution c
of lead (Goulard's extract), add to It by small quantities at a time liquor
potaatat until all the oxide of lead is precipitated. Then continue to add
more until nearly, but not quite, all this precipitate is redissolved. By thus
leaving a little oxide of lead, the operator is assured that liquor potaissi has
not been added in excess.

G. H. Balding (Hastings) wishes to know how to make crucibles for
chemical experiments. He is not sufficiently precise. What sort or
crucibles ? and what kind of experiments ? The crucible adapted for one
use is totally unfitted for others. The chemist employs crucibles of day-
ware, German porcelain, blacklead-ware, iron, silver, platinum, and, os-
casionally, gold ; but he does not prepare those crucibles himself ; tney ejf
the manufacture of various trades.

LESSONS IN PHYSICS.

317

ON PHYSICS, OR NATURAL PHILOSOPHY.
No. XXII.

[Continued from page 304.)
PNEUMATIC AND HYDRAULIC MACHINES.

The Condenser, — The condenser is an apparatus which is em-
ployed to condense air or any other gas. As its form differs
but little from that of the air-pump, with the exception of the
valves, it will be sufficient to give here a longitudinal section
of this machine, in order to show the action of the valves,
which open downwards, whereas in the air-pump they open
upwards. These valves, of which the one is represented at a
in the bottom of the piston, and the other at o in the bottom
of the barrel, fig. 103, are conical, and are kept shut by a

Fig. 103.

* K

r A

coiled spring. When the piston p is raised, the air is rarefied
below it, the valve o is kept shut by the spring, and the valve
a opens by the pressure of the atmosphere, which permits the
exterior air to enter the barrel. When the piston is lowered,
the air which is below it is compressed, the valve a is shut,
whilst the valve o is opened and admits .the compressed air,
which is transmitted to the receiver b. At every stroke of the
piston, the mass of air contained in the barrel is passed into
the receiver* Yet there is a limit to the tension of the con-
densed air ; for during the condensation, a period will arrive
when the elastic force of the air in the barrel, even when the
piston is at the bottom, is no longer equal to that of the air in
the receiver, and then no more air will pass into the latter,
because the valves will remain shut, in consequence of the
pressure of the interior air.

In the condenser, the tension of the air is measured by means
of a small manometer of compressed air communicating with
the receiver. In this machine, the receiver must be strongly
fastened to the platen, otherwise it would be driven off by the
elastic force of the condensed air. For this purpose, the re-
ceiver is constructed of a strong glass cylindric vessel open at
both ends, and having its edges well ground and well greased.
The lower edge rests on the platen a, and the upper edge is
shut by a strong glass plate b, perforated at equal distances by
four holes, through which pass four iron rods d, fastened to
the platen. By means of these rods and the screws b, the
glass plate B is firmly fixed to the cylinder, and the whole to
the platen. In order to prevent accidents by the breaking of
the cylinder, in consequence of the pressure of the condensed
air or gas, it is surrounded by an iron grating. This machine
has few practical applications ; but under the following form
it is of very frequent use.

Condensing Syringe, — The condensing syringe is a kind of
forcing pump, composed of a single barrel, a, fig. 104, of
small diameter, in which a solid piston (that is, a piston with-
out valves) is made to work by the operation of the hand.
The barrel is furnished with a screw by which it can be
fastened to the vessel in which the air or any gas is to be con-
densed. Fig. 104 represents the condensing syringe a c,
with a handle for working it, and screwed, to a vessel x, in
which the air is to be condensed. Fig. 105 shows the arrange-
ment of the valves, which are constructed so that the side
valve o open* inwardly, and the bottom valve s opens out-

TOL. IT.

wardly. These valves are kept shut by small coiled springs.
The action of the valves is the same as that of the valves in
the condenser; and as in the latter there is a limit to the
condensation, so there is the same limit in the condensing
syringe. This limit depends on the ratio which exists between
the two volumes of air included under the piston, when it is
at the top or at the bottom of the barrel. If the volume of
air, when the piston is at the bottom of the barrel, be one-
sixtieth part of the volume of air when it is at the top of the
barrel, we can only condense the air up to 60 atmospheres ;

Fig. 105.

Fig. 104.

for beyond that pressure, the tension of the air in the receiver
x would be greater than that of the air in the barrel, and
then the bottom valve would not open to give admission to an
additional quantity of air.

Condensed Air Fountain. — The condensed air fountain is re-
presented in fig. 104. It is composed of a brass cylinder x,
furnished at the top with a tube and stop* cock c, upon which
the condensing syringe is screwed. A tube n, open at both
ends, projects to the bottom of the cylinder, or reservoir k.
A quantity of water is put into this reservoir, the stop-cock
c is opened, and the condensing syringe a is put in opera-
tion. The condensed air enters the reservoir by the tube h,
and presses on the upper surface of the water. If then the
stop-cock c be shut, and the syringe A be unscrewed, and,
instead of it, a tube or ajutage be fastened to the tube h, the
water will instantly issue vertically, like a spring or fountain,
as soon as the stop-cock c is opened.

The apparatus in fig. 104 is also employed in the absorption
of gases by water. To effect this, the stop-cock b, by means
of the tube d, is made to communicate with the vessel full of
gas which is to be absorbed, as, for instance, carbonic acid.
The condensing syringe draws the gas from the vessel and
condenses it in the reservoir x, where it is absorbed ; and tho
quantity thus absorbed increases, as before observed, in pro-
portion to the degree of condensation to which the gas is sub-
jected. By the application of a similar apparatus, aerated or
gaseous waters are manufactured.

The Air-gun: — This instrument is a gun in which the ex-
pansive force of condensed air forms a substitute for that of
the gas produced by the ignition of gunpowder On the
stock, which is hollow and made of wrought-iron, is screwed
a force-pump, by means of which the stock may be filled with
air of 10 or 15 atmospheres of pressure. A projectile bein,
placed in the usual manner in the barrel, a valve comiw

100

818

THE POPULAR EDUCATOR.

eating with the stock and the barrel, is opened by means of a
trigger, and the air escaping from the former with great force,
the projectile is discharged from the latter. The valve closing
immediately that this is done, the air contained in the stock still
possesses a very considerable elastio force, and several balls
can be discharged without the introduction of a fresh quantity
of air.

The Fountain of Btro, — A variety of hydraulic machines
have in modern times been constructed on the principle of
Hero's fountain ; such as the Hungarian machine employed
for raising water from the mines of Schemmtz, the machine of
Detrouville, the mechanism of Girard's lamps, &c. It is re-
presented in fig. 106, No. 1, and is composed of three vessels ; an

Fig. 106. No.l.

Fig. 106. No. 2.

upper vessel a, a middle vessel b % and a lower vessel c. These
vessels are connected by three tubes : the first, x, descends
from the bottom of the upper vessel, nearly to the bottom of
the lower vessel; the second, y, rises from the top of the
lower vessel nearly to the top of the middle vessel ; and the
third, s, rises nearly from the bottom of the middle vessel, and
terminates in a jet a little above the upper vessel. The opera-
tion is as follows : — Water is put into the vessel b, by means
of the stop-cock p, it is then closed ; water is also put into the
vessel a ; the stop-cock r in. the tube x is then opened, and the
water rushes from the upper vessel into the lower one ; in this
vessel the water is immediately acted on by the compression of
the air which it contains, and is forced up the tube y into the
vessel b ; here the water is again acted on by the compression
of the air which this vessel contains, and is forced up the tube
s, through the jet, into the atmosphere, rising to a height
above the upper vessel, which, theoretically speaking, is as
much aljove the level of the water in the middle vessel as the
level of the water in the upper vessel is above the level of the
water in the lower vessel. The reason is that the air which is
contained in the lower vessel, and in the middle one, supports
a pressure determined by a height of water equal to the differ-
ence between the two levels of the water in the upper and
lower vessels ; the water contained in the middle vessel must
therefore rise in the tube s, to the height due to this pressure.

For the purpose of lecture-room illustration, the following
representation of this fountain will be better understood, as seen

in fig. 106, No. 2. In this figure d is a brass cup or Teasel, and x
and n are two glass globes about four or five inches in diame-
ter ; b is the long brass tube connecting the cup d with the
lower part of the globe n ; 4 is the tube connecting the upper
portions of the two globes x and n. Between these two tubes
is seen a third, connecting the lower part of the globe m with
the atmosphere above the level of the water in d ; but this tube
is, in this construction, withdrawn, in order to admit of the
pouring of water into the globe x, until it be half-fall. This
being done, the tube is replaced, and water is poured" into the
cup or cistern. This water descends by the tube b, into the
lower globe, and drives the air out of it ; this air is condensed
in the upper globe, where it acts upon the water and causes it
to spring up, as in the diagram. Abstracting the resistance
of the air and friction, the water should rise above the cup to
a height equal to the difference of the level of {he water in the
two globes.

The Intermittent Fountain.— The models of the intermittent
fountain exhibited in our lecture-rooms explain in a plausible
manner the causes of intermittent springs. The upper part of
this apparatus', fig. 107, No. 1, is a close vessel or reservoir.

Fig. Va. No.l.

Fig. 107. No. S.

filled with water up to the level ab. A vertical tuba T
into this vessel from below, has its upper orifice open, anJ
raised above the level of the liquid ab t and its lower orifice at
c is also open. The bottom-piece of the apparatus it double,
and the orifice t allows the water which falls on ' the first
bottom to escape into the second, a b. with leas velocity than
it falls from the ajutages, c, *,/, d. The flow of water from
the upper vessel or reservoir continues untU the crater, by its
accumulation, closes up the orifice, at c, of the vertical tube,
and the pressure on at becomes less than the pressure of the
atmosphere. This flow begins again after the qiseharm of a
sufficient quantity of water has tajten place at tlffi orifice t;
and it continues until it is again interrupted in the fftqp man-
ner ss before ; and so on.

This apparatus is, perhaps, more vividly shown fn fig, 107,
No. 2, where the upper reservoir for the water is a dees •&*•
or pear-shaped vessel, made air-tight by a grouna Stopper,
and having two or three short capillary tubes, p, through
which the water runs, a is a strong glass-tube, open at both
ends, which is inserted in the globe 0, having on* end raised
above the water-level in the globe, and the other terminatinr
near the central orifice in the brass basin or stand b, which
supports the apparatus. Here, the globe being about two-
thirds full of water, this liquid issues from the orifice », At

LESSONS IN PHYSICS.

319

interior pressure or the surface being equal to the sum of that
of the atmosphere which is transmitted through the tube a,
an4 that of the column of water above o ; whilst the exterior
pressure is only that of the atmosphere, Theae circumstances
continue so long as the lower end of the tube is open, that is,
so long as the tension of the interior air is equal to that of the
ajmosphere, for the air is admitted into the globe in propor-
tion, as the water runs off. But the apparatus being adjusted
so that the orifice in the basin or stand b allows less water to
escape than that delivered by the orifices d, the level rises by
degrees in the basin, and ultimately covers the lower aperture
of the tube. The exterior air no longer obtaining admittance
into the globe o, the air within it is rarefied in proportion as
the water continues to flow, until the sum of the pressures
of the column of water od and of the tension of the air above
it, is equal to the exterior pressure of the atmosphere at d ;
then the flow of the water is stopt ; but the basin continuing
to empty itself, the extremity of the tube is again uncovered,
and the air entering as before, the flow recommences ; and the
same process is repeated until there be no water left in the
globe o.

The Siphon. — The siphon is a bent tube having two unequal
branches used for drawing off liquids, as in fig. 108, No. 1 ;

Fig. 108, No. 1,

Fig. 106, No. 2.

and when in action, the hend is uppermost. In order to make
use of this instrument, it is first inverted, and the shorter
branch being kept closed, it is filled to the top of the longer
branch with the liquid to be drawn off. This branch is then
closed, and the instrument being restored to its right position,
the shorter branch is inserted in the vessel containing the
liquid, and the longer in the vessel to be filled; both ends
being then opened, the liquid will flow from the one vessel
into the other tin tit the level of the liquid be the same in both.
Another mode of putting the instrument in operation, is to
insert the shorter o ranch into the liquid at c, as in fig. 108,
No. 2, and with the mouth to c)raw out the air contained in
the tube at the orifice a of the longer branch. This being
4one 4 vacuum is formed, arid the liquid in the vessel o rises
in the tube by the pressure of the atmosphere, fills it, and
continues to flow as before. When the liquid is unfit to
touch the mouth, a siphon is used, to which is soldered a
second tube m, as in fig. 109, parallel to the longer branch.
The ajr is withdrawn from the siphon by the orifice o of this
Additional tube, the orifice p of the siphon betas kept shut
only until the liquid reaches it ; otherwise the liquid might
rise to the mouth in the additional tube.

In order to understand how the flow of the liquid takes
place, let it be observed that the force which presses on the
liquid at o, in fig. 108, No. 2, and draws it in the direction
C d b, is that of the pressure of the atmosphere, minus that of a
column ox water whose height is c d. Also, the force which
presses on the liquid at b and urges it in the direction room
the pressure of the atmosphere, minus that of the weight of a
column of water whose height is a b. Now the latter column
being greater than the former, it follows that the effective force
which acts at b is less than that which acts at c. The flow
then takes place in consequence of the difference of these
forces. Consequently, according to the theorem of Torricelli,

the velocity of the flow will be greater or less in proportion to
the difference of level between the orifice b and the surface of
the liquid at o. From this, it is evident, that the siphon cannot
act in a vacuum j and that it equally fails, when the height of
the column co is greater than that of a column of the liquid
whose weight is equal to the pressure of the atmosphere.

Fig. 109.

Fig. no.

Siphon with Constant Flow. — In order that the flow of the
siphon may be always the same, it is evident from the prece-
ding observations, that the difference between the levels of the
liquid in its two branches must be invariable. This object is
attained by the arrangement shown in fig. 110. The siphon
is preserved in equilibrium by a float a and a weight p, in such
a manner that in proportion as the level of the liquid in the
vessel h is lowered, the siphon is lowered With it ; hence, the
difference between the heights a b and b e remains always the
same.

The Intermittent Siphon. — The intermittent siphon, aa its
name indicates, is one in which the flow is not continuous.
This siphon is arranged in a vessel so that the shorter branch
is open near the bottom, while the greater branch passes through
it and opens below it. The vessel being supplied with a con-
stant flow of water, the level rises by degrees, both in the
vessel and in the shorter branoh. up to the top or bend of the
siphon. The siphon is then filled in consequence of the ptes- •
sure of the liquid, and the flow takes place as shown in fig. 111.

Fig. ill.

But as the discharge of the siphon is so adjusted that it is
greater than that of the tube which supplies the vessel, the
level sinks in the vessel, and the shorter branch of the siphon
soon ceases to be immersed in the liquid ; the siphon is then
emptied and the flow is interrupted. The vessel, however,
continuing to be supplied by the constant source, the level again
rises, and the same series of operations is periodically
renewed.
In the large water-works, oonstrueted for the supply of towns,

320

THE POPULAR EDUCATOR.

apparatus with intermittent flows are often employed to open
or shut the stop-cocks of main-pipes at certain fixed periods.
For this purpose, vessels supplied by a small but constant run
of water, empty themselves at intervals, and becoming some-
times heavy and sometimes light, they act, by the aid of counter-
weights, fir«t in one direction and then in another, on the
keys of the stop-cocks, and produce the effect required. The
theory of the intermittent siphon gives ihe explanation of
natural intermittent fountains which are to be found in various
places of the globe. Some of these fountains yield a supply
of water during several days or months, then they stop during
a longer or shorter interval, and after this they begin again to
flow. Others stop and resume their flow several times in an
hour. These phenomena are explained by supposing the
existence of subterranean cavities which are filled more or less
slowly with water from springs, and which empty themselves
again by fissures which exist under ground, in the same manner
as the intermittent siphon.

LE8SON8 IN CHEMISTRY -No. XXI.

Inasmuch as the metal silver is one that admits of being obtained
bodily, evidently, from all its solutions with remarkable facility, by
first precipitating it as a chloride, and then decomposing that
chloride by either of the means already described, the student may
perhaps imagine that, for this very reason, the discovery and the
quantitative estimation of silver are matters of peculiar certainty,
ft is true that this discovery and quantitative estimation are matters
of great ease and certainty, but not for the reason adverted to.
Young chemists are in the habit of committing the great error of
assuming that chemical estimation of any given substance neces-
sarily involves bodily presence of that substance. The idea is
natural, but it is not si ways correct ; on the contrary, the actual
bodily presence of a substance is seldom effected during the course
of analysis. Chemistry, in this respect, furnishes an exception to
the usual rules of evidence : collateral and indirect, being frequently
of greater value than immediate and direct evidence. The chemical
relations of the metal silver furnish a remarkable illustration of
this proposition. We can easily get the metal out of any solution ;
nevertheless, in practice it is found more correct to estimate the
amount of silver by collecting and weighing the amount of chloride
generated. So much more correct is the latter process, that it is
adopted as the means of testing the purity of silver in the French
mint. "We English do not adopt that process in our mint, because
it occupies more time ; but as to its superior correctness there can-
not be two opinions.

In order, however, that the amount of chloride generated should
be a faithful index of the quantity of silver present, one postulate
•is necessary. It will have occurred to the student, no doubt; for
I have taken several opportunities of expatiating upon parallel
cases. The composition of chloride of silver must be fixed and un-
vstjxnr ; a given weight of it must always contain the same relative
» meant of silver and chlorine. Now this is the case, and the pro-
position holds good for all chemical compounds whatsoever. Per-
haps hereafter I shall treat of the philosophy of chemistry, as I
now treat of its practice, and I shall describe the laws of definite
proportionality, and expatiate on the beauties and the probabilities
of the atomic theory. Meantime remember, if you please — that
the fact of chloride of silver being fixed and invariable as to
composition, however prepared, furnishes one of the many proofs
that the composition of chemical compounds generally is fixed and
invariable, end supplies one of the strongest arguments in favour of
the atomic theory.

Well, to proceed. The composition of chloride of silver, dried
and fused, to drive off the last remnant of moisture, is, as near as
our most delicate balances can inform us, as follows : — Every 144
parts by weight are made up of 108 parts by weight of silver, and
36 parts by weight of chlorine ; whence it follows, that, having
generated a certain given weight of chloride of silver, absolutely
pure and dry, we may ascertain the quantity of silver present in it
by a rule of simple proportion. If we choose to extract the silver,
we can easily do so ; but the resulting indication will not be so
exact, for the very simple reason, that the manipulative processes
involved in effecting reduction, however carefully exercised, must
be necessarily attended with some slight loss.

Proceeding with the mental investigation of the circumstances

of the case, perhaps the student will have already anticipated the
statement that the troublesome process of collecting, washing,
fusing, and weighing the chloride, may be altogether dispensed
with, simply by preparing a chlorine solution of known invariable
and definite strength, weighing a vessel full of this solution, add-
ing portions of this solution, drop by drop, to the silver solution,
until no more chloride of silver is deposited ; and finally esti-
mating the amount of loss in weight of the standard teat solution
thus employed.

Fig. 7.

For example, let us suppose a. and b to be two test-glasses, of
which a contains an unknown quantity of silver, and B a known
quantity of chlorine, in any convenient form of combination (for
pure chlorine is a gas). This known amount of chlorine, we will
furthermore assume to be 36 grains in weight. Suppose, now,
the contents of B to be added to the contents of a, and that exactly
the whole of b is required to precipitate the whole of A ; no more,
no less. Then does it not follow, as clearly as the simplest demon-
stration in geo etry, that the quantity of silver in A must be equal
to 108 grains?

Nothing, then, can be easier than the theory of this operation ;
but, as usual, certain difficulties present themselves in practice,
and have to be provided for. In the first place, the solution of
chlorine compound must be absolutely pure ; secondly, means
must be taken to prevent evaporation of the standard solution,
otherwise its strength would be continually increasing. These
matters, however, exclusively refer to quantitative chemistry, hence
I need not further advert to them here.

Mercury — As it is my object, in the present course .of lessons, to
treat of chemical substances according to the groups in which they
present themselves to a practical operator, I cannot do better than
follow the investigation of silver by that of the only other metal
which affords a chloride absolutely insoluble in water. I have al-
ready mentioned (Lesson xix.), that any dilute metallic solution
which yields a white precipitate on the addition of hydrochloric
acid or a chloride — I might have also said a solution of chlorine--
must either be mercury or silver. I lay stress on the word dilute,
because strong lead solutions produce a similar effect, as we shall
recognise when discussing that metal. If you have any doubt,
therefore, dilute the suspected solution and apply heat. If the
white precipitate disappears, the metal under examination will be
lead ; if it remain, the metal will be mercury or silver.

Having reference to their chlorides, therefore, it is evident that
silver, mercury, and lead arrange themselves in one analytical
group. Mercury differs from the greater number of metals, we
have already considered, in forming two classes of combinations —
proto combinations and per combinations. Thus we have protoxide
and peroxide of mercury ; protochloride and perohloride of mer-
cury ; protobromide and perbromide of mercury, and so on. These
various salts I shall not treat of in detail, but I shall merely group
them into proto and per salts.

Now the best solutions on which to display the peculiarities of
these classes will be protonitrate, protochloride, and perekkride of
mercury. I may also as well say at once, that the insoluble chlo-
ride of mercury, of which I have spoken, is the protochlotids com-
monly known as " calomel," under which name you will do well
to procure some. As regards the protonitrate, you will have to
make it, directions for effecting which will be presently given. The
perchloride is corrosive sublimate of she shops, otherwise known as
" oxy muriate of mercury," xix. p. 292 : of this you will require a
few grains. It is a violent poison, as you have been already in-
formed ; and its antidote, as you already know, is white of egg.

Protonitrate of mercury is made by adding aquafortis, mixed
with about an equal bulk of water, to quicksilver, and applying

LESSONS IN GEOMETRY.

321

heat. The quicksilver should be more iu quantity than the nitric
acid employed can dissolve.

We Will now proceed with a comparative testing of a protoaal
and a perult of mercury, using protonitrate and protochloride a
our specimen of the former, perchloride as our specimen of th
latter.

For this purpose, begin with pouring into one glass (a wine-glas
will do) a few drops of protonitrate, then nil the glass with water
Repeat the operation, using a few drops of the perchloride solution
in another glass. Let us now assume the nature of the metal to be
totally unknown, and begin to examine it analytically. The stu-
dent knows by this time that the first witnesses to be brought into
court are hydrosulphuric acid solution, hydrosulphate of ammonia,
and ferrocyanide of potassium. Let both protosalt and persalt be
tested with the first of these tests, and we shall get a result, it may
be, of a very peculiar character. If the amounts of the two solutions
be duly apportioned, the precipitate will be black ; nevertheless, if
the admixture be effected within certain limits, a white precipitate
may ensue ; or, finally, we may have a white changing to black, or
black changing to white. This variable indication is characteristic
of mercury ; we will, however, let it pass, and will assume the
precipitate, to have been black from the beginning. This being the
case, what does our operation teach us ? That the solution under |
consideration contains a metal — a caldgenous metal — not zinc, or
iron, or manganese, or uranium, or nickel ; not arsenic or antimony,
cadmium or persalt of tin.

Test next with ferrocyanide of potassium (prussiate of potash).
We now get a white precipitate, hence the metal in question is not
copper, molybdenum, uranium, or titanium. Thus far our process
of testing has been equally applied to both protosalt and persalt.

Let us now try what a solution containing chlorine will effect
— a solution of common salt, for example. Adding a little
of this to the perchloride of mercury, we get no precipitate,
hence the information conveyed by our test is very little, and that
little negative ; but adding a portion of the same test -solution to
the protochloride, we get a white precipitate. Now this white pre-
cipitate may be indicative of silver, mercury, or perhaps of lead. If
it represent the latter, it will dissolve wnen boiled in contact with
water. Remove therefore a little to a test-tube ; half fill the test-
tube with water, and boil. The white substance does not dissolve ;
it cannot therefore represent lead. But does it stand for silver ?
Let us see. If it be chloride of silver, it will readily dissolve in
haruhcrn. It does not, but turns black. Now this characteristic
is indicative of mercury — nothing but mercury. If therefore the
unknown metal had come before us as a protosalt, we should have
already made it out. Directing our attention now to the other
solution, place a few drops of it upon a piece of gold (say a coin),
. and bring into contact with the liquid and the coin at once a piece
of clean iron, say a key ; after the lapse of a few seconds a white
metallic stain, growing resplendent when dried and rubbed, will
appear on the coin. This result is indicative of mercury ; and here
let us take our leave of the metal mercury for the present.

LESSONS IN GEOMETRY.— No. XXVIII.

LECTURES ON EUCLID.

PROPOSITION XXVIII.— THEOREM.

{Continued from page 313.)

In the analytical proof reference is made to what is denominated
the principle of homogeneity', a principle in itself irrefragable,
but like all others, capable of being ill applied. Wherever
Quantities are to be equal, it is necessary that they be homoge-
neous, or of the same kind; for equality is nothing but the
capability of coincidence, and things heterogeneous cannot 1
coincide. A mile of length, or two or three or four miles, can I
by no possibility be equal to an hour of time; the assertion would
be ip$o facto foolish and unmeaning. But there is no objection
tosayiwtthat fo«J miles ^ ten hours because ^ tot of ihtae

" v ^" two miles five hours

expressions means only the number of times that the quantity
two miles can be taken in the quantity four miles, which is the
number two: and five hours may be taken the same number of
times in ten hours. The thine* finally declared equal are not
heterogeneous, for they are both of them numbers. And by the

same rule, there is no objection to saying that four miles = two

miles x n onrs ; f or this means nothing but that four miles «
five hours

two miles X the number which results from seeing how often
five hours can be taken in ten hours. It follows therefore that
heterogeneous quantities enter equation* by pairs ; or at all events
are reducible to pairs by running some two or more of them into
one by the operation of addition or subtraction. There cannot
be the slightest idea of questioning this, or any of the legitimate
results of what has been called the principle of homogeneity.

But the application in this instance was not legitimate, or at
all events not legitimately conducted. There was on the face of
it an unjustifiable operation, consisting in substituting: .for the
angles the numbers which expressed , their ratios. Professor
Leslie brought this into full light, by pointing out that if the
same reasoning were applied to the case where two sides (a and
6; were given and the angle between them p. it would produce
the statement that the remaining side e = * : (a t 6, p) : in which,
on substituting for a, 6, c> the numbers which express their ratios,
there would be the same argument for inferring that c would be
the same whatever was the angle, which is notoriously untrue.
And this brought out the avowal, that his opponents in the case of
[the angles intended to substitute the ratios, and in the case of the
sides, not ; a mode of arguing comparable only to the ingenuity
of the artist, who in playing at " odd or even," nolds a ball which
be has the power of projecting or not, as shall be required to
make him win.

When pushed on this point, they replied, that their reason for
| Substituting the ratios in the case of the angles and not of the
sides, was u because the right angle was the natural unit of
angles.'* But the fact of a right angle (or more properly four
Tight angles, or a turning from the place started from till arriving
it it again) being a convenient object of reference for the compari-
son ofangles in general, is devoid of any proved connexion with
the propriety of substituting the ratios in one case, and not sub-
stituting them in the other.

When pressed, however, they produced a reason. They said
It was because 'the angle is a portion of a. finite whole, the
straight line a portion of an infinite whole ; so that every given
angle is a finito quantity, while every given straight line is a
quantity infinitely small, and only the ratios of given straight
fines can enter into our calculations with given angles."t And
this was repeated as " a very subtle and very just metaphysical
dea ; and at the same time strictly analytical. X On which all
that can be done, is to remark on the absence of any reasonable
or demonstrated connexion (even supposing the facts indisputable,
which might be questioned), between the facts alleged and the
consequences assigned to them.

But a circumstance which appears to have escaped Professor
Leslie is, that his opponents, till his counter case appeared, had
i >een at the expense of an unnecessary wrong. There was not
the slightest necessity for substituting numbers, to produce their
argument ; for p was just as heterogeneous and intractable when
A, b, o wero angles, as after numbers had been substituted. It
s difficult therefore to surmise any reason for the substitution
unless they had a foresight of Leslie's reply. And when that
ame, they should havo said that they would eject p the side, as
Incapable of homogeneity, but for p the angle tney would substi-
tute-^ , y and then it would be a number, which need not be

a
jected. because c, a, and 6 may by possibility compound a num-
ber. This would at least have held together ; but it would have
ank under the unreasonableness of the substitution demanded
in one case with intention to refuse it in tho other.
And this leads to the substantial inference from the whole of
lie somewhat perplexed controversy which took place at the time ;
vhich is, that the original mistake consisted in confounding two
lets of things essentially distinct : the quantities, the fixation of
which causes another quantity to be necessarily fixed, or what
Buciid, in his Book of Data, calls given, and the quantities which

• " L'angle est une quanta^ que je mesure toujourt par son rapport avec
angle droit, car Tangle droit est l'unlie uatuieUe des angles. Danseette
otion tr&« simple, un angle est toujour! uu uoutbre. 11 n'en eft pas de
tame des lignes : uoe ligne tic peut entrer dans le calcul, dans une equation
uelcouque, qu'avec une autre ligue qui sera pri»e pour unite, oa qui aura
a rapport connu avee la ligne unittf."— • Letter q/ M. Legendrc. Leslie's
udiments of Plana Geometry. Fouith Euitiou. flows and Illustrations,

^tVtper of M. le Baron Maurice, in the Bibliothiqur Vniverxclle de
enire, Oct. 1810; as given in Dr. Brewster's Edition of U-*.\.d:e's
eometry, Motes, p. 235.
X Note by M. Legaadre, Ibid.
\ a standing for a right angle

322

THE POPULAR EDUCATOR.

27. M. Lacroix avow* the difficulty which exists ; and

himself with simplifying the Axiom of Bustid bj eoaftning it
the ease where two strait ht lines are intersected by a third, to

be employed as elements in its actual calculation. These
two sett are not necessarily the same, either in number or kind.
Take, for example, Professor Leslie's case, where e = f : (a, 6, p).

It is quite true that when a, 6, P are fixed, e is fixed. But pro- ^fcieh they both are perpendicular. On which he suppose* it to
coed to the actual calculation of e. and very different things be taken for granted, that if one of the straight line* torn* inwards
appear upon the scene. For the value of c has to be collected either way, it will cut the opposite perpendicular on the side em
from the well-known trigonometrical formula, that a + 6: a — 6 which it turns inwards.* Which, excepting the simplification

: : tang of

2b — p ,

tang, of semi-difference of the angles at the

base e. Here then, in lieu of the solitary and heterogeneous
angle P, start np among the practical elements of the calculation
two straight lines, in the shape of the tangents of two arcs, which
of course do not afterwards fail to conduct themselves with

arising from taking the case where the angles are right angle*,
appears to be the same argument as Professor Leslie**.

28. A demonstration is offered in the KUmens de (komHrk of M.
Lacroix,f and attributed to M. Bertrand, which i* the hardest of
any to convince of weakness, and takes the strongest hold of the
difficulty which exists in distinguishing between dbeervation and
mathematical proof. It proceeds by stating, that any angle) snay

perfect submission to the law of homogeneity. And with all ' be multiplied till it equals or exceeds a right angle. If then there

this the proposers of the analytical proof are "bound to make
their argument square ; for the concession of their own demands
ends in establishing the results of vulgar trigonometry, and not
in altering them . On the whole, therefore, the pretence of know-
ing what quantities must be ejected to preserve the law of homo-
geneity, is visionary till it is xnown what quantities may or may
not fturseqnentlr appear among the practical elements of the
calculation ; which is impossible in the preliminary stag*.

The point, then, which the supporters of the analytical proof
Will be called on to establish, is why the possibility o'f the appa-
rition of new elements which is visible in other cases (and which
in Professor Leslie's case they actually claim by demanding the
admission of B), is necessarily non-existent in their own. Take,
for example, the hyperbolic triangle A H O, towards the end of
16 of this collection. In this it is plain that if the line a b and
the straight lines AG and OH are fixed and determined,. the
angle a h o most be one certain angle and no other. But proceed
to calculate the comparative magnitude of the angle to different
values of a o. and there immediately start into action new elements
in no stinted number, viz., two constant straight lines under the
denominations of a major and a minor axis, ana a varying straight
line under tne title of abscissa, to say nothing of the radius of a
circle and such sines or tangents of different arcs thereof as may
be found necessary in the process. How then do the opponents
know thai there are no more elements in the other ease ? it nature
had contrived that the three angles of a triangle should not be
always equal to two right angles, the proportionality of the sides
of similar triangles would not nave nelcl good, and in making
Tables (for example) of the tangents to different arcs of a circle,
the magnitude of the radios of the circle must in some guise or
other have been an element. The tangent of 45° to a radins of
one foot would have borne some given ratio to a foot, and the
tangent of the same angle to a radius of two feet, instead of bear-
ing the same ratio to two feet, would have borne some different
one. There must have been a column of numbers to be applied
according to the length of the radius, to obtain the true tangent
of the angle to a given length of radius ; in the same manner as
would be necessary if it was desired to frame a Table for finding
the perpendiculars in the hyperbolic triangle for different lengths
of baae. In other words, there would have been more elements.
That this is not so, may be a happy event; but by what evidence
included in their proposed demonstration, do they know that it
is not ? All they can say is, that they have no evidence that it
is so. Their fallacy, therefore, is that of putting what they do
not know to be, for what they know not to be. Or if they trust
to the difficulty of finding anything in the case of straight lines
by which the variation of the angle* could have been regulated,
how do they know, for example, that natnro, instead of making

the angle c=2r-(a + b), has not made it =2b— (a + b)+

m "~"" , where m the modulus is some given straight line ; m

be taken a right angle, and angles cut off from it equal to the
supposed angle till they equal or exceed the whole, and at any
distance from the angular point be drawn a perpendicular from
one of the straight lines that make the right angle, and of coarse
a parallel to the other, and other perpendiculars at the same
distance in succession from one another ; on all the line* being
prolonged without limit, a certain number of the angular space*
will fill up or exceed the whole of the indefinite space included
between the sides of the right angle, but the same number of the
parallel band*, it is argued, will not. Whence, it is inferred, the
sum of the angular spaces is greater than the sum of the parallel
bands, and therefore one of the angular space* g re at* * than one
of the bands ; the consequence of which Is, that the line making
the supposed angle with the first perpendicular, will have eat the
second!.

All references to the equality of magnitude of infinite surfaces,
in respect of the parts where they are avowedly without boundaries,
are intrinsically paralogisms; for it is tantamount to saying that
boundaries coincide, where boundaries are none. And the only
way to arrive at safe conclusions in such cases, is to demand to
be shown the magnitudes asserted to be equal, in some stage
where boundaries exist, and then sec what cab be established
touching the consequences of extending the boundaries without
restriction assigned. When it is shinned that the surface of the
sngles is equal to or greater than the surface of the right angle,
and the surface of the bands is not, to reduce this to anything
reasonable and precise, it is necessary that it be understood to
mean, that if circles of greater aud greater radii be drawn about
the angular point d, there will at some time be a portion of the
quadrant exterior to the bands, greater than all the portions of
bands of an altitude equal to the radius, which are exterior to the
quadrant — , and further, that this will be the case^however the
distance between the parallels may be increased. Wow that this

again being equal in triangles with different angles, * to t x

A+B,

where m shall be some grand modulus existing in nature, which
(for the sake of removing the argument from vulgar experience)
may be supposed to be of very great dimension, as for instance
equal to the radius of the earth's orbit ? If an astronomer should
arise and declare he had found astronomical evidence that this
was true, how would the supporters of tho analytical proof pro-
ceed to put him down ? Ana would they not find themselves in
the, situation of those prophets, who find it easier to prophesy
after the fact, than while tne result is in abeyance ? f

• Without tome provision of thia kind, the expression would pretent a
straight line m such, that no straight lines making angles with iU ex-
tremities would ever meet ; which could not be, for to the extremities of say
straight line others may be drawn making angles with it, from any point

. not in the same straight Hue with the first.

•> ♦ For reference to a numbtr of places where this subject is agitated in

various senses, see Legendre's JRsmens at OSomHrie, Items ewttfea,
ifote».p.287. *

* E 6 mens de Geometric, par 8. F. Laeroix. lSeme edition, p. 22.
+ " On doit cependant excepter de ce reproche la demonstration donnee
par M. Bertrand; elle me paru la plus simple et la plus inggnieuse de totttes
celles que Je connais; en void le fond.'*

" II est d'aborri evident que si on ajoute un angle qutlconqas edh an
nombre sufflsaut de foi* a lui-n>6me, en hdh\ k'dh", h"dk'" t *'"<**"", on
parviendra toujours a former un angle total edh"" plifs grand que Tangle
dioitedo; mai* si l'on Sieve snr la drolte D B les perpendicnlaires Diet
F o, prvlongees iudlfininient, on formera une bande indennie bdfo, qui
ne samMit remplir Tangle droit kdb, quelque nombre de fois qu'elle soit
»Joute> a elU-meuoe. En effet, si Ton prend fk=df, et qu'on eUeve kl
perpendiculaire sur AD, que Ton pile eusuite la figure le long de FO, la
bande idpo couvrira exautement la bande ofil; ear les angles Q F D,
o F x, Sunt droits, la partte o r tombera sur F x ; et comme o f=F x par
construction, le point d se placera sur le point a ; de plus. Tangle fxl
SUnt droit aussl bien que b d P, fa ligne d B ss placera Stfr a l. Cela post,
puisqu'ou peut prendre sur la droite indSrinie d B autant qu'on voudra de
parlies egales a d f, sans arriver a son terme, on formera un nombre aoati
grand qu r on voudra de bandes e^ales aiDFO, sans ponvoir couvrir Tespaee
Inddflni compris entre les deux cdtes de Tangle droit BI»B. Jl eaitde 14
que, considers relativement a leurs limltes laterals*, la surface de Tangle
edh est plus grande que oelle de la bande isfo. 81 done on eofiatrnU
dans oette bande, sur la droite b n, un angle idh e*gal I edh, il ne poftfra
demeurer contenu entre les lignes b D et r o ; son cote ft a eotrpefl asvss-
sairement la droite r a."

" Pour sentir la force de cette demonstration, II faut blett mjnetvev ens
lorvqu'on applique Tangle droit edh sur Tangle droll idi.csi dans Seriaeas
doiveni toujours cotncider entre leurs limites laterales de et ds, o a et am,
quelque loin qu'on les prolonge : aiors on verra que si les angles eonstreiti
dans les bandes n'en sortaient pas, ils laisseraient un vide indeflni, apres la
dernfere bande et un autre dans chaque bande; mala eelui-ci, qui a toujours
lieu prd* de leur somraet, est plus que compense* par les espaees out leur
devieonent commune qoand ils sont sortis dea bandes, parce que lean cotes
ss croisant, ile ae recouvrent en partie : tsl est Tespaee it » 0. een uuun aax
angles BDH.aiH'. Avec eette explication, il ne doH raster, a ee que je
crois, auoun Br-' - #—j* ••«_-_. ,. - . ,.-_..

LESSONS IN GEOMETRY.

823

will be true, is founded solely upon saying, "Make the experiment
by drawing on a piece of paper, and you will find it alwat s u so."
But what the geometrician wants to know, is the principle upon
which one of these areas will necessarily in -all cases grow larger
than the other ; not tu be shown the fact, that it croWs lamer in
instances produced to him ; for by the same rule he might set
down that spheres are as the cubes of their diameters, on being
shown that an iron ball of two inches diameter weighs eight
times as much as another of one inch. He does not want the fact,
bat the reason of the fact.

The point really taken for granted in the formation of the con-
clusion above, is that the perpendiculars will at all events cut
some of the straight lines that divide the right angle into smaller
angles ; for if this did not happen, there Would be an end of the
persuasion that, of the areas above mentioned, one will necessarily
grow greater than the other. Arid that these Straight lines or
any of them will ever cut, is a mere taking for granted of the
mutter in question, viz., of Euclid's axiom that straight linen
making with another straight line, angles on the same side
together less than two right angles, will meet. It may be a Case
in which the empirical indication is very prominent, but still it is
only empirical. There is no tttigle where tome perpendicular may
not be drawn from the base that shall meet the other line; for a
perpendicular may always be let fall upon the base. Bnt the
Question is, whether it has been geometrically proved of any angle,
however small, that the perpendicular on removing to a greater
distance, as for instance to the distance of the fixed stars, may
not make smaller and smaller angles at the section, and at last
cease to cut at all. There is no use in saying, it does not look as
if it would ; the question on which the bet is depending, is whether
any universal reason has been pointed out, why it never can.
The preaent, therefore, may be concluded to be another, though a
very complicated and ingenious case, in which empirical inference
is substituted tor geometrical proof.

29. A demonstration, attributed to Mr. Ivory, is presented in
the Notes to Professor Young's " Elements of Geometry," which,
curiously enough, contains the elements of its own dissolution.
It must be premised that it has previously been demonstrated fas
may be done irrefragably in many ways) that the three angles
of a rectilinear triangle cannot be together greater than two right
at* $?!(•«.•

• -The three angles of any triangle are equal to two righi angles »
" If what is affirmed be not true, let the three angles of the trianf le aob
be lets than two right angles, and let the defeet from two right angles be
equal to the angle x. Let P stand for a right angle, and And a multiple
of the angle z, vis., mx, such that 4 p-hm, or the excess of four right
angles above the multiple angle shall be less than the sum of the two angles
aob and abo ofthe proposed triangle."

"Produce the side c b, snd cut off b x, l r, r o, fcc., each equal lb * o, so
that the whole co shall contain ob, m times ; and construct the triangles
iui,bkf,plo, &c, having their sides equal to the sides of the triangle
aob, and, consequently, their angles equal to the angles of the same tri-
angle. In o a produced take any point M, and draw uu, km, lm, &e. ;
A II. H x. x L, ftc."

" All the angles of all the triangles into whjeh the quadrilateral figure
oolm Is divided, constitute the four angles of that figure, together with
the angles round each of the points h, k, fee., and the angles directed into
the iuterior of the figure, at the points a, b, b, V, &c. But all the angles
round the points h, x, &c, of whleh points the number is *v- 3, are equal
to (m— 8)4p, or to 4mr— 8r; and all the angles at the point* a, B,x, P,
&c, are equal to m times 2 r. Wherefore the sum of all the angles of all the
triangles into whleh the quadrilateral OQLX is divided, is equal to the four
angles of that figure, together with 4mr— *p-f JwP=6m r— 8 p."

" Again: the three angles of the triangle ABC are, by hypothesis, equal to
2p-«; and, as the number of the triangles o A b, bhx,bkp, flo, is equal
to m, the turn of all the angles of all these triangles Will be equal to
2»p- mm. Upon each of the lines a a, hi, xl, there stand two tri-
angles, one above, and one below ; and, as the three angles Of a triangle
cannot exeeed two right angles, it follows that all the angles of those tri-
angles, the number of which is equal to Jm-2, cannot exceed 4»p— 4P.
Wherefore the sum of all the angles of all the triangles into which the
quadrilateral culm la divided cannot eseeed 4 MP— 4P+ta»P— s*#*s«sjii
-4H4HSf"

** It follows from what has now bean proved, that the four angles of the

The infirmity bf this is, that it is taken for granted there will be
formed (ro— 1) triangles at M as represented, in the same manner
as if Ahkl was one straight line. Whereas it is demonstrable,
that A UK, hkl, Ac, must all be angles less than the sum of two
right angles on the side towards c o, and that before the number
of points H, Kt fee., at whieh new triangles are formed further aha
further from A amounts to m — 2, the formation bf new triangles in
that direction must cease, in consequence of the angles mkl, &<♦.,
becoming greater than two right angles on the side removed from
A. By which the intended proof falls to the ground.

For since the angles of the triangle abc are (by the Hyp.)
less by x than two right angles, and the angles of the triangle H tiA
(by the Proposition preceding) are not greater than two right
angles ; the four angles of the quadrilateral figure A OB h must be
less than four right angles, by at the least x ; and because the
angles use and hbb, or hdc and a c b are equal to two right
angles* the remaining angles of the quadrilateral figure, A h b and
fl a o (and consequently ahd and khboi the angle ihk) must
be less than two right angles, by at the. least x; and in like manner
the angles hkl, &c. Wherefore if a h, h x, &c. be prolonged,
the angles sun, lro, &c., must be each equal at the least to
m. And because b a c, b a m arc together equal to two right
angles, and b a c, a c b, a b c are (by the tiyp ) less by x than
two right angles ; b a m — x must be equal to the sum of A ob ahd
abo; and because 4 p — mx.is (by the Hyp.) less than the sum of
acb and abo, it must be less than bam— « and 4p— (m — 1)*
must be less than bam, and (m — l)x must be greater than 4 P —
bam; and because bam is less than two right angles, 4 p— bam
is greater than two right angles, still more therefore must (m— l)ar
be greater than two right angles. And because the angles h AC,
ahb have been shown to be together less than two right angles
by at the least x, hao must be less than two right angles by
more than x, and still more must the angle nea (which is If ss
than H a c the exterior and opposite). Whence, because (m — 1)*
is greater than two right angles, and m h a is less than two right
angles by more than i|MBA must be less than (as— 2)*, and
mhn must be greater than 2 p— (m — 2)«, and mhk must
be greater than 2 P — (m — 2)a?+«. And because the angle xxo
ia greater than mhk (for it is the exterior and opposite) it
must be greater than Sp — (m — 9)*-fa; and the angle axL
must be greater than 2p— (in— s)*+2*» and soon. Wherefore,
before there have been taken (*»— 2) points as h, x, &c.,the angle,
as mxl, must be greater than 2p, and there must fail to be
formed a new triangle on the side removed from a as required for
the Intended proof.

30. Professor Young proposes this demonstration with an altera-
tion*, consisting in taking such a multiple of a?, that mm may
exceed 4 p. But if there cannot be constructed (m — I) triangles

4 p— sum of acb and abc;
aa supposed, when m is greater than ■

m 4p

still mora cannot (m— 8) be constructed when m is greater than — •

*
The number of demonstrations proposed on the subject of
Parallel lines is evidence of the anxiety felt by geometrical writers
upon the subject. If an erroneous account haa been given of any
efted abort, the references will supply the means of correction.

JuadrilateraleOLM, together with Imr- 8r, cannot exceed 8mr— 8p+
p— mx. Wherefore, by taking the same thing, vis.. 6m r— 8 p, from the
two unequal things, the four angles of the quadrilateral colm cannot
exeeed 4p— mar. But if—mx is less than the sum of the two angles
acb and lop : wherefore, a fortiori, the four angles of the quadrilateral
cannot exeeed the sum of the two angles aob, lo p j that is, a whole cannot
exceed a part of it, which is absurd. Therefore the three angles or the
triangle abo cannot be less than two right angles."

"And because the three angles of a triangle can neither be greater nor
less than two right angles, they are equal to two right angles."

'* By help of this proposition,** observes Mr. Ivory, " the defect in Euclid's
Theory of Parallel Lines tiny be removed."— Iftemeytf* of Geometry, bjf
J. B. Young, Professor of Mathematics in Belfast College, notes, p. 170.

• «• I shall, however, venture to suggest a trifling improvement, which
the above reasoning appears to admit of, and thereby obviate an objection
that might be brought against it."

" It might be said, and with reason, that we have no right to assume that,
in every case, a multiple of m may be taken, such that 4r — mm may be lees

than the sum of the two angles aob and abo; for these angles may be so
Small that their sum shall be much less than the angle m, however small
this be assumed; snd although 4r— mm must also be less than *, it may
nevertheless be comparatively mueh greater than the sum of the angles
AOB. ABO t in which case the above conclusion caauot be drawn."

" It appears, therefore, preferable to assume the multiple of «, such that
mx may exeeed 4p, whieh Is unquestionably allowable: then the subsequent
reasoning may remain the same till we come to the inference, that the lour
angles of the quadrilateral, together with 6m P— Sp, cannot exceed 6mr-
8r+4p— mx, whieh obviously involves an absurdity, because 6wr-8?
alpne exceeds 6m P— 8p+4p— mx; since this latter expression results from
adding to the former a leu magnitude, viz., 4 p, and taking away a greater,
vis,, mm, for by hypothesis 4 r> m*.»-£tements of Qeemeiry, by S. M.
Young, p. 17».

324

THE POPULAR EDUCATOR.

The following ii the passage referred to, in p. 313, and ww
insert it because of its great ingenuity and value : —

By superposition, it can be shown immediately, and without
any preliminary propositions, that two triangles are equal when
they have two angles and an interjacent side in each equal. Lei
us call this side p, ihe two adjacent angles a and B, the third
angle c This third angle c, tnercforo, is entirely determined-
when the angles a and b ; with the side p, are known ; for if
-several different angles c might correspond to the three given mag*
nitudes a, b> p, there would be several different triangles, eacjt
having two angles, and the interjacent side equal, which is impossi-
ble ; hence the anglo c must bo a determinate function ofthe three
quantities A,B,p, which we shall express thus, c = *: (a, B,p).

Let the right angle be equal to unity, then the angles a, b, d
will be numbers included between and 2; and since c=*;
A, B, »), the lino p cannot enter into the function 0. For we
jave already seen that c must be entirely determined by the given
quantities a, b, p alone, without any other line or anglo whatever*
Sat the line v is heterogeneous with the numbers a, b, o ; and if
there existed any equation between a, b, c, p, the value of «
might bo found from it in terms of a, b, c ; whence it would fol-
low, that j> is canal to a number ; which is absurd : hence p can-
not enter into tho functiou ^, and wo have simply c = <p : (a, b). #

This formula already proves, that if two angles of ouo triangle
are equal t > two angles of another, the third anglo of the former
must also be equal to tho third of the latter ; and this granted, it
is easy to arrive at the theorem wo have in view.

First, let a b c be a triangle right-angled at v

A ; from the poiut a draw a d perpendicular /\

to tho hypotenuse. Tho angles B and o of the /

trianglo abd are equal to the angles b and a x '
of the trianglo B a c ; hence, from what has ** ' - j — ^ C

just been proved, the third angle B a d is equal
to the third c. For a like reason, the angle d a c = b, hence
B ad -h D a c, or B A c= B 4- c ; but the augle B a c is right ; hence
the two acute angles of a right-angled triangle are together equal
to a right augle.

Now, let b a c be any triangle, and b c a side of it not less than
either of tho other sides; if from tho opposite angle a the peri
pendicular a d is let fall on b c, this perpendicular will fall within
tho trianglo a b c, and divide it into two right-angled triangles
bad, d a c. But in the right angled triangle bad, the two
angles bao,abd are together equal to a right angle ; in the
right-angled triangle dac, the two d a c, a c d are also equal to
a right angle ; henco all the four taken together, or, which
amounts to the same thing, all three, bag, abc, a c b, are
together equal to two right angles ; hence in every triangle, tlie
sum of its three angles is equal to two right angles.

It thus apoears, that the theorem in question does not depend,
when considered a priori, upon any series of propositions, but
may be deduced immediately from the principle of homogeneity *
a principle which must display itself in a relation subsisting
between all quantities of whatever sort. Let us continue the
investigation, and show that, from the same source, the other
fundamental theorems of geometry may likewise be derived.

Retaining the same denominations as abovo, let us further call
the side opposite the angle a by the name of m, and the side
opposite b by that of n. The quantity m must be entirely
determined by the quantities a, b, p alone ; hence m is a function

of a, b, p, and — is ono also ; so that we may put ~ = * : (a, b,
p p

p). But — is a number as well as a and b ; hence the fuuctiou *
P

eannot contain the line p, and we shall have simply — =■ * : (a,

P
b;, or m s*p + : (a, b). Hence, also, in like manner, n -p ^ (b. a)

Now, let another triangle be formed with the same angles a, b,

c, and .with* sides m', n'y, respectively opposite to them. Since
a and B are not changed; we shall still, in this new triangle, have
m' = y + : (a, b), and n' -p 1 ^: (a, b) Hence m:m* =zn:ii* = p :
p'. Hence, in equiangular triangles, the sides opposite the equal
angles are proportional.

The proposition concerning the square of the hypotenuse is a
consequence of that concerning equiangular triangles. Here
then are three fundamental propositions of geometry, — tliat con-
cerning the three angles of a triangle, that concerning equiangular
triangles, and that concerning the square of the hypotenuse,
which may be very simply and directly deduced from the
consideration of functions. In the same way, the propositions
relating to similar figures and similar solids may be demon-
strated with great ease.

Let a b c d b be any polygon. Having taken
any side a b, upon a b as a base, form as many
triangles a b c, a b d, &c. as there are angles c,

d, k. &c. lying out-of it. Put tho base ab = p;
let a and « represent tho two angles of the
triangle abc, which arc adjacent to the side
a b ; a' and b' the two angles of the trianglo ,
abd, which are adjacent to the same side a b,
and so on. Tho figure abcde will bo entirely
determined, if the side p with tho angles a, b,
a', b', a", b", &c. are known, and the number of
data will in all amount to 2 u —3, n being the

number of the polygon's sides. This beiug granted, any side or
lino x, any how drawn in the polygon, and from the data alone
whiob serve to determine this polygon, will be a function of those

given quantities ; and since — must be a number, we may suppose

= *: (a, b,

&«•.) or xz

=p * (a, b, a', n', kc.\ and the

• Against this demonstration it has been objected, that if it were applied
word lor word to spherical triangle?, we should find that two angles being
known, are sufficient to deteimine the third, which ia not the eaae in that
species of triangles. The answer is, that in spherisal triangles there exists
one element more than in plane triangles, the radius of the sphere, namely,
which must not be omitted in our reasoning. Let r be the radius; Instead
of c s 4> v a, b, p) we shall now have c = <p (a, b, p, r), or by the law of

homogeneity, simply o = f a, b,— j . Bat since the ratio —is a number

as well ai a, b, c, there is nothing to hinder — from entering the function
t). and oonseqnently, we hare no right to infer from it, that o = <p (a, b).

function ^ will not contain p. If with the same angles, and another
I sidep*, a second polygon be formed, the linear' corresponding or
I homologous to x will have for its value x* = p*': (a, b, a , B' t

tot.); hence x : x' —p :p'. Figures thus constructed might be
I defined as similar figures', hence in simi ar fi'jures the homo-
I logons lines are proportional. Thus, not only the homologous
I sides and the homologous diagonals, but also any lines terminat-
I ing the same way in the two figures, are to each other as any
I other two homologous lines whatever.

Let us name the surfaco of the first polygon 8 ; that surface is

I homogeneous with the square />'; henco — must be a number,

P %
I containing nothing but the angles a, b, a', b', &c.; bo that wo
I shall have S=p*v: (s B, a', b\ &c); for the same reason, S'
I being the surface of the second polygon, we shall have S' = //* <f> :
I (a, b. a', b', &c.) Hence S : S' = p* : ;/' ; heuco the surf acts of
I similar figures are to each other as the squares of their homolo-
gous sides.

Let us now proceed to polyedrons. We may take it for
grantod. that a race is determined by means of a given side j',
and ofthe several given angles a, b, c, &c. Next, the vertices of
tho solid angles which lie out of this face, will be determined
each by means of three given quantities, which may be regarded
ns so many angles; so that the whole determination of the poly-
edron depends on one side, p, and several angles a. b, c, Ac., the
number of which varies according to the nature of the polyedron.
I This being granted, a line which joins to no vertices, or more
I generally, any line x drawn in a determinate manner in the poly-
edron. and from the data alone which serve to construct it, will
be a function of the given quantities p, a, h, c, &c ; and since

— must be a number, the function equal toJH will contain
p p

nothing but the angles a, b, c, &c, and we may put x=pt:
[a, b, c. &c.) The surface of the solid is homogeneous to p»;
hence that surface may be represented by ft * : ( a, b, c, Ac) : its
solidity is homogeneous with p 3 , and may be represented by p %
: (a, b, c, etc.), the functions designated by *, and n being tnoe-
dent of p.

Suppose a second solid to be formed with the same angle a, b, c.
kc., and a side p' different from p j and that the solids so formed
are called similar solids. The line which in the former solid
was p a (a, b, c, &c), or simply p £, will in this new solid become
p' <t> ; the surface which was p* * in the one. will now become pi
I, in the other; and, lastly, the solidity which waspMi in the oue,
will now become p'* n in the other. Hence, first, in similar
Molids, the homologous lines are proportional: secondlv, their
surfaces are as the squares of the homologous sides; thirdly, their
solidities are as the cubes of those same sides.

The same principles are easily applicable to the circle. Let Q

LESSONS IN GERMAN.

325

be the circumference, and * the surface of the circle whose radiui
is r ; since there cannot be two unequal circles with the same)

radius, the quantities - C - and — must be determinate functions of
r ; but as these quantities are numbers, the expression of them

cannot contain r ; and thus we shall have -1 = «, and J- = ft, o,

r f*

and ft being constant numbers. Let c' be the circumference, and
s' the surface of another circle whose radius is r* ; we shall, as

before, have il = a, and il = ft. Hence e : e' = r :r* f and t : ** i

r' r"

= H : f« : hence tlie circumferences of circle* are to each other a$
their radii, and the turf aces area* the squares of those radii.

Let us now examine a sector whose radius is r. A being the
angle at the centre, let * be the arc which terminates the sector,
and y the surface of that sector. Since the sector is entirely
determined when r and A are known, x and y must be determi-
nate functions of r and A : hence ~ and ^L are also similar funo-

r r*

tions. But — is a number, as well as J^ ; hence those quantities

r t*

cannot contain r, and are simply functions of A ; so that we have

-^L = *: A, and •£. = *: A. Let *' and y be the arc, and the sur-
r r*

face of another sector, whose angle is A, and radius r' ; we shall
call those two sectors similar : and since the angle A is the same

in both, we shall have ~ = 9 : A,and.£ = * : A. Hence x : x*

r* r'*

= r : *•*, and y:y' = r* it"*; hence similar arcs, or the arcs of
similar sectors, are to each other as their radii; and the sectors
themselves are as the squares of the radii.

By the same method we could evidently show, that spheres are
as the cubes of their radii.

In all this we liavo supposed that surfaces are measured by the
product of two lines, and solids by the product of three ; a truth
which is easy to demonstrate by analysis, in like manner. Let
us examine a rectangle, whose sides are p and q ; its surface,
which must be a function of p and q, we shall represent by 4> :
(p y q). If we examine another rectangle, whose dimensions are
p+p' and a, this rectangle is evidently composed of two others ;
of one having p and q for its dimensions, of another having p*
and q ; so that we may put 4, : (p + />', q) = 9 : {p,q) + * : (p*, q).
Let p'=p; we shall have * (2 />, q) = 2 * (p, q). Letp'=2p;
we shall have * (3p, q) = *(p, q) +*(2p, q) = 3* (p,q). Let
p' = 3n; we shall have * (4 p, q) = <p (p, q) + * (3 p, q) = 4 <p
(p, q). Henoe generally, if k is any whole number, we shall have

♦ (*P, <l) = * ♦ (P, q) or ±&3l=L<?Pi3l ; from which it fol-
P k P

lows that t \Ei V is such a function of p as not to be changed by

P
substituting in place of p any multiple of it kp. Hence this
function is independent of p, and cannot include any thing except

q. But for the same reason * ^' V

hence * 2S1 V includes neither p nor q, and must therefore be
pq

limited to a constant quant : tv a. Henoe we shall have * (p, a)
= a » 9; : and as there :s nothing to prevent us from taking a = 1,
wo shall h&ve <p(p,q)=pq; thus the surface of a rectangle la
equal to the product of its two dimensions.

In the very same manner, we could show, that the solidity of
a right-angled parallelopipedon, whose dimensions are p, q, r, is
equal to the product p q r of its three dimensions.

We may observe, in conclusion, that the doctrine of functions,
which thus affords a very simple demonstration of the fundamen-
tal propositions of geometry, has already been employed with
success in demonstrating the fundamental principles of Mechanics.
See the Memoirs of Turin, vol ii.

\/ront f is put in the genitive: as, bU mciflen Qtarlufc fun> find
Qxf&^tt fa$ig, most losses are capable of reparation ; tie dxU ift
blU irz ®&te td $crrn, the earth is full of the goodness of the
Lord.

Observations.

il! The adjectives comprehended under this rule are such as
follow :

. must be independent of q;

LESSONS IN G E R M A N.— No. LXXXHL
S 124. Rule.

A noun limiting the application of an adjective, when in
English the relation would be expressed by such words as of or

Umuftig, in want ; needing.
©* eftflat, needing, wanting,
©aij 11 ft, conscious,
^tnjctfnt mindful.
jiahi.v- capable; susceptible.
5r»4 glad.
(JknMi^r, aware.

Qtauattio/ waiting; in expecta-
tion,
tifciviff, sure ; certain.
(Scurtfynt, used to ; in the habit.
£u£ili& having a knowledge ;
skilled.
I 1 cci.j, empty ; void.
Ikrr, void.

Sort, free ; rid.

3ftA$tig, having; in possession.
SRute, tired ; weary,
©alt, satiated; weary,
©ctyulbig, guilty ; indebted.
Styeityafi, partaking.
Utberbvuffig, tired ; weary.
SGerfeActytig, suspicious.
93crluflig, having lost; deprived
of.

a?ott, full.

SBcrty, worth ; worthy.
SBurtig, worthy.
Ouitt, rid ; free from.

(2) After flctt>a v r, flewotynt, lot, mutt, fatt, »ott and totnff, the accu-
tative is often used : as, tr unirbfcintn JBruter flewa&T, he was aware
of (the presence of) his brother, i. e. he observed his brother

% 125. Rule.

A . ; ■ un limiting the application of any of the following verbs
ii put in the genitive:

ft4i<n. to mind, or regard.
QtHifts, to want.
^(^tJicn, to desire.
'JJianL^n, to use.
G itttchi'L'n, to need.
(SntcntK'it, to do without.
tycm wudn, to want, or be with-
out.
(fr.vdhien, to mention.
flhilBlfli, to think, or ponder.
&ttfit$t», to enioy.
Okma^rtn, to observe.

barren, to wait.

£a$cn ( to laugh.

$flejcn to foster.

<5$onen, to spare.

iStxittytn, to miss, or fuiL

iUergeffen, to forget.

gBatyrcn, to guard.

SOa^mc^mrn, to observe.

SBaUcn, to manage.

SBartcn, to attend to, or mind.

Observations.

iiciiirftn, bt$tf)vtn, htnud^tn, tntbtifxtn, tvmtfncn, gfnicfen, pfit^tn
ifyvutn, v<rfe$len, tergeffen, nja^rnc^men, loarnt and ttxirtcn, take more
frpqueudy, in common conversation, the accusative. Sl^tcn,
[v.. lui and tvarten are more commonly construed with auf, and
1.1 .j v.: fycttcn and nwltw with ufrcr, before an accusative.

§ 126. Rule.

The following reflexive verbs take, in addition to the pronoun
peculiar to them, a word of limitation in the genitive:

■ikii aiunajien, to claim.
n . ne^men, to engage in.
1 aicnen, to use.

ci^tn, to attend to.

tipigen, to apply to.

tUn, to yield up.^
tcm44>tiflen, to acquire.
I tiutifhrn, to seize.
: '*! \)6btn, to acquiesce in.
[eftnncn, to ponder.
tnUufcrn, to abstain.

&Ub«i, to dare, or be bold.
cm foremen, to forbear,
v fatten, to refrain.

id)ia%tn, to get rid.

[tonen, to recollect.
1 1 ' armen, to pity.

$i$ erfre^cn, to presume.

„ eriiinem, to remember.

„ crfuyncn, to venture.

„ arotfxtn, to resist.

„ freucn, to rejoice.

„ gttroflen, to hope for.

„ tubmen, to boast.

„ ftyamen, to be ashamed.

„ ufa$cfen, to be haughty.

„ untcrfangen, to undertake.

„ untcrmintcn, to undertake.

„ vecmcjfcii, to presume.

„ wrfc^en, to be aware.

„ tw^rtn, to resist.

„ twicjcm, to refuse.

„ tvuntero, to wonder.

386

the Popular educator.

OBSERVATIONS.

(1) The genitive is ill like manner put after the following »•»•
versonoU :

Hi geluflet mic$, I desire, or am pleased with.

<&i jammrrt \ri\a), 1 pity, or compassionate.

9< rent tttta}, I repents or regret.

(Si U>f}i\t ficy, It is worth while.

The verbs following
iking and an accusative

ttntfagen, to accuse.
£Jelc v ren, to inform.
iBerou&in, to rob.
JBefcyiiungen, to accuse,
(fntbinrtn, to liberate,
ffntbtofen, to strip,
©ntyeben, to exempt,
tfrnttabea, to disburden.
(Jirtfleibcn, to undrWB.
©mlaffen, to free from.
Qntletoigen, to free from
(JntfeStn, to displace.

§ 127. Kulb.
require after them a genitive denoting a
signifying a person :

Gntmftynen, to wean.
£e«fore($en, to acquit.
QHaljnen, to remind.
Ue&erf Hyrea, to convier?
lleseryeben, to exempt.
Ueberjeugen, to convince.
iBetfttjtnt, to assure,
gtertrijten, to amuse) or pus off
with hope.
20urtigen, to deem worthy.
3ctyfn, to accuse ; to charge.

Examples.
<&t y at mxa) meinel QfitlUt btxaubt, he has robbed me of my money.
£>rr Siftyof yat feen $rttigec fcinc* 9lmte* entfe^t, the bishop has
removed tho preacher from his office.

Observations.

(1) The verbs above, when in the passive voice, take for their
nominative the word denoting the person, the genitive of the
thing remaining the same; as, cr ijt eine* &etftre$cnf angeffagt
ttortcn, he has been accused of a crime.

| 128. Rule.

Nouns denoting the lime, place, manner, intent or cause of an
action, are often put absolutely in the genitive and treated as
adverbs: as,

£el SWorgenl ge y e \a) aut, in the morning I go out.

SKan fu$t i y n after Drten, they seek him everywhere.

3$ bin JffliUcn« yinntgeyen, I am willing to go there.

Obsbhyatiohb.

(1) This adverbial use of the genitive is quite common in
German. In order, however, to express the particular point, or
the duration of time, the accusative is generally employed, or a
preposition with its proper case ; as, 3$ merle nd$fttn iDhmtag an*
bet Stafct geytn, I shall go out of town next Monday.

»' 129. Rule.

A noun or pronoun used to represent the object in reference
to which an action is done or directed, is put in the dative : as,

3c$ feanfe btc, I thank (or am thankful to) you.
dx gefaUt vititn £euten, he pleases many people*
<fc tft tern %stt entgangen, he has escaped from death.

Observations.

(1) The dative is the case employed to denote the person or
the thing in relation to Which the subject of the Verb is repre-
sented as acting. Compared with the accusative, it is the case
of the remote object : the accusative being the case of the im-
mediate object. Thus, in the example, ity ftyrleb tttttttcm 93ater
einen $rtef, I Wrote (to) my father a letter, the immediate object
is a letter ; while father, the person to whom I wrote, is the
remote object. The number of verbs thus taking the accusative
with the dative, is large.

(2) On the principle expluined in the preceding observation
may be resolved such cases as the following : f« t$nt mir kit, it
causes me sorrow, or I am sorry, e4 tvirfe mir tm $erjen tt*y* tyitn, it
will cause pain to me in the heart lit will pain me to the heart).

(8) A right regard to the obaetvation made above, namely,
that the dative merely marks that person or thing ill N/fcitnw
to which an action is performed, will serve, also, to explain all
such examples as these : 3$nen btUutei fciefe* Cpfer ixxdfyit, to you
(i« e. so far as you are concerned) this sacrifice means nothing ;
tie ZfcraneR, lit ffurem ®rreit gefloffen, the tears which have flowed
in relation to (i. e.from) your dispute ; mit bfcttte tin €<**# feel
$ferb, a shot killed a horse for me, i. e. killed my horse ; falle
mir nva)t, jttriiter, fall not for me, little* One. ttt Men Instances is
the last two, the dative is often omitted in translating.

(4) The rule comprehends all such verbs as the following:
antteertcn, to answer ; fcanfen, to thank ; tienm, to serve ; state*, to
threaten j ftyitn, to fall short; jlntytn, to curse } fsffta, to follow;
fttynen, to do homage ;• geMh)rrn, to be due ; tfaSta, to please ;
geydwn, to pertain to; gefcercytn, to obey; genfgrn, to satisfy: at*
rcuytn, to be adequate ; gteU$eri, to resemble ; Jelfrii, to help, Ac

(5) This rule, also, comprehends all reflexive tetbi that
govern the dative : as, ia) mafe mir teinen Xittl art, toefcytn ia) nty
fa**, I claim to myself no title which I hate not} as, also,
impersonals requiring the dative : as, <• beftebt mir, it pleases me,
or I am pleased ; el mangelt mir, it is wanting to me, or I am
wanting, &c.

(6) The dative is also often used after passive verbs: as,
u)nen murbe n>ie*erfhmfeen, it was resisted to them, i. e. they were
resisted : toon fteiftern toirb ter 2Beg boju fefe}flfct, the wty thereto is
guarded by angels ; i v m totrb gefoyiit, (literally) it ia rewarded to
him, i. e. he is rewarded.

1 130. Rule.

Many Compound verbs, particularly those compounded with
er, *er, tnt, an, ah, duf, set, ncicf, vtt, ga and itittr, require
after them the dative ; as,

3<$ y afee i^m (Belt cingctotcn, I have ottered him money.

S 181. Role.

An adjective used to limit the application of a noun, where in
English the relation would be expressed by such words aa t
or for, governs the dative : as,

3ei brinem ferrn gerreii, be faithful to four inaatef.
$al SBetter if* un* nie}t gunftig, the weather it nOt favourable
to us.

"OBSEttVAtlONS.

(1) Under this rule are embraced (among others) the follow-
ing adjectives: aynlufc like; angcraeflen, appropriate; angettefm,
agreeable; anflftfi^ offensive; Utanid, knowni ttjayMM, destined;
etgen, peculiar ; fremfc, foreign ; gemdf, according to ; ganein, com-
monj genxutfen, competent; gndtig, graeious; leitfam, healthful
Ucb, agreeable ; na v c, near ; uberlegen, superior ; wtflhrnuneu, wel
come ; tttbrio, adverse ; vUafl^ar, serviceable ; ff^prfsm, obedient
nfl|n^, useful.

§ 132. RtTLK.

A noun or pronoun which is the immediate object of an active
transitive verb, is put in the accusative :

SBir (ie&en iinfete 8renrt*e, we love our friends,

$er £unfc Umty bal #<tuf, the dog guards the house*

O&SERVAflONS.

(1) The accusative! as before said, being the case of the direct
or immediate object (% 129. L)* is Used with all verbs* whatever
their classification in other respects, that have a frsmstfnrt sig-
nification. - Accordingly, under this rule tome all those imper-
sonal and reflrxive verbs that take after them the i<*uMtive;
all those Verbs having a causatlv* signification, fit, fattrt, to fell,
i. e. to cause to fall ; as also nearly all Verbs Crjfflpotmded with
the prefix be. The exceptions are, fcegegnrn, feyagen, fctffeyen, U*
v arren and fcen>a$feii.

(2) ?t^ttri, to teach ; fiennen, to name j ^etperi/ to call) fa)clten, to
reproach (with vile names) j taufen^ to baptize (christen) ; take
after them two accusatives : as, cr le y rt mic^ tie teutfe^c %vtaa)t t he
teaches me the German language t ft neftftt u)a frtata Hitter, ae
calls him hit deUVerer. Bee Sect. 63

LESSONS IN ALGEBRA.

(3) The accusative is used with such terms as xoit$tn, to weigh ;
toficn, to cost; getten, to pass for; tixttb, worth; ftytoer, heavy;
ttia), rich ; tang, long ; n*it, wide ; to mark definitely the measure
or distance indicated by these words ; as, tiefto <St<xf ift ein $u$
long, this stick is a foot long ; <r $ tier CRwtate tit, he is four
months old. In the earlier German, these words of measure or
distance were put in the genitive : as, einet @9ttttftt ttttt, a span
wide.

(4) At words expressing time indefinitely are put in the ge-
nitive ({ 128. 1.), so those denoting a particular point, or du-
ration of time, are put in the accusative ; as, i<$ ertoartttc ten
gtoeiten $09, I waited two days.

(5) A substantive construed with a participle, is sometimes
put absolutely in the accusative ; as, titfen Umfianb autgenommen,
finte i$ fttte* xta)t, this circumstance excepted, I find all right.

§ 133. Rule.

A noun Or pronoun used merely to explain or specify that
which is signified by a preceding noun or pronoun, must be in
the same case : at,

(Stcrto, tin grof cr fltether, Cicefo, a great orator.
3$m, mrtnem 2Botyltl)rttcr, to him, my benefactor.
£)tt ftaty meincs JBtufccrt, toti $Ren)t«g«lt$rten, the advice of my
brother, the lawyer.

Observations.

(1) The explanatory noun is said to-be in apposition with that
which it explains : the latter being called the principal term.
Between these two, that is, between the principal and the- ex.
planatory term, there often intervenes some connective particle.
Thus er $ot fia) alt Gkfctyjefer rofcient gcma$t, he, as a lawgiver, has
rendered himself meritorious ; mein Sftactybar, ndmli$ Ut JJPaucr,
my neighbour, namely, the farmer. This latter mode of speci-
fying (that is, with the word aamlty), is far more common in
German than in English.

(2) The proper names of months, countries, towns, and the
like appellatives, are put in apposition with their common
names ; where, in English, the two words stand connected, for
the most part, by the preposition of; as, tec fDtonat ftuguft, the
month {of) August; tie ©tabt Sonton, the city {of) London ; tie
Unnxrfliat Qrfors, the university (of) Oxford.

LESSONS IN ALGEBRA.— No. XI.

(Continued from p. 272.)
REDUCTION BY MULTIPLICATION.

159. When the unknown quantity is connected with a known
quantity by the sign of division, the reduction is effected by
multiplying both members of the equation by the latter, if. it
be the divisor ; and by the former, if it be the divisor.

In this case, it will be particularly useful to remember a
rule formerly given : vis., that a fraction is multiplied by its
denominator, by removing the denominator; or, in other
words, putting down the numerator as the product. Also,
that after this process has been performed, transposition is still
to be employed as in the preceding examples.

Examples.
x

13. Reduce the equation — |- a = b -f- d,

e
Here, multiplying both sides by 0, We have, for the product,
x-\-ac=fo+cd; and, by transposition, x=bc-\-cd—ac.
x 4

14. Reduce the equation — — (-5=20. Ana. «=94.

15. Reduce the equation^-pr+dbsA. Ans.<K=(a4-6)X0fc— <*)•
»«+s

16. Reduce the equation

10-

+7=±8. Ana.<r=4.

160. Though it is hot always nmssary, yet it is often conve-
nient, to remove the denominators from fractions Consisting of
known quantities only. This is done in the same mantlet as
in the preceding rule.

17. Reduce the equation — =— -1 — *

• b* e

Here, multiplying by a, we have ar= —{ — ' again, multi-

plying by *, we have bx=a&\ ; lastly, multiplying by c,

we have bcxesacd-\-abh. "Whence #=— z_j!_ . Answer.

161. An equation may be cleared of fractions by multiplying both
members by all the denominators.

162. In clearing an equation of fractions, it often happens that
a numerator becomes a multiple of its denominator (i. e. can be
divided by it without a remainder), or that some of the frae*
tions can be reduced to lower terms. When this occurs, the
operation may be shortened by performing the division indi-
cated and by reducing the fractions to their lowest terms.

b . e A.
d g m

Ans* a? as

18. Reduce the equation •

abgm+ad em—adfh.
dgm

x 2 4 ft

19. Reduce the equation ■— =3 ~ + — + -=■. Ani. c =-

2 3 5 2

• -A.

168. In clearing an equation of fractions, it will be necessary
to observe, that the sign — prefixed to any fraction, denotes
that the whole value is to be subtracted, which is done by
changing the signs of all the terms in the numerator.

20. Reduce

Examples.
1 — d 3&—2A»— 6» .

Ans. 2 =

(a — d)r

cr — 3b+ 2hm +&n

21. Reduce -£ — 4 = •• ***• * = **•
8 4

- + ^ + 9

Ans. * 3K 7.

Ans. x = 10.

23. Reduce 2*-- = ^ + 4.

5 25 ^5

a. « •« . x . Zx 2x . x 10

24. tteduce-*+ Y + T - y + 1 -j« S - r

REDUCTION BY DIVISION.

Ans. * =2 70.

164. When the unknown quantity contains any known Quantity,
as a f actor 1 the equation is reduced by dividing every term on both
members by this known quantity,

25. Reduce the equation «# + b -— &h se &

Huie, by transposition, we have ax=zd+Zh — b\ and

dividing by #, we haye x = — - . Ans.

26. Reduce the equation 2* = — — •*+ lb. Ans. x sa

»(?-*)+»

THE FOFULAR EDUCATOR.

lit l£ the unknown u— HJtifi hi ec-ewaente m era
^/tbc eq>«tioo »i^ It divided 1^ tbe mm of all these

imn^!

fer*M,

27. Seduce the equation &x — *x= « — d.

H*re, 3x-** = '3 — 'y*. ** d (3-*;X*=«— *

Whence, dividing by 3 — *, we have* =£-3^ Ana.

28. Reduce the equation « + * = A — 4. Ana. x =

A-4
e+T

29. Reduce the equation * j- = —

Exawpuu.

«. Be**. -^ + -5^- = i.

Here, by tuV* 4 — ^ a fee 750; » fee 3 ; end * 6* 875; the
equation 1 em - + - = 1- Sow ckatine; of fractions,

e*
we hare a* + «* = «*: endr = e— y. On laafuaisi the

munbera, we hare jr= 750-

{a+J) h—\b
V(A-i) '
166. If any quantity, either known or unknown, is found ai la

to it. In this way, the factor or nuujuj
the reduction may be effected u brief e.

30 Reduce Ihi- ♦fju«iion ax -J- 3ai = 6ed+ «.

llVre, dividing by a, we have * + 3* = W+l; aud by
tiaiiepoeUion,* = 6d+l-- 3*. Ana.

31. Reduce the equation — - = — - — .

lUt* multiplying by x, we have * + 1 — £ = A — <f ; and,
by tr*nepoatUmt, j ^iA — e* -|- A — 1. Am.

32. Reduce the equation x X («+ *) — « — *= d X («+*;•
Ans.x = e , + 1.

167. -d proportion is converted into an equation by makin* ths
product of the extreme*, one member of the equation ; and the product
of the dm, the other member.

33. Reduce to an equation ax : b : : eh : d.

Here the product of the extreme* is adx, and the product of
the meana be h ; the equation is, therefore, adx = beh. Whence

beh A
x = — —. Ana.
ad

34. Reduce to an equation e -f- b : e : : h - w : y. AnB. y =
g( A— w)

a + a '

108. An equation may be converted into a proportion, by resolvituj
one tide of the equation into two factors, for the middle terms of
the proportion ; and the other side into two factors t for the rttrcuus,

35. Convert the equation adx = trA, into a proportion.
Here the nrit member may bv divided into the two factor*

ax and d ; the eecoud into eh and 6. From these factors we
may form the proportion ax: b :: ch : d.

Examples.

36. Reduce to a proportion the equation ay + fy = a* — aw.
Ana. a + b : h — m : : e : b.

37. Reduce the equation lGr + 2 = 3-1. Ana. x = 2.

38. Reduce the equation 4x — 8 = — 3* + 13. Ans. x= 3.

39. Reduce the equation 10* — 19 = 7 a + 17. Ans. x = 12.

40. Reduce the equation 8* — 3 + 9 = — 7x + 9 + 27.
Ans. x = 2.

NUMERICAL SUBSTITUTION.

169. In the reduction of an equrttiwi, a* well n in other parts
of algebra, a romptitatett procean can often be rendered more
ehnpte, by uhLiak letter* for the gii?cn numbers, Md sJao by in-
troriucinpr a Mill flat*** which ah all Ije made to repiceerit a
toholrt filffrfmris rj-presnioii* This prfceti is calkd sun&TnuTiON.
Alter ibe elgsbrtta operation la completed, the number* t or the
compound quantity for which a iiugh letter ha* been substi-
tuted, must be restored, in order to obtain the numerical
Talue.

375

42. Reduce

43.

44. Reduce

45. Reduce

- + 6=84. Ane.x = 104.

860

= 10. Ana. x = 3176.

/ — M — N

(aie — d) (i — m — n)

* + *+*•

Ans. x =z med +

ExaMPLaa foe Pnacnci.

1. Reduce^ + 6 = ^ + 7. Ans.» = 8.

4 o

2. Reduce~ + A=4~ ~+'-

a ' b c

abc{d — h)

Ans. x = -7 "TTr -

ab — ac + it

3. Reduce 40 — Bx — 16 = 120 — 14a*. Ans. x = 12.
* — 3 . x .. ar— 19

4. Reduce ■

+ 3=20-

6. Reduce-|- + y = 20— ^.

6. Reduce

7. Reduce

8. Reduce

1 — a

3
*+4

4 = 6.
.2 = 8.

* + *

= 1.

9. Reduce *+ | + ^ = U.

10. Reduce Y + T - r = B .

11. Reduce

x — 6

6x =

284 — *

12. Reduce 3x +

2* + 6_

=6 +

5
1U

Ans. x = 23i.
Ans. = 13».

Ans. x=|(l— *)•

Ans. x-= — 3.7.

Ana. x = i.

Ans. * =6.

Ana. * = 1}.

Ans. x =s 9.

Ans. x=7.

LESSONS IN ALGEBRA.

32*

,o t> , *<* — * „ 18 — 4*
13. Reduce — 2 = —

14. Reduce 21 -f

3*- 11

x. An*, x = 4.

5x — 5 . 97 — 7*

Ana. * =3 9.

,r»j « * — * , 5x + 14 1
15. Beduc Zx 4 = — T _.

10. Reduce

17. Reduce

18. Reduce x-

7r + 5 16 + 4*

-6 =

Ans. * = 7.
3*4-9

4* + 2_

5 — 6*4

Ans. #= 1.
7*4-14

3x — 3

■4 =

Ans. x == 4.
20— a; 6a:— 8 , 4* — 4

7^5
Ant. i = 6.

19. Reduce^ 4 '*

2*4-4

6jr + 3

20. Reduce ^±i:ii^ :: 7:4 .

21. Reduce 2*— 9 = 72 4- -^.

22. Reduce* — 11 =^±-^4- 7.

23. Reduce i-.is-f.4-1.

24. Reduce 11 — i = 13 — ^ .

o 4

25. Reduce 1±1 4-—--

26. Riduce ^— - 4

6
* + 9

= 8.
_3*4-7

Ans. * = 4.
Ans. * = 2.

Ans. x =z 45.

Ans. * = 23.

Ans. x = 12.

Ans. * = 40.

Ans. * = 19.

4-3. Ans. a: = 51.

«» « * 2* . 4* 6.r * , 3a; 5x . _ .

27. Reduce 3 4. --- y = ~ 4.-— g 4*81. Ans.*=420.

x — 1 x — 2 x — 3

28. Reduce — 1 — = 6. Ans. x = 1J.

2 3 4

80LUTION OF PROBLEM&

170. For the solution of problems in Simple Equations, we
'derive from the preceding principles the following general
rule ; —

Rulb. 1st. Transitu the statement of the question from the ordi-
nary language into algebraic language, in such a manner at to form
an equation ; that is, put the question into the form of an equation.

2nd. Clear the equation of fractions by multiplying every term in
both members by all the denominators successively^ or by their least
common multiple.

3rd. Transpose all the terms containing the unknown quantity to
the one side of the equation, and all the known quantities to the
other, taking care to change the eigne of the terms transposed,' and
incorporate the terms that are alike.

4th. Remove the co-efficient of the unknown quantity, by di-
viding all the terms in the equation by it ; the result will be the
sotutuyn required.

Peoof.— Substitute the value of the unknown quantity for the
letter which stands for it in the equation ; and if the number satis-
JUs the conditions of the question, it is the answer sought.

Problem I. A man being asked how much he gave for hie
watch, replied : If you multiply the price by 4, to the product

add 70, and from this sum subtract 60, the remainder will be
equal to 220 pounds.

In order to solve this question, we must first translate the
conditions of the problem into such an algebraic expression as
will form an equation.

Let * be the price of the watch.

This price is to be multiplied by 4, which makes 4* ; to the
product 70 is to be added, making ix 4- 70 ; from this, 50 is
to be subtracted, making 4x4*70 — 50.

Here we have a number of the conditions, expressed in
algebraic terms ; but we have as yet no equation. We must
observe, then, that by the last condition of the problem, tho
preceding terms are said to be equal to 220.

We have, therefore, this equation 4*4-70 — 50=220;
which reduced, gives * = 60. Ans.

Here the value of x is found to be 60 pounds, which is the
price of the watch.

Pboov. — The original equation is 4* + 70 — 50 =s 220 ; sub-
stituting 60 for x, it becomes 4 X 60 + 70 — 60 = 22Qi that
is, 220 = 220.

Prob. 2.— What number is that to which, if its half be
added, and from the sum 20 be subtracted, the remainder will
be a fourth of the number itself?

In stating questions of this kind, where fractions are con-
cerned, it should be recollected, that \x is the same as

|; that*r = -, &c.

Let x be the number required.

Then by the conditions, we have x 4-

reducing the equation, we have *= 16. Ans.

Pboop. Thus 16 4- ^ — 20 = !?.
2 4

Prob. 3. — A father divides his estate among his three sons
in such a manner, that the first has £1,000 less than the whole ;
the second has £800 less than one-third of the whole ; the
the third has £600 leas than one-fourth of the whole? what is
the value of the estate ? Ans. £28,800.

Prob. 4. — Divide 48 into two such parts, that if the less be
divided by 4, and the greater by 6, the sum of the quotients
will be 9.

Let x be the smaller part; then 48 — • is the greater part ;

48 — *

20=—; and

and, by the conditions of the problem, we have, \

= 9. Whence x « 12 ; therefore, 12 is the less part, and 36
the greater part.

171. Letters may be employed to express the known quantities
in an equation, as well as the unknown. A particular value is
assigned to the letters, when they are introduced into the cal-
culation ; and at its close, the numbers are restored.

Prob. 6. — If to a certain number, 720 be added, and the sum
be divided by 125, the quotient will be equal to 7392 divided
by 462. What is the number ?

Let m be the number required ; and let a = 720, * = 125,
d « 7392, and h - 462.

x-Ua
Then, by the conditions of the problem, we have-— ~~

d . , . . M— ah
« —; and reducing, we have * « .

; * -A

Restoring the numbers, we have,. ( ^X 7392)- (720 X 462)

462
- 1280.

Prob. 6. Divide 11 into two parts, such that the sum of twice
the first and half the second may be 16. Ans. 7 and 4.

Prob. 7. Divide 39 into four parts, such, that if the first be in-
creased by I, the second diminished by 2, the third multiplied by
3, and the fourth divided by 4, the results may be all equal.

Ans. 5, 8, 2, 24.

Prob. 1. If a certain number is divided by 12, the quotient,

THE POPULAB EDUCATOR.

dividend, and divisor, added together, will amount to 64.
What it the number ? Ana, 48.

Prob. 9. An estate is divided among four children, in such
a manner that the first has £200 more than ± of the whole,
the second has £340 more than * of the whole, the third has
£800 more than £ of the whole, the fourth has £400 more than
i of the whole. What is the value of the estate * Ans. £4800.

Prob. 10. What is that number which is as much less than
500, as a fifth part of it is greater than 40 ? Ans. 450.

Prob. 11. There are two numbers whose difference is 40, and
which are to each other as 6 to 5. What are the numbers ?

Ans. 240 and 200.

Prob. 12. Suppose two coaches to start at the same hour, one
from London for Glasgow, and the other from Glasgow fpr Lon-
don, the former travelling 10} and the latter 9} miles per hour :
where will they meet, the distance between the two cities being
400 miles ? Ans. 210 miles from London.

Prob. 18. Buppose every thing to be as in the last oueation,
except that the coach from Glasgow starts two hours earlier than
the other ; where will they meet ? Ans. 200^ miles from London.

Prob. 14. A dealer purchases 6Q yards of cloth for 30/. ; and
by selling one part of it at 12*., another, twice u great, at 14*.,
and the rest at 10*. per yard, he gains 8/. How many yards
were in the several lots ? Ans. 16, 32, and 12.

Prob. 16. Suppose two dealers each annually to double his
capital, except an expenditure of 100/. ; and, that at the end of
three years, the capital of one is found to be doubled, while the
other has only half what he had at first ; how much had each to
commence with? Ans. 116/. 13*. id. and 93/. 6*. Sd.

Prob. 16. If a person each year double his capital except an
expenditure of 300/. the first year, 400/. the next year, and 500/.
the third, and at the end of three years be found to be worth
5600/., what was his original capital ? Ans. 1000/.

Prob. 17 . A father's age is now treble of his eon's, while five
years ago it was quadruple : what are their present ages ?

Ans. 45 and 15 years,

Prob. 18. Divide 1000/. between A, B, and C, giving A 100/.
more, and B 501. less, than O. Ans. A's share 416/. 13*. id. ;
B's 266/. 18s. 4sf. ; and C's 316/. 13s. id.

Prob. 19. A spirit merchant finds that if he add 10 gallons to a
cask of brandy, the mixture will be worth 21s. per gallon ; but
that if he add ten gallons more, the value will be reduced to 18s.
How many gallons were in the cask } Ans. 50.

Prob. 20. Find a number, such that if it be divided successively
by 2, 3, 4, 6, 6, 7, 8, 9, and 10, half the sum of the first four
quotients increased by 20 shall be equal to the sum of the remain-
ing five. Ans. 5040.

Prob. 21. Find two numbers differing by 6, and such that
three times the leas may exceed twice the greater by 7.

Ans. 25 and 19.

Prob. 22. Find a number such, that if it be increased suooes-
atvelv by 1, 8, and 8, the turn of one-half of the first result and
one third of the second shall exceed one-fourth of the third by 8.

. Ans. 13.

LB880N8 IN READING AND ELOCUTION.-No. III.
PUNCTUATION.

THE COMMA.

22. TK$ mark used for the comma is a round dot with a small
curve appended to it,' turning from right to left.

23. When you come to a comma in reading, you must, in
general, make a short pause or stop, so long as would enable you
to count one.

24. The last word before a comma is most frequently read with
the falling inflection of the voice.

Examples,

25. In reading, when you come to a comma, you must keep

tout voice suspended as if some one had stopped you before yon
had read all that you intended to read.

26. In the following examples keep your breath suspended
when you come to thftomroa : but let the abort pause or stop
which you make, be h total cessation of the voice.

Diligence, industry, and proper improvement of time, are
material duties of the young.

He is religious, generous, just, charitable and humane.

By wisdom, by art, by the united strength of a civil oun sj s u ui i ly,
men have been enabled to subdue the whole race of lions, bean
and serpents.

The genuine glory, the proper distinction of the rational species,
arises from the perfection of the mental powers.

Courage is apt to be fierce, and strength is often exerted in acts
of oppression.

Wisdom is the associate of justice. It assists her to form equal
laws, to pursue right measures, to correct power, to protect weak-
ness, and to unite individuals in a common interest and general
welfare.

Heroes may kill tyrants, but it is wisdom and laws that prevent
tyranny and oppression.

27. When a note of interrogation occurs at the end of a sen-
tence, the parts, and even the words, of the sentence separated by
commas, should each be' read like a question.

Examples.

Did you read as correctly, speak as properly, or behave as well
as James r

Art thou the Thracian robber, of whose exploits I have heard
so much ?

Who shall separate us from the love of Christ? shall tribula-
tion, or distress, or persecution, or famine, or peril or sword ?

How are the dead raised up, and with what body do they come ?

For what is our hope, our joy, or crown of rejoicing }

Have you not misemployed your time, wasted your talents,
and passed your life in idleness and vice ?

Have you been taught any thing of the nature, structure and
laws of the body which you inhabit ?

Were you ever made to understand the operation of diet, air,
exercise, and modes of dress, upon the human frame )

28. Sometimes the word preceding a comma, is to be read like
that preceding a period, with the falling inflection of the voice.

Examples.

It is said by unbelievers that religion is dull, "—«fH. tu>
charitable, enthusiastic, a damper of human joy, a morose intruder
upon human pleasure.

Nothing is more erroneous, unjust, or untrue, than the state-
ment in the preceding sentence.

Perhaps you have mistaken sobriety for dulnesf , equanimity
for moroseness, disinclination to bad company for aversion to
society, abhorrence of vice for uncharitablenesa, and piety for
enthusiasm.

Henry was careless, thoughtless, heedless, and inattentive.

This is partial, unjust, uncharitable, and iniquitous.

The history of religion is ransacked by its enemies, for instan-
ces of persecution, of austerities, and of enthusiastic irregularities.

Religion is often supposed to be something whiah mutt be
practised apart from every thing else, a 4jstinct profession, %
peculiar occupation.

29. Sometimes the word preceding teomme, is to he seed hke
that preceding an exclamation.

Examples.

How can you destroy those beautiful thinga whiah ymr sasher
procured for you ! that beautiful top, those pfiliahed MrUe**
that excellent ball, and that beautifully painted kite, oh how sen
you destroy them, and) expect that he will buy you new ones !

How canst thou renounce the boundless store of oharms tfeat
Nature t«> her vo'ary yields! the warbling woodland, the resound*
ing.ehore, the pomp of groves, the garniture of fields, all thattbc
genial ray of morning gilds, and all that echoes to the song of
even, all that the mountain's sheltering bosom shields, and ailing
dre&d magnificence of heaven, how canst thou renounce them ajoa
hope to be forgiven !

CORRESPONDENCE.

381

Ok wintet ! ruler of the inverted year I thy Mattered hair with
aleetlike ashes filled, thy breath congealed upon thy lips, thy
cheeks fringed with a beard made white with other mows than
those of age, thy forehead wrapped in elands, a leafless branch
thy sceptre. %nd thy throne a sliding ear, indebted to no wheels,
but urged oy storms along its slippery way, I lore thee, all uu-'
lovely as thou seemest, and dreaded as thou art !

Lovely art thou, Peace ! and lovely are thy children, and
lovely are the prints of thy footsteps in the preen valleys. '

30- Sometimes the word preceding a comma and other marks,
II to be read without any pause or inflection ef the voice.

Bsawpkt.

You Me* my aon, this wide and large firmament over our
heads, where the sun and moon, and all the stars appear in their
turns.

Therefore } my child, fear and worship, and love God.

He that can read as well as you can, James, need not be
ashamed to read aloud.

I consider it my duty, at this time, to tell you, that you have
done something of whioh you ought to be ashamed.

The Spaniards, while thus employed, were surrounded by
many of the natives, who gazed, in silent admiration, upon
actions which they could not comprehend, and of whioh they did
not foresee the consequences. The dress of the Spaniards, the
whiteness of their skins, their beards, their arms, appeared strange
and surprising.

Yet, fair as thou art. thou shunnest to glide, beautiful stream !
by the village side, but windest away from the haunts of men, to
silent valley and ■haded glen.

But it is not for man, either solely or principally, that night is
made.

We imagine, thatf in a world of our own creation, there would
always be a blessing in the air, and flowers and fruits on the
earth.

Share with you ! said his father— so the industrious must lose
his labour to feed the idle.

31. Sometimes the pause of a comma must he made where
there is no pause in the book. Spaces are left in the following
sentences where the pause is proper to be made*

Bwmplv.

The Europeans TO"o hardly less amazed at the scene now set
before them.

Their black hair long and curled floated upon their shoulders
or was bound in tresses around their head.

Persons of reflection and sensibility contemplate with interest
the scenes of nature.

The succession and contrast of the seasons give scope to
care and foresight diligence and industry which are essential to
the dignity and enjoyment of human beings.

The eye is sweetly rested on every object to which it turns.
It is grateful to perceive how widely yet chastely nature;
hath mixed her colours and painted her robe.

Winter oompen sates for the want of attractions abroad by
fireside delights and homefelt joys. In all this interchange
and variety we find reason to acknowledge the wise and
benevolent care of the God of seasons.

89. The pupil may read the following sentences ; but before
reading them, he should tell after what word the pause should be
made. The pause is not printed in the sentences, but it must be |
made when reading them* And here it may be observed, that j
the comma is more frequently used to point out the grammatical
divisions of a sentence, than to indicate a rest or cessation of the
voice. Good reading depends much upon skill and judgment in
making those pauses which the meaning of the sentence dictates,
hut whioh are not noted in the book ; and the sooner the pupil is
taught to make them, with proper discrimination, the surer and
the more rapid will be his progress in the art of reading.

The golden head that was wont to rise at that part of-the table
was now wanting.
For even though absent from school I shall get the lesson.
For even though dead I will control the trophies ef the capitol.

Jt is now two hundred years since attempts have been made to
civilize the North American savage.

Doing well has something more in it than the fulfilling of a
duty.

| You will expeot me to say something of the lonely records of
■ the former races that inhabited this country.

There is no virtue without a characteristic beauty to make it
[particularly loved by the good, ana" to make the bad ashamed of
\ their neglect of it.

A sacrifice was never yet offered to a principle, that was not
made up to us by self-approval, and the consideration of what
our degradation would have been had we done otherwise.

The succession and contrast of the seasons give scope to that
care and foresight, vigilance and industry, which are essential to
the dignity and enjoyment of human beings, whose happiness is
connected with the exertion of their faculties.

A lion of the largest size measures from eight to nine feet from
the muzzle to the origin of the tail whioh last is of itself about
four feet long. The height of the larger specimens is four or five
feet,

A benison upon thee gentle huntsman. Whose towers are
these that overlook the wood ?

The incidents of the last few days have been such as will
probably neve? again be witnessed by the people of America and
such aa were never before witnessed by any nation under heaven.
a To the memory of Andre' his country has erected the most mag-
nificent monument, and -bestowed on his family the highest
honours and most liberal rewards. To the memory of Hale not
a stone has been erected and the traveller asks in vain for the
place of his long sleep.

CORRESPONDENCE.

MUTUAL INSTRUCTION CLASSES.

Sir, — This is an old mode of instruction, but one too muoh
neglected. It* importance will be disputed by few, affording as it
doe* such facilities for acquiring and exercising knowledge, quick-
ening the perceptive faculties by wholesome and stimulating com-
petition, and enlarging and correcting our views hj association. It
has struck me that the success and prosperity of the " Popular
Educator " would be even more permanently established, and
the students themselves more interested and benefited by its lessons,
if classes of this description could be generally established in con-
nexion with this publication. The students of the " Popular
Educator" do not sufficiently know their brother students.
Many of them in the same town may be individually studying the
Same subject, unknown to each other, who would be very glad to
meet for the purpose of mutual instruction. Difficulties frequently
Ocour to one person, which are easily removed by another ; and,
where necessary, an instructor for the whole class might be engaged
at a trifling expense to each, instead of paying exorbitantly for
private lessons.

Now, Sir, if a plan could be devised for collecting together all
the students belonging to a particular locality, little difficulty
would be experienced by them in subdividing themselves into classes,
according to their different studies. The machinery required for
this would be very simple. Tou would have to exercise your
indulgence by sparing a corner of the P. B. for it; and any
person wishing to collect together the students of the locality in
which he resides, would merely have to send you his name and
address for insertion, thus :— Norwich, w. B. " News " office.
Any students in the place referred to, seeing this announcement^
could at once communicate with him, and he might immediately
bring them together by calling a meeting, when arrangements
sould be made for the formation of classes.

I should like that this experiment were made in Norwich,
believing that many students here would at once embrace the
bpportunitT. If such persons, therefore, will send to the address I
have just given as an example Ms. W. B. "News" office, Norwioh),
[ shall .feel most happy in calling them together, and assisting in
(he necessary arrangements.

Should this effort prove effectual for Norwich, of course many
other places could do the same. A system of National Adult
Education of no mean character would thus be established through-
put the kingdom ; and the anxious desire of many great and good
pien of the present day, would be in a great measure realised,
through the simple instrumentality of the Popular Educator and
the exertions of a few spirited individuals in eajh laoslity.
. Trusting that you will lend your iniuenoe in aid of this move-

332

THE POPULAR EDUCATOR.

meot, lod bcoeac tb*$ md »o»i »xt aeerae fc^a* iti ~can?fetn or
T.art:*l adop-'./n by ▼•>«*• r*ie*t« f I nt, **.— W. B.

NomA, FA. %w4 t If M.

" W» bare \*.%*TV*i tv.s letter, "vers as* w* thick ti* t*aa a fa*
o- *. v "- r '." *« i-i ff« «'**■ '.3,»TT:--Ai wz.ic:. we bare has :-,
* X'. ■•••t-r r --* wiiti La*»">«- ;::x.+(J. Of ersnc tie xnior
has zl -? f.r>t"e"y ii« ai=* ir.-i a.::rt%\«, a »e«
isiiepeiiss*!? to -.tj p— ponl *f •-
rece.se.]

'Lsarttn.- Ar-

irtw, a *aea?t.rt? q%ztc ' j 11 ? *
a* k:-.i wh "ci w? ssay ; ^_J

to m.—+tnnzcrr l* Trmjm -. Ba mm at the seiataoa of tbe Mathe-

*ir Mcnrurans is tbe V. at L, it Terr fab? ; bat a littse

vs*s.i£ »_r»* Ws-t s ca tia sVw worn rrotoriwriiw, Piim

bt wis wheats as to feemaaaassae a taatsr, saaont giro felt

bd ao. r-t», aad free as of i«m ia the matter.— J. Wood (Maav

.t.iT::>;lii« Dar'^cte t »« caaTt ad*a*e thessu— D. E. B.

Tv. IL cc* 'CassniVtGa

i iter Ea» W?ssnawnrV ,e y s e t u« (ura; qnsfisn. which is '

eagnvt-ra^sn oil erf sraSer is w be sfcradcsl <

bs has* ae a w asue af snrr kind,
lr«ai:toka«r
M * E»o*x a Tsaanr £oaafar< <c t : Wtk a ne wer scan o r beard a f ay
..__— ._-^_ _.-. _r^^_ -_ _--^.^-- ■ ■■ »j — •'■•■BBf *aerf rwaBBaa Sreai tfca «ap5aatlaa af Maaaaaafai to theaaaor"

ANSWERS TO CORRESPONDENTS. 7m u LwaVu *«« - ■ • - ^ ■

* ~ .. . _ - t _*. - m_ j ... aroeers u u u t« tie West raje ;

T. C. !I. U : We nrswt refer yaw. ta p i t i i ta s renaarhs with regard ta ft e - p.^ ateasrt-f t imarw«ed aw
'•thaw U?fi0oarf. T>-« ass^tt v*X be aaJy i w^n i i. Wxta rvfari to tt* M«tLem*t:T».— W MACYiaJOX

K ^.^*r fc " M ^ to ' J>< tofia^lai a» to ab^af ibgi^T b^ ajaak r. ,»»« ^ r p«r «e«C. sa W^ eaT Vy the aK«al aafaaeat af a certain aoat
m^d hxuiiMU the yr.^rw af *~« earaeat yay^ T^f* the aal ef a . Wa*» «a«i: tkat aaa •-» be ! - Beta, tbe aaai • is aa aavaJty. Vow
sau^bct at ti» euae b«a fsxtber tbe aOaaasa r€ by far t^a freay. , p,. T^KsaaaTia k» - Antbaaeoe,- * f^. tbe«i, Ibat ia order • to to4
aaaaber. T« »sC«f> tbetx c-snon:?. taay wsj* easapare tbe Key vnb tbe ' .., entire *asa tfs* far aa «sasmr leassccaaf; -4-" far a aire*
eaer*iMa ef tbe jnrvn* »<*k, aad eaosadcr IbriieN'ea exess^ted Cross . ^ * - - c •

f .be tub of tnaatetiaf iteaL. A L"rur lac^-afe is r« karasd, obe a s>»4 t
<k>«, exrelj for tbe parpose of re*4tar . bat also Jot tbe pxrp ss e cf fswabixf |
and wnti-f ; aaal with reavd ta tbis latter asoat aasjnrtaat atjeet, tb* j W( .

*e^-acti«itv of tbe aaack stcat be kept ip ty a£ sieaaa ia Ue paver af a I « — I

'eseber. H<nrn«r # a Key af all tbe srrrMos E?afbb-IbLisc Excreiacs sr.U ! 'ar>— ^-

1 iatersst bebaj ajcrrf -« aB tbe sMSjey tbas

faractee
reasaiaaor.

—X •

1 ;xa«4 i = -

; wbere * , a, aad a, hare the

be rrrea after the tena:sa*wi of eac^ cf th» priadpal dl-H*-:-;-!
fraaisMr. a d taen we think wi:bo<st tbe abore-ttsied s^ad*-&=tKfe.

H. Mtt BirattBfbufi.: See oar asuwer ta T. kL. Oatmrta. Tie
t*abtrm sn'.m oat witbaot eefTeaee t> saj soafras. u bumM; sr«-.
Write to t*<a LdilAr of tbe P. B- K. as ;>« i' t-) u —J. D. B>=ia?biaj -
Wbm tbe chord of si arc. and the ra£:«« rf tbe c:rr> are ctrra, tbe e^ori
'. f t.elf tbe are avaj be frr:ad wUbont Trtr- uui<tij. tbss : I rasa tbe »)sare
«f tbe r*-1iat «abvaet lite square of hfeif' tbe (irea catard. sod tbe s^asre
roof of tbe reBr.aiadtr miZ be th* di*tas<e of the catre cf lie e.re> frws tbe
uudcleof lfce<V'-rd; ssbtrar! thi» '.-fUme 'r .es :be red:*!*, v>4 tberestvni«r
»r;ll be tbe m$itta '.x CM'ao.e frc-i tie ai^ieof tbe chord I . tbe sili'jt zt
tbe arc. : aii 'be sqnare of thit ta|~.t*« to tbe *qisxe of b» f tLe r/.^es '
ri.',ril, ail t'e »-j i**e n:--' o' tr.e » :=i *:1! be *h* r»rj .ii^-i • vird cf Lif
the *re. Gtk+nri*e : i--b»nr: tLe iqatre of ha I f.e ch rd fret: •..»
»qu*'e of tbe r»-ijat, sad extr*et the eqavr- rc«: of t^e re-=«-*id*r. Sa 1 !- '
ua*"t :ou r*>t (rem tt»e r»; u», ivt aiul-pij tb* rrxv«vi*r *-y tirise tbe j
r»dja.; tbea estrart tbe ^;ire r-.? # . of tr-e prod if, acd it « 11 te tbe ■
req?*r»d -h^r i of half tbe af. 1 * e terse! l:se it :*» d-tfe.-ft-e btlsreea i
-«• rvdlm a* d the cosm-. *cc No-. Tl, pir*. H. — J. F. Trti» G!ifyow : !
JwJnttd it pTono-jcced lee-c-Ut-ed. —

i. K. (Clerktoireli;: We «».» Lis aa>v«r to tie Ij^t CL". qiestira
bad hren rirli:; we hare hid or-i) sr-l ^t*c-a. fc-it ;l 5t net yt sixssrerei.—
Us Ltudiajct ^Dir.ine;toa : Mo»: h^'.r a Gr *\ Dittlorarr. Jcc.,wi.l be
p-WUhed.— T. F. 'Hoi *.ru, : Tse dlflcnUj wfci'h h* soeets wi:h ia refard
to esercMri in parsir.s:. or icy otber e«erri»es, wanld be sae*. by hit jnuinr
a cc atia' m**..-ticUi-n sccety. s tb ar, we bswe cf:ea reo?xai*a.«d. If saj '
six jounr in* a. or rid cieti. or men of nvx-d are*, seree to men xr.l anl.t i
ascb crh^r, rber can tapdy tbe flace cf a tat^r am ay th^vxKrs: an i If I
any mrrum» dtfieulty '•erar#, we »«•? «U.ia« to becnee ass^r*. It is qui> '
pea*: vie to b«ov.z»e a enrr** t Latin seh lir. <--r any st.Ser scar-lar. by d«.f-
f~£'.j •tndtinr the Le»s , :!:» !n the P. *-; b'jt the mat-ial taf:reet>?n 9t»:*m
wr.1fTe%*I/ rn!-jffiten *nd «h-->rf- tie process. It wrali e«en rres'Jj ;
srii **> 'be prj-wer of tbe «}»Urn, at *el. at to ;:» :nterett aid iu hni^aciU*. ■
xi *...< »:x KQ*ail inscr-acti? :»*«*.« ^onA tjke «ocnc raf<ed and de*titate '
,<"*».'* 4*l**twmi fross the s'reet*. anl try t? isaunct bim aad make bun ,
of - • •

ra!a»t fLr*t atcre, aa! a — . Ia order to solra the preeediaf

by a sisaple Als^brate

qteitaoa, tbea, we bar* c~ '.j ta re«Taa tbe

(a,-: t
p- ;»a?.this- ■ = . Ei«;:j: If the rata of £7,9» lCs. 4Jd.

«. — *
were borrowed far J : year*, at i

off u tu lx: : a-.#.. £;■.•:■.

l»-4 a

i — =IjC£; a-. I a. = s.

!■:•>

= '. y : * .* -. ■- lie i"s*w#r i»« £\ X sast be pal] yearly.

per cent., what aaamal aaai woa!d pay it

F * XTMQl9I«9 It the mm borrowed;

7*kx«l83S.C6

= 5.7I3I»1 ; tberetbrr a =

5.74M91-1

LITERARY NOTICES.

GRAND DOrBLE NUMBER OF

-TEX lUITSTmATBD FAKXX.T Fi

-Ovk::'. Iirutrarr! Fa=i:.r Psperr >" - 15. bexrinf data March 25. will
»e a D i > Naaber. exitaininr la Pares, prise Twopeaea. This
D-?h!c Si^\*r will he maraificeo*. t Illaftrated, aal will be tare to
coasma.nl the L:^h*st apyrcvii of all rsrehasers.

THE WORKING MAN'S FRIEND AND FAMILY INSTRUCTOR.
Be-usme cf tk-'t ctUbrsS*-! aad popmlcr Wmk.

Thi< Wcrk it effered. f r a Exited period, at a redaced price. Tbe set

«c»n:p-:#-* ftt-. T^Iaues. ero»a ceta'-j. For the excellency and genera^

iiterrf -f u crier.u it i# oct be # jrpa«aed. U forms a library in itself*

in* Ta!e< and Namuves b\ V.i!iamaad Mary Howir, Miss Mete-

B- Tdearo iriny to Imlr^ct saeh s on?, they ' T ^ Si^erre-. . ar.d" «tber writer, of em:aeace : leadta^ articles on topics

io*r if sor.ety. __ _ _

**-..:•. >ari in ^!h better tbe.TT.*«:^..s^d t-ey moi'A teeth; ha-r.xn min'i i & J wp ir.terest to :Le worki**; clas«es; the cekbrateJ letters of Martha
•rK.ykrA-.vi *- 4+T^*dlir*, Ike a -ironc:nr pan; tranfplsnt^-! m'.ot.o*w M«ker*a*e r n Doxefti? Eertn^^mr; Pspm and Extracts oo Saeaec and

*?A z*vtrt nil. Ob tae ^ieatare • f do.cz go>~d ! Tbey w--:id be s n:<ly
r»»art«f. Tbe*.r avrrry w il: bv # w. e ».>-»-d; it w-.uH blest xth tteao
'bV. rare vA Wem tbat rocaiTrd V.- prerioi* boon. Kemeccber *' t^iat tnc
•r^t* a» sj;tii;«a* s.-.o«!«ds;* is w«t z-wl."

EcoLtea W^-jecb, : We sftall t»se -p the tihjeet of Architecture
arata, wh-o we can fet an opem*? in ?h* P. F.— i. Child ;Tenb} > : Lor*-
ritbaas sj^ti we can yet room in tae V. K.— l^getaia (Bi1ef>rd): We don't
•bias anch cf th» b">ks to whieh Le refers : a« to the Elementary Bxiit*
ia Ceveasastry, we boUi in inr ha/Kft a «>,rk » f * <xe value, nhicb sires s l;»t
of 41 wtto tb»ir aaases. cq ura.-a'j. ke. T » *■?. of con-se, w;U be fi*cn in
'.rder, ia t^e Lesv.ns :a Lie P. h. — A. B. Car- arr^n; : We d^ n^t know any
CoLf w.^re aT.-s-nta are adn-.ittf-i crati«; S-it what onnexi«n this has
with bet* % a Brtt:*b Cocr:. or An»tss*a-1or. we do not »e* !— Toat . Dubl a):
Saeowr Claris unj Les*on no Mo*l- — 'irrtx Eitoo Square, will finds
descnp'.ao'i sad drawiaz oi tbe Mmrquoii Scales, or parallel ruler, iu tkr
P. EL. ▼ 4. 1.. p. 13, eel. i, Af . 5, aawi :io# 13 from Lie bottom. — Coqucs
(London) : Tuere i» no ta-rh th;or a« perpetnal motion iarentible by man.
M. Gl'TsiaiE ^LiTeipool, Box W. 90. wisKet an a-ceati^n to anxiety cf
yoaaa; ir.*n wb> are earned In carryinz on a mamifcript marpz-ne. As
roan; a.cn best onderstaad or.? another, we bepe this inttmatiua wiU
incite rome tanfleds^nl g eniaue* to come forward «r d aid the ?Oi>d catue
by tbefr co-.tribotior.*. We hope, howerar, tbat theav: comlribmiiotu mill
aot belike those which the Professor, who o«ed to caeat bis stodents li his
own dkmmbers Jimelm carpeted, instead of the dbvs-rooas, requested the.-n
t> Unte at Ike door.—l. GairriTus (Ah^ryttw.tb): aee pp. 13? and 213,
to!. II , P. E. ; also pp. Il9 ( 295, and 323, to!. III.; and pp. 907 et sexu
aal. IV.

U. J. Chcki«tx ,'Bamlet) : Rirht— Ho Hrroxxxox, D. Josirn (San-
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LESSONS IN PHYSICS.

833

ON PHYSia OR NATURAL PHILOSOPHY.
No. XXIII.
PNEUMATIC AND HYDRAULIC MACHINES.
(Continued from page 320.)

Pumps .— Pamps are machines employed to raise water, by
suction, by pressure, or by the united effect of both: hence,
their division into three kinds, the suction or common lifting
pump ; the forcing pump ; and the suction and forcing pump, cr
Hft and force-pump. Before the time of Galileo, who died in
1642, the ascent of water in suction-pumps was attributed to
Nature* » abhorrence of a vacuum ; but we now know that the
cause is the pressure of the atmosphere.

The Suction-Pump. — The suction or common lifting pump
has been already so far explained in a former lesson ; but in
order to make the subject clearer to some readers, we shall
explain a model adapted for lecture-room demonstration, as
shown in fig. 112. This model is composed, 1st, of a cylin-

Fif . 112.

dries! barrel made of strong glass, at the bottom of which is a
valve s opening upwards ; v 2nd, of a suction-pipe a, which is
immersed in the reservoir containing the water to be lifted;
3rd, of a piston with piston-rod which rises and falls in the
barrel, the piston being perforated in the centre, and having
the orifice covered at top by a valve o opening upwards. The
pump-handle p is employed to put the piston-rod and piston
in motion. When the piston is raised from the bottom of the
barrel, a partial vacuum is formed below it, and the valve o
remains closed in consequence of the pressure of the atmo-
sphere ; while the air in the suction-pipe a rises by its elsstic
force, raises the valves, and partly forces its way into the barrel.
The air below the valve s, being thus rarefied, the water rises
in the auction-pipe until the pressure of the liquid column so
raised, added to the tension of the rarefied air remaining in the
pipe, balances the external atmospheric pressure on the water
in the reservoir.

When the piston is lowered, the valve s is closed by its own
weight, and prevents the return of the air from the barrel into
the suction-pipe. The air in the barrel, being now condensed
by the pressure of the piston, opens the valve o, and escapes
into the atmosphere by the pipe above the barrel, which is

TOL. IT.

called the ascension-pipe. At a second stroke of the piston, the
same series of phenomena are reproduced ; and after . a few
strokes, the water,, following the air, finds its way into the
barrel. The effect of the succeeding strokes is now modified.
During the descent of the piston, the valve is closed, the com-
pressed water raises the valve e, rises above the piston, which
then lifts it up and causes it to rise by degrees to the upper
reservoir. There is, after this, no more air in the barrel, and
the water, urged by the atmospheric pressure, rises with the
piston, provided that the top of the barrel is no higher than 34
feet above the level of the water in the lower reservoir, which
receives the lower end of the suction-pipe ; for we have seen,
in a former lesson, that a column of water of about 34 feet
balances the pressure of the atmosphere.

In order to ascertain the proper height which may be given
to the suction-pipe a, it should be observed that in practice
the piston is never brought down exactly to the bottom of the
barrel, and that there is always below it a small quantity of
air having the force of the atmospheric pressure. Suppose the
space which this quantity occupies to be -fa of the barrel.
Then the air in this space expands as the piston ascends, and
when it is at the top of the barrel, the tension of the air in the
barrel is ^<j of that of the atmospheric air, according to Mari-
otte's law. The air of the suction-pipe, therefore, cannot be
rarefied beyond this limit ; and consequently the water, in this
case, can only be raised to the height of fj of 34 feet, that is,
to the height of about 33 feet. This height is still too great,
because the water must be raised by a certain quantity above
the valve s ; so that, in general, we cannot give to the suction-
pipe a greater height between the limits above mentioned,
than that of about 26 or 27 feet. Thus we see that in the suc-
tion-pump the water is first raised in the suction-pipe by the
force of atmospheric pressure, and that the height thus
obtained does not in general exceed 27 feet ; but when once
the water has passed through the piston, it is the ascensional
force of the piston which raises it, and the height to which it
may then ascend depends only on the force which moves the
piston.

The Forcing-Pump. — Having explained the nature of the
common pump, erroneously called suction-pump — seeing that
the suction of the water, or its ascent in following the piston, is
due simply to the pressure of the atmosphere, ana that it
would fail in bo doing as soon as the column of water exceeded
that pressure, the limit being at the utmost within 34 feet — we
proceed to describe the operation of the forcing-pump, repre-
sented in fig. 11*3 : a is the suction -tube, having its lower end

Fif. 113.

immersed in the water as before, p is a solid piston without a
valve, which moves in the body of the pump c t by means of a
lever as in the common pump. The air is withdrawn from
the suction-tube as before ; but instead of escaping through a
valve in the piston, as it cannot return through the valve r, it
is forced by the descent of the piston^ up through the valve I,
into the ascension-tube s ; the water then follows by the pres-
sure of the atmosphere and the ascent of the piston, and is
forced through the valve r ; this valve is then closed by the
descent of the piston, and the water in the body of the pump
is forced through the valve /, and up the ascension-tube *,
om which it cannot return, as its weight shuts the ^alve /.
This process is cninued untiUhe water in the ascension-tube

101

THE POPULAR EDGCATOR.

, the force muu e m i to me it
ccc£rsa!2j increasing until H
nd a discharged frrSa the as ter skm - tube.
ar=. of th* ftr=t-'pz;, there b no use Bade
* -A the a^mospherel The scetion-ahe, of course,
with, sad the pump-barrel is itself immersed in
lie iliLii. c f± water Vj be raised. The eontinuiry of the jet
of vcs fnct ti* MwcBec-pis* £* «-baiced by the action of
»ilml2 v .mnii cf air, which we shall explain in the foOow-
ag d c a cr^ci :*; if is p aj ealled the /(^ mmdfmt saap, tad
— .— ■ m <±e nwrfari w*J ftrcmf pmmp, which ddBers tut little
thai jat desenbed. "except m the application of the air-
. is jrzduse eoctfuuity in the flow. Thai object ia also
;brit sperad on of two pumps acting alternately,
a a t2he eeKstrueti:^ cf the eonunon ^to-os/ar.

H* LA c*f F:re* Paam.— Thfa pomp niaea water both by
■acaon asd by preaure, that ia, both by atmospheric a e auie
sad by aachxeseal pressure. It has a solid piston, and at tie
accaoa of the barrel on the top of the suction-pipe, a valve
a op wing up n aids , fig. 114. Another Tare o> aiao opening

n*. 114.

upwards, closes the aperture cf a bent pipe, finch, pissing
under the metal plate a, connects the valve s with the air-resacl
m. From this Teasel or reservoir of air, proceeds the ascension
pipe d, which is employed to raise the water to ar.v ciTen
height. At every ascent of the piston b, the *a:er rises in the
suction-pipe a and enters the barrel. \l~£:i the pi*:on
descends again, the valves is shut, and the c: repressed witer
raises the valve o in order to enter the leservcir m, and thence
paa into the ascension-pipe d, in which Ue height attained by
the water is only limited by the force cf the moving power
which keeps the pump in operation. If the pipe n were only
theoontinuaticcofthe pipe/, the flower jet of water would
be mtermittert, taking place enly when the piston descended,
and stopping as seen a it ascend e d . But the c on t inuity of
these tubes is interrupted by the air-vessel m, by «fyi of
which a continued jet is msizrtazsed. The water thrown into
thia vessel is civiiei iat* two parts, cf which the one raised in
the tuba d compresses the water in the reserron x ; while the
other, in consequence cf this pressure, is raised in the reservoir
above the lower oxide* of the pipe r, br the compressi on of
th e air which is above h. Consequently, when the piston
ifiaarendi and no onger acts so a to eanpraa the water, the
air of the reservoir at, by the excea of pcaaure which it ha

received, reacts on the water and
the piston re-descends ; and ia thii
with: at intermxttanee.

Tkt L*U #/ tU Putem.—In the pump just described, i
the water ha filled the suction-pipe and the barrel up a the
mouth of the jet. the farce necessary a raise the piston ia equal
to the weight of a column cf water having for its ban the
horiaontal section of the piston, and for iti height the TextJal
distance of the orifice of the jet from the level of the water la
the r eam oil from which it it drawn. Thus let ■ be the pea-
sure of the atmosphere, A the height of the water above a
piston, and A' the nexeht of the column of wear which nib tan
§uetiju«y:pe end the lower part of the barrel- The pi i aim
above th^ pt*ton it evidently u-\-t* and that below the frstou
h— A', since the weight cf the column A' tends a balance the
pressure of the annosphere. Xow, the pressure n — A* lends a
raise the piston; the elective resistance, therefore, is the excea
of H+A, above a— A' ; that a, A-f-A', which wa a be proved,

FrmMmL Applkaivm cf Pvmsw.— In aaetiecfc the fallowing
rules are olarred in the construction of pumps. The velocity
of the piston i» calculated to vary from six a nine inches per
second. The area of the aperture covered by the valves ■
about half that of the ksr.el of the pump. The «*;«w»«»> of the
suctioc-pipe, and of the ascension a djschane-pipe, is about
two- third* cf that of the barren of the panp. The stroke of the
piston in Urge pumps viries from tnree and a half to five feet.
In good pumps the las occasioned by the time required for
shutting the valva reduces the effect to about four-fifths of
that produced ^y the piston. The allowing figures present
different model* of pistons and vilves employed in the con-
struction of pumps. Fig. 1 1-5. a pxsan packed with leather ;
fig. 115, a piston packed with aafl lr. 117, a piston fur-
nished with a single cl&ck-vsve; ML US, a piston with a
double-clack or butterfly valve ; fi£. lift interior of the barrel
of a pump, in the bottom of which u eagle clack-valve works ;
fig. 120, separate view of a tingle tack- valve; fig. 121, a
conical valve.

Flf. UX

IfeUft.

BreaaA'f rTiaVisssTi 2Vat.f-We here
explanation of this mTentiou: Mails

wahi

LB88QN8 IN PHYSICS,

explanation of the forcing-pump, we repeat it here under
another form, its importance demanding additional elucidation.
The hydrostatic press is a beautiful application of a principle
previously known for nearly two centuries, and commonly
called the hydrostatic paradox ; via., that any quantity of water,
however small, may be made to balance any quantity how-
ever great. The practical effect of this principle is, that when
water enclosed in a vessel quite full of the liquid, is pressed
by a piston at any aperture with a given force, this pressure is
at once communicated to every part of the vessel of the same
siae as the aperture, with the same force. Mr. Bramah, by an
ingenious application of the forcing-pump to an apparatus con-
structed on this principle, produced one of the most powerful
and useful machines used in the present day. It is represented
in fig. 122, where s is the piston which moves in the cylindrical

succession ; and lei us suppose that the lower extremity of
the tube g is placed between the two ajutages b and e.

1st. If we open first the ajutage b y the water runs out, its
level is lowered in the tube g t and as soon as this level reaches
that of by the run of water is stopped. This phenomenon is
explained by the fact of the excess of inward pressure which
took place first at b; an excess which disappears when tho
level of the water in the tube g is brought down to b. For,
before the water issued from b, the pressure on all points of the
horizontal stratum b e was not the same. At *, it was composed
of the pressure of the atmosphere and the weight of the column
of water g #, whilst at ft, the pressure was that of the atmosphere
only. But as soon as the level of the water is the same at e
and at 6, there is an equilibrium, because that in the bottle
and in the tube the pressure is then the samefon all points if

Ifeltt.

tube /, or small barrel of the pump ; p is the piston which
moves in the cylinder ce\ or large barrel of the pump; and
mtbuis the tube of communication between the two barrels of
the pump. A lever of the second kind / raises the piston «,
and the water in the reservoir b' is drawn into the barrel of the
pump/. When the lever is pressed downward, a valve shuts,
and prevents the water from returning into the reservoir b\
and forces it along the tube tbu, in order to act upon the
lower extremity of the piston p, to which is attached the plate
p; efia another plate, against which the objects to be com-
pressed by the machine are pushed by the former. In con-
sequence of the guaquavertal pressure of the water forced into
the large barrel of the pump from the small one, the pressure of
one pound on every square inch of the surface of the liquid in
the latter will be communicated to every square inch of the
surface of the liquid in the former. Hence, if the diameter of
the piston $ be one inch, and that of the piston b be ten inches,
the pressure of one pound on the former will be 100 lbs. on the
latter. A noble specimen of this press was exhibited in the
Crystal Palace by the Bank Quay Foundry Company,
Warrington ; via, that which was used for raising the Bri-
tannia Tubular Bridge. The greatest weight lifted by this
press was 1,144 tons, and the quantity of water used for every
lift of six feet, was 81 J gallons. The internal diameter of the
great cylinder was twenty-two inches, and that of the ram or
piston twenty inches.

MariotU's Bottle.— The bottle of Mariolte is an apparatus
which exhibits some remarkable examples of the pressure of
the atmosphere, and by means of which we may obtain a con-
stant flow. The neck of this bottle is closed by a cork, through
which a glass tube passes, open at both ends ; in the side of
the bottle there are three apertures furnished with ajutages,
a, b, c t at right angles to the side and closed by wooden pegs.
When the bottle and the tube are quite full of water, let us
consider the effect of opening one of the ajutages, e>#> «, in

the horiaontal stratum be. Thus, the pressure at* and at«
being equal to that of the atmosphere, it is easy to demonstrate
that it is the same pressure which acta at any point o of the
stratum b e. For this purpose, let n denote the pressure of
the atmosphere ; this force acting^at b and #, is transmitted in

Fig. 123.

all directions in the interior of the bottle, according to the
principle of Pascal formerly explained, and the upper side *
resists an upward pressure equal to h— ko ; for the weight of
the column of water ko partially counteracts the pressure
which is transmitted to *. Now, according to the mechanical
principle, that reaction i$ alwayt equal and contrary to actum, the
pressure h— ko is urged downward by tho side k on the stratum
be i so that the particle of water at o, supports in reality two
pressures, the one equal to the weight of the column of water
ko, the other, the pressure h—*o, resulting from the reaction

886

THE POPULAR EDUCATOR.

of the side A. The real pressure, therefore, which the particle
at o supports is *o+h— *o, that is, r the pressure of the atmo-
sphere ; which it was proposed to demonstrate.

2nd. If we shut the ajutage b, and open the ajutage a, there
will be no run of water ; on the contrary, the air will enter the
bottle by the aperture a, and the water will rise in the tube g
to the level a d t when the equilibrium will be restored. For it
is easy to perceive by reasoning, as in the preceding case, that
the pressure is then the same at all points of the horizontal
stratum a d.

3rd. Let the apertures a and b be closed, and the aperture e
be open. In this case, there will be a run of water with a con-
stant velocity so long as the level of the water in the bottle
docs not fall below the level of the lower orifice / of the tube :
for then the air would enter tliis orifice and fill the upper part
of the bottle, where it would take the place of the water run
off. In order to demonstrate that the flow of water at c is con-
stant, it is necessary to show that the pressure on the horizon-
tal stratum c A is always equal to the pressure of the atmo-
phere increased by that of the column A /. Suppose, then, that
in the bottle the level of the water is lowered to the stratum
ad. The air which has entered the bottle supports a pressure
equal to h— pn. In consequence of its elasticity, the air
transmits this pressure to the stratum e A. Now, this stratum
supports besides this the weight of the column of water pm.
Therefore, the' pressure transmitted to m is in reality, j>m+ h
— pn % orH-f-mw, that is, h + AJ. In the same manner, it
would be demonstrated that this pressure is the same, when
the level is lowered to e b ; and so on, so long as the level is
above the orifice /; the pressure on the stratum c A is therefore
conhtant, and so is the velocity of the flow. But as soon as the
level falls below the point /, this pre>surc decreases, and con-
sequently the velocity of the flow diminishes. Thus, we see
that the bottle of Mariotte is a means of obtaining a constant
flow; namely, by filling it with water and opening the ajutage
or aperture placed below the orifice / of the tube. The
velocity is then proportional to the square root of the height
/ A, as shown in a former lesson.

LESSONS IN CHEMISTRY.— No. XXII.

Ik the course of any chemical examination, and more espe-
cially of metals, we find certain compounds demanding our
especial attention. Amongst all the combinations of mercury,
perhaps the bichloride, or corrosive sublimate, is that which
claims our prominent notice. It is a terrible poison : its dis-
covery and identification, when mixed with animal fluids,
involve many points of chemical interest, and the manipula-
tive processes employed in its extraction are of great beauty
and delicacy.

I must premise by directing the student's attention to the
fact of there being two chlorides of mercury — one the proto-
chloride, ordinarily known as calomel ; the other, bichloride,
ordinarily known as corrosive sublimate : the respective com-
positions of which are as follow :—

Calomel, or Proto-chloride of
Mercury

Corrosive Sublimate, or Bi-
chloride of Mercury . . .

Parts by weight.
Chlorine. Mercury.

3G
72

200
200

Hence the ratio of chlorine in these two chlorides is as one to
two. Calomel may be generated in various ways. The stu-
dent has already generated it by the addition of common-salt
solution to proto-nitrate of mercury, and he will not fail to see,
by reference to the preceding tabular exposition, that if by any

{>rocess we can succeed in taking from a given weight of sub-
imate half the chlorine it contains, the result will be calomel ;
and if we can succeed in removing the whole of its chlorine,
the result will be metallic mercury.

Chemical instigation of Bichloride of Mercury in simple and
complex fluid*.— Taking a portion of the solution of bichloride
of mercury already prepared, let us master the appearances it
affords with testa in simple solution. And here it will be

remembered that inasmuch as our desire is not merely to
discover a certain metal, but a given compound of a certain
metal, we shall require not merely a test for mercury, but for
that which is combined with the mercury and holds it in solu-
tion. Let us begin with a very characteristic test for soluble
persalts of mercury generally — a solution of iodide of potas-
sium. The effects of this test are most remarkable, as will be
seen. Having poured a weak solution of bichloride of mer-
cury into a test-tube or a conical glass, add to it, drop by drop,
another solution of iodide of potassium, and remark the beau-
tiful play of colours which result, also the disappearance of all
colour, all precipitate, and the resumption of perfect trans-
parency in certain states of dilution ; that is to say, to soon as
a certain amount of test liquor has been added. It is useless
to expatiate on changes which can be seen very much better
than they can be described, but I may remark that by revers-
ing the order of experiment in testing, and adding the bichlo-
ride Sdlution to the iodide of potassium solution, instead of
adding the latter to the former, the chromatic effects will vary.
Now the peculiar effects here detailed are characteristic of a
persalt of mercury; and the only persalt of mercury at all
likely to come under one's notice in a case of poisoning is the
perchloride of mercury ; however, any doubt can be at once
cleared up by the addition of the test for chlorine. Now what
is the test f >r chlorine ? Tou remember, I presume, that it is
nitrate of silver— the reaction of that substance having already k
under the head of " Silver," come before us. Add, then, a little
nitrate of silver solution, and a white precipitate results. But
there are thousands of white precipitates ; how shall we know
what this one is ? Simply by adding hartshorn (liquor aramo-
niie) to it, the white precipitate dissolves. It has been pro-
duced, therefore, by chlorine. We" have already determined
the presence of mercury, therefore our substance must be a
chloride of mercury. But as there are two chlorides of mercury,
which is this ? It cannot be the proto-chloride of mercury
because that substance is insoluble ; it must, therefore, be the
per- or bichloride of mercury. Thus, at length, we arrive at
the demonstration.

The next test we shall employ is ether ; a liquid which, by
the way, is rather to be considered as a separator than a test
in the ordinary acceptation of the term.

Having poured a little bichloride solution into a narrow
test-tube, add to it about an equal volume of rectified ether
(when the term "ether" without prefix, is used, chemists
always mean sulphuric ether), then closing the tube with
the thumb, agitate the tube. Proceeding thus, the ether and
the bichloride solution will become intimately mixed. This
mixture being effected, cork the tube (to prevent evaporation
of the ether) and allow it to stand for the space of a few
minutes at rest. Presently two distinct fluid layers will be
recognisable ; so well marked, so thoroughly individualised,
that one may be readily separated from the other. The best
means of effecting the separation is, as represented below, fig.
8, by the use of a little glass instrument termed a pipette.

Fig. ft.

The student, however, who does not possess the instrument
may accomplish his result perfectly well by means of a glass

LESSONS IN GREEK.

887

tube drawn out into a capillary termination, as represented in
the acoompanying diagram, fig. 9. I need not stop to describe

Fif.t.

how such an instrument is made. The student has only to
refer to some previously described glass manipulations, and he
will see.

Well, having separated the supernatant layer of fluid, deposit
it on a watch-glass, and allow evaporation to take place.
Ether is a fluid so exceedingly volatile in its nature, that the
application of a very slight amount of heat is necessary to effect
this volatilisation. It suffices for this purpose to hold the
watch-glass in the palm of the hand. Evaporation having
ceased, that is to say, all the ether having been removed, the
watch-glass will be found to contain a portion of white solid
material. If the white solid material be viewed through a lens it
will be seen to be crystalline. What is it ? Nothing more nor
less than solid bichloride of mercury, which happens to possets
the quality of being more soluble in ether than in water; hence
ether removes it from water as we have seen. This is a very
elegant test, and most useful under certain conditions. It is
not, however, a good quantitative test; that is to say, the
operator can never depend on removing by its agency the
whole of the bichloride actually existing in a liquid. This
/act was first demonstrated by the French chemist Devergie.
Nevertheless we must not underrate the value of the test. In
poisoning cases it is a great point to make out the existence of
a poison in any quantity, seeing that the law does not propound
to the analytical chemist the question — M Have you extracted
all the poison?" but, "Have you extracted a sufficiency to
account for death ?" Again, the ether test has the rare advan-
tage of acting equally well in animal and vegetable fluids as
in pure water.

The next test we will employ is the white of egg. For this
purpose it will be well to beat up the substance, white of egg,
with water, and strain through muslin ; by proceeding thus
we shall get rid of much animal membrane that would be em-
barrassing to the result. Having prepared the test as described,
add a portion of it to the bichloride solution, and remark the
white curdy deposit which results. At one time this precipi-
tate was imagined to be oalomel, — the action of the white of
egg being assumed to accomplish the removal of one half of the
chlorine. It is not thus : the precipitate is an actual chemical
compound of white of egg (albumen) and the bichloride. At any
rate it is almost, if not quite, insoluble in water and the gastric
fluids; hence it is innocuous, and this is the great point to be
remembered in practice. Under the head of" Tin " (during the
investigation of which metal we had occasion to employ bichlo-
ride of mercury as a test), I stated that white of egg was the
antidote to bichloride of mercury. Tou will now clearly see
why, for what reason, in virtue of what chemical reactions, it
is an antidote.

In our next lesson we will consider the best means of extract-
ing bichloride of mercury from complex animal and vegetable
solutions,

LESSONS IN GREEK.— No. XXm.

By John R. Bbahd, D.D.

Conjugation, Preliminary Notions.

Let us take this word, namely, tXvaaprjv, and study it. The
word signifies, J looted myself, I untied or unbound myself.
| Now, suppose that I unbound myself was written as -though
it formed one word, as thus: — Iunboundmyself. Let us
1 mark off the several elements of this compound by hyphens,
\ and assign names to the several parts : —

Personal Prefix. Adverbial Prefix, Verbal Stem. Personal Suffix.
I - un bound - myself.

You have now some idea how the Greek form above pre-
sented has been produced. Here it is divided, and the parts
named : —

Augment. Root. Aorist Stem. Middle Personal- ending.
i - Xv era pnv.

You thus see that the root of the form is Xv. This is called
the root because it remains permanent under all the changes.
Thus you find it in Xvw, in Xvoo/uvoc, t\vOnv 9 &c. By pre*
fixing certain letters to Xv, and by adding certain letters to Xv,
you make all the varieties of form and signification. Thus, if
you want to say / loose, you add « as Xv-« ; if you want to say
they loosed, you prefix t and add oav, thus, t-\v-aav. The
prefixes and suffixes, bv whose aid the root is thus modified,
may be termed formative syllables. A knowledge of these
formative syllables, combined with a knowledge of the several
roots, will make you proficient in the grammar of the verbs.
You will do well to make a distinction between the root of a
verb and the stem. The root of a verb is the verb reduced to
its ultimate or most simple form. It agrees with the stem in
being generally the stem of the present tense, active voice.
But it differs from the stem, inasmuch as it is one primitive
form ; and there are several stems — the stem of the present,
the stem of the imperfect, the stem of the perfect, &c. The
stem of a tense is that form which remains when the personal
endings and the mood characteristics are taken away. I
present the stems of the root, and of several tenses of rvirrw,
I strike. ,

Personal-endings.

*""""

Third Person.

Second Person.

Root

rvir

Present Stem

rtnrr -

f» he strikes

ft£ thou, Ac.

Imperfect Stem

trvirr -

e he struck

«C

First Aorist Stem

trwl* -

s he has struck

Perfect Stem

verve* -

s he has struck

Pluperfect Stem

trtrvf -

ct he had struck

ttg.

That is to say, if to the present stem I add ci, I get 1
which means he strikes; if to the pluperfect stem I add tig t I
get crcrveitg, which means thou hadst struck. So, if from
rtrvfag I take away ag, I get the perfect stem rtrve). If I want
to make the perfect stem into the pluperfect stem, I prefix the
augment t, and make irtrup. If, again, I wish to resolve
rervf into the root, I cut off the augment rt, and change the
aspirate <f> into the corresponding soft ir, and so obtain rvw.
This the root I may raise into the present stem by affixing r,
thus— rvxr. And rvwr I may. change into the imperfect
stem by prefixing the augment of that tense, namely, s.

The Auombnt.

After these general explanations, you are, I presume, pre-
pared to enter into particulars. First, then, let us consider
the augment or temporal prefix. I call the augment temporal,
because its function is to denote past time ; and I call it a
prefix, because it is put at the beginning of the root or stem.
The augment is of two kinds; first, syllebio; second, temporal,
lit is syllabic when it adds a syllable to the verb ; it is tempoial
I when it lengthens the initial vowel of the verb. The syllabic
i augment is of two kinds, it is simple or reduplicative ; for
| instance, it is simple when it merely prefixes a vowel, as In
tXsiirov, X was leaving t it is reduplicative when it doubles

Aft:

THE POT ULAA EI>OCATOB.

the initial consonant, se XiXtnra ; here « is ealled the simple
syllabic augment, and Xc the reduplicative. The syllabic
augment is employed when the rerb begins with a consonant.
If the verb begins with a vowel, the temporal augment is
used, the vowels a and < being changed into ij or tt, and
i and v (iota short and uptilon short) being changed into I and
9 ; o is changed into «. The simple syllabic augment is found
ill only the indicative mood ; the reduplicative extends
thrown all the moods. The simple syllabic augment is used
with the imperfect tense and with the aorist. The reduplica-
tive augment is used with the perfect tense, the pluperfect
tense, and the third future, sometimes called the paulo-post-
future. li, however, tlie verb begins with a vowel, the perfect
and the pluperfect have, instead of the reduplicative, merely
the temporal augment. The pluperfect ha* a double augment,
inasmuch as it prefixes the simple augment t to the reduplica-
tive rt, &c; for instance, mrv^uv. Fuller details will be
given hereafter. My object in these general remarks is to afford
you assistance to understand and commit to memory a general
paradigm of the verb.

Chabacte&istic Ltrnss.

I have previously used the terms pure teres. This is one
class into which verbs are divided. Verbs are divided gene-
rally into.classes, according to the characteristic letters of the
present tense, or the stem of the present tense. The letter
which stands immediately before the «* of the present tense is
called the verbal characteristic ; thus, in Xvw, the v is the cha-
racteristic of the verb ; and in rvvrut the r is the characteristic
of the verb; and in o-rcXAw, the X is the characteristic of the
verb. If the characteristic is a vowel, the verb is called pure,
e.g. \vto ; if the characteristic is a consonant, the verb is called
mute, e.g.rvirrw ; if the characteristic is a liquid, the verb is
ealled liquid, e. g. <m XXw, I ten*. Thus there are three kinds
of verbs.

Fure.
Tifiato, I honour.

MuU.
rpc/fo, I rub.

Flexion ax Terminations.

Liquid.
fenvm y I ekotc.

Another kind of characteristic letters or syllables are the
inflexions, which mark the time (tense), the manner (mood),
and the persons of the verb. Look at Xvevpat, I will loose my-
wdf. Analyse it, and you will find the parts stand thus :—

Boot.
Xv

Tense Sign.

Mood Sign.

Person Sign.
fiat

Here Xv is the root, <r is the characteristic of the future, o of
the indicative mood, and uai of the first person singular. Let
us vary these forms a little.

Root. Zen* Sign. Mood Sign. Person Sign.

\v o ot fit9a

Here the sign of the indicative mood o has become ot, to indi-
\/*«» of the first person singular is

cate the optative ; and uai of

changed into utQa of the first person plural.

sXvoavro.

Again, take

Augment.

Moot.

fiovXtv
flovXtv

A u g m e n t Root.

i povXtv

Tenet Sign. Mood Sign, Person Sign.

Voios Sign.
9

uai
utjv

Person Sign,
nv

The tense sign, in union with the person sign, is termed the
tense-ending. Thus, in Xvota the <r is the tense sign, being the
sign of the future, and ow is the ending of the future tense,
active voice, commonly called the first future active. The
stem of the verb, in connexion with the tense sign and with
the augment, is called the tense-stem. Thus, in s^evXcvow the
tense-etem is t/3ovXfwr, that is, the stem of the first aorist
active.

r giro a gsjssjfsjl view of

TkbTbtib-]

Active.

Middle.

0y*opMt

Present

Imperfect

Perfect a mmi*

Pluperfect ay snrr 9

Aorist first oa * a p**

Future first ou oonai

Aorist second or oum* m>

Future second frxrum

This arrangement places onto the middle voice some tenses,
those marked with an asterisk, which are commonly ascribed
to the passive voice. If the atudent bears in mind what was
said in the last lesson of the intimate relation of the two, he
will see a ground for this diversity of view. Of comae, the
arrangement here presented is believed to be the beat.

Pebsowax EiroixGa awd Vowel 8im.
The personal endings are the terminations by which the

variations of person are indicated. They are closely connected
with the a sood - ' — * ■■•»**»*» •— > **»- — -— -*- *i — -. /i_^*__^_ -» _
several moods,

with the ssood-sijrns, which are the vowels that
toods. for example: —

lPer.Sin.Ind.Pres.M. fiovXivo-uw
3 Pers. Sing. Ind. Fut, povXev-v-i-rm

1 Pen. Plur.Ind. Pres. PovXiv-o-fu9a

2 Pers. Plur.Ind. Pres. /3et*£v-«-«0f

lPers. Sin. IrkLAor. 1 e/SovXtv-o'-c-enjv Subj. flmltv m m pen
3 Pers. Sin. Ind. Aor. 1 c/8evXcv-e-a-ro Opt. /SovXsv-ewtt-ro

Subj. /3ovXrv-«#-juu
Opt. povXtv-o-ot-ro
Subj. p*v\M»-*-ju9a
8ubj. PooXtv-w-wQe

In these instances /SoeXsv is the root, and c/3o«Xssw is the atesa
of the first aorist, while /SoaXcve-is the stem of the future. The
personal endings arejuu, rm, fuBa, ro, sec And the aaoosV
ejgna are the vowels •,«»; «, 9 ; a , «. Mark how readily the
one permanent form /SovXcv takes to itself other forma, to suit
modifications in the sense. Mark, also, that the short vowels
represent the indicative, and that these short vowels are
changed into their corresponding long ones for the subjunc-
tive. Ton may also note that i enters as an essential into the
optative forms, as in /3owX» -wiro and povkevoeuro. These two
tenses are, you see, very near in form, differing in this only,
that the latter has an a where the former has an o.

The personal endings join on immediately to the mood-signs,
and unite so closely with them that they are blended together,
and may appear as one; e.g., Bov\ewr-fc f instead of /SosXcsw-
e-tc, and /SovXtv-e; instead of povXev-t-au

The distinction between the principal tenses and the histo-
rical tenses is important. The principal tenses, that is, the
present, the perfect, and the future, form the seoend and the
third person of the dual with the same ending ; that is, ov, as
jSovXcv-c-rov, povXev-i-rov, /3oi'\<tN£-<r0ov,/3otA«u-€-dftov ; while
the historical tenses form the second person of the dual in ov,
but the third in nv ; as, cjSovXc v-£-roy, tpovXtv-e-rnv ; c/Sov-
Xcv-t-oQov, tpovXiv-t- oBtjv. Further, the principal tenses form
the third person plural, active Voice, with the termination si,
which before a vowel becomes otr (abbreviated from »rt, tnrt),
and the third person plural middle with vrai ; hut the histo-
rical or secondary tenses have in the active », and in the
middle vro : as

povXxv-o-voi = PovKt w see i (v)
j3ovXfv-o«i

Lastly, the, principal tenses in the singular of the present
middle run thus, pai, cat, rat ; but the hatoritml tenses thus,
ftijv, ov, to ; as,

/SovXcv-o-fiac
PovXtv-t-oai = f$ov\ev-y
povXiV't-rat

t-fiovXeif-o-Hnv

t povXrv-t-oo sz c /SouXev-ov

t-fiovXev-t-ro.

The person-endings of fte subjunctive of4hepiinoipel Tensas
correspond to those of the indicative of the principals

UM801I8 IV HERMAN.

839

2 and 3 Dual Ind. Pres. /SovXcve-rov Subj. fiovktyn-rov
f&ovXtvt-vQov — - pavKtfi'oBav
S Plural )3ovX(v0v-ai(v) — j3ov\ctw-?t(v)

/3ou\«vo-vrai ' — jBovXcvw-vrat

1 Sing. BQliMvo-pqi — povXevw-fiai

2 — povXtv y — fiov\tv-y

3 — fiovKtvt-Tcu — fiovXtpw-rai
2an4 3Du. Impf. Indie. f-/3ovA«/e-rw, i-rajy Opt jSoyXiuot- rov,

l-fiovXlVl-ffQoV, i -ffOlfV— floVAtWH'OQoV,

S Plural f-0ovXcvo-v — /SovXcuoi-o'

••/SovXtvo-yro — /SovXcvM-vro

1 Sing. f-/9ovXfvo-pjfy — fiovktvot-finv

2 — (<-/3ovXcve-<ro) c/?ov- — ( /3vX«voi-<ro )

&iv-ov pfluX«VPt-a

3 — * «-/3ei/X«i/s-n> — ? /JflvX* t/oi-ro.

As already intimated, the mood- vowel of the subjunctive of
the historical tenses aiflers from that of the indicative in its
being lengthened : thus o is lengthened into « ; « and a into n ;
and u into y ; as,

Judicative /3ovX*u-o-/wv, j3ovXiv-fif, £ovX#v-*-00e
Subjunctive /3ovXcv-*j-jkp, /feuXcv-yf* povX«*f-sj-<r0f.

The mood-vowel, or mood-sign, of the optative is t, in con-
nexion with the preceding mood-vowel of the first person sin-
gular Indicative ; the ptatoeriect forms an exception, since its
optative assumes the toood-vowel of the present ; e.g.

I Sin. Imp. Act. Indie, o Opt. oi t-fiovXev-o-v /3ovXh/-<m-/h
Plural Aor. 1 a — at ipovktve-a-fuv /SovAsw-ai,

utp
1 Sin. flnp. Act Opt. <*

Present oi — /Se-jSovXetuc-oifu, /SovXcv-otpt.

Person.

N ^ **

0OfcO*-O»tOH-0pfcO»-i
£;*»*» m m I J * J 2

h» Ja ?»

O **» C

* I 8 8 E Zl

b* §

• «oM>«»OM«e

&« a* »< Ac j* | •*<&« r*
w

.3 |«S«* C

&B&&&&&&

— • fM

3 H ooooooooo

° rl

a — — a — a $

si. a.

.3 *

I *?t

K '

Gxksbal View op to* Pjeson-JSnotngs of ▲ Vssb xh *».

.drtfw Ifrm.

Middle Form.

Indie, ft 8ubj. of Indie, ft Opt. of Iniic. ft Sub. of Ind. ft Opt of

the Prin. Tenses, the Prin.Tentes. th* Hut. Tenses, the Hist.Tens.

S. 1 v ficti \lt\v

2 c C vai <ro, o

3 — — rai ' to
I). 1 — — ftfOov ptfop

2 top rov &0ov aOov

3 rov rnv oBov aBtjv
P. 1 fitv fitv fttOa ptOa

2 r« r« <r0f <rfo

3 (vri)ff* v t aav vrai (arai) vro [aro)

Imperative,

Imperative.

S. 2 3 rw S. 2
D. 2 rov 3 r«v D. 2
P. 2 r* 3 rwav P. 2

(<70) O 3 000)

<r0ov 3 cr&oiv
<r0c 3 ffOwavi

Infinitive.

Infinitive,

Pres., Future and Aoriat 2
Perf. Act. and Aor. 1 and 2 Pass.
Aorjst 1 Active

v aBai

vai

ParticipU.

Stem vr f except the Perfect whose
Stem ends in or

ParticipU.

'/UVOft fuvtit pivov
ptvoc, iuvq, ptvov, Perf.

LESSONS IN GEBMAN.— No. LXXXIV.

§134. THE PRONOUNS.

Rule.

A pronoun must agree with the noun or pronoun which it re-
presents, in person, number and gender : as,

3>er SWann, ttetyfr toctfe i% the man who is wise.
£>i< gran, ftttyc f[ei§ig iff, the woman who is diligent.
S>aS JTinb, xixltyi ftrin ift, the child that is small.

Observations.

(1) The neuter pronoun, « «, is used in a general and indefi-
nite way to represent words of all genders and numbers: as, ti
{ft htt anami, it is the men; d ift tie ffrau, it is the woman ; «« ifl
t& Jttnb, ii is the child / e4 finb bitlKinncr, they are the men, &c.
In like manner, also, often are used the pronouns bat, (that) :
bie«, (/Ait) ; »a«, (what) ; as also the neuter adjective allel,
(atf) ; as, bctf jtnb mcine 0n^tet, these are my judges.

(2) When the antecedent is a personal appellation formed by
one of the diminutive (neuter) terminations, Qtn and teiti, the
pronoun, instead of being in the neuter, takes generally the
gender natural to the person represented t as, too ifl i$r 6obiu$en?
Sfl er (not c«) im ©orten f Where is your litde son ? Is he in the
garden ? The same remark applies to flBet* (toomon) and grautn*
jtmmer, (Wy). When, however, a child or servant U referred
to, the neuter is often employed.

(8) A collective noun may in German, as in English, be re-
presented by a pronoun in the pkural number : as, bie GkifUUhfcit
war fttt ibre Recite fe$t Ufottf, the clergy were very anxious about
their righto.

(4) The relative in German, can never, as in English, be sup-

Sressed : thus, in English, we say, the letter (which) you wrote;
ut in German it must be, bet ©riff, toefefcen bu fefcricbeft.

(5) The neuter pronoun tt, at the beginning of a sentence,
is often merely expletive, and answers to the English word
"there " in the like situation : as, tt tpor niemonb bier, there was
no one here ; tt fotnnun Scute, there are people coming.

(6) The English forms, he is a friend of mine; it U a stable ^
of owe, &c., cannot be literally rendered into German ; for
there we must say, et i£ mein gteiwb, he is my friend ; or, er ift
ciaer mciner greunbe, he is one of my friends, &c.

(7) The definite article in German is often used where in
English a possessive pronoun is required: as, er tointte i$m arit
bee ^anb, he beckoned to him with his (the) hand.

;jft

THE POPULAR EDUCATOR.

(8) The datives of the personal pronouns are often in fami-
liar style employed in a manner merely expletive : as, \a) leftc
nrir ben Hfainnxtn, I like Rhenish wine for me, Le. I prefer
Rhenish wine. See § 129. 3.

§ 135. THE ADJECTIVES.

Rule.

Adjectives, when they precede their nouns (expressed or un-
derstood), agree with them in gender,- number, and case ; as,

$>iefc fcbeitc $ame, this handsome lady.
Gin gutigcr unt gerec^ter fttatcr, a good and just father.
Ttn jwotftcn ticfc* 2Ronat«, the twelfth {day) of this month, Ac.
£ier if* cin Cftiffocrflant, — tin £antgicifli$cr here is a misunder-
standing,— a palpable {one).

% Observations.

(1) This rule of course has reference to those adjectives
which are used attributively ; for predicative adjectives, it will
be remembered, are not declined. For the several circum-
stances under which adjectives are varied in declension, consult
§ 27, § 28., Ac

(2) This rule applies equally to adjectives of all degrees of
comparison ; as, befferc SucQtr, better books ; tec bcjlc fficin, the
best wine ; Ui beften SBcinc*, of the best wine, &c. So, too, it
applies equally to all classes of adjectives ; as, adjective pro-
nouns, numerals, and participles.

(3) The word " one" which, in English, so often supplies the
place of a preceding noun after an adjective, cannot be trans-
lated literally into German: its office being rendered needless in
the latter tongue by the terminations of declension. See last
example under the rule.

(4) So, also, the English " one'**' is the proper equivalent of
the German fcin in such cases as the following: gibt ti ctwas ;
(Jtlcie*, al* fciucit £eintcn ;u vcrgcbcnY is any thing more noble than i
to forgive one's enemies? !

(5) When the same adjective is made to refer to several sin-
gular nouns differiug in gender, it must be repeated with each (
and varied in form accordingly ; as, tin gefebrtec 5i$r unt tine go
Uf)xtt Scrttcr, a learned sou and a learned daughter. The adjec-
tives are, also, often repeated, though the nouns be all of the
same gender.

S 136. THE VERBS.

Rlle.

A verb agrees with its subject or nominative in number and
person ; as,

3cicr «ugcnblicf if* fcftbar, every moment is precious.
Sic Sdumc Mutycn im frilling, the trees bloom in spring.

Observations.

li) When the subject is the pronoun c*, tat or bid, used in-
definitely (See $ 134. 1.), the predicate, if a noun, determines
the number and person of the verb ; as, ti finb tic ffruittc 3$rrt
£$un#, these are the fruits of your actions.

(2) In the second person (singular and plural) of the Impe-
rative mood, the pronoun which forms the subject is commonly
omitted ; as, gefcet $in unb fagct Sobanni n&tcr, trol 3$r fe^rt unt
$frrct, go and tell John what ye see and hear.

(3) When the verb has two or more singular subjects con-
nected by unb, it is generally put in the plural ; as, £ap unb (*i.
ferfud)t finb ficftigc Scibcnf*aficn, hatred and jealousy are violent
passions.

(4) When the subject is a collective noun, that is, one con-
veying the idea of many individuals taken together as unity,
the verb must (generally) be in the singular ; as, bos cnglifityc $olf
fpt grofe Jrcifrcit, the English people have (has) great liberty. In
a few cases only, as, cin 9Jaar, a pair ; cine SMcnge, I number ; cin
l&uftcnt, a dozen, the verb stands in the plural.

(5) When a verb has several subjects, and they are of diffe-
rent perssns, the verb agrees with the first rather than the third;
as, tn, tcin 'Brutct unb i<$ wottcn fpajicrcn geben, thou, thy brother,
and I will go take a walk \ tu unt tciu 2*rutcr sautfget uiel, you
and your brother avail much.

S 137. USE OF THE TENSES.

Rule.

The Present tense properly expresses what exists or is taking
place at the time being; as, tie nwu)rc gapftrfett bcf$ufct tea
&dm*a)tu, true valour protects the weak.

OhSEEVATIONS.

(1) The Present in German, as in other languages, is often,
in lively narrative, employed in place of the Imperfect ; as,

Sic ©enne gebt (for ging) untrr, t a fir$t (for ftant) cr am 3$«r, w.,
the sun goes down, while he stands at the door, Ac

(2) The Present is not unfrequently used for the Future, when
the true time is sufficiently clear from the context ; or when,
for the sake of emphasis, a future event is regarded and treated
as already certain ; as,

3$ rrifc mcrgra afr, I start (i. e. will start) to-morrow.

Set tetif, wet tnergen ubct un* beficbU, who knows who commands

(i. e. will command) us to-morrow ?
Salt fefren Sic mia) met ex, soon you (wiil) see me again.
£tt* S&l*?s rrfteigen air in ticfer ilaa)t, this castle scale we (i. e.
trill we scale) this very night.

(3) It should be noted that the Present is, moreover, the
proper tense for the expression of general or universal truths
or propositions ; as, tic »4Segel flicgen iu bcr ?aff, birds fly in the
air.

' (4) In English we have several forms of the Present tense ;
as, I praise, I do praise, or I am praising In German there is
but one form (id) tebe) for the* expression of these several
shades of meaning.

(5) The Present in connection with the adverb fa)en (already)
often supplies the place of a Perfect ; as, nrir teobntn fa)cn ffeben
3abw tyicr, already dwell we here (i e. have we dwelt) seven years.

(0) In English, often we say, "I do walk, I did wal^," and
the like : where the verb do (Present and Imperfect) is em-
ployed as an auxiliary. This cannot properly be done with the
corresponding verb (t^un, to do) iu German.

§ 138. Rule.

The Imjterfect tense is used to express what existed, or was
taking place at some past time indicated by the context : as, uf

f*rieb an Sic, alt icft 3: >rcn S?ricf elicit, I was writing to you, when
1 received your letter.

Observations.

(1) The Imperfect is the historical tense of the Germans.
Its proper office is to mark what is incomplete, or going on,
while something else is going on. It is the tense adopted by
the narrator, who speaks as an eye-witness ; though it may be
used by such as have not been eye-witnesses of the events
narrated : provided the statement be introduced or accom-
panied by such expressions as, he said (fagte cr), il is said, or
they say (fagt man). When the speaker has not been an eye-
witness, the Perfect should be used.

(2) From the use of the Imperfect in expressing the conti-
nuance of a thing, i. e. what was going on at a given time, comes
the kindred power which it has of expressing repeated or
customary action : as, cr pflcgte gu fogen, he used to say, i. e. was
in the habit of saying.

(3) The Imperfect in German, like the Present, has but one
form ; which, according to circumstances, is to be rendered by
any oue of the three English forms of that tense. 3$ UUt,
therefore, is either I praised, did praise, or was praising,

§ 139. Rule.

The Perfect tense is that which represent* the being, actios,
or passion, as past and complete at the time being: as, tie

@$iffc finb angctommen, the ships have arrived; cr if* vorigc ffi«$e
geftorben, he died last week.

Observations.

(1) The German Perfect, as a general thing, corresponds
closely to our Imperfect, when used as au aerist ; that is, when
used to express an event simply and absolutely, and without

FRENCH READINGS.

841

regard to other events or circumstance!. Hence it often hap-
pens, that where io English we use the Imperfect, the Germans
employ their Perfect: thus, t$ babe fectnen ©rubor geftem gefefcen,
oBcr nia)t fjeftmx^en, I saw your brother yesterday, but did not
speak to him.

(2) The auxiliary participle (toorten) in the perfect passive, is
sometimes omitted. (See % 84. 2.)

(3) We may remark here also, that, though in English we
have a double form for the Prefect (thus, I have written and I
have been writing), the Germans have but the one. By which
of the English forms, therefore, the German Perfect is, in any
given case, to be rendered, must be determined by the context.

• FRENCH READING S.— No. IV.
LE SAPEUR DE DI£ ANS.
Section VII.

Le general qui commandait, voyant* que lc salut d'une
partie de Tannee dependait de la destruction do ce pont, 1
voulut envoyer quelques sapeurs pour abattre cettc poutre
et cntrafner b le reste de la charpente : 2 mais, au moment
ou ils s'appretaient a s'embarquer, l'ennemi arrive dc
l'autre cot6 de la riviere, 3 et commence un feu si terrible de
coups de fusil, qu'il ne paraissait i*as probable qu'aucun
sapeur put d arriver vivant pusau'a la fatale poutre.* Aussi
allait-on se retirer en se defendant, 5 lorsque tout a coup on
voit s'elancer un soldat dans la riviere,* uno haehc sur
l'epaule; il plonge et reparait bientot, 7 et a* sa grande
barbe* on reconnalt que e'est un sapeur qui se d&voue au
salut de tous. Tout le regiment attentif le suit f des yeux 9
tandis qu'il naeo et que les ennemis font* bouillonner l'cau
autoui* de lui d'une gr£le de balles ; 10 mais lc brave sapeur
n'cn h avance pas moins vigourcuscment. Enfin il arrive
apres des efforts inoufe, monte sur le pied do la pile, 11 et,
en quelques coups do hache, abat 1 le reste de la poutre qui
do loin semblait enormc, mais qui 6tait aux trois quarts
brisee. Aussitot la charpente des deux arches s'abtme
dans la riviere, 12 l'eau iaillit en Fair avec un fracas terrible,
et Ton ne voit plus le brave sapeur. Mais tout a coup,
parmi les debris qui surnagent,J on l'apercoit se dirigeant k
vers la rive. 13 Tout le monde s'y elance rempli d'aSmira-
tion et de joie ; u car malgre tant de malheurs, on etait
joyeux de voir fairc de si nobles actions; on tend des
perches au nageur, on l'excite, on Tencourage ; le general
lui-memc s'approche jusqu'au bord de l'eau, et n'est pas pen
etonne de voir sortir Bilboquet avec une grandc barbe noire
pendue au nienton. 14

— Qu'est-ce que cela? s'ecrie-t-il et que signifie cette
mascarade? 16

C'est moi l dit le tambour, e'est Bilboquet, 17 a qui vous
avez promis qu'on lui donnerait la croix, quand il aurait de
la barbo au menton. En voici une qui est fameuse, j'es-
pere. 19 .... Allcz, allez,™ je n'y ai rien epargne ;
il y en a pour" votro argent, et vos vingt francs y ont

Le general demeura stupefait de tant de courage et de
finesse a la fois. 19 II prit ° la main a Bilboquet, comme s'il
cut kik un homme et lui donna sur-le-champ la croix que
lui-meme port ait a sa boutonniero,'- et qu'il avait gagneei»
uussi, a force dc bravoure et de services. Dcpuis ce temps,
les anciens du regiment saluoicnt Bilboquet avec amitifc, 31
et le tambour-maitrc ne lui donna plus de coups de canne.
E. Marco de Saint-Hilairk.

Colloquial Exercise.
pont

1. La destruction du
etait-elle necessaire ?

2. Qu'est-ce que le general
voulut faire?

3. Que sepassa-t-il lorsque les
sapeurs aUaient s'embarquer?

4. Qu'est-ce qui ne paraissait
pas probable ?

5. Qu'aUait-on faire alors ?

6. Que vit-on tout a coup ?

7. Que fit co soldat ?

8. A quoi le reconnut-on pour
un sapeur?

9- te regiment lercgardait-il?

10. Que faisaient les ennemis
pendant co temps-la ?

11. Arriva-t-il enfin au pont ?

12. Qu'arriva-t-il aussitot ?

13. Que vit-on parmi les debris
qui surnageaient ?

14. Que s'empressa-t-on de faire
alors?

15. Pourquoi le general fnt-il
surpris?

16. Que dit-il au petit tam-
bour?

17. Que rdpondit Bilboquet?

18. Que dit-il en montrant sa
barbe?

19. Quel sentiment lc general
eprouva-t-il ?

20. Comment recompensa-t-on
notre heros ?

21. De quelle manicre fut-il
traite* depuis, par les anciens
du regiment?

Notes and References. — a. from voir ; L. part ii., p. 110.
— b. en trainer, throw down. — c. from paraitre ; i. part ii., p. 98.
— d. from pouvoir; L. part ii., p. 100.— e. a, by ; L. S. 86, R. 4.
— /. from suivre'; L. part ii., p. 106.— g. from faire ; L. part ii.,
p. 92, also S. 31, R. 3.— h. en, on that account.— i. from abattre ;
L. part ii., p. 76.—,;. surnagent^/fcxrf ; L. part il, § 19, R. (1) .—
k. se dirigeant vers, swimming toroards; L. part ii., § 49, R. (1)
— I. L. S. 80, R. 1. — m. aUez, allez, I assure you; literally, go,
go — n. il y en a pour votre argent, there is the north of your
money,— o. from prendre; L. part ii., p. 100. -p. L. S 41, R. 7.

l des Parthes,

LE CHATEAU DE CARTES.

Un bon mari, sa femme, et deux jolis enfants, 1
Coulaient a en paix leurs jours dans le simple ermitage*
Ou, paisibles, comme eux, v§curent b leurs parents.
Ces epoux, partageant c les doux soins du menage,
Cultivaient leur jardin, recueillaient d leurs moissons j 3
Et lc soir, dans l'ete" soupant sous le fcuillage,

Dans lTiiver devant leurs c tisons,*
Ils preehaient a leurs fils la vertu, la sagesse ; *
Leur parlaient du bonheur qu'ils f procurent toujours. 6
Lc p£ro par un contc egayait ses discourn,

La mere par une caresse. 7
L'aine de ces enfants, n6* grave, studieux,

Lisait h et meditait sans ccsse;*
Lc cadet, vif, leger, mais plein de gentillessc,
Sautait, riait 1 toujours, ne sc plaisaitJ qu'aux jeux. 9
Un soir, selon l'usage, a cote de leur i)^re,
Assis prds d'une table ou s'appuyait la mere,
L'alne lisait Rollin: 10 le cadet, peu soigncux k
D'apprendre les hauts faits 1 des Romania ou d<
Employait tout son art, toutes ses faeultes,
A joindre, a soutenir par les quatre cotes

Un fragile chateau de cartes. 11
II n'en respirait pas m d'attcntion, de peur.

Tout a coup voici le lecteur
Qui 8'interrompt; n Papa, dit-il daigne ni'instruirc
Porquoi certains guemers sont nommes conqu§rants,
Et d'autres fondateurs d'cmpii'e :
Ces deux noms sont-ils difierents ? 12
Lc pere meditait une reponse sage, 13
IiOrsque sou fils cadet, transporte de plaisir,
Apres tant de travail, d'avoir pu° parvenir
A placer son second 6tage, ! *
S'ecrie : Il est fini ! lft Son fr^re murmurant,
Se fache,p et d'un seul coup d6truit < » son long ouvrage ; M
Et voil4 le cadet pleurant.
Mon fils repond alors le p£re
Le fondateur c'est votre frere
Et vous eti^s le conquerant." Florian.

Colloquial Exercise.'

1. Combicn de personnes j
avait-il dans cette famille ?

2. Quelle &ait leur habita-
tion?

8. Quelles e^aient les occupa-
tions de ces epoux f

4. Ou soupeient-ils dans l'C'te
et dans 1 hiver ?

5. Que recommandaient-ils a
leurs enfants P

6. Deauoilcur parlaient-ilif

THE POPULAR EDUCATOR.

7. De quells manure
ils ieur conversation

8. Quel etait le caractero da
I'aine?

0. Le oadet ressemblait-il a
I'aine?

10. Que faisait i'aine', un soir a
eotl de wa pere ?

11. De quoi le oadet s'oeeupait-
ilalon?

12. Quelle queatk»rain^u>a'
a son pere?

13. Le pere lui repondit-il sur
le champ P

14. De quoi le cadet Aait-il
joyeux?

15. Quedit-il?

16. Quefitalorsl'ainl?

17. Quelle fat enfin la rlponse
dupere?

Nona afd BiFEBEKOES. — *. Coulaient, spent — b. from vivre;
L.partii.,p. 110. — o. L. part ii., §49. B. (l).—d. from reeueillir;
L. part ii., p. 102.—*. leurs tisons, their fire; literally, fire-
brands.—/. The ils is here a poetical liocuso ; the pronoun should
be eUe*> as it relates to vertu and sagesse t which arc feminine.— ^.
ne\ by nature; litcrallv, born; from nattre ; L. part ii., p. 96. —
A from /ire ; L. part ii., p. 94. — t. from rire; L. part il, p. 104.
—j. se plaisait, delighted ; L. S. 39, K 6. — k. soigncux, desirous.
— I faite, oVedf. — r». il n*en rcspirait pas, he hardly ventured to
breaths. — n. from interrompre; L. part ii., p. 94. — o. from pou-
voir; L. part ii., p. 100.— p. L. S. 39, B. 4 — q. from de'truire,
L, part ii, p. 88.— r. from /aire ; L. S. 63, B. 2.

M«* DE LAJOLAIS.
Section I.

La galerie que dcvait* traverser rEmpcrcur, pour so
rendre au conseiV etait une vasto piece longuc, gciairee par
dee croisees paxallcles, 2 les unes oyont vuo b sur la cour
d'entree, les autres sur les jordins. 3 Neuf heures venaiont
dc c sonncr et peu a peu lea deux cotes de cette galeric ee
remplircnt de d monde,* de curieux, de solliciteurs, des offi-
cers de service, des gens e de la maison. Panni tout ce
monde deux femmes sc faisaient remarquer, 5 la premiere
par sa beaute, et l'air gracieux avec lequel ell© accueillait*
les saluts respectucux de tous ceux qui passaient pro's
d'clle; 6 et la scconde par son extreme jeunessc, 7 par la
palcur qui donnait a sa beaute un caractero extraordinaire,
et par sea beaux cheveux blonds 8 tombant en boucles non\-
breuses sur ses epaules.

— Allons,* du courage! disait' 1 la premiere a la secondc, 9
du courage !

— Jc nc vous quittcrai pas, disait encore la premiere.
Puis, pour donner plus de poids a ses paroles, sa main allait
chercher la main de la jeune fille et la serrait avec amitie. 10

Le regard le plus cxprossif et le plus triste repondait a
cette favour ; ll et incontinent ics beaux yeux de r enfant se
retournaient vers la porto 1 - par laquelle dpvait' paraitre
1'Kmpereur. Toute cette amc jeune, aimante, exaltee, scm-
blait avoir passe dans ses yeux ; i tout le restc de son corps
paraissait k inanime.

Deux heures se passerent ainsi ; u deux heures d'attentc,
de pcines, d'nngoisses, et, pendant ces deux heures, ni Tune
ni rautre de ces onfants n'avait bouge.

La plus jeune, tenant 1 les yeux attach6s sur cette porto
ferraee, attendait qu'elle s'ouvrit pour respirer, 14 pour vi\tc;
l'autre nc detournait pas les yeux de dessus sa compagne. 15
Lo plus pro fond silence rcgnait dans cette galerie ; on n'en-
tenoait que la respiration plus ou moins agitec de tout ce
monde, 16 qui attendait aussi.

Enfin onze heures sonnent, les deux battants de la porte
s'ouvrcnt, 17 et un huissier annoncc l'Empereur. 1 "

Plusieurs pcrsonnes jparaisscnt 111 a la fois.

Lequel ? demande Maria dans la plus vivo anxiete.

Le seul qui ait" son chapeau sur la tete, 19 lui rcpond
vivement Hortense.

La jeune flile n'en Gcoute pas davantage ; nc voyant "
plus qu un seul etre dans toutc cette foule qui l'environnait,
ello sort'' des rangs, Balance aux pieds do eclui quon lui a
dengne, 80 sfecric : grace ! grace ! et joint i les mains avec
force en les levant vers le ciel. 2l

CoZXOCjOTAi

1. Poorquoi rBmperenr de-
vait-il traverser la galerie ?

2. Comment e^aitcette galerie?

3. Surquoi lea fenetrea avaient-
elles vue?

4. Qne vit-on lonque neuf
heures furent sonnees ?

5. Que remarquait-on parmi
tout oe moods?

6. Par quoi se faisait remarquer
la premiere?

7. Aquoipouvait-ondistinguer

la seconae ?
8 Do quelle couleur e^aiont

ses cheveux?
9. Quo disait la premiere a la

plus jeune ?
10. Que faisait-elle pour donner

plus do poids a ses paroles ?

Notes and Bxfbmxom. — a, devak, was; from devoir ;Tr
8. 84, B. 5.—*. ayant vue, looking towards.—*. L. 8. 16, B. «.—
d. L. 8. 95, B. 1.— e. L. S. 94. B. l.—f.frvmaccneillir; L.pert
ii., p. 76.—^. aliens, du courage ! tome, ekeer an /—A. from mre;
L. part ii., p. 88.— f. see note a, also L. S. 66, fc. 1 — ^'. L. a 9,
B. 7. — k. from paraitre; h part ii., p. 98.—/. tenant, Htpinj ;
from tenir; L. part ii., p. 108. — a«. see note k, — ». from avow;
L. S. 73, B. 4k — o. from voir ; L. part ii., p. XJuQ.— p.from sorHr;
L. part ii, p. 106.— q. from joindre ; L. part ii , p. 94.

11. De Quelle maniere Vmmjknt
repondau>eUe a cette &-
veur?

15. DequelouU se tournaieiit
les yeux de l'enfast ?

18. Combien de tempe laf deux

femmes attendirent-elleal
14. Qu*attendait la jeune fille P

16. Que fai*ait alora rautre?

16. Kntendait-ondu bruit dans
la galerie ?

17. Qu'arriva-t-il a onxe heures?

18. Qu'annonca rhuissier ?

19. Comment Hortenae desig-
na-t-clle rEmpereur ? "

20. Quo fit auora la
fille?

21. Que fit-elle en s'ecriant,
grftoe! grace?

jeune

LES60N8 IN ALGEBRA.— No. XII.

(Coulintud from p. 330.)
PBOBLEMS IN SIMPLE EQUATIONS.

1. What two numbers are those whose difference is 10 ; and
if 16 be added to their sum, the amount will be 43 ? Ana*
9 and 19.

2. There are two numbers whose difference is 14 • and if 9
times the less be subtracted from 6 times the greater, the
remainder will be 33. What are the numbers ? Ana. 17 and
31.

3. What number is that to which if 20 be added, and from
<j of this sum 12 be subtracted, the remainder will be 10?
Ana. 13.

4. A and B lay out equal sums of money in trade | A gains
£120, and B loses £80 ; and now A'e money is triple that of B.
What sum had each at first ? Ans. £ 180.

6. What number is that, I of which exceeds J by 72? Ans.
864.

G. There are two numbers whose sum is 37 ; and if 3 times
the less be subtracted from 4 times the greater, end the re-
mainder be divided by G, the quotient will be 6. What are
the numbers ? Ans. 21 and 16.

7. A man has two children, to & of the sum of whose ages
if 13 be added, the amount will be 17 ; but if from half the
difference of their ages 1 be subtracted, the remainder will be
2. What is the age of each? Ana. 9 and 8 years.

8. A messenger being sent on business, goes at £ha rate of
6 miles an hour ; 8 hours afterwards, another is despatched
with countermanding orders, and goes at the rate of M> miles
an hour. How long will it take the latter to overtake the Jfec-
mer ? Ans. 12 hours.

9. To nud two numbers in the proportion of 2 to 3 whose
product shall be 54. Ans. 6 and 0.

10. A man agreed to give a labourer 12s. a day for every
day he worked, but for every day he was idle he should forfeit
8s. After 390 days they settled, and their account was even.
How many days did he work ? Ans. 156 days.

11. Three persons, A, B, and C draw prizes in a lottery. A
draws £200 ; B draws as much as A, together with a thVdef
what C draws ; and C draws as much as A and B hoth.. yfeat
is the amount ef the three prizes ? Ans. £1 ,200.

LBS80N8 IK ALGEBRA.

348

12. What number it that which is to 12 increased by three
times the number, as 2 to 9 ? Ans. 8.

IS. A ship and a boat are descending a rivet at the same
time. The ship passes a certain fort, when the boat is 18 miles
below. The ship descends 6 miles, while the boat descends
3. At what distance below the fort will they be together ?
Ans. 32} miles.

14. What number is that, a sixth part of which exeeeds an
eighth pari of it by 20 ? Ans. 480.

15. Divide a prize of £2,000 into two such parts that one of
them shall be to the other as 9 to 7. Ans. £1,125 and £875.

16. What sum of money is that, whose third part, fourth
part, and fifth part, added together, amount to £94 ? Ans.
£120.

17. Two travellers, A and B, 800 miles apart, travel towards
each other till they meet. A's progress is 10 miles an hour,
and B's 8. How far does each travel before they meet ? Ans.
A 200 mUes and B 160 miles.

18. A man spent one-third of his life in England, one-fourth
of it in Scotland, and the remainder of it, which was 20 years,
in the United States. To what age did he live? Ans. 48
years.

19. What number is that, i of which is greater than i of it
by 96? Ans. 1,920.

20. A post is i in the earth, $ in the water, and 13 feet
above the water, Wfaat is the length of the post? An*. 86.

21. WhatMMaberis that, to which 10 being as\ded v f of the
sum will be 66 ? Ans. 91.

22. Of the trees in on orchard, £ are apple-trees, ^ pear-
trees, and the remainder peach-trees, which are 20 more than
i of the whole. What is the whole number of trees in the
orchard ? Ans. 800 trees.

23. A gentleman bought several gallons of wine for £94 ;
and after using 7 gallons himself, sold J of the remainder tor
£20. How many gallons had he at first ? Ans. 47.

24. A and B have the same income. A contracts an annual
debt amounting to $ of it ; B Uvea upon $ of it ; at the end of
ten years B lends to A enough to pay off his debts, and fee*
£160 to spare. What is the income of each? Ans. £280.

25. A gentleman lived single $ of his whole life ; and after
having been married & years more than y of his life, he bad a
son who died 4 years befose him, and who reached only half
the age of his father. To what age did the father live ? Ana.'
84 years.

26. What number is ths^ of which if i, i, and # be added
together, the sum will be 73? Ans. 84.

27. A person after spending £100 more than J of his income*
had remaining £35 more than i of it. Required his income.
Ans. £450.

28. In the composition of a quantity of gnnpowder, the nitre
was 10 lbs. more than | of the whole, the sulphur 4 J lbs. lets
than i of the whole, the charcoal 2 lbs. less than r of the nitre.
What was the amount of gunpowder ? Ans. 147 lbs.

29. A cask which held 146 gallons, was filled with a mix-
ture of brandy, wine, and water. There were 15 gallons of
wine more than of brandy, and as much water as the brandy
and nine together. What quantity was there of each ? Ans.
29 gals, brandy, 44 gals, wine, and 73 sals, water.

30. "Four persons purchased a farm m company for £4,755 ;
of which B paid three times as much as A ; C paid as much as
A and B ; and D paid as much as C and B. What did each
pay? Ans. A £317, B £951, C £1,268, and D £2,219.

31. It is required to divide the number 99 into five such,
parts that the first may exceed the second by 3, be less than
the third by 10, greater than the fourth by 9, and less than the
fifth by 16. Ans. 17, 14, 27, 8, and 38.

32. A father divided a small sum among four sons: the
third had 9 shillings more than the fourth, the second had 12
shillings more than the third, the first had 18 shillings more
than the second, and the whole sum was 6 shillings more than
7 times the sum which the youngest received. What was the
sum divided ? Ans. 153 shillings.

88. A farmer had two flocks of sheep, each containing the
same number. Having sold from one of these 39, and from
the other 98, he finds twice as many remaining in the one as in
the other. How many did each flock originally contain ? Ans.
147 steep.

84. An •express fcsvellfcig at the rate trft)ftmTles-aday,'hva

been despatched 6 days, when a second was sent after him,
travelling 75 miles a day. In what time will the one overtake
the other? Ans. 20 days.

86. The age of A is double that of B, the age of B triple
that of C, and the sum of all their ages 140. What is the age
of each ? Ans. A 84, B 42, and C 14.

36. Two pieces of cloth, at the same price by the yard, but
of different lengths, were bought, the one for £5, the other for
£6}. If 10 yards be added to the length of each, the sums
will be as 6 to 6. Required the length of each piece. Ans.
20 yards and 26 yards.

37. A and B began trade with equal sums of money. The
first year A gained £40, and B lost £40. The second year A
lost J of what he had at the end of the first, and B gained £40
less than twice the sum which A had lost. B had then twice
as much money as A. What sum did each begin with ? Ans.
£220.

38* What number is that, which being severally added to 36
and 52, will make the former sum to the latter as 3 to 4 ?
Ans. 12.

39. A gentleman bought a chaise, horse, and harness for
£360. The horse cost twice as much as the harness, and the
chaise cost twice as much as the harness and horse together.
What was the price of each ? Ans. Chaise £240, horse £80,
harness £40.

40. Out of a cask of wine, from which had leaked J part, 21

gallons were afterwards drawn ; when the cask was found to
» half full. How much did it hold ? Ans. 126 gallons.

41. A man has 6 sons, each of whom is 4 years older than
his next younger brother ; and the eldest is three times as old
as the youngest. What is the age of each? Ans. 10, 14, 18,
22, 26, and 30.

42. Divide the number 49 into two such parts, that the
gaeater increased by 6, shall be to the less diminished by 11, as
9 to 2. Ans. 30 and 19.

43. What two numbers are as 2 to 3 ; to each of which, if
4 be added, the sums will be as 5 to 7 ? Ans. 16 and 24.

44. A person bought two casks of porter, one of which held
just 3 times as much as the other ; from each of these he drew
4 gallons, and then found that there were 4 times as many
gallons remaking in the larger as in the other. How many
gallons were there in oaoh ? Ans. 36 and 12.

45. Divide the number 68 into two such parts, that the dif-
ference ^between the greater and 84 shall be equal to 3 times
the difference between the less and 40. Ans. 42 and 26.

46. Four places arc situated in the order of the letters A, B,
O, D. The distance from A to D is 84 miles. The distance
from A to B is to the distance from C to D as 2 to 3. And £
of the distance from A to B, added to half the distance from C
to D, is three times the distance from B to C. What are the
respective distances ? Ans. 12, 4, and 16 miles.

47. Divide the number 36 into 3 such parts, that £ of the
first, J of the second, and £ of the third, shall be equal to each
other. Ans. 8, 12, and 16.

48. A merchant supported himself 3 years for £50 a year,
and at the end of each year added to that part of his stock
which was not thus expended, a sum equal to one-third of this
part. At the end of the third year his original stock was
doubled. What was that stock ? Ans. £740.

49. A general having lost a battle, found that he had only
half of his army+3,600 men loft fit for action ; $ of the army
4-600 men being wounded ; and the rest, who were £ of the
whole, either slain, taken prisoners, or missing. Of how many
men did his army consist'. Ans. 24,000 men.

50. To find a number to the sum of whose digits if 7 be
added, the result will be 3 times the left hand digit ; and if
from the number itself 18 be taken, the digits will be inverted.
Ans. 53.

51. To find a number consisting of two digits, the sum of
which is 5 ; and if 9 be added to the number itself, the digits
will be inverted. Ans. 23.

52. There is a certain fraction such, that if you add 1 to its
numerator it becomes J ; but if you add 3 to its denominator,
it becomes \. Required the fraction. Ans. Jr.

53. It is required to find two numbers whose difference u 7,
and their sum 33. Ans. 20 and 13.

5*. At a town meeting, 876 votes were oast, and the person

344

THE POPULAR EDUCATOR.

elected to office had a majority of 91. How many votes had
each candidate } Ana. 233 and 142.

46. A post stand* J in the ground, J in the water, and 10
feet above the water. What U the whole length of it r Ana.
24 fret.

66. A young man the first day after hi* arrival in London,
spent \ of hia money, the second day J, the third day ■£, and
he then had only 24 pence left. How much did he hare at
ft rut r An*. 10 shil lings.

67. A person being asked his age, answered that } of his
age multiplied by ?V of his age, would give a product equal to
his age. How many yean old was he r Ans. 16 years.

68. A man leased a house for r J'J yean ; and being asked
how much of the time had expired, replied that two-thirds of
the time past was equal to four-fifths of the time to come.
How many years had expired r Ans. 64 years.

69. On commencing the study of his profession, a man found
that } of his life had been spent before he learned his letters,
1 at a public school. $ at an academy, and 4 years a: college.
How old was he r Ann. 21.

60. It is required to find a number such, that whether it
be divided into two equal parts, or three equal parts, the pro-
duct of its parts will \#- equal. Ans. 6J hours.

61. Two persons, 164 miles apart, set out at the same time
to meet each other, one travelling at the rate of 3 miles in 2
hours, the other 6 miles in 4. How long will it be before they
meet r Ans. 6fi hours.

62. A man and his wife usually drank a cask of beer in 12
days, but when the man was absent, it lasted the wife 30 days.
How long would it last the man, if hU wife were absent ? Ans.
20 days.

63. A shepherd being asked how many sheep he had, replied,
if he ha/1 as many mote, half as many "more, and 7£ sheep, he
would then hare 600. How many had he ? Ans. 197.

64. A farmer hired two men to do a job of work for him;
one could do the work in 10 days, the other in 16. How long
would it lake both together to do the same job? Ans. 6
days.

66. A and B together can build a boat in 20 days ; with tho
assistance of C, they can do it in 12 days. How long would
it take C to build the boat r Ans. 30 days.

66. There is a cistern with two aqueducts ; one will fill it in
30 minutes, the other will empty it in 40. How long will it
take to fill it, if both run together? Ans. 120 minutes.

67. Required to divide 1 shilling into pence and farthings
in such a proportion that there may be 39 pieces. Ans. 36
farthings and 3 pence.

68. A man divided a small sum of money among his children
in the following manner, viz. to the first he gave J of the whole
•4-4 pence, to the second \ of the remainder +8 pence, to the
third « of the remainder + 12 pence, and so on, giving to all
an equal «um till he had distributed the whole. Required the
number of shares and the sum distributed. Ans. 6 shares and
120 pence.

69. A hare has 60 leaps the start of a hound, and takes 4 lesps
while the hound takes 3 ; but 2 leaps of the hound are equal
to 3 of (he hsre. How many leaps will the hound take in
catching tho hare ? Ans. 300.

70. A and B start at the same time and place to go round an
island 600 miles in circumference. A goes 30 miles a day,
and B 20. How long before they will both be at the starling
point together, and how far will each have travelled? Ans. 60
days; and 1,800 and 1,200 miles.

71. A has £100, B £48. A robber takes twice as much
from A us from B. A now has 3 times as much as B. What
wtih tuken from each? Ans. £44 from B.

72. I' is required to divide £1,200 between A, B, and C ; B
has £256+ i of A's share; C has £270 + * of B's. What
was the share of each ? Ans. A £312, B £412, and C £476.

73. There arc 3 pieces of cloth of different value. The
average price of the first and second id 7s. per yard, tha,t of the
second and third is 9*., and the average price of all is— i of the
third. What are the several prices ? Ans. 12s., 2s., and 16s.

74. A pipe will fill a cistern in 11 hours. After running
6 hours another is opened, and then the two fill it in 2 hours.
In what time would the last fill it ? Ans. 6£ hours.

76. A man bought a cask of wine, and £ of it leaking out,
ha sold the rest at 26s. per gallon, and neither gained nor lost

by his bargain. What did he give per gallon for hia wine ?
Ans. 20s.

76. A and B a. art at the same time and in the same direc-
tion, but directly opposite each other, to go round a circular
pond 636 yards in circumference ; A goes 11 yards a minute,
and B 34 in 3 minutes. In how long time will B overtake A ?
Ans. 804 minute*.

77. A cask contains a certain number of gallons of rum, and
an mth part of that quantity of water : but, if a gallons of rum
and b of water be added to the mixture, the water in the whole
compound will be an ath part of the rum. Required the
quantity of each contained in the cask at first. Examine also
and explain the case, in which, as being equal to n, * is equal
to nb, and the one in which it is not equal to it ; and also the
case in which z and y come out negative, x denoting the original
number of gallons of the rum, and y those of the water.

Ans. y= — ^— , and x= — When *• = », and

at — n m — n

az=.nb, the question is indeterminate : when **=*, and
a greater or leas than nb, the values of x and y are infi-
nite, and the question absurd. When x and jr are
negative, the question will be changed into one in which
the quantity of rum is diminished by a gallons, and that
of the water by b gallons.

78. Find a fraction, such that if its denominator be increased
by 1, the value becomes £ ; while if the numerator he increased
by 1 , the value is }. Ans. -ft.

79. Required a fraction, such that if the numerator and
denominator be each increased by 1, the value is changed into
}; but, if they be each diminished by 1, the value becomes
i. Ans.*.

80. One person says to another : " If you sive me half your
money, I shall have a hundred pounds." The other replies :
" I shall have a hundred pounds, if you give me a third of your
money." How much had each ? Ans. £60 and £80.

81. At what time between 10' 1 and ll b o'clock, are the hour
and minute hands of a common clock exactly together ? Ans.
At 5\\ minutes before 1 1 o'clock.

82. Find two numbers, such that one-third of the first
exceeds one-fourth of the second by 3, and that one-fourth of
the first and one-fifth of the second are together equal to 10.
Ana. 24 and 20.

83. Required two numbers, such that the sum of one-half of
the first and one-third of the second may be 29, and that one-
third of the first and one-fourth of the second may amount to
21. Ans. 18 and 60.

84. A number expressed by three digits, whoee sum is 22, is
less by 297 than the number expressed by the same digits in a
reversed order, and its first digit is less by one than its second.
What is the number r Ans. 679.

86. A bill of £100 may be paid by 60 bank notes of one value
each, and by 38 of another; or it may be paid by means of 76
of the former kind, and 17 of the latter. What are the values
of the notes ? Ans. Those of the first kind 21 shillings each,
and those of the second 26 shillings.

86. Two persons set out from a certain place on the same
day, and proceed in the same direction, the one travelling 30
miles the first day, and going each day a mile less than he did
on the preceding ; while the other travels at the constant rate
of 20 miles a day. When will they next be together ? Ans.
At the end of 21 days.

87. How many lines are contained in a page of a book, and
how many letters at an average in each line of that page, if it
be found that by adding one line to each page, and making
each line contain an additional letter, the page will be increased
by 96 letters ; while, by adding two lines to the original page,
and making each line contain four additional letters, the nuss-
ber of letters will be increased by 286 ? Ans. 44 lines, each
containing 61 letters.

88. Two persons get each a legacy of £300, and one of them
is then found to be worth three times as much as the other;
but had the legacy to each been £800, the one would hate
been worth only twice as much as the other. How much had
each originally ? Ans. £1200 and £200.

89. A cistern can be filled by three pipes ; by the first in 80
minutes, by the seoond in 200 minutes, and by the third in WO

LONDON UNIVERSITY.

345

minutes. In what time will the cittern be filled when all three
pipes are open at once ? Ans. In 48 minutes.

90. Two gentlemen play at billiards ; A, before he began to
play, had £42, and B £247 Each lost and won in turn, when
A found he had five times as much as B had remaining. How
much did A win ? Ans. £13.

91. What capital is that which, with five years' interest at 4
per cent., will amount to £8,208. Ans. £6,840.

92. A capital was put out for one year at 4J per cent, per
annum ; at trie expiration of the year there was received back,
es capital and interest, £13,167. What was the amount of the
capital ? Ans. £12,600.

93. A fortress has a garrison of 2,600 men, among whom are
nine times as many foot soldiers and three times as many
artillery as cavalry. How many are there in each corps ? Ans.
200 cavalry, 6S0 artillery, and 1,800 foot.

94. Divide the number 46 into two parts, so that when the
one is divided by 7, and the other by 3, the quotients together
may amount to 10. What are the parts ? Ans. 28 and 18.

95. From the first of two mortars in a battery 36 shells are
thrown before the second is readv for firing. Shells are then
thrown from both in the proportion of 8 from the first to 7 of
the second ; the second mortar requiring as much powder for
3 charges as the first does for 4. It is required to determine
after how many discharges of the second mortar the quantity
of powder consumed by it is equal to the quantity consumed
by the first. Ans. 189.

96. Suppose the crown of Hiero of Syracuse weighed 100
ounces ; suppose the two crowns, one gold and the other silver,
weighed the same, 100 ounces each ; and supposing what would
be very nearly the case, that the gold crown, weighed in water,
lost 5 ounces : the silver one lost 9 ounces ; and supposing the
compound or mixed crown lost 6 ounces ; it is required to find
the proportion of gold and silver in the crown of Hiero. Ans.
75 oz. gold, and 25 oz. silver.

97. A footman agreed to serve his master for £8 a year and
a livery, but was turned away at the end of 7 months, and re-
ceived only £2 13*. id. and his livery. What was its value?
Ans. £4 16*.

98. A fish was caught whose tail weighed 9lbs. ; his head
weighed as much as his tail and half his body ; and his body
weighed as much as his head and tail ; what is the weight of
the whole fish ? Ans. 721bs.

99. If A and B together can perform a piece of work in eight
days, A and|C together in nine days, and B and C together in
ten dftys,Jhow long will each person take to perform it alone ?
Ans. A, 13}$ ; B, 17}?; and C, 23A.

100. The forewheel of a carriage makes 6 revolutions more
than the hind wheel in going 120 yards ; but if the circumfer-
ence of each wheel be increased by 3 feet, the forewheel makes
only 4 revolutions more than the hindwheel ; what is the cir-
cumference of each wheel ? Ans. 12 feet and 15 feet.

[We have here given our students a centenary of problems to
exercise themselves in Algebra. We hope they will do their
best to solve them ; we shall be happy to insert their solutions,
with their names attached to them, if they be performed in the
shortest and easiest possible manner, just as we have done
with the Exercises in Geometry.]

UNIVERSITY OF LONDON.— No. VI.

Ws feel assured that all of our subscribers will be gratified by
the perusal of the following papers which we have the pleasure
to lay before them in reference to our efforts on behalf of the
self-educating students and others of the British realms. These
papers were presented to the Senate of the University of Lon-
don, on the 1st of the present month, and read at the meeting
on that day. It will now be necessary, if our self-educating
students be in real earnest, and we have every reason to believe
that very many of them are so, from the letters which we have
received, that this movement should be followed up not only
by an application and petition to the Senate of the University
of London, but by an application and petition also to Govern-
ment itself. We know that Her Majesty's present Government,

with the illustrious Lord Palmerston at the head of the inquiry,
are anxiously and earnestly engaged with the great question
of the education of the people in general, with that of the pro-
priety of opening the old Universities to the public generally,
without regard to religious creed, and with that of the utility
of giving a still more liberal constitution to the University of
London. This is therefore the nick of time for our students
to come forward in a body by petition and representation,
respectfully to urge their claims to be examined as to the learning
which they have most industriously and often painfully
acquired, and to be rewarded with those sweet honours which
ought to be conferred on them if they succeed. Let us not
be behind ancient Greece in this respect ; but let us be up and
be doing what we can to rescue the sons of the soil from the
pressure of antiquated monopoly.

The following communications are recorded, printed and
circulated in the Minutes of the University of London.

•• « The Popular Educator' OffLo,
La Belle^fcauvage Yard,

Ladgate Hill, London,
lit February, 1854.

" Sib, — I have the honour to request that you will have the
goodness to lay the accompanying Memorial before the meet-
ing of the Senate of the University of London this day ; and
permit me also to request that a number of letters addressed
to me, as Editor of * The Popular Educator/ on the subject of
the Memorial, and nlaced by me in the hands of Mr. Moore,
Clerk to the Senate, may also be laid before the meeting as
evidence of the statements 6et forth in the Memorial. I hope
that at the next meeting I shall be able to submit further evi-
dence of the same description, and also to add many names to
the prayer of the Memorial, which it was impossible to obtain,
owing to the rapidity with which the Memorial was prepared,
and to tho non-arrival of the members of Parliament and
others in town, who should hare been most willing to put
their names to the document.

'* I have the honour to be,
"Sir,
" Tour most obedient servant,

" Robert Wallace."
"R. W. Rothtnan, Esq.,
Registrar, %e."

Inchsure.]

" To the Right Honourable the Earl of Burlington,
LL.D., F.R.S., Chancellor, the Honourable
John George Shaw Lefevre, Esq., C.B., M.A.,
F.R.S., Vice-Chancellor, and the Right Reve-
rend and Honourable the Senate of the Univer.
sity of London :

" The Memorial of the Subscribers,
" Sheveth,
" That in consequence of the increasing demand for the dif-
fusion of useful knowledge, the extension of the blessings of
education, and the equitable distribution of the honours and
rewards of learning, among all classes of the community, it
would seem to be both wise and politic, on the part of a liberal
and paternal Government, to throw open the Royal Road to
the valuable and permanent distinctions which the University
of London confers upon its members, to all the aspiring and
self-taught 8tudents of the British Empire, irrespective of their
various conditions in life, or of the different places and ways in
which they may have acquired their learning.

THE POPULAR EDUCATOR.

" With this view, your Memorialists are induced, by the
accustomed suavity, kindness, and liberality for which the
Noblemen and Gentlemen composing the Senate of the Uni-
versity of London are distinguished, to solicit on behalf of all
such Students, and especially of the self-taught, that you would,
as a body, apply to Her Majesty's GoTernment for such a
renewal and extension of the Royal Charter as will enable you
to confer the honours and degrees of the Unirersity upon
them, without requiring their attendance for a term of years at
any of the affiliated Colleges or Institutions connected there-
with, provided that they be found competent at the period of
the Annual Examinations of the Unirersity, upon the payment
of the necessary fees, and upon their presenting at the same
time such certificates of moral character as shall be deemed
satisfactory to the members.of the Senate, or to the Inspectors
that may be appointed by that body to decide upon the merit
and validity of such certificates, and for the following rea-
sons: —

" FirtL That it appears from the present Royal Charter and
from the Laws and Regulations of the Unirersity, that no
student, however well qualified he mag be t is permitted to come
forward to the Annual Examinations for degrees, unless he
has attended a certain number of academical years at one of
tho affiliated Colleges or Institutions connected with the
University.

" SWotul. That by the said Charter, Laws, and Regulations,
nutntnm* »clf- taught ami vthvr student* in the British Empire
ni» i-fti.lutU'cl from tho attainment of those honours and the
|i<jft*mi»i<iii of those degrees, to which their perseverance in the
jii<|ui«itioti of literary uiul scientific knowledge would justly

Mltltln ttliilll.

" Third. That tho University of London, by its metropolitan
|i<i«iiloti, lis freti and liberal constitution, its high and impartial
ilufitliiiK, iitul the well-known ability of its Examiners, is better
fjiiiilillfil thnii any other Aeadiuuical Hody in the Kingdom, to
imImcI uiul eoiiNoliilnti' thi> advantages of s literary and scien-
tific mIiii-nIIou among thu masses of the people.

•* f'Uttth. Tlml theio riists among the community at large,
hufli in Urn United Kingdom and in tho Colonies, a desire for
tli« iiM|iiUiiinii nf that honour which arises from the possession
i.f nnl kiifiwli'dw 1 * tn tho exclusion of that surreptitious honour
whi'-h »i fonfi'iied by tho purchase of titles and degrees to
"; •< !■ Mi<> prHMfHiHi Iihm no claim on the score of literary and

.'i ■ ■■ ni« ft'

/ /'/, ii..< M, i. iiii'l'lltnir uiul lower classes of the people
r .., .,./. **•*<«. <#./.•, i i.t *m li honours and degrees as the
. ...., :! f — *!•,

'.•wi n/iiiti, from a sincere conviction

ij.«i/ *oi nJ, le and praiseworthy, and constitute

. ';;jijj»i.M'/ff biiiojig men.

i.'»ia ii..t the ton vie- Lion just mentioned is ono of the

. , *->.-* n*;*i hurtful signs of a great chango for tho

. , . * v. i >i.;**. classes of tho community; that it is fraught

... . w* '.J *ujJi an amelioration in tho condition of the

«.-.- <v *ti*\. nut to lib overlooked by a wise and intel-

. u . r •• ^-vu«.xi ; uud Unit it is, iu truth, tho harbinger of
• y.^-u^u of that aucieiiL prophecy referred to by
.%*..,. «. ua muAIj; in hi* * Instauratio Magna,' namely,
4 . . 4 / j^-.mwU, u fcciuttia augebitur.'

• . ;/. i < M u*<> y.i.^uu.ntsd improvement of the Postage

r w^aJ--/ f.(#<«ii4ii.(sd to tha diffusion of useful

.. v n ■>.*•» u.,*+,+u,*i *«-s*jli mquirbs to bo fostered and

. . j . . I***. w#'< g u.4.< <*um onuuiug of the honours and

h .; ■— ',>„ ivi#»i./ '/I Iwluh v$ ull Uur Majesty's sub-

js+u.v* ..- ^ *^*JU4Uu*t t mutut proper regulations as

Rghih. That ignorance being the mother of i
rice, and the father of crime and violence, sedition and anarchy,
it seems to behove the Senate of the said Unirersity, on the
principles of its free constitution and liberal administration, to
employ the mighty lever which it possesses, in raising all classes
to the level of an honourable and useful rank in society, by the
bestowment of its valuable honours and degrees on all who art
found duly qualified, irrespective of their original condition.

"And lastly. That the security of Government, the advance-
ment of religion and morality, the suppression of crime, the
removal of juvenile delinquency, and the rapid pr og r e ss of
humanity towards a peaceful and happy state of civilisation,
are greatly dependent on the free extension of the M— fap of
education to all classes of the community, and on the free ad-
mission to the distinction which it confers on its enlightened
possessors, In whatever manner it may have been acq uir ed ;
and that though there be no Boyal Bead to Learnlnf, yet there
may be a generous, noble, and illustrious road to its
thrown open to the Learned by Boyal Favour ; a <
tion which your Memorialists earnestly with, and raspeetfully
press upon your attention.

11 Robert Wallace, A.M, Glasguensis, formerly
First Professor of Mathematics fat the Ad-
disonian University, Glasgow, and Pro-
fessor of Mathematics and Physios in
Homerton and Stepney Colleges.

M. D. Hill, Q.C., Recorder of Birmiiighaam.

Edwin Hill, Inland Revenue Office.

8. Moblbt, Wood Street,

Rowland Hill, General Post Office.

William Ellis, Champion HilL

John Moblet, Wood Street.

Thoxab Muul, formerly one of the Magistrates of
the City of Glasgow.

Frederic Hill, Late Inspector of Prisons fa
Scotland.

Arthur Hill, Bruce Castle 8chool, Tottenham.

John Cassbll, Ludgate Hill."

In order to assist our stu ents in following up the preceding
efforts on their behalf, we propose that the following short
petition to the Senate of the University of London should have
as many of the names as possible of our Subscribers, readers,
and others whom it may concern, appended to it, and that it
should be forwarded by us immediately to that learned body tor
its serious consideration. We shall be glad to receive these names
by post as soon as possible, so that no time may he lost, whOe
the subject is fresh in the minds of the members of the Senate,
and while the questions connected with it are just on the point
of being brought before Parliament.

lb the Bight Honourable the Earl of Burlington^
LL.D. y F.&.S., Chancellor, tka BonomraUe
John George Shaw Lefevre, Eoq. t CA, MJL,
F.RS. t rice-Chancellor, and Hut Bight Mm*
rend and honourable the Senate of the Ma>
city of London :

The Petition of the Subscriber*,

Humbly Sheweth,
That, having careful ly perused a memorial presented
by the Editor of the Popular Eduoatob and others, to the
Senate, on the 1st of February, 1854, In reference to the sub-
ject of throwing open the University of London to all sap

CORRESPONDENCE.

srr

tmaht and other Students belonging to the British Empire, so
that they may be permitted to obtain the honours, distinctions,
and degrees which it has to confer on those who are found
sufficiently qualified , at its public Examinations-, without their
attendance being required for a given period at any of the affi-
liated Colleges of the University, we, your petitioners, entirely
agree in the sentiments expressed in that memorial on our be-
half, and earnestly pray that you would be pleased to take the
matter into your most serious consideration,
"And your Petitioners shall ever pray."

(Signed)

Such is the form of the petition to the Senate, to which we
moat respectfully request our Students to send in their signa-
tures ; if any of them choose to assign their reasons for so
doing in their own way, the^ may rest assured that the utmost
attention will be paid to their statements, not only by our-
selves, but by the noblemen and gentlemen composing the
Senate of the tJniversity ; and we may just add, in conclusion,
that we shall take the earliest opportunity of calling the atten-
tion of the liberal members of Government, as well as of both
Houses of Parliament, to the subject both of the petition and
the memorial.

MR. CASSELL'8 PUBLICATIONS.

Batuunihg, however, to our cheap periodicals, which, from,
the quick and regular succession of their discharge must con-
tinue to be among the most powerful artillery of literature, we
find encouraging tokens of advancement. The "Illustrated
Family Newspaper" of Mr. Cassell, as yet only seven weeks
old, already equals in circulation, if indeed it do not exceed, the
11 London Journal," which up to that recent date stood in this
respect at the head of the weekly periodicals. This magazine,
for such it is, is another of the marvels wrought by the bene-
volent enterprise of its publisher. At the price of one penny it
contains eight folio pages of interesting and instructive matter,
crowded with illustrations, in many cases of wonderful merit.
At present it is largely occupied with Russian and Turkish sub-
jects, which must, of course, increase its immediate interest ; but
its pleasant historical treatment of them secures their permanent
value. Here we remark, as in the other publications of Mr.
Cassell, an unobtrusive infusion of religious sentiment ; and
while the excellence of the publication is thus in our eyes
enhanced, it is done with so much propriety that none
but a Mephistopheles could find in it matter for a sneer.
Among the benefactors of his country, Mr. Cassell, by the
singular versatility and vigour of his efforts in the eleva-
tion of the popular taste, must undoubtedly rank. We
have heard disparaging allusions to the unusual connexion
of Literature and Coffee. The more honour, we say, to
the man who, sprung from the lower ranks of the people, is not
content with a flourishing business as a coffee- merchant, but
steps out of his way to lend a hand in the great work of popular
education. Mr. Cassell seems to us to have earned peculiar
praise in his literary enterprises : for he has not merely sent
forth a large array of educational works, embracing the widest
range of liberal culture, but he has aimed at popularising
Art as a special department of the work of civilisation. The
humanising effect of the masterpieces of art on the popular
tastes can hardly be overrated. Compare one of the gentle
landscapes of Cuyp, with its sleeping sunshine, its cattle

r° 3tly rejoicing in the stream, and its homely peasants re-
ing in the shadow of the trees, with one of those startling
tableaux which illustrate the literature of the Mysteries and
Bandit school. The one is suggestive of peace, and hope, and
beauty — it awakens the love of nature, and appeals with
unutterable power to what is highest and purest in the bosom
of man ; the other mav strike the eVe by its cleverness,
but it strikes no chord in the soul— it nas no inner meaning,
nothing to speak of but frantic passion, or vulgar cunning,
or idle sentimentalism. Our blessings go with the man who

would offer the purer gift to his fellows ! We know not how.
Mr. Cassell manages to give the public the series of engravings
in his " Illustrated Magazine of Art " and " Works of Emi-
nent Masters " at the price marked on the covers. All we
know is that we feel personally indebted to him, and that he
puts a valuable collection of works of art Within reach even of
the labouring man. We might plead for fewer Dutch boors
and Frenchmen, and more of our native art, but we really can-
not complain. Mr. Millais' "Proscribed Royalist" alone is a
treasure to keep us quiet for a good while. To those who are
benevolently disposed, we could recommend no better outlay
of a few shillings, even at the price of a little self-denial, than
the presentation of such works to any poor family Who are lit-
tle able to taste the " grace and the glory of life. — BMwfk
Guardian.

CORRESPONDENCE.

TJNIVERSITY OF LONDON.

< Sib, — Gould you kindly inform me, through the medium of the
P. E., what are the appointed selections from the classics which
have to be more especially studied for the ensuing July examina-
tion of the London University ? Last year you gave your readers
a list of those selections, and informed them that it was taken from
the TJniversity Calendar. I have written for the calendar, but
have been unsuccessful in obtaining it. I know of no otaet way,
therefore, in which to get the information I want, than by applying
to you. Minimus.

[For the use of our correspondent and our students generally, w*
insert the required information.

CLASSICAL SUBJECTS.
MATRICULATION.
1854. — Xenophon: Anabasis, Book III.

Virgil: Oeorgics, Book I.
1866.— Xenopton: Hellenics, Book I.
Cicero t Pro Milone.

BACHELOR O* A*T8.
1854.— Euripides: The Iphigenia in Aulis.

Cicero : The Somnium Scipionis, and the Orations for the
Manilian Law, for Marcellus, and for Archias.
1855.— Demosthenes : Speech against Leptincs.

Tacitus: Agricola; Germania; Historiet, Book I.

To this information we add the red letter days of the calendar,
because they are the days appointed for the examinations this
year.

6 M

1-5

Th 1

JUNE. 1&M +
MA. Examination, Branch I.

Id ,.„

Id 0*f* Trio. Term Ve*>

14 *

MAE lamination , Branc h 1 1 ♦

JH,

Af.

Id. g Trin Term end*,

M.A. Exam id at. Branch 111. LL»B* Eaaminit' an

/*. Id

Id, ♦

[Etc ction of Yicc-ChoR&Uor mnd titer OjUc$>\

m. *

JITLT.

Matriculation Examination.

Id Oxford A^U andCam-

Jtf, [bridgtUommeacemt.

&L • . • * . itiiiti • *«**

LL.D. Examination.

Id. .,,,* ,.♦

Matriculation Examination for Honours.

/* "».

Id.

«. ..,„.

Id. >*••»***/

Is\ „ »«.* +

3**

TEE POPULAR EDUCATOR.

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^r« 11: •_» i«— «tr siir *uw Briwc t«* :»£:+. 11 t.v »^iT «erl 'ahieh ii tbt
t- fl«rr.^i :£ iai« :?i Bibe> u lu aksk <u»«l' . ;: i* ?►.— r. 1-3 the very vordt
•: « t j*t .: ji coruAei.. ux: Uit miu 1: LtC w u.* *M»e u hit metl worth

«: i-i .4 -?* rdir-rr ■ ir t ■■ :»i vai-* n* m^mit t c t — / : nodei«!imfiBf
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re=.u&.» en the n#e of
r Sl Lake'*; : We

Tut C*a% cU tcr,Jeeft kboTe n.*r.tic7i*'i tre iL*>*e which pory fr cm
y»« v# y«r ; for tr*« *Ht '/f t&Ofe tuv«ct« wLki ire invariabe,
•u 1 . h, *i»»i* :;« «ura from jtir t> jeir, oee pp. 137 and 213,

ANSWERS TO C0RRESP0XDENT8.

',«ii<r'T.( wfc^-.i * 4rkw'b^ a-'.'J itv.rip'.i'j*. 'A a Lett c'uerticil tUn-i
w*->x-'*. i'** '.»»*»»:■. or* *.f »?.;'.•» te Uz.t.tt a«> v* u»t'ai t-j our chen:e«:
r«!*-C-ri. "#< w< .•'..■-•£ V/ fjt..*^f. I*j*-:.*t, ti^at »«i §• p&rAt« rraJer
b«4, ,ik« '.L*.ri,',fct, c.i-.-«t*r*'l i'K.tforai of aU&d fii!AbL« ta bu wr.'.i.
*.u*u.s.*i* -mu l! ,n*u''"*: "'-■ It-'?.''* '-*•;» .% ;*>rtion <-i hit ap^&ra'.s*. if
/.^ »»f» v» : - j*:. »'. .: ^. ". * '.Vit'i ■•»•.'* for a.-;' mo;..; ♦l.iny r<«utr>rj coti:-r..
7\»« r • •', . *: *'»../ ff.f *y. ••> v.* ::.-.-- Ir.t'.Kn '#f z vxflrn pey, roti'jny
1". * vs **\ :\ 'y r*. * # ^- -j • f •.-. « • :r**l *r^ ••.H *jt m^riufactureri of ^i.i-
• •-*'#j.f. '.ii :r.t*r •.'/.«.:■.

A ',MfcMi'.4L "!-f:#*--T it,:- 'j»i'!.¥.r.;,V/i »ri4 illattrattd dnwin;
**f b %"..!-*A..tii ','*■* •f.'s-.-.t Ti\:.*.t % A.'*\.y..i. Ir.ttrustr.U cf tb» kind are
*s,tt*ui'.n *t*/i<t, \w Mitp.ij'/wo! \*,\\iu% »al*r r*^H;jr, bj: th*y do no:
fjl'-l '.ii« V/f« lit '#o* '.f % X'/O'J M'^wpip*. A b^owf/ip* fitir>« »!.0'iid cori.it
of* tf^x'.'ir* of c#»ib'i«ijli •: rn»tlrr, knd a g at«ou« Mp^rter of roiobmt.on.
Now it,* iritu<*rr;*M t+wi-.'-l ^> o ir corral pond*r.t yi^id* a j*t of com-
b'>iti'#.« natter »lon« ; h«r.c« j* • rom^iUft on i* on I;. p-;rl»rct ezterniliy —
•JiT* it to-ti ti«i tb« air. 1 k«r« i* r.otLwjg 10 good a« the mouth blow.
pip* f»>r ail purfK/ft of niir.traioyiciil r*i«»rcn. fi»rz«liut oiatntaioed that
*-t«rr oUier form «,f mitrunent ua»d f-r the ilx..e purpoee wai worthleas.
Flattr.er f a modern wnur on th* bl*.wpi^«, do« not coincide witb this
view. |f« u««i a p«cu!i«r in«charjlcal aid for obtaining hie jet— under
certain tircunuUneea. Hut Flattner ui« the blowpipe ae an agent of
fiMftfiAfJtce a»»ay, causing it to do the work cf a furnace. In our humble
opinion, JWz»liu»— who restricted the blowpipe U> qualitative inTettigationi
— entertained a more correct idea of the true gemui and powera of the in-
strument. For flaae-blowing, a pair of donb.e bellows is generallly em-
ployed. |p our own ease, we Seldom uke the trouble of using this
instrumeri ■ tif mouth hloirpipe accorepiishuig all that we require.

IfAkTLkT Wikdle (Karby) : The Letsons in English are published in a
separate form.

John McKbwxii (Thames DilUm) and Rob but II umbeb (Hartlepool):
Your wishea »ball receive our careful consideration.

C. 11. Y. (Irishtown-road, Dublin) t The third number of the ,: Classical
Library" Will not be published for four or fire weeks. The Latin which
our correspondent wishes explained, cot. sis ts of fragments of two verses,
ihe word tunt is understood after the nominative, or they arc in apposition
with something gone before, and the sense appears to be, that the difficul-
ties of a journey or life in a desert are welcome to a courageous spirit,
(literally, sweet to courage)*

W. D. C. (Dover) is rtgbU-R. D. 0. (Byde) : Bight; but as he justly sup-
pose*, there is a reaeon for teery thing ; we cannot, however, make him one

Lm» -M.-..:-- -t ■ w? iLn.c in
»-: if s< ij-rwrrr-^rA — Z~ia ah; . : » 2i

:* ▼ l. : star -» i_t ilbh ant soitree* :■■ v *ron:d be glad J f he
• :;..: •*_ \>-t u — L. 1- •c*i.rtK .-* n:*l: Knf^ tt* Ltgluh poets.

— T. E.-T l-ar-rAci.-* : ix**-. -*■: s-iiirs.

a "» ifa.T ?tt:i^t :m ^~ isit rjT.: ^aet •* ib* pce": : oa of the /bar
: _+. ii-: a.-: :( v 1 <;".i :? jL m *rs.r :n.^.: i-t La ejarolauon is wrokg.—
1 »ttji- l:-i*r . •■• la«* tr. :■:•.!. .31 sf- Th^sta* Csr^lv's works at
._, tii ii.:* -li: i:-» ■ rji w«i : r-s ."-»« as »t-w*t»*a: them. Ditto
::is>seruaf :at L •• u' >"*;— 3»- — Mm: i SaJjfd} aad * -H.X.O.: We
rfci*: :t_ -Aim . 7 : ■ ■.•••is-:: r-s . -. . k =^. xxii. 39. ia not extant.

— Y. . P .•: E\* r : •r:*:'-^ : Z it ixa: i.» rtA -r« u are sab printed.

i *j:::=a w— *-» a*?*: .r i.:»-T. II. I".*. Cxeieea : The number
£ :-T_*K i*ri* s«az.« :«".;j £ >c -si i :"*».•« cwi a j r/sw ibmss). For "Lce-
-::.+ ii «.mt:-i^:.;" i«* t . ... r .»".—». f. Br»;i^rc •. The lines 00

— X ■ ra. itt-n * are }ctzrj fvi.-. »^,i u«f f=. ^.: M au»: eaeellent; but we
w .^ f :♦•■«:« i a ic-^r a" f r.»i:j wr_*a. ;f tie M Bri'jh Poets " before
»:u=r=** a-;ti^g ua.: »:-i-= »-=;. mei. time before the taste was
:-:pr-.t<:.

N m : : N«+r-: — X. : T"r rrr a - : rrs^-f y 1 1: patience for a bad marriage.

— H iiAiTi t Ik**t : F:-:n :i tie Nuttiirale is quite ssckeoing to us,
etiiTt^ktK a as*, rf it — I PH. T:*a - TursrfmJness, even if admissible

i w-.tirg j a-tl i^"er.:rt /rr-;f.

C Oaii j it LWMtre-: w* rair :t t*l. the order in which the differ-
t : artr/^ges w-Jl a^p^x.-. w* ^nt xk: seta the work of 3J. Le Page
l . - . td t . Tie living of *i.s i £ it. ?t»it etoth ie Is. 6d.— T. G. YaTze

i»i:i v : B:s rf^-**: ita.. tf i::o:ri :: soon, for the sake of the Bolton
Lir-«tn.-C.occ>ii v^ier.fa:T-s.rr#c : some new things are preparing.

— U'OBk-G naac ate, C ;iL 1 _* iftr eeatury is one of the darkest
p-ri>£s of hsaxory: «e caz^:: ai»-*^. Search the Library of the British
M^ieua. — E. Coorra -.l»*;c:.-r. . . Ts answer his queries would tequire a
vy.ose.

T. L. Ell: »3X C:ti^ - L -irgraphy.— Dokcb (Holborn Hill): Wa
st-.^li ait ta«e ins* cm ti=. tai he c:t gi*en as hie real name and
ad^refi : to assume *— * tt-e s* u.real Lumi.iiy: for his wish to learn proves
tbs: he u no sfeaace. Tie &:•:*_*<* p*:ir ia the P. E. I* sufflcitnt. CmnetV&
Arithmetic j tie be*i we caa reccc^r.ead ; learn the whole of it from begin-
ning to end.

J. J.G. Psr.d'ctca : Bf«xi*s your bockbiader's nre^a, yon most have a
mt:h:nc fpt cc.tirg tie e J res rf y:-ii b^oka, technically called a pUmgk,
li oar cases for s:tgl* T>'.i»es ci the P. E. will hold saw, make them do so;
we think, &» a^ Eig^iicai. tiat joj possess this Uberty. O. H. u. (Has-
J^ti^.z. : We hare »e*= w-a: was called a writing alphabet of the Greek
l*Lzxi?e: tut we w?-jid. if we dars^ advise every language to be written
ai i: :t' priced, ar. i especially Greek.— J. J. Gaavas (Northampton): Yon
mai be?;- the t'.L.~x •:*. tic Greek T^stairect whenever you please; as you
rocs, jour d&cu.ues »il. disappear as you study the Greek lessons ia the
1*. K. We cocuder that it is every man and woman's duty to learn to read
the New Testament in the i-rigimal foapue. if by any means he or she can
t£T:ri tie time a*;d expesiT. tt* latter t.ow beir.g enmparatively small; and
our reaton if. that this knowledge throws a flood of light on the 6criptores
which cacz.ot otherwise be ru-ide oa?'s own. We are much pleased with
the S.Utcry cf his steady prorjrss through difEcu'.tler, and we heartily wish
h:m all succcas.

J. PaTaxCK r .Lubenh«m: : Your ipirit-Lunp doubtleet ie euffldently
effective. We desenbed one something Uke it at the eommeneemtsnt of our
lesions, advising the i-tudent notwithstanding to procure a real spirit-lamp,
which only costs a trifle, and soon reimburses the student for his outlay by
preventing t-';e evaporation of his spirit:

Thokas Wallace: A eoda-water bottle may be used instead of a
Florence flask in all experiments not requiring the application of heat. Ia
proportion as class i* thicker, so Is it more easily fractured by the applica-
tion of heat ; therefore, in selecting Florence flasks and retorts, choose those
of which the bottoms are thin.

J.Macmsh: The term verdigris is somewhat indefinitely applied. It
should be limited to express »ubaeettte of copper, that is to say. acetate of
copper having an excess of oxide. It is, however, frequently employed to
designate the green pulverulent substance which appears upon copper
after long exposure to air and moisture (carbonate). Acetate of copper,

that ii to sa> , neutral acetate, Is known to druggists generally, if not 1
sally, by the very absurd name of "sKsn'JZed verdigris." Cryetalliaed
grta would be right, but distillation is no way concerned In evolvi

product.

evolving the

Studbst op tub P. E. (London): You have applied the heat too and*
denly. The sudden application of heat to glass vessels render them areee
to break at any time— especially during cold weather. Probably, also, you
toucbe 1 the glass whilst hot with the wet wick of Che lamp. That treat-
ment will infallibly lead to a fracture.

Music: Timothy PFWNO.E88 will find sufficient instructions for play-
ing the German Concertina, with the help of a little " gumption,'* in one of
our earlier Music Lei sons.— John Mass: Our glass harmonicon has two
octaves, from below the treble staff to c above. The lowest glass (cosa-
mon window-glass) is five Inches and two-eighths long. The highest is tws
inches and five-eighths. You tune the glasses by chipping off the ends with
a key, If you ha?e not anything better.

LESSONS IN PHYSICS.

149

ON PHYSICS, OR NATURAL PHILOSOPHY.
No. XXIV.

(Continued from page 336.)

ACOUSTICS.

PRODUCTION, PROPAGATION, AND REFLECTION OF
SOUND.

Object of Acoustics.— -The science of Acoustics has for its object
the study of the laws of sound, and of the vibrations of elastic
bodies. Music treats of sounds, with regard to the feelings and
passions which they excite in us ; acoustics only treats of the
properties of sounds, the sensations which they produce not
being taken into consideration.

Sound is a particular sensation excited in the organ of hear-
ing by the vibratory motion of bodies, when this motion can
be conveyed to the ear by an intervening medium. All sounds
are not alike ; they are distinguished by differences so sensible
that we can compare them with each other and determine their
ratios of intonsity.

Noise, in general, is distinguished from sound. Sound,
properly so called, is that which produces a continuous sensa-
tion, and of which we can appreciate the musical value ; but
noise is a Bound too short in its duration to permit of its being
appreciated, as the roar of a cannon ; or rather it is a confused
mixture of several discordant sounds, as the rolling of thunder
or the dashing of the waves of the sea. Yet the difference
between sound and noise is not always distinctly marked ; there
are some ears so finely organised that they can determine the
musical value of the noise produced by the rolling of a carriage
on the street.

Cause of Sound.— Sound is always the result of the rapid
oscillations impressed on the particles of elastic bodies, when,
under the influence of a blow or of friction, the state of equi-
librium among these particles has been disturbed. They tend
then to resume their original position ; but they cannot return
to this position at once, for they oscillate on each side of it by
vibratory or going and coming motions, which are extremely
rapid, and whose amplitude very quickly decreases.

A body which emits a sound is called sonorous ; and the
motion which takes place among the particles of the sonorous
body, and which consists of a go or a come of these particles, is
called a single oscillation or vibration ; a double or complete vibra-
tion consists both of a go and a come. The vibrations are easily
put to the test of experiment ; if we throw a light powder on
a body emitting a sound, this powder will take a rapid motion,
and thus render the vibrations of the body visible ; and if we
strike a long tense {stretched) cord, its vibrations will be appa-
rent to the eye.

Sound not propagated in a vacuum. — The vibrations of elastic
bodies can only produce in us the sensation of sound by the
intervention of a material medium placed between the ear
and the sonorous body, and vibrating with it. This medium is
commonly the air ; but gases, vapours, liquids, and solids also
transmit sound. In order to show that the presence of a
material medium is necessary to the propagation of sound, the
following experiment is resorted to ; place under the receiver
of an air-pump, a bell which a small hammer strikes in a con-
tinuous manner, being put in motion by clock-work, fig. 124.
While the receiver is full of air at the ordinary atmospheric
pressure, the sound of the bell under the strokes of the hammer
is distinctly heard ; but in proportion as the air is rarefied, the
sound loses its intensity, and it ceases to be perceptible when
the receiver is exhausted. Whence, we conclude that spund
is not propagated in a vacuum. In order that the experiment
may succeed well, the sonorous body should be placed on a
cushion ; for the pieces of metal of which the apparatus is made
would otherwise transmit the sound to the platen of the air-
pump, and the platen to the exterior air. The same experi-
ment can be made in a simpler manner by means of a glass
globe, with a stop-cock, in which is suspended a little bell. If
we shake the globe when it is full of air, we distinctly hear the
sound of the bell ; but after the air within the globe has been
exhausted, by means of the exhausting syringe, the bell is no
longer heard.

YOL. IY.

Sound is propagated in all elastic bodies. — If in the two experi-
ments just mentioned, after having made the vacuum, we
introduce into the receiver or into the globe any gas or vapour,
the sound of the bell is again heard, which proves that sound
is propagated in gases and vapours, as in common air. Sound
is also propagated in liquids. When two bodies strike against
each other under water, the sound of the shock is distinctly

heard. A diver who is at the bottom of the water of a river
can hear what is said on the bank. As to solids, their conduct-
ing power is so great that a very slight noise, as the scratch of
a pin, at the one extremity of a piece of wood is easily heard at
the other extremity. The ground conducts sound so well, that
at night, by applying the ear to it, the footsteps of horses and
other noises at a great distance can be distinctly heard. ^

Mode of the propagation of sound in air. — In order to simplify
the theory of the propagation of sound, let us first consider the
case where it is propagated in an indefinite cylindrical tube.
Let m n, fig. 125, be such a tube filled with air at a constant
temperature and pressure ; and in this tube let there be a
piston p oscillating with great velocity between a and a. ^ This
piston when it passes from a to a compresses the air in the
tube ; but by reason of the great compressibility of this fluid,
the condensation does not act throughout the whole length of
the tube, but only on a certain length a h, which is called the
condensed wave. All the parts of the condensed wave are not
equally condensed and their velocity is not the same ; for the
piston in its oscillatory motion is animated with variable velo-
cities. The velocity at first is nothing at a, it increases pro-
gressively to the middle of its course, then decreases to a, where
it becomes nothing again.

Whence arise in the wave a h, variable densities of air and
velocities, varying with the velocity of the piston. At a, where
the piston is at rest, the velocity of the air is nothing, and
this fluid has resumed its primitive density. At u, where
the wave terminates, the velocity and density are the same as
at a ; but in the intervening points, these quantities increase
from the point a to the middle section of the wave, and then
decrease towards h. By conceiving the tube it x to be divided
into equal lengths such as a h, and each of these lengths
divided into sections parallel to the piston, it can be demon-
strated that at the moment when the first section of the wave
a h is at rest, the first section of the part n h' begins to parti-
cipate in the motion ; then, when the second section of the
wave a u is at rest, the motion is communicated to the second
section of h h'; and so on, section by section, in the parts n' h",
h"h"\ etc. The condensed wave proceeds therefore through
the tube, each of its parts passing successively through the
same degrees of velocity and condensation.

When th? piston moves in the contrary direction from a to

102

35rt

THE POPULAR EDUCATOR.

<s, it produces behind it a vacuum in -which the section or
stratum of air in contact "with the posterior face of the piston
is expanded. Then the following section or stratum expand-
ing in its turn, the first returns to its primitive state of conden-
sation, and so on from section to section, or from stratum to
stratum; so that when the piston has reached the point a,
there is produced an expanded or dilated wave of the same length
as the condensed wave, and immediately following it in the
cylindric tube, where they are propagated in succession, the
corresponding sections of the two waves having equal and
contrary velocities. These two waves taken together constitute
one undulation ; that is, that an undulation comprises the part
of the column of air which is modified during a go and come of
the piston ; the length of the undulation is the space which the
sound describes during the time of a complete vibration of the
body which produces it. This length diminishes with the
rapidity of the vibrations.

air in the place where it is produced. If we place a bell put
in motion by clock-work under the receiver of an air-pump, we
hear the intensity of the sound diminishing as the air becomes
rarefied. In hydrogen, which is about fourteen times rarer
than air, the sound has much less intensity, although the pres-
sure be the same. In carbonic acid, on the contrary, of which
the density is about one and a half times that of air, the sound
is more intense. On high mountains, where the air is much
rarefied, we must speak with considerable effort in order to
be heard, and the explosion of a gun produces but a weak
sound.

4th. The intensity of sound is modified by the* agitation of
the air and the direction of the winds. It is found that in
calm weather sound is alwajrs more easily propagated than in
windy weather ; and that, in the latter case, the strand ft mere
intense, at the tame distance, when heard in the direction of
the wind than when heard in the Opposite direction.

Fig. 125.

n n H A rr

fT j

i :

From the consideration of the motion of sonorous waves in
a cylinder, we majr now pass to that of their motion in a
medium indefinite in extent in all directions. By supposing
what has been said regarding a moveable piston in a tube to
be applied in every direction to the particles of vibratory
bodies, we shall be enabled to arrive at the explanation of
this case also. On this supposition, there will be produced
around every centre of disturbance a scries of spherical waves
alternately condensed and rarefied. These waves being con-
tained between two spherical concentric surfaces whose radii
are gradually increasing, whilst the breadth of the waves
remains the same, their mass Will increase in proportion as
they recede from the centre of disturbance ; whence the velo-
city of vibration imparted to the particles will be gradually
diminished, and the intensity of the Bound lessened in the
same proportion. It is the spherical waves thus alternately
condensed and rarefied, which, in spreading themselves through
space, become the medium for the propagation of sound. If, at
several points of space, disturbances take place at the same
time, there will be produced around each, a system of waves
similar to the preceding. Now all these waves spread them-
selves across each other, without having either their length or
their velocity modified. Sometimes the condensed or rarefied
waves are placed upon others of the same kind in such a man-
ner as to produce an effect equal to their sum ; sometimes they
meet and produce an effect equal to their difference. The co-
existence of waves is rendered visible to the eye, by disturbing
smooth water at several points of its surface.

Causes of variation in the intensity of sound. — Several causes
modify the force or intensity of sound, such as the distance of
the sonorous body, the amplitude of the vibrations, the density
of the air in the place where the sound is produced, the direc-
tion of the currents of the sir, and the vicinity of other sonorous
bodies. 1st, The intensity of sound is in the inverse ratio of
the square of the distance of the sonorous body from the ear.
This law, demonstrable by analysis, is the consequence of the
mode of the propagation of sonorous waves. Indeed, the
intensity of the vibrations of the air being, in every spherical
wave, in the inverse ratio of the square of the radius of the
/.phere, that is, of the square of the distance from the point of
disturbance, this is necessarily the case al6o with the intensity
of the sound.

2nd. The intensity of sound increases with the amplitude of
the vibrations of the sonorous body ; and consequently, with
the velocity of the oscillation of the waves. The connection
which exists between the intensity of sound and the ampli-
tude of the vibrations is easily proved by means of vibrating
cords ; they show that when the amplitude of the oscillations
diminishes, the intensity of the sound is diminished also.

3rd. The intensity of sound depends on the density of the

6th. Sound is increased in the vicinity of a sbnbftus boty.
The string of an instrument stretched in free air, Vielfls but a
feeble sound when it is made to vibrate at a distance from
every sonorous body ; but if it be stretched above a sonorous
case, as in the guitar, the vidllh, or the violoncello, it emits a
full and strong sound, because that the case and the air vibrate
in Unison with the string. Hehce aWkeS the ustB of sdhbrous
cases in Stringed instruments.

Apparatus for increasing sound.— To demonstrate the tibwer of
cose* or vessels full of air td increase the Intensity of ttmftj.
M. Savart constructed the Apparatus shown in Bg. 1*6. It

Ft*, ite.

consists of a hemispherical vessel a, made of b«ll-mel«], wlakfa
is made to vibrate by means of a strong bow \ near tt a pineal
a hollow cylinder a made of paste- board, open at the anterior
extremity and closed at the other. By means of a handle, thi*
cylinder is turned at pleasure on a support fixed in an arm c,
whicb slides freely in the stand oif the apparatus; thus the
cylinder B can be easily turned aside from the vessel k* Tht
apparatus being arranged as shown in the figure, when ft i*
made to vibrate, the sounds emitted taXe a force and a fulness
of which no idea can be formed without hearing them ; e-uj
the sound lose* almost all its intensity if the- cylinder be turnea
aside, and it is gradually diminished as the cylinder ti drawn
back ; ah experiment which proves that the increase In n
intensity of the sound arises from the vibrations of fte aft tin-

LESSONS IN PHYSICS.

farmed in the cylinder. In this apparatus, the cylinder must
have a determinate depth, in order that the air which it con-
taint may be in uniaon with the Teasel a, otherwise the lattnt
would Tibrate alone. VitruTios relates that the ancients
placed Sounding Teasels in their theatres, in order to strengthen
the sounds of the actors' Voices,

jyirf of tubs en the intensity of §omd.— The law aboTe Stat*
that the intensity of sound is in the inverse ratio of the sous:
of the distance, is not applicable to sounds transmitted through
tubes, especially if they be cylindrical and straight. Tl
sonorous waves are not then propagated under the form of
increasing concentric spheres, and consequently the sound
may be carried to a considerable distance without any tery
sensible alteration in its intensity. M. Biot has proved by
experiment, that in one of the pipes employed for conducting
the water in Paris, about 3,120 feet long, the voice lost so little
of its intensity, that from one extremity of this tube to the
other a conversation could be carried on in a low voice. Yet
the diminution of the sound becomes sensible in tubes of great
diameter, or in those in which the sides present many turnings
and windings. Such effects are observed in vaults and long
galleries.

The property which tubes possess of conveying sounds to ft
distance first received its most useful application among on
selves. The speaking-tubes used in our hotels and large
establishments are well known. These tubes are made of
caoutchouc, and of small diameter ; they pass from one place
to another through the walls of the house. If one speaks with
a voice a little raised above the ordinary tone at one of the
extremities of such a tube, it is very distinctly heard at the
other extremity. According to the experiments of M. Biot
already mentioned, it is evident that by means of acoustic
tubes a correspondence with the living voice could be main-
tained between two towns at a given distance from each other.
As sound passes over about 1,100 feet in a second, a distance
of about 50 miles would be passed over in four minutes.

Velocity of sound in gases. — The propagation of sonoroi
waves being successive, sound is transmitted from place
to place in an interval varying with their distance. On
this principle, a great number of phenomena are explained.
For example, the noise of thunder is heard a certain time after
we have seen the flash of lightning, although the noise and
the flash are produced simultaneously in the cloud.

Numerous experiments have been made in order to deter-
mine the velocity of sound in the air, that is, the space which
it describes in a second. The latest appears to have been ma<:
in the summer of 1822, during the night, by the members ; f
the French Board of Longitude. Two eminences were chosen
as stations for this purpose, the one at Villejuif and the other
at Montlhery, near Paris. At each station, every ten minutes
a cannon was fired. The observers at Villejuif heard very
distinctly the twelve shots fired at Montlhery; but those at
the latter station heard only seven shots out of the twelve fired
at Villejuif, the direction of the wind being contrary. At each
station, the observers marked, by means of chronomoters, thi
time which elapsed between the sight of the flash at the moment
of explosion, and the hearinc of the sound. This time was
taken for that which the sound required in order to travel from
the one station to the other ; for the distance between the two
stations was only 61066*127 feet, and we shall see, when we
treat of Optics, that light takes an inappreciable time to de
cribe a short distance like this. They found also that the
mean duration of the propagation of sound from the one
station to the other was 54*6 seconds. Now dividing the
distance between the two stations by this number of
seconds, we find that the velocity of the sound per secoi
was about 1118*4 feet, at the temperature of 60°*8 Fahrenheit,
which was that of the atmosphere at the time of the experi-
ments. The velocity of sound in the air decreases with tie
temperature : at 50° Fahrenheit it is only about 1105*7 feet p i
second ; and at 88* Fahrenheit it ia about 1092*5 feet per second.
But at the same temperature, this velocity is independent of
the density of the air, and consequently of the pressure. At
the same temperature the velocity is the same for all sound
weak or strong, sharp or flat. M. Biot found in his expei
ments above-mentioned on the conductibility of tubes, that
when a flute was played at the extremity of the tube 3,180 feet
long, the sounds preserved their harmony at the other extt

[ mitv, which indicates that the different sound! were propagated
I with equal velocity.

The velocity of sound varies in different gases, although
the temperature be the same in all. By making the same pipe
of an organ sound with different Kates, Dulong found that at
32° Fahrenheit the velocities in these gases were as follows :

Carbonic acid 708*7 feet per second

Oxygen 1040*1 „

Air 1092*5 „

Carbonic oxide 1105*7 „

Hydrogen 4163-6 „

Velocity of sound in liquids and solids.— The velocity of
sound in liquids is greater than in air. MM. Colladon and
8turm found, by experiments made in 1827, on the Lake of
Geneva, that the velocity of sound in water is about 4,708 feet
per second. This is more than four times its velocity in air.
In solids, the velocity is still greater. In experimenting on
the east-iron pipes used in conducting water, M. Biot found
that sound is propagated in cast iron with a velocity ten and a
half times that of its velocity in air. The velocity of sound in
other solids has been determined theoretically by Chladni,
Savartg M. Masson and M. Wertheim, by means of the number
of longitudinal or transversal vibrations of the bodies, or by
means of their coefficient of elasticity. Chladni has found by
means of the longitudinal vibrations that in wood the velocity
of sound is from ten to sixteen times greater than it is in air.
In metals, this velocity is more variable) the velocities
varying from four to sixteen times greater than its velocity in
air.

Reflection of sound.— So long as the sonorous waves are Hot
retarded in their development, thejrare propagated under the
form of concentric spheres ; but when they meet an obstacle,
they follow the general law of elastic bodies, they are thrown
back upon themselves, and form new concentric waves, which
seem to emanate from a second centre on the other side of the
obstacle: this is expressed by saying that the waves are
reflected. Fig. 127 represents a series of waves first incident

on and then reflected from an obstacle fo. If we consider,
for Instance, the incident wave modn, emitted from the centre

a, the corresponding rejected wave is represented by the arc
oxn, of which the point aiBtke virtual centra. If we join any
point o of the reflecting body to the sonorous centre a> aha
draw oh perpendicular to the surface of this body, the angle
▲ob is called the angle of incidence, and the angle bob formed
by the production of a o, the ancle of reflection. Whence the
reflection of sound is regulated by the two following laws,
which are also the same for light and for heat :

1st. The angle of reflection ia equal to the angle of inci-
dence.

2nd. The angle of reflection and the angle of incidence are
situated in the same planet which is perpendicular to the reflect-
ing surface.

According to these laws, the sound which in fig. 127 is pro-
pagated along the straight line ag, takes after reflection the
direction of the straight line 01; so that an observer placed at

b, will hear, besides the sound procaedisw from a, a second
sound, which will seem to him to be emitted from the point a.

3*3

THE POPULAR EDUCATOR.

LE880N8 IN G R E E K .-No. XXIV.
By John R. Beabd, D.D.

Verbs in w. The pure verb Aw*, I hat*,— Active Voice,

Tub Greek Ave* and (he English loose are obviously connected
in form as well as meaning. From the same root is our to
bee, which is the same word as loose, differently spelt and
pronounced ; to lost is the result of loosing.

I proceed to exhibit in full an example of a verb pure, m
take as my instance this verb Avw, / loose, or unbind. But i
the pure verbs do not possess the second tenses, that is, tl
second perfect active, the second pluperfect active, the aeeos
future passive, and the second aorist active, middle, an
passive ; these second forma are taken from two mute verb
namely, rpt0«#, I rub, and Act*--** (root Aor), I leave; and froi
one liquid verb, namely, +cuv* (root fav), I show. By th
means a complete example is piesented.

CONJUGATION OF A PURE VERB IN «.

ACTIVE VOICE. PARADIOM.

Tbxsxi

Indicative.

SUBJUNCTIVB

Optative,

Imperative.

Inpikitivp.

Pabticiplx,

Numb, and

Or the

That is. the

Principal

Sabjunctire of the

Fnu.

Tenae*.

Historical Teniae.

I loose, &c.

I may loose, &c.

Loose thou, &c.

To loose.

Loosing.

I
2

Av-ccg

A v-***
Av-yc

At/-e

Xv-uv

Xv-mv

Av-fi

Xv-y*

Xv trot

Xvsrov*

Av-ijrov*

Xv-erov*

Xv'trov*

Xv-nrov

Xv-irw

Au-o/ifv

\v wuiv

Xv-erf*

\v-n.rt

Xv-tn*

\v-ovoi*
I was loosing.

Xv-kKTl

I might loose.

Xv-trwoav or

OVTUiV

t-Xv-ov*

Xv-oifu

f-Av-ic

Xt/'Otc

c-Xv-(

Xv-o«

t-Aw-trov

Xv-oirov

3
1

•-Au-tmv

C-Av-OfMV

Xv-oiriji>
Xv-otfuv

•-Xu-eri

Xv-oirt

£-Au-ov*
/ «Aatf loose.

Xvouv

I would loose.

To be about to loose.

About loosing.

Au-ff-4*+

Xv-tr-oifii

Xv-ff'tiv

Xw-ff-wv

Xu-*-ccc

Xv-a, he. like the

Xv-*-«c

Xv-a Imperfect

Xv-?-&c.

Xv-o

a B

Au-<r- ft&* M*

Xv-ff

£§

Ai/-<r- Present

Xv'ff

2
3

Ave-

At/-*-

Xv'ff
Xv-o

•

I loosed.

I may have loosed.

I might have loosed.

Loose thou.

2b have loosed.

Having loosed.

c-Au-ff-a

At;-?.***,'

Xv"ff"Otfu

Xva-at

Av-<r-ac

c-Av-ir-ac

At/-«r-yc like the

Xv-a-aiQ or tiag

Xv-a-ov*

t-At/-«r-#

Xv-«r- Pr«. £«#.

Av-<r-ai* or m

Xv-o-arta

€-Av-^-orov

Av-*-

Xv-9-airov

Xv-a-arov

c Aw-a" arijv

Av-a-

Xv-o-airnv

Xv-a-arwv

c-Xv-e-a/icv

Aw-e'-

Xv~<T-aiutv

c-Av- a-are

Xu-«r-

Aw-<r-atr«

Xv-9-art

/ Aatw footaf .

X»-*-

T may have loosed.

Xv-o-auv or tiav

Xv-9-arvoav or
ffavruiv*

To hare loosed.

Having wotSm.

Af-Av-c-a

Xc-Xu-c-**

2
3

Ac-Av-c-ag
Ai-Av-*-«*

Af-Av-K-yg.&o. like
Xf-Av-K- thePres.

Xt'Xv-K't*

Xt'Xv'K'tna

\i'Xv-K tvai

Af-Av-c set

J).

Ai-Au-e-arov*

Xc-Xv-ie- Sttbj.

Xt-Xv-Ktrov

Xc-Av-r-arov*

Xf-Xv-K-

Xt-XV'K-tTWV

Af-Av-c a/«v

Xi-Xv-r-

Xi-Xv-K-art

Xc-Xv-r-

Xt-Xv-K'tri

XtXv-K &<Tt

Af-Av-c*

Xf-Xv ««tfwwv*

or ovrvv

LESSONS IN GREEK.

333

PARADIGM - continued.

Tenses,

Indicativp.

Subjunctive

Optative,

Imperative.

Infinitive.

Participlp.

Numb, and
Pbrs.

OfUM

Principal
Tenses.

That It, the
8utiJanctir«ofthe
Historical Ten.e.'.

/ had loosed.

I might have loosed .

-¥ S. 1
t4 2
Ki 3

Is 3

JS P, 1
§'/> 2

S 3

c-Xc-Xv-r-fiv

f-Xf-Xv-K-fiC

C-Xf-Xv-K-ft

t-Xt'Xv-K-tlTOV

i-Xc-Xv-r-cirifv

*-Xt-XvK-tlfttl>

t-Xi-Xv-K-ttre
*~Xt'Xv~K-ii<7ai>

Xt-Xv-K-oqu
Xc-Xv-c-otC) &c
Xc-Xu-c- like the
Xc-Xv-e- OptJmpf.
Xt-Xv K-

Xt-XV'K-
Xf-Xv-K-

Xc-Xv-c-

Pbrpbct
Sbcond.

or te>av.
1 have appeared

The flexions
are the same
as in the
First Per-
fect.

vt-ttyv-a

wt-fyvu

•

irt'^rjv't*

irt-<pj) vivai

iri*$n.v wq

Pluperfect
Sbcond.

/ had appiaral.

The flexions
are the same
as in the
First Plu-
perfect.

l'Wk-<pt)V-UV

wi-fiiv-cipi

Aoeist

8ECOND.

Stem «-Xir

8. 1
2

*-Xiw-oi>
s-Xir-tc, &c. like
the Ltd. Imp/,

Xnr-*»

Xtv-yCt &c. like
the Subj. Fret.

XlK-Olfll

XiK-oiQ like the
Opt. Imp/.

Xiir*< like the
Free, Imperat.

Xiir-*7v

Xix-utv

• The connexion of the parts will become obvious if I put the Stems together.

Stems.
Present. Imperfect. Future. First Aorist. First Perfect. Firet Plup. Second Perfect. Second Plup. Second Aorist.
Xv iXv Xv9 tXva XiXvk • fXcXvc xt+n.v iwifnv tXi*.

The Stems arrange themselves in pairs, thus —
1 Xv, Aw. 2 Xvcr» tXvcr. 3 XfXvc, cXf Xv«.

The first thing which I advise the Student to do, is to
make himself familiar with the stems. Having got the steins
he will easily acquire the rest.

The Student should carefully copy out the whole several
times. After he has learnt to recognise the connexion and
derivation of the several parts, and so formed some idea of the
beautiful harmony of the whole, let him commit the entire
paradigm to memory; and let him not pass on until he has
accomplished the task. The effort will save a world of
trouble.

It is customary in Greek Grammar to give three parts of
the verb, as the principal parts, or those parts from which
the others may be formed; namely, the present, the future,
the perfect. The connexion of the other parts with these
hree is shown in the Table of Stems given above. I present

an example or two, as inniu, I honour: /SovXciw, t advise; and
Xovv, I wash :—

Present.

Future.

Ptrfed.

nut

PovXivu

Xovm

now

fiovXivffut

Xovau)

rt-ruta
fiefiovXivica
Xi-Xovica. -

I present the same parts in their steins :—

Present Stem. Future Stem. Perfect Stem.

n- ri9- rt ruc-

jSovXfv- fiovXtvo- pt-povXtvK*

Aov- Xovff* Xt-Aovc-

~- =-nz -n^= : ye might
. ~. :_-*- i-l:: ;mi«; tc

.-: ^-i=. . «*-? Z .L&T* Ix-sed ;
•^1. m m^iz iiT* iootcd ;

ti^^ j'.-.-:r ~: !:•:*= : having
— . ■-•^■i 7; :«o might

. ;*-="- ET^e-LTri . T* tWO hire

■fi^j. h:-pL;C-- yi^-elves to
.-ir» U4 M^Tn". r ins of the

*s ^= pi — ^i^cil relations
*.r*tBL% zizwtrtr, we have to

> a r i.i y-:i to thoroughly

■r: La regard, thee, to the
v*tL u *.j other parts to be

'ar*i"u~y. and correct what
uronl parts of the Greek-

m. ar> ^r_r.zr-Ji^n.:— ".. :de root; 2. the aug-

_:■. - :--n. -. ::l- 'inie: -5. the mood-rowel;

zs-= rsz -»•- --■ 3u:cc-Tom-ei ; 7. the person-

: — r 12 !sis kcl Tipi'Jiir with ihe mood- vowel and

1. t:-. ij.- :« irrlis-i :hus, «-A>i'\«t-ff-.s-ro.

-.— s-z.--- Mf.utf ■ "Jif r:-:v. ii* the augment; c,

•■ -- - t-__ ..•.•■. :zrns •i^t'Vii-, which U the tense

~ _i ==*=*.: zaicau"* active ; the a, the tenie

__- — . =::- : --; irst Lunar, in-i thus the item of this

-_ ::- .r«r- 'lie x a the mood-vowel of the

. zr irat. ? r:n ? ^* sj«/i*u*a ; finally, the

■sr:---:^ini i" -he uiri pers-n singular of an
--__ sea* .: :.e xi^ulc mite : nan: el y, iJovXivaa-ro,

^ ^ zzz. perscn 5-.naxar =uz.ber trst a.rist middle

■^_-_ ->^=r ji-t 'troiio* . "±c iLU-re :or= sf which it fiovXtw* ;

_ ■_ ...ii -ara ire £or<ci:«. :oi.\r.r«. 5i3ovXfv-ca; for,

^_-^_ -*. — s it* * . 4"- T -: "-it r:-:: u found in the

.- ^_ j_r -r^-ir*-. par*, is ▼■:"- is :: tell— 1. the per-

_r "x:-:i 4 ".==«: :. the vuice, of eferjr

_: — - : -r=rr -*-- m -_:±: t:j. meet with.

_.r - T -^~-- *~ -i" -- *-h* paradigm are—

.-—. . -.. w.— d a:r:at f Xnrwv ; nr*t

r? rr =--- - .*.. 5*-: :r.d perfect, 7r«yijMuc.

r>. — _ -1: art declined like wr, which

.t*. r. .. it-: and znprjiiog is declined

^^ :?.-. I i— — 'l the forms uf Xvoac and

^. *. ... .:>7* -. ■»"-■ -t immediately under your

; ^- ■ ■-•a»a. Xrvai', ff*t"/ /w*

-e

■

--;--

Xv-aav

■ -"ir;,

Xvoavroe

""-■■»

Xv-oaiTi
Xv-crav

*- T

XvoaiTt

--:-:...

Xv'travroiv

Jftiri.

. -

-JBJ--

\i-oavra

a -i

\t~tavr<*v
Xp-ffarra

.^ 4.*L*=»*

«.- . vryiu. it' i<t(«

kawy /dostjf.

\i\v-titav

X«Xu roc
AfXu-fc-oroc

Xf*v-jccc

3*6

THE POPULAR KDUCATOH.

directed to the ease of albumen, yet it happens in practice that all,
or nearly all, animal and vegetable sabstances are capable of solu-
tion in liquor potassse. Therefore the content* of the most orani-
verous stomach may be committed to the potash flask with the
almost perfect assurance that every thing, except the mercurial
compound, will be dissolved.

The latter, as we have already seen, would be converted by this
treatment into the red or peroxide, which, being collected, might
be reduced to the metallic state by a method to be presently de-
scribed. The second plan is carried into execution by boiling the
contents of the stomach with nitromuriatic acid ; is. a mixture of
aquafortis and spirit of salt (two to one by measure). This liquid has
the property of rendering soluble all otherwise insoluble compounds
of mercury. (Demonstrate this proposition on calomel. Use a
test-tube. The boiling must be prolonged ; and the fluid result of
such ebullition will be bichloride of mercury. Demonstrate this
by the tests for bichloride of mercury.)

By proceeding thus, we disembarrass the mercury from its
organic associates, and obtain a solution, from which it may be
thrown down ; for which purpose, no agent is better than proto-
cbloride of tin, the nature and uses of which have been so fully
described under the head of tin, that further notice here is
unnecessary.

The student will not fail to remark that the latter mode of pro-
cedure, although unexceptionable as a means of extracting mer-
cury, destroys all evidence as to the condition in which the mercury
existed. For aught we might know to the contrary, calomel might
have been the specific mercurial compound from which the result
was obtained, inasmuch as the treatment with nitromuriatic acid
had for its prime object the conversion of insoluble mercurial pre-
parations, of whatever nature, into a soluble one, and that bichlo-
ride. Supposing the existence of bichloride to have been previ-
ously made out, the objection would not lie : otherwise it would be
fatal to the medical testimony.

Finally, it may be stated that all mercurial solid compounds are
decomposed when mixed with black flux and heated in a tube,
metallic mercury subliming. The method of discriminating it
when thus sublimed, from all other substances, and especially
from arsenic, have been already detailed under the head of tin. It
was to this mode of proceeding that I alluded just now, in stating
that the red or " peroxide " of mercury being collected might be
reduced to the metallic state by a method to be presently described.

LESSONS IN ITALIAN GRAMMAR.— No. XXI.

By CHARLES TAUSENAU, M.D..

Of the University of Patia, and Professor of the German and Italian
Languages at the Kensington Proprietary Grammar School;

Per.

This preposition denotes :—

I. The pottage through a place, or, more generally speaking,
a relation between two objects, one of which gets moving
along, piercing, penetrating, etc., through another, e.g. e-gli
pas- to per la cd-me-ra, he went through the room ; a R6-ma si
pud an-dd-re per Fi-rin-ze, o per Lo-ri-to, one may go to Rome
by way of Florence or of Loretto; pat-td-reper u-na eit-td, to
pass through a town ; /' a-cqua ehe scor-re per que-sto ea-nd-le,
the water which runs through this canal ; man-dd-re u-na lit'
tcra per Rb-ma aNd-po-li, to send a letter to Naples via* Rome ;
per di qua, per di Id, through this place, through here, through
that place ; per di s6t-to, per di sb-pra, through under there,
through above there.

II. The cause, motive, meant by which any purpose is or can
be effected, instrumentality. The latter idea, however, is most
frequently expressed by the words me-didn-te, per mis-zo di,
pervi-a di, by means of, by the agency of, through ; e. g. e-gli
td-ceper ti-md-re, per ver-gb-gna, he is silent out of fear, for
shame. La-vb-ra per qua-dd-gno, he works for the sake of
interest, gain, or lucre ; lo-go-rd-to per il Ikn-go u-so, worn out
by a long use ; k-gli e* in pri-gib-ne per de-bi-ti, he is in prison
for debt ; lo fa pel sii-o van-tdg-gio, he does it for his own
benefit ; per va-na-glb-ria, non per mi-se-ri-cbr-dia, for the sake
of a foolish pride or vainglory, not of mercy; non po-ti-va far
tnbt-to per rdb-bia, per do-lb-re, he could not speak with rage,
with pain ; dd-re per V a-mbr di Bio, to give for the love of
God; perlaqualob-ta, on that account, for that; per oa-gib-ne, J

per can-so, per ra-gib-ne, per mo-ti-vo, on account of, for, by
reason of, for the purpose of, with a view to, etc. ; per me,
per te, per lui, per U-i, per not, per voi, for my, thy, his, her,

our, your sake, on my, thy account, for me, thee, him,

her, us, you.

III. A purpose, end, or aim in view, object, tendency, endeavour t
effort. This is a most frequent and important ate of per, which
in this case exactly coincides with the English conjunctions tt,
in order to, to at to; e.g. e ve-nu-to per ve-der-vi, he has come
to see you ; ttu-did-re, Ug-ge-re, tra-diir-re per im-pa-rd-re, to
study, to read, to translate in order to learn; giuo-ed-re per
di-ver-tir-si, man-gid-re per vi-ve-re, to play, to be amused or
diverted with, to eat in order to live ; lo di-ce per bur-ldr-ti, he
says so to laugh at you ; per ter-vir-la, to serve or wait on you
(i. e. I am at your service, sir, yes, sir, etc. ; e. g. il pa-drb-ne
e in cd-sa f Per ter-vir-la, ti-gnb-re. Is master within ? Yes,
sir).

IV. An ability or qualification to do a thing, alto in this ease
corresponding to the English conjunction to, or to suitable
prepositions with present participles ; e. g. el-la ha in-gi-gno
ab-ba-ttdn-za per fdr-lo nU-glio di lui, she has sufficient intellect
to do it better than he, or of (for) doing it better than he ; i-gh
e trbp-po o-ni-sto per in-gan-ndr-vi, he is too honest to deceive
you.

V. The state of being about to do or on the point of doing any-
thing; e.g. is-se-re, std-re per fd-re qudl-che cd-sa, to be about
to do something ; sb-no, ttd per an-dd-re in Frdn-cia, I am on
the point of starting for France ; ttd-re per mo-ri-re, to be a'
the point of death.

VI. Any substitution qf persons and things, exchange, barter,
etc., corresponding to the English prepositions in the place of,
instead of, in lieu of, for, etc. ; e. g. ho ven-dk-to ilmi-o ca-pdl-h
per dii-ci dop-pie, I have sold my horse for ten pistoles ; prin-
der r u-no per V dltro, to take one for or in the place of the
other ; fd-re u-na c6 saper un dl-tra, to make one thing for or
in the place of another ; quci dit-e sb-no fdt-ti t u-noper C dl-Uo,
those two are made one for the other ; an-dd-te Id per me, gc
there instead of me.

VII. A continuation with regard to space or time; e. g. cbr-ri-
re per un mi-glio, to run a mile ; fa-ti-cd-re per titt-to un gibr-no,
to work hard for a whole day ; an-dd-re per ter-ra, per md-re,
to go by land, by sea; stra-tci nd-re per tir-ra, to drag or trail
along the ground ; e par-ti-to per tit gibr-ni, he has departed
for six days ; la mi- a md-dre e ttd-to ma-la-tic-cia per al-cu-ni
gi6r-ni, my mother has been indisposed for several days.

VIII. Distributive portions ; e.g. tdn-to per gior-no, per me'-st,
so much a day, a month ; tan?to per u6-mo, per ti-sta, so much
a man, a head ; tre soUdd-ti per ed-sa, tre ub-vaper u-n&, three
soldiers for every house, three eggs for one.

In addition to these uses the preposition per frequently
coincides with by ; e. g. fd-re qudl-che eb-ta per 6r-di-ne delpe*-
dru-ne, to do something by order of the master ; per co-mdn-d*
del re, by order of the king ; per vb-stro con-ti-glio, by your
advice ; prin-de-re, te-ner u-no per la md-no, per nn brde-cio, to
take, hold one by the hand, by one arm ; ti-rdr pe* ca-pe-gh,
to pull by the hair ; me-nd-re pel nd-to, to lead by the nose;
appic-cd-re pe* pii-di, to hang up by the feet ; chia-md-re i-no
per iltu-o nb-me, to call one by his name ; — with/br : eg. i-opar-
le-rdper voi (instead of a fa-vbr vb-ttro), I shall speak in your
favour; pre-gd-re Di-oper u-no, to pray to God for one; ho
fdMo que'-sto per te, I have done this for thee, for thy benefit,
on thy account ; man-dd-re, an-dd-re per u-na cd-sa, to send,
go for a thing ; so-tpi-rd-re per una cb-ta, to sigh for a thing ;
pel bin pub-bli-co, for the general good; per esan-pio, for
example ;— with at or to be, particularly in those cases when
after some verbs, as te-ni-re, ri-pu-td-re, etc., per is used instead
of cb-me, as, e. g. te-nire, ri-pu-td-re u-no per va-lo-rb-to, to look
upon one as brave, or take him to be brave ; U-ni-te-mi per
vb-stro, consider me as yours, or think me to be yours ; U-ntr
per fir-mo (instead of cb-me fir-mo), to look upon it as certain ;
cri-der or a-ver per vi-ro (instead oieb-me vi-ro), to believe it
to be true ; a-ver per ni-in-te,* to look upon it as nothing, t. #.
to think lightly of it ; dd- re al-cu-no per i-spac-cid-to, to give one
up as lost ; vel do per ti-eu-ro, I give you this as quite sure;—
with on the part or side of: e. g. per pd-dre, per md-dre, on the

• This phrase also means : to h*ve something ridieulousfy
cheap, or almost for nothing.

LE8S0NS IN ITALIAN.

357

part or side of the father, of the mother, by or on the paternal,
maternal side ; perpdr-ts mi-a, on my part, for my part, as for
me ;— with in : e. g. per mi-o pa-ri-re, in my opinion ; al-cu-
niper logiar-di-no si ri-md-se-ro, some remained in the garden ;
ce-nid-mo per lo fresco, let us take our supper in the cool ; le
bid-de on-deg-gia-no per % cdm-pi, the corn waves to and fro in
the fields; — with the preposition to : e.g. get-td-re per Ur-ra,
to throw, hurl, or pitch to ground.

An important use of per is the following : — Per quanto, or
merely jtw (along with the noun, adjective, verb, etc., imme-
diately connected with it) in the course of the sentence fol-
lowed by che (thus : per... che), signify as much as : however, as,
whatever, etc. : e. g. per p6-co cK i>o bd-va, however little I may
drink, or little as I may drink ; perbH-la cK ellasi-a, however
beautiful she may be, or beautiful as she may be ; per po-td-re
ch' d-gli db-bia a hu6-ce-re, whatever power he may have to do
harm ; per qudn-to ac-cvr-to u-no si-a (or per ac-cdr-to che it-no
si-a), however wise any one may be; per qudn-to pd-co la-v6-ri
(or per po-co che la-vo-ri) gua-dd-gna pe-rd da vi-ve-re, however
little he may work, still he gains his livelihood (i. e. to live).

It is obvious that even this detailed illustration of the uses
of per cannot do full justice to the great variety of its mean-
ings ; and only a judicious reading of good authors will enable
the pupil to make up this deficiency. Many phrases not ex-
plained in the preceding remarks will be clear to him at first
sight, and without an effort ; e. g. d-gli ha per mollis u-na Bo-
md-na, he has married a Roman; a-vd re it-no per a-mi-co, to
have a friend in one, etc. .

A careful study of the following exercise and vocabulary,
and indeed of all the exercises and vocabularies on the prepo-
sitions hitherto explained, will perhaps be the best preparation
for a more thorough knowledge of the language in this direc-
tion.

Exercises.— Italian-English.

Lo fd per pia-ce'-re, e non per do-ve-re. L' ba pre-so per I
man-tdl-lo. I'-o lo t£n-ni per un ga-lant-ud-mo, I'-o par-lo
per vd-stro van-tag-gio. rer ver-g6-gna di-v6n-ne r6s-so.
Per ri-guar-do deli* a-mi-co. Lo in-dus-se per vi-a di mi-nac-
ce. Sof-fre per ca-gio-ne di lui. M61-ti da lui ve-ni-va-no
per con-si -glio. VSn-ne per le p6-ste. E'-gli vi«m gi6r-no per
gi6r-no. £o di-co per vo-stro b£-ne. I'-o per me sa-re-i di
pa-re-re. Ah Si-gn6-re ! per ca-ri-ta non mi pre-ci-pi-ta-te.
11 Ban-gue per le ve'-ne ag-ghiac-cia. Per le vil-le, per i cam-
pi, per le vi-e e per le ca-se di dl e di not-te mo-rig-no (Boc-
caccio^. Per p6-co sa-rg-i ca-dh-to. Per lo con-si-glio di
co-lu-i. Fu sep-pel-li-to per mdr-to. Li la-scia-ro-no per
raor-ti. L' ha pre*-sa per m6-glie. An-da-re per u-na c6-sa.
Me-na-rc per la ma-no. Per un tgm-po de-ter-mi-na-to.
L' ha im-pre-Bta-to per quin-di-ci gi6r-ni. Per lo pas-sa-to
(per 1' ad-did-tro) si vi-ve-va bS-ne. Pan- no per un ve-sti-to.
En-tra-re per la fi-nd-stra, per 1' u-scio. Por-te-rd le spe'-se
perme-U. Va-lu-ta-ne la ll-ra ster-ll-na per v6n-ti scel-li-ni.
Non lo pds-so da-re per mi-no di difi-ci fio-ri-ni. Per la pri-
ma, per T ul-ti-ma volta. An-no per an-no. Per pd-co tem-
po, per bre-ve spa-zio di tdm-po. Per man-can-za di da-
rt a-ro. Per a-m6r su-o. Per mi-a fe. Per tdm-po. TJ'-na
\61-ta per sSm-pre. Per su-o li-be-ro vo-ld-re. Per viag-gio,
per i-stra-da. Per 6-ra non pds-so. Va per gra-di. Per qual
ra-gi6-ne? Per bud-na s8r-te. Per bno-na ven-tu-ra. Per
av-ven-tu-ra. Per dis-gra-zia. Per at-to di a-mi-ci-zia, di
ca-ii-ta, di con-ve-nien-za. Ci va per ma-re o per ter-ra?
P6z-zo per p$z-zo, par-te per par-te. Per Di-o ! per ca-ri-ta !
Co-n6-scer per fi-ma. Per i-spa-ven-ta-re. Per lo che, per
lo qua-le. Per lo me'-no, per lo piii. Per p6-co (or qud-si)
sa-re-i m6r-to. Per un an-no, per un* 6-ra, per un gi6r-no.
Chia-mar per n6-me. Perpo-ter ch* el-la ab-bia. Per pen-
si6-ri che a-v£s-se. Per quan-ti si-a-no i nd-stri ne-mi-ci.
Per quan-te la-gri-me ei spar-ga. Per quan-ta ffhr-za a-veY
ma-i pda-sa.

Vocabulary.

Lo fu, I do it.

Piacere, pleasure.

Dovere, duty, obligation.

V liapreso, he seized him.

Mantel lo, cloak.

Io lo tenni, I took him.

Golantuonto, honest man.

Io parlo, I speak.

Vantaggio, advantage, benefit,

profit, good.
Vergogna, shame, bashfulness.
Divenne rosso, he turned red,

blushed, coloured.

Lo indusse, he induced him,
prevailed on him.

Via, way, road, street, route ;
course, manner, means (per
via di, by way of, through,
by, by means of, by dint of,
by the help of).

Minaccia, (., threat, menace.

Soffrc, he suffers.

Cagione, cause, occasion, rea-
son, motive (per cagione di
or a cagione di, on account
of, for, by reason of, in con-
sequence of).

Lui, him.

Molti, many.

Venivano, came.

Consiglio, counsel, advice.

Venne, he came.

Posta, f., post (in potia or per
le po$te t in great haste, in
the greatest haste or hurry,
post-haste, post, by, with,
or on the mail).

Egli vten, he comes.

Giorno, day (giorno per giorno,
every day).

Lo dieo, I say so.

Bene, good, profit, advantage.

Io, I.

Me, me (per me, te, as far
as I am, thou art, con-
cerned, as to or as for me,
thee, for my, thy, part).

Sarei, should be.

Parere, opinion.

Caritd, charity, compassion,

mercy (per caritd, for the

love oi ~

sake)

love of God, for God's

Non mi precipitate, do not ruin
me.

Sangue, blood.

Vena, f„ vein.

Agghiaceia, freezes or curdles.

Villa, {., villa, country-houBe,
country-seat.

Campo, m., field.

Di di e di notte, day and night.

Morieno, they died.

Poco, little (per poco, almost,
nearly, well nigh, within a
hair's breath, I, he, we,
you, etc. ... had like to, etc.
... I, he, etc. ... was near
being, etc.)

Sarei caduto, I should have
made a fall (per poco sarei
caduto, I had like to have
made a fall).

Colui, he, that (per lo consiglio
di colui or per lo colui consi-
glio, by his advice).

Fu seppelito, he was buried.

Morto, dead.

Li laseiarono, they left them
on the spot (li laseiarono per
morti, they left them on the
spot for dead;.

L* haprcsa, he took her.

Moglie, wife.

Menare, to lead or guide.

Mano, f., hand.

Tempo, time.

Determinate, definite.

X* ha imprestato, he has lent
it.

Qvindici, fifteen.

Passato, the past, time past,
times of yore, antiquity.

Addietro, behind, back, behind-
hand, backwards (per lo pas-
sato or per t addietro, before
now, heretofore, formerly,
of old).

& viveva bene, people lived
happy or high.

Panno, cloth.

Vestito, dress, suit of clothes.

Entrare, to enter, step in.

Finestra, window.

XJscio, streetdoor, outside door,
entrance, opening, passage.

Portero, I shall bear.

Spesa, t, expense.

Metd, one half, a moiety (por-
tero le spese per metd, I shall
bear half the expense).

Valutano, they compute, esti-
mate, or rate.

Lira sterlina, pound sterling.

Venti, twenty.

Scellino, shilling.

Non lo posso dare, I cannot give
it.

Meno, less.

Dieci t ten.

Fiorina, florin.

Prima, m., prima, f., first.

Ultimo, m., ultima, {., last.

Volta, time.

Anno, year (anno per anno, year
by year).

Breve, short.

Spazio, space or interval.

Mancanza, want.

Danaro, money.

Amor, love ( per amors, for love,
for ... sake, on account of,
for").

Suo, his (per amor suo, out jof
love for him, for his sake,
to oblige him).

Mio, no., mia, f., my*

Fe, faith (per mia ft, upon my
faith).

Tempo, time (per tempo, in time,
in right time, in the nick of
time; early, early in the
morning ; for all times, for
ever).

Una volta, once (una volta per
sempre, once for all).

Libero, free.

Voters, will, pleasure (per suo
libero volere, of one's own
will, freely, spontaneously,
voluntarily).

Viaggio, journey (per viaggio,
on a journey or voyage, on
one's travels).

Slrada, road, way, route (per
istrada, on the way, by the
way, on the route, while
going along).

Ora, now, at present (per ora,
for the present, for this time,
at present, now, just now).

Va, it goes.

Orado, degree, step (pergradi,
by steps, step by step, gra-
dually, by degrees).

Qual, which, what.

Bagione, reason, cause, motive.

Sorts, luck, fortune, chance
lot, hap, hazard.

THE POPULAR EDUCATOR.

Tentura, fortune, lack, adven-
tare, chance (buona tort*,
kuana ventura, good lack,
per buona sorte, per buona
ventura, luckily, fortunately,
by good fortune).

Awentura, accident, event, ad-
Tenture (per awentura or
per ventura, a ventura, by
haphazard, by chance, by
accident).

Disgrazia, misfortune, disaster,
disgrace (per diegraaia, un-
fortunately).

Atto, act, action, deed {per otto
di, out of, through).

Amicizia, friendship.

Convenient*, propriety, deco-
rum, decency, politeness.

Ci va, does he go.

Mart, sea.

Terra, earth, land (per mare,
per terra, by sea, by land).

Petto, piece.

Parte, part, portion (petto per
peao, parte per part*, piece
by piece, piecemeal, by
pieces or morsels, in bits).

Dio, God (per Die, for God's
sake).

Conoseere, to know.

Fama, fame, reputation, re-
nown.

Spaventare, to frighten, terrify,
alarm.

C5U, which (per la cfa, per h
quale, wherefore, on what
account, for what reason,
why; on that account,

for that or this
that).

Piu, more (per le mem, at least,
per la pirn or i7 pii, most,
mostly, for the most part,
generally, commonly, usu-
ally, ordinarily, customa-
rily).

Quasi, almost, as if.

Arret morts, I should hare
died.

Ora, hour.

CA taster, to call*

Some, to name.

Pot€r % power.

Ch' ella abbia, she may have
(perpsttr ek'flla «Ww, what-
ever power she may hare).

Pensiero, though!.

Che aretee, he rnUht haTe
(per pemieri rke arette,
however much he may have
to think).

Quanto, m., quanta, f., how
much, how many.

Siano, may be.

Semico, enemy (per fuarnti
suino i naetri memie i, now-
ever numerous may be our
enemies).

Logrima, f., tear.

JSi eparfa, he may shed (per
quemte lagrime' ei apery*,
however many tears he may
shed).

Fbrza y strength.

Aver maipe a e m , he may have
(per quanta fbrta over mat
poaea y however strong he
may be).

Coxloquux Bxmacists.— Itujax-Exolish.

TlR-bra, the book.

IU-bri, the books.

La pen-no, the pen.

Lepin-nty the pens.

Upd-dre, the rather.

I pa-dri, the fathers.

La rnd-dre, the mcther.

Le md-dri, the mothers.

I btt6-ni U-lri, the &ood bocks.

Le fa£-n* pcn-ne, the good pens.

La ciUta, the city, town.

La eri-M, the house.

Al-to, high, tall.

Con-un-io, content, contested,

satisfied, pleased.
Si-no, are.

St'^-nodi, belong to (i.e. are of).
Sp-i~so t often, frequently.
&m-pre, always continually,

invariably, ever.
Ivsi-ittifra-Ul-ii, our brothers.
Le n-'-stre so-ret-fc, our sisters.
7/cT-fc-m, the tree.
Oh nl-ie-riy the trees.

V c-mi-co, the friend (m.)
Gli a-mi-H, the friends (m.)

V a-mi-ca. the female friend.
Le a- zil-fhe, the female friends.
La sptc-cnio, the looking-glass,

mirror.
GHtpi;-chj, the looking-glasses,
mirrors.

V uo-wio t the humm being,
man.

GtiuA-mi-pi, the human beings,
men.

Uti-ma, the theme, exercise
on a rule of grammar, sub-
ject, thesis.

Iti-mi, the themes, exercises,
etc.

Ilgio-ra-ne #*>-«tf, the young
servant-man or man-ser-
vant.

I git-ea-ni ser-ft, the young
servant-men or men-ser-
vants.

Ilfic-re, the flower.

Mai com-tfn-tey discontented,
dissatisfied, displeased.

ZT-ti4e, useful, profitable, lu-
crative.

Fii-ci-Uy ecsy.

Dtf-fj ci-le, difficult.

Ra-gio-nc-vo-U, reasonable, ra-
tional, sensible.

IT -no, one.

D*-e, two.

Tre, three.

Qmt-tro, four.

Cm-qm t five.

&-i, six.

SSt-te, seven.

6t- to, eight.

-V.I-C*, nine.

Du-ci. ten.

Un-di-ci, eleven.

D -di-ci, twelve.

'i r«-flKJ, thirteen.

Quat-t-sr-di-ei, fourteen.

Qfe r i-di»£i, fifteen.

S4-di-ci, sixteen.

Die-ei-eH-te, seventeen.
Dk-ci-St-ta, eighteen.
Dii-ei-nA-ve, nineteen.
Ven-ti, twenty.

V ar-md-dio, the press, clothe**
press, cupboard.

La *4-dia, the chair, seat.

V en- no, the year.

tl «a/-ia, the month.

Lamt-tUmd***,ihtj weak.

Itp*r>m,\h*&Mf.

CTI,e'e, there is*

d so-no, there are.

Vha fin multiplication), timet,

multipled by.
O,oo\oe.

iTAUAN-BHOUBb.

I pa-dri e le ma-dri. I bud-ni pa-dri e le buA-ne mi-dri.
1 11-bri so-no buft-ni. Le pen-ne &6-no bud-rie. Qu6-eti il-
be-ri *6-no al-ti. Le ck-se di que-sta cit-ta so-no al-tis-ai-me
e bel-Ms-si-me. Que-sto p6-ve-ro e s6m-pre con-tkn-to. Le
fi-glie di r.d-»tro zi-o so-no con-ten-*is-ai-mei A'n-cha i po"-
ve-ri so-no speVso con -ten- ti. Le pen-ne di ml-a eo-rel-la so-
no pic-co-le. Le eu-gi-ne di Gio-van-ni so-no pft-ve-re. Qu£>
ste iei-te-re s6-no m61-to pic-co-le. A«v$-te voi tro-va-to
que'-ste pen-ne nel no-stro cor-ti-le } Ab-bik-mo tio-vk-to i
ii-bri e le pen-ne di rd-atro fra-tel-lo. Hai tu ve-dfi-to le
let-te-re di mi-o cu-gi-no ? Que-ati giar-di-ni ao-no di mf-o
ri-o. I H-bri di mi-o xi-o so-no u-ti-li I fan-ciul-li di que-
sto uo-mo so-no ra-sio-ne^vo-lL La mi-dre d'Bn-ri-oo e-ma t
fi6-ri ed i fan-ciul-U. Gli a-mi-ci di Gio-vkn-ni s6-no ar-ri-
vk-ti. Le a-mi-che di mi-a so-rel-la so-no par-tl-u per H6*
ma. Gli 41-be-ri nel no-stro giar-df-no ao-no an-c6-r4 mol-to
ric-co-li. Que'-sti ud-mi-ni so-no sem-nre mal-oon-ten-tL Ls
n-glie dique-sto giar-di-nie~re so-no an-co-ra m61-to rio-ta-ni.
I te mi di mi-o cu-gi-no s6-no fk-ci-li; ma i tl-ml di mf-o
fra-te!-Io so-no mol-to dif-fiT-ci-li. I v6^-atri cu-gi-ni s6-no
ric-chi. ma le vd-stre ao-rel-le so-no po-ve-rfs-si-me. Hai tu
ve-du-to gli kUbe-ri ed i 66- ri nel nft-atro giar-dl-no? Kel
nd-stro giar-di-no v* c un* al-be-ro che e mol-to al-to. Nel-la
n6-stra c«-.«a ci s6-no quat-t6r-dl-ci stkn-«S. In que-su s tin-
ea ci so-no du-e tk-ro-le e do-di-ei aeV-dia. II n6-stro vi-ci*no
ha cin-qme mn-eiul-li, tre fi-gU e du-« fr-glie. In %ue-ato
giar-di-no ci so-no ven-ti gran-di al-be-rL Mi-o ai-ohn com*
pr4-to quat-tro cn-vsi-H. Ab-bia-mo ve-du-to nel4a scud-ln
tre-di-ci sco-lk-ri. Mi-o pk-dre ha quin-di-ci a-nH-li e se-i
ta-bac-ehie-re. Noi ab-bik-sno un' ar-mk-dio. akt-ta Ut-ti •
n6-ve spee-ehj. L* kn-no ha do-di-ei aae-ai, la asUti-ak-aa
ha set-te gi6r-nu H me-ee ha qukt-tro aet-ti-aaa-ae, e dk-o o
tre g.6r-ni. Xel-la nostra scno-la ao-no dik-oi aeka-ni. Tie
vi-a quat-tro do-di-ci. Tre vi-a tre n6-ve.

Coixoqoal T^iaosm.--EyoiJsm-ItaMAK,
The friends of my uncle are very rich. I haTe often seta
these men. The children of our gardener's wife are reason*
able. Our books are useful. London is a large town. The
houses of Paris are very high. Francis and William have
(tL *. are)anived. The daughters of this poor woman are vet
little. We have found Henry's sisters in the ohurch. Due
mother is always satisfied, but our (female) neighbours are
often dissatisfied. Tour exercises are difficult, but tie exer-
cises of Lewis are very easy. Have you received these beau-
tiful flowers from John? Our cousin has three snuff-boxes.
I have received from my uncle a pen-knife and twenty pens.
The (female) friend of my sister has five caps. This lady hat
seven children. I have bought two looking-glssset and six
chairs. This man has four sons and two daughters, who are
very reasonable. We have received five setters from oar
aunt. My friend has found a pen-knife and eight pens. I
have lost in the school ten pens. Four multiplied by five
predme* twenty.

LES80NS IN GERMAN.— Mo. LXXXV.

I 140. Rim
The Pluperfect /ease is used to express what find taken plate
at some past time denoted by the context: as,

Stai^fctm tic Game artrrjnjeftjnt aw, $1113 ft «§, after the sum

had gone down, he went off.
vr tone wdfrmtr m«rm Uatrmvaaa ^cwftfafca. he had slept during
our conversation.

• —»■
• English words in the Colloquial BxeretSM r*hrted in itanes
must be left out in the Italian.

L«6fiOKfc IN G*fcMA&

869

| 14l> ftuLi.

Tfrejfrtf Future tense Is fcmrildfred toertly lb exptett What
as*'/ or sris? take place hereafter j while law second £taar# Is
used to denote what tftaff tort* occurred at tome future period.

ObsbrVatiohs.

(1) The Future tenses, both first and second, have their
precise equivalents in the corresponding English tenses* and
should be used accordingly.

(2) When a future action is represented* or is mentioned, as
a thing ween***? to be done> as in tht English phrases* T*m to
go, he is to have, and the lis*, tnfc OeMnatt employs a distinct
verb expressive of obligation or necessity ; as, i<$ fott el ljafceri, I
am (shall be oblfrd) to have it. tr fott ftJtt^tn, ftc.

S 142. Rulb.

The IWdtcaYfo* mood is used in affirming or denying that
which is conceived to be eerhUh or undoubted; **

#r talrs atvearu itttBttfumtnen, he will return to-morrow.

OBSiaVAtlONB.

(1) Since the prober ottee of the Indicative is to empress
reaHfa It is employed in all absolute or independent sentences.
Even in conditional sentences, moreover, it is used, it the con-
dition is assumed ah ifacit bjs> sift tn reUfc fb git xht, art thou
rich (i. e. f/thbu hrt Hen), Mve much.

(2) Sometimes the indicative is employed instead of the /at-
perative, where that which is enjoined is treated as something
already in progress; as, tu trittfl w>r, thou steppest forward, i. e.
step (thou) forward. This il regarded IB the strongest form of
command.

j 148. feuLiv

The Subjunctive mood is used when that which is expressed by
the verb is conceived to be uncertain, though possible; as,

3$ tybt At$>rt» ta$ cr tie getounf$te Crefle er$a(ten $aBe, t have
heard, that he has obtained the desired situation.

3a) umnftye, Wfi et glutflla) toerbe, I wish that he may become
happy.

Observations.

(1) The Subjunctive, from its very nature, stands chiefly in
dependent clauses; and in these appears under various cir&
eu'thstances. Thus, it Is employed :

(£) When the design of the Speaker is merely to rtpeai cr
quote a statement, without vouching foe its accuracy % as, er fogt,
ter *3asm Mn$c, he says, that the tree blossoms; er melt* te mir, tag
cr fty ter$eir«t$et $a6e, he told me, that he had been married.
When* on the contrary, the design of the speaker is to set forth
the thihg repeated or quoted, as something real and undoubted,
the Indicative mutt be used j as, er tariff ei etyt afetiten, tag fein
sCrutct gtfkcrfccii ift, he will not believe that his brother is dead.

(3) In like manner, the Subjunctive is used in subordinate
clauses, after such verbs as fofjen, to hope; fur<*teit, to fear 5
n miftfcn, to wish $ ttwften, to desire $ titten, to ask j ratten, to ad- 1
vise; verfrimn, to forbid; cnh*$nen, to exhort; since the event,
in such cases, may be supposed to be always more or less un-
certain ; as, er fimtrct, tap tr Ctrafc ers>i(te> he is afraid that he
may be punished.

(4) 80. also, the Subjunctive is employed in clauses which
indicate ah *>i«f, ohfeet, with, or result; and which are intro-
duced by tap, a:tf tap, tamit, or by a relative ; as, fprtc^ tout, tomtit I
er tin) vetitcV, speak loud, that he may understand you ; er fua)t I
Arbeit, mlty if m *3nto gete, he seeks work, which may give him I
bread<.

(•) In cases such as those, explained in the observations
above, the student must note that that tense of the Subjunctive
is employed which corresponds with the one wed by the sub-
ject of the dependent clause, of the time token he said or did
that which is affirmed of him : as, er fagte, tr fate tielmet feint
Seit, he said, that ha had (literally hoe} no time at present; er
tytfte nut aefsgt, tof er « fctym fast, ha had told sae,.that he had
done it.

(6) The Subjunctive appears, also, in asking indirect ques-
tion < 1 m, i$ friftte u)n, et er mlt tal 6et» 0ien ttnne, I asked him,
whether he could five me the money. When the question is
mode directly, of course the Indicative is used.

( M The Subjunctive is sometimes employed as a sort of
ioftened Imperative, to express a #hh vtj&mhtion; as, #*e H
ttt %mmi t may heaven grant it ! ttefet »aum trase ate nritstt grn<$t,
Let this (or may this) tree never again bear fruit 1 et t ¥ se ttaf er
iv ill, let him do what ha will !

S 144. Rule.

The Conditional mood is used where a condition is supposed
which may or may not be conceived to be possible; as,

®iati « aso) fetter f* »«tte tr 60 3<u)re aft fein, if he yet lived, he
would be firV y«aH bid.

OasaaVATtoNS.

(1) besides the two tenses ranged in the paradigms under
the head of the Conditional, it must be observed that the Im*
perfect and the Pluperfect of the Subjunctive are equally often
employed in expressing conditional propositions. In point of
time, indeed, there is no dinVrence between the Imperfect of
the Subjunctive and the first Conditional, and between the Plu-
perfect of the Subjunctive and the second Conditional. OrdU
rtftnLy > where both forms are employed in the same sentence,
fte Subjunctive will be round in the clause expressing the ton-
dition, while the form peculiar to the Conditional appears in the
mher ; as, ty a>nrtt el ttjun, torn* d atdaftt* Mitt, I would do it* if
it were possible ; n*im et tyirt ttftrt, Ysftrh et tin) etfto$t ^aben, if he
were There, he would have visited you.

1,-1 When the condition is assumed and treated as A/act, it
is expressed* not by the Conditional* but by the Indicative ; as,
Hft ty rrifc f» glet *M, art thou (i. e. if thou art) rich, then give
much.

(3) Sometimes the verb expressing the condition is merely
understood ; as, tty ftaitt tie «ac$t snterl $em$t, I should have
done it otherwise (if it had been committed to me); itt joiner
Uv hjtte tcs> ti nkit getfcn, (if 1 had been), in hk situaUon, I
would not have done it.

(4) Sometimes, in the way of exclamation, the condition is
expressed, white that Which depends upon it is omitted i in
which ease the whole expression being of the nature of a «>Ssh
or fSfttiMsSa is often introduced (in translation) by" O," " I wish
that, n and the like: as, ^atte \a) \e$ Heftn Sraaft alt gtft^eh! as,
O t that 1 had never seen, this man ! literally, had I never seen
this man (how happy I should be)! urtrt et tas) am (esen! 0,
that he were yet alive !

(5) Hie Conditional is frequently employed in questions de-
signed to elicit a negative answer; as, toare H tean totfr* could
it be true? (it could not be true;) tu tearrft fb faff^s) B*»efen?
would you have been so faithless? (yoa would not.)

(6) Not unfrequently the Conditional of the auxiliaries ntigen,
tvlrft", ftftfn, Wasen and nwUrn, is employed to render an expres-
sion lea* positive, or to give it an air of diftdence; as, tc^ xootttt,
&\t Uqttlttttn wid^, I could wish (instead of, \ wish) you would
accompany me; ty m«Q>te fn>er ja fthrreten fein, I Should be
hard to be persuaded, Or. it would be difficult' to persuade me;
Mirfte ^ Sie am uk Aeffer Ktren* might I (be permitted to)
ask you for the knife ?

I 145. Rulb.

The Imperative mood is used in expressing a command, en-
treaty, or exhortation ; as, *

%ur<$re Qtott ant e$re ten jtdnia, fear God and honour the king.

Observations.

(1) The Imperative is sometimes employed to indicate a eon.
dition on which something is declared to depend; as, fei fbti
nab Va sMsjk a*at& «s>iiu%j ftaka, be Itatt^hly (i e W you be
haughty) and you wtU ind regard.

THE POPULAR EDUCATOR-

, (2) In order to make a request in a manner modest and po-
lite, instead of the Imperative, the Subjunctive of megen and
motttn is often employed ; as, tu uwlUtft fcinrt nic wrgrffen, pray,
never forget him ; megen &ic rtmncv getmfen, may you remember,
or remember me, I pray. To express a decided command,
however, the Indicative is frequently used. Sec $ 142. 2.

(3) 8ometimcs, by a peculiar ellipsis, the past Participle is
employed in place of the Imperative ; as, nur nictyt langr grfragt!
do not atk long ! where the full phrnsc would be, r* tatxu nur
ni4t fang t ]M ;jf, let it not long be asked ! 5tn tie ftritit argangen,
ttt them go to tli'.ir work!

ANSWERS TO CORRESPONDENTS.

T, Q. <l, li Informed that a rlui for initrviction in Mr. Curwen's
*,*\*tn of mimic |g hkrly to t>« opened near tbe entrance to Waterloo-lutdge.
IU th'fiilil writ" t«i Mr. It. (iilfllihs, 4, Cullunvstreet, Fenciiurch-s;rrvt.

'1'nr. Koin IUi.l Qi'icmtion.— Wo hare received numerous solutions of
t!ii« iju»-»tl'»ii, hut with ono or two exceptions, they are all erroneous. The
< Mrf mtur nt tTMir in tin- : opposition that theceutres of thr four boll* uiu*t
llr «l| In one pt.un>. N'»w this cannot be the rase ; for if so, then the four
bait* <mhM imt dy nii> unsiihillty be put all in ctmtact tcith each other, a
tiling tvhlili nm iiijiilinl by the question. Hut if thrre ball* b* put in con-
tact *ith rich utliiT, tit id the fourth ball be pUoeil above them to as to
touch each of the three, then the four balls will be in contact with each
other. Now the ball which is to touch each ot the four must be placed in
the interior t pace among the four balls, aud mm: be of ion*iderably loss
diameter than thclis. We have received a correct and ingenious solution
from Quimin I'htNOiM (IIUmio*), in which the 4?th of Euclid's l*t
Itook is the onl) element in the <M/i*«Ialto*. a matter ol some impoitance to
a learner, and we would at oiiee insert it ; but, like the Won** cub. it tracts
1-cking Into than*, so «» to be tit for the public eje. Moreover, he has in
his soluUou.av.unnd the principle of the ceutre of graviij of a pv ra-i id, a
saedtosiiosi I'liinipl* which cannot be admitted int > a gccxetr.cal liemvD-
> trains. What has become of the »oiation*whuh inuht h*ve been ex peered
Ir.m so-re ,f our old corraponlents, such a* Full Simili, 3L rtcs Y. ,
J oh a Bat s>, etc. '

J. S. Window Mc«3mouth»\ir;' : Eagl.sh Dictionaries are as r.'ectT as '
1-lackbemes in U.rir teason ; tier* fot*. Cass* ~*s d.tie won't be publahed j
f.w some tjme. :1 at a-i.~ W. MtiuXii ; Manchester; and J. \*iLSOS.
\\rdwick'. wi..- *•«:= to i« the #*w? prrym. are very aakioaa about Astro- .
unay. Wesloal- ..ke*ery cacl taat xitj woa!J »t.>fy spelling and c.*r !
Lessons in Etrlish ia the P. L- — Ax:, is Lcami-gtect: Laplace oc j
Asaonosnj.— Fjeivte* : The \rcz.:h Leto-** of the P. E. =ay te had In a
t-epsnte i^uaf f:r tie students jou wish to instruct in that lanf j^jt. I
Mr. Caaseil w-..: »h>rt-y pcMish a w ik ©a Botany.— Coxmsr Scbscbib** '
•Hertford*: Wa a :'s AlgctrazcGe'cetry or H..raer*s t\:::c S--rtio s; 5i:u- i

Han D. Dat:§ 'MaiiaHL! : His answer to l\e Four Ball Q-:e«uoi !
■•Tears t: be ririt. tu: bj njelhod is a little -irk^ard.— T. M.-a : in j
L^sae-y' Ttas f:**= =*ar*Tti* sx»e arawee is t^.e ;-<co!: ccrrcp.'-Ji- :,
'.at he «xi:>ct» s-^c of "th* cperati:=.— Hiset lux Web 3 roc. : lLe
•jmzin cf Nest:*.t en 5arreyi=- is, we beier-. arery ircod or.e. — .
'JtchaSa* A:rine, : All tlLat w« k=ow «f ih-* "S-rtccl of \ltnLc°
r .e fw fr:x a >:o\ jutiiCoc-r haada by Dr. Ljoz PLi>fair. ••Metro-
?>:ttaa 8<rh.:cl -f x:ence ar-?Ue-i to Miainy asi the Art*. M-i-
fcwai of Practical Geology. Toe folio win r _*-?ur«e» of leetarr* will be
i;T*a<lir:~x ie $«*iu?a l*."i3-4. I. C .c 21 s^try. with special re'ereace to
■:* apfLcat... : .3 the Art* as i M a:: n: acta res. — A. W. Hc^mira, Pc. D.,
r'.&-5. t. ^af^ral H.Tt*^. a"P-i*« to (.eU:fj ir. i th « Art*.— EJwi/d
* :rbca. F.B.S. 3. Ph>»:eal Scxc=.:e. with iz* #p^r.al A?;lxcat.ons. — Sober t
H«.t, Keeper of Mzaior Rtcoris. -L }l;ti-iur*y. - .:~v ::* spveial AppU.-a-
V-csu— Jota Perry, M.D.. F.S.5. 5. Geology, a. i 1 j ^M-ti^al Appliratiro.
— %. v.". Cj. . *ai. FJLS. < 3l^::r.raz<l Mineral. #..— w«i--:oo W. Sm^tt,
M.A_. F«».*. 7. AppLe-: Mechanic*.— Rcbert W I.*. 3I.A-. T.R S "Tie
fee ::r >iair:iv.'_»>U st^Jcct* :-;r L.« coarse ^f :*•> >ear« :s ore pay.
asertef £+), ..- ;«o a^-aJ payrstEts o: aTi>. T: :? :<e'i=clud«s pract cal
lutrcccoc ii tbe 5«id *r.i a^hir-.aJ JTawiac. I < fee* f?r tLe che=>ica:
aaj Bwcailvrpcal ji«r*icrie» ax.' a, 10 fcr the !<r=~ «. : f.urt.ca wevks. Ojv
A the •* Duke cf Cocr^AiT* Exbir :a. =*.**of £<.$ p-r m:ax,!j be h«1 1 .or
:^» yean, zrxrtd by HJt.H. the 1 r;- :e <i Wale*, wij be competed ic; at
i_e esd cf the S^tio-v Aeticf a:s^; agenu or ausagen may attend tbe
lecture* at half th* u> *al chargee. The tame role is app'a- d to oCcers ia
thr QeK*:.*» or tac Hca. E I.Coccjv }'% Serrfre. aieiEbers of the Col.c£* of
Prvceptors, *=d certiaeated. «chool=a*ters. Tkkets for eepara'e Ccarscs
areie^ued at £ teach, r £\S far the « bole cf tLe lecturtsdonog tteS<cft:c.
I'yt further i- fcrsatk-n apply to Mr. Trenhao Beek*, Cu*a:or, ?t the
Uaeesa. Jcrmyc-s^cet, Louden.— D. T. De Li Bicub, D^re^tor."

opinWois, of an opinion ; In like manner, Veritas, itis. means that the nom
native is rental, truth, and the genitive, Tertt&lis, oja truth.

A. J, calls our attention to a diagram at p. 1 13, Lesson VI I., which he cannot
understand. Partly this arise* from an omission in printing, partly from a
misapprehension of oor correspondent himself. Let A. J. begin by sapplying
the printer's omission, namely, two diagonal junction line* ; one bet ween the
figures 9 (water) and 8 ( ox j gen), the other between the figures 31 (tnlpfco-
rous acid) and 16 1 oxygen). Let A. J. then attend to the following remark*.
Throughout this diagram the figure* hare reference to parts by weight, not
to atoms; indeed this non-reference to atoms is sufficiently indicated by the
expression immediately following, i e. "/n this diamrmm J ham nwoidoi mil
fractional numbers for the sake of greater clearness. >' ow there can be no
tractions of an atom, and had we been treating of atoms we should hare had
no fractions to avoid. A. J. says our diagram represents the at m osp here as
composed ol 7 equivalent* (atoms) nearly of nitrogen and three of oxygen.
whereas he goes on to say " if 1* see// aSsosns that fonr-Aflls of the oiaso-
sphere consist of nitrogen and the other fifth of oxygen." Well, this composi-
tion is immediately deducible from our numbers :— thus,

1-20 : 0-96 : : l'OO : f (Nitrogen)

and
1-20 : 024 : : 100 : i (Oxygen)

Throughout we hare assumed that which in point of fact is not strict*?
true. viz. that the sp. gr«. of ot)gen and of nitrogen are eqaaL Our dia-
gram, in joint of fact, is not atomic, but approximate. yfevenheJessj His
a near approximation. We have no right to make the aim osnluis smeaebJe
to thr laws of the atomic theory, inasmuch as it is not even /ro e eaf tobea
compound, much less an atomic mixture.

A. Jouxsoic : Hydrosulphite of lime may be made by boiling together
lime, sulphur, and water, filtering, exposing the filtered liquid to the air.
breaking the scum en the surface of the liquid as often aa formed, and

filtering again. Hyposulphite of soda is made by adding a sotmtaon of
carbonate of soda tc h\ ;o*uIpbite of lime, filtering, and evaporating. Hy-
posulphuroui acid can barely be obtained. Herscheu thought he had mo-
cured it, I vadditnt'il; hune acid to hyposulphite of baryta ; bat the evolved
add was almost immediately decomposed. Our co r re sp ondent will purchare
hyposulphite of soda much cheaper than he can make it.

; 3. Tts; I. 8ee rnsver*iy of Leaden. No. VI.
Dublin': Le&osson Beadirs aid Execution are

Wsi. B: 1. No; ». Ye*
ii tbe P. E.— J. S. A. A. C.

robag on.— Tsuaxgls : We do cct *ec how Tri^o£.«.xeu> can le practical.
vales* i» is appl:ei W :>.o** practi*ai branch* s to which be refers.— A
Y.-rsc Ecuis.vu Macie= : W- can*: auvtr, ttcauie we dr r.': uader-
fotdhii^.tf.: a.-N.: Vc*.

H. Rowrsx Lcn ; .Cc::: v . rvvk : Ye*.—TH1 Eat'SH jElisno-tis . Go en; we
are preparing.— W h. >nui ^taSordsaire Pi.tUiw*: : Ue thai^ be is
rig v t ; the BT le acd :he P. E. are the best books. TL«ie is a ae« ctiition
ct the " Wcrkrcg Ma- ** Fnend • being iasned at a ch^ap rate. As 10 hit Latiu
njeries. 1. Tes, r. Slew; 3. Tea; 4. No. la the vora'v:**'- . : ^1-.^-!*
. .. s .», t . .. -:r;-v t* ?• of mi-. <iv prt«^-», •■n-'S ire p»r.»rire \t

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LESSONS IN PHYSICS.

3ftl

ON PHYSICS OR NATURAL PHILOSOPHY.

No. XXV.

ACOUSTICS.
(Continued from page 351.)

Sohoes and Ringing Sound*.— The repetition of a sound in the
air by reflection from any obstacle, is called an echo. In order
that the phenomenon of an echo may take place, the sound
must be- reflected in the direction of the observer, and the
reflecting obstacle must be at the distance of at least 66 feet ;
for it is scarcely possible to distinguish one sound from another,
unless about one-tenth of a second elapses between the two
sounds. Now, the Telocity of sound being about 1,120 feet
per second, it is plain that in a tenth of a second, sound would
pass over a space of about 66 feet; consequently, if the
reflecting obstacle is at or beyond a distance of 66 feet, the
sound in going to the obstacle and returning from it would
have at least 112 feet to pass over. The time which elapses
between the direct and the reflected sound will therefore be, at
least, one-tenth of a second; thus, the two sounds will not
confound each other, and the reflected sound will be distinctly
heard. According to these remarks, it is evident that if we
speak in a high voice before a reflecting body at the distance
of 56 feet, we can only distinguish the last reflected syllable ;
whence the echo is monosyllabic \ if the reflecting body be dis-
tant two, three, or more times the distance of 66 feet, the
echo will be dissyllabic, trisyllabic, and so on.

When the distance of the reflecting body is less than 66
feet, the direct and the reflected Bounds have a tendency to
mingle and produce confusion of sound. They cannot be
heard separately, but the sound is strengthened, and this effect
is called a resonance, or ringing tottttd. This phenomenon is
observed in large rooms; empty halls are very resonant or
resounding, but curtains and drapery, which are bad reflec-
tors oi sound, remove the effect of such resonances- in halls and
large apartments.

Multiplying echoes are those which repeat the same sound
several times; this takes place when two obstacles placed
opposite to each other, as, for instance, two walls parallel to
one another, mutually reflect the sound emitted. At Ader-
nach, in Bohemia, there is an echo that repeats seven syllables
three times; and at Lurley-Fells, on the Rhine, there is
another that repeats the*same sound seventeen times. There
is a famous echo at Woodstock, in Oxfordshire, which is said
to repeat the same sound fifty times. At Rosneath, in Dum-
bartonshire, there is an echo which is said faithfully to repeat
eight or ten notes of a tune played with a trumpet, but a third
lower ; after a short interval, another repetition is heard in a
still lower tone ; and after a similar interval, a third repetition
in a tone a third lower still.

Among the ancients, the echo at Capo-di-Bove was reckoned
famous ; so also was that at the tomb of the Me tell i, at Rome,
which is said to have distinctly repeated eight times the first
verse of the JEneid of Virgil, which contains fifteen syllables.
There is an echo on the Villa Simonetta, near Milan, which
repeats a shout thirty times ; and another in Pavia repeats the
last syllable of a question the same number of times.

The laws of the reflection of sound being the same as those
of the reflection of light and heat, the curve surfaces on which
it falls give rise to acoustic foci analogous to the luminous and
calorifie foci which are produced by concave reflectors. For ex-
ample, if we speak under the arch of a stone bridge, with the face
turned to one of the piers, the words will be reproduced with
so much intensity at the opposite pier, that a conversation can
be carried on in a low voice without being heard by persons
situated in the intermediate space. In the ground-floor of the
"Conservatoire des Arts et Metiers," at Paris, there is a
square hall with an arched ceiling which exhibits this pheno-
menon in a remarkable manner, when two persons place
themselves at two opposite corners. The Whispering QalUrus
both of ancient and modern times have their origin in the
similar architecture of their roofs and ceilings ; as in the Ear
or grotto of Dionysius of Syracuse, and in the whispering
gallery of St Paul's Cathedral! London.

Sound is reflected not only from the surface of solid todies,

vol. rr.

such as the walls of a building, woods, and rocks ; but also
from the clouds, at their meeting with a stratum of air having
a different density from that through which they have been
passing ; and even from the vesicles of which fogs are com-
posed. Thus, when the atmosphere is foggy, sounds undergo
a considerable number of partial reflections, which extend
themselves through the air with immense rapidity. At night,
when the air is clear, calm, and of uniform density, sounds are
heard at by far the greatest distance.

The Speaking and the Bearing Trumpets. — The speaking-
trumpet and the hearing-trumpet are two small instruments
constructed on the principles of the reflection of sound, and on
its conductibility in cylindrical tubes. The former, as its
name indicates, is intended to carry the sound of tho voice to
peat distances. It consists of a tube made of tin-plate or
brass, fig. 128, whicft is slightly conical throughout its length,

Fig. 188.

but funnel or bell-shaped at the one end, and which is held to
the mouth at the other end in order to convey the sound of
the voice to a distance. The principle of the instrument is
explained by the successive reflections of the waves of sound
from the sides of the tube ; reflections which, in consequence
of its form, tend to render the waves more and more diver-
gent. In the theory of this instrument, it is shown that to the
increase of the Amplitude of the oscillations which the particles
of the air undergo near the funnel, must be assigned the prin-
cipal cause of the effects which it produces in practice.

The hearing-trumpet is employed by persons who are very
hard of hearing. It is also a conical metal tube, one of the
extremities of which terminates in a funnel or bell, by which
the sound enters, and the other extremity of which is placed
close against the ear. The funnel or bell, in this case, is the
mouth-piece, that is, it receives the sounds which come from
the speaker. These sounds are transmitted by a series of
reflections in the interior of the instrument, so that the waves
which had taken a wide development are concentrated in the
auditory portion of the instrument, and there produce a much
more sensible effect than if they had proceeded from divergent
waves of sound.

VIBRATIONS OF CORDS, THEIR NUMBER AND
INTENSITY.

Two hinds of VibraUon m Cords.— In acoustics, cords are
thread-snaped bodies rendered elastic by tension. In tense
cords two kinds of vibration are observed, the one transversal f
or in a direction perpendicular to the cords ; the other longitu-

103

302

1HK tOfULAK JiDlJCAfOR

dinaly or in the direction of their length. The transversal
Tibrationg are produced by a bow, as on the violin, or by
pulling them quickly in the direction perpendicular to their
length, as on the harp and the guitar. Tne longitudinal vibra-
tions are produced by rubbing the cords in (he direction of their
length with a piece of Bilk sprinkled with rosin. As the
transversal vibrations are those only which are concerned in
the theory of music, wc shall confine our inquiries to this kind
of vibrations in cord*.

The Sonometer or Jlfonochord. — The sonometer is an apparatus
which in employed in the investigation of the transversal
vibrations of cords. It is also called the monochord, because it
is constructed only with a single chord. This apparatus is
composed of a case ot box of thin wood, which is intended to
increase th* sound ; on this case are fixed two bridges, a and
d, fig. 129 No. 1, over which a metallic cord passes, fixed at one

the vibrations attain their maximum of altitude, is called a
swell.

In order to prove the existence of nodes and swells in the
vibrations of cords, one is fixed at both ends, and under it a
small bridge is successively placed at a third, a fourth, and a
fifth part of the cord. If the bridge be placed at one-third of
the cord, as represented in fig. 129, No. 1, and the part b d be
made to vibrate with a bow, the ether part a m will then
divide itself into two parts, a c and c b, which will vibrate
separately, the point c remaining sensibly fixed. This will be
clearly seen by placing small pieces of paper on the cord, one
at c, "one between b and c, and one between o and a. As
soon as the cord is put into vibration, the piece of paper at c
will only be slightly disturbed, while the other pieces will be
thrown to a distance. There is, therefore, a node at the first
point, and there are swells at the other two points. If the

l Fig. 130. No. 1.

I r

i /

/ /

£M9?ZsV^ ja ■ ■■■',

- / /

Bat

/ /

/ ./

end, and stretched at the other by a series of weights which
can be increased at pleasure. A third bridge, n, is made
moveable along the case, in order to vary the length of the
cord which is put into the vibratory state.

Laws of the Transversal Vibrations of Cords. — It has been
found by analysis that if / be made to represent the length of
the cord, that is, the part whioh vibrates between the two
bridges a and b, in fig. 129; r the radius of a transverse
section ; d the density of the cord;.* the weight which keeps
it stretched ; and n the number of vibrations per second ; the

formula n = — \/ , in which w denotes the ratio of the

rind

circumference to the diameter of a circle, and the relation
which subsists among the quantities just enumerated. Whence
the four following laws are easily deduced : —

1st. The tension of a cord being; constant, tho number of
vibrations in the same time is in the inverse ratio of the length.

2nd. Other things being equal, the number of the vibrations
is in the inverse ratio of the radius of a transverse section of
the cord.

3rd. The number of the vibrations of the same cord is
directly proportional to the square root of the weight by
which it is kept stretched.

4th. Other things being equal, the number of the vibrations
of a cord is inversely proportional to tho square root of its
density.

The first of these laws* which is the most important, may
bo verified by experiment, if we employ a cord sufficiently
long and sufficiently. tenso to admit of the number of its oscil-
lations being counted by the observer.

Nodts and Nodal Lines.— When a body is made to vibrate, it
does so not only in its whole mass, but it divides itself gene-
rally into a number of aliquot parts, of which each is animated
with its own proper vibrations. Between these different parts
certain points or lines exist which vibrato less than the rest,
and which may be considered as sensibly fixed. Such points
are denominated nodes ; and such lines are denominated nodal
ww. The vibrating parts comprised between two nodes and
two nodal lines are called a eoncamerdlion, that is, an arching
^or vaulting. The middle of a concameration, the place where

bridge be placed at a fourth part of the cord, it will produce
between a and b two nodes and three swells; if at a fifth
psrt, it will form between the same points three nodes and four
swells , and so on.
The following side view of a monochord, fig. 129, No. 2,

Fig. 129, No. 3.
if

f^S

may suggest a simpler construction than 1Kb Preceding to
some readers ; c p is the. case or box, a the pbjnt where the
cord is fixed, i and b the, fixed bridges at the^ extremities of
the case, ii' the place o^ the moveable bridge', v^hicli is deter-
mined in any experiment by means of. a graduated scale on the
box placed below the cord, p the pulley over which the cord
passes, and 8 the weight which keeps it .tense.

The existence and the form ox nodat lines, in vibrating pistes
and membranes will be proved in a subsequent lesson.

SavarVs Toothed Wheel— The toothed wheel ,of M. gavart,
wh|ch bears the name of its inventor, is an apparatus con-
structed to show the absolute number of vibrations which
correspond to a determinate sound. It is formed of solid
pieces of oak nrmly tixed together on a stand,, like a book-
binder's bench, having an aperture in the puddle through
nearly its wbole length. In the aperture *ro placed twg
wheels, A and b, fig. ISO, So, 1, of which the first, a, ii
employed to communicate a great velocity to the second, s ;
and the second, which is toothed, is employed to produce
vibrations in a card or flexible plate, c, JUeo at one end of the
bench. This card, being struck by each tooth on iis passu j*ft
makes, by the revolution uf the toothed wheel, n* lunny com*
plete vibrations as there are teeth. On a small, dial. It, U
placed. a counter, which receives its motion from the axis of
the toothed wheel, and which indie a tea the number of turns
per second, and consequently the number of vibration* If a

LESSONS IN PHYSICS.

363

•low motion be given at first to the toothed wheel, the succes-
sive strokes of the teeth upon the card are distinctly heard ;
but if the velocity be gradually increased, a continued sound
is obtained, which gradually rises higher and higher. When,
by this means, the sound is produced whose number of vibra-
tions oro required, the same velocity is kept up during a deter-
minate number of seconds ; and by reading off on the counter
the number of turns of the toothed wheel b, we have only to

the toothed wheel, e is the place where the card is fixed which
catches the teeth of the wheel.

The Sinn.— -The siren is a small apparatus employed, like
the preceding, for the purpose of measuring the exact num-
ber of the vibrations of a sonorous body in a given time. M.
Cagniard de Latour, the inventor, gave this name to the
instrument, because it can be made to yield sounds under
water. It is made wholly of brass, and is represented in

Fij. 130, No. 1.

multiply this ijtli

to obtain

product

will be 1

representation of the stint inslrttnibn^

rig. iio, No. 2.

improvement fcr simplicity in the construction, fig. 130, No. 1
4« Is the oaken bench, b is the large wheel furnished with a
winch *, d is an axle on which is placed the toothed wheel d'
and a pulley of small radius, x is the band which passes over tie
large -wheel and the pulley, and communicates the motion to

fig. 131, mounted on the box of a blowing, machine or bellows*
hereafter described, which is employed to send a continued
current of air into the siren. Fig. 132, No. 1, and fig. 133,
show the inferior details of the siren. The lower part of this
instrument consists of a cylindrical box, o, surmounted by a
fixed plate, ii. On this plate rests a vertical rod t, to which
is fastened a disk a, that turns freely with the rod; several
holes are made at equal distances, in a circular form, in the
plate n ; and jn the disk ▲ an equal number, of the tame size
and at the same distance from the centre as those of the plate,
are perforated. These holes arc not perpendicular to the
planes of the plate and the disk; but they are all inclined to
them at the same angle, those in the plate being inclined in
one direction, and those in the disk in the contrary direction,
in such a manner that when the holes in the plate and the
dLsk face each other they are arranged as seen at m «, fig. 133.
From this arrangement it follows, that when a rapid current of
air comes from the bellows into the cylindrical box and into
the hole iw, it obliquely strikes the sides of the hole n, and
imparts to the disk a, a motion of rotation in the directions
n a.

In order to simplify the explanation oi the play of the siren,
we shall first suppose that the moveable disk ▲ is pierced with

Us. 13\

Tig. 133.

Fig. 13*., No. 1.

364

THE POPULAR EDUCATOR.

eighteen holes, and that the plate b is pierced with only one
hole, and we shall consider the case where the latter coincides
with one of the upper holes. When the wind from the bellows
strikes the sides of this upper hole, the moveable disk begins
to revolve, and the space between two consecutive holes
covers the lower hole. But as the disk continues to revolve
in consequence of its acquired velocity, two holes again face
each other ; whence a new impulse is given, and so on. Thus,
during a complete revolution of the disk, the lower hole is
eighteen times open and eighteen times shut ; whence arises
a series of blasts and stops which puts the air into vibration,
and produces a sound when the successive impulses are very
rapid. If we now suppose that the fixed plate n has eighteen
holes, when the disk revolves each hole will produce at once
the same effect as a single hole ; the sound will, therefore, be
eighteen times more intense, but the number of vibrations will
not be increased.

In order to find the number of vibrations corresponding to
the sound which the apparatus gives during its motion of
rotation, we must know how many revolutions the disk makes
in a second. This is effected in the following manner : — on
the rod t is placed an endless screw, which transmits its
motion to a wheel of 100 teeth. This wheel, which advances
one tooth at every revolution of the disk, carries on it a pin, p ;
and this pin causes a second wheel to advance one tooth at
every revolution, as seen to the left in fig. 132, No. 1. The
axes of these wheels carry two indexes or hands, which move
round the dials shown in fig. 131. One of these indexes shows
the number of the revolutions of the disk, and the other the
hundreds of these revolutions. Two knobs, c and D, are used
to engage or disengage at pleasure the small wheel and the
endless screw. As the sound rises in proportion as the
velocity of the disk increases, a determinate sound may be
obtained by increasing the force of the wind from the bellows.
By keeping up the same current of air during a certain time,
say two minutes, we can then read on the dials the number of
revolutions which have been made by the disk. Next, by
multiplying this number by 18, and dividing the product by
the number of seconds, the quotient will give the number of
vibrations per second. Fig. 132, No. 2, shows some of the

Fiff. 132, No. 3.

pares of the siren more distinctly, and it is added here on this
account, ee is the cylindrical box, communicating, at the
bottom, with a tube through which any fluid, liquid or
gaseous, is made to flow for the production of sound; tttt
the metallic frame- work in which the apparatus is contained ;
x the rod or vertical axis which revolves on itself; qq the
moveable circular disk, placed as near as possible to the fixed
circular plate without touching it ; and 11 the toothed wheels
which indicate the number of vibrations.

The siren, with equal velocity, gives the same sound in
water as in air ; the same sound also takes place in all eases,
a fact which shows that a determinate sound depends only on
the number of vibrations and not on the nature of the sonorous
body,

Blowing Machine, — In acoustics, a blowing machine is a
bellows, with a reservoir of air, which keeps up a continued

blast for wind instruments, such as the siren and the organ*
Under the feet of a wooden table, fig. 134, is placed a bellows*
c, which is put in motion by a pedal or foot-board, p. A
reservoir, n, made of flexible leather or skin, is employed to
collect the air thrown into it by the bellows. If this reservoir
be compressed by weights placed above it, or by means of a
rod, t, moved by the hand, the air is forced by a pipe, a, into

Fig. 134.

a box fixed on the table. This box is pierced with holes, to
which are fitted small metal valves, which can be opened at
pleasure by pressing on stops or keys placed in front of the
box. On these holes are placed the box of the siren or the
pipes of the organ, p.

Limits of Perceptible Sound.— Before the experimental re-
searches of M. Savart, philosophers believed that the ear
ceased to perceive sound when the number of simple vibra-
tions per second was below thirty-two for low sounds, and
above 18,000 for high sounds. But this experimenter has
shown that these limits were too contracted, and that the
faculty of perceiving, more or less easily, low sounds and high
sounds depends more on intensity than height ; so that when
the extreme sounds are not heard, it is because that these
sounds are not produced with sufficient intensity to make an
impression on the organ of hearing. By increasing the diame-
ter of his toothed wheel, and consequently the amplitude
and intensity of the vibrations, M. Savart has extended the
limit of high sounds to 48,000 simple vibrations per second.
For low sounds he substituted for his toothed wheel a bar of
iron of about 26 inches in length, revolving between two thin
slips of wood distant from the bar only about one-thirteenth
part of an inch. At every passage it produced only a dry
sound, arising from the displacement of the air. When
the motion was accelerated, the sound became continuous,
extremely full and deafening. Savart, by the aid of this
apparatus, found that when it produced from fourteen to six-
teen simple vibrations per second, the ear still recognised a
sound well determined, but extremely low.

Whatever may be the method employed to count the num-
ber of vibrations, the results obtained are sufficiently concor-
dant to admit of our considering them as the expression of the
truth by a very close approximation. In the middle portion of
the scale of sounds, one has been particularly selected as a
starting point. This selection is entirely arbitrary ; but it has
been fixed by custom ; and the la of the diapason represents
in musical language a sound of very determinate height; vis.
that which corresponds to 880 simple vibrations ; that is, 880
excursions of the particles of the sonorous body.

LESSONS IN GREEK.

360

LESSONS IN GREEK.— No. XXV.
By John.R. Beard, D.D.

PARADIGM OF THE REGULAR VERB Xt/«, I LOOSE.-MIDDLE VOICE.

Tenses,

Indicative.

Subjunctive

Optativf,

Imperative.

Infinitive.

Participles.

NlHB. AStD

of the

Subjun. of the

Tuns.

Principal Tens ee.

Historical Tenses.

2 foot* myself or

I may loose

I might loose

Loose thou

To loose one's self

Loosing one's

am loosed.

myself.

myself

thyself.

or ttt be loosed.

self

s.- 1

Xv-opat

Xv'Ufiat

Xv-t-oQai

Xv-optvog

* 2

X«/-y»

Xt/-y*

Xv-ov

Xv-irax

Xv-ijrai

Xv-to9u>

si D - 1
l! 1

"1 *-i

\v-opt9ov

Xv-OJfitOop

Xv-to9ov*

Xv-tjo9ov m

Xv-tc9ov*

Xv-to9ov*

Xvrjo9ov*

Xv-to9<i>v*

Xv-OfuBa

Xv u>fii9a

Xv-ioOt*

Xv-qoBt

Xv-io9i*

Xv-ovrai

I was looting
myself

Xv-tavrai

Xv-icr9w€tav t
commonly io9u>v %

i * *

t-Xv-oprjv

Xu-oifitjv

i 2

e-Xv-ov

Xv oio

IT i 3

c-Xv-cro

Xv-oiro

la a J

*'Xv-ofii9ov

Xv-oifiiOcv

i-Xv-io9ov

Xv-ot<r9vv

t'XvtoBnv

Xv-ototirjv

J 2

i-Xv-ofitOa

Xv oifitUa

i-Xv-to9t

Xv-otoBi

H 3

t'Xv-OVTO

I thall loose
myself.

Xv-oivro

J would host.
myself

. S. 1

Xv-o-oftai, the

Xvo-oiftrjv, the

Perton-

Person-

endings

cndings

like the

like Opt.

Present.

Jatjicrf

I loosed myself.

I m ty luive loosed
myself.

I n'ght have loosed
myself.

Loose thyself

To have loosed
one's self.

Having looted.

* tf. 1

t-Xv-O'Ctfitiv

\v o-wfiat

Xv a aifAtfv

Xv*9-ao- 9ai

Xve-apims

-i 2

i'Xv-O'ia

Xvo-y* like

Xv-o-aio

Xv-e-ai*

*1 3

t'Xv-o aro

ISnhj. Pret,

Xv-v-atTo

Xt/-<r-a<r0(i>

•g a D. 1

i-Xvo-api9ov

Xv-o-aipt9ov

i-Xv-o-aoQov

Xv-o-ato9ov

Xvo aoOov

S ? 3

t-Xv-o-ao9tjv

Xv-oatodrjv

Xv-o--ao9(t>v*

S s r. i

*S 2

i~Xvo~afn6a

Xvo-aipiOa

f-Xt/-<T-acr0*

Xv- a-aio9t

Xv-a-aaQi

*- 3

t-Xv-o-avro

I have loosed my-

self or have been

loosed.

I may have loosed

myself or been

looted.

Xv-a-aivTo

I might have loosed

myself or been

loosed

Xv oaaQ<ij<rav t
commonly a*9wv+

, * l

X 2

Xi-Xv-fiai

Xt'Xv-fuvos <*

Xe-Xv-eOai

Xt-Xv-fiivoc

Xi-Xv-eai

X«-Xv-//«i*oc yc

Xt-Xv-oo

-i 3

Xt'Xv-rai

Xt'Xv'ftivog y

X*-Xv-o9io

•Si 2

Xt-Xv-fu9ov

Xe-Xv~o9ov*

XtXv-fltt'U tJTOV

Xe-Xv'o9ov*

£? 3
g P. 1

Xt-Xv~o9ov*

Xt-Xv fUV(t> TJTOV

Xt~Xv-o9utv m

Xi'Xv'fu9a

Xt-Xvfiivot ojfiiv

J 2

\z-\v-o9t*

Xl-Xv-fitVOl fJTl

X« Xt/-<T0€*

H 3

\t~Xv'Vrai

Xi Xv pivot VOl

Xt-Xv- o9id<rav t
commonly adwr*

366

THE POPULAR EDUCATOR.

PARADIGM— «/i/i'ww«f.

TENSES,

INDICATIVE.

S- DJLXCUVE

OrTATITE,

Imfeujltivx.

Infinitive

PAJtTIClTLn.

NiMH. AND

of the

Stibjun. of the

FrRB.

Priii'. ipalTtt.f.-s

Ilis'.crical Tenses.

ntji('f. Or iitf.i

s. S. 1

*< 2

ri a

^2 2
S..=i 3

1 % '■ I

I Xc-)-f-'-?j
t-\i-\v-TO

i Sc-Xr-m'-i :■
f-Xc-Xi; ««/. v
*-Al .\ l -»:";/ r

f Xi-Xv '»!
e-At-Xu-j.ro

A*-Xr-/nroc «o;v
Xi-Ar /ut'i-c fiifc
Ai-A.*-/ *»-*; cirf

A«-\r /'(iwtuj'ti'
Xt -A !•-;'? rw *if/ri;i'
A « ■ X t?-/u rui f i #//* t A'
At-.Xj' utvnt 4t;/r€
■Xt-\f [Uicititjvav

PrKI'lCT

I''UTUKB,01i
TlIIKD

Futiue ;
T.S.Xi Xv-v

/ khall hie: loo,. (1
mysi'J\o Inn

•

I wul.l have
I sited .flyse?/.

To lc about to
loose yourself*

Being about to
lomyoMTvlf*

S. 1

X«-Xl* G-VHtl

Ltd. ins.

Xe Xu<r-oifi^v
like Optative
hnperf.

\t-\v-9-t90at

\t-\VG-OfltVO%

Second
Aoui&t ;

' i re 'nali^d
bthind.

I mat/ have
remained behind.

I tuigU or
would, &c.

Remain b. hind.

T.3. e-XtT

S. 1

i-Xiir-of.ijv /<av
//«„• /.#«»/'. bid.

\nr-tofiai like
the Subj. iVcs.

XiTr-ut-ujy /i"A<r

Ojd. Imof.

\l7TOV, -i<j9u>
1 Ik' ih- Prwht.

Xnr-trrQai

Xcx-o/ievot

EXEIICIFKS.— GUCEK-EXULISU.

Avoifitjv, Xvffoi/uji'; Xuo/mt ; At/w/rat; «Xi\»//j;i'; fNrTi'/tijv ;
XeXv/uzt; 1X1X174171/ ; XtXvaofxat. \ Xi'<ro/iat ; iXnrofujv; \vuvTai ;
«Xuovro ; cXv<ravro; XcXurrai ; cXtXvi/ro; XtXiyHvoc w;
Xt/<#ac<r0c ; XeXvrat ; XcXu/ierot ioai ; XfXr/icCa; Xnrotfiijv;
XnrioOar, XtTru/isroc ; \voatfVai\ Xnef-'ai ; Xru/itroc; Xi»«ra<x0i;
X{Xu/i«voc ftijffj XnriofKu.

EXQLISH-GllEIIK.

I might loose myself; he might loose himself; they might

loose themselves; to loose one's self; to have loosed one's
self; loosing one's self ; loose yourselves; I have loosed my-
self; they have loosed themselves; they might have loosed
themselves; thou miyest have loosed thyself; they shall
have loosed themselves; they remained behind; he may
have remained behind ; do ye remain behind; let him loose
himself ; to have loosed one's self.

Conjugate, according to the active and middle paradigms,
these verbs: — iraittv*, I instruct, educate; fiaetXtv*. J reign:
the chief parts arc — iracfovw, iraifcwrw, vrtwaiitVKa, a-cxat-
Uvpai; ana fiaoiXivto, fiaciXtvau, /3c/3affiXiv*a, /fy3a<r«X*tyiat.

LI5SSONS IN CHEMISTRY.— No. XXIV.

Befoxie entering any further upon the investigation of chemi-
cal bodies, it will bo necessary to pause awhile and describe
certain manipulative operations having reference to the appli-
cation of heat. An examination of the contributions to the
editorial letter-file points out the neccsMiy of this. One
correspondent desires to know whether a gas flame may not
be substituted for a spirit-lamp flame ; another wishes to be
instructed as to the best means of conducting distillation. I
■hall proceed, therefore, in this lesson, to impart a notion of
the economy of heat chiefly in reference to gas. Hitherto I
have directed the employment of charcoal and of spirit as
sources of heat. This course was pursued in reference to the
necessities of ihose who could not i—mmaml the agency of
coal gis, which whenever at hand, titiords u cheap, commo-

dious, and an elegant means of conducting many chemical
operations.

' Until within the last few years, the most usual method of
employing coal gas in chemical laboratories as a source of heat,
consisted in utilising the flame of a common argand burner,
the construction of which is so well Known that it scarcely
need be detailed. At present, the argand burner is almost
thrown out of uso by the mixed gas flame presently to be
described.

The great advantage possessed by the mixed gasbnmer over
the argand flame is the absence of all smo|te. The student
may here reply, that a well-regulated argand burner does not
smoke. True enough ; but it nevertheless deposits a thick
coating of smoke or soot on the surface of any body held
within it, whereas, on the contrary, a mixed gas flame, if well
regulated, deposits no soot whatever. The theory of this soot
deposition cannot bo understood, until we have fully investi-

LESSONS IN CHEMISTRY.

367

gated the chemical nature of carbon. Suffice it to say, that
the combustion of coal gas alone yields smoke, whereas the
combustion of coal gas and atmospheric air, or coal gas and
oxygen, tjie latter being the effective constituent in atmos-
pheric air, yields no smoke.

But most people know, J assume, that a mixture of coal gas
and atmospheric sir constitutes the terribly explosive fire-damp
of the miner; how, then, are ire to burn this mixture without
danger ? $ot only does this problem admit of being solved,
but the most explosive gaseous, mixture in nature can be
tranquilly burned by the method, slightly modified, that we
shall adopt (or producing ihb mixed gas flame, namely, outside
a piece of wire gauge, the effect of Which material in checking
the progress of flame can be admirably recognised in the
following experiment, for conducting which, either a spirit-
lamp flame or a gas jet flame admits of being employed. Pro-
cure a piece of wire gauze (of copper wire by preference), and
about six inches square. IJoJd this wire gauze horizontally
over the apex of tho flame, 'and gradually lower it to the base
of the same, as represented in the annexed diagram, fig. 11.

Fi*. 11.

If, in the preceding experiment, tho wire gauze be held at a
sufficient distance from the jet, and the resulting flame ex-
amined, it will be seen to yield a very diminished amount of
smoke ; indeed, if the wire gauze bo held exactly at the cor-
rect distance from the issue jet, a flame absolutely devoid of
smoke may resulr. See now how these principles are applied
to the construction of a mixed gas burner.

Commence by taking an iron or brass or copper tube, having
an internal diameter of about two inches, and a length of about
four.

Tightly whip, by means of wire, a sheet of wire gauze over
one end of the tube, as represented at a, and scollop the other
end as represented at b fig. 13. These directions being
followed, the student will have made a contrivance for using
the mixed gas flame.

Fig. 13.

By proceeding in this manner, tho flame will be seen unable
to extend through the wire gauze, that is to say, will be unable
to traverse tt and reappear at its upper surface. If a spirit-
lamp be employed, the extinguished gaseous contents Which
permeate the gauze will be invisible; if,however, a gas flame be
the subject of experiment, the volatile emanations will be seen
to be charged with smoke. Before proceeding to expatiate
upon these phenomena, I ought to remark that a common
candle 'will serve the purpose of a gas flame, though' on a
smaller, and therefore a less evident and less satisfactory
scale. Two important facts will have been learned by the
performance of the preceding experiments. The first is, that
coal gas contains the matter of smoke, although it may not
smoke on burning, and a spirit-ianip flame does not. The
second fact is,' that flame cannot, or rather cannot readily, pass
through small apertures.

Advancing now a step further, the operator may demonstrate
by means of a spirit-lamp, a gas jet, or a candle flame, that
although flame does not pass through wiro gauze, yet the
gaseous material, the mod of flame (thus to express one's self),
does. Consequently it admits of being ignited on the other or
upper side of the wire gauze and conversely, supposing a gas
jet employed (a spirit-lamp or candle will no longer aid our
illustration) — supposing, I say, a gas jet employed, and cuused to
pass through the wire gauze, that portion which traverses the
wire gauze may be burned on the upper surface of the latter,
without the transmission of flame through the wire gauze down
to the orifice of the jet, fig. 12.

Fir. 12.

The use of the scollops at the lower end of the tube b t is
for the double purpose of admitting free passage to the atmos-
pheric air and to the end of a gaS-pipe c, and the rationale of the
instrument will soon be rendered evident. Very slight consi-
deration of what has been said will show that the conditions
of the arrangement are such as to cause the admixture of gas
with atmospheric air ; which xnjxture ascending, must pass
through the wire gauze layer at «, and escape. Being there
ignited, we get a flame without smoke, because the material
burned is no longer gas, but a mixture of gas and atmospheric
air.

I have described this instrument in its simplest form, which,
if not better than, is at least as good as any other. Nothing so
simple can be procured in the shops of philosophic instrument
makers ; these gentlemen devoting much time and material to
the manufacture of an apparatus very pretty to look at cer-
tainly, but not better in practice than that just described. It
may here be remarked, that the tiv'o great points to bo attended
to in the use of this instrument, are (I) to apportion the
amount of gas to that of air, and (2) to promote accurate admix-
ture between thb two. The former condition is secured by the
very obvious means of a stop- cock, the second by well distri-
buting the issue of gas : to which latter end one of a few very
simple expedients will suffice.

Supposing the laboratory tube employed for conveying the
gas to be made of indh-rubbcr or gutta-percha, to one end of
it should be attached about a foot length of pewter or lead gas-
tubing, a material which admits of being readily bent or other-
wise manipulated. If such a terminal leaden pipe be made to
open without further preparation directly into the cylinder, it
is probable that perfect mixture of the gas and the air will not
result ; in which case the operator should proceed' as follows.

Taking a pair of pliers, let him tightly compress the
delivery end of the metallic tube as represented in a, or more
evidently in the section 6, fig. 14. In this manner it is evident the
gas will be delivered in a sort of fish-tail jet, and an admixture
sufficiently perfect will usually ensue. If not, little holes may
be bored through the sides of the tube, until the exact condi-
tion of perfect admixture is achieved. This may be known to
have occurcd when a piece of glass held in the flame is no

THE POPULAR KDUCATOK.

covered
1fcis~ seemingly
the dimensions
ft cobidoii iron

with imoke. Let not the reader undervalue
rude apparatus. The writer possesses one of
indicated, which boils four quarts of water in
kettle at the expiration of a few minutes.

Fig. U.

The discovery of the method of employing the mixed gas
has been a great boon to chemists, enabling them to accomplish
bv its means many results for which furnaces had been
hitherto required.

Although the flame produced by the method detailed is
powerful enough for the generality of purposes, its power

rig. 15.

admits of being further increased. A very usual way of
accomplishing this consists in superimposing a short chimney
on the wire cauzo top. This chimney affords convenient
bearing for little tiiangulur supports of platinum or iron wire,
and these in their turn can be used for tho support of crucibles,
retorts, 4c. In the last diagram, lig. 15, a crucible is repre-
sented thus exposed to the action ot tho flume.

Modification of this Flame Ay riatmised iWuW £7ojii». — Thq
metal platinum, in the state of minute divUion, has tho remark-
able property of causing the ignition of inflammable gases.
Taking advantage of this quality, 1 have used it with great
satisfaction for the purpose of adding power, of modifying and
imparting steadiness to the mixed gss flame.

To this end proceed as follows : Immerse small fragments
of pumice stone, about the sise of hasei nuts, and irregularly
angular, in a solution of chloride of platinum, and ignite the
pieces to redness. By this treatment the pumice stone will be
covered and imbued with'metullic platinum in the ttnest state
of division. If some pieces of this prepared pumice stone be
heated so as to expel all moisture, then laid upon the wire
gauxe platform, and mixed gas passed between, the pieces will
soon begin to glow like ignited iharcoal, and this state of glow-
ing will continue as long aa theses is mado to pass. Usually
• - gas does not burst into flame under these circumstances ;

indeed the result described only occurs when the gas is in
very small proportions as compared with the air; nevertheless,
the heat thus developed is very regular and gentle, and well
adapted for many chemical operations. If the amount of gas be
larger, the natural incandescence does not usually occur, but
if the inflammable mixture be ignited, the platinised stone will
increase the body and regularity of the flame. It may here be
well to remark, that instead of the iron-plate chimney just
described, one made by boring a hole in a large piece of pumice-
stone filed into the shape of a cylinder externally, is equally
good, if not preferable. The further consideration of coal-gas
as a source of heat, as well as the general principles of distilla-
tion, must be deferred until next week.

LESSONS IN READING AND ELOCUTION.— No. IV.
THE SEMICOLON.

33. The Semicolon Is formed by a period placed above a
comma.

34. When you come to a semicolon in reading, you must in
general make a pause twice as long as you would make at a
comma.

35. Sometimes you must use the falling inflection of the
voice when you come to a semicolon, and sometimes yon must
keep your Voice suspended, as directed in the case of the
comma. Whatever may be the length of the pause, let it be a
total testation of the voice.

Example*.

That God whom >ou »ee me daily worship ; whom I daily
call upon to bless both you and me, and all mankind ; whose
wondrous acts are recorded in those Scriptures which you
constantly read ; that God who created the heaven and "the
earth is your Father and Friend.

My son, as you have been used to look to me in all your
actions, and have been afraid to do anything unless you fir>t
knew my will ; so let it now be a rule of your life to 'look up
to God in all your actions.

If I have seen any perish for want of clothing, or any poor
without covering ; if his loins have not blessed me, and if he
were not warmed with the fleece of my sheep ; if I have lifted
up my hand against the fatherless, when I saw my help in the
gate ; then let mine arm fall from my shoulder blade, and mine
arm be broken from the bone.

The stranger did not lodge in the street ; but I opened my
doors to the traveller.

If my land cry against me, or the furrows thereof complain ;
if I have eaten the fruits thereof without money, or have
caused the owners thereof to lose their life ; let thistles grow
instead of wheat, and cockles instead of barley.

When the fair moon, refulgent lamp of night, o'er heaven's
clear axure spreads her sacred light ; when not a breath dis-
turbs the deep serene, and not a cloud o'ercasts the solemn
scene; around her throne the vivid planets roll, and stars
unnumbered gild the glowing pole; o'er the dark trees a
Yellower verdure shed, snd tip with silver every mountain's
head ; then shine the vales, the rocks in prospect rise, a flood
of glory bursts from all the skies ; the conscious swains, re-
joicing in the sight, eye the blue vault, and bless the useful
light.

When the battle wss ended, the stranger disappeared ; and
ne person knew whence he had come, nor whither he had
gone.

The relief was io timely, so sudden, so unexpected, and so
providential ; the appearance and the retreat of him who fur-
nished it were so unaccountable ; his person was so dignified
and commanding ; his resolution so superior, and his inter-
ference so decisive, that the inhabitants believed him to be an
angel, sent by heaven for their preservation.

36. Sometimes you must use the falling inflection of the
voice when you come to a semicolon, in reading.

LESSONS IN READING AND ELOCUTION.

369

Example $

Let your drets be sober, clean, and modest ; not to set off the
beauty of your person, but to declare the sobriety of your mind ;
that your outward garb may resemble the inward plainness
and simplicity of your heart.

In meat and drink, observe the rules of Christian temperance
and sobriety; consider your body only as the servant and
minister of your soul ; and only so nourish it, as it may best
perform an humble and obedient service.

Condescend to all the weaknesses and infirmities of your fel-
low-creatures ; cover their frailties ; love their excellences ; en-
rage their virtues ; relieve their wants ; rejoice in their pros-
perity ; compassionate their distress ; receive their friendship ;
overlook their unkindness ; forgive their malice ; be a servant
of servants ; and condescend to do the lowest offices for the
lowest of mankind.

Struck with the sight of so fine a tree, he hastened to his
own, hoping to find as large a crop upon it; but, to his great
surprise, he saw scarcely any thing, except branches, covered
with moss, and a few yellow leaves.

In sleep's serene oblivion laid, I've safely passed the silent
night ; again 1 see the breaking shade, again behold the morn-
ing light.

New-born, I bless the waking hour ; once more, with awe,
rejoice to be ; -my conscious soul resumes her power, and soars,
my guardian God, to thee.

That deeper shade shall break away ; that deeper sleep shall
leave mine eyes ; thy light shall give eternal day ; thy love,
the rapture of the skies.

In the sight of our law the African slave trader is a pirate
and a felon ; and in the sight of heaven, an offender far beyond
the ordinary depth of human guilt.

What hope of liberty is there remaining, if whatever is their
pleasure, it is lawful for them to do ; if what is lawful
for them to do, they are able to do ; if what they are
able to do, they dare do ; if what they dare do, they really
execute; and if what they execute, is in no way offensive to
you?

It is not the use of the innocent amusements of life which
is dangerous, but the abuse of them ; it is not when they are
occasionally, but when they are constantly pursued ; when the
love of amusement degenerates into a passion ; and when, from
being an occasional indulgence, it becomes an habitual desire.

The prevailing colour of the body of a tiger is a deep tawnv,
or orange yellow ; the face, throat, and lower part of the belly
are nearly white; and the whole is traversed by numerous
long black stripes.

The horse, next to the Hottentot, is the favourite prey of the
lion ; and the elephant and camel are ^oth highly relished ;
while the sheep, owing probably to its woolly fleece, is seldom
molested.

The horse is quick-sighted ; he ean see things in the night
which his rider cannot perceive ; but when it is too dark for
his sight, his sense of smelling is his guide.

37. The semicolon is sometimes used as a note of interrogation,
and sometimes as an exclamation.

Example*.

Hist thou not set at defiance my authority; violated the
public peace, and passed thy life in injuring the persons and
properties of thy fellow-subjects ?

Oh, it was impious ; it was unmanly ; it was poor and
pitiful !

Hive not you too gone about the earth like an evil genius ;
blasting the fair fruits of peace and industry; plundering,
ravaging, killing without law, without justice, merely to gratify
an insatiable lust for dominion r

Art thou not, fatal vision, sensible to feeling as to sight ?
Or art thou but a dagger of the mind ; a false creation, proceed-
ing from the heat-eppreased brain ?

By such apologies shall man insult his Creator ; and shall
he hope to flatter the ear of Omnipotence ? Think you that
such excuses will gain new importance in their ascent to the
Majesty on high ; and will you trust the interests of eternity
in the hands of these superficial advocates ? j

And shall not the Christian blush to repine ; the Christian,

from before whom the veil is removed ; to whose eyes are
revealed the glories of heaven ?

Why, for so many a year, has the poet and the philosopher
wandered amidst the fragments of Athens or of Rome ; and
paused, with strange and kindling feelings, amidst their
broken columns, their mouldering temples, their deserted
plains r It is because their day of glory is passed ; it is because
their name is obscured; their power is departed ; their influence
is lost !

Where are they who taught these stones to grieve ; where
are the hands that hewed them ; and the hearts that reared
them ? *fc»

Hope ye by these to avert oblivion's doom; in grief
ambitious, and in ashes vain ?

Can no support be offered ; can no source of confidence be
named.?

Is this the man that made the earth to tremble ; that thook
the kingdoms; that made the world like a desert; that de-
stroyed the cities ?

Falsely luxurious, will not man awake ; and, springing from
the bed of sloth, enjoy the cool, the fragrant, and the silent
hour, to meditation due, and sacred song?

But who shall speak before the king when he is troubled ;
and who shall boast of knowledge when he is distressed by
doubt ?

Who would in such a gloomy state remain longer than
nature craves ; when every muse and every blooming pleasure
wait without, to bless the wildly devious morning walk ?

What a glorious monument of human invention, that has
thus triumphed over wind and wave ; has brought the ends of
the earth in communion; has established an interchange of
blessings, pouring into the sterile regions of the north all the
luxuries of the south ; diffused the light of knowledge and
the charities of cultivated life; and has thus bound together
those scattered portions of the human race, between which
nature seems to have thrown an insurmountable barrier !

Who that bears a human bosom, hath not often felt, how
dear are all those ties which bind our race in gentleness
together ; and how sweet their force, let fortune's wayward
hand the while be kind or cruel ?

THE COLON.

38. The Colon is composed of two periods placed one above
the other.

39. Sometimes the passage ending with a colon is* to be read
with the voice suspended; but it should generally be read
with the falling inflection of the voice.

40. Tn reading, be careful to let the pause of the colon be a
total cessation of the voie^ and three times longer than that
indicated by a comma.

Examples,

The smile of gaiety is often assumed while the heart aches
within : though folly may laugh, guilt will sting.

There is no mortal truly wise and restless at the same time :
wisdom is the repose of the mind.

Nature felt her inability to extricate herself from the conse-
quences of guilt: the gospel reveals the plan of Divine inter-
position and aid.

Nature confessed some atonement to be necessary : the gos-
pel discovers that the atonement is made.

Law and order are forgotten : violence and rapine are abroad:
the golden cords of society are loosed.

The temples are profaned : the soldiers curse resounds in the
house of God : the marble pavement is trampled by iron hoofs :
horses neigh beside the altar.

Blue wreaths of smoke ascend through the trees, and betray
the half-hidden cottage : the eye contemplates well-thatched
ricks, and barns bursting with plenty : the peasant laughs at
the approach of winter.

The necessaries of life are few, and industry secures them
to every man : it is the elegancies of life that empty the purse:
the superfluities of fashion, the gratification of pride, and the
indulgence of luxury, make a man poor.

My dear children, I give you these trees : you see that they

370

THE POPULAR EDUCATOR.

are in good condition. They will thrive as much by your care
as they will decline by your negligence : their fruits will re-
ward you in proportion to your labour.

A bee among the flowers in spring U one of the most cheerful
objects that can be looked upon. Its lite appears to be all en-
joyment : so busy and so pleased : yet it is only a i pecimen of
iiihcci life, with which, by reason of the animal being half-
domesticatcd, we hnppc-n to be better acquainted.

'Tis a picture in memory distinctly defined, with the strong
and unperishing colours of mind : a part of my being beyond
my control, beheld on that cloud, and transcribed on my soul.

Yet such is the destiny of all 04 earth : so fiouxishes and
fades majestic man.

Let those deplore their doom whoso hopes still grovel in this
dark sojourn : but lofty soul*, who look beyond the tomb, can
smile at fate, and wonder why they mourn.

If for my faded brow thy hand prepare some future wreath,
let me the gift resign : transfer the rosy garland : let it bloom
around the temples of that friend beloved, on whose maternal
bosom, even now, I lay my aching head.

Do not flatter yourselves with the hope of perfect happiness :
there is no such thing in the world.

But when old age has on your temples shed her silver frost,
there's no returning sun : swift flies our summer, swift our
autumn's fled, when youth, and spring, and golden joys, are
gone.

A divine legislator, uttering his voice from heaven ; an al-
mighty governor, stretching forth his arm Jo punish or reward :
informing us of perpetual rest prepared hereafter for the
righteous, and of indignation and wrath awaiting the wicked :
these are the considerations which overawe the world, which
support integrity, and check guilt.

It is not only in the sacred fane that homage should be paid
to the Most High: there is a temple, one not made with hands,
the vaulted firmament : far in the woods, almost beyond the
sound of city-chime, at intervals heard through the brcezcicss
air.

Ah we perceive the shadow to have moved along the dial,
but did not perceive its moving ; and it appears that the grass
has grown, though nobody ever saw it grow : so the advances
we make in knowledge, as they consist of such minute steps,
are perceivable only by the distance gone over.

Thou shalt pronounce this parublo upon the king of Babylon;
and shalt say : How hath the oppressor ceased ?

THE I'AIIE^TIIHSIS, CROTCHETS, AND BRACKETS.

41. A Parenthesis is a sentence, or part of a sentence, en-
closed between two curved lines, thus ( )

42. The curved lines in which the parenthesis is enclosed
arc called Crotchets.

43. The parenthesis, with the crotchets which enclose it, is
generally inserted between the words of another sentence, and
may he omitted without injuring the sense.

41. The parenthesis should generally be read in a quicker!
and lower tone of voice than the other parts of the sentence in
which it stands.

•15. Sometimes a sentence is enclosed in marks like these [ ],
which are called Brackets.

4(5. Sentences which are included within crotchets or brac-
kets, should generally be read in a quicker and lower tone of
voice.

47. Although tlio crotchet and the bracket are sometimes
indiscriminately used, the following difference in their use may
be noticed :— Crotchets arc used to enclose a sentence, or part
of a sentence, which is inserted between the part* of another sen-
tence : brackets arc generally used to separate two subjects, or
to enclose an explanation, note, or observation, standing by
itself. When a parenthesis occurs within another parenthesis,
brackets enclose the former, and crotchets enclose the latter.

Examples.

I asked my eldest son (a boy who never was guilty of a false-
hood) to give me a correct account of the matter.

The master told me that the lesson (which was a very diffi-
cult one) was recited correctly by every pupil in the class.

When they were both turned of forty (an age in which,
according to Mr. Cowley, there is no dallying with life), they

determined to retire, and piss the remainder of their days in
the country.

Notwithstanding all this care of Cicero, history informs us,
that Marcus proved a mere blockhead ; and that nature (who,
it seems, was even with the son for her prodigality to 1 the
father) rendered him incapable' of Improving, by all the rules;
of eloquence, the precepts of philosophy, his own endeavours;
and the most refined conversation in Athens.

Natural liistoriaris observe (for whilst I am in the country I
must fetch my allusions from thence) that only the male birds
have voices ; that their songs begin a little before breeding-
time, and end a little after.

Dr. Clark has observed, that Qomer is more perspicuous
than any other author ; but if he is so (which yet may be
questioned), \\ie perspicuity arises from his subject, and no}
from the language itself in which he writes.

The many letters which come to mefrom persons of the best
sense of both, sexes (C*r I may pronounce' their characters from
their way of writing) do not a little encourage me in the pro-
secution of this my undertaking.

It is this sense which furnishes the imagination with its
idea* ; so that by the pleasures of the imagination, or fancy
(terms which I shall use promiscuously), 1 here mean such as
arise from visible objects.

'Hie stomach (crammed from every dish, a tomb of boiled
and roast, and flesh and fish, where bile, and wind, and phlegm,
and add, jar, and all the man is one intestine war) remembers
oil the school-boy's simple fare,' the temperate sleep*, and
spirits light as air.

' William Fenn was distinguished from his companions by
wearing a blue sash of silk network (which, it seems, is still
preserved by Mr. Rett, of Seething-hall, near Norwich), and by
naving in his Jmnd a roll of parchment, on which was engrossed
the confirmation of the treaty of purchase 'and amity.

Again, would your worship a moment suppose (it is a case
that has happened, and may be again), that the visage or coun-
tenance had not a nose, pray who would, or who could, wear
spectacles then ?

Upon this the dial-plate (if we may credit the fable) changed
countenance with alarm.

To speak of nothing else, the arrival of the English in her
father's dominions must have appeared (as indeed it turned out
to be) a most portentous phenomenon.

Surely, jn this age of invention, something may be struck
out to obviate the necessity (if such necessity exists; of so task-
ing the human intellect.

I compassionate the unfortunates now (at this very moment,
perhaps) screwed up perpendicularly in the scat of torture,
having in the right hand a fresh-nibbed patent pen, dipped ever
and anon into the ink-bottle, as if to hook up ideas, and under
the outspread palm of the left hand a fair sheet of best Bath
post (ready to receive thoughts yet unhatched); on which their
eyes are ri vetted with a stare of disconsolate perplexity, infi-
nitely touching to a feeling mind.

O the unspeakable relief (could such a machine be invented)
of having only to grind an answer to one of one's dear five
hundred friends !

Have I not groaned under similar horrors, from the hour
when I was first shut up (under lock and key, I believe) to in-
dite a dutiful epistle to an honoured aunt ?

To such unhappy persons, then, I would fain offer a few
hints (the fruit of long experience) which may prove service-
able in t)ie hour of emergency.

If ever you should come to Modena (where, among other
relics, you may seeTassoni's bucket), stop at a palace near the
Ileggio gate, dwelt in of old by one of the Donati.

My father and my uncle Toby (clever soul) were sitting by
the tire with Dr. Slop ; and Corporal Trim (a brave and honest
fellow) was reading a sermon to them. — As the sermon contains
many parentheses, and affords an opportunity also' of showing
you a sentence in brackets (you will observe that all the pre-
vious parentheses in this lesion are enclosed 'in crotchets), I
shall insert some parts of it in the following numbers.

To have the fear of God before our eyes, and in our mutual
dealings with each other, to govern our actions by the eternal
measures of right and wrong : the first of these will compre-
hend the duties of religion ; the second those of morality,
which are so inseparably connected together, that you cannot

LESSONS IN GERMAN.

371

divide these two tables, even in imagination (phough the au
tempt is often made in practice), without breaking and mutu-
ally destroying them both. [Here my father observed that
Dr. Slop was fust asleep]. I said the attempt is often made
and so it is ; there being nothing more common than to see a
man who has no sense at all of religion, and, indeed, has so
much henesty as to pretend to none, who would take it as tht
bitterest nffront, should you but hint at a suspicion of hi»
moral character, cr imagine he was not conscientiously jusl
and scrupulous to the uttermost mite.

I know the banker t deal with,' or the physician I usually
call in [There is no need, cried Dr. Slop (vak|ng) tq call in any
physician in this case], to bo neither of thejn njen oT'ihuca
religion.

Experienced schoolmasters may quickly make a grammar of
boys' natures, and reduce them all (saving pome few excep-
tions) to certain general rules."

Ingenious boys, who are idle, think, with the hare in the
fable, that, running with snails (so they count the rest of their
school-fellows), they shall corao soon enough to }ho post J
though sleeping a good while before their starting."

LESSONS IN GERMAN.— No. LXXXVI.
S 140. Rule.

The Infinitive mood either with or without the particle ju (to)
preceding, is used to represent the being, action or passion, \a
a manner unlimited : as,
etcrfcen tjl 9ti<$», tcc$ ftfccu tint nia)t fetyen, U$ ifl tin Unolncf, to di<
is nothing, yet to live and not to see, that is a misfortune
indeed.
Ttx 3Bmifc$ aele$t ju tocrten, the wish to be praised.

Observations.

(1) The Infinitive without ju. (to) appears,

a. When, as a v. rbal substantive (§ 146, 3.), it is made cither
the subject or the object of a verb : as, ficben ij* felt^cr all
Wctymen, to give is more blessed than to receive.: US aenni cr at
tcrtcn, that he calls working.

a. When it stands alone, as in a dictionary: as, Itfen, to
praise ; "Urictt, to love,

c. After the verbs
firijicn, to bid : as, i$ (n'cji ifm ackn, I bad him go.
iclfca, to help : as, cr I;iljt mil fifyrcitch, he helps me to write.
Icijrcn, to teach: as, cr Ufnt t«s3 SL\:\t Icfcii, he teaches the

child to read
I:rnc;», to learn : as, n>ir lerncn tanjen, we learn to dance.
Ijoren, to hear : as, id? Knc ftc flaxen, } hear fheni sing,

fetyen, to sec : as, \$ fc&e if;n fwiuicr., I see him come,

fufilcit, to feel : as, i$ fiij)le ten %v.U fa h$cn, I feel hi? pulse

fl:itcn, to fmd : as. i.f; fanfc ta« Shicty auf rem Sijtyc liqcji, |
found the book lying on the table.

The verbs Ichon and Icrncii form exceptions to the observation
in the text : admitting, as tbey do sometimes, the particle ju
between them and an Infinitive succeeding. The student will
note, also, that the Infinitive after all these verbs, is, jn English,
often best rendered by a participle : as, cr fw£Uc fcia Slut g&frcn,
he felt his blood boiling.

d. After the auxiliaries of mood, mfa.cn, feuncn, hffen, burfen,
follcu, nuftcn and mujfcn, and after irtrten, when employed as an
auxiliary in forming the future tense.

e. After the verbs following, in certain phrases,

blci&cn, to remain : as, cr elcttt ft$en, he continues

sitting,
fafcicn, to go in a carriage : as, id) fafre fiujicrcn, I ride out

for an airing,
fltfccn, to go or walk ; a«, cr ge^t bcttcln, he goes begging.

fpbtii, to have : as, cr M gut rctcn, be has easy

talking, i. g. it is easy for
him to talk.
Iffcn, to lay : as, ic$ lege mi$ f$(afcit, I lay my-

sell down to sleep. [

maa)cn,

to make :

nennen,

rcitcn,
tfiun,

to name :
to ride :
to do:

as, cr •mactyte mi$ fao)en, he made

me laugh.

as, id) fann \h\ ncnucn, I can name

him.

as, i$ rettc fpajicrfn, I ride out for

exercise.

as, er t§ut nic$t$ aft fd)cltcn, he

docs nothing but scold.

SiA^rrij however, cannot, as in English, be used to signify to

make or cause l*j forte: thus, to translate; the English phrase,

male Htm tjo cuf, tie German i say* laf "(pot'marje) tt)n IjincntSgcf ch.

Tlu* Infinitive without m cornea after 'tfjjn, pnlv when nicjjti aft

precedes, In the example above*

(2) The Infinitive with j« is employed:
a. Artcr'nouha and adjectives which, in English, are followed
elttjer by the preposition to with the Infinitive, or by of with a
participle: as, iej \$ix fivj ij« jti fcluit H I was glad to see him ; £tc
friifen Buft jb fvlcfen'p you have a desire to plaj"; ie$ (itt mute t$ £U
J&fcn, I am tired of hearing it';

(5) After verba, to express the end or object of their action :
aa, irfj l;nvut nijt 3£iwu ju u \rf;m, T come to (ii c. in order to)
apeak with you ; in which cbsc, u\so, the particle urn bftcn comes
before $u, to render the expression more forcible: as, licBc't tie
"tujfnr, urn ^imllift! in fchi, love virtue, in order (um) to be happy,
c. After (Jie verbs followjpg and others of like impoft :

fHnfanjcn, to begin. Sdacrn, to delay.

33cfc^(cn, to command. ^tenen, to serve.

$ittcn, to beg. <&inrci$cn, to suffice,

(irmartcn, to expect. 2$ a men, to warn.

£offcn, to hope. SBcigcrn, to refuge.

&urc$tcn, to fear. Qrfcnncn, to acknowledge. ,

2)rc^cn, to threaten. iBcfcnncn, to confess.

SicJ frcucn, to rejoice. Gcjcineh) to appear/

@tc^ fc^flmen, to be ashamed. SSunfcr)cn, to wish.'

iBcrcucn, to regret. (Stfaufcn, to permit,

oVrtf.iprcn, to proceed. Scrltcncn, to deserve,

ftntcrlaffch, to neglect. SBagcn/to venture.

| iafcen, Ipohave. "' 4 SBijfciu to know.

£«n, to dc." * Stu^cfi, to be of use.

Grfciuun and fcefenaen are construed mainly with the preterit of
the Infinitive : as, cr crfcunt, fi$ gctrrt ju \)aU\\, he acknowledges
tfiat he has been in prror.

i. After tlie prepositiops efcic (without) and (tatt or anflatt (m.
stead of), as, crjnc cin Sport iu fagen, without saying a word ; an*
flatt ju fct)rci6cn, instead of wrjfiug.

(3) The tufinitlve in German, as intimated before, often
performs the office of a verbal substantive. It is then com-
monly preceded by the neuter of the article, and has all the
various cases : as, tq* Sugcn tyatrt tern Sugncr am mciftnt, lying
injures the liar most; id; bin U4 <5Jc^cn« mtitc, I am weary
of walking; jum Kcifcn tujl tu nia)t acf$icfr, you are not fit for
journeying.

(•1) The Infinitive active, in German, after certain verbs, as,

, fcin, lajfen, wrfcictcn, {»cfc|j(cn, &c., is not unfrcquently employed

I passively : thus, lap tyn rufen, which (literally) means, let him

I pall, may, also, signify, let him }e called; t\ ifl fcinc 3eit ju vcrlic*

ccn, t jiere is no time to lQse, pr to be lost.

(5) *flie Germans often employ the Indicative or Subjunctive,
preceded by tap, where, in English, the Infinitive, preceded by
to, is used : as, ity tt?ci&, tap cr tcr Q?2ann ifl, I know him to be
(litcrallv, I know that he is) the man.

(6) Tlie Infinitive, in English, preceded by the words how,
iphere, wkat, when, and the like, after such verbs a% tell, know,

ay, and teach, cannot be rendered literally into German : the
j er in an s, in such coses, always using the Indicative or Subjunc-

five of such verbs as fdtcn, mujfcn, fonncn : as, i$ ujcif, ttic \6f cl

tyun mufi, I know how to do it, or (literally) I know how I roust
lo it ; Ic^rcn ®ic inicfc, xoM i*^ fagcit foil, teach me what to say.

For the use of the Infinitive of mtyn, rwttcii, fcNcn, &c. f in place

Of the past Participle, See § 74. 3.

37*

THE POPULAR EDUCATOR.

S 147 THE PARTICIPLES.

(1) The Participles, in German, are varied by cases, follow-
ing the tame rules of inflection as the adjectives. Having the
nature of adjectives, the Present in a few, and the Preterit in
many instances, readily admit the degrees of comparison.

(2) The use of the Participle, as such, however, in German,
is far more restricted than in Eoglish. For, in English, it is
commonly used to form a distinct clause of a sentence ; and is
thus made to indicate the time, cause, or meant of effecting
that which is expressed in the main clause: thus, we say:
Walking (that is, by or when walking) uprightly, we walk surely.
This mode of expression can rarely, if ever, be adopted in
German; into which language, if we desire to translate the
above sentence, we must say : toenn wit aafrie^ttg icantctn, fo nun
tew mix ftycr, that is, when we walk uprightly, we walk surely.

(3) So, too, we say in English : Having given him the money,
he went away; but since there is nothing in German to cor-
respond to this English compound Participle, it would be a
gross error to attempt to render the sentence literally Resort
must be had, as in the other case, to a different structure :
thus, all ft i$m taf GMt gegeben $atte, ging er ireg, that is, after or
when he had given him the money, he went away. In this way
must all similar cases be managed : wc must employ a verb in I
each clause, and connect the two together by means of suitable |
conjunctions ; such as, nxi(, roenn, all, ta and intern.

S 148. Rule.

The Present Participle, like an attributive adjective, agrees
with its noun in gender, number, and case; and may, also,
govern the same case as the verb whence it is derived : as,

Set la$cnfcc grilling, the smiling spring.

Jtttylentel (ftetranfc, cooling drink.

Sic add bctefentc Sonne, the all animating sun, i. e. the sun
that animates all.

Observations

fl) This Participle is seldom, if ever, otherwise employed
witn a noun than in an attributive sense. Its predicative use is
found almost altogether in those words that have so far lost
character as Participles as to be commonly recognised only as
adjectives : as,

Steijent, charming. Drutfcnt, oppressive.

Jtranfent, mortifying. Slicfcnt, flowing.

Ginncfrmcnt, captivating. Ginreipfnt, overpowering.

IDringcnt, pressing.

Such a combination, therefore, as, / am reading, we are
walking, and the like, which is so common in English, is wholly
inadmissible in German ; save in the instance of tho*c Parti-
ciples that have lost, as just said, their true participial character:
as, tic Slot!) til fctingent, the necessity is pressing.

(2) The Present Participle, in connection with the article, is
often used substantively, the noun being understood ; as tcr
8efcnre, the reader, (literally) the (one) reading; tic Stcrfrcntc,
the dying (female).

(3) This Participle, however, cannot in German, as in Eng-
lish, be, by means of an article, turned into an abstract verbal
noun. But in order properly to render such phrases as, the \
reading, the writing, into German, we must use the present of
the Infinitive : thus, taf Scftn, feat §cfyrcibtn.

(4) The Present Participle, as stated in the Role, may govern
the case of its own verb ; but it must be noted that the word so
governed always precedes the Participle : tool unf vcrfelgente GJc
fcfctrf, the us pursuing fate, i. e. the fate that pursues us. In
some instances, the words actually united, forming compounds:!
as, c$r(ie6cnfc, honour-loving, that is, ambitious ; gefetgebenfe, law-
giving, &c.

(5) The Present Participle is sometimes u*od with the power
of an Adverb ; that is, to express some circumstance of manner
or condition: thus, lvcincn* fpradj cr ju mir, weeping (i. e. wee-
pixyly) he spoke to me; cr fc&tc fcc$ frfjrceigcnfc meter, keeping silent
(i. e. silently) he sat down.

§ 119. Rule.
Thft Preterit Participle is not only used in the formation of

the compound tenses, but may, also, be construed with nouns,
after the manner of Adjectives: as,

3$ babe tatte taf 9n<$ gelc'cn, I have read the book to-day.

<fia ocltcfctef Slim, a be tared child.

iter Tlatm ft grlrirt, the man is learned.

Obseevations.

(1) This Participle; in its character as an Adjective, is far
more frequently employed in German than in English. Indeed,
many Preterites in German, havin? lost all character as Parti-
ciples, are now used exclusively as Adjectives.

(2) The Preterit, like the Present Participle, is sometimes
used in an adverbial manner : thus, ta! iBue$ ift tcrlcrcn aegacacn,
the book is lost (literally, gone, lost).

(3) This is especially the case with certain Participles em-
ployed with the verb fommen; as, cr femmt gefa^ren, he comes
driven, i. e. driving in a carriage ; cr frmmt ocrittrn, he comes
ridden, i. e. riding on horseback ; cr fimmt geflegcn, he comes
flying ; crfdmntt ocloufcn, he comes running, &c.

(4) Kindred to this, is its use, when connected with a verb,
to express the condition or state of the subject : as. jefct fieri' td>
teruhigt. now I die content ; in fcinc Sujtnt grfuflt, treat cr tcr $rt>
(eumtnng, wrapped in his virtue, he defies calumny.

(5) The Preterit Participle, usually in connection with the
accusative, is iu some phrases employed absolutely: as, tic
nugen gen <$immel gcri4»tct. his eyes being directed towards heaven ;
ten (Stomnn a*gercc$net the profit being deducted ; tiefrn gall auf •
aenemmen, this case being excepted.

(6) This Participle is sometimes elliptically used for the Im-
perative. (See $ 145. 3.)

S 150. Rule.

The Future Participle is used, when tne subject is to be re-
presented as a thing that must or ought to take place : as,
dine )u lofrenre Ibzt, a deed to be (i. e. that ought to be) praised.

Observations.

(1) What is called the Future Participle in German* is pro-
duced by placing ju before the present participle as above. It
can be formed from transitive verbs only, and is always to be '
taken in a passive sense. It is chiefly to be found in the case
of compound verbs: thus, $o$}uefcrcnter -Scrr, the-highly-to-be
honoured, i. e. the honourable, Sir. See Section XLII.

§ 151. THE ADVERBS.
Rule.

Adverbs qualify verbs, participles, adjectives and other ad-
verbs : as,

6r fareibt fdten, he writes seldom.

<5r $at ten ©egcnftanb vortrefflicft befcanteft, he has treated the sub-
ject admirably.
Xicfel $uc$ ift: fctyr gut, this book is very good.
(Jr arfrcitet ni$t gem, he works unwillingly.

Observations.

Almost all adjectives in the absolute form are, in German,
employed as Adverbs. See § 102. 3. For remarks on the
position of Adverbs in sentences, see the section on the arrange-
ment of words, $ 158.

S 152. THE PREPOSITIONS.

Rule.

The Prepositions aajiatt, aupcr$al6, tiejfktS, <fcc. (See the List
f 109.) are construed with the genitive.

Observations.

(1) Wheu the same Preposition governs several nouns in the
same construction, it is put before the first only ; as, i<$ (in ten
nictner $ttmatft, tnetnem SSaterlante unt meinen ffrennten gttrcnnt, from
my home, my country, and my friends, am I separated.

(2) For the right use and position of some of the Preposi-
tions, much attention is required. See the Observations on
those construed with the genitive: $ 110.

FRENCH READINGS.

373

§ 153. Rule.

The Prepositions auf, aufer, &i, &c. (See List § 111.) are con-
strued with the dative. (See Obs. § 1 12.)

§ 154. Rule.

The Prepositions bur<$, fur, gcjcn, &c. (See List § 113) are
construed with the accusative. (See Obs § 114.)

§ 155. Rule.
The Preposition! an, auf, gutter, &c. (See List § 115) govern
the dative or accusative : the accusative, when motion or ten-
dency toioard* ')% signified, but in the other situations the dative.
(See Obs. §116.)

S 15G. THE CONJUNCTIONS.
Rule.

Conjunctions connects words and sentences in construction,
and show their mutual relation and dependence ; as,
3o$ann unb SBityetm ge$en jur G$uTr, John and William are

going to school
3$ fa$ ti ; ba$er toeif t$ tS, I saw it ; therefore I know it.
dx if* altar all \a), he is older than I.

Observations.

(1) Under the general name of Conjunctions in this Rule,
must be included all words performing the office of Conjunc-
tions, whether properly such or not Of these connective
words three classes are to be distinguished : 1. those that do not
affect the order of the words of a sentence in which they occur
(§ 160. 8.) ; 2. those that always remove the copula to the end
of the sentence (§ 160. 7.) ; 3. and finally, those that do or do
not remove the copula to the end, according as they stand be-
fore or after the subject ($ 160. 8.).

(2) The true force and use of the Conjunctions is best learned
from examples; of which see a large collection in Section C.
We subjoin, however, a few remarks in explanation of the
following:

a. 9l&er, atlctn, funbern. 216ft is less adversative than either of
the others. It is often merely continuative. 2lfl«u always in-
troduces what is contrary to what might be inferred from
what precedes : as, er ifl feljr fJetpig, aflcin ft font fe$r toenig, he is
very industrious, but he learns very little, ®onbern serves to in-
troduce what is contradictory. It is used only when a negative
precedes ; n\a)t fbft, fonbern flrinmuttyig, not noble, but pusillani-
mous; el ifl merer ftytvari noa) braun, fonbern grun, it is neither
black nor brown, but green.

b. &a$, also auf baf, introduces a clause expressing the end,
object or result; as, ty toeif, baf ft fommt, I know that he is
coming. This form of expression is more common in German
than in English. When bap is left out, the copula comes im-
mediately after the subject.

c. S><4 introduces something unexpected' or not properly pro-
ceeding from the antecedent : as, ct ifl feljr rei<$, unb $at too) toeni<j
gearbeitci, he is very rich, yet has he worked little. It is some-
times elliptically employed to indicate certainty, entreaty, and
the like : as, fagen ©if mtr bod), tell me, pray.

d. 3c, like the definite article in English, is put before com-
paratives to denote proportion. It, then, has bfflo for its cor-
relative : thus, je ftaptger ct ifl, bfflo gele$rter toirb er, the more dili-
gent he is, the more learned he becomes. JDeflo sometimes
comes before if : as, fin Jtunftotr! ifl befto fi»Jner, j[e wflfommener el
ifl, a work of art is the more beautiful, the more perfect it is.
Sometimes if is employed before both comparatives : thus, je
mtyr, if befler, the more, the better. Sometimes befto stands be-
fore a comparative without if answering to it : as, id) ertoortete
ntyt meincn grtunb ju finben, befto proper aber mar metne 9rcube, aU ty
u)n fa$, I did not expect to find my friend, but the greater was
my joy when I saw him.

e. Obotacb, »bf<$on, obtoo^l, indicate concession. The parts are
often separated, especially by monosyllables : such as, \a), ba, rr,

'cf, »er, ibr, fte Often two or three such little words come be-
tween : as, e& er glricb alt ifl, *., although he is old, &c. j tt to
mty tfety ftcite, k. t although I rejoice, &c

f. Go, after such conjunctions as, totif, at*, ba, toenn, naa)ttm
obg(ei<^ obtyott, obtt>o$l, n>ennglei<$ and toie»o$l, introduces the sub-
sequent clause. This is chiefly the case, when the antecedent
clause is long, or consists of several members : Ex. 9Bci( bi$
<&ott bie« and getixibr toerben lief, fo ifl flttemanb fo toeife al« bu. since
God hath given thee to know all this, so (therefore) is no one
so wise as thou. @o commonly, however, denotes comparison :
as, bee *nabe ifl fo gut, at* bas 2Ra<$en, the boy is so (as) good as
the girl. So in the phrases, fotoo$l all au$, or fo»o$l att, to (as)
well as: fobatb all, so (as) soon as, &c. With ana) (fo— «u<$) fol-
lowing, it signifies however: as, fogwji bie GfyttdtnU* «ticgf« au$,
ic , however great the terrors of war, &c. ; fo xtxa) et aud> ifl, w.
however rich he is, &c.

g. The following are the more common correlatives • as,

Gnti»eter # either, ober, or.

SSBeber, neither, vaa), nor.

SBenn, if, fo, so, or then.

5>a, when fo, then.

3e, the, je, * the.

3e, the, befto, the.

@obalb, as soon, all, as.

@0»cM, as well, all, as.

2Bie, as, fo, so.

(go, so, fo, so.

Sltyt, not, fonbern, but.

9l\a)t aOein, not only, fonbern, but.

9tic$t nur, not only, fonbern ana), but also.

$ 157. THE INTERJECTIONS.

Rule.

Interjections have no dependent construction.

Observations.
(1) Interjections stand generally before the nominative or the
vocative; as, O! tyuerfier Stater! But sometimes the genitive,
and sometimes the dative, is preceded by an Interjection : as,
O, be r Breube '. O the joy ! SBe$ mit ! Woe to me !

FRENCH READINGS.—No. V.
M"* DE LAJOLAIS.
Section II.

A ces cris, a cette action imprSvue, l'Empereur stardte
en froncant les soureils. 1

— Encoro ! . . . . s'ecrie-t-il d'un ton d'impatience, j'avais
pourtant dit que je ne voulais plus de ces scenes-la ! *

Et croisant ses bras snr sa poitrine, il voulut passer
outre.*

— Sire ! cria la jeune fille, a laquello la position de son
pere donnait une Anergic au-dessus de son age, je you* en
conjure, ^coutez-moi ! 3 . . . . au nom de votre mdre, sire,
6coutez-moi ! au nom de votre p£re, accordcz-moi la grace
du mien ! . . . . C'cst mon pere, sire ; il aura b §te entratne,
seduit ,• pardonnez-lui ! .... Oh ! sire, vous tenez la vie de

mon pere, la mienne dans vous mains Ayez pitied

d'une malheureuse enfant qui vous demando la vie de son
pere Sire ! sire ! grace pitie pardon.

— Laissez-moi, Mademoiselle, dit l'Empereur, la repous-
sant assez c rudement. 4

Mais, sans se laisser intimider, (il y allait d d'une exis-
tence trop ohere), 5 M"e do Lajolais, se trainant sur les
dalles" de marbre de la galerie, criait avee angoisse :

— Oh ! pitie;, pitie, sire ! . . . . grace ! . . . . pour mon pere !
Oh ! jetez au moins un regard sur moi, sire ! '

II y avait f quelque chose de si dechirant' dans cctte voix
d'enfant demandant la vie de son pdrc, que l'Empereur
s'arre'ta malgTe lui, et regarda cellc qui fimplorait avec
tant h d'instance. 7

MU« de Lajolais etait fort bien, mais, dans ce moment, sa
beaute tenait 1 de 1'ange. Blanche comme un cygne, la

374

THE POPULAtt EDUCATOR.

douleur donnait a scs traits un caracte're encrgiqne et pas*
sionn6; 9 scs beaux chevoux blonds ruissolaient J sur set
epaulcs; scs pttitos mains, crispfces par la fievre, avaicnt
fini par k saisir unc des mains clc rLmpcreur," et lui com*

muuiquaient leur chalcur brulante Ajrenouillee, le

visage baigne dc larmes, levant scs grands yciix bleus vera
celui duquel ellc scmblait attendre la vie ou la mort, 10 clle
no pouvait plus ni parler, ni pleurer, ni respirer.

— N'etes-vous pns M''c de Lajolais? 11 lui dunanda TEm-
pereur.

Sans repondrc, Maria prcssa la main de TEmpcrem- avee
plus de force. 1J

II repi it 1 avee sevcrito : Savez-vous que e'est la seconds
fois que votre pere se rend eoupablc d'un crime clivers
l'Ktat, Mademoiselle?^

— Jc le sais ! - lvpondit M lle de Lajolais, avec la plus
grandc ingenuitC ; mais la premiere ibis il etait innocent,
sire. 14

— Mais, ccttc fois, il nc Tcot n pas, repliqua Bonaparte.'* 3

— Aussi e'est sa grace que jc vous demande, sire, reprit
Maria, grace .... ou jc mourrai devant vous.

L'i'mpercur, ne pouvaut plus mai t riser lfJ son emotion, sc
baissa vers ellc en lui disant :

~-Kk ! l)icn, oui, Mademoiselle, oui je vous l'aecordc.
Mais, rclevoz-vous. 17

innumerable scientific truths for the benefit and to the asto-
nishment of man ; and in the midst of our wonder, we are
forced to acknowledge and admire the omnipotence of study
in exploring the secret bosom of Nature, and snatching there- ^
from the hidden treasures she would willingly conceal; but in^
the child, Zarah Colburn, we find the young and powerful
mental giant, with amazing alacrity, performing his incredible
feats of intellectual gymnastics over the rugged play-ground
of mathematical calculation.

Zarah Colburn, the subject of the present short memoir, was
an American boy belonging to the state of Vermont; according
to our authority he was born in 1807. When only six years
of age, his knowledge of arithmetic began to be discovered, his
father having, to his astonishment, accidentally heard him tell
| the product of two numbers ; and on asking him the multi-
plication table, and a scries of similar questions in the rule of
multiplication, he found that the little prodigy answered them
all with the greatest possible ease.

In November, 1813, this astonishing youth, accompanied by
his father, happened, to be in Newry for a few fyours, on his
way from Dublin to Belfast, whence he intended to proceed to
Glasgow College. During his short stay in Newry. he had
scarcely time to take his hurried refreshment ; for the people
of that intelligent town were too eager to see and to hear tne
young philosopher, of whom they had previously heard bo
much. Here, many intricate questions were proposed to him,
and, as if by instinct, he solved them all with the greatest

Eti lui jetant un sourirc d'encouragement et de bonte, il rapidity and accuracy ; and " all by the mere operation of the
degagcaP scs mains tcmicsi toujour* avec force " et sY-loigna m . ind » without the assistance of any visible symbol or con-
vive men t.

CoixoQriAL ExrncisE.

1. Que fit i'Kmpereurenenten-
dant ces eris ?

2. Quo dit-il d'un ton d'impa-
tiencc ?

3. Quelle* paroles cncrgupies la
jnine fillcadnssa-t-cllc a Uo«
r.aparlt 1 ?

4. Qik» (lit rKiiinereur et que
fit-il?

5. Pourquoi W-** clefcuVlru.* ne
pc laissa-t-olle pas ini hinder?

C. Qu'ajouta-K-lle on :-s trai-
nant sur les dalles de inarbrc?

7. Que fit alors lTinpcrcur?

8. Quel earnetevo la douleur
donnait-cllc aux traits dc
Maria P

9. Ou ctaicut les mains do
renfant?'

10. Que faisait-clle aux pieib dc
Napoleon ?

11. Que lui dVinanua-t-il alow?
12 Quelle repon«c lui fit

Maria ?
13. Que lui (lit Xapnlt'un, rela- 1

tivcmenl a son pore?
1 1. Que ri'p^.ndit-elle ?
15. Que rvpliqua l?onapartt>?
IG. L'Kmpeivur eeinblait • il

c*mu ?

17. Que dit-il?

18. Quj fit-il avant de s'cloi-
gncr?

Notes AND Re?E»je;:ces.— a. passer outre, to yo on, to pro-
ceed. — b. aura, has without doubt, probably ; the future tense, in
French, is often used to express probability.— -c. assez rudement,
frith some abruptness.— d. il y allait, etc., so precious a life was in
danger, at stake.— e. dalles, floor; literally, flat stones.— f. L.
part ii., § 61-2. — g. duchirant, Jiearl-rending . — h. avec lantd'in-
stance, to earnestly.— i. tenait, resembled Viat.—j. L. part ii., §
49. R. (d-). — 1\ fini par, mechanically, unconsciously ; literally, at
last. — I. from rcprendre ; L. part ii., p. 100.— m. from savoir ;
L. part ii , p. 101. — n. P, so. — o. from mourir ; L. part ii., p. 96.
— p. L. part ii., § 49, K. (1).— q. tenuos, held; from tenir ; L.
j>art ii., p. 108.

BIOGRAPH Y.— No. XIII.
ZARAU COLBURN.

When Nature, ai if to show her own dignity, bestows on a
mere child, extraordinary mental powers, exceeding in magni-
tude what experience and the most wonderful development
can scarcely approach, our pride is so completely humbled,
that the pleasure we feel in contemplating the sublime pheno-
menon is almost lost in the disappointment we meet in being
unable to reach its superlative grandeur.

In men such as Newton and La Place, wo find genius, by
the force of culture and indefatigable application, calling forth

trivance." Zarah Colburn, be it remembered, never made
use of pen or pencil in solving the most difficult problems, no
matter how long or how abstiuse the process might be that
was required. I have been often told that an humble house
in Water-street, Newry, was for many years afterwards
pointed out to the inquisitive tourist as the place where " tks
:alculatitig bog'* once stopped.

In hi« progress on his journey, before Zarah Colburn reached
Belfast, his extraordinary intellectual capacity was a favourite
topic; and many a juvenile arithmetician was ransacking hit
y wn brains in order that he might find " a few puzzlers, aa
questions, to propose to the much tall^ed-of youth.

Z «rah, shortly after his arrival in Belfast, was, on the 16th
of November, 1813, introduced to a meeting of the members
Of the Royal Academical Institution ; and the young readers
Of the PoruLAii Kbucatob may rest assured that his capa-
bilities were sufficiently tested under a high standard by those
literary gentlemen, and that to a degree that raised wonder
imd delight to their very climax.

Here the amazing •* calculating boy," oF only nine years of
ige, stood to be questioned ; and here it. was that he called
forth such a strength of .intellectual energy as to be almost
without a parallel in history^. He was fiist asked the product
of 365 and 13, and his answer, on the moment, was simply
#,715. But it was soon seen that such questions as this were
too easy for such a pet of Nature's choosing. He was next told
to extract the cube root of 307,546,875, and with the greatest
readiness he answered (675. Other questions of a similar
nature were proposed, and their solutions were effected by
him with the same readiness and accuracy. A writer in one
fcf the journals of the day says, •' in short, there appeared to
be no limits to the powers of his mind in calculation."

^.fter exhibiting such rare proficiency at the Institution, and
before such a learned body, tho result of his examination
naturally spread through all parts of the town, to garret,
cellar, and drawing-room alike, as if carried on the wings of
electric agency *, so that crowds of the literati thronged to the
joffec-room of the inn where he resided for the time, in order
to Jirove by their own experience what the most flexible ere*
iiility could scarcely believe.

Of the complex nature of the numerous question's proposed
to Zarah at this exhibition, our readers may form some remote
idea from the few following examples. He was requested to
extract the cube root of 51,230,158,344 ; his answer, immedi-
ately given, was 8,714.

lie, in an instant, multiplied 349,621 by 6, and gave the cot-
feet product, 1,748,105.

Ag.iin, he divided 2,008,732 by 4> and gave lor answer
962,183. Here, it is to be expected that the aatosishmem and

LESSONS IN INSTRUMENTAL ARITHMETIC.

375

pleasure of his auditors were great indeed ; arid it may be
safely inferred that the problems proposed were still becoming
more and more abstruse.

Now, it was proposed to him, given the sum and difference
of two numbers, 728, and ifi, to find the numbers themselves;
he answered 372 and 356. On being asked what factors would
produce 763.G21, his answer was 85,069, multiplied by 9.
Again, 877 was given as one of the factors of the same number
to find the other; and he instantaneously gave 873 as the
answer.

Agairi, he was required tell the fourth toot of 3,701,506 ; but
he immediately said there was no root, which was indeed true,
the proposer having intentionally read the number wrong, for
the puipose, if possible, of '* flooring " trie young genius.

But the active powers of his mind seemed by far too great
to be taken by surprise on the broad arena of culculation.

Shortly after the proposal of the preceding question, he was
asked the fourth root of 37,015,056 (the right number), and
the modest little arithmetician, with his usual expertness, ease,
and accuracy, answered 78, to the great surprise, and delight
of the whole auditory. Thus it was that the " American Cal-
culating Boy,'' Zarah Colburn, spent some Ume in Belfast,
experiencing kindness wherever lie Went, and exciting ,the
admiration of all by his truly wonderful facililty of managing
numbers, through the unassisted instrumentality of mental
operation.

Uke those of many an. eminent genius in humb)e liffy nil
parents were poor, his father, was struggling to send nim to
the University, but he had no money ; it was therefore sug-
gested that a memoir of his life should be published, that it
should cost a guinea and a half, and that with the money

obtained by this means he should be enabled to get a college
education. An eminent literary gentleman even undertook to
write nis life; but whether the laudable proposal was ever
executed or not, I cannot tell, or whether the " calculating
boy " .ever got to college I never was able to ascertain.

Perhaps, indeed, the vigorous flame of his intellect, so early
kindled^ by " nature's touch," and so often called on to act
mechanically, was neglected, suffered to run to waste, flicker,
and die, without ever knowing the, blessings of a proper
development ! For the sake of humanity and science, I hope
not—but I cannot banish my doubts on the subject, as I never
heard bf him figuring in the mathematical world after he left
Belfast.

In disposition, Zarah was modest arid playful, arid in
appearance presented nothing singular beyond other children
of his age, not even in the formation of his forehead, that
portion of the human fabric to which critics so eagerly direct
attention. Yet there is rip doubt that, ih after years, the gradual
development of such a mind would have acted on the counte-
nance of such an extraordinary person.

As some of the correspondents of the Popular Educator (of
which I have been a constant reader from the first) expressed
a desire to know something bf this wonderful boy, 1 have
endeavoured thus hurriedly to place before tnem this rather
seamy memoir, collected from what I had heard of him, and
from my old papers of the year 1813.

My fellow -readers, keep good heart ; my promise concern-
ing the memoir of out celebrated Dr. Thomson will be fulfilled.
The PoruiAit Educator shall have it when finished, before
the ink is quite drjr ; but some time must yet elapse.

Katesbridge, February 20th f 1834. H. II. Ulidia.

INSTRUMENTAL ARITHMETIC.-No. IV.
SCALES OF VARIOUS EQUAL PARTS TO AN INCH.

In Lesson No. itl. on Instrumental Arithmetic, we gave a
drawing and description of an instrument called a Plane Scale
and Protractor ; we then omitted the drawing of the other side
of the instrument for want of room; but we now insert it below,
fig. 1, with a short description of its nature and use.

are contained 10 of such equal parts, or f J of an inch ; from 2
to ihc same point, are contained 20 of such equal parts or
f $ of an inch ; from 3 to the same point, 30 equal parts, or •? J}
of an inch ; and so on. A unit of this line, the first one adja-
cent to the number 10, which should have been marked with
sero or 0, at its extremity on the right hand, is subdivided into
X0 equal parts af the bottom of the space which it occupies, and
into 1 2 equal parts at the top of this space. Of the former sub-
divisions, each one is a tenth part of an inch ; hence this line

Fiff.l.

V~6T"7] ^ *\ *|p^|Qz JJ3 „ ,/U " <[ JF ^tg ~j[7T?fs~?Tg~ij 5^r^

g S ii Jl >l >l >l ' *l n rf A *1p iH > 'its' £g ' ■i|3^tr jjT7 r ff~?g

i \ "zl 3i 41 . , si M 1\ S\ Al *\9 ii/ J|Z ~*Vi ,if±

71 i\\ r, 41 Jl 6\ » b\ M d\o i\t i\t

t*t

o 3i

fr e C0~ 7I

_?L

> i

.7. _

"3T

In this scale there arc fourteen lines of equal parts, ail of
which contain a certain. number of, equal parts to an inch.
The numbers placed at the left-hand s^de .of £he scale sfybw
how many equal parts of the line on which it stands, one inch
contains, each unit of the line containing ten of these equal
parts. Thus, the first lpie on thjs scale at t)ie bottom has ID
narked at the lett-hand side, and the units 1, 2, 3, and 4»
marked along the line from left to right ; this means that an
inch contains ten e4^ J?*rto or Mi^friripu of this line, each
unit on this line containing jft of an inch ; hence, from 1 to
the beginning of the matter divisions on the line on the right,

wjtn. the %oltom. subdivisions is a. decimal scale of inches, and
from it we can lake on! or measure any number of inches and
tenths of an inch us far ns the scale wfll permit, as, 1*7, 2*5,
3-8, etc. inches. Of the top subdivisions, each one is a twelfth
part of an inch ; hence this line with the top subdivisions is a
duodecimal scate of inched, and frorh it we can take off or mea-
sure any number of inches and primes or twelfths of an inch as
fnr as the scale will allow, as 1 ih. 7% 2 in. 5', 3 in. 8', etc.

Afiaiflj the tccond line on the scale, reckoning from the
bottom upwards, has 11 marked at the left-hand side, and the
units I, 2> 3, 4, and 5, marked along the line from left to right :

376

THE POPULAR EDUCATOR.

thU means that an inch contains 11 equal parts or subdivisions
of this line, each unit on this line containing |f of an inch ;
hence, from 1 to the beginning of the subdivisions on the
right, are contained 10 of such equal parts, or xi of an inch;
from 2 to the same point, are contained 20 of such equal parts,
or f f of an inch ; and so on. A unit of this line, the first one
adjacent to the number 11, ia subdivided into 10 equal parts at
the bottom of the space it occupies, and into 12 equal parts at
the top of this space. Of the former subdivisions, each one is
a tenth part of a unit of this line, or a tenth part of ten-elevenths
of an inch, that is, one-eleventh of an inch ; hence any number
of elevenths of an inch may be obtained from this line as far as
the scale will permit, as 7, 12, 25, etc. elevenths of an inch.
Of the top subdivisions, each one is a twelfth part of a unit of
the scale ; this is intended for those who uie this line merely
as a line of equal parts, and prefer the duodecimal to the deci-
mal subdivision of the unit.

Again, the third line on the scale, reckoning upwards, has
12 marked at the left-hand side, and the units 1, 2, 3, 4, 6,
marked along the line from left to right ; this means that an
inch contains 12 equal parts or subdivisions of this line, each
unit on tne line containing \ % of an inch ; hence, from 1 to the
beginning of the subdivisions on the right, are contained 10
of such equal parts, or \ % of an inch ; from 2 to the same point,
are contained 20 of such equal parts or {J of an inch ; and so
on. A unit of this line, the first adjacent to the number 12, is
subdivided into 10 equal parts at the bottom of the space it
occupies, and into 12 equal parts at the top of this space. Of
the former subdivisions, each is a tenth part of a unit of this
line, or a tenth part of ten-twelfths of an inch, that is, one-
twelfth of an inch ; hence any number of twelfths of an inch
may be obtained from this line as far as the scale will permit,
as 7, 14, 27, etc. twelfths of an inch. Of the top suldivinons,
each one is a twelfth part of a unit of the scale.

Next, ihe fourth line on the scale, reckoning upwards, has
13$ marked at the left-hand side, and the unite 1, 2, 3, 4, 5, 6,
marked along tho line from left to right ; this means that an
inch contains 13} equal parts or subdivisions of this line, each

unit on the line containing .VL of an inch, or _ of an inch \
139 27

hence, from 1 to the beginning of the subdivisions on the right,
are contained 10 of such equal parts, or f? of an inch ; from 2
to the same point, are contained 20 of such equal parts, or f? of
an inch ; and co on. A unit of this line, the first adjacent to
the number 13}, is subdivided into 10 equal parts at the bot-
tom of the space it occupies, and into 12 equal parts at the top
of this space. Of the former subdivisions, each one is a tenth

part of a unit of this line, or a tenth part of — of an inch, or

13}

a tenth paxt of twenty twenty- seventh of an inch, that is, two
twenty-sevenths of an inch ; hence any number of parts of which
13} make an inch may be obtained from this line as before,
only as far as the scale will permit. Of the top subdivisions,
each one is a twelfth part of a unit of the scale. In the latter
case, the part of an inch thus obtained is a compound and

complex fraction denoted by — of — , or JL of _, that is,
12 13} 12 27

— of an inch.
81

^ In the same way we might proceed to explain the remaining
lines of this scale ; but we presume that we have sufficiently
explained the first four lines on the scale, to render the remain-
ing ten lines equally easy of comprehension. Besides, we
must leave a little to the ingenuity of our students, otherwise
there would be no excitement for them to study. Moreover, all
these different lines may be used as scales of equal parts differ-
ing from one another in the magnitude of the unit by very
small and gradual differences, so that a student from amongst
ihem may get almost any scale that will answer his drawings.
The relation of the units of these scales to an inch is a matter
in general of small importance to a vast variety of mechanical
drawings; still, if such relation be wanted, it can be fully
obtained on the principles which we have already explained.
Some plane scales of the kind which we have described may
be had with twenty lines on them adapted to different scales
of measurement, namely, the one half or ten on the one side,

and the other half or ten on the other side. The range of
these scales is as follows :—

On the one side, the numbers of the subdivisions to an inch
are—

10, 11, 12, 13J, 15, 16}, 18, 20, 22, 25;
and on the other side, the numbers of the subdivisions to an
inch are —

28, 32, 36, 40, 45, 50, 60, 70, 85, 100.

The left-hand primary division or unit of the lines on these
scales is sometimes subdivided into 10, 12, and 8 eq-ial parts ;
as these subdivisions are of great use in drawing the parts of a
fortress, a piece of cannon, an engine, or of the different orders
of architecture.

In our next Lesson we shall explain the Logarithmic lines
on the Engineer's Rule and on Gunter's Scale.

ANSWERS TO CORRESPONDENTS.

Tobiok : The only fluids adapted 'tor burning in lamps without wicks
are some of the highly volatile hydrocarbon*, of which thoee are best whicH
approach nearest to the composition of Beniole. The lamp, however, for
this purpose, must be constructed on peculiar principles ; ordinary limps
will not do. Is our correspondent aware that a patent has been taken oat
for this description of lamp by Mr. Hollo way T He has a depot in Hoiboru
(No. 117. we believe). Wickless lamps are attended with considerable
inconvenience, and have riven ri-e to numerous accident?, tome of them
fatal.

Iaco: The employment of the words " either ••" or M certainly art am-
biguous ; let our correspondent supply the words " both** "and" in their
plane. What we meant to state was, that iron, manganese, cobalt, and
nickel, are not precipitated from their solutions by hydrosulphurte acid
alone, but are precipitated from their solutions by hydtosulphate of
ammonia.— R. G. Smith: The precipitate lurnlshed by sulphuretted
hydrogen iu a pure solution of silver, is black.

W. U. Hudson (llarby): It is not necessary to study Logic before
Euclid ; the geometry of Luclid is the finest specimen or Logic the world
ever saw. Whateley'* Logic 1* reckoned among onr best modern Utilises.—
II. K. W. (Brixton) : Won't do; must try again ; but before doing to, read
much good poetry, a«]Milton, Cowper, etc.— PouiiTruL (Bisnop-Aucklaud):
Moody is quite ctrrtct as lar as Latin is concerned. The English has no
ablative.

E. II. B. ( Birkenhead) should study Cassell's Arithmetic, Algebra, and
Geometry in their order, that is, Arithmetic first ; then Algvbra ; and
then Ueometr) ; or if he prefers It, the lessons on these subjects l.i the P. E.
will do as well. The French Dictionary will soon be finished, ii not so
already. The suggestions made will be kept in view.— H. Uborgx (Bristol):
It is most likely that the Lessons in Geology will assume a separate form.
Any book on navigation U a guide to the eompaa.'.

Wilton (Bebtington) : The Geography will be tstntd with an Atlas; the
Lessons In English are published at 3s.— J. Chadwick (B0.1t.1n) should
make the experiment referred to ; we have never seen the statru:ent. It is *
generally considered that the best glass for an electrical machine is tat
whitest, the most transparent, the hardest, and freest from tabbies, and
that which contains a large proportion of silex ; and it should not be too
thick.

errata.

Vol. iv. page 2, col. 2, line 23 from bottom, for 400th. read 40,000th.
page 126, col. 2, line 1ft from top. for £170 read lift',
page 126, col. 2, lint 10 from bottom, for Liverpool real Manchester.

LITERARY NOTICES.

Cassbll's Latin Dictionary, by J. B. Bbabd, D.D. — Tha publica-
tion of this Dictionary has commenced, and will be completed in about
T went j- six Number*, .Tbbebfexcb each, or in Monthly Parts, One
Shilling tach. Part the First is now ready ; Part the Second will be ready
with the Magazim » for April.

Cassbll's Frrnch and English Dictionary*— The French, and
English portion of this important Dictionary is now complete J, and maybe
had, price 4s , or strongly bound, 6s. The English and > hknoh portion
ii* in the course of publication, and will be completed lu about Twelve
Numbers, Thrrkfbnce each. The entire Dictionary, forming one handsome
volume, will be ready with the Magazines for April, price ifc? GJ.

Cassbll's Grrman Pronouncing Dictionary.— The Orexan-
English Portion of this Dictionary is now ready, price 6t iu stiff covers,
or 5s. 6d. strong cloth.— Tne English-Gbbman Portion wlil bt coaapteted
as quickly as possible, in Numbers, Thbbbfbncb each; nod the entire
Volume, strongly bound, at 9s., will shortly be issued.

Cassbll's 8hillino Edition of First Lessons in Latin. • By Pis-
lessors E. A. Andrews and 8. Stoddard. Revised and Corrected. Prkt
Is. paper covers, or Is. 6d. neat cloth.

Cassbll's Latin GrAm mar. For the use of Schools and Colleges. Bf
Professors E. A. Andrews and S. Stoddard. Btvised and Corrected.
Price 3s. 6d. in cloth boards.

Cassell's Lessons in Latin. These Lessons hare been pronounced
unrivalled by thousands of students. Many who have studied Latin from
other grammars and on other systems, and have completely uiled. hart
acquired more real knowledge of the Latin Tongue from theft Lessons la
six months, than they have acquired In as many years by the means bithtrtt
adopted. Price 2s. 6d. In paper covers, or 3s. I* oloth.

A Key to Cassbll's Lbssons in Latin. Containing; TrarslaUcns at
all the Exercises. Price 1 s. In paper covers, or Is, 6d, doth.

LESSONS IN PHYSICS.

377

on physics, or Natural philosophy.

No. XXVI.

{Continued from page 364.)
PHY8ICAL THEORY OF MUSIC

Quality ef Musical Sound,— The result of continued, rapid,
and isochronous vibrations, which produce on the organ of
hearing a prolonged eeneation, ia called a musical sound. Such
a sound oan always be compared with others of the same kind
aa to their unison or discord ; and in this respect it is to be
wholly distinguished from mere noise. The ear can perceive
in musical sounds three particular qualities — height, intensity,
and distinctness ; the last of which the French call timbre.

'The impression made upon the organ of hearing by the
greater or less number of yibrations made in a given time, U
called the height of a musical sound. Sounds which are pro-
duced by a email number of vibrations, are called low ; and
those which arise from a great number of vibrations, are called
high. Those sounds, therefore, which are at the extrem ;
of the scale of perceptible sounds, are properly called low
or high. All the intermediate sounds are called low or high
only m a relative manner. Yet we speak of a low sound or a
hign sound, as we spesk of a low temperature or a high
temperature, by comparing the sound with those which moat
commonly mil upon the ear. The relative depth or height of
two sounds is called tone ; that is, this word expresses the
degree of the height of a given sound ; and in a musical point
of view, it expresses the degree of the height of the scale to
which it belongs.

It has been already shown that the intensity or the force of
the sound depends on the amplitude of the oscillations, and not
on their number. The same sound may preserve the same
degree of height ox depth, and yet assume a greater or lees
intensity, according to the amplitude of the oscillations which
produce it. This is seen in a tense cord, as it is mad to
depart more or less from its position of equilibrium.

Distinctness, or timbre.iB observed in the case of two dif-
ferent instruments which yield each a sound of the same
height or intensity ; and yet these two sounds can be per-
fectly distinguished from each other. Thus, the sound of the
hautboy is very different from that of the flute; or the sound
of the horn from that of the bassoon. In the same way, the
human voice varies much; that is, it presents a very different
timbre, according to the individual, the sge, or the sex. The
cause of this quality is unknown. ^ It appears to depend not
only on die matter of which the instruments are composed,
but also on their form, and on the mode in which they are put
in action. Thus, the sound of a brass trumpet is completely
changed by being strongly heated in an oven, and a straight
trumpet has a louder sound than a curved one.

Unison. — When two sounds are produced by the same
number of vibrations per second, they are said to be in unison ;
that is, they are equally low or equally high. Thus, tbe
wheel of Savart and the siren are in unison when their counters
indicate the same number of vibrations in the same time. The
unison of a musical sound can always be determined ; but not
that of a noise. The number of vibrations of any sonorous
body is, in fact, determined by putting it in unison with the
siren.

The Musical Scale, or Gamut.— VTe give the name of the
Musical Scale to a series of sounds separated from one another
by intervals, which appear to have their origin in the nature of
our organisation. In this series, the sounds are reproduced
in the same order by periods of seven sounds, each period being
denominated a Gamut, and the seven sounds, or notes of each
gamut, are known by the names, ut, ri, mi, fa, sol, la, si.

The notes of the Gamut are represented to the eye by
placing them on what is called the staff, which consists of fire
parallel straight lines and four intervening spaces. The
double staff used for the music of the pianoforte represents,
within its extent, a series of three octaves, aa exhibited in the
following table, fig. 135.

When it is necessary to go beyond the extent of this staff;:
two methods are used. The one consists in giving to the
notes which exceed the normal staff, a supplementary staff, by

YOL. IY.

means of fragments of lines which indicate their relative
position. The other consists in the use of keys or clefs, which
are signs employed to raise or lower the gamut by several
tones, id even several octaves. The clefs are commonly at
the beginning of a piece of music, and the normal intonation
is determined by them. They are accompanied with a variety
of other signs which .regulate the different conditions of the
performance ; these will be afterwards explained.

Fig. 135.

j jjjJ^prrf

«i r< mi ftaolltfei utrtmlfi

i-j jj^rr^

The notes of the g&nut can be represented by number?.
For this purpose, we take for ut, the fundamental sound of the
sonometer explained in a former Lesson ; that is, the sound
produced by a cord vibrating throughout its whole length.
By varying the position of the moveable bridge B, fig. 129, No. 1,
page 362, an experimenter, who has a practised ear, can easily
find the lengtn which must be successively given to the
vibrating part A b, in order to produce the six other notes.
Thus, by representing by unity or 1, the length of the cord
which gives ut, we find that the lengths of toe cords which
give the other notes will be represented by the following
settle of numbers containing fractions of unity : —

/.i /Names of the Notes . . . ut, ri % mi, fa, sol, la, si;
w t Relative lengths of the Cords 1, i, t, f, |, f, ft.

Thus, the length of the cord which gives the note rV, is only
!■ of the length of that which gives the note ut ; the length of
the cord which produces the note mi, is only *, of that which
produces the note ut; and so on. Such are the numbers
which are employed to represent the notes of the gamut,
according to the relative length of the cords which produce
them. By continuing to advance the place of the bridge on
the sonometer, we find that the eighth sound produced by the
half of the length of the cord is the same as the fundamental
sound, The same series of ratios already given recommences
at this sound, and we obtain a new gamut, perfectly cor-
respond in g to the first ; the length of the cord corresponding
to each note of this second gamut, being the half of that
which answers to the note of the same name in the preceding
gamut ; and so on, for a third and a fourth gamut.

In order to ascertain the relative number of vibrations in
the same time corresponding to each note, we have only to take
the reciprocals of the fractions in the preceding table ; for,
according to the first law of the vibrations of cords, formerly
stated, the number of the vibrations of a cord is in the inverse
ratio of its length. Representing, therefore, the number of
the vibrations of a cord which give the fundamental sound ut
hy unity or 1, we have the following table (B) of the reci-
procals of the preceding table (A) :—

m% f Notes of the Gamut . . . ut, re, mi, fa, sol, la, si;
W(llelative Num. of Vibrations 1, f, *, J, J, $, \\

The gamut, of which the ratios of the vibrations of the notes
have now been given, is called the Diatonic Scale ; the gamut
which proceeds by semitones, and which contains thirteen
sounds, is called the Chromatic Scale.

Absolute Number of Vibrations to each Note. — The siren affords
a simple method of deducing from the preceding table the
real number of vibrations which are produced by each of the
notes of the musical scale. Thus, if we put this apparatus in
unison with the fundamental note ut, it will point out to us
the exact number of vibrations which correspond to this note.
Wo have then only to multiply this number by the ratios f ,
j, etc., of the preceding table, in order to find the exact
number of the vibrations of the other notes.

Now, as the fundamental sound which is taken for the note
ut, varies with the length of the cord of the sonometer, with its
tension and with its nature, so the number of vibrations cor-

104

378

THE POPULAR EDUCATOR.

responding to this note will also vary. The real number of
vibrations, calculated as we have now shown, maj.be repre-
sented by an infinity of numbers, to which will correspond as
many different gamuts. Among all the scales which may be
thus represented, that has been selected of which the note ut
corresponds to the lowest sound of the bass, and in physics the
notes of this gamut are indicated by giving the index 1, as ut x ;
whilst to the notes of the higher gamuts are given the indices
2, 3, etc., as ut 29 ut a , etc. ; and to the notes of the lower gamuts,
the indices — 1, — 2, etc., as ut lf ut_ % , re_ lt r/_ a , etc.

Having ascertained by experiment, that the number of vibra-
tions corresponding to the lowest sound ot the bass is 128, we
have only to multiply this number by the ratios given in table
(B), in order to obtain the absolute number of vibrations for
each note ; whence, we hare the following table : —

fr x ( Notes of the Gamut ~ ui, re", mi, fa, sol, la, si.
w \ Abs. No. of Sim. Vib. 128, 144, 160, 170|, 192, 213£, 240.

The absolute numbers of vibrations for the notes of the
higher scales, are obtained by multiplying the numbers of this
table (C), by 2, by 4, by 8, etc. ; and for those of the lower
scales, by dividing the sama numbers by 2, by 4, by 8, etc.
Thus, the number of simple vibrations corresponding to sol B , is
equal to 192 X 4, or 768 per second ; and the number corres-
ponding to ft 8 , is equal to 240 -f- 4, or sixty per second.

length of the Waves.— When we have ascertained the num-
ber of simple vibrations which a sonorous body makes per
second, it is easy to deduce from them the length of the waves.
We know that sound passes over about 1,120 feet per second,
at a mean state of the atmosphere, or about 60° Fahrenheit.
If, therefore, a body made only one simple vibration per
second, the length osVthe wave would be 1,120 feet ; if it made
two such vibrations, the length of the wave would be half of
1,120 feet ; and so on. Now we have seen that 128 simple
vibrations per second correspond to the note ut x ; the length
of the waves, therefore, is the quotient of 1,120 feet divided by
128, that is, 8*75 feet. The following table shows the length
of the wave corresponding to the first note of the successive
gamuts or scales

Number of

First Notts.

Lengths of Waves.

Vibrations.

Ut ,

... •

7000 feet ...

«<-«

... •

3500 „ ...

«Li

... •

1750 „ ...

utx

8-75 „ ...

... 128

ut 2

... •

.. ... 4*375 ,, ...

... 256

«/ 3

... •

•* •*. 2*18/5 „ •*•

... 512

«**

...

1-09375,, ...

... 1024

Intervals, Sharps and Flats. — The ratio of one sound to
another in music is called an interval, that is, the quantity
which indicates by how much one sound is higher than another.
The interval from ut to ri is called a second ; from ut to mi, a
third ; from ut to fa, & fourth ; from ut to sol, a fifth ; from ut to la,
a sixth ; from ut to si, a seventh ; and from ut to ut, an octave.
The following table shows the intervals ef the consecutive
notes, which are obtained by dividing the number of the
vibrations of any note by that of the vibrations of the note
immediately below it : —

{Notes of the scale ... ut, re, mi, fa, sol, la, si, ut.
Relative No. of vibrations 1, $ t i, i, f, $, V. 2.
Intervals . I, V, «• t. V. I,«.

From this table we perceive that the different intervals are
reduced to three, which are $, V. and if* The first o£ these,
which is the greatest, is called the tone major ; the second, the
tone minor; and the third, which is the least, is called the
semitone major. The interval between the tone major and the
tone minor is fj . This is the smallest interval which is taken
into consideration ; it is only a practised ear which can appre-
ciate this interval, a quantity known in music by the name of
comma. Composers have been led to intercalate between the
notes of the Gamut certain intermediate notes, which are
distinguished by the names of sharps and flats. To sharpen a
note, is to increase the number of its vibrations in the ratio of
24 to 25 ; to flatten it, is to diminish the same number in the
ratio of 25 to 24. In music, the sharp is denoted by the sign $ ,
and the flat by the sign \) .
Harmony, Discord. — The co-existence of several sounds

which produce on the ear an agreeable sensation, is generally
denominated harmony, concord, or accord. There is harmony
only when the numbers of the vibrations of the simultaneous
sounds are connected with each other by a simple ratio ; if the
ratio is complex, the ear is affected in a disagreeable manner,
and the simultaneous sounds are called a discord or dissonance.
The simplest concord is unison ; then follow the octave, the
fifth, the third, the fourth, and the sixth. A perfect harmony
or concord is the name given to three simultaneous sounds,
such as the first and the second forming a third major, the
second and the third forming a third minor, and the first and
the third forming a fifth ; that is, to three sounds, such that
the numbers of their corresponding vibrations are to each other
as the numbers 4, 5, and 6. Thus, the three notes /a, la, ut; or
ut, mi, sol ; or sol, si, re', form three perfect concords. These
are the harmonies which produce on the ear the most agreeable
musical sensation.

Pulsation. — When two sounds, which are not in unison, are
produced simultaneously, there is heard at equal intervals a
strengthening of sound which is called a pulsation. Thus, if
the numbers of the vibrations of two sounds are SO and 31,
after 30 vibrations of the first, or 31 of the second, there will
be a coincidence, and consequently a pulsation.

If the pulsations are sufficiently near each other to produce
a continued sound, it will be evidently lower than those from
which it is derived, since it proceeds from a single vibration,
when the other sounds make 30 and 31 vibrations.

The Tuning Fork. — The tuning-fork is a small instrument by
the aid of which we can reproduce at pleasure an invariable
note ; it thus becomes a suitable apparatus for regulating
musical instruments as well as the human voice. It consists
of a steel rod bent into the form of a pair of sugar tongs ;
fig. 136. It is made to vibrate by drawing a bow across its

Fif.136.

edges, or by suddenly separating its two branches by means of
a cylindrical piece of iron which is forcibly drawn between
them, as shown in the figure. The two branches being thus
forced out of their state of equilibrium, return to it after a
certain number of vibrations, and produce a constant sound
for each instrument of this kind. The sound of this apparatus
is greatly increased by fixing it on a wooden box, open at one
or both of its extremities, ft may also be put into vibration
by holding it in the hand by the piece attached to the bend in
the instrument, and striking either end of it against a wooden
board.

VIBRATION OF RODS, PLATES, AND MEMBRANES.

Vibration of Rods and Lamina. — Rods and thin laminae in
wood, glass, and especially in tempered steel, vitiate in con-
sequence of their elasticity, and exhibit, like cords, two kinds
of vibrations ; the one transversal, and the other longitudinal.
The transversal are produced by fixing the rods or lamina at
one extremity, and passing a bow oyer the part whicfe is fr*

LESSONS IN PHYSICS.

879

or unfixed. The longitudinal vibrations in a rod are produced
by fixing it at one of its points, and by rubbing it in the
direction of its length with a piece of cloth wetted, or powdered
with rosin. Yet, in. the latter case, we do not produce a
sound, unless the fixed point of the rod be at its half, its
third, its fourth, and, in short, a certain aliquot part. Analysis
proves that the number of the transversal vibrations of rods
and lamina? of the same nature is in the direct ratio of their
thickness, and in the inverse ratio of the square of their length.
The breadth of the laminae has no effect on the number of
their vibrations ; it only causes the force which produces the
vibrations to vary in its intensity. In elastic rods of the same
nature, the number of longitudinal vibrations is in the inverse
ratio of their length, whatever may be their diameter and the
form of their transversal section. In fig. 137 is a representa-
Fif . 137.

tion of an instrument, the construction of which is founded on
the longitudinal vibrations of rods.

This instrument, constructed by M. Marloye, consists of a
solid wooden stand, on which are fixed twenty cylindrical
fir rods, some coloured and some white. Their lengths are
determined in such a manner, that the white rods give the
diatonic scale, whilst the coloured rods give the semitones and
complete the scale, rendering it chromatic. In order to play
an air with this instrument, the rods are rubbed in the direc-
tion of their length, between the thumb and the fore-finger,
which have been previously dipped in powdered resin. The
sounds which are thus obtained have a strong resemblance to
ih«»-o of the Pandion reed.

Vibration of Plates. — When we jrisb to put a plate "into a
state of vibration, we fix it at the middle point, as represented
in fig. 138, and wc draw a bow across its edges ; or, as may be

considered preferable, we fix it at some point in its surface,
and, through a hole pierced in the middle, we produce friction
by means of horse-hair powdered with rosin.

Vibrating plates present nodal lines which vary in number
and position, according to their form, their elasticity, the

Fig. 138.

mode of putting them in action, and the number of their
vibrations. The nodal lines are rendered obvious to the sight
by covering the plates with a thin stratum of sand before
putting them into the vibratory state. As soon as the vibra-
tions commence, the sand leaves the vibrating parts and dis-
poses itself along the' nodal lines as shown in the preceding
figure.

The vibrations of plates are subject to the following general
laws : In plates of the same nature and of the same form,

S'ving the same figures, the number of vibrations is in the
rect ratio of their thickness and in the inverse ratio of their
surface. Any particular note "will always produce the same
figure with the same piste ; but a small change may be pro-
duced in the figure by slightly changing the place at which
the pla£e is held, without causing any difference in the tone.
If the tone be changed, the existing figure disappears at once,
and a new one makes its appearance. The lowest note which
any plate yields produces the simplest figure ; and the higher
the note is the more complex the figure, or, in other word*,
the more nodal lines there will be. If similar plates of various
sizes be made to vibrate in the same manner, similar figures
will be produced in each. The notes, however, will differ ; the
larger plates will yield the lower notes; and under equal
dimensions, the thicker or stronger plates will yield the highei
notes.

Vibrations of Membranes, — The flexibility of membranes pre-
vents them from vibrating unless they are stretched like the
top of a drum. Then they yield a sound which is higher in
proportion to the smallness of their dimensions and the force
with which they are stretched. M. Savart constructed
vibrating membranes, by pasting very flexible goldbeater's
skin on wooden frames. Membranes are made to vibrate by
percussion, as in the drum; or by the influence of other vibrat-
ing bodies. Thus, M. Savart has observed that a membrane
can be put into a vibratory state by the influence of the vibra-
tions of the air, whatever may be the number of these vibr" •
tions, provided that they are sufficiently intense. Fig. 1*3
represents a membrane vibrating under the influence of vibra-
tions impressed up m the air by a sonorous bell. Same fine
sand spread over the membrane shows the formation of swells
and nodes in it, in the same manner as in plates.

Fig. 139,

380

THE POPULAR EDUCATOR.

LESSONS IN CHEMISTRY^-No. XXV.

Thb apparatus for burning a mixture of coal-gas and atmo-
spheric air, as represented and described in the preceding lesson,
may be considered as the representative of a wind-furnace on
a small scale. By slightly modifying .'t, in a manner now to
be described, it admits of being changed into the representative
of a blast-furnace. To this end, the apparatus, as already de-

Flf. 16.

scribed in the preceding lesson, is supplied with a central jet,
perforating the wire-gauze and communicating with a flexible
tube. To the latter a mouthpiece being adapted, the breath
can be directed in a current upwards through the flame, thus
concentrating the energies of the latter against one point, after
the manner of a blowpipe, flg. 16. By means of a blast of this
description, gold and silver admit of ready fusion, provided
the crucible holding them be of Ttot too great dimensions.

Although the mixed gis flame is that which answers the
greatest variety of purposes, nevertheless other descriptions of
flame are occasionally advantageous. Of these, the, flame
resulting from a circular burner with small lateral orifices is
amongst the most useful. One great advantage it possesses is
the following : instead of heating the lowest point of a flask or
retort, its energies are rather directed on the sides ; thus les-
sening the depth of fluid through which the bubbles resulting
from ebullition have to pass, and thus diminishing the chances
of fracture.

The Argattd Gat Burner. — As a specific source of heat, the
Argnnd gas burner is not so much employed at this time as
formerly ; nevertheless it affords the best means of using gas
for the purposes of illumination, and will therefore be found in
many laboratories. A prudent chemist will never allow the
heat from such a source to go to waste ; he will get some sort

of rough work out of it. For example, he will use H as the
source of heat for keeping up a supply of distilled water. This
is the plan I adopt in my own laboratory, and as its descrip-
tion will serve to initiate the matter of distillation, displaying
that process in its simplest form, I shall describe it somewhat
in detail.

Flf . 17.

First of all, what do we mean by distillation ? Most persons
associate with this process some intricate operation, involving
the use, as a necessity, of much apparatus ; but it is not neces-
sarily of this kind. Viewed in its simplest aspect, distillation
only differs from evaporation in this, — that whilst in the latter
case the vaporised product goes to waste, in the former case it
is condensed and preserved ; such, at least, is true as regards
the distillation of liquids and solids ; but the liberation of gases
from certain substances by the application of heat is also termed
distillation. The apparatus employed in my laboratory for the
distillation of water is as follows. The source of heat, I have
already mentioned, is an Argand burner ; over this is placed a
permanent loop of strong wire, securely fixed to the wall in
such a manner that a convenient support for a large glass flask
results, as indicated in the accompanying diagram fig. 17. This
support, before use, is wound round with a little tow, in such a
manner that the glass flask does not directly bear upon the
iron. The tow rapidly chars, but the carbonaceous residue

Fiff. 18.

LESSONS IN ALGEBRA.

981

remains still, affording a soft cushion for the flask, which holds
about three quarts, to rest upon.

To the mouth of this flask is loosely adapted a cork, to which
a length of glass tubing, about the eighth of an inch in dia-
meter (no more), is attached by perforation. This tube is
attached to another by means of an india-rubber connecter
b, and tube after tube is then attached, until a length of about
18 feet results, fig. 18. This total length is suspended by cord
loop9 from the ceiling, and finally terminates, as represented,
in a large wide-mouthed glass jar e, passing loosely through a
cover of tinned wood /. This cover, it will be seen, is supplied
with a second perforation, admitting the bent glass tube *, which
is joined by means of an india-rubber tube t to another glass
tube j9, the latter represented in our diagram as looking upward,
and secured in that position by a wire hook h. Perhaps it is
scarcely necessary to indicate that the tube passing from the
flask to the receiving jar must have a gradual fall $ this fall
need, however, only be of the slightest.

Turn we now to the apparatus in action. The flask being
removed from its stand and charged with water (about three-
parts f ulH , is replaced and the cork inserted, a very slight
amount ot pressure being sufficient and the rotation of the cork
unnecessary. The gas may now be lighted, taking care that
the flame is small for the first minute or two ; the gas may then
be turned on fully, and the apparatus left to itself. Ebullition
soon ensues and vapour is eliminated ; this vapour passing
along the tube, gets partially condensed into water, which be-
ing driven onward by the force of uncondensed steam, both
enter the receiving iar together. Here the greater part of the
remaining steam is condensed, not enough escaping to produce
inconvenience, nor, indeed, to be for the most part appreciable.
"When it is desired to withdraw a portion of water from the re-
ceiving jar, this is accomplished by merely unhooking the tube
p, bending it on its india-rubber joint t, and bringing it to the
position of the dotted line «'. This arrangement being made,
a syphon will result and water will flow ; the delivery being
perfectly at command, and ceasing so soon as the tube p is bent
back upon *. The apparatus just described illustrates the pro-
cess of distillation under its most simple form. The operation of
cooling, or condensation, the student will observe, is left pretty
much to itself; and so long as water is the liquid to be distilled,
the contrivance answers perfectly ; but liquids whose volatility is
greater than water require a different treatment when distilled.
Sometimes artificial means must be had recourse to for conden-
sing them, and hence the necessity for instruments presently to
be described. On the large scale, in various operations of manu-
facturing chemistry, the usual plan of accomplishing distillation
is by means of a still and worm, as the respective parts of the ar-
rangement are termed. The still is subject to considerable vari-
ations, but in general terms it may be described as a vessel of
copper or other metal, formed on the type of a flask, to which
a head* and delivery-tube are attached, usually by means of
cement or lute ; a small model of this hhi:l is represented in
the accompanying diagram, fig. 19.

Fig. 19.

arranged inside a vessel holding water. The operation of this
worm is almost too obvious for comment. The heat of vapori-
sation being first communicated to the metal, the latter imparts
it to the water, which in its turn becomes gradually so hot that
it has to be renewed, and the condensed vapour passes through
the lower extremity of the worm into a receiving vessel.
The still and worm, though not a bad contrivance for Jarge
commercial operations, may be said to be obsolete in labora-
tories for analysis and general research; flasks and retorts,
properly arranged, and connected with instruments of conden-
sation, taking their place. *

A retort, I believe, is always associated with the idea of
distillation in the amateur chemist's mind; but on trial he
will be surprised to find to what an extent this comparatively
expensive instrument may be discarded in favour of flasks on
the large scale and tubes on the small. There are certain
liquids, of course, which do not admit of being distilled in
flasks. Mineral acids are of this kind ; their vapour being so
corrosive, that the cork wherewith the mouth of the flask is
necessarily closed up being rapidly destroyed ; thus not only
disarranging the apparatus, but contaminating the result ; but
even in many cases of this kind the operation may ^e con-
ducted in flasks, provided india-rubber stoppers be made to
take the place of corks. In general terms it may be stated, that
the success of distillation does not so much depend on the kind
of evaporating vessel, as on the perfection of the means em-
ployed in bringing about condensation. The chief contrivances
to this end will be described in our next lesson.

Attached to this instrument is its necessary complement — a
worm or refrigerator, consisting of a metallic pipe spirallv

LESSONS IN ALGEBRA.— No. XIII.

(Continued from p. 345.)

INVOLUTION, OR RAISING OF POWERS.

172. When a number is composed of the product of the tame
factor any number of times, the result is called a power of the
faelor. Towers are divided into different orders or degrees ; as the
first, second, third, fourth, fifth powers, $c, which are also called
the root, square, cube, biquadrate, $c.

The powers take their names from the number of times the
root, or first power, is used as a factor in producing the given
power.

The original quantity is called the first power or root of all
the other powers, because they are all derived from it.

Thus, if 2 be the root or first power, then

2x2 = 4, the square or second power of 2.
2 X 2 X 2 = 8, the cube or third power.
2x2X2X2 = 1 6, the biquadrate or fourth power, &c.

And, if a be the root or first power, then

a X a = aa, the second power of a.
a X a X a = <*<"*» the third power.
aXflX«X« = aaaa, the fourth power, &c.

173. The nutnber of times a quantity is employed as a factor
to produce the given power is generally indicated by a figure or
letter placed above it on the right hand. This figure or letter
is called the index or exponent, Thus a X » = <w, is written a*
instead of aa ; and a X « X * = *«*t * 8 written a 3 .

The index of the first power is 1 ; but this is commonly omitted,
that is, a 1 = a.

An index is totally different from a co-efficient. The latter
shows how many times a quantity is taken as Apart of a whole;
the former how many times tho quantity is taken as a factor.
Thus 4fl = rt + o-(-tf-(-a; but a* = aX<*XflX<>= aaaa.
If a = 4, then 4a = 16 ; and a 4 = 256.

174. Powers are also divided into direct and reciprocal.
Direct Powers are those which have positive indices, as d\

rf 5 , &c, and are produced by multiplying a quantity by itself,
as above described. Thus d X d = d 2 ; d X d X d = <P » and
dX dXdXdz=:dK

The Reciprocal Power of a quantity is the quotient arising
from dividing a unit by the direct power of that quantity, as

1 1 1

<f» d* d*

, &c.

362

THE POPULAR EDUCATOR.

A reciprocal power is produced by dividing a direct power by
its root, till we como to the root itself; and then continuing the

division, we obtain the reciprocal powers.

Thus -:=&; and
a

- 1 - d = -=■ : and — — a = — . &c

d* d 1

-=rf: - = <*° = 1 ; and -
d —a, rf _» —i, anu d

175. For convenience of calculation and expression) reci-
procal powers arc written like direct powers with the sign —

before the index ; thus -^ = d •
a*

, &c. The direct and red-
d-\ o\- 3 ,

procal powers of d, are rf 4 , a" 3 , d 3 , a* 1 , d°, rf- 1 ,
J"- 4 , &e. in which d°= 1.

16. Involution •'« *A« process of finding any power of a
quantity as explained in Art. 172.

177. To involve a quantity to any required power.

Bulb. — Multiply the quantity by itself, and by its successive pro-
duets, till it is taken as a factor as many times as tliere are units in
ike index of the power to which the quantity is to be raised.

All powers of unity or 1 are the same, viz. 1. For 1 X 1 X
1 x 1, &c = 1.

178. A single letter is involved or raised to any power, by
giving it the index of the proposed power ; or by repeating it
as a factor as many times as there are units in that index.

If the letter or quantity has a co- efficient, it must be raised
to the required power by actual multiplication.

Examples.

1. The 4th power of a, is a*, or aaa ;.

2. The 6th power of y, is y°, or yyyyyy.

3. The nth power of*, is x n , or xxx ... repeated n times.

4. Required the 3rd power of 3x. Ans. 27x 3 .

5. Required the 4th power of 4y. Ans. 256^'.

6. Required the 7th power of 2a, Ans. 128a 7 .

179. The method of involving a quantity which constats of
several factors, depends on the principle, that the jwwer of the
product of several factors is equal to the product of their powers.

21. Find the #ith power of (* + »)*. Ans. (* 4- «)*».

22. Find the 2nd power of («» X P). Ana. V£.

23. Find the 3rd power of (a***A«). Ana. aW*".

192. A fraction is raised to a power by involving tntk 4L
numerator and the denominator to the power required.

Examples.

24. Find the square of -£.
b

By the rule for the multiplication of fractions we have ~

X b — bb~b 2 '

Ans.

Examples.
7. What is the square of ay. Hero,

For by

(ay) 2 = <*'-y,
Art. 177, {ay) 2 =. ay X ay.

But ay X ay = ay ay =: aayy z=z a-y 2 , Ans.

8. What is the 3rd power of bmx } Ans. ^//i 3 * 3 .

9. What is the ;*th power of ady} Ans. a n d n y a .

In finding the power of a product, therefore, we may either
involve the whole at once ; or we may involve each of the factor*
s.parately, and then multiply their several powers into each
other.

10. What is the 4th power of dhy } Ans. dWyK

11. What is the 3rd power of 46 ? Ans. 64 ft 3 .

12. What is the wth power of 6ad } Ans. e^rf".

13. What is the 3rd power of 3w X 2y ? Ans. 216roy

180. When the root is positive, all its powers are positive also ;
but when the root is negative, the odd powers are negative, while
the even powers are positive.

Hence any odd power has the same sign as its root But
an even power is positive, whether its root is positive or nega-
tive. Thus (+ a) X (+ a) = a\ And (— a) X (— a) = a\

181. To involve a quantity which is already a power.

Rule. — Multiply the index of the quantity by the index of the
to which it is to be raised.

Examples.

14. Find the 3rd power of a 2 . Here, (a 2 ) 3 = a 6 .

For a 2 z=zaa: and the cube of aa is aa X aa X aa =r= aaaaaa
=s efi ;"which is the 6th power of a, but the third power of a 2 .

15. Find the 4th power of aW*. Ans. a 1 -'**.

16. Find the 3rd power of 4a\r. Ans. 64a r v\

17. Find the 4th power of 2a a X 3*-rf. Ans. 1296« ! 'W l .

18. Find the 5th power of (a + b) 2 . An*, (a + u) w ,

19. Find the 2nd power of {a + b) a . Ans. (a + b)' in .

20. Find the nih. power of (x — y) ' . Ans. (.-•; — y) mn .

25. Find the 2nd, 3rd, and nth powers of — . Ans.

1 1

26. Find the cube of

2xr 2

3y '

Ans.

27y»*

27. Find the nth power of .

Ans.

%**r*
ay*'

28. Find the square t*~~**S d + m \

Ana. *<'+»>'

183. A compound quantity consisting of terms connected
by -f- and — , is involved by an actual multiplication of its
several parts.

Examples.

29. Find the second, third, and fourth powers of a + 6.
Here (« + b) 1 = a + b, the first power

a + b

the second power

a 2 + ab
+ ab + b*

+ by

= a*+2ab + b 2 , . . .
a + b

a- + 2a-* + a*-

+ *"b + 2a* 3 + 6*

(«

+ by

= a + 3a 3 * + 3a* 3 + * 3 ,
a + *

the third power

a* + 3a 8 * + 3a 3 * 3 4- a*»

+ a 3 * + 3q2* 3 + 3a* 3 + *«
(a + by = a* + 4a 3 * + 6a 3 * 3 + 4a* 3 + **, toe fourth

30. Find the square of a — *. Ads. a 2 — 2a*-f- * 3 .

31. Find the cube of a +1. Ans. a 3 + 3« 3 4- 3« + 1.

32. Find the square of a + * + A. Ans. a 2 4- 2ab -4- 2«A -4-
*3 + 2*A + A 2 . i -T- -r

33. Required the square of a -f- 2rf 4- 3. Ana. a- 4- 4<zrf 4- 6*
+ 4^ + 12d 4- 9. ^

34. Required the 4th power of * + 2. Ans. * l 4- 8** 4- 24*-
+ 16* + 16. ' T

35. Required the 5th power of x 4- 1. Ans. ** 4- ** 4- «i
+ * 3 4-* + l. ^ ^

36. Required the 6th power of 1 — *. Ans. 1 — 6* 4- 15**
— 20*3+15** — 6** + fc. T

184. The squares of binomial and residual quantities occur so
frequently in algebraic processes, that it is important to make
them familiar. Thus,

If we multiply a + A into itself, and also a — A into itself,
we have

a + h
a + h

<i — A
<i — A

a 2 + ah
+ ah + fc

a 2 + 2a"A + h l .

■~ah
— «A + A»
1 - 2«A + k\

LESSONS IN ALGEBRA.

383

Here it will be seen, that in each case, the first and last
terms are the squares of a and A ; and that the middle term is
twice the product of a by A. Hence the squares of binomial
and residual quantities, without multiplying each of the terms
separately, may be found by the following rule : —

(1.) The square ef a binomial, the terms of which are both
vostticc, is equal to the squares of the first and last terms, plus twice
the product of the two terms,

(2.) The squire of a residual quantity is equal to the squares
of the first and l%st Urms, minus twice the product of the two terms.

Examples.

39. Fina the square of 2a + b.

40. Find the square of h -f- 1.

Ans. 4« 2 + & + iab.
Ans. A 2 4- 1 + 2A.

» 2 h + 1

41. Find the square of a* + cd. Ans. a 2 & 2 + e 2 rf 2 + 2abed.

42. Find the square of 6 y + 3. Ans. 36 y 2 + 9 + 36y.

43. Find the square of Zd — A. Ans. 9 d* + A 2 — 6dh.

44. Find the square of a — 1 . Ans. a* + 1 — 2a.
183. For many purposes it will be sufficient to express the

powers of compound quantities by exponents without an actual
multiplication.

Examples.

45. Find the square of a + b. Ans. (a + A) 2 .

46. Find the nth power of be + 8 + x. Ans. (be + 8 + *)« .
In cases of this kind, all the terms of which the compound

quantity consists must be included in the parenthesis.

186. But if the root consists of several factors, the paren-
thesis used in expressing the power, may either extend over
the whole, or may be applied to each of the factors separately,
as convenience may require.

Thus the square of (a + b) X (o + d),ia either

{(<+*) X(«+«0J'i or(« + ^X (« + *)».

The first of these expressions s the square of the product of
the two factors, end the last is the product of their squares,
and tliese are equal to eich other.

In like manner the cube of a X (b + <0, is ( a X (b + d) ) \
or «* X (* + «*)'. C J

187. When a quantity, whose power has been expressed by
a parenthesis, with an index, is afterwards involved by an
actual multiplication of the terms, it is said to be expanded.

Thus (a + b) l t when expanded, becomes a 2 -f- 2rt * + b\ and
( a _L. b + hy becomes a J + lab + 2ah + 6 2 + 2bh + h\

BINOMIAL THEOREM.

188. To involve a binomial to a high power by actual multi-
plication is a long and tedious process, A much easier and more
expeditions way to obtain the required power, is by means of
what is called the Binomial Theorem. This ingenious and
beautiful method was invented by Sir Isaac Newton, and was
deemed of so great importance to mathematical investigation,
that it was inscribed on hie monument in Westminster Abbey.

To illustrate this theorem, let the pupil involve the binomial
a + b, and the residual a — b t to the 2nd, 3rd, and 4th powers.
Thus, (a + *) 2 = a 2 + 2ab + 6 2 .

(a 4- b)* = a 2 4- 3a?* + 3aP + b\

[a + by = a* + Aa*b + 6a 2 * 2 + 4a#» + b*.
Also (a - by = a 2 — 2ab + b\

(a -- 6)3 = « 3 — 3a 2 6 + 3a* 2 — 4*.

\m — by = a 1 — ia*b + 6a 2 * 2 — 4c# + bK

of the first, third, and fifth terms are + , while those of the
second tm&fourt A are — .

3. As to the indices, it will be seen that the index of the first
term, or the leading quantity* in each power, always begins with
the index of the proposed power, and decreases by 1 in each suc-
cessive term towards the right, till we come to the last term
from which the letter itself is excluded. . Thus in (* + *)*
the indices <pf the leading quantity a, are 4, 8, 2, 1.

4. The index of the following quantity begins with 1 in the
second term, and increases regularly by 1 to the last term, whose
index, like that of the first, is the index of the required power.
Thus in {a + by the indices of the following quantity b, are
1,2,3,4.

5. We also perceive, that the sum of the indices is the satne
in eacA term ex any given power ; and this sum is equal to the
index of tAat power. Thus the sum of the indices in each of
terms of the 4th power is 4.

6. As to the co-efficients of the several terms, that of the first
j and last terms in each power is 1 ; the co-efficient of the second

and next to the last terms, is the index of the required power.
Thus, in the' 3rd power, the co- efficient of the second and next
to the last terms, is 3 ; and in the same terms in the 4th power,
it is 4, &c.

It is to be observed, also, that the co-efficients increase in a
regular manner through the first half of the terms, and then
decrease at the samirate through the last half. Thus,

in the 4th power they are
in the 6th power they are

1. 4, 6, 4, 1,
1, 6, 15, 20, 15, 6, 1.

7. The co-efficients of any two terms equally distant from the
extremes are equal to each other. Thus, in the 4th power, the
second co-efficient from each extreme is 4 ; in the 6th power,
the second co-efficient from each extreme is 6; and the third
is 15.

8. The sum of all the co-efficients in each power is equal to
the number 2 raised to that power. Thus, (2) l = 16; also,
the sum of the co-efficients in the 4th power, is 16; and (2) G =
64; so the sum of the co-efficients in the 6th power, is 64.

189. If we involve any other binomial, or residual, to any
required power whatever, wc shall find the foregoing principles
true in all cases, and applicable to all examples. Hence, we may
safely conclude, that they are universal principles, and may bo
employed in raising all binomials to any require^ power.
'They ure the basis or elements of what is called the Binomial
Theorem.

The Binomial Theorem my be, therefore,. defined, a general
methodof involving binomial quantities to finy propostd power. It
is comprised in the following general rule : —

I. Sions. — Jf both terms of the binomial luivc the sign +, all
the signs in every power wiH be -f- ; but if the given quantify is a
residual, all the odd terms in each power, reckoning from't/te left,
will have the sign 4-, and the even terms — .

II. Indices. — The index of the first term or leading quantity,
must always be the index of the required power ; and this decreasis
regularly by 1 through the other terms. Tfie index of tfif \ following

fuantUy begins witA 1 in the second term, and increases regularly by
through the others.

III. Co- efficients. — The co-efficient of the first term is 1 ; that
of the second is equal to the index of the power ; and, universally,
if the co-efficient of any term be multiplied by the index of the leading

I quantity in tAat term, and divided by tAe index of the following
1 quantity increased by 1, it will give the co-efficient of the suecoca'iny
I term.

By a careful inspection of the several parts of the preceding I IV. Number op Terms.— The number of terms will ansa** he
operation, the following particulars will be observed to be one greater than the power reqwred.

applicable to each power, especially if carried out to a greater
number of powers.

1. By counting the terms, it will be found that their number
in each power, is greater by 1 than the index of that power ;
thus, in the 3rd power the number of terms is 4 ; in the 4th
power, it is 5, and so on.

2. If we examine the signs, we shall perceive, when both
terms of the binomial are positive, that all the signs in every
power are + ; but when the quantity is a residual, all the odd
terms, reckoning from the left, have the sign + , and all the
even terms have the sign — . Thus in the 4th power, the signs

In algebraic characters, the theorem is expressed thus —

»— 1

(0 -f b) n = a n + n a n - b + «.

- 2 * 2 +

m— 1

i — 2 n — 3

b* + &c.

* The first letter of a binomial is called the leading quantity, aad
1 he other, the following quantity.

384

THE POPULAR EDUCATOR.

It is here supposed that the terms of the binomial have no
other co-efficients or exponents than 1, but other binomials
may be reduced to this form by substitution.

ExAMPLBS.

1. What is the 6th power of x + V ?

Here, the terms without the co-efficients aro

And the co-efficients, by the rule, are

i a 6 * 5 16 X 4 20X3

6, 1.

2
or 1, 6, 15, 20, 16, 6, 1.

Now, prefixing these co-efficients to the several terms, and
observing the rule of signs, we have the power required as
folio ws : —

afi + 6r>y + 15ar«y- + 20rV + 1&*V + **¥* + **• Ans.

2. What is the 5th power of (d -f h) }

Ans. <*> + 6d*h + 1<WW + lOrfW + 5<tt* + A*.

3. What is the »th power of (b + y) ?

% Ans. i n +^ n — I y4-56 n - V + ^ n — y + D3» — V +
&c M in which the co-efficients which are here represented by
A, J?, C, &c, are respectively

*,«.

tt— 1

W — 1

-, &c.

4. What is the 5th power of x 2 + 3y 3 ?

Here, substituting a for x* % and * for 3y*, we have (a + £) 8
~a» + 5a 4 * + lOtfW + lOaW + So** + **.

And restoring the values of a and b, we have (** + 3y-) 5 =
*u + 15*»y 3 + 90*«y* + 270.iV -f 405*V + 243y w .

5. What is the 6th power of (3* + 2y) ?

Ans. 729*« + 2916*»y + 4860*V + 4320*<y + 2160*V +
576*y* + 64y«.

6. What is the 2nd power of (a — b) } Ans. a 2 — 2ab -\- b*.

7. What is the 3rd power of (a — b) }

Ans. a» — Zarb + Zab* — **.

8. What is the 4th power of (« — *)>

Ans. a* — 4a a 6 + 6a-* 3 — 4a*s + 6*.

9. What is the 6th power of {x - y) ?

Ans. x« — 6^y + ISjtV — 20*V .±_ i5*y — 6xy* +y«.

10. What is the «th power of (a — b) ?

n — 1 n — lr

Ans. a n — na b -{■ n — 5 — a

• 2 *-„-"- 1

2 » — 3

*>+,&c.

] 90. When one of the terms of a binomial is a unit, it is
generally omitted in the power, except in the first or last term ;
because every power of 1 is 1 ; and this, when it is a factor,
has no .effect upon the quantity with which it is connected.

11. Find the cube of (x 4- 1).

Ans. x* + 3a*X 1 + 3* X i a + I s . or a* + 3*« +3* + l.

12. What is the 4th power of (a -— 1)?

Ans. a* — 4a 3 + 6a 2 + 6a + 1.

191. The insertion of the powers of 1 is of no use, unless it
be to preserve the exponents of both the leading and the follow-
ing quantity in each term, lor the purpose of finding the co-
efficients. But this will be unnecessary, if we bear in mind,
that the sum of the two exponents, in each term, is equal to
the index of the power. So that, if we have the exponent of
the leading quantity, we may know that of the following quan-
tity, and vice versa,

13. What is the 6th power of (1 — y) }

Ans. 1 — 6y + Ibif — 20^ + 15yi — 6y 5 + y a .
" 14. What is the wth power of (1 -f x) ?

Ans. 1 + tix + h. '

2 +,&c.

192. The binomial theorem may also be applied to quanti-
ties consisting of tnor$ than two terms. By substitution, several

terms may be reduced to two ; and when the compound 1
sions are restored, such of them as have exponents may be
separately expanded.

Iff. What is the cube of a 4- b + e f

Here, substituting h for (b + e) t we have a + (6 + *) =:
c4-A.

And by the theorem, (a + h)* = a* + 3a»A + 3aA» -|- #.

Now, restoring the value of A, we have

(a + b + ey = a> + Wx(b + e) + 3aX(*+ey
+ (* + ')>.

The last two terms contain powers of (b -\- c); but these may
be separately involved, and the whole expanded.

193. Binomials, in which one of the terms is a fraction, may
be involved by actual multiplication, or by reducing the given
quantity to an improper fraction, and then involving the
fraction. It may also be done by substitution,

Examples.
16. Find the squares of x 4- i ; and of x — J.

H^.-j-J

Also, x — J
x — i

+ ** + *

a? —

-CsH

** + * + * x* — x + l.

Otherwise, reducing the mixed quantities to improper frac-
tions, we have .

x+l

_ 2x + 1

and x — I =

2jp — 1

Whence,

/2*+lY 4** + 4* + l >(** — lY 4*»-4*+i

v-f-J = 4 ; and v-2-/ = — r 111 -*

2 ^ ~~ 4

or x 2 + * + i» anc * * 2 "" * + i* «* oeforo.
2
17. Find the square of a +- Ans. a 3 + •

■+f

18. Find the square of x -

Ans. a: 3 — bx +

19. Find the square of r- 3.ry.

Ans.

-5 + 9jr 8 y a .

M a ill ' ^

20. Find the square of -

• ~ + 2abc.
7

Ans. — — yo^+4a a A

1. Expand Ci +y) 8 .

3. Expand (a — bS*.

5. Expand t^ — y) 9 «

7. Expand (a + bj 9 .

9. Eicpand (* — y) 1 . 8 .
11. Expand ffl + b)*.
13. Expand {<* — bx +
15. Expand (lab — *)*.

Examples fob Practice.

2. Expand (a

« + *) 4 .
(* + *)*.

17. Expand {

4. Expand (*
6. Expand («i

8. Expand ?a?-fy) lo »
10. Expand (o — M 7 .
12. Expand (2 + x)K
14. Expand (a -f 3s«)».
16. Expand hob 4- 6V*)'.
18. Expand (&» -f &Q*.

The Answers to these will he given in our next Lesson.

LESSONS IN GERMA N.— No. LXXXV1L

§ 158. COLLOCATION OF WORDS.

(1) In the arrangement of words in sentences, the German
differs widely from the English. Many differences of colloca-
tion, accordingly, have already been noted and explained in
various other parts of these lessons. But, as every word and
member of a sentence in German takes its position according
to a definite law of arrangement, and cannot, without great

LESSONS IN GERMAN.

385

offence against euphony, be thrown out of its proper place, we
subjoin here some general instructions on this topic.

(2) The essential parts of every sentence, as already re-
marked (§ 119.), are the Subject and the Predicate. That
which is used (properly some part of the verb of existence,
fein) to couple the subject and the predicate, is called the
Copula. Now. arranging these three parts in their natural
order, the subject will come first, the copula next, the predicate
lust: thus,

which a noun or adjective is made to play the same part in
respect to a verb that is sustained by a separable particle.
This will account for the position of urn Staff in the sentence : it
being treated just like a separable prefix. Other phrases be-
longing to this class are :

Subject.

Copula.

Predicate.

JDie ©fume

tyott.

The flower

beautiful.

JDai $ftrb

wet

fart.

The horse

was

strong.

Predicate.

(3) When, as in the case of simple tenses, the copula and
the predicate are both contained in a single word, that word
holds the place of the copula ; while the place of the predicate
either remains vacant, or is occupied by the object of the verb.
Examples :

Copula.

t>mt.

blooms.

lefeit

read

fc$ten.

fight.

ffyf

$ulfe leijlen, to render aid.

Bu £ulfe fommen, to come to the

aid.
3u SRtttag effen, to dine.
Gorge fragen, to take care.
Bu Qntnbt geyen, to perish.
Bu ©runt* ricyten, to ruin.
3nl ffietf fefcen, to execute.
Bn Stonbefcringen, to accomplish.
9$t geften, to pay attention*

Urn* 8eben fomjen, to deprive of

life.
£ro| fcieten, to bid defiance.
Bu £$ei( werben, to fall to one's

part.
&a$ geBcn, to give advice.
Offer ge&en, to grant a hearing.
Qcfcu)r lauftn, to run a risk.
@tiH ftey*n, to stand still.
Bfefi fatten, to hold fast.

bae 2Bucf>.
the book

btefen SRann.
this man.

Subject.

$ie 3Huute

The flower

©it

JDie ©olbaten

The soldiers

(4) In the case of compound tenses, however, the auxiliary
takes the place of the copula ; which place is also held by the
auxiliaries of mood (S 74.) : the place of the predicate being
occupied by the infinitive or participle. If the verb be a com-
pound separable (5 90), the particle stands in the place of the
predicate, while the radical forms the copula. Examples :

Subject. Copula. Predicate.

3$ . y-a&e getefen.

I have read

SBit flnb getoefen.

We have been,

(ft fann fn)rri*en.

He can write,

They were seen.

(5c geyt ant.

He goes out

(5) When any of those verbs which assume the place of the
copula are employed in the compound form, the participle or
infinitive belonging to them stands after the proper predicate
Examples :

Copula.

(7) Should both objects, however, be persons, the accusative
comes first : except the oblique cases of the personal pronouns
(i*, bu, et, fie, c*, tvir, i y r, fie), which always take the precedence.
Examples :

Subject.

(ft

Sic

<Sie

<5rt

has
nrirb
will

yAUfll
ftnb
ttnrb
iH

Predicate.

ty&ti^t geftefen.
foolish been,
gelefcn yafren.
read have.
f$reifcen fctlen.
ge$drt trorten.
gefeytn ttwrben fein.
auegegangen.

(6) The object of a sentence comes between the copula and
the predicate ; and, if there be two objects, that of the person
precedes that of the thing. Examples :

Subject. Copula. 1st Object. 2m) Olject. Predicate.

(fft fat elncn fflrief — gefo)rie&it.

(Jr tjl feinem flxeunbe — geroogen.

eir flnb eines 95etfcr«$cn* — fcefaulbtgt toorben.

3ty yalf bent StuaUn fin fBua) gegefcen.

3c| tyfo meinen 8reun» — ttm ftaty gefragt.

Subj. Copula. 1st Object. 2nd Object. Predicate.
3<$ fate beinen 9o$n meinem fjteunbe empfoyren.

<Sr nrirb i y m feme Softer geton.

(8) When two personal pronouns form the objects of a sen-
tence, the accusative comes before the dative and the genitive.
Examples :

' Subj. Copula. 1st Object . 2nd Object. Predicate.
@te $a*en rt mir gegefcen.

SBir nefcmen tin* feinet an.

to fat fi<$ mir cmtfcyfrn.

(9) Adverbs of degree and manner, or nouns governed by
prepositions and serving in the place of adverbs, when they
refer exclusively to the verb, stand immediately after the object.
Examples :

Subj. Copula. Object. Adverb. Predicate.

(St Bey" anbett feinen Gegenflanb *crtreffli{$. —
9c ffat feinen Oegenftanb wrtreffltcj frfanbeft.

Oh Ipt fell (Skit mit &reub«t aulgegefcen.

(10) Adverbs of time, and phrases used instead of adverbs o f
time, commonly come before the object and before adverbs of
place. Examples :

Subj. Copula. Adverb* Object. Predicate.

3$ $abt geflrra einen Brief gefarieBen.

Crr if* t>or tret JIagen in Swtbon — angefpmmen.

(11) Adverbs of place, and nouns with prepositions, used as
such, generally come immediately before the predicate. Ex-
amples :

Subj. Copula. Object. Adverb. Predicate.

(12) Nouns and pronouns, with the prepositions appropriate
to the verb employed in the sentence, generally come immedi-
ately before the predicate. Examples :

3$ ya&c nlemat* fi&er ben Qegenfianb mit u}m gefrrwytn.
3$ tterbt niemafc in meinem Se&cn gu u)m gef en.

When, however, the preposition with its noun is merely used
to denote the cause or purpose, Ac., of what is expressed by the
verb, it stands before the object. Examples :

SBit tranfen geftern aul Mangel an 93icr JBSaffet.
3<^ ronnte t y m «ot Steuben fetne ftnnwrt geben.

$ 159. Inversion.

(1) In all the cases preceding, the natural order of the lead,
ing parts has been preserved : that is, the subject first, the co-
pula next, and the predicate last. But for the sake of giving
special emphasis to particular words, this order is often inverted.
Thus, the real, or logical subject is made emphatic by being

11m 9fa$ with fragen forms a phrase (um Slaty fragen, to ask for put after the copula : the pronoun ef taking its place as a gram!
advice,) which belongs to a class of phrases in German, in | matical subject : as, es fpU bie 9rtu)cit tyre 9ayne auf, liberty up-

386

THE POPULAR EDUCATOR.

lifts her standard. When, again, either the copula or the pre-
dicate is to be rendered emphatic, they exchange places : Ihm,
(predicate emphatic) flfrfcen mujfen «fle, die must all. The chief
places in which the copula receives the stress, arc,

a. in direct questions ; as, ftyrei&t tcr SWann ?

b. in imperatives ; as, fprectycn ®ic mit tym ;

c. in the case of itipgtn, when used to express a wish ; as,

mcge tt t« $immrf grbcn !

d. in cases where surprise (generally with Ufy) is to be ex*

pressed ; as, ifl tec$ tie Statt tote grff^rt !

(3) When, on any one of those words which, in the natural
order, come between the copula and the predicate, we wish to
lay special emphasis, it must be put either before the other
words standing between the copula and the predicate, or else
before the subject. In this laiter case, however, the subject
and the copula exchange places : thus, nur ven Gtfcm fa it it (frlr*
ftammen ; where the common order would be : (StUt fann sun wn
(ft tan flammen. These inversions, however, chiefly occur when
principal and subordinate sentences are connected by conjunc-
tions.

S 160. Sentences : Principal and Subordinate

(1) A principal sentence is one that expresses by itself an in-
dependent proposition : thus, // wat reported ; He demrvet ;
John toils.

(2) A subordinate sentence is one that serves as the com-
plement to a principal sentence ; and without which it convey*
no complete idea. Thus, in the expressions, It was reported t
that the town woe taken ; He deserves^ that we should dtfi tid
him ; John toils, although he is rich: the first, in each case, is
the principal, and the second the subordinate sentence.

(3) In the natural order, the principal precedes the subor-
dinate sentence But this order is often reversed; in which
case the order of the subject and the copula in the principal
sentence is also reversed. Thus, in the natural order we viy.
ty weis, bap cr tt n\a)t t$un fann, / know, that he cannot do it.
Putting the subordinate sentence first, it will stand : kaj n a
nu$t t|un fann, n>eijj i$, that he cannot do it, know I.

(4) When, however, the subordinate sentence comes in after
the copula (i. e. before a part only) of the principal sentence,
the natural order of the latter remains unchanged : as, tfi frnfy
ait ia) in gontoon curiam, meinen grrunb nic^t.

(5) In subordinate sentence, the common order of the
leading parts differs from that of principal sentences, in making
the copula come last, i. e. in making the copula and the pre-
dicate exchange places. Examples :

Copula.

<5r, tt>f(ctycr mir ten JBrtcf bradjtc.

lie, who to me the letter brought.

2)fr, tcffoi J&crj rein ifl.

3$ rocip too xeb iljn geftfcii babt.

(art fenjt tap cr tt nntt tyun fann.

<fx ift arm, tocil tv fctyr trdge iff*.

(G) The subordinate sentence is usually connected with the
principal one by means of some conjunctive word. The con.
junctive word so employed in either a relative pronoun, a rela-
tive adverb, or some conjunction proper, expressing cause, con-
dition, purpose, limitation, or the like. Sec the examples under
the preceding paragraph.

(7) The conjunction employed in connecting principal with
subordinate sentences, are : ala, auf fcafi, frcwr, bit, ta, tafern, taunt,
taf, tim*i(, fa, fatti, [t, [t na$b<m, intmt, na$tcni, nun, cb, l-ivLlu-i-.
eOfc^pn, ebtooty, fcittcm, ungca<$tct, iD&tyrtnb, tot'xl, »cnn, iMtut ni^t
wenn g(rtcj», twnn ftyon, n*nn aud>, toit, trie aurt, nrietuo$(, n-.-. u ■ ,•
fern, efconar. These all remove the copula to the end of the
sentence.

3)ap is sometimes omitted ; in which case the copula stands,
not at the end, but just as in a principal sentence : thus, cr fagtr,
cr tonne tyrtiben.

When istnn is left out, the subject and copula stand as in n
question : thus, tuenn id» tS gftftyriefcen Mttc, k. or (without mtm)
^aate ty tt gefff>tief»c-, fe toiirtc M> ti 36ncn gcfsigt htkn.

(8) The following are the conjunctive adverbs, which are
used to connect subordinate sentences with principal ones, after
the manner of real conjunctions : aujtttcm, fcafrr, tann, alftann,
tarum, beftvegen, te§$alfe, ttnnc$, trf(tnungf«$tft, nictytftcftavtnigrr, tcp*
gttu$fn, ttfio, rintrfeiM, anbrrftitt, cntti*. frmrr, fc(glic$, gt«<$n>cbl, in*
trffen, tytn&a), nad^er, i&rify, Jintrffcn, (intcp), ingtti$cn, in fo fern, in
fo tveit (fo writ), taunt, mityin, nic^t altan, n\a)t nur, ni$t felcj, noefc,
nur, fonft, fatlt tfeUl, fibrigen*, ubertic*, vtclmc^r, tw|(, juttm, |trar
These all reverse the order of subject and copula, when they
stand be/ore the subject : when, however, they come after the
copula, the natural order of the sentence obtains.

(9) ftftcin, tenn, fontern, tint and ctcr always stand at the head
of a sentence without influencing the order of the other words.
ftber and mlrnlid) may, also, occupy the first place without chang-
ing the position of the other words.

(10) Where a mood-auxiliary, or any such verb as takes the
infinitive without $u, occurs together with another infinitive, the
copula stands before the two infinitives : thus, ttxun i$ r* blttc
t$un muffen, k., not nxnn tc^ t^un muffen ^Att^.

FRENCH HEADING S.— No. VI.

M".* DE LAJOLAIS.

Seotiox III.

Le saisisscment de In joic fut plus dangerous pour M u * de
Lajolais que la douleur. 1 La pauvre enfanttomba lourdement
et sans conuaissance* sur lc marbro do la galerie.*

Grace aux soins de l'impera trice, de la princosse Hortonse
et dc leurs dames, M Ue de Lajolais repnt bientot connais-
sance>— Mon pere, mon p^rc! murmura-t-elle aussit^tqu'elle
put r parler. Oh ! que jc sois d la premiere a lui annoncer sa
grace. 3

Et se levant, ellc voulut s'echappcr des bras qui la rete-
naient ; 4 mais trop faibic pour tant demotions divcrses, elley
retomba sans force.

— Rien nc prcssc maintcnant, Mademoiselle, dit une des
dames ; prenez* un peu de repos et de nourriture ; vous ircz r
une heure plus tard.*

— Une heure plus tard ! sc reeria Maria ; vous voulez que
je retarde d'une heure Tannonco de la vie a un hommc eon-
damne a mort, 6 surtout quand cet hommc est mon pere.
Oh! Madame ajouta-t-cllc, se tournant vers l'imperatru-c,
laissez-moi partir 7 . . . . dc grace;? songez que cVst mon
p£re : qu'il a sa grace, et qu*il ne le sait h pas encore.

— Soit,' mon enfant, lui repondit l'cxccllento Josephine ;
mais vous ne pouvez aller scute a sa prison. 8

— Je suis bicn venue sculc a votre chateau, repondit- elle
vivcment.J

— Que v votre majeste nouspcnnetted'accompagiier M u « dc
Lajolais, 10 demanderent a la fois plusieurs orKciers ct aidt»>-
de-camp do 1'Empereur, que Taction pourtant bien natuivlle
de M l,e de Lajolais avait remplis d'admiration.

— M. dc Lavalette* me rendraec service, 11 ditrimperntrioc
souriant 1 gracieusement a Tun d'eux ; ainsi que Monsieur (de-
signant un aide-de-camp de service}. — Vous vous ser\*ire/. ! *
d'unc dc mes voitures ; 15 .... ailcz, Slessicurs, jevous contie
M llc de Lajolais.

Bicn qu epuiace dc fatigue, dc besoin et demotion, Maria
rcfusa de prendre ct nourriture et repos. 16 Ellc voulut clle-
menie voir atteler les chevaux, presser les gens, 1 ' ct no se tint
en place que lorsqu'clle et ses conducteurs furent installed
sur les coussins de la voiture. 18

* Leg^ndral Lavalette avait epouse* uneniftcc de riinp^ratrice. 1 -
Concilium^ ft mort on 1815, il fut same par lc g^ne'rvux devouemont
de sa feinine, 13 qui s'intro(N:i?it dans sa prison, v\ changes de fete-
incuts avec lui. 1 *

KOYAL SCOTTISH SOCIETY OF ARTS.

38?

Colloquial Ezxbciss.

1. Lajeune filleput-elle reaister
a tuht de joie r

2. Ou tomba la pauvre enfant ?
3 Que dit-elle aussitdt qu'elle

put parler ?

4. Quo Toulut-elle faire en so re-
levant?

5. Que lui dit une des dames ?

6. Quo repondit-elle a cetto
dame?

7. Que dit-elle alors a riinpere-
trice?

8. Que lui repondit la bonne Jo-
sephine ?

9. Qu'ajouta vivement MUe.de
Lajolais ?

10. Quelle dcmandc les ofBciers
adresserent-ils a l'impera-
trice?

11. QueditJoB^phinecnparlant
deM. deLavalette?

12. Le general e"tait-il allic" a la
famiUe de Josephine ?

13. Far qui fut-il sauvc en
1815.

14. Comment le sauva-t-elle ?

15. De quelle voiture devait-on
Be servir?

16. Maria pritn-eile du repos
alors?

17. Que yolut-elle faire ?

18. Quand sc tint-clle en place ?

mime, 15 il faut avoir et£ separe de* auteurs de ses jours,* ct
avoir tremble pour leur vie, pour comprendre tout co que
ce moment de reunion avait de * saint, de delicieux, d in-
effable.

E. Marco de Sawt-Hilaire.

Colloquial Exercise.

Notes and References. — a. Sans connaissance, senseless. —
b. reprit bientot connaissance, soon recovered ; from reprendre ;
L. part ii., p. 104.— c. from pouvoir ; L. part ii., p. 100. — d. que
je Qoia'let tne be. — e. from prendre; L. part ii., p. 100. ~-f. from
aller ; L. part ii., p. 76. — g. de grace, I beseech you. —h. from
savoir; L. part ii., p. 104. — i. soit, be it so.—j. vivement, hastily.
— k. que, will ; literally, let.— I. from sourire ; L.partii., p. 106.
— m. vous vous servirez, you will use ; L. S. 38, K. 2. — n. ne se
tint en place, did not rest ; literally, did not keep herself in one
place. — o. alii*?, related, connected.— p. from prendre ; L. part, ii.,
p. 100.

Section IV.

Alors la voiture partit au galop de six bons chevaux : elle
franchit avec une rapidite incroyable la distance qui se"-
varait Saint-Cloud de la prison/ Pendant tout le trajet,
Maria, droitc et roide, 2 tenait* les yeux fixes sur le cherain
quelle avait encore a parcourir : b son regard scmblait vou-
loir d&vorcr la distance ; 3 sa poitrinc haletait, comme si
e.'etait elle, au lieu des chevaux, qui trafnat c le carosse, et
rile etaitpale, si pale, que deuxoutrois fois ses compagnonslui
adresserent la parole, mais inutilement, elle nc les entendait
pas.* Quand la voiture s'arreta, elle s'elanca pardessus le
marchepied 3 avant que M. de Lavalctte cut cu le temps de
lui offnr la main jjour descendre, c f , ne pouvant d articuler
que ce mot : vite, vite ! elle parcourait les longs corridors de
la prison,* prec£dant le goolier et ses guides, et repliant
toujours : vite, vite ! Arrivee a la porte du cachot, il fallut
bien e qu'elle attendk f que le geolicr en cut ouvert la sernmy
et tire deux enorines verrous ; mais a peine 8 la poi*te cut-cllc
ced£, h que, se precipitant dans rinterieur, elle alia tomber
dans les bras de son pere, 8 en criant : Papa .... TEmpcrem*
.... la vie ... . grace .... Elle ne put Reliever : sa voix sc
perdait en longs l cris, chaque parole coinmencecJ finissait par
un sanglot.

Le general de Lajolais crut k un instant qu'on venait le
chercher 1 pour le conduire a la mort, 9 et que 6a fille ay ant
trompe la vigilance des gardiens, avait tout brave pour lui
faire ses adieux.™

Mais M. de Lavalctte le detrompa bientot : 10 voyant que
Maria vaincue D par Temotion ne pouvait articuler un son, il
prit la parole :

— L'Empereur vous accorde votro grace, general, lui dit-
il, et vous la devez au courage ct a la tendresse de votro
fille."

Puis avec une Amotion dont il ne pouvait se defendre, il
raconta au general de Lajolais tout ce que sa fille avait fait
pour lui. 12

Oh ! combien elle etait heureuse cette jcunc fille P 3 eom-
bien ce moment conmensait ct bien au dela, tout ce qu'elle
avait souffert jusqu alors ; souifcrt! avait-elle reellemcnt
souffert? Elle ne s'en souvenait n plus. Toutes ses souf-
rrances s'etaient p effacees u devant son pere qui la serrait
avec transport dans ses bras. 11 faut avoir souffert soi-

1. La voiture transporta-t-elle
Maria rapidement ?

2. Que faisait-olle pendant tout
le trajet ?

3. Ou son regard se portait-il ?

4. Entendait-elle ce qu'on lui
disait?

5. Que fit-elle quand la voiture
s'arreta ?

6. Entra-t-elle dans les corri-
dors de la prison ?

7. Ne lui fallut-il pas attendro
a la porte du caenot ?

8. Quo fit-elle quand la porte
fut ouverte ?

Notes and Reeebences. — a. Tenait, kept; L. S. 89, R. 1 —
b. parcourir, to travel ; L. part ii., p. 98. — c. from trainer ; L. S.
73, R. 3.— d. from pouvoir ; L. part ii., p. 100, also L. part ii.,
§ 138, R. (2).— <?. il fallut bien qu'elle attendit, she was obliged
to wait.—f. L. S. 72, R. 1. — g. a peine, scarcely. — A. cecltf, been
opened; literally, yielded, given way. — i. longs, prolonged.— j.
L. S. 98, R. 1. — k. from croire ; L. part ii., p. 84. — /. chercher,
to take. — m. L. S. 36, R. 2. — n. vaincue, overcome ; from vaincre;
L. part ii., p. 108.— o. L. S 36, R. 2. — p. s'e'taient eflacecs, were
forgotten ; literally, obliterated. — q. auteurs de ses jours, parents.

9. Que crut d'abord le ge-
neral P

10. Par ouifutildetrompe*? ,

11. Queliiidit-il alors M. de
Lavalette ?

12. Que lui raconta- t-il en-
suite?

13. Que dit l'auteur, du bon-
hcur de la jeune fille ?

14. Ses souflranoes e'taient-eRea
presenter a son esprit P

15. Quo faut-il pour comprcn-
dre le plaisir d'une telle reu-
nion?

ROYAL SCOTTISH SOCIETY OF ARTS.

{From the Edinburgh Evening Courani).

8HORT-HAND.

" The Society met in their Hall, 61, George-street, on Thursday,
16th February, 1854-Rev. Professor Kelland, M.A., President, in
the chair.

The following communication was made :—

On a New Principle of Stenography or Short-hand Writing.
By Alexander Melville Bell, Esq., Edinburgh.

The author stated that the novelty of this system consists in the
adoption of a principle of writing the consonants of words, which
renders altogether superfluous the insertion of vowel point r, either
at the beginning or in the middle of words— the presence or
absence of preceding vowels being indicated by the mode in which
the consonants are written. The following is the principle: —
"Those letters only that, preceded by a vowel sound, are written of
the full alp/iaUtic size (this size being optional), and consonant*
that are not preceded by a vowel are written of such a manifestly
subordinate size, as plainly and at a glance to indicate that they are
not syllabic letters,** Thus the writing not only shows at once where
vowels do and where they do not occur, but also indicates, in the
number of full-sized characters, the number of syllables of which
words are composed. The alphabet consists of simple straight and
curved lines, to all of which the above principle of notation is
applicable — each elementary sound being denoted by a single line.
Distinctive vowel marks may be inserted in thin system ; but they
arc never necessary except in the writing of foreign wordi t proper
names, etc. The consonant delineation pnsents this important
peculiarity, that the full-sized wiiting of those letters whi< h have
a preceding vowel admits of tie free insertion of vowel marks
where they may be required ; while the contracted writing of the
letters which have no preceding vowel precludes their insertion in
the wrong places, or where they do not occur. The rudimenxal
principle of contracting the less important letters of syllables is
also applied to the less important syllables of words, and words of
sentences, by writing without full-sized characters all prefixes and
terminations, and words of the subordinate part* of speech — articles,
prepositions, protfouns, and connectives. The effect of this in tu

f;ive prominence to the radical syllables in each word, and the
eading word in every sentence; and thus to make the words
which are most important to tl.e feme cmp'xitic to the eye, as if
presented in bold capitals on a printed page. A further application

388

THE POPULAB EDUCATOR.

of the same principle consists in writing but one full-sized character
in any word, thus giving prominence to the most distinctive
syllable, that on which the accent falls. In this way words which
occur with a double accentuation — such as present, present', desert,
desert', etc. — are distinguished in their different senses, without the
use of separate accentual marks. This system claims a degree of
simplicity in the acquisition, and an ease of legibility, which have
haraly been approached— which, perhaps, can never be surpassed.
The full alphabetic writing may be learned in an thour ; and this,
when familiarised by practice, may, with almost nothing new to
learn, be contracted at pleasure, either into the curt or manuscript,
or the more abbreviated reporting style.

After tome complimentary remarks made by the President and
others, the thanks of the Society were voted to Mr. Bell for this
communication ; and were given to him from the chair."

CORRESPONDENCE.
MUTUAL IMPROVEMENT CLASS.

81 k, —I take up my pen to trouble you in answering me a ques-
tion, which, as it will be the last for some time, perhaps you will
the more excuse. I am to sail for Alexandria, in Egypt, on the
20th of this month, to erect, or at least to aid in erecting, two
bridges over the Nile, for the railway from that town to Cairo ; and
as I will be, comparatively speaking, in the vicinity of the Holy
Land, I wri' 1 ask if you could give me information as to the
best r"ute i . either of these cities to Jerusalem, which, at the
same time •*• at be economical enough to suit a toorkwg man.

I am an . neer, and a Scotchman, inheriting many of the
peculiarities o my countrymen, and among these a love of travel ;
aod as the days of my manhood have not been many, and my life
has not as yet been ruined by vice, I think you will approve the
step I am about to take, especially when you know that I will have
abundant leisure for study.

In order to fill up profitably these leisure hours, I have taken a
good supply of books, and of the Popular Educator from the
beginning to the " present number." Could I get the French
Dictionary bound by the 16th inst., as I have a smattering of
French which must be carefully improved in the short time I have
to stay ? Before I came to London in October last, I wan in Gala-
shiels, and there I originated and carried ont" Mutual Improve-
ment Class " in geometry and arithmetic, whieh, I am happy to
say, still goes on well. All the members did not take in the P. E. f
as their means toeing apprentices^ did not allow them ; but some
of them did take it in, and I studied the Arithmetical Lessons in it
in order to prepare me for my duties ; and I must say that I found '•
not a few practical hints therein. .

It is true that I did not get my own education from the pages of
the P. E., but in an ancient city on the east coast of Fifeshire,
which you will recognise on the envelope of my letter. There I
spent the winter of 1852-3, and benefited much by the classes
taught in that city.

One thing that greatly prevents private study is " extra time;" •
for when one has to work hard from 6 a.m. till 9 p.m., I wonder [
where the spare time is to come from. I write this letter to you at
five in the morning, as I have no other time at present.

People may talk about " supply and demand" as much as they
like; but a "ten hours' bill" would " supply the time" which
study requires; and nothing else will accomplish this much-needed
boon. As the early-closing movement, however, in some branches
of labour, gains much attention from the publio, wo would fain hope
that our trade will be benefited before long. Indeed, were the men
to respect themselves (which, alas ! few do), instead of debasing
themselves by vice, we would be able to overpower every opposi-
tion ; but until the Maine Law is passed, hopo keeps far in the
distance.

I will now draw to a close this too long letter (for an editor), and
trusting you will answer me per post, for which purpose I enclose
an envelope, etc., I am, Sir, yours respectfully,

March 3rd, 1854. Hoxtoniknbis.

feet and syllables. Indeed, we cannot see the use of poetry, unlet* it be
written in that rythmical cadence which distinguishes it from prose.— T.
Clayton (Maoclesfleld) : His answer to the Four Ball Question is correct.

W. W. Bmillino (Stamford-street) : His answer to the question about
the 3, 6, and 8 gallons is right*~YouNQ Beginner: The home trade U
quite finished; we know no better lessons in Bookkeeping than those in
the P. E.— A. H. Wood: 8ee Blair's Lectures on Rhetoric and Belles
Lettves. The best way to study blank verse is to read poetry so written,
especially Milton's Paradise Lost.

J. M. (Greenock): Liddell and Scott'*.— A. Subscriber (Oldham) 7
Cassell's " Element* of Algebra" is the best.— J. Plodd (Luton) : We don't
know the best and cheapest. Craig's is 'pretty fair.— Jo. Pott b a (Ashton-
under-Lrne) : Navigation must take Its turn.— A Movies (New North-
road) : Study Dr. Beard's Lessons in English, especially the early one?,
over and orer again, and don't despair;. have patience, and you will conquer.
—9. B.: Immediately.— Iqxoramus (Wollaston) : Blair's grammar is too
old now ; you have not solved the Dean's riddle.

Mutual Instruction Classis. Free: M. De Langue, Professor of
the French and Italian Languages, 14, Bulwark-street, Dover, Kent. Also,
D. H., Mrs. Owen, Bookseller, Greenock, Renfrewshire. Nearly rasa : W.
Y.. Christ Church, Bermondsey.— J as. Green (Dunmow): We know nothing
tf the book to which he refers ; we advise him to study Dr. Beard's lessons
in the P. E.— J. L. N. (Dublin): Under consideration.— A. M'Leod (High
Holborn) must study all the Rules In CasseU's Arithmetic, and all the
Lessons in Penmanship in the P. E., as well as those in Bookkee.piug.— J. B.
(Sldmouth-etreet) : Water can be made to attain a much higher tempera-
ture than 219° Fahrenheit by inclosing it in a strong vetnel; Perkins, who
made experiments on the subject, asserted that water could be made rrd
hot, provided that vessels could be obtained stseag enough to re»lst the
pressure of the water in endeavouring to assume the lorm of steawi. In
mvny high-pressure engines the water is carried much above the boiling
point.— Fauo (Manchester); Meni at the end of French adverbs is pro-
nounced according to the rules laid down in CasseU's French Dictionary.—
Edouard (Louth): 8ee Caesell's French Dictionary.— Osa who* tiik
P. E. &c: The solution is too complicated : try again.

Esperanza (Barnsley) : Inquire at the French consulate in the nearest
town.— Ignorance (Great Ayton): Astronomy as soon as possible. — A
Weekly Purchaser (St. Mary-street): Surely the capital most have been
a receipt and not * payment ; surely the transactions with the b*nk are real
cash transactions ; surely stock account and the London and Westminster
Bank are sundries, i.e. two or more accounts —J. C. (Eltham): Wroug on
the Four Ball QnesUon.— U.Smith (Birmingham): "CasseU's Lesson* in
English," and "CasseU's Lessons in Latin."— A. W. F. (Cambiulang) : You
may get a very good old Latin Dictionary for a shilling or two at a book-stall
in Glasgow, Edinburgh, or Loudon, which will serve your nmrpot-e tiil
" CasseU's Latin Dictionary " be ready ; and you will get it in America,
when published, through Mr. Cassell's agent in New York.— A Cuanp.s-
roNDiNT (Chester), who&e name we can't read, wishes his Cestrian brethren
to form a •• Mutual Instruction Class." We hope they will begin with our
Lessons in Penmanship.

M. W. N. may get a second-hand copy of an English Herodotus for three
or four § hillings. The translation published b> Bohn is very good Mid
pretty cheap. A copy of the Greek, without notes, might be got for five or
six shillings. We are not aware that Colonel Bawllnson has published any
other work.

ANSWERS TO CORRESPONDENTS.

T. M. C. (Plymouth): Number is a necessiry adjunct to true poetry,
though not to true poetical ideas. Pope says "he spake in numbers, for tfle
numbers came." Milton alio writes his poetry in numbers, or in measured

LITERARY NOTICES.

Cassill's Latin Dictionary, by J. R. Biard, D.D. — The public »-
tion of this Dictionary has commenced, and will be completed in ab,-»ui
Twenty-six Numbers, Threepence each, or in Monthly Part*, »xr
Shilling each. Eight Numbers, ai well as the First Two Part*, are now

ready. ' «. „

Cassell's French and English Dictionary.— The Frrnch and
English portion of this important Dictionary is now completed, ami maybe
had, price 4s., or strongly bound, 5*.— The English and Frkncii portion
is in the courte of publication, and will be completed in about Twelve
Numbers, Threepence each. The entire Dictionary, forming one handr oine
Yolume, will be ready in a few days, price 9».6d.

Cassell's Gbrmah Pronouncing Dictionary.— The Oermvn-
English Portion of this Dictionary is now ready, price f»s iu«tifT covers,
or 0s. 6d. strong cloth.— The English-German Portion will be completed
as quickly as possible, in Numbers, Threepence each; and the entire
Volume, strongly bound, at Us., will shortly be issued.

Cassell's Lessons in German. Parts I. and II.— These Lostons have
been ackowledged by those who have studied them to be the easiest intro-
duction to the German Tongue which has ever bcon published It; the
English^ Language. Price 2s. each, in paper covers, or 2«. Cd. cloth.— The
Two Parts bound together, price 4s. 6d.

Cassell's Eclectic German Header : containing choice selection*
from the best German Authors, in Prosre and Verse, with a complete
Dictionary of all the Words employed, and copious references to •• Gat*eil>
Lessons in German," Parts I. and II., to whieh It is intended to serve as a
Supplement. Price 8s. in paper covers, or 9s. <W. bound in cloth.

Cassill's Lessons in German Pronunciation : consisting of easy
Extracts from German Writers, with interlinear directions for the Pronun-
ciation of every Word, and a Dictionary explaining the in. aiimg of eacb.
By means of these directions, a person knowing nothing of German pre-
viously, may at once pronounce the language so as to be easily understood
by a native. Price is. in stiff covers, or Is. 6d. neatly bound.

END OP VOL. IV.

I.OX1HIX : JOHN CA88ISLI1, PRINTER, LU DO ATE- HILL.

I.6Z68S0(

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Full text of "The popular educator"

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