S\N

THE

LONDON, EDINBURGH, ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

| CONDUCTED BY

SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & E. &e.
RICHARD TAYLOR, F.L.S. G.S. Astr. S. Nat. H. Mose. &e.
SIR ROBERT KANE, M.D. M.R.LA.

WILLIAM FRANCIS, Pa.D. F.L.S. F.B.A.S. F.C.S.
JOHN TYNDALL, Pu.D. F.R.S. &e.

“Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster
yilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not.

VOL. VII.—FOURTH SERIES.
JANUARY—JUNE, 1854.

LONDON.

TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Printers and Publishers to the University of London ;

SOLD BY LONGMAN, BROWN, GREEN, AND LONGMANS ; SIMPKIN, MARSHALI.
AND CO.; S. HIGHLEY ; WHITTAKER AND CO.; AND PIPER AND
€O,, LONDON: —— BY ADAM AND CHARLES BLACK, AND
THOMAS CLARK, EDINBURGH; SMITH AND SON,

GLASGOW ; HODGES AND SMITH, DUBLIN 5;

AND WILEY AND PUTNAM, NEW YORK,

“Meditationis est perscrutari occulta ; contemplationis est admirari
perspicua..... Admiratio generat questionem, questio investigationem,
investigatio inventionem.”’—Hugo de S. Victore.

—* Cur spirent venti, cur terra dehiscat,
Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Phoebus ferrugine condat,
Quid toties diros cogat flagrare cometas ;
Quid pariat nubes, veniant cur fulmina ccelo,
Quo micet igne Iris, superos quis conciat orbes
Tam vario motu.”
J. B. Pinelli ad Mazonium.

CONTENTS OF VOL. VII.

(FOURTH SERIES.)

NUMBER XLII.—JANUARY 1854.

Mr. W. J. M. Rankine on the Mechanical Action of Heat
Dr. Stenhouse on the dried Coffee-leaf of Sumatra, which is
employed in that and some of the adjacent Islands as a sub-
stitute for Tea or for the Coffee-héan .......-...-.---0-
Dr. Stenhouse’s Examination of the Crystalline Deposit which
forms in Oil of Bitter Almonds? <2. 2... 20: ons aneeeue ne
Dr. Stenhouse on Xanthoxyline, a new Crystalline principle
from Japanese Pepper, the fruit of the Xanthoxylum pipe-
Pee AD WOCCANGOUE ooo. a aytinie'oia's sg A taco < oe wip ciees~e»
Prof. Boole’s Solution of a Question in the Theory of Proba-
ae We Se 2 citar. co mae etials aides Seg
Dr. Tyndall’s Reports on the Progress of the Physical Sciences.
On the Conductibility of Metals for Heat. By G. Wiede-
mann and R. Franz. (With a Plate.) ..............
Mr. A. Cayley on the Theory of Groups, as depending on the
MSEC MIURHOM mE se. Deke eect ts teas | is te te
Mr. W. R. Grove on the Electricity of the Blowpipe Flame ..

Mr. J. J. Sylvester’s Note on a Point of Notation.......

Erececdinps of the Royal Society... ic. juice ss ce nets es eee
On the Products of the Decomposition of Rocks under the In-

fluence of Sulphurous Therma] Waters, by J. Bouis ......
Meteorological Observations for November 1853............

Meteorological Observations made by Mr. Thompson at the
Garden of the Horticultural Society at Chiswick, near
London; by Mr. Veall at Boston; and by the Rev. C.
Clouston at Sandwick Manse, Orkney.......... wae ese on

-

NUMBER XLIII.—FEBRUARY.

The Rev. Prof. Callan on the Results of a series of Experiments
on the Decomposition of Water by the Galvanic Battery, with
a view to obtain a constant and brilliant Lime light........
Mr. J. P. Gassiot on some Experiments made with Ruhmkorff’s
1 OES A rs Meg AS BR Bi SER DEAT S RS aU A
M. Delesse on the Action of Alkalies on Rocks
Mr. F. C. Calvert on the Adulteration of Oils..............
Mr. W.J.M. Rankine on the Mechanical Action of Heat (con-
tinued)

COMSSCH SECS ROVE SHORES E Seco pert eene Bese nvnenseeonne

Page
1

21

26

28
29

33
40
47

50
51

71

101

IV CONTENTS OF VOL. VII.—FOURTH SERIES,

Page

Prof. H. Buff on the Electricity of Plants ..... es a
Dr. Percy and Mr. R. Smith on the Detection of Gold in Lead

Bnd dte COMmpgnnds. 5 29s 5.0 ds va se repack = Soir Mae 126

Mr. J. Cockle on the Methodof Symmetric Products (concluded). 130
Prof. W. Thomson on the C£conomy of the Heating or Cooling

of Buildings by means of Currents of Air..,............. 138
Proceedings of the RoyaliSoaiebystce.-. 33.2 4); ie geese eee 142
On the Genareae of Nickel and Cobalt in some Mineral Springs,

and on a Method for their Isolation, by Ossian Henry .... 149
On the Influence of Pressure upon the Formation of Chemical

Compounds, ‘by Brat, SWAG BIER fs." 4 «fois p55 ailst « 9 ah'g « nis wer han 150
Meteorological Observations for December 1853............ 151
at PAINE. oie actin ct ere Staged dete at xe We]! dle owe wie 152

NUMBER XLIV.—MARCH.

Dr. Hirst’s Reports on the Progress of the Physical Sciences. 153
On the Application of Magnetic Induction to the determi-
nation of the Magnetic Inclination. By Prof. W.Weber.

(With wn Plates)s bis: vate. cote titanate ade Aan 153
Mr. P. J. Martin on the Anticlinal Line of the London and
Hanypahire; Basing’; ss ame ape) 2s atdtesatd Pedals gasusl etek 166

Sir D. Brewster on the Date of the Discovery of the Optical
Properties of Chrysammate of Potash. In a Letter to Prof.

RSGIGCS ec eratede deni eek n aah Oblawee yt skualetne e b e 171
Mr. W. J. M. Rankine on the Mechanical Action of Heat (con-
PINUEDY ia coe, nec ake ee wet spa beinite bey ci umsietns csthis indo. bes eRe 172
M. F. Savart on some Acoustic Phzenomena produced by the
motion of Liquids through short Efflux Tubes............ 186
Prof. W.. Thomson on the Mechanical Values of Distributions of
Electricity, Magnetism and Galvanism ................ 192
Prof. Faraday on Electric Induction—Associated cases of Cur-
rentand Static Mircets oes cme tucheteaniteciea as, «phen 197
Mr. A. Cayley on the Homographic Transformation of a Sur-
face of the Second Order into itself.......... 2... ss eee 208
Dr. Booth on a particular case of Elliptic Integrals whose Para-
miocters are) LMARMIAEY. is pale wiere so kyay Sais | ok ee os eee 213
M. W. Haidinger on the Colours of Mausite .............. 215
Proceedings of the Royal Society’. .s, 0... 0sia.«atés'o: ¢o-0b <oald 218
——___—_—— Royal Institution.................... 223
Electro - deposition of Aluminium and Silicium, by George
MOBSTER y 6 ccirate, 6:55, nUiso hues; dn/e, sree, on0) Sie yske la ook cae enor 227
Experiments on the Artificial Production of Sub cck in Cry-
stallized Substances, by M. De Sénarmont . F aati h one
On Aluminium and its Compounds, by M. Deville. /.cn iy aac 230
Meteorological Observations for January 1854 ............ 231
ee ft a re aR Ue We pi & oa odie 232

CONTENTS OF VOL. VII.— FOURTH SERIES.
NUMBER XLV.—APRIL.

Mr. T. S. Hunt on the Composition and Metamorphoses of
some Sedimentary Rocks ......-.-+-- +s eset eereceee
Mr. W. J. M. Rankine on the Mechanical Action of Heat (con-
cluded). (With a Plate.)......------ BES R RAIN BINNS
Prof. Grassmann on the Theory of Compound Colours. (With
EPP lsaeyias «fie Se rAd cate = habia eo en~ SIE To eee
Prof. Faraday on Electro-dynamic Induction in Liquids ......
Mr. T. Dobson on the Storm-tracks of the South Pacific Ocean.
Wate ra: Pllisties ieee oc cree tca Rane 1) Se ws ety
Prof. Magnus on an Apparatus for the illustration of various
phenomena of Rotating Bodies. (With a Plate.) ........
Mr. A. H. Church on the Spheroidal State of Bodies.. . ;
Prof. Challis on two new Theorems relating to the Moon’s
ie ee Foe AS Pee tans Seras ovina test «lar's olieviate
Mr. A. Normandy on the Spheroidal State of Water in Steam-
boilers.....-0« sever tens ee eum ee BERENS Me cA amhioie =.) Ses! «/ 5s
Proceedings of the Royal Society.....-.-.-++-+++++s5 007s
Royal Institution .. ....----++++-+ +20
On the Heat produced by an Electric Discharge, by R. Clausius.
On some peculiar Reductions of Metals in the Humid way, by
Pe Wohlers vee ee wens Sms es = ap sw nie
On the Decomposition of Water by the Pile, by oy, JanQITE 6
Lithologic Studies, by C. Sainte-Claire Deville ...
Meteorological Observations for February 1854 ........-.--
Wabledoc-ches.02 hn a0) ee aps hast op os 5

eee ee nee

NUMBER XLVI.—MAY.

M. R. Koblrausch’s Theory of the Electric Residue in the
Beyden Jars law 02 Sinai as eee gies aie" so 2°
Mr. §. V. Wood on some Tubular Cavities in the Coralline
Crag at Sudbourn and Gedgrave near Orford. (With a Plate.)
The Rev. J. B. Reade on some early Experiments in Photo-
graphy, being the substance of a Letter addressed to Robert
Hants Baqi. oi Qsos eee Pn Mn a aiere + 09's Nei
Mr. J. J. Sylvester’s Note on the “ Enumeration of the Contacts
of Lines and Surfaces of the Second Order” .....+--+---
Messrs. W. E. Logan and T. S. Hunt on the Chemical Com-
position of Recent and Fossil Lingule, and some other Shells.
Mr. A. Cayley’s Developments on the Porism of the In-and-
circumscribed Polygon ....--++ cesses errs eecerteecces
Dr. Martin Barry’s Note on the Penetration of the Spermatozoon
into the Interior of the Ovum ......00-- sees secs ereeee
Prof. W. Thomson on the Heat produced by an Electric Discharge.
M. P. Riess on the Generation of Heat by Electricity ......
Messrs. J. Spiller and W. Crookes on a Method for preserving
the Sensitiveness of Collodion Plates for a considerable time.

Page
233
239

254
265

268

vi CONTENTS OF VOL. VII.—FOURTH SERTES.

Page
Dr. Herapath’s Additional Directions and Improvements in the
Process for the Manufacture of Artificial Tourmalines...... 352
Sir David Brewster’s Notice on Barometrical, Thermometrical,
and Hygrometrical Clocks..........020---0- SS chon: 358
Proceedings of the Royal Society. ............. ce. se eee 358
— Royal Institution ...............0-.6- 372
On a new Meteorite from New Mexico, by Dr. F. A. Genth.. 378
On M. Foucault’s Pendulum Experiments ............-.-. 379
On the supposed Conversion of Ammonia into Nitric Acid in the
Animal Organism, by Christian Jaffé .......... 0222 ceee 381
Meteorological Observations for March 1854 .............. 383
—_———_ a eaNes fe Apatite 2 Maatieete. een South se RS . 384

NUMBER XLVII.—JUNE.

Dr. E. W. Davy on a new and simple Method of determining

the amount of Urea in the Urinary Secretion ............ 385
The Rev. S. Haughton’s Account of Experiments to determine
the Velocities of the Rifle Bullets commonly used ........ 390

Prof. Faraday on Subterraneous Electro-telegraph Wires .... 396
The Rev. B. Powell onsome Experiments on Rotatory Motion. 398
Prof. Collins on the Attraction of Ellipsoids considered geome-

arate. °F. ose SD DBI ORE ONE eto GE tee ee OF 401
Mr. A. Cayley on the Theory of Groups, as depending on the

Symbolic Equation 6"=1.—Part II..............e ce eee . 408
Dr. Roxburgh on the Cartesian Barometer ................ 410
M. R. Kohlrausch’s Theory of the Electric Residue in the

Leyden Jar (continued). (With a Plate.)................ 412
Prof. Connell on the Voltaic Decomposition of Water ...... 426
M. P. Riess on the Generation of Heat by Electricity ...... 428

Prof. Challis on certain questions relating to the Moon’s Orbit. 429
Mr. J. J. Sylvester’s Note on a Formula by aid of which and
of a table of single entry the continued product of any set of
numbers (or at least a given constant multiple thereof) may
be effected by additions and subtractions only without the

mse of Logarithms '< a: [52 1- sicker este Se to AE ok 430
Proceedings of the Royal Society.............. ihe is 'evevet death 437
——__————— Cambridge Philosophical Society........ 442
On the Production of Ozone by the Decomposition of Water

at Low Temperatures, by M. Goret...........0...000 0 459

On the Separation of Nickel from Cobalt, by Prof. Liebig.... 461
On the Preparation of Hydroferrocyanic Acid, by Prof. Liebig.. 461
Observations on the Nomenclature of the Metals contained in
Columbite and Tantalite, by Prof. A. Connell............
Meteorological Observations for April 1854................ 463
re UN ba ode Wiss dv od bid dled. whe RRC TIC ES .-. 464

CONTENTS OF VOL. VII.—FOURTH SERIES. vant

NUMBER XLVIII.—SUPPLEMENT TO VOL. VII.

Page

Mr. H. Wilbraham on‘ the Theory of Chances developed in .

Professor Boole’s “‘ Laws of Thought”.................. 465
M. R. Kohlrausch’s Theory of the Electric Residue in the

wevyoen Jar (concluded) «05 20o8s « «sue amas weet teins 476
M. Becquerel on a new Electro-Magnetic Engine invented by

Dg ae IOV. oN ee tate a Ss isa alte on ees. 489

Sir W. R. Hamilton on some Extensions of Quaternions .... 492
Mr. T. S. Hunt’s Description and Analysis of two Mineral

LSE Te nee Sy ale hi kr prin eee ae ten eo ope © aia tel 499
Dr. Stenhouse on Fraxinine, the crystallizable principle in the
Bark of the Frazinus excelsior, or Common Ash .......... 501

Prof. W. Thomson on the Uniform Motion of Heat in Homoge-
neous Solid Bodies, and its connexion with the Mathematical

PUN OL MACOUNEIE oets is ox in cin ne coe cs 502
Proceedings of the Royal Society..............ee0000% i. OLD
Second Note on the Decomposition of Water by the Pile, by

cua Fe TT aaa Ste ha alee na hea aa Ras ‘le eipnl 526
Hansen’s Electro-magnetic Engraving Machine ............ 527

On the Force which governs Chemical Actions, by M. Wittwer. 528
Note on the Magnetism of Liquids, by M. Quet............ 529
os RRs NOI ERD Sa LE ge ea i pe hace ea

PLATES.

J. Illustrative of MM. Wiedemann and Franz’s Paper on the Conducti-
bility of Metals for Heat.

IL. Illustrative of Prof. Weber’s Paper on the Application of Magnetic
Induction to the determination of the Magnetic Inclination.

III. Illustrative of Mr. W. J. M. Rankine’s Paper on the Mechanical
Action of Heat; Prof. Grassmann’s Paper on the Theory of Com-
pound Colours; and Mr. T. Dobson’s Paper on the Storm-tracks
of the South Pacifie Ocean.

IV. Mlustrative of Prof. Magnus’s Paper on an Apparatus for the Ilustra-
tien of various phenomena of Rotating Bodies.

V. Illustrative of Mr. 8. V. Wood’s Paper on some Tubular Cavities in
the Coralline Crag at Sudbourn and Gedgrave, near Orford.

VI. Illustrative of M. R. Kohlrausch’s Theory of the Electric Residue in
the Leyden Jar.

ERRATUM

Page 193, line 14 from top, for multiplied read divided.

THE

LONDON, EDINBURGH anv DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

JANUARY 1854.

I. On the Mechanical Action of Heat. By Witu1am Joun
Macquorn Rankine, C.E., F.R.SS. Lond. and Edinb. &e.*

Prefatory Remarks.

BY the permission of the Council of the Royal Society of
Edinburgh, the following series of communications are
republished, which, having been read to the meetings of that
body at various periods during the sessions of 1849-50 and
1850-51, were first printed in the First and Second Parts of
the Twentieth Volume of their Transactions.

These investigations may be considered under a twofold
aspect,—either as determining the theoretical and practical re-
sults, so far as heat and expansive power are concerned, of the
law of the mutual convertibility of physical powers, or as deve-
loping the consequences of an hypothesis respecting the consti-
tution of matter, called that of Molecular Vortices, whereby that
law, as respects heat and elasticity, is made a particular case of
the mechanical principle of the conservation of vis viva.

The law of the mutual convertibility of physical powers has
long been a subject of abstract speculation, and may appear to
some minds in the light of a necessary truth. As we cannot,
however, expect it to be generally received as such, its practical
demonstration must be considered as having been effected by
the experiments of Mr. Joule.

In the following paper, as it originally appeared, the mecha-
nical equivalent of the heat required to raise the temperature of
a given mass of liquid water by one degree was calculated inde-
pendently of those experiments, from the observed velocity of
sound in air, and from the specific heat of air under constant

* Communicated by the Author,

Phil. Mag. 8. 4, Vol. 7. No. 42. Jan, 1854. B

2 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

pressure as compared with that of water, according to the expe-
riments of De la Roche and Bérard. The result thus obtamed
was 695 feet of fall per degree of Fahrenheit, being about one-
tenth part less than Joule’s equivalent. But shortly afterwards
Mr. Joule’s latest and most accurate series of experiments were
published, the mutual agreement of which made it evident that
his determination of the value of one degree of Fahrenheit’s
scale in liquid water, viz. 772 feet of fall, is correct to about
sddth of its amount. All the numerical results in the fol-
lowing paper, therefore, have been corrected to correspond with
this value; and amongst others, the specific heat of air, the
theoretical computation of which has recently been exactly con-
firmed by the experiments of M. Regnault.

With respect to the consequences of the law of the mutual
convertibility of heat and expansive power, the results of the
following investigations will be found to comeide in many points
with those arrived at by Messrs. Mayer, Helmholtz, Holtzmann,
Clausius, and Thomson.

Considered as the development of the consequences of the hy-
pothesis of molecular vortices, these researches constitute the
second part of a paper on the Centrifugal Theory of Elasticity,
the first part of which, treating of the Statical Relations of Heat
and Elasticity, was read to the Royal Society of Edinburgh along
with the present investigation, and published in the Philosophical
Magazine for December 1851.

The introduction of an hypothesis into the theory of a phy-
sical science has for its sole legitimate object, to deduce the laws
of one class of phenomena from those of another class whose
laws are better known, and thus to diminish the number and
the complexity of first principles.

Motion and force being the only phenomena of which we
thoroughly and exactly know the laws, and mechanics the only
complete physical science, it has been the constant endeavour of
natural philosophers, by conceiving the other phenomena of
nature as modifications of motion and force, to reduce the other
physical sciences to branches of mechanics.

In the preface to the Principia, we find Newton expressing a
wish for the extension of this kind of investigation in these
words :—“ UTINAM CHTERA NATURE PHANOMENA EX PRINCI-
PIIS MECHANICIS DERIVARE LICERET.”

The theory of radiant heat and light having been reduced to
a branch of mechanics by means of the hypothesis of undulations,
it is the object of the hypothesis of molecular vortices to reduce
the theory of thermometric heat and elasticity also to a branch
of mechanies, by so conceiving the molecular structure of matter,
that the laws of these phznomena shall be consequences of those
of motion and force.

Mr. W.J. M. Rankine on the Mechanical Action of Heat. 3

This hypothesis, like all others, is neither demonstrably true
nor demonstrably false, but merely probable in proportion to the
extent of the class of facts with which its consequences agree. It
must however be remarked, that whether the hypothesis be pro-
bable or improbable, the theoretical and practical results arrived
at in the following paper respecting the mechanical action of heat
remain unaffected, being deduced from principles which have
been established by experiment and demonstration.

The chief contents are as follows :—

The Introduction explains the hypothesis.

The First Section treats generally of the mutual conversion of
heat and expansive power ;

The Second Section, of real and apparent specific heat, espe-
cially in the state of perfect gas ;

The Third Section, of the latent and total heat of evaporation,
especially for water.

The Fourth Section treats of the mechanical action of steam,
treated as a perfect gas, and the power of the steam-engine, and
contains practical formule and tables. In a supplement to this
section, the results of these formule and tables are compared
with the experiments of Mr. Wicksteed on the Cornish engine
at Old Ford; and a graphic solution is given of the problem, to
determine the rate of expansion in a Cornish engine, so that the
sum of the annual cost of fuel, and the interest of capital, shall
be the least possible as compared with the work done.

The Fifth Section treats of the ceconomy of heat in expansive
machines generally.

A sixth section was read to the Royal Society of Edinburgh
in January 1853, and is published in their Transactions.

Besides the numerical corrections already referred to, the only
alterations which this paper has received consist in the addition
of some notes, the cancelling of some statements and calcula-
tions which have been superseded by subsequent researches, and
a few slight improvements in the notation.

Glasgow, November 1853.

On the Mechanical Action of Heat, especially in Gases and
Vapours*,

INTRODUCTION.
Summary of the Principles of the Hypothesis of Molecular Vor-

tices, and its application to the Theory of Temperature, Elasti-
city, and real Specific Heat.

_ The ensuing paper forms part of a series of researches respect-

ing the consequences of an hypothesis called that of Molecular

* Read to the Royal Society of Edinburgh, February 4, 1850, [With
B2

4 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

Vortices, the object of which is, to deduce the laws of elasticity,
and of heat as connected with elasticity, by means of the prin-
ciples of mechanics, from a physical supposition consistent and
connected with the theory which deduces the laws of radiant
light and heat from the hypothesis of undulations. Those
researches were commenced in 1842, and after having been laid
aside for nearly seven years, from the want of experimental data,
were resumed in consequence of the appearance of the experi-
ments of M. Regnault on gases and vapours.

The investigation which I have now to describe, relates to the
mutual conversion of heat and mechanical power by means of
the expansion and contraction of gases and vapours*.

In the introduction which I here prefix to it, I purpose to
give such a summary of the principles of the hypothesis as is
necessary to render the subsequent investigation intelligible.

The fundamental suppositions are the following :—

First,—That each atom of matter consists of a nucleus, or cen-
tral physical point, enveloped by an elastic atmosphere, which is
retained in its position by forces attractive towards the nucleus or
centre.

Suppositions similar to this have been brought forward by
Franklin, A’pinus, Mossotti, and others. They have in general,
however, conceived the atmosphere of each nucleus to be of
variable mass. I have treated it, on the contrary, as an essential
part of the atom. I have left the question indeterminate, whether
the nucleus is a small body of a character distinct from that of
the atmosphere, or merely a portion of the atmosphere in a highly
condensed state, owing to the mutual attraction of its parts.

According to this first supposition, the boundary between two
contiguous atoms of a body is an imaginary surface at which the
attractions of all the atomic centres of the body balance each
other; and the elasticity of the body is made up of two parts:
First, the elasticity of the atomic atmospheres at the imaginary
boundaries of the atoms, which I shall call the superficial-atomic
elasticity ; and, secondly, the force resulting from the mutual
actions of distinct atoms. If the atmospheres are so much con-
densed round their nuclei or centres that the superficial-atomic
elasticity is insensible, and that the resultants of the mutual

the original paper are incorporated some corrected numerical results for-
merly contained in a supplementary paper read on the 2nd of December
1850, which were deduced from Mr. Joule’s latest experiments on the me-
chanical equivalent of heat. The foot-notes have all been added since the
original paper was read. |

* The statical relations between the density, heat, temperature, and pres-
sure of gaseous bodies, as deduced from this hypothesis, form the subject
of a paper ‘On the Centrifugal Theory of Elasticity,” published in the
Philosophical Magazine for Deeember 1851.

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 5

actions of all parts of the distinct atoms are forces acting along
the lines joining the nuclei or centres, then the body is a perfect
solid, having a tendency to preserve not only a certain bulk, but
a certain figure; and the elasticity of figure, or rigidity, bears
certain definite relations to the elasticity of volume.

If the atmospheres are less condensed about their centres, so
that the mutual actions of distinct atoms are not reducible to a
system of forces acting along the lines joining the atomic centres,
but produce merely a cohesive force sufficient to balance the
superficial-atomic elasticity, then the condition is that of a per-
fect liquid; and the intermediate conditions between this and
perfect solidity constitute the gelatinous, plastic, and viscous
states*.

When the mutual actions of distinct atoms are very small as
compared with the superficial-atomic elasticity, the condition 1s
that of gas or vapour; and when the substance is so far rarefied
that the influence of the atomic nuclei or centres in modifying
the superficial elasticity of their atmospheres is insensible, it is
then in the state of perfect gas.

So far as our experimental knowledge goes, the elasticity of a
perfect gas at a given temperature varies simply in proportion to
its density. I have therefore assumed this to be the law of the
elasticity of the atomic atmospheres, ascribing a specific coeffi-
cient of elasticity to each substance.

The second supposition, being that from which the hypothesis
of molecular vortices derives its name, is the following :—That
the elasticity due to heat arises from the centrifugal force of revo-
lutions or oscillations among the particles of the atomic atmospheres ;
so that quantity of heat is the vis viva of those revolutions or oscil-
lations.

This supposition appears to have been first definitely stated
by Sir Humphry Davy. It has since been supported by Mr.
Joule, whose valuable experiments to establish the convertibility
of heat and mechanical power are well known. So far as I am
aware, however, its consequences have not hitherto been mathe-
matically developed.

To connect this hypothesis with the undulatory theory of
radiation, I have introduced a third supposition:—That the me-
dium which transmits light and radiant heat consists of the nuclei
of the atoms, vibrating independently, or almost independently, of

* I have applied these ideas to the laws of the elasticity of solid bodies,
in a paper teak to the British Association for the Advancement of Science
on the Ist of August 1850, and published in the Cambridge and Dublin
Mathematical Journal for February 1851. Further developments of this
view of the theory of the elasticity of solids were published in the numbers
of the same journal for November 1851 and November 1852.

6 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

their atmospheres ;—so that the absorption of light and of radiant
heat is the transference of motion from the nuclei to their atmo-
spheres, and the emission of light and of radiant heat, the trans-
ference of motion from the atmospheres to their nuclei*.

Although in all undulations of sensible length and amplitude,
such as those of sound, the nuclei must carry their atmospheres
along with them, and vibrating thus loaded, produce a compara-
tively slow velocity of propagation; yet in all probability the
minute vibrations of light and radiant heat may be performed by
the atomic nuclei in transparent and diathermanous bodies,
without moving the atmospheres more than by that amount
which constitutes absorption ; and those vibrations will therefore
be transmitted according to the laws of the elasticity of perfect
solids, and with a rapidity corresponding to the extreme small-
ness of the masses set in motion, as compared with the mutual
forces exerted by them.

This supposition is peculiar to my own view of the hypothesis,
and is, in fact, the converse of the idea hitherto adopted, of an
ther surrounding ponderable particles.

The second and third suppositions involve the assumption,
that motion can be communicated between the nuclei and their
atmospheres, and between the different parts of the atmospheres ;
so that there is a tendency to produce some permanent condition
of motion, which constitutes equilibrium of heat. It is now to
be considered what kind of motion is capable of producing in-
crease of elasticity, and what are the conditions of permanency
of that motion.

It is obvious, that the parts of the atomic atmospheres may
have motions of alternate expansion and contraction, or of recti-
linear oscillation about a position of equilibrium, without affecting
the superficial atomic elasticity, except by small periodical
changes. Should they have motions, however, of revolution
about centres, so as to form a group of vortices, the centrifugal
force will have the effect of increasing the density of the atmo-
sphere at what I have called the bounding surfaces of the atoms,
and thus of augmenting the elasticity of the body.

In this summary, I shall not enter into the details of mathe-
matical analysis, but shall state results only. The following,

* The consequences of this supposition, in the theory of polarization and
double refraction, are pointed out in a paper read to the Royal Society of
Edinburgh on the 2nd of December 1850, and published in the Philoso-
phical Magazine for June 1851. A modification of this third supposition,
according to which the motion constituting light is an oscillation of the
atomic nuclei round transverse axes, and is’transmitted by means of a
species of polarity, forms the subject of a paper read to the British Asso-
ganen at Hull, and published in the Philosophical Magazine for Decem-

er 1853.

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 7

then, are the conditions which must be fulfilled, in order that a
group of vortices, of small size as compared with the bulk of an
atom, and of various diameters, may permanently coexist, whether
side by side, or end to end, in the atomic atmospheres of one
substance, or of various substances mixed.

First, The mean elasticity must vary continuously ; which in-
volves the condition, that at the surface of contact of two vor-
tices of different substances, side by side, or end to end, the
respective densities at each point of contact must be inversely
proportional to the coefficients of elasticity. Hence the specific
gravities of the atmospheric parts of all substances, under pre-
cisely similar circumstances as to heat and molecular forces (a.con-
dition realized in perfect gases at the same pressure and tempe-
rature), are inversely proportional to the coefficients of atmospheric
elasticity. Therefore let ~ represent the mass of the atmosphere
of one atom of any substance, 4 its coefficient of elasticity, and
n the number of atoms which, in the state of perfect gas, occupy
unity of volume under unity of pressure at the temperature of
melting ice ;—then

i ip oye pain, oe vaainctaats | BA

is a constant quantity for all substances.

Secondly, The superficial elasticity of a vortex must not be a
function of its diameter: to fulfill which condition, the linear
velocity of revolution must be equal throughout all parts of each
individual vortex.

Thirdly, In all contiguous vortices of the same substance, the
velocities of revolution must be equal; and in contiguous vor-
tices of different substances, the squares of the velocities must be
proportional to the coefficients of elasticity of the molecular
atmospheres.

The second and third conditions are those of equilibrium of
heat, and are equivalent to this law :—

TEMPERATURE is a function of the square of the velocity of
revolution in the molecular vortices divided by the coefficient of
elasticity of the atomic atmospheres ; or,

w
Temperature=$("), ete

where w represents that velocity.
The mean elasticity which a vortex exerts endways is not
affected by its motion, being equal to
Bas “iter itis Blush. SGD)
where p is its mean density. The superficial clasticity at its
lateral surfaces, however, is expressed by
2

af y
ag ayer game Scie hs Aa

8 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

2
The additional elasticity Se being that which is due to the

motion, is independent of the diameter. The divisor g (the force
of gravity) is introduced, on the supposition of the density p
being measured by weight.

Supposing the atmosphere of an atom to be divided into con-
centric spherical layers, it may be shown that the effect of the
coexistence of a great number of small vortices in one of those
layers whose radius is 7, and mean density p, is to give it a cen-
trifugal force, expressed by

we

i nian is igh a conde EEE
which tends to increase the density and elasticity of the atmo-
sphere at the surface, which I have called the boundary of the
atom. The layer is also acted upon by the difference between
the mean elasticities at its two surfaces, and by the attraction
towards the atomic centre; and these three forces must balance
each other.

I have integrated the differential equation which results from
this condition, for substances in the gaseous state, in which the
forces that interfere with the centrifugal force and atmospheric
elasticity are comparatively small; and the result is

=40(S ) ="
P=bD gb (l—F)+/f(D). . . (VI)

P is the entire elasticity of the gas, and D its mean density.
M represents the total mass of an atom, measured by weight,
and yw that of its atmospheric part; so that iD is the mean
density of the atomic atmospheres*.

J(D) denotes the effect of the mutual actions of separate atoms.

The first term represents the superficial-atomic elasticity. F de-
notes the effect of the attraction of the nucleus in modifying that
elasticity, and can be represented approximately by a converging

2

series, in terms of the negative powers of 596% 1, commencing
with the inverse square, the coefficients being functions of the
density D.

By using the first term of such a series, and determining its
coefficient, and the quantity f(D) empirically, I have obtained
formule agreeing closely with the results of M. Regnault’s ex-

* The corresponding differential equation for substances in any state
whatsoever is integrated in a paper on the Centrifugal Theory of Elasticity,
published in the Transactions of the Royal Society of Edinburgh, vol. xx.
part 3,

_ Mr. W. J. M. Rankine on the Mechanical Action of Heat. 9

periments on the expansion of atmospheric air, carbonic acid and
hydrogen*.
In a perfect gas, the above expression is reduced to

pH p(& )
pare p(so41 p or noe ove! PVE.)

Let n, as before, denote the number of atoms of a substance
which, in the state of perfect gas, occupy unity of volume under
unity of pressure at the temperature of melting ice, so that nM
is its specific gravity in that state : then

D w?
Ps nM nub (x + 1). cory ere (VIII.)
The factor by which =! is here multiplied fulfills the con-
2
ditionof being a function of a and of constants which are the

same for all substances, and is therefore fitted for a measure of
temperature. It obviously varies proportionally to the pressure
of a perfect gas of a given density, or its volume under a given
pressure.

Let 7, therefore, denote temperature, as measured from an
imaginary zero, C degrees of the scale adopted, below the tem-
perature of melting ice, at which
w2
agp +1=0:
then for all substances

w2

and in perfect gases FY es bed a Rs 3 325)
as D
~ CnM’

+ may be termed absolute temperature, and the point from
which it is measured, the absolute zero of temperature. This, as
I have observed, is an imaginary point, beg lower than the
absolute zero of heat by the quantity Crp, which is the same
for all substances.

The value of C, or the absolute temperature of melting ice, as
determined from M. Regnault’s experiments, is

274°-6 Centigrade,
being the reciprocal of
0:00364166 per Centigrade degree,

the value to which the coefficients of dilatation of gases at the
temperature of melting ice approximate as they are rarefied.

* Philosophical Magazine, December 1851.

10 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

For Fahrenheit’s scale C=494°-28. -
In the sequel I shall represent temperatures measured from
that of melting ice by pas aly

We have now to consider the absolute quantity of heat, or of
molecular vis viva, which corresponds to a given temperature in
a given substance, It is obvious that

pw?

2g
represents, in terms of gravity, the portion of vis viva, m one
atom, due to the molecular vortices; but besides the vortical
motion, there may be oscillations of expansion and contraction,
or of rectilinear vibration about a position of equilibrium. The
velocity with which these additional motions are performed will
be in a permanent condition when the mean value of its square,
independent of small periodic changes, is equal throughout the
atomic atmosphere. We may therefore represent by

2 2
Bee iy 2k, ene

the total vis viva of the atomic atmosphere. To this we have to
add that of the nucleus, raising the quantity of heat in one
atom to Mv?

Elia

while the quantity of heat in unity of weight is of - ot EE)
v

2
ye

The coefficient & (which enters into the value of specific heat)
being the ratio of the vis viva of the entire motion impressed on
the atomic atmospheres by the action of their nuclei, to the vis
viva of a peculiar kind of motion, may be conjectured to have
a specific value for each substance depending in a manner yet
unknown on some circumstance in the constitution of its atoms.
Although it varies in some cases for the same substance in the
solid, liquid and gaseous states, there is no experimental evidence
that it varies for the same substance in the same condition. In
the investigation which follows, therefore, I have treated it as
sensibly constant.

The following, then, are the expressions for quantity of heat
in terms of temperature. In one atom :—

v 3kM
In unity of weight :— at ae bree
2
Q=- ae (r—Cnpb)

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 11
Real specific heat is consequently expressed by the following

equations :—
For one atom :—
dy _ 3iM )
dr 2Cnp’ ek oF
For unity of weight :—
dQ 3k
Grn DOne bib Sanda stieuareyc Sani)

For so much of a perfect gas as occupies |
unity of volume under unity of pressure at
the temperature of melting ice :—

Fa 5) Ch’ de oda ee J
The laws established experimentally by Dulong, that the spe-
cific heats of simple atoms, and of certain groups of compound

atoms, bear to each other simple ratios, generally that of equality,
and that the specific heats of equal volumes of all simple gases

are equal, show that the specific factor A™ depends on the che-

mical constitution of the atom, and thus confirm the conjecture
I have stated respecting the coefficient k.

As I shall have occasion, in the investigation which follows,
to refer to and to use the equation for the elasticity of vapours
in contact with their liquids, which I published in the Edinburgh
New Philosophical Journal for July 1849, I shall here state ge-
nerally the nature of the reasoning from which it was deduced.

The equilibrium of a vapour in contact with its liquid depends
on three conditions :—

First. The total elasticity of the substance in the two states
must be the same.

Secondly. The superficial-atomic elasticity must vary conti-
nuously ; so that if at the surface which reflects light there is an
abrupt change of density (which seems almost certain), there
must there be two densities corresponding to the same super-
ficial-atomic elasticity.

Thirdly. The two forces, which act on each stratum of vapour
parallel to the surface of the liquid, namely, the preponderance
of molecular attraction towards the liquid, and the difference of
the superficial-atomic elasticities at the two sides of the stratum,
must be in equilibrio,

Close to the surface of the liquid, therefore, the vapour is
highly condensed. The density diminishes rapidly as the di-
stance from the liquid increases, and at all appreciable distances

12 Mr.W. J. M. Rankine on the Mechanical Action of Heat.

has a sensibly uniform value, which is a function of the tempe-
rature and of certain unknown molecular forces.

The integration of a differential equation representing the
third condition of equilibrium, indicates the form of the approxi-
mate equation

logP=a—2_Y XIV

og ir=a— a _— » op pl ep eq ier: Peay te ( )
the coefficients of which have been determined empirically by
three experimental data for each fluid. For proofs of the extreme
closeness with which the formule thus obtained agree with ex-
periment, I refer to the Journal in which they first appeared.

In the Philosophical Magazine for December 1851 is given a
table of the coefficients for water, alcohol, ether, turpentine,
petroleum, and mercury, in the direct equation, and also in the
inverse formula

Ling /abe? #_E EE °'S
T Y An? 2h
by which the temperature of vapour at saturation may be caleu-
lated from the pressure.

For turpentine, petroleum, and mercury, the formula consists

of two terms only,

log P=a—E, = i yeljca oh ae ieee

the small range of the experiments rendering the determination
of y impossible.

Section I.—Of the Mutual Conversion of Heat and Expansive
Power.

1. The quantity of heat in a given mass of matter, according
to the hypothesis of molecular vortices, as well as every other
hypothesis which ascribes the phenomena of heat to motion, is
measured by the mechanical power to which that motion is
equivalent, that being a quantity the total amount of which in a
given system of bodies cannot be altered by their mutual actions,
although its distribution and form may be altered. This is ex-
pressed in equation XII. of the Introduction, where the quantity

3
of heat in unity of weight, Q, is represented by the height = ;

from which a body must fall in order to acquire the velocity of
the molecular oscillations. This height, being multiplied by the
weight of a body, gives the mechanical power to which the
oscillations constituting its heat are equivalent. The real specific
heat of unity of weight, as given in equation XIII, of the In-
troduction, dQ 3k

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 13

represents the depth of fall, which is equivalent to one degree of
rise of temperature 1 any given weight of the substance under
consideration.

We know, to a greater or less degree of precision, the ratios
of the specific heats of many substances to each other, and they
are commonly expressed bytaking that of water at the temperature
of melting ice as unity.

9. Mr. Joule has made several very interesting series of ex-
periments, in order to ascertain the quantity of heat developed
in various substances by mechanical power employed in different
ways, viz. by electric currents excited by the rotation of a
magnet, by the foremg of water through narrow tubes, by the
agitation of water, mercury and oil with a paddle, by the friction
of cast iron, by the compression of air, and by the friction of air
rushing through a narrow orifice. In his latest and best series
of experiments (Phil. Trans. 1850), the mechanical equivalent
of heat in liquid water was determined by means of the friction
of water, mercury, and cast iron, the mean results being as
follows :—

One Centigrade degree in liquid water=the action of gravity
through 1389°6 feet =452°54 metres. One degree of Fahrenheit
in liquid water =the action of gravity through 772 feet. So far
as I can judge from the mutual agreement of the experiments,
the probable error of this result does not exceed x},dth of its
amount.

3. Means of determining the mechanical equivalent of heat in
air and other gases are furnished by experiments on the velocity
of sound, which, according to the received and well-known theory
of Laplace, is accelerated by the heat developed by the compres-
sion of the medium.

The accuracy of this theory has lately been called in question.
There can be no doubt that it deviates from absolute exactness,
in so far that the magnitude of the displacements of the particles
of air is neglected in comparison with the length of a wave. It
appears to me, however, that the Astronomer Royal, in his re-
marks on the subject in the London and Edinburgh Philosophical
Magazine for July 1849, has Shown, in a satisfactory manner,
that although the effect of the appreciable magnitude of those
displacements, as compared with the length of a wave of sound,
is to alter slowly the form of the function representing the wave,
still that effect is not sufficiently great to make Laplace’s theory
practically erroneous.

4. The expression already given for the real specific heat of
unity of weight of a given substance may be resolved into two

factors, thus :—
GQ Danish PRB itisis \» 0 voinetenen
dr CnM” 2p

14 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

The first factor, cow may be considered in general as a known

quantity ; for C represents, as already stated, 274-6 Centigrade
degrees, the absolute temperature of melting ice, and nM the theo-
retical weight, in the perfectly gaseous state, of unity of volume
of the substance, under unity of pressure, at that temperature ;
; ; ee ‘ pune
or what is the same thing, aM the height of an imaginary
column of the substance, of uniform density, and at the tempe-
rature of melting ice, whose pressure by weight upon a given
area of base is equal to its pressure by elasticity, supposing it

to be perfectly gaseous. The determination of the ratio ‘ere
is necessary, to complete the solution of the problem.

5. The relation now to be investigated between heat and me-
chanical power, is that which exists between the power expended
in compressing a body into a smaller volume, and the increase
of heat in consequence of such a compression, and conversely,
between the heat which disappears, or, as it is said, becomes
latent, during the expansion of a body to a greater volume, and
the mechanical power gained or developed by that expansion.
Those phenomena, according to the hypothesis now under con-
sideration, as well as every hypothesis which ascribes heat to
motion, are simply the transformation of mechanical power from
one shape into another.

It is obvious, in the first place, without the aid of algebraical
symbols, that the general effect of the compression of an oscilla-
ting atomic atmosphere, or molecular vortex, must be to accele-
rate its motion, and of its dilatation, to retard its motion; for
every portion of such an atmosphere is urged towards the nucleus
or atomic centre by a centripetal force equal to the centrifugal
force arising from the oscillation ; so that when, by compression,
each portion of the atmosphere is made to approach the centre
by a given distance, the vis viva of its motion will be increased
by the amount corresponding to the centripetal force acting
through that distance; and conversely, when by expansion each
portion of the atmosphere is made to retreat from the centre, the
vis viva of its motion will be diminished by a similar amount.

It is not, however, to be taken for granted, that adJ the power
expended in compressing a body appears in the form of heat.
More or less power may be consumed or developed by changes
of molecular arrangement, or of the internal distribution of the
density of the atomic atmospheres; and changes of molecular
arrangement or distribution may develope or consume heat, in-
dependently of changes of volume.

6. We shall now investigate, according to the hypothesis of

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 15

molecular vortices, the amount of heat produced by an indefinitely
small compression of one atom of a body in that state of perfect
fluidity which admits of the bounding surface of theZatom; being
treated as if it were spherical ; its radius being denoted by R,
and the radius of any internal spherical layer of the atmosphere
by multiplying R by a fraction w*.

I shall denote by the ordinary symbol of differentiation d, such
changes as depend on the various positions of portions of the
atomic atmosphere relatively to each other, when changes of
volume and temperature are not taken into consideration ; while
by the symbol 6 of the calculus of variations, I shall represent
such changes as arise from the variations of volume and tempe-
rature.

Let us consider the case of an indefinitely thin spherical layer
of the atomic atmosphere, whose distance from the nucleus is Ru,
its thickness Rdu, its area 4m R*u?, and its density

M DY (D,7).
The weight, then, of this layer is
dor? af Dut (u, D, 7) du.

Its velocity of oscillation is v, and having, in virtue of that
velocity, a mean centrifugal force, as explained in the Introduc-
tion (Equation V.), equal to
sa Stal ( v — 2Q
Se aa gkRu kRu/?
it is kept in equilibrio by an equal and opposite centripetal force,

arising from attraction and elastic pressure, which is consequently
represented by

am? ™ Dunp (u, D, 7) du
M gk 3 ’

=8rR? my QDu (u, D, 7) du.

Let the mean density of the atom now be increased by the
indefinitely small quantity 5D, Then the layer will approach
the nucleus through the distance —6(Ru)= —uwdR—Rou, and
being acted upon through that distance by the centripetal force
already stated, the vis viva of oscillation will be increased by a

* In a subsequent paper, read to the Royal Society of Edinburgh on the
15th of December 1851, I have shown, that the same results, though by a
more complicated analysis, are obtained, supposing the boundaries of the
atoms to be of any figure whatsoever. The supposition that they are spheri-
eal, therefore, is to be regarded as merely an expedient to simplify calcula-
tion, and not as an essential part of the theory. (See Trans. Royal Soc.
Edinb. vol. xx. part 3.)

16 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

quantity corresponding to the mechanical power (that is to say,
the heat), represented by the product of that distance by that

force, or by
—87R? = QDuh(u, D, 7)du x 8(Ru)’

=—8nR? # QDy(u, D, 2)? fe i . ie

: 6k 1 8D 4a R3D f
which, because E=-3°D? and 3 =M, is equal to

2 5D ou
+QM. Hay(u, D, ra! = 3 3) ae

We must suppose that the velocity of oscillation is equalized
throughout the atomic atmosphere, by a propagation of motion
so rapid as to be practically instantaneous.

Then if the above expression be integrated with respect to du,
from u=0 to u=1, the result will give the whole increase of heat
in the atom arising from the condensation 6D ; and dividing that
integral by the atomic weight M, we shall obtain the correspond-
ing development of heat in unity of weight. This is expressed
by the following equation :—

_3Q'=2Q td ak me nae ene
=8 f du. ubuh(u,D,7) } fd Ae

The letter Q! is here introduced to denote, when positive, that
heat which is consumed in producing changes of volume and of
molecular arrangement, and when negative, as in the above equa-
tion, the heat which is produced by such changes.

The following substitutions have to be made in equation (1)
of this Section.

For Q is to be substituted its value, according to equation XII.
of the Introduction ; or abbreviating Cnyd into «,—

3k
Q= 2Cnu Cat) ee Se |
The value of the first integral in equation (2) of this Section is
1
if du .wr»p(u, D, r)= &
0 3
The value of the second integral,
1
3 ae du .uBurp(u, D7);

remains to be investigated. The first step in this inquiry is given
by the condition, that whatsoever changes of magnitude a given

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 17

spherical layer undergoes, the portion of atmosphere between it
and the nucleus is invariable. This condition is expressed by
the equation

d d d u .
o= (ou 5 +84 +8 5) f du.urr(u,D,7), ~ (A)

from which it follows that

au 1 d d # F
su= — ®ru, D, 7) (ar5 +6D alee du .u*r(u, D, 7),
and consequently that

3 f du , uduryp(u, D, r)=

d d ) Ndy (2% 4. oe
+(ar. = +80 5) 8 ff" du.vp(u,D, 2).
Hence, making
1 du u
9 — du .urp(u,D,r)=U, . « 6
So Sf te yu, Ds 7) (5)
the second integral in equation (2) is transformed into
1 d d
+ 5(or4-+8D =p):
By means of those substitutions we obtain, for the mechanical
value of the heat consumed in unity of weight of a fluid by any
indefinitely small change of volume or of molecular distribution—

or taking V= 5 to denote the volume of unity

of weight of the substance,
pT (agi f eee ag aU
82 = GoM (av (¥ av cee ds

Of this expression, the portion har aa
represents the variation of heat arising from mere change of
volume. ,
TOK py dU _ _ TH 5) dU
CnM- = dV” CnM dD
produced by change of molecular distribution dependent on
change of volume.

Phil. Mag.8. 4. Vol. 7. No. 42. Jan. 1854. C

, denotes the variation of heat

18 Mr. W.J.'M. Rankine on the Mechanical Action of Heat.

t—x. aU Si .
— Gal or a expresses the variation of heat due to change of

molecular distribution dependent on change of temperature.

7. The function U is one depending on molecular forces, the
nature of which is yet unknown. The only case in which it can
be calculated directly is that of a perfect gas. Without giving
the details of the integration, it may be sufficient to state, that
in this case

K
p=; |
and therefore that Fae a Oya
Dy 2 ye dU ==0 |
Eger Wehbe nk

In all other cases, however, the value of this function can be
determined indirectly, by introducing into the investigation the
principle of the conservation of vis viva*.

Suppose a portion of any substance, of the weight unity, to
pass through a yariety of changes of temperature and volume,
and at length to be brought back to its primitive volume and
temperature. Then the absolute quantity of heat in the substance,
and the molecular arrangement and distribution, bemg the same
as at first, the effect of their changes is elimmated ; and the
algebraical sum of the vis viva expended and produced, whether in
the shape of expansion and compression, or in that of heat, must be
equal to zero :—that is to say, if, on the whole, any mechanical
power has appeared and been given out from the body in the
fom of expansion, an equal amount must have been communi-
cated to the body, and must have disappeared in the form of
heat ; and if any mechanical power has appeared and been given
out from the body in the form of heat, an equal amount must
have been communicated to the body, and must have disappeared
in the form of compression.» This principle, expressed symboli-
cally, is .

ATI —AQ! Oy ya) BS a fe SS)

where IT, when positive, represents expansive power given out,
when negative, compressive power absorbed ; and Q! represents,
when negative, heat given out, when positive, heat absorbed.
To take the simplest case possible, let the changes of tempe-
rature and of yolume be supposed to be indefinitely small, and to
occur during distinct intervals of time, so that 7 and V are in-
dependent variables. Let the initial absolute temperature be 7,

* The function U is determined by direct integration in a paper already
referred to on the Centrifugal Theory of Elasticity (Trans. Roy. Soc. Edinb.
yol, xx. part 3).

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 19

the initial volume V, and the initial total elasticity P;. and let
. the substance go through the followmg four changes:— __
First. Let its temperature be raised from t to 7+6r7, the
volume remaining unchanged. Then the quantity of heat
absorbed is
dQ- tr—K dU
"dr CnM dr ye
and there is no expansion nor compression.
Secondly. Let the body expand, without change of temperature,
from the volume V to the volume V+6V. Then the quantity
of heat absorbed is

t+étr—xk/l d
ov. cCam (Vv av
while the power given out by expansion is

dU
. (U+ 581),

Thirdly. Let the temperature fall from 7+r to its original
value rT, the volume V+6V continuing unchanged; then the
heat given out is

dQ t-—«d dU ..
-§ (F-tate U+ a),
and there is no expansion nor compression.

Fourthly. Let the body be compressed, without change of
temperature, to its original volume V ; then the heat given out is

t—K (1 dU
¥ Moar ty — av)
while the power absorbed in compression is
—dV.P.

The body being now restored in all respects to its primitive
state, the sum of the two portions of power connected with
change of yolume, must, in virtue of the principle of vis viva, be
equal to the sum of the four quantities of heat. Those additions
being made, and the sums divided by the common factor dVoér,
the following equation is obtained :—

dP DRS Fe

ar — CaM V av . . . . . . (9)
The integral of this partial differential equation is

U=$.r4 fav(+ —CoM SE). rat}
C2

20 Mr. W.J. M. Rankine on the Mechanical Action of Heat.
Now #.7 being the same for all densities, is the value of U for
the perfectly gaseous state, or . ; for inthatstatetheintegral =0.

The values of the partial differential coefficients are accordingly

dU 1 dP

Wa ye ae i =
dU K d°P r

ee ey le j

and they can, therefore, be determined in all cases in which the
quantity «=Cnyb, and the law of variation of the total elasticity
with the volume and temperature are known, so as to complete
the data required in order to apply equation 6 of this section to
the calculation of the mechanical value of the variations of heat
due to changes of volume and molecular arrangement.
The total elasticity of an imperfect gas, according to equations

VI. and XII. of the introduction, being ;

P= gay (t-¥ (0.2) +0»

its first and second partial differential coefficients with respect to
the temperature are

dP 1 d T

i = ov} (1473) F(D,5)),
gy DL el d? %
3 = — tan ar +a) P(D,5).
Consequently, for the imperfectly gaseous state,

K d r(D,*)
US3 +(1475) fav."

ay (rg)e(.2) —
a

qU__* (94 ©) fav (0,7)

drt ae ae ie

(8.) It is to be observed, that the process followed in ascer-
taining the nature of the function U is analogous to that em-

* The substitution of these values in equation 6 reduces it to the follow-
ing form, which, being the more convenient, has been employed in most
subsequent investigations :—

BE": i ao" @P 4. dP
a 6): {or(aret [Ga av) tev.

On the dried Coffec-leaf of Sumatra. 21

ployed by M. Carnot in his theory of the motive power of heat,
although founded on contrary principles, and leading to different
results.

Carnot, in fact, considers heat to be something of a peculiar
kind, whether a condition or a substance, the total amount of
which in nature is incapable of increase or of diminution. It is
not, therefore, according to his theory, convertible into mecha-
nical power; but is capable, by its transmission through sub-
stances under particular circumstances, of causing mechanical
power to be developed. He supposes a body to go through
certain changes of temperature and volume, and to return at last
to its primitive volume and temperature, and conceives, in accord-
ance with his view of the nature of heat, that it must have given
out exactly the same quantity of heat that it has absorbed. The
transmission of this heat he regards as the cause of the produc-
tion of an amount of mechanical power, depending on the quan-
tity of heat transmitted and on the temperature at which the
transmission has taken place. According to these principles, a
body, having received a certain quantity of heat, is capable of
giving out not only all the heat it has received, but also a quan-
tity of mechanical power which did not before exist.

According to the theory of this Essay, on the contrary, and
to every conceivable theory which regards heat as a modification
of motion, no mechanical power can be given out in the shape
of expansion unless the quantity of heat emitted by the body in
returning to its primitive temperature and volume is less than
the quantity of heat originally received ; the excess of the latter
quantity above the former disappearmg as heat, to appear as
expansive power, so that the sum of the vis viva in those two
forms continues unchanged.

[To be continued. |

pees Siri ie) adr t i ee

II. On the dried Coffee-leaf of Sumatra, which is employed in
that and some of the adjacent Islands as a substitute for Tea or
for the Coffee-bean. By Joun Stun HOUSE, LL.Dat Res. ™

RECENTLY reccived from my friend Daniel Hanbury, Jun.,
Esq., a quantity of dried coffee-leaves which had been pre-
pared in Sumatra, under the direction of N. M. Ward, Esq. of
Padang+. The sample had a deep brown colour, and consisted
of the leaves of the coffee-tree mixed with fragments of the
stalks. ‘The leaves had been very strongly roasted in rather a
rough manner, and had consequently acquired a slightly empy~

* Communicated by the Author.
T Seea paper by Mr. Hanbury in the 13th volume of the Pharmaceutical
Journal, p. 207,

22 Dr. Stenhouse on the dried Coffee-leaf of Sumatra

reumatic odour. In this respect they pretty closely resemble
Paraguay tea, the leaves and twigs of the Ilex paraguayensis,
which is subjected to a somewhat similar process. The coffee-
leaves when digested with boiling water yielded a deep brown
infusion, which in taste and odour closely resembled an infusion
of a mixture of coffee and tea. On the addition of milk and
sugar, it formed a very tolerable beverage; and as the roasted
coffee-leaf can be imported into Europe for rather less than two-
pence per pound, the poorer classes of society are likely to find
it a very useful substitute for tea and coffee. Should a more
moderate temperature be employed in drying the coffee-leaf, I
think its flavour would be greatly improved.

The coffee-leaf, as might almost have been expected, contains
the two characteristic constituents of the coffee-bean, viz. theine
or caffeine, and caffeic acid. In this respect the coffee-leaf dif-
fers essentially from chicory or any of its adulterations, such as
roasted turnips, mangelwurzel, carrots, &c., the usual substitutes
for coffee, which do not contain a trace of either of these prin-
ciples.

The theine or caffeine was extracted from the coffee-leaves in
the usual way, by precipitating the colourmg matter and other
impurities, first by acetate and then by subacetate of lead. The
acetate of lead threw down a dark brown precipitate -containing
all the caffeic acid, and the subacetate produced a scanty bright
yellow precipitate. The excess of lead was then removed from
the clear solution by sulphuretted hydrogen, and the sulphide of
lead having been collected by filtration, the theine crystallized
when the liquid, after being sufficiently concentrated, had been
set aside in a cool place for some days.

The crystals of theine as first ohtained were of a brownish
colour, but after being strongly pressed between folds of blotting-
paper and repeatedly crystallized, they were rendered nearly
colourless,

I. 1000 grains of dried coffee-leaves, when treated in the way
just described, yielded 12°5 grains theine =1:25 per cent.

II. 1000 grains of coffee-leaves in a subsequent trial gave
11°54 grains =1°15 per cent.

The amount of nitrogen in the dried coffee-leaves was also
determined by Will’s method.

1:344 grm., substance gave 0:2005 platinum =2°118 per cent.
nitrogen.

0:7775 grm. gave 01185 platinum =2°165 per cent.

Now it has been ascertained as the result of numerous experi-
ments*, that “ coffee contains from 0°80 to 1 per cent. of theme,

* See the 32nd page of “ The Chemical Report on the mode of detect-
ing Vegetable Substances mixed with Coffee for the purposes of adultera-

as a substitute for Tea or for the Coffee-bean. 23

and that tea contains 2 per cent. of the same principle.” “ And
the nitrogen in coffee-beans (see page 27 of the same Report)
lies between 24 and 3 per cent.”

By a recent determination I found that 1000 grains of a good
black tea gave 21°3 grains of theine = 2°18 per cent.

1000 grains of a black tea grown in the East India Company’s
tea plantations at Kemaon on the Himalayas, gave 19°7 grains
=1-97 per cent.

0°4705 grm. of the same Kemaon tea gave 0°1175 platinum
=3°5 per cent. nitrogen. :

Many years ago I detected the existence of theine in what is
called Paraguay tea, the dried leaves and twigs of the Lew para-
guayensis, but I neglected to determine its amount. I have
recently found that 1000: grains of Paraguay tea yielded 12°3
grains of theme =1:23 per cent.

If. 1000 grains ditto gave 11 grains =1°1 per cent.

1:748 grm. gave 0°:1865 platinum =1°51 nitrogen.

1-031 grm. gave 0°123 platinum =1°70 nitrogen per cent.

From these results it is clear that dried coffee-leaves are some-
what richer in theine than the coffee-bean, and contain, as nearly
as may be, the same amount of that principle as Paraguay tea.

From the violent roasting to which the coffee-leaves had been
subjected, I feel convinced a portion of their theine has been dis-
sipated; and were they only dried at a moderate tempera-
ture, I confidently expect that they would yield 13 per cent. of
theine. The theine obtained from the coffee-leaves was not
subjected to analysis. This I considered unnecessary, as it pos-
sessed all the well-known properties of ordinary theine, ery-
stallizing in fine silky crystals, which readily sublimed when
heated ; and when digested with nitric acid and cautiously eva-
porated to dryness, they gave when treated with ammonia the
characteristic red coloration so closely resembling that from uric
acid when acted on by the same reagents.

With regard to caffeic acid, the other characteristic proximate
principle of coffee, the leaf of the coffee plant contains it also in
larger quantity than the berry. Caffeic acid is precipitated of a
deep yellow colour by acetate of lead, but is apparently uncry-
stallizable ; at least the numerous attempts which I have made
to obtain it in a crystalline state have hitherto proved unsuc-
cessful. Caffeic acid does not precipitate solutions of gelatine,
and it is therefore not a species of tannin, as has been sometimes
asserted. ‘The most remarkable property of caffeic acid is that
first stated at the 34th page of the joint Report on the adultera-
tion of coffee already quoted. ‘ Caffeic acid appears to be ana-

tion,” drawn up by Professor Graham, Dugald Campbell,*Esq. and myself,
for the British Government, and communicated to it in December 1852.

24 Dr. Stenhouse on the dried Coffee-leaf of Sumatra

logous to kinic acid, the acid of cinchona barks, for it yields
kinone when oxidated by means of sulphuric acid and binoxide
of manganese. To observe this property, the coffee is boiled
with water aud a little slaked lime, the infusion filtered and
evaporated down to the consistence of a syrup. The syrupy
liquid is then mixed in a retort with four times its weight of
binoxide of manganese and one part of oil of vitriol diluted with
an equal bulk of water. Sufficient heat is produced by the
action of the sulphuric acid upon the other materials to bring
over the greater portion of the kinone, and the lamp need not
be applied till towards the close of the operation. The distillate
consists of yellow crystals of kinone, which usually coat the neck
and sides of the retort, and a bright yellow liquid which is a
saturated aqueous solution of kinone with a considerable quan-
tity of formic acid. Kinone is easily discernible by its volatility
and peculiarly acrid odour, which greatly resembles that of chlo-
rine. The solution of kinone gives with ammonia a sepia black
colour. It is decoiorized by sulphurous acid. The beautiful
green hydrokinone is obtained by exactly neutralizing the solu-
tion of the yellow kinone with sulphurous acid, great care being »
taken not to introduce the latter in excess.

“The peculiar acid in Paraguay tea agrees with caffeic acid,
to which it is no doubt related, in yielding kinone to similar
oxidizing agencies ; so does the acid of the leaves of the common
holly, Ilex aquifolium, and the whole of the Cinchona tribe.”

When coffee-leaves are boiled with a considerable quantity of
water and a slight excess of milk of lime, the dark brown strongly
alkaline liquor is cautiously evaporated to dryness, and then
treated in the way already described with three times its weight
of black oxide of manganese and one part of sulphuric acid
diluted with its own bulk of water, a much larger quantity of
crystals of kinone are obtained than can be procured from an
equal weight of the coffee-bean. This clearly shows that the
leaves are richer in caffeic acid than the beans.

Kinone may, I find, be obtained in small quantity by a similar
process from a great number of our commonest plants. Thus I
also obtained indications of kinone from the leaves and branches
of the privet, Ligustrum vulgare ; from the common ivy, Hedera
heliz ; from the Quercus Ilex, the evergreen oak of our gardens
and shrubberies, a native of Turkey; from the Quercus robur,
the common British oak; from the Udmus campestris, the com-
mon small-leaved elm; from the ash, Frawinus eaxcelsior ; and
from the bush-tea of the Cape of Good Hope, the Cyclopia lati-
folia of DeCandolle, a plant of the natural order Leguminosee.

From numerous plants which I tried I could not obtain a
trace of kinone, This was the case among others with laburnum,

as a substitute for Tea or for the Coffee-bean. 25

Cytisus laburnum, with tobacco, with Prunus spinosa, the sloe,
and others too numerous to mention.

The kinone was only obtained in crystals from the coffee-bean,
from the coffee-leaf, and from the holly, the Ilex aquifolium.
In all the other cases its existence was detected by the deep
yellow liquid which distilled over at a comparatively low tempe-
rature, and which yielded the dark humus-like coloration with
ammonia, so characteristic of solutions of kinone. Kinone is so
exceedingly soluble in water, that unless a considerable amount
of it is evolved, and proper precautions are employed, a deep-
coloured solution of it only is obtained either from the coffee-
leaf, the berry or the leaves of the holly. The comparatively small
amount of the kmone yieldimg substance, or perhaps we should
say substances, present in such plants as the privet, the oak, &c.,
is most probably the only reason why crystals of kinone have
not likewise been obtained from these plants.

In order to assist in forming an estimate of the comparative
value of coffee-leaves as a beverage as compared with the bean,
I determined the amount of soluble matter which each of them
yielded to boiling water. 6-048 grms. of dried coffee-leaves and
6-038 grms. of roasted and ground coffee-beans were repeatedly
treated with precisely similar quantities of boiling water, till the
liquid which came off from them was nearly colourless. The
6:048 grms. coffee-leaves were found to have lost 2:348 grms.
=38'8 per cent., while the 6:038 grms. roasted coffee-beans had
lost 1:759 grms. =29°1 per cent. From this determination it
is clear that coffee-leaves yield to boiling water nearly 10 per
cent. more soluble matter than the bean. In this respect, there-
fore, the coffee-leaf has an advantage over the berry.

So far as regards the two characteristic principles of coffee,
viz. caffeic acid and theine or caffeine, these are common both to
the leaf and the bean, the leaf being decidedly richer in both.
In other respects, however, they differ considerably. The coffee-
leaf contains some tannin, and scarcely any sugar or fat. The
coffee-bean contains about 12 per cent. of fat and “8 per cent.
of cane-sugar.”’ (See Joint Report.)

So far as I can judge, the infusion of the coffee-leaf has a
much greater resemblance to that of tea than to a decoction of
the coffee-bean ; so that should the coffee-leaf ever come into
general use in European countries, it will be rather as a substi-
tute for tea than for coffee. If the coffee-leaves were only dried
at a somewhat lower and better regulated temperature, I have
little doubt that they would yield a much more agreeable beve-
rage than can be made with the present roughly-roasted and
partially empyreumatized product.

Chemical Laboratory, St. Bartholomew’s Hospital,
December 1, 1853.

[ 26 ]

III. Examination of the Crystalline Deposit which forms in Oil
of Bitter Almonds. By Joun Stennovss, LL.D., F.RS*

HEN oil of bitter almonds is kept for some time in
loosely-stoppered bottles, a crystalline deposit not un-
frequently forms in it, especially if the oil is exposed to the
influence of the light. So long ago as 1823, M. Stange declared
this crystalline deposit to be simply benzoic acid produced by the
oxidation of the oil, a statement which was confirmed in 1830
by Robiquet and Boutron-Challard. (Ann. de Chim. et de Phys.
yol. xliy. p. 364.) It does not appear, however, that any of
these chemists subjected the supposed benzoic acid to the test of
analysis. Subsequently the late Dr. Jonathan Pereira, in the
first edition of his Elements of Materia Medica, page 1107,
stated that he had met with “three kinds of a crystalline sub-
stance from oil of bitter almonds, differing essentially from each
other and from benzoic acid.” These deposits were examined
by Dr. Pereira, and one of them, that marked No. 3, by Dr.
Letheby. None of them were subjected to analysis, but they
were tested by the action upon them of oil of vitriol, caustic
potassa, &e. These crystalline deposits were given to Dr. Pereira
by Mr. George Whipple, who kindly furnished me a few weeks
ago with no fewer than ten different specimens of a similar
character which had formed in as many portions of oil of bitter
almonds. The weight of the crystals exceeded three ounces.
The crystals had a deep yellow colour, and were strongly im-
pregnated with oil of bitter almonds. As much of the oil as
possible was removed by strongly compressing the crystals
between folds of blotting-paper. The crystals were then digested
with boiling water, in which they readily dissolved. After
repeated solutions and crystallizations they presented the usual
characters of benzoic acid. On analysis, 0°4215 grm. substance
dried at 212° F., when burnt in a current of oxygen gas, gave
1:069 carbonic acid and 0:2005 water =

Calculated numbers. Found numbers.
14C 4 68°853 69°167
6jEly Beton 4915 52838
40 26'282 25°460
100-000 100-000

The silver salt was prepared by neutralizing the acid with
ammonia and then adding a solution of nitrate of silver. When
subjected to analysis, 0°3883 grm. salt gave 0°525 carbonic acid
and 0°317 water.

* Communicated by the Author.

On the Crystalline Deposit from Oil of Bitter Almonds. 27
1:1711 grm. salt gave 0°5516 silver.

Calculated numbers. Found numbers.
AgO = 50°654 50°5383
WGC ar... poGod 36:909
5H 2'183 2:317
30 10°479 10:24]
100°000 100-000

From these results it is clear that the crystalline deposits from
oil of bitter almonds examined by me were simply benzoic acid,
and this I have reason to believe was also the case with two out
of the three samples described by Dr. Pereira; for through the
kindness of Professor Redwood I obtained three small specimens
of these deposits from Dr. Pereira’s collection, now in the pos-
session of the Pharmaceutical Society. That marked No. 1
I found to be simply benzoic acid. I received also a specimen
given to the Pharmaceutical Society by Mr. Whipple; it was
also benzoic acid. The specimen marked No. 8, and which
amounted only to a few grains in weight, was that examined by
Drs, Pereira and Letheby. © It consisted of small, acicular,
lemon-yellow crystals, which were insoluble in water, alcohol,
zther and acetic acid. Sulphuric acid reddened and then dis-
solved them, forming a deep yellow solution. They were not
dissolved by a solution of caustic potassa in the cold; when
heated with it, however, ammonia was evolved, which proved
that the crystals contained nitrogen. When the crystals were
strongly heated on platinum foil they melted and were decom-
posed, a small amount of sublimate only being produced.

The origin of the crystalline deposit No. 3 is very obscure.
Mr. Whipple informs me that he only obtained it on one occa-
sion, many years ago, when the essential oil of almonds was
prepared by distillation over the naked fire; but ever since the
operation has been effected by means of a steam apparatus, he
has never met with it again, and has merely obtained deposits
of benzoic acid. I strongly suspect that the yellow insoluble
erystals marked No. 3 were produced by the action of ammonia
on oil of bitter almonds, and that the ammonia on that occasion
was probably evolved by the charring of a portion of the nitro-
genous pulp of the almonds by the overheating of the bottom of
the retort. The crystalline deposits which form in oil of bitter
almonds must be regarded therefore (unless in the single some-
what inexplicable instance just stated) as simply benzoic acid
resulting from the oxidation of the oil.

L 28 ]

IV. On Xanthoxyline, a new Crystalline principle from Japanese
Pepper, the fruit of the Xanthoxylum piperitum of DeCan-
dolle. By Joun Stennovuss, LL.D., F.RS*

FEW months ago I received from my friend Daniel Han-

bury, Jun., Esq., a small quantity of a very singular fruit

from Japan, known in commerce as Japanese pepper. Mr. Han-

bury likewise kindly furnished me with the subjoined botanical
account of the tree from which it is obtained.

“ Japanese pepper is the produce of Zanthoxylum piperitum,
DeCand. (Fagara piperita, Linn.), a tree of Japan of the natural
order Rutacee, figured and described by Keempfer in 17127.

“Tt consists of roundish sessile capsules of the size of a pep-
percorn, which appear to have been normally four in number,
situated at the extremity of a peduncle, though but one or two
are usually fully developed. The capsules, which are externally
reddish-brown, have their outer covering beset with numerous
prominent tubercles enclosing an acrid liquid to which the pepper
owes its pungent flavour. The seeds are black, shining, and
devoid of pungency; from dehiscence of the capsules, they are
generally wanting in the sample which we have examined.

“The flavour of Japanese pepper is aromatic and agreeable,
with a pungency not unlike that of pellitory (Radix pyrethri).
Its odour when bruised is remarkably fragrant.

Tt is employed as a condiment by the Japanese and Chinese.”

The Japanese pepper, after being reduced to a coarse powder,
was digested with successive portions of spirits of wine till it was
rendered nearly tasteless; the greater portion of the spirit was
then drawn off by distillation, and the residue on standing for a
few days became filled with dark-coloured crystals of considerable
size. Their colour was owing to the presence of a resinous
matter, which adhered to them very tenaciously. The best way
of removing this dark-coloured resin is to wash the crystals with
cold liquor ammoniz, which dissolves the resin, leaving the
crystals unacted on. The crystals were rendered quite white,
and were easily obtained an inch in length by repeatedly dis-
solving them in ether, or in a mixture of alcohol and ether.

Through the kindness of Professor W. H. Miller of Cam-
bridge, 1 am enabled to subjoin the following figure and descrip-
tion of the crystalline form of xanthoxyline.

The crystals of xanthoxyline belong to the oblique system.

The angles between normals to the faces are :—

* Communicated by the Author.
t+ Amenitates, pp. 892-895.

Solution of a Question in the Theory of Probabilities. 29

be: SRR
vhs if i coeelel
TC 52 50
mh. 58 5
ee

Cleavage. , very perfect and easily obtained ; ¢, perfect.
The crystals are extremely thin in a direction perpendicular
to the face c.

The faces 7, m were so
imperfect that the angles Seen a
they make with b and c
could not be determined c’

with much accuracy.

Xanthoxyline is quite insoluble either in cold or hot water,
but it readily dissolves in alcohol or xther. Its solutions are
quite neutral to test-paper, and do not appear to possess either
acid or basic properties, The crystals of xanthoxyline melt at
80° C. Their taste is aromatic and resinous, not unlike that of
elemi or olibanum. The amount of xanthoxyline in Japanese
pepper is very considerable. A quantity of xanthoxyline, after
being dried at 100° Centigrade, was subjected to analysis in the
usual way.

I. 0°179 grm. substance gave 0°401 CO? and 0°104 water.

II. 0°1142 grm. substance gave 0°2558 CO? and 0:07 water.

I. Il.
Carbon . . 61:09 61:09
Hydrogen . 6°45 63
I subsequently found that xanthoxyline contains a small
quantity of nitrogen, the amount of which I was unable to deter-
mine from want of material. I confidently expect to obtain in
the course of a few months a considerable quantity of Japanese
pepper, when I hope to be able to complete its analysis. Not-
withstanding that xanthoxyline contains nitrogen, it does not
exhibit any basic properties, but in its general properties con-
siderably resembles the so-called stearoptens.

V. Solution of a Question in the Theory of Probabilities. By
Grorce Booin, LL.D., Professor of Mathematics in Queen’s
College, Cork*.,

HE question considered by Mr. Cayley in the Philosophical
Magazine for October 1853, p. 259, is a particular case of a
problem proposed by me in the Cambridge and Dublin Mathe-

* Communicated by the Author.

30 Mr. G. Boole’s Solution of a Question in

matical Journal in the month of November 1851. This may
justify my offermg a few remarks upon the subject.
The problem as considered by Mr. Cayley is thus stated.
Given the probability « that a cause A will act, and the pro-
bability p that A acting the effect will happen; also the proba-
bility @ that a cause B will act, and the probability g that B
acting the effect will happen: required the total probability of
the effect, supposed impossible in the absence of both the causes.
The solution given by Mr. Cayley is as follows. Let % be the
probability that the cause A acting will act efficaciously, yw. the
probability that the cause B acting will act efficaciously, Then
PHAAUL—AYWAS Pos ». Hees Ota)
g=e+(1—p)ra, deen ieee ts Sr pe ws
which determines A, uw, and the total probability u of the effect
will be given by
u=rAa+pB—ApoeB. . . . . . . (3)
Mr. Cayley shows that this leads to a correct result when
a=1. He further remarks, that the problem presents no dif-
ficulty.
I think it to be one of the peculiar difficulties of the theory of
probabilities, that its difficulties sometimes are not seen. The
solution of a problem may appear to be conducted according to
the principles of the theory as usually stated; it may lead to a
result susceptible of verification in particular instances ; and yet
it may be an erroneous solution. The problem which Mr. Cay-
ley has considered seems to me to afford a good illustration of
this remark. Several attempts at its solution have been for-
warded to me, all of them by mathematicians of great eminence,
all of them admitting of particular verification, yet differing from
each other and from the truth. Mr. Cayley’s solution is the
only published one I have seen, and I feel I must extend to it
the same observations. But in doing this, I willingly add that
I have two or three times attempted to solve the problem by the
same kind of reasoning, and have not approached so near the
truth as Mr. Cayley has done. ‘To illustrate these remarks, I
will first complete Mr. Cayley’s solution, and give one or two
apparent verifications, then exhibit the true solution ; and lastly,
make a few observations upon the general subject.
Ist. To complete Mr. Cayley’s solution, eliminate \ and u
from (1), (2), and (3); the result is

l—a(1—p)—u)(1—A(1—q)—u

Amali=—) 9080-9) —) Gig,
a quadratic equation from which wv must be determined. Sup-
pose that p=1 and g=1, the above equation gives

the Theory of Probabilities. 31
1—u=(1—a)(1—A),
oe u=1—(1 —a)(1—£),
a result obviously correct. For if either cause necessarily pro-
duces the effect, the probability of the effect is equal to the pro-
bability that both the causes will not be absent.

Again, suppose that « and § are very small, so that their
product may be neglected, then the solution gives

(1—u)?— (a(1—p) + A(1—g) )(1—u) = (1-2) (1-8) (1—u),

whence we find
u=ap + Bq. :

Now this is the known form of the solution when the causes
are mutually exclusive, so that they cannot coincide. But the
smaller their separate probabilities, the smaller is the probability
of their coincidence. And in the limit the two probabilities
correspond.

I suppose that few persons, after reading Mr. Cayley’s solu-
tion and noticing the above verifications, would feel any doubt of
its correctness; and yet it is certainly erroneous. Take the
particular cases of p=1 and g=0. It is evident that the pro-
bability of the effect ought then to be a. If the cause A always
produces the effect, and the cause B never, the probability of the
effect, there being no other causes to which it can be ascribed,
will be equal to that of the cause A. The equation (4), however,
becomes on clearing of fractions,

(l—u)(1—B—a) =(1—a)(1—8)(1—u),
whence either u=1, or

1—B8—u=(1—a)(1—8),

u=(1—8)—(1— )(1—8)
=a(1—f).
But neither of these results is correct.
2nd. I will now exhibit the true solution of the problem,
Representing, as before, by u the probability of the effect, the
value of that quantity will be determined by the solution of the
quadratic equation

RE Dad rl A ad) eA
l—u - «p+Bq—u ~~

Of this equation that root must be taken which is at the same
time not less than each of the two quantities

apand 8, °. 5 2) Oe ee 6)

wherefore

32 Solution of a Question in the Theory of Probabilities.

and not greater than any one of the three quantities

1—a(1—p), 1—B(1—g), ap+Bg. . « (7)
Moreover, whenever the data of the problem are real, 2. e. repre-
sent a possible experience, there will exist one root, and only
one root, of the above equation satisfying the conditions described.
The conditions of a possible experience are, that each of the
three quantities in (7) exceeds each of the two in (6).

The above solution may readily be verified in the case con-
sidered by Mr. Cayley, and in the three cases discussed in this
paper. Of these I will here confine myself to the last.

Clearing the equation of fractions, and making p=1, g=0,

we have
(1—u)(1—R—u)(a—u) =(1—u)(u—a)u.

This equation is satisfied by the values
tier — fi

but the conditions above stated restrict our choice to the first,
which we have before seen to be the true one.

8rd. Upon the nature of the errors which are most to be
apprehended in the solution of questions in the theory of pro-
babilities, I will only remark that they are not usually mathe-
matical, in the ordmary sense of that term, but arise from the
necessity of employing a logic of a peculiarly subtle or highly
complex character. When the data are the probabilities of in-
dependent simple events, the method of procedure is sufficiently
easy; but if those data relate to events occurrmg in combina-
tions, or connected by causal relations, the principles which
suffice for the former case become either inadequate or inappli-
cable. Laplace has to some extent vestigated the additional
new principles (derivable from the prior definitions and axioms
of the science) of which it is then necessary to take account.
But all these aids carry us but a short way in advance; and of
this I am fully assured, that no general method for the solution
of questions in the theory of probabilities can be established
which does not explicitly recognize, not only the special nume-
rical bases of the science, but also those universal laws of thought
which are the basis of all reasoning, and which, whatever they
may be as to their essence, are at least mathematical as to their
form. Such a method I have exhibited in a treatise now on the
eve of publication, and to which I must refer for the investiga-
tion of the problem, the solution of which has been exemplified
in this paper.

5 Grenville Place, Cork,

Noy. 30, 1853.

[ 33 ]

VI. Reports on the Progress of the Physical Sciences.
By Dr. Joun Tynpatt, F.R.S.

On the Conductibility of Metals for Heat. By G. WinDEMANN and
; R. Franz, Poggendorff’s Annalen, vol. Ixxxix. p. 497.

[With a Plate. |

oi the sense of touch as a thermoscope in experiments on

the conduction of heat succeeded the expedient of Ingen-.
housz, which consisted in coating rods of the substances to be
examined with wax, brmging one end into connexion with a
source of heat and observing the distance to which the wax
melted on the surface. Exact numerical results were, however,
wanting until Despretz took up the subject nearly thirty years
ago. In his experiments the bodies examined were reduced
to the shape of prismatic bars; in each bar, and at equal di-
stances apart, cavities were hollowed out for the reception of
mercury, into which dipped the bulbs of a number of sensitive
thermometers. One end of the bar was heated by a lamp with
a constant flame, and the heating was suffered to continue until
the temperature of the bar became constant. This of course
took place when the amount of heat received by any- cross section
of the bar from the section immediately preceding, was equal to
the quantity imparted to the following section and lost by radia-
tion in the same time. The thermometers under these circum-
stances formed a series decreasing in height from the hottest end
of the bar onwards. From the temperatures thus observed, it is
possible, by means of Fourier’s formula, to calculate the con-
ductive power of the bar for heat. In these experiments, however,
the breach of continuity caused by the introduction of the cavi-
ties and their contents must have exerted a disturbing influ-
ence. In the subsequent experiments of Langberg this difficulty
was avoided by the application of a thermo-electric element,
which was caused to press against the heated bar; the tempe-
rature being estimated from the deflection which it produced
upon a suitable galvanometer. A little reflection, however, will
suggest various expedients by which the accuracy of the mode
of observation introduced by Langberg may be increased ; and
this appears to have led to the recent resumption of the subject
by MM. Wiedemann and Franz, whose careful experiments con-
stitute the matter of the present report.

In an inquiry of this nature it is necessary that the exterior
conductivity, as it is called, should be the same in all the sub-
stances examined. Despretz secured this by coating all his bars
with the same description of varnish, thus imparting to them
the same radiative power. In the experiments of Wiedemann

Phil, Mag, 8. 4. Vol. 7. No, 42, Jan, 1854, D

34 Dr. Tyndall on the Progress of the Physical Sciences :

and Franz the same object is attained by silvering the bars. As
the latter were thin, a very necessary precaution was to shelter
them from currents of air, and to preserve the surrounding air
at a constant temperature. The arrangement also permitted of
the bars being examined in vacuo. The following description
will, we doubt not, render the manner of experiment sufficiently
plain without having recourse to a figure.

Each bar was caused to oceupy the axis of a cylindrical vessel -
of glass, being retained in this position by causing the ends of
the bar to rest in two tubes fixed in the ends of the cylinder.
The tube at one end was extended, and surrounded by a space
which communicated with a vessel of boiling water. ‘When this
space was filled with steam, heat was communicated to the tube
and to the bar within it, whence it propagated itself through
the mass of the bar. Through the opposite end of the glass
cylinder, and at some distance from its centre, a rod was caused
to pass which was capable of sliding up and downair-tight. To
the end of this rod was attached the thermo-electric element,
which by turning the rod could be caused to press against the
heated bar. Two thin wires, one of iron, the other of German
silver, formed the thermo-electric element, the wires being cut
across obliquely and thus soldered together. The moveable rod.
was graduated, and a fixed index was attached to the end of the
cylinder; it was thus in the experimenter’s power to cause the
thermo-electric element to press against the bar at any required
distance from its heated end. The points of the bar thus ex-
amined were at a constant distance of two inches apart. By
means of a tube which communicated with the interior of the
glass cylinder, the latter could be connected with an air-pump
and exhausted. During the experiments the entire cylinder
was immersed in a vessel of water, which was preserved at a con-
stant temperature of 12° C.

The following tables contain the results of the experiments
with the substances therein mentioned. To facilitate compa-
rison, the temperature of the zero-point of each bar is reduced to
100 by multiplying each entire series of observations by a suit-
able factor. ‘The figures under w represent the distances reckoned
from zero, and taken, as before remarked, from two to two
inches ; the adjacent figures represent the corresponding tempe-
ratures, and the last column in each case contains the mean of
experiments made with different bars.

Wiedemann and Franz on the Conductibity of Metals for Heat. 35

I, Experiments with the cylindrical vessel full of Air.
1. Silver, 5 millims. thick.

z. Mean.
0 100-0 100:0 100-0 100:0
2 78-2 731 73:1 781
4 61-1 60°6 61:0 60°9
6 48-0 46:7 47-0 472
8 37°4 365 36-4 36°38
10 27-7 28°5 27°5 27°9
12 - 19:0 21-9 20°3 20°4
14 12-2 Liesl ce bierssee 14:4

ba
i
—
$
5

0

2 75°4 75°6 76:2 7671 76:0 758
4 2

6

8 32°6 80°5 32-9 33°5 31:7 32'2

10 23:0 21-6 23°6 24:1 22°4 23°0
12 15:9 141 16:3 16-4 14:9 15°5
14 Uae 3 Pca eee Fasene eabanss || usersss 9°8

8. Gold, 5 millims. thick, 4. Brass, 5 millims. thick.

—————— TT nn

a Mean. Mean.

0 100-0 100-0 100-0 100-0 100:0 1000 | 100-0
2 74:5 74:1 74:3 61:4 60°7 60:9 61:0
4 53°1 53°6 53°3 38°'8 35°9 37°6 37-4
. 37:2 38°9 38:0 246 23:3 25°6 24:5
0
2

25°6 271 26:3 15:7 12:7 173 16°5
15-7 18°1 16:9 DD} = casters |i teste 9-2
apsane 10°8 10°8 4:3 stesns BEA 4:3

5. Iron, 6. Steel, 7. Platinum,
5 millims. thick. 5 millims. thick. 4°75 millims. thick.

6 Dr. Tyndall on the Progress of the Physical Sciences :

8. German silver,
5 millims. thick. 6°2

4). Brass,
millims.thick.

9. Tin,
6:2 millims. thick.

x Mean
0 100:0 100-0 100-0 100:0 100-0
2 39°1 65:1 57-4 58-1 Sy rf
4 16:2 42-1 338 SHR; 34°5
6 6:4 25:9 19-7 21:3 20°5
8 2-0 14:7 117 12°6 12-1
10 8-0 72 76
12 | 46 38 42
10. Lead, 11. Rose’s fusible metal, 12. Bismuth,
6:2 millims. thick. 6 millims. thick. 6 millims. thick.
a |
0 100-0 1000 100-0
2 47'3 29°7 17:9
4 239 10:2 4-4
6 12:1 41
8 6-4
10 34
12 1:2

Il. Experiments with cylinder exhausted.

1. Silver, 3. Gold,
5 millims. thick. 5 millims. thick.

2. Copper,
5 millims. thick.

a. Mean. Mean
0 |100-0 | 100-0 | 100-0 100:0 100:0 | 100-0 | 100:0
2 86:8 | 86:1 | 86-4 82:0 82:9 | 82:9 | 82-9
4 74:0 | 73:7 | 73:9 68°5 67°5 | 67:5 | 67°5
6 64:1 | 62:9 | 63:5 568 54:1 | 53:4 | 53:7
8 541] 53:6 | 53:9 45-3 | 43:1 | 43:4 | 43:3

10 45-4 | 45°6 | 45°5 35°0 33°6 | 33°6 | 33°6

12 37:9 | 389 | 38-4 ATE ae oma, gi | eee 8 23°8 | 23°8

14 BOB Se taiheL GO ilty. fe 2 pees. ON Lac dves 16:0 | 16:0

4. Brass, 5. Iron, 6. Steel,

5 millims. thick. 5 millims. thick. 5 millims. thick.

z | | Mean. Mean.
0 1000 || 100-0 100-0 100-0 190:0 100:0 | 100°0
2 73:0 | 67°4 66:7 67:1 €3°9 64:2 64:0
4 59°5 453 43°7 445 42:6 408 41°7
6 46:0 i 29'8 29-4 29°6 27:4 26°5 26°9
8 35'0 | 19°'8 18-2 19:0 18:3 16°2 17-2

10 27°0 || 14: 1 11-2 12-6 VOD ah Poe. 10:9

12 | 205 ||

14 15:5 |! |

Wiedemann and Franz on the Conductibility of Metals for Heat. 37

7. Platinum, 8. German silver, 4b. Brass.

4°75 millims. thick. 5 millims. thick. 6°2 millims. thick.
x. Mean.

0 | 100-0 | 100-0 | 100-0 100:0 . 190:0 Hs

2 63°5 | 64:8 | 64:2 63:1 792

4 40°7 | 43:7 | 42:2 35:0 61-2

6 29:1 | 29°9 | 29-0 24:0 47-0

8 20:2 | 20:3 | 20:2 15:8 35'2

10 1299 | 14:1 | lod 8-9 25°8

12 8-6 | 10:9 96 56 19-1

14 | 33 123

11. Rose’s
9. Tin, 10. Lead, fusible metal,
6:2 millims. thick. 6:2 mullims. thick. 6 millims. thick.

x Mean. Mean
0 | 100-0 | 100-0 | 100-0 100°0 100-0 | 100°0 100:°0
2 72°38 | 73-7 | 73:2 66:5 63-9 | 65:2 60°1
4 53:5 | 548 | 54:2 44-6 ALS 43°1 36:2
6 391 | 39:9 | 39-5 27°9 26°5 27°2 22°9
8 28:5 | 28:5 | 28°5 18:6 166 | 17°6 15°6
| 10 20:4 | 20-6 | 20°5 117 97 10°7 8:5
12 140 | 145 | 14:2 66 Aches oO 53
| 14 90 8:8 8:9

Taking the bar experimented with in each case as a datum
line, marking the points at which the observations were made
along it, and erecting at each point a perpendicular to express
the temperature at that point, we obtain, by uniting the ends
of all the perpendiculars, a curve which represents the manner
in which the heat is distributed throughout the bar. In Plate I.
this process is carried out for each bar, the curves which refer to
the thicker bars being distinguished from the others by being
drawn in dotted lines.

Remembering that the steepest curves belong to the substances
which conduct heat the most imperfectly, we obtain from the
diagram the order of conductivity as follows :—

I. Thin bars.
Silver,
Copper,

Gold,

Brass,

Tron,

Steel,
Platinum,
German silver.

38 Dr. Tyndall on the Progress of the Physical Sciences :

II. Thicker bars.
Brass!
Tin,
Lead,
Rose’s metal,
Bismuth.

The foregoing results enable us, however, to give numerical
expression to the relative conductivity of the various bars. Ifa
metallic rod with the transverse section © and periphery y be
heated at two points above the surrounding medium, and if the
temperature Up, V,, V2 of three different points which are separated
from each other and a constant interval « be determined, then,
according to Fourier, we have the following relation :—

g= vy +0, n/t an J hy

la+e di
>, + Q;

where / denotes the interior, and / the exterior conductivity of
the rod.

ee Ae! 1
Setting e " @=z, we have r+ — eg: and
TOY ge: ot
- 0% Toga)

In the experiments at present under consideration, the distance
a, and also the exterior conductivity /, are in all cases the same.
Further, the cross section of the bar is a circle ; andif its thick-

ness =d, we have += ~ If two different bars, therefore, pos-
sess the conductivities 7 and /,, the thicknesses d and d,, and the
values x and 2, calculated from the observed quotients q and q,,

we have

“dy (log a)”

It is easy to see that a very small alteration of the quotient g
is sufficient to cause a considerable change in the conductivity /
calculated from it. If, for example, the quotient varies between
the numbers2°032 and 2:035, the calculated conductivities change
from 152 to 166. Since, therefore, a small error of observation
carries along with it a large alteration of the calculated conduc-
tivity, the numerical values obtained from the quotients in
question must not be considered more than approximate. The
curves to which we have already referred the reader are certainly
calculated to give a more correct notion of the distribution
throughout the different bars than the numbers derived from the
application of the foregoing formula. Nevertheless, as a nume-

Wiedemann and Franz on the Conductibilityof Metals for Heat. 39

rical comparison may be desirable, we here present it to the
reader. In the following table the conductivity of silver is as-
sumed to be 100, and certain trifling corrections are introduced
for the purpose of translating the indications of the galvano-
meter into those of the ordinary thermometer :—

Cylinder full of air. | Cylinder exhausted.

Metals.
q: i. q- i
BilVEE wis. ccssestii. 2:0456 | 100 2:0145 | 100
Copper ssissesessee 2062 73°6 20195 74:8
Gold) ccascveor-sesssli 2000 53-2 2-027 54:8
Stabs) -cstececsscsee4 2200 23°1 2-058 25-0

Brass 2 (thick) ...) 2154 24:1 | 2-051 230
ssssees| 2°264 14:5 | 2-076 15-4

TB ps n0500dees

NEON: Tektvcakics sacs 2-393 11:9 2-144 10-1
MGGEL Eloceccavsaases 2-405 11°6 2°1395 10:3
BiGAG! sii asiecaas 2-445 85 2-149 79
Platinum ......... 2597 8-4 2-163 9:4
German silver .,.| 2°772 63 2-201 73
Rose’s metal ...... 3434 2°8 2°44] 2°8
Bismuth ............ 4565 1:8

Twenty years ago Professor Forbes was led to suspect that
those metals which conducted heat most perfectly were also the
best conductors of electricity*. We here transcribe a table,
comparing the results arrived at by Wiedemann and Franz on
heat, with those obtained by Riess, Becquerel and Lenz, upon
electricity.

Conductivity for electricity. Conductivity for heat.
Name of body. oe
@ iess. | Becquerel.| Lenz, Wiedemann and Franz.
EIGER sscesefasases 100 100 100 100

Copper ..s.ss.s.00 66°7 91:5 733 736
Gold « seusstccsiss ees 59:0 64:9 58°5 53°2
PATBSS ha rs caacinn stas 1? a Re 21°5 23°6
BAN a oawaes¥noes oo 10-0 14:0 22°6 14:5
POT Vek cedddssostas 12:0 12°35 13:0 119
BAGG) Hye) is -<pypesst-| |) stexie yi] 5 - sees dr fur | Hohaess 116
1 ts a ere 70 8-27 10-7 85
Platinum ....... ; 10°5 7:93 10:3 84
German silver Bi [ee ears Salty. 63
18

Whatever the quality may be upon which calorific conduction
depends, the above table renders it exceedingly probable that
the same quality influences in a similar manner the transmission
of electricity ; for the divergences of the numbers expressing
the conductivity for heat from those expressing the conductivity
for electricity are not greater than the divergences of the latter
alone, exhibited by the results of the different observers.

* Phil. Mag. S, 3. vol. iv. p. 27.

[ 40 J

VII. On the Theory of Groups, as depending on the Symbolic
Equation 0’°=1. By A. Cayiry, Esq.*

: Bae 6 be a symbol of operation, which may, if we please,

have for its operand, not a single quantity z, but a system
(z, y...), so that

Olin ace (at sof see)

Where 2’, y'.. are any functions whatever of v, y..., it is not
even necessary that a’, y!.. should be the same in number with
z,y... In particular 2’, y', &e. may represent a permutation
of x, y, &e. @ isin this case what is termed a substitution ;
and if, instead of a set v,y.., the operand is a single quantity z,
so that 6v=z'=fzx, @ is an ordinary functional symbol. It is
not necessary (even if this could be done) to attach any meaning
to a symbol such as 6+¢, or to the symbol 0, nor consequently
to an equation such as 6=0, or 0+¢=0; but the symbol 1
will naturally denote an operation which (either generally or in
regard to the particular operand) leaves the operand unaltered,
and the equation @=¢ will denote that the operation @ is (either
generally or in regard to the particular operand) equivalent to ¢,
and of course 0=1 will in like manner denote the equivalence
of the operation @ to the operation 1. A symbol @¢ denotes the
compound operation, the performance of which is equivalent to
the performance, first of the operation ¢, and then of the opera-
tion 6; @¢ is of course in general different from $0. But the
symbols 0, @.. are in general such that 6. dby=0¢.x, &e., so
that Opy, Odyw, &c. have a definite signification independent of
the particular mode of compounding the symbols; this will be
the case even if the functional operations involved in the symbols
0, ¢, &e. contain parameters such as the quaternion imaginaries
2,7, k; but not if these functional operations contain parameters
such as the imaginaries which enter into the theory of octaves,
&c., and for which, e. g. «.@ry is something different from «8.y,
a supposition which is altogether excluded from the present
paper. The order of the factors of a product @dy.. must of
course be attended to, simce even in the case of a product of ©
two factors the order is material ; it is very convenient to speak
of the symbols 6, ¢. . as the first or furthest, second, third, &c.,
and last or nearest factor. What precedes may be almost entirely
summed up in the remark, that the distributive law has no ap-
plication to the symbols 0¢..; and that these symbols are not
in general convertible, but are associative. It is easy to see that
6°=1, and that the index law 6”. 6"=0”"", holds for all posi-
tive or negative integer values, not excluding 0. It should

* Communicated by the Author.

On the Theory of Groups. Al

be noticed also, that if 0=¢, then, whatever the symbols a, @
may be, a08=a¢8, and conversely.
A set of symbols,
Le faias

all of them different, and such that the product of any two of
them (no matter in what order), or the product of any one of
them into itself belongs to the set, is said to be a group*. It
follows that if the entire group is multiplied by any one of the
symbols, either as further or nearer factor, the effect is simply
to reproduce the group; or what is the same thing, that if the
symbols of the group are multiplied together so as to form a
table, thus :-—
Further factors.

1 Sia B
1 peat PTB apo Pal im

a a? | Ba

8| 8 |ee| &

Nearer factors.
g

that as well each line as each column of the square will contain
all the symbols 1, 4, 8.. It also follows that the product of
any number of the symbols, with or without repetitions, and in
any order whatever, is a symbol of the group. Suppose that the

group
ae: ee

contains 7 symbols, it may be shown that each of these symbols
satisfies the equation
items le

so that a group may be considered as representing a system
of roots of this symbolic binomial equation. It is, moreover,
easy to show that if any symbol « of the group satisfies the
equation 6’=1, where r is less than n, then that 7 must be a
submultiple of 2; it follows that when n is a prime number, the
group is of necessity of the form

Lee on ee, lane),
And the same may be, but is not necessarily the case, when
n is a composite number. But whether x be prime or com-
posite, the group, assumed to be of the form in question, is in
* The idea of a group as applied to permutations or substitutions is due

to Galois, and the introduction of it may be considered as marking an
epoch in the progress of the theory of algebraical equations.

42 Mr. A. Uayley on the Theory of Groups,

every respect analogous to the system of the roots of the ordi-
nary binomial equation «"—1=0; thus, when is prime, all the
roots (except the root 1) are prime roots; but when 2 is com-
posite, there are only as many prime roots as there are num-
bers less than m and prime to it, &c.

The distinction between the theory of the symbolic equation

6"=1, and that of the ordinary equation 2”"—1=0, presents
itself in the very simplest case n=4. For, consider the group
1, «, By,

which are a system of roots of the symbolic equation
Ce as

There is, it is clear, at least one root 8, such that 8? =1; we
may therefore represent the group thus,

|e a, B, af, (B?=1) ;
then multiplying each term by @ as further factor, we have for
the group 1, 2”, «@, «8, so that a* must be equal either to 8 or
else to 1. In the former case the group is

a a, ae”, a3, («#=1),
which is analogous to the system of roots of the ordinary equa-

tion at—1=0. For the sake of comparison with what follows,
I remark, that, representing the last-mentioned group by

1 » ay B yo ETS

A a, B, fy

we have the table

Bale ae a oe

(eyo nea el ee

If, on the other hand, «?=1, then it is easy by similar reasoning
to show that we must have «8= fa, so that the group in the

case 18
1, a, B, 4B, (#=1, P=1, «B=Ba) ;
or if we represent the group by

1, a, B, Y
we have the table

as depending on the Symbolic Equation 6"=1. 43
] a) iBiaoy

Bel J pom Bae

iy a i) BFR ey
Bs Bi pomek 1

a

ea ena. ae tL

Or, if we please, the symbols are such that

— a? = 8B? =y?=1]
a=By=y8
B=ya=a8
y=aB=Ba.

Systems of this form are of frequent occurrence in analysis,
and it is only on account of their extreme simplicity that they
have not been expressly remarked. For instance, in the theory
of elliptic functions, if n be the parameter, and

c +n c(l+n
a)=< B()=—F42 (ny = —- 0 4),

then a, 8, y form a group of the species in question. Soin the
theory of quadratic forms, if

a(a,b,c)=(c, 0, a)

B(a, b, e)=(a, —b, e)

(a, 6, c)=(c, —d, a) ;
although, indeed, in this case (treating forms which are pro-
perly equivalent as identical) we have «=, and therefore y=1,
in which point of view the group is simply a group of two symbols
1, a(a®=1),

Again, in the theory of matrices, if J denote the operation of
inversion, and ¢r that of transposition, (I do not stop to explain
the terms as the example may be passed over), we may write

a7, BH vel .ir=sitrl.
I proceed to the case of a group of six symbols,
I, a, B, ve 6, €,
which may be considered as representing a system of roots of the
symbolic equation
ae
It is in the first place to be shown that there is at least one

ded. Mr. A. Cayley on the Theory of Groups,

root which is a prime root of 6°=1, or (to use a simpler expres-
sion) a root having the index 3. It 1s clear that if there were a
prime root, or root having the index 6, the square of this root
would have the index 3, it is therefore only necessary to show
that it is impossible that ad/ the roots should have the index 2.
This may be done by means of a theorem which I shali for the
present assume, viz. that if among the roots of the symbolic
equation 6”=1, there are contained a system of roots of the sym-
bolic equation 6”=1 (or, in other words, if among the symbols
forming a group of the order there are contained symbols form-
ing a group of the order p), then p is a submultiple of n. In
the particular case in question, a group of the order 4 awe
form part of the group of the order 6. Suppose, then, that y,
are two roots of 6®=1, having each of them the index 2; then
if yd had also the index 2, we should have yo=6y; and 1, y,
6, dy, which is part of the group of the order 6, would be a
group of the order 4. It is easy to see that yS must have the
index 3, and that the group is, in fact, 1, 6, dy, y, 6, yoy, which
is, in fact, one of the groups to be presently obtained ; I prefer
commencing with the assumption of a root having the index 3.
Suppose that « is such a root, the group must clearly be of the
form
1, a, a, y, ay, ay, (#8=1);

and multiplying the entire group by ¥ as nearer factor, it becomes
ry, ary, ce-ry, ry?, cery?, ey? ; we must therefore have y?=1, a, or a”.
But the supposition y*=«? gives y4=at=a, and the group is
in this case 1, y, ¥”, y°, y4, y° (y8=1); and the supposition
y°=« gives also this same group. It only remains, therefore,
to assume y?=1; then we must have either ya=ay or else
ya=a’y. The former assumption leads to the group

1, a, a, y, ay, wy, (#=1, =1, ye=ay),
which is, in fact, analogous to the system of roots of the ordinary
equation a—1=0; and by putting ay=A, might be exhibited
in the form 1, A, A%, A3, A4, A®, (A°=1), in which this system
has previously been considered. The latter assumption leads to
the group

1, a, a, y, ay, ay, (08 =1, y?=1, ya=a*y).
And we have thus two, and only two, essentially distinct forms
of a group of six. If we represent the first of these two forms,
viz. the group

1, a, a, ry, ay, any, (= 1, y?=1, yas ary)
by the general symbols

1, od) B, Y> 5, €,

we have the table

as depending on the Symbolic Equation 0"=1. 45

1 3 a, B 3 % 8, E

BAcBeh 9 ) € 1 a
Y
)

is
)

Epreiah darlece | a aan

while if we represent the second of these two forms, viz. the
Beep

1, a, a, y, ay, ay, (e=1, y=1, ya=a*y),
by the same general symbols
ibe a, B, Y 5, é,

we have the table

or, what is the same thing, the system of equations

1=fa=aB=y? ==?

a= 2? =by =ed =e

B=a? =ey =75 =de

y= ba =eB =Bd=ae

S=ca =yB =ay=Pe

e= ya =58 =By=a6.

An instance of a group of this kind is given by the permuta-

46 On the Theory of Groups.

tion of three letters ; the group
1; a, B, > 8, €
may represent a group of substitutions as follows :—
abe, cab, bea, acb, cha, bac
abe abe abe abe abe abe.

Another singular instance is given by the optical theorem
proved in my paper “On a property of the Caustics by refrac-
tion of a Circle.”

It is, I think, worth noticing, that if, imstead of considering
a, 8, &c. as symbols of operation, we consider them as quan-
tities (or, to use a more abstract term, ‘ cogitables’) such as the
quaternion imaginaries ; the equations expressing the existence
of the group are, in fact, the equations defining the meaning of
the product of two complex quantities of the form

w+aa+bB+...
Thus, in the system just considered,
(w+aae+bB+cy+d8+ ee) (w! +aa+B+cy+d's+ee)
=W-+Aa+B6+Cy+D6-+ He,
where
We=ww! +ab! +db+ ce +dd'+ee
A=wd +w'a+ bb! + de! + ed! + ce!
B=w! + w'b + aa! +ec! + cd'+de!
C=we +w'c+da' + eb! + bd'+ae
D=wd! + w'd+ ea! + cb! + ac + be
B=we +w'e+ca! + db! + be 4- ad’.

It does not appear that there is in this system anything ana-
logous to the modulus w?+a?+y?+2*, so important in the
theory of quaternions.

I hope shortly to resume the subject of the present paper,
which is closely connected, not only with the theory of alge-
braical equations, but also with that of the composition of
quadratic forms, and the ‘irregularity’ in certain cases of the
determinants of these forms. But I conclude for the present
with the following two examples of groups of higher orders.
The first of these is a group of eighteen, viz.

# a, B, Y ap, Ba, aY, V4 By; ¥B, apy, Bye, yaB,
aa, ByB; YeY> apyB, ByBa,
where

rt —t i =i, y=1, (By)>=1, (ye)? =1, («P)?=1,
(aBy)?=1, (Bya)?=1, (ya8)P=1 ;

Mr. W. R. Grove on the Electricity of the Blowpipe Flame. 47
and the other a group of twenty-seven, viz.

1, a, a, ¥; V7, V4) &Y; ya, ary, 7, ay”, ya, ary”,
caryce, eury7ce, otrycr, ary 2ee, crrycn®, cary?ar®, cxPryen”, cxry?ee?,
yay, yey, pray, yay,
aya, yayra?,
where
aF=1, FP =1, (ya)2=1, (y2a)2=1, (ya?) =1, (y*o?)P=1.
It is hardly necessary to remark, that each of these groups is
in reality perfectly symmetric, the omitted terms being, in virtue
of the equations defining the nature of the symbols, identical
with some of the terms of the group: thus, in the group of 18,
the equations 22=1, 6?=1, y?=1, («Py)*=1 give aBy=yfa,
and similarly for all the other omitted terms. It is easy to see
that in the group of 18 the index of each term is 2 or else 3,
while in the group of 27 the index of each term is 3.

2 Stone Buildings, Nov. 2, 1853.

VIII. On the Electricity of the Blowpipe Flame.
By W. R. Grove, F.R.S. &c.*

OLTA and Erman made known the first indications of the

production of electricity by flame. Pouillet and Becquerel

have experimented and reasoned on the statical effects of such

electricity, while Andrews, and more recently Hankel and Buff,

have published very interesting results on the effects of flame as
to conduction and production of voltaic electricity.

The experiments of which I am about to give a notice were
for the greater part made before I had read the papers of the
two last authors; and while they in many respects differ from
theirs, they give a means of producing a voltaic current from
flame far more distinct and powerful than any which I have tried
or read of.

The flame I have worked with is that of naphtha or spirits of
wine, urged by an ordinary glass-worker’s blowpipe ; and with a
galvanometer, the needles of which are barely deflected to 2° by
any current which I can procure by the flame of a common
spirit-lamp, I can by the blowpipe flame procure deflections of
20° or even 30°, and with great certainty and uniformity of
direction.

I am not aware that the blowpipe flame has ever been used
for the production of electricity, though I see by M. H. Bec-

* Communicated by the Author.

48 Mr. W. R. Grove on the Electricity of the Blowpipe Flame.

querel’s recent paper that M. Becquerel, sen. has used it asa
means of adventitiously heating a spiral placed in another
flame.

Two platinum wires of 6 inches long and =4,th of an inch dia-
meter have their ends formed into coils of 3th of an inch long and
wide ; these wires are attached to copper wires insulated by glass
stands, and having their further extremities connected with a
galvanometer. My galvanometer is by Ruhmkorf; the wire is
not as long as those now constructed, being only 544 feet, but
I have magnetized the needles so as to render them highly
astatic; they take four minutes to make one oscillation.

An additional binding screw is connected with the wire at 54
feet, so that I can ascertain by the same instrument the effect
of a slighter resistance.

When the flame of a spirit-lamp is urged by the blowpipe,
one of the above-mentioned coils is placed in the full yellow flame
just beyond the apex of the blue cone, and the other near the
orifice of the brass jet, or at what may be called the root of the
flame, just above the base of the blue cone, the distance between
the two coils being 23 inches. The coil in the full flame is at a
white heat brilliantly incandescent, the coil near the orifice or at
the commencement of the flame is cherry-red. The galvano-
meter is deflected to an average of 6°, the coil near the orifice or
at the root of the flame being positive, or related to the further
coil as zine to platinum in the voltaic trough. On reversing the
position of the wires, the galvanometer is deflected 6° in the
opposite direction.

This current is not due to thermo-electricity excited in the
wires at the poimt of junction of the platinum and copper, for it
is unaltered in direction by a powerful thermo-current excited
in these by heating the points of junction by another spirit-
lamp.

By making this thermo-current aid or counteract the flame-
current, a slight difference in degree is perceptible in the deflec-
tion according as the point of junction of the one or other wire
is heated, but no difference in direction.

The flame-current, moreover, scarcely affects the short wired
galvanometer, while the thermo-current of copper and platinum
whirls the needle to 90°.

It is not a thermo-electrie current arising from the unequal
heating of the two coils, for it is in the same direction when the
further coil is removed from the full flame so as to be less heated
than the coil at the root of the flame. It is also different im
direction from the thermo-current produced by unequally heating
the coils in similar parts of the flame, or the current described
by M. Buff, and to which he ascribes the electricity of flame.

Mr. W. R. Grove on the Electricity of the Blowpipe Flame. 49

The flame-current proper in my experiments is opposed to, and
conquers the thermo-current.

On advancing the coil from the root of the flame towards the
further coil, the deflection lessens, but still preserves its direction
until the wires get very closely approximated, when the deflec-
tion of the flame-current yields to that of the thermo-current,
and the direction of the needle depends on the relative heat of
the coils.

A wire of zine near the root of the flame with the platinum
coil in the full flame gave a much smaller deflection, only 2° ;
when the direction of these wires was reversed, the current was
stronger, the galvanometer marking 5°: the direction of the
deviation was in both instances the same as with platinum and
platinum.

Iron and copper acted as zinc, but rather more feebly. As
in these experiments the wires of zinc, iron, and copper respect-
ively were stouter than the platinum wire, I attribute the supe-
rior amount of deflection when the oxidable metal was in full
flame to the greater cooling effect of the thicker wire reducing
the antagonizing thermic current.

As the above experiments seemed to show that there was a
proper flame-current irrespective of, and even overcoming the
thermic flame-current, I was led to expect that by uniting in
direction these two currents I might get more marked results.
The following experiment, it will be seen, realized this expec-
tation.

I formed a little cone of platinum foil of {ths of an inch in
depth, and the same width at the widest part ; I suspended this
in a ring of platinum wire and substituted it for one of the
coils.

Being placed in the full flame, the coil being at the root, it
was filled with water, and water dropped into it from a pipette to
supply that which was boiled away. I now readily obtained a
deflection of 20° in the same direction as in my original experi-
ment, and frequently the needles deviated to 30°. When the
cone filled with water was placed at the root and the coil in the
full flame, the deviation was only 5°.

In all the above experiments with the blowpipe it will be seen
that the direction of the current was, as far as a comparison can
be instituted, the reverse of that indicated in the experiments of
Hankel, excepting his experiment with the flame of hydrogen ;
and also the reverse of the greater part of the experiments of
Buff, which he rightly attributes to thermo-electricity.

One result of M. Buff (Archives d’ Electricité, vol. xvii. p. 275)
when he places one wire in the centre and the other at the outer
margin of the flame, is probably dependent on a similar cause to

Phil, Mag. 8. 4. Vol. 7. No, 42. Jan, 1854. K

50 Mr. J. J. Sylvester on a Point of Notation.

mine ; though when he places the second wire in the full flame,
the current is in a contrary direction to that which I obtain.

My experiments prove, I think, distinctly, that there is a vol-
taic current, and that of no mean intensity, due to flame and
not dependent on thermo-electricity.

I know of no better theory to account for these results than
that which Pouillet applied to the effects on the condenser, viz.
that it is the result of combustion ; the platinum at the com-
mencement of chemical action, or where the elements are enter-
ing into combination, being as the zinc of the voltaic battery ;
and that at the termination of combustion, or at the points
where the chemical action is completed, being as the platinum
of the voltaic combination.

Although there is a distinct thermo-current produced by the
contact of two unequally heated bodies with flame, yet when we
see, as in the above experiments, a marked current, in a contrary
direction to, and overcoming that which is excited by the thermo-
current in the flame, and also that at the points of junction of
the wires without the flame, I see no means of viewing the re-
sulting current as a thermo-current. The blowpipe flame, from
its definiteness of direction, brings out most distinctly this cur-
rent; in other flames, from the more confused circulation of the
heated and burning particles, the results are less significant ;
and the various flame-currents counteracting each other, the
thermic current obtains a predominance.

The current from the blowpipe flame, when the platinum in
the full flame is cooled, is so marked, that I have little doubt, by
attaching to a powerful pair of bellows a tube from which a row
of jets proceeds, and alternating pairs of platinum in flames urged
by the jets, a flame-battery might be constructed which would
produce chemical decomposition and all the usual effects of the
voltaic pile.

IX. Note ona Point of Notation. By J.J. Syivester, F.R.S*

| frequently becomes important in algebraical investigations,

and in the representation of results, to have a means of

expressing that the sign + or — is to be affixed to an algebraical
expression, according as certain indices 0,, 05, 03,...@, which
occur therein, and which represent the natural numbers from 1 to
nin some regular or regular order, can be derived from the fun-
damental arrangement 1, 2, 3,...2 by an even or by an odd
number of interchanges. An example of this occurred in my

* Communicated by the Author.

ee ee ond

se See ee ee

Royal Society. 51

short paper in the last Number of the Philosophical Magazine,
on the extension of Lagrange’s Rule of Interpolation, where I
used to denote that such a choice of signs was to be made, the
awkward and unsuggestive symbol “?” There exists, however,
a very simple algebraical mode of denoting the presence of the
factor +1 or —1, according to the order of the natural num-
bers in the scale 0), 05, @3,...@,,.

fhas been always consecrated by me to the purpose of signifying
that the product of the squared differences is to be taken of the
elements with which it is in regimen ; and in the paper adverted to
I introduced the highly convenient new symbol ¢? to denote that
the product is to be taken of the simple differences obtained by
subtracting from each element in regimen therewith every sub-
sequent element in the arrangement of the elements as set down.
By aid of this new symbol ¢?, the positive or negative character
of any permutation, as 0,, 0,,... @,, can be completely expressed;
for £4(0,, Ao, 03, ... 9,)+€#(1, 2, 3,...n) will be +1 or —1
according as 1, 2, 3,...nand 6,, 6, 3,...@, belong to the
same group, or to opposite groups in the natural dichotomous
separation of the permutations of the m symbols in question, and
thereby the desired object of giving a functional representation
of the ambiguous sign is perfectly attained.

X. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from vol. vi. p. 306.]
Nov. 17, 1853.—Dr. Wallich, V.P., in the Chair.

ig following papers were read :

1. “On the Nerves which supply the Muscular Structure of
the Heart.” By Robert Lee, M.D., F.R.S.

The author remarks that, in a paper entitled ‘“‘ On the Ganglia
and Nerves of the Heart,” published in the Philosophical Trans-
actions, Part I. 1839, it is asserted, that ‘‘it can be clearly demon-
strated that every artery distributed throughout the walls of the
uterus and heart, and every muscular fasciculus of these organs, is
supplied with nerves upon which ganglia are formed.”

He then states that ‘“ recent dissections which I have made of
the heart of the race-horse, in which both the muscular and ner-
vous structures are largely developed, demonstrate, that from the
outer surface to the lining membrane the walls are universally per-
vaded with nerves, on which ganglia are formed, or enlargements
invested with neurilemma, into which nerves enter and from which
they issue, as in all the other ganglia of the great sympathetic
nerve.

“From these dissections it is seen that the ganglionic nerves

E 2

52 Royal Society.

which ramify on the surface of the heart, those which have hitherto
been delineated in the works of anatomists, are few in number com-
pared to those which are distributed throughout the muscular struc-
ture of the organ, many of which are wholly independent of the
blood-vyessels.

«This anatomical demonstration of the ganglia and nerves of the
muscular structure of the heart, completely subverts the opinion
still entertained by some physiologists, that the sensitive and con-
tractile powers of the heart are independent of nervous influence.
It further indicates the real source of the action of the heart as an
entire organ, from the commencement to the termination of life;
how the circulation of the blood is carried on when the foetus has
neither brain nor spinal cord, and how the detached parts of the
heart continue to contract for a time in some animals after its total
separation from the body.

«These dissections are now open to examination by any gen-
tleman who may feel interested in the anatomy and physiology of
the heart.

“ When Mr. West’s drawings of the nerves displayed in these
dissections have been completed, they will be presented to the Royal
Society, with a description of the appearances delineated.”’

2. “On the Influence of the Moon on the magnetic direction at
Toronto, St. Helena, and Hobarton.” By Colonel Edward Sabine,
R.A., V.P. and Treas.

Having noticed the inference drawn by M. Kreil from the mag-
netic observations at Milan and Prague, that the moon exercises an
influence on the magnetic direction at the surface of our globe, cog-
nisable by a variation in the declination depending on the moon’s
hour-angle and completing its period in a lunar day, the author pro-
ceeds in this paper to state the results of an examination, analogous
to that pursued by M. Kreil, into the influence of the moon on the
magnetic declination at the three stations of Toronto, St. Helena,
and Hobarton.

The observations employed in this investigation consisted of six
years of hourly observation at Toronto, five years at St. Helena, and
five years at Hobarton, forming, exclusive of observations omitted
on account of excessive disturbance, a total of 105,747 observations.

The processes are related by which, after the separation of the
disturbances of largest amount, the observations were treated,
for the purpose of eliminating the variations due to solar influence,
and of re-arrangement in a form by which the inequality of the moon’s
action at the different hours of each lunar day might be brought
distinctly into view. ‘The results are shown in tables exhibiting the
amount of inequality at each of the three stations corresponding to
each of the twenty-four lunar hours.

It appears from these results that the existence of a lunar diurnal
variation in the magnetic declination is shown at each of the three
stations of ‘Toronto, St. Helena, and Hobarton, and that it has the
same general character at each, viz. that of a double progression in

Royal Society. 53

a lunar day, having two easterly maxima nearly at opposite points
of the hour-circle, and two westerly maxima also at nearly two op-
posite points of the hour-circle. The extreme elongations are not
at precisely opposite points of the hour-circle at any of the three
stations, nor have the amounts of the two elongations which take
place in the same direction always precisely the same value; but
the slight inequalities in these respects are within the limits which
might be ascribed to accidental variations, and might therefore dis-
appear with longer continued observations. It is otherwise, how-
ever, in the author’s opinion, with the disparity between the amounts
of easterly and westerly extreme elongations which presents itself at
each of the three stations. At Hobarton and St. Helena the westerly
elongations have the larger values, at Toronto the easterly (the north
end of the magnet being referred to in all cases).

The times at which the extreme clongations in the two directions
take place are not the same at the three stations, and are as follows:—
At Toronto the easterly extremes take place about the hours of 0
and 12, being the hours of the upper and lower culminations ; at
St. Helena the westerly extremes about two hours before the culmi-
nations; and at Hobarton about two hours after the culminations.
At Toronto the westerly extremes take place about the hours of 6
and 18; at St. Helena and Hobarton the easterly extremes respect-
ively two hours before and two hours after the same hours of 6 and
18. The extreme inequality, or the amount of lunar variation
measured from one extreme elongation to the other, is about 28" of
are at Toronto, 20 at Hobarton, and 11" at St. Helena. The
resolved portion of the terrestrial magnetic force which acts in the
horizontal direction, and is opposed to any disturbing influence, is
approximately 3°54 at Toronto, 4°51 at Hobarton, and 5°57 at St.
Helena.

Nov. 24.—The Earl of Rosse, President, in the Chair.

The following extract of a letter from Lieut. Gilliss, U.S.N. to

Colonel Sabine, R.A., was read :—
Washington, 12 Sept. 1853.

Lieut. Mackai returned to the United States in April, having made
his magnetical observations successfully at all the elevations and at
distances of 100 miles, entirely across the Pampas. Soon after leaving
Mendoza he was thrown from his horse, breaking his barometer and
so injuring his chronometer, that he has neither the longitudes of
his magnetical stations nor barometric profile of the country. Being
desirous to make his work complete, he volunteered to retrace his
ground, and left the United States for the purpose more than a month
ago, taking with him the declinometer and dip-circle, two Bunten’s
barometers, an apparatus for determining altitudes from the boiling-
point, and some smaller instruments.

Conveyance of the unifilar would have required another mule.

Cursory inspection of the observations already made afforded evi-
dence of their reliability, and as repetition would have involved

54 Royal Society.

many hours’ detention at each station, it was not considered essen-
tiul to cumber him. Should the Argentine provinces have become
sufficiently quiet, he will first cross the Andes at the Planchan Pass,
lat. 35° 20’, next at the Partillo (the most elevated) Pass, lat. 33° 40!,
and finally at the Cumbre and Uspalata Pass, in lat. 32° 50', where
observations have already been made. ‘

As he will remain at Santiago only a short time, I look for him
home during February next.

His and all the magnetical observations will then be discussed,
and the volume be ready for press by the close of 1854. Those on
meteorology are very far advanced.

The astronomical observations will fill three volumes, one of which
(Mars and Venus) will be ready about the same time as the mag-
netical and meterological volume; the zones not until two years
later.

My report, embracing those of Lieut. Mackai and the naturalists,

with the maps, plans, and drawings, will probably be the first pub-.

lished; and should Congress extend its usual liberality to my pro-
positions, all the volumes will be presented to the world in a
creditable manner.

A paper was also read, entitled “‘ On the Typical Forms of the
large Secreting Organs of the Human Body.” By Thomas H.
Silvester, M.D.

The author in this paper offers some observations on the large
secreting organs of the human body, namely,—

The lungs,

The liver,

The kidney,

The stomach,

The intestines, and

The developments connected with reproduction.

He observes that there are great: obstacles to an attempt to re-
duce them to a uniform type, but that further observation reveals
a typical uniformity, in adaptation to special purposes, unequalled in
the rest of the human ceconomy. ‘The greatest hindrance to the
discovery of this law of formation has been the habit of regarding a
single element of the glandular organ as the whole and not a mere
part of the glandular apparatus; for instance, the ovary has been
described as the ovuliferous gland, although in reality the latter
consists of the ovary, the Fallopian tubes, the uterus, and the vagina:
also the lung has been said to be a gland, meaning by this expres-
sion the secreting portion; whereas the lung-gland is composed of
the vesicular structure, the excretory ducts, the bronchi, larynx,
thyroid body, and even the nasal passages. The aim of the author
has been to discover the constant elements of the glandular system
and to compare them together in the several organs.

A secreting gland is described as a more or less developed fold of

> yen

Royai Society. 55

mucous membrane, or even a plain surface-—in its simplest forma
follicle ; but in the organs to be described it is a highly complicated
apparatus, composed of many parts, each possessing a peculiar func-
tion. It is an unvarying characteristic of these structures that the
elements of which they are composed always bear the same relation
to each other in position. An accompanying diagram exhibited the
type of a perfect gland, constituted of five elements and an ap-
pendage.

1. The secreting element...... SE ce atte aiateinS Red.
ag by EMSS Togs 3 A) 2117 Ae I I ee Blue.

~ 3, The receptacle element ... ci dt CHOW a
4. The cervix with its glandular appendage ~. Eure:
5. The efferent duct, , Sg CIECoals

Sketches of the several i of the human ved accompanied the
paper, coloured in the same manner, so that the corresponding parts
might be seen at a glance. The elements are seldom wanting
though sometimes scarcely discernible in their rudimentary condi-
tion, and retained apparently only in conformity to typical law.

There is great difference in degree of development of the elements.
The secreting part of the liver is of large size compared to the ducts,
whilst that of the generative organ in the female, namely, the ovarium,
is comparatively minute. The appendage of the cervix is very large
in the biliferous apparatus, but scarcely discoverable in the stomach
and sigmoid flexure. The excretory duct in the digestive organ,
represented by a contraction across the middle of the stomach, is of
enormous length in the seminiferous gland, as the vas deferens.

The popular terms being inexact or without meaning, it was
proposed to substitute for the ordinary names of the secreting
organs designations more aptly descriptive of their functions and
more in accordance with the principles of scientific nomenclature, as
follows :—

The uriniferous gland.
The seminiferous gland.
The biliferous gland,

The pneumatiferous gland.
The intestinal gland.

The oyuliferous gland.
The lactiferous gland; and
The digestive gland.

The kidney, or uriniferous gland, presents an almost typical re-
gularity of development. The secreting element or cortical portion
is composed of small convoluted tubes covered with a net-work of
blood-vessels.

The excretory duct or medullary structure arises from the cor-
tical part by numerous straight tubuli, which terminate in a duct
for the conveyance of the urine into

The receptacle or bladder. This organ has a cervix lined with

56 Royal Society.

mucous membrane in longitudinal folds, studded with minute fol-
licles and a rudimentary glandular appendage in the male.

The efferent duct is constituted of the membranous portion of
the urethra.

The seminiferous gland consists of the testicle, a collection of
convoluted tubercles, of an excretory duct called the vas deferens,
of a receptacle the analogue of the uterus, the vesicule seminales
being the body, the prostate the glandular appendage surrounding
the cervix. The efferent duct is of considerable length; the re-
ceptacle is lined with an alveolar fissure like the gall-bladder and
some muscular fibres.

The ovuliferous organ consists of the ovarium or secretory ele-
ment, the fallopian tubes or excretory duct, the uterus or recep-
tacle, the cervix and its glandular appendage in the shape of mucous
follices, and the vagina or efferent duct. ‘The secretory structure is
not tubular, but vesicular ; the excretory duct is connected with the
ovarium by its fimbriated extremity at certain periods only, in con-
formity with its peculiar function.

The lactiferous gland is remarkable for the singular distribution
of its elements; the secreting portion or breast, and the excretory
duct or nipple, being attached to one individual, and the receptacle
or mouth, cervix, glandular appendage or tonsils, and efferent duct
or cesophagus belonging to another, of which the mother and child
afford an illustration.

The stomach or digestive. gland does not appear at first sight to
be formed upon the same type as the other glands; it is however
divisible into three distinct cavities—the secreting or cardiac, the
receptacular or pyloric, and the efferent or duodenum. It is a tube
of enormous calibre, divided into three compartments of unequal
area. The excretory tube is recognized in the central contraction
of the muscles during digestion; the cervix, lined with plicated
mucous membrane, has been poetically described as the pylorus.

Comparative anatomy as well as microscopical bear testimony to
the correctness of this view with regard to structure and develop-
ment.

The biliferous gland is constituted as follows :

The secreting element, popularly called the liver.

The hepatic duct is the excretory tube.

The gall-bladder is the receptacle terminating in the duodenum
in conjunction with the pancreatic duct, the pancreas being the
glandular appendage surrounding the slender cervix of the recep-
tacle, and the duodenum performing the function of an efferent
canal to the digestive and biliferous glands.

The glandular appendages are subject to great variety of deve-
lopment. ‘The thyroid, the pancreas, and the prostate are large
structures, whilst in the pylorus, the sigmoid flexure of the colon
and the cervix uteri, the same element is little more than a fold of
mucous membrane with follicles interspersed. This element, like the
glandular apparatus, is greatly predisposed to cancerous degeneration.

Royal Society. 57

The writer of the paper now proceeds to describe the most re-
markable and important gland of the human economy, namely, the
sanguiferous.

The jejunum and ileum constitute the secreting element of this
organ. The ileo-cecal valve or verminiferous appendage is the ex-
cretory duct in a rudimentary state. The colon, though enormously
developed in a longitudinal direction, must be regarded as the re-
ceptacle ; the sigmoid flexure folded upon itself like the letter S (as
in the cervix of the gall-bladder) is the cervix of the colon recep-
tacle; the rectum or the efferent duct completes the system.

The function of this system is not fully known; the tract is lined
with mucous membrane and glandule for the secretion of air and
other products of the blood. It can scarcely be denied that the in-
testinal tube, in its structure and form and arrangement of the ele-
ments, bears the closest analogy to the glandular apparatus as seen
in the other large viscera of the human body.

The jejunum, as its name implies, is generally empty; it is con-
voluted, and its parietes are covered with a net-work of capillaries ;
it resembles therefore in all these particulars the tubes which form
the secreting tissue of the testicle and kidney, and differs from them
but in size. The jejunum and ileum, regarded as a continuous tube,
constitute a magnificent secreting structure, and its function is pro-
bably something more than the supply of the air and mucus gene-
rally contained in its canal. It has been suggested, that the blood,
the lymph and the feces owe their existence to the active capillaries
of the mesenteric arteries, but some certain proofs are still wanting
in confirmation of this opinion.

In the lung-gland, or pneumatiferous organ, the vesicular struc-
ture is the secreting element ; it secretes carbonic acid: the rami-
fications of the bronchia ending in the two bronchi represent the
excretory duct; the trachea is the receptacle; and the glandular
appendage covering the cervix (or cricoid cartilage) and marking
its position, passes by the name of the thyroid.

The efferent duct commences at the cricoid and ends at the carti-
laginous orifice of the nostrils.

The lacrymiferous organ is formed upon the same plan as the
preceding ; but in consequence of some peculiarities of development,
that, together with the simpler secreting structures, will be reserved
for a future opportunity.

Nov. 30.—Anniversary Meeting. —'The President, the Earl of
Rosse, K.P., M.A., addressed the Society as follows :—

GENTLEMEN,

I am happy that it is in my power again to congratulate you on the
progress made in the researches which have been carried on, aided
by the Grant the Government have placed at your disposal: after
an experience of more than three years we may say with confidence
that much has been accomplished. At first there were some mis-

58 Royal Society.

givings: continental experience was not altogether relied upon. Al-
though it had been very much the practice of foreign governments
to take an active part in encouraging the pursuit of science, and with
decided success, here the smallest effort in that direction was looked
upon by some as an experiment little harmonizing with our institu-
tions, our feelings, perhaps our prejudices, and only to be followed
by failure and disappointment. It was feared that because occasion-
ally there had been some difficulty in employing effectively the small
fund which had been bequeathed to us, that therefore there would
be increased difficulty in employing a larger fund; and this no doubt
would have happened if there had been restrictions limiting the
application of the larger fund to certain specific objects, or if the
field of discovery had been of limited extent: the reverse however
was the case. Your Council were not embarrassed by any unwise
restrictions, and in science there is room for every one. It is one
of the deductions of economic science that labour creates a demand
for labour; in fact, that where a community is industrious, and
labour accumulates and becomes capital, that there the people will be
fully employed: the same is true in the inductive sciences, and it
is true universally; there no modifying causes interfere to diminish
the force, or limit the application of the great principle, and we see
strikingly that as facts accumulate, and facts are the capital of
inductive science, fresh employment is everywhere provided for
those who are willing to work. Take any one of the inductive
sciences as an example, and we at once see how this is. Take for
instance chemistry, compare it as it now is with what it was when
Priestley commenced his career. The whole of the science then con-
sisted of an imperfect knowledge of the properties of a few of the
metals, of sulphur, phosphorus, and the three alkalies as they were
then called. There was a little known also about salts and acids, and
the existence of hydrogen and carbonic acid gas had recently been
ascertained. In a range so limited there was little room but for one
master mind, when Priestley discovered oxygen, and at once an open-
ing was made for researches into the nature of the atmosphere, of
water, and of combustion, of the acids and the alkalies, and ample
employment was provided for a host of distinguished philosophers
for years to come. Other important discoveries were soon made,
each becoming as it were a new origin of light, throwing perhaps
at first but feeble rays upon the objects around us, but revealing so
much of their strange forms as to excite curiosity, and awaken the
strongest passion of the human mind,—the desire to discover the
truth. Inorganie chemistry was then rapidly becoming a great
science, when the foundations of organic chemistry were laid in a
succession of brilliant discoveries. ‘That was but a few years ago,
but there were many men then ready trained for the work, and the
progress was proportionally rapid. To take a few of the disco-
veries in organic chemistry, and show how each has been the germ
of others, as it were the first term of a diverging series, and thus
to exhibit the great principle at work that in science labour creates

Royal Society. 59

a demand for labour, might perhaps be of some interest, but it would
lead me from the object which I have in view, which is simply to
point out the grounds upon which I have ever felt a strong con-
viction, that whatever means were placed at the disposal of the Royal
Society, no lasting difficulty could occur in turning them to useful
account.

During the last year considerable progress has been made by Mr.
Hopkins in the important experiments which he has been carrying
on in conjunction with Mr. Fairbairn and Mr. Joule. You no
doubt are aware, that, as we descend below the surface of the earth,
it has been found that the temperature increases : numerous experi-
ments made in different places with all the necessary precautions to
guard against fallacy, seem clearly to have established the fact. The
increase is about one degree of Fahrenheit for a depth of from 50 to
60 feet. If therefore the conducting power of the materials of the
globe was the same at all depths, we should have a series, which
would give us the depth proportional to every required temperature.
Reasoning in this way, we conclude that a temperature higher than
that of melting iron exists at a depth of thirty miles, and that at
double that depth the materials of thesurface of the globe, combined as
we find them in nature, would enter into fusion. It has therefore been
supposed by many that the solid crust beneath our feet is not more
than forty or fifty miles thick. It has however been assumed that the
increasing pressure at increasing depths does not alter either the
conducting power of materials, or the temperature at which they
melt. This no doubt is to a certain extent incorrect, and it is highly
probable that the conducting power of the different strata increases
considerably with the depth, the materials becoming more compact
under augmented pressure. It is not improbable also that pressure
may raise the temperature of fluidity. In either case the solid crust
of the globe would be thicker than it had been supposed to be on
the assumed data. With the view of throwing lhght upon this
question so interesting to all geologists, Mr. Hopkins undertook,
with the assistance of Mr. Fairbairn and Mr. Joule, to subject
various substances under different temperatures to enormous pres-
sure. Considerable time was required, even with Mr. Fairbairn’s
unlimited mechanical means, to construct the necessary apparatus ;
however, recently it has been completed, and in the few substances
examined it has been found that the temperature of fusion has
increased with the pressure: in the case of wax, by a pressure of
13,000 pounds to the square inch, the fusing-point was raised 3U°.
Whatever may be the influence of these experiments as-affecting the
great questions of Lerrestrial Physics, we may predict with certainty
that data will be obtained most valuable in philosophical research.

Mr. Joule, I find, has been actively engaged, in conjunction with
Professor Thomson, in his experiments on. the thermal effects of
fluids in motion, and has determined with considerable accuracy,
operating on a great scale, the depression of temperature when com-
pressed air escapes into the atmosphere through a porous plug. ‘The

60 Royal Society.

laws of the phenomena as to the temperature and pressure of the
confined gas, will also soon be determined.

Carbonic acid gas has been found to give a depression four and
a half times as great as atmospheric air, while it passes through
the porous plug with greater facility than atmospheric air; equal
volumes requiring pressures of 1 and 1°05 respectively in order to
be transmitted in equal times. Certain heating effects of air rushing
through a single orifice have been observed, which will probably
lead to a further development of the mechanical theory of the tem-
perature of elastic fluids in rapid motion.

The examination of the sedimentary deposits in the Nile valley,
mentioned at the last Anniversary, is still going on. Mr. Horner
states, that by the munificent aid of His Highness Abbas Pacha, the
Viceroy of Egypt, a series of operations have been carried on at
Heliopolis, and at another station thirteen miles above Cairo, which
have led to interesting results. A pit has been sunk to the depth of
24 feet below the pedestal of the colossal statue of Ramses the
Second, who reigned, according to the chronology of Bunsen, about
1400 years before Christ, and borings have been continued by which
cylinders of soil have been extracted at an additional depth of 48
feet. A series of thirty-two pits has been sunk across the valley in
a line between the Libyan and Arabian deserts, occupying a line of
about five miles, passing through the site of the statue alluded to;
and it is proposed to sink a similar line of pits next year about twenty
miles lower down the river, passing through the site of the obelisk
of Heliopolis. Above sixty persons were employed in the operations
at Memphis. The plan, as proposed by Mr. Horner, was, through the
intervention of the Hon. Charles Augustus Murray, Her Majesty’s
late Consul-General in Egypt, submitted to the Viceroy, and met with
the most ready acceptance. He gave directions to his government
that every assistance should be afforded for carrying on the proposed
researches ; he appointed an able engineer officer high in his service,
M. Hekekyan Bey, to conduct them, and ordered that the whole
expense should be defrayed by his government. Such enlightened
liberality on the part of His Highness Abbas Pacha justly entitles
him to the gratitude of all cultivators of science.

The other researches alluded to on the last occasion are proceeding
satisfactorily, but there is nothing which seems to call for especial
notice at present; I will therefore at once proceed to give some
account of the steps which have been taken by your Council for the
advancement of science in another direction.

In the history of individual sciences we perceive there have been
always successive periods of activity and repose. In Astronomy, for
many years we have had a period of activity. Physical Astronomy
has achieved perhaps its greatest triumph within the last few years
in the discovery of Neptune; and the discovery of the numerous
Asteroids and Comets is evidence that Practical Astronomy has kept
pace with it. Within the same period the nebulous contents of the
Southern Hemisphere have for the first time been made known to us;

Royal Society. 61

we have now a catalogue of the highest excellence, with an ample
guarantee for its accuracy in the zeal, ability, and experience of Sir
John Herschel.

That catalogue will be a record for future ages, leading probably
to the detection of change in the wonderful objects revealed by the
telescope, and so giving a clue to the mysterious laws which rule
the remote universe.

The Cape observations were not long before the world when some
astronomers expressed a desire that it should not be left to posterity
to turn them to account, but that some effort should be made to
employ them in the service of the present generation. It was sug-
gested, that with such an admirable working list, much might be ef-
fected ina short time. A comparisonof the Northern and Southern cata-
logues had led many to believe that the same instrument had effected
more in the Southern than in the Northern Hemisphere. Whether
that had been owing to a better atmosphere, or whether the objects
themselves were more remarkable, in either case it was reasonable
to expect that an instrument of great power would do more ina
well-selected situation in the Southern Hemisphere than in these
islands; and on that account alone there seemed to be grounds for
a well-founded hope that interesting discoveries would be made ;
but there were other grounds.

In the present state of Nebular Astronomy, the best prospect we
have of extending our knowledge, seems to be by carefully sketching
and measuring every object sufficiently within reach of our instru-
ments, to make details discernible. It is highly probable that the
objects we see are presented to us in every variety of position, that
they often differ in form merely because we see them in a different
aspect, and that if all were similarly placed as to the line of sight, a
few normal forms would represent the whole. _ If this is the case,
had we a sufficient number of accurate sketches, it is probable that
out of the apparent confusion we should succeed in extracting the
normal forms. It is also probable that in the nebular systems
motion exists. If we see a system with a distinct spiral arrangement,
all analogy leads us to conclude that there has been motion, and
that if there has been motion that it still continues. The apparent
motion is probably very slow, owing to the immense distance of the
nebulz; still there are double stars known to be physically double
from their motions, which are probably as distant as some of the
nebule. In certain nebule stars are so peculiarly situated that we
can scarcely doubt their connection with the nebular system in
which we see them, and some of these stars are as bright as some
of the stars known to be physically double; as bright even as some
of the stars which the latest Pulkowa observations have shown to
have sensible parallax, and whose distance therefore is approximately
known. We have therefore some vague idea, resting on probable
evidence, even of the distance of the nearest nebule. It seems there-
fore not unreasonable to expect that measurements perseveringly
carried on will detect motion, and that a fulcrum will thus be

62 Royal Society.

obtained, by which the powers of analysis may be brought to bear
upon the laws which govern these mysterious systems.

In the northern catalogue of Nebule, and the same observation
no doubt applies to the southern also, there are vast numbers much
too faint to be sketched, or measured, with any prospect of advan-
tage; the most powerful instruments we possess, showing in them
nothing of an organized structure, but merely a confused mass of
nebulosity of varying brightness. The number of nebule in the
northern hemisphere, in which details are well brought out,
is not very large, and even in these, a great proportion of the
measurements are necessarily rough, and wanting in that precision
by which the motion of certain double stars was so soon detected.
It is evident therefore that to obtain a true knowledge of the forms
of the nebular systems, our sketches must be as numerous as possi-
ble ; and to obtain evidence of motion with rough measures, our
measures should be very numerous also; but the northern hemi-
sphere presents but a very limited list of suitable objects, therefore
it is desirable to take in the southern hemisphere also.

I have thus, I believe, in part at least, explained the views of
those who felt anxious that the southern hemisphere should be exa-
mined with a telescope of great power: the first attempt to give
practical effect to their wishes was at the meeting of the British
Association held at Birmingham in 1849.

The President of the Association was on that occasion directed to
apply to Government to send a telescope of great power, in charge
of an experienced observer, to the southern hemisphere. That
application was unsuccessful ; the Government, while they acknow-
ledged the importance of the proposed object, declined to proceed, from
an apprehension of difficulties, through which they did not then see
their way clearly. At asubsequent meeting of the British Association,
the matter was again discussed, and a Committee was appointed, to
take such measures as they considered best calculated to effect the
object. The Committee, in the first instance, laid the whole matter
before your Council, and the Council, approving of the suggestion,
appointed a Committee to consider the subject in detail.

It was necessary before the Government could be applied to with
a reasonable prospect of success, that a specific plan should be in
readiness, complete in all its details: the size of the imstrument, its
optical principle, its mounting, and its site.

With the view of obtaining the best information, the Committee
consulted several eminent men, conversant with the management of
large instruments. ‘The first question proposed was, whether the
instrument should be a refractor or reflector, and it was decided in
favour of the reflector—there was in fact no choice. In the present
state of knowledge, there was no probability that a good refractor
could be constructed of sufficient power. As to size, the Committee
were disposed to recommend a telescope of 4 feet aperture, and
35 feet focal length, to be mounted equatorially; not that an instru-
ment of that size was the best, a much larger no doubt would have

a

a

Royal Society. 63

been better, but it would have been obviously unwise to have re-
commended a plan involving a very large expenditure. The Com-
mittee proceeded one step further, they pointed out a mechanical
engineer of character and experience in the construction of optical
instruments, who was willing to undertake to make the instrument
for a specific sum, and having proceeded thus far, they laid the
whole matter before Government, with whom it at present rests.

Another application is also before the Government of a very
different character, but with the same great object, the advancement
of human knowledge: it is to provide a building for the reception
of the Scientific Societies of the metropolis. That application did
not proceed from your Council, but from a large number of indivi-
duals, many of them Fellows of this Sociefy, the remainder distin-
guished members of the other Scientific bodies of the metropolis.
The application was made in the shape of a Memorial to Govern-
ment, the signatures amounting to about 200. There had been no
effort, I believe, on the part of those who brought the subject for-
ward to procure a large number of signatures, or in any way to
obtain a direct representation of the Scientific bodies : the Memorial
was a preliminary step, and in that stage nothing more was required,
than to show that it was supported by a large number of persons of
that class, from which science, if called upon, would have selected
her representatives. The Memorial was presented by a deputation,
and care was taken to explain to Government, that it did not ema-
nate officially from this Society or from any other.

A detailed explanation was also entered into, showing in what
way the cultivation of science would be promoted, by providing
suitable accommodation for the scientific societies. Carleton ride
was suggested as a convenient situation, and other sites were named
in the same neighbourhood.

Reference was made to the suggested site at Kensington, and it was
explained that it would be inconvenient to a large proportion of the
working men of the Societies, many of them engaged in business, and
whose time was most valuable, that they would be unable to attend
regularly, and that the usefulness of the Societies would be thereby
greatly impaired. It was also intimated that the purchase of a large
tract of land at Kensington did not materially affect the question ;
as a small space would be sufficient for all the Societies, and there-
fore that a free grant at Kensington could be but little object. Should
the Government accede to the Memorial, I presume that then the
Societies will be regularly consulted. The site will then be pointed
out, the plan of the building laid before you, and you will form your
own opinion; you will decide whether to remain as you are, or to
accept the enlarged accommodation, which the far-sighted liberality
of the nation will have provided for you.

The interests of science appear to me to be deeply involved in the
question of providing a suitable building for the Scientific Societies.
It is a practical question, and we must look at it in all its bearings,
as men of the world, Had there been no Societies, science would

64 Royal Society.

not therefore have stood still; but its progress would have been
much slower. The desire of discovering the truth, which is so
strongly implanted in every educated mind, would have been to
some a sufficient motive for exertion; but the aid and inspiriting
influence of association would have been wanting, and many active
members of our scientific bodies would probably never have taken
up science as a pursuit at all. The love of ease, the fascinations of
society, the little prospect of advancing their material interests,
through the path of scientific discovery, would have been to them a
sufficient excuse for indolence. ‘This point was very well put at the
last Anniversary, by one of the distinguished men to whom you award-
ed a medal; he said, had he been like Robinson Crusoe on a desert
island, the desire of discovering the truth would have been an induce-
ment to work, but to obtain the good opinion of his fellow-men,
associated together, was with him avery strong additional inducement.
If a man, naturally gifted, and well-educated, attends scientific meet-
ings, he will feel himself constrained to work, and therefore it is so
important for the advancement of knowledge, that able men should be
induced to join and attend the different societies ; but nothing I think
would have greater attractions than a building in a convenient central
situation, where the business of science would be transacted, where
there would be access to the best libraries, and where that kind of
society most valued by scientific men would always be within reach.’

Where the question is, shall a great country like England provide
a suitable place of meeting for its scientific bodies, I should hope
there are not many who would be disposed to count the cost, I scarcely
think the question, cui bono, could be asked; should any one however
ask it, I should answer, the object is to promote the increase of human
knowledge, to extend the domain of reason ; and “‘it is the understand-
ing that sets man above the rest of sensible beings, and gives him all the
advantage and dominion which he has over them.’ To take lower
ground, science is a part of England’s greatness: without science En-
gland would be nothing, and in the race with the world, if she is for-
saken by science, she will fall far behind. The exact sciences are
the foundation of navigation; they are the foundation of engineer-
ing; and many of our manufactures are based on principles, which
have been evolved in the researches of a refined chemistry. Besides,
have we not sometimes been at fault where science was not ready
to guide us? We have heard of failures in ship-building: some
ships sail slowly, and are therefore of little use; others roll, and
strain, and are also condemned; where we have succeeded best we
have taken our models from abroad, where high science has long
been urged to lend its aid in naval construction; where such men
as the two Bernouillis, Euler, Chapman and others, have been in-
duced to examine and discuss the questions of most interest to the
practical builder. In civil engineering too, our most eminent men,
I am sure, would not hesitate to acknowledge their obligations to
our neighbours. We have long been almost unrivalled in the appli-
cations of steam ; and yet, who is there who has not sought for the

Royal Society. 65

theory of the locomotive in the essay of De Pampour, or the prin-
ciples of steam in general in the researches of Regnault ?

In military engineering too, as well as in naval architecture,
has not science been sometimes on the side of our adversaries? and
have we not in consequence suffered severely? But let me not be
mistaken. I do not contend that science can in a moment increase
our success in the arts, upon which the greatness of this country de-
pends. If we were to. say to the mathematician, give us the best
lines for a ship suited to a given purpose, however profound his ma-
thematical knowledge might be, he would fail; practice must be com-
bined, but in due subordination with theory. It is where ina nation
science is cultivated profoundly by a large class of persons, and cir-
cumstances exist tending to direct it to practice, that some men will
always be found, gifted with the faculty of applying it in whatever
way the interests of the country may require.

Popular science, however, will not do: it has its uses, subordinate
as they are; it must be science of a high order; science as taught
at our universities: there a power is created capable of effecting
great objects, but in too many cases it is not applied at all, and it
soon passes away without useful result. Were it possible to enlist
that gigantic power into the service of the country by making our
scientific Associations more inviting, by placing science in this me-
tropolis in a position more attractive, a result would be obtained
which the merest utilitarian would consider of immense value.

I deeply regret that the last accounts have brought no intelli-
gence of Sir J. Franklin’s expedition, and that science has sustained
a heavy loss in the death of a distinguished French officer; the
latest sacrifice to the perils of Arctic discovery.

Many now present were acquainted with Lieut. Bellot, and I am
sure they will bear me out in this, that there was a singleness of
purpose, and a propriety of feeling in everything he said and did,
in perfect keeping with the tenor of his previous life; and though
he was here so short a time, he was regarded as a friend by all who
knew him.

You have heard no doubt with sincere pride, that British valour,
and British perseverance, have at length solved the problem of the
north-west passage. A question of great geographical interest has
thus been settled, and an important fact has been added to the data
of terrestrial physics. In all future inquiries relative to the oceanic
currents, the tides, the variations of temperature, the winds, and
meteorological phenomena generally, it will no longer be a doubtful
assumption, that the sea flows freely around the northern coast of
America.

It now only remains for me to state, and I have the greatest plea-
sure in doing so, that your Society is prosperous. The publication
of your Transactions proceeds regularly, and they continue to be,
as they have been for two centuries, the records of every important
addition to British science. There is no indication of a diminished
anxiety to share in your labours, the candidates for admission are

Phil. Mag. 8. 4. Vol. 7. No, 42. Jan. 1854. F

66 Royal Society.

numerous, and your Council have had no difficulty, though acting
under a heavy responsibility, in pointing out to you the required
number of persons in every way worthy of the Fellowship.

So far the present system of election appears to me to have worked
extremely well. ‘The Fellowship is sought for as a high honour, and
here, as at the Universities, the claims of the respective candidates are
tested by responsible persons.

In this, the Royal Society differs from every other Society; and
I think upon the preservation of that distinction, the welfare, the
position, perhaps the existence of our Society depends. For 150
years the Royal Society stood alone; unaided it bore the whole
labour of wielding the power of Association, in the cause of pro-
gressing science. Recently other Societies were formed to meet more
fully the wants of individual sciences; not as rivals to the Royal
Society, (in all of them our Fellows have held very prominent places)
but as the most friendly allies; not dependent on the Royal Society,
but fully admitting its pre-eminence.

These Societies have rendered important services; much has been
effected through their means which otherwise would not have been
attempted. Science has been carried out by them in the utmost
detail. Besides, it is a law of human nature, that we usually form
a high estimate of the importance of the pursuit we are engaged in;
and in a Society limited to one science, that feeling will necessarily
predominate, and will act as a stimulus to exertion. Under its in-
fluence, labour will be cheerfully borne, from which under other cir-
cumstances we should recoil with disgust. That feeling, however,
would proceed too far were there not here a power to restrain it:
you hold that power: you exercise a presiding influence over all the
Societies. The leading members of the scientific bodies have their
places here, and science is fully represented.

You look at science as a whole, and you weigh the value of every
new discovery as adding to the mass of human knowledge. The
honour of contributing to your Transactions is eagerly sought for,
the medals you award are in high estimation, and science is stimu-
lated to its grandest efforts, because you are viewed by all as just
and able judges. To hold securely that proud position, learning
must be your distinguishing attribute; in the altered state of things
it is learning which fits you for your new duties, and so long as the
Fellowship is regarded as the reward of services in the cause of
science of no common order, or of proved scientific eminence at the
universities, so long, I think, we may predict with confidence that
the Royal Society will flourish.

Dec. 15.—Thomas Bell, Esq., V.P. in the Chair.

The following communications were read :—

1. Extract of a Letter from Dr. Edward Vogel to Colonel Sabine,
dated Mourzuk, Oct. 14, 1853.

“ You will receive through the Foreign Office a packet of Astro-
nomical, Meteorological, and Magnetical Observations, made on the

Royal Society. 67

way from Tripoli and since my arrival here. My instruments are
almost all in good conditicn, although their cases have split from
the effects of heat and dryness, notwithstanding their double, and in
some instances triple, leather protection. I saw the great comet for
the first time on August 23, but others had seen it three or four
days sooner. Its nucleus was very bright, resembling a star of the
first magnitude, with a distinctly defined disc of the apparent dia-
meter of Jupiter. The tail made an angle of 86° or 87° with the
horizon, inclining to the north. It was a single tail with almost
precisely parallel sides. Its length was 10° on the 25th of August,
12° on the 26th, and 15° on the 27th and 29th of August. I have
seen here repeatedly the apparent fluctuation in the position of stars
which is spoken of in the third volume of Cosmos, and have sent the
particulars of my observations to Baron von Humboldt. There is
no regular rainy season at Mourzuk, but slight showers occur
sometimes in the winter and spring, seldom in the autumn. A heavy
rain is considered a great calamity, as it destroys all the houses,
which are built of mud dried in the sun. It would likewise kill the
date trees, by dissolving the salt which is in large quantities in the
soil. About twelve years ago there perished above 10,000 date
trees in the neighbourhood of Mourzuk, on account of a rain which
continued for seven days. The prevailing winds are south and east,
the strongest generally west or north-west. ‘T'wice or three times
I have seen whirlwinds pass through the town, a phenomenon which
was common in the deserts between Benioleed and Mourzuk. All the
whirlwinds I observed turned in the direction from east by north
and west to south. In December and the first half of January the
thermometer falls at sunrise (at Moorzuk) as low as 42°, and in
places exposed to the wind water freezes during the night. At
Sokna I found no one who could remember having seen snow; but
at Ghadamis snow was seen by Mr. F. Warrington on the 15th of
January 1851. At Tripoli we had heavy dews at night; and I
observed the same until we had passed a small chain of mountains
fifteen miles north of Sokna; from thence we had no dew, and it was
even often impossible to get the dew-point with Daniell’s hygro-
meter. In the desert the thermometer generally rose till 4p.m.,
from the sand (which was sometimes heated to 140° at 1 p.m.) giving
out its heat. Earthquakes are unknown in Fezzan; slight shocks
are sometimes felt at Benioleed and Sokna, as was the case the end
of last May. Shooting stars were observed in great quantities
(about forty an hour) on the 7th, 8th, and 31st of July; very few
on the evenings of the 9th, 10th, and 11th of August, averaging
fifteen an hour, mostly coming from Cassiopea and Ursa Minor. On
the 10th, at 8 a.m., I saw in ten minutes three shooting stars coming
from a Cassiopez, and rising right upwards towards the zenith.
About 4 a.m. on the 11th, J observed in a quarter of an hour about
twenty very bright ones in Pegasus and Aries. Shooting stars were
numerous also on the Ist, 2nd and 8rd of October.”

F2

68 Intelligence and Miscellaneous Articles.

2. Notice of a Comet seen from H.M. Brig Penguin off the Coast
of South Africa.

« Sir,—I am not aware that it can be of any service, still I have
thought proper to write you, for the information of the Royal Society,
that on the lst of May 1853, on board H.M. brig Penguin, in lat.
35° 0' S., long. 21° 52! E., at 6" 30™ p.m. I observed a comet
bearing N.W. by W.1W., measuring from the centre star in the
belt of Orion 14° 30’, the altitude of the comet being 26° 19’, its
length being about 5°. It went down at 95 10™, bearing W.1N.,
and from the altitude, time, and rate it appeared to move at, it must
have been the first evening of being seen. On first observing it, it
appeared to be making a retrograde motion, or tail first, and not
travelling as fast as the two small stars above it, as by the time it
set it had approached very close to them: the weather fine, warm,
and cloudy. On the 3rd of May a gale came on which lasted till
the 7th, after that time it became rather indistinct, not being seen
but when very clear, or by the aid of a glass. Having sailed on the
29th April from Simon’s Bay, Cape of Good Hope, and not hearing
there, or seeing anything of a comet, in either the Nautical or Cape
Almanacs, I concluded it had not as yet been observed, and there-
fore have thought it my duty to forward a rough sketch of its
appearance on the days mentioned, and its positions, as near as 1
could place it with my left hand, my right unfortunately having been
partially smashed and disabled on the night the gale commenced,
and which also prevented me from measuring its distance from any
of the stars, &c. A copy of the latitude, longitude, and bearings is
from the ship’s log. I found on our arrival at Quilemane that it had
been observed by the other two cruisers, but not till the 6th of May.
I must apologize for troubling you with the above, but considering
it as a point of duty that I should do so, I have the honour to be,

“ Sir, your very obedient Servant,
‘«< W.B. Epwarps,
‘Master H.M. Brig Penguin.”

XI. Intelligence and Miscellaneous Articles.

ON THE PRODUCTS OF THE DECOMPOSITION OF ROCKS UNDER
THE INFLUENCE OF SULPHUROUS THERMAL WATERS. By
J. BOUIS.

AM the products analysed by the author were derived from the
strata whence issue the remarkable waters of Olette (Pyrénées
Orientales), particularly the source of the cascade, the temperature
of which rises to 181° F. Some alterations having led to the re-
moval of the blocks of stone which closed the opening of the spring,
the effects of the corrosive action of the water upon the rock became
observable.
The rock is gray, veined with white quartz; its fracture is dull;

Intelligence and Miscellaneous Articles. 69

its specific gravity is 2°86; it resembles petrosilex. Its composition
on an average of several analyses is as follows :—

SUG SB ae Sid tsaeperoiate a. Seo
je Qqupenyht Re pom eta Grane oo
Protoxide of iron .......- 12
Lime ..... mir ciate levepsiar sisters lees
Soda: ac.cce se: PR ie Sovevetcct 4:2
Potastte, ceric cc ct excce.c diene’ = 0°7
Water Berns ota tin her os 1°6

The rock when reduced to powder still retains a certain quantity
of water which can only be got rid of at a red heat. In this cir-
cumstance, and its composition, this rock approaches the aquiferous
granites and the petrosilex of China, of which analyses have been

iven by Ebelmen and Salvétat. In its transformation by the action
of the water it first acquires a very bright red colour, due to some
peroxide of iron; it then cracks as though it had undergone the
action of a very high temperature, and afterwards becomes white
and friable, acquires the appearance of pumice-stone, and consists
only of pure silica.

Analyses of decomposed rocks gave 95°97, 98°00, 99°5, and lastly
100°00 per cent. of silica, according as their change advanced. The
silica is usually snow-white, friable and porous, sometimes coloured
by iron and manganese. In the clefts of the rock the silica is formed
in stalactites, consisting of concentric layers which indicate the re-
sult of a gradual deposit. This variety of silica is often covered with
crystals of sulphate of lime; it sometimes also contains very small
crystals of quartz, a circumstance which may perhaps be appealed to
by those geologists who admit that quartz has been formed by
aqueous crystallization. The surface of the stalactiform silica is
often of a very fine green colour, owing to the presence of crypto-
gamic vegetation. Lastly, the silica is met with in a gelatinous
state, constituting transparent masses which are often confounded
with glairine, or sometimes imbedding plants growing upon the
rocks, and forming by spontaneous desiccation a gray felt-like sub-
stance, which might readily be mistaken for pasteboard.

The silica is consequently derived from two different sources : in
one case it is due to the action of the water on the rock removing
all the other elements; in the other it is deposited from the water
holding it in solution by the aid of a high temperature, just as lime
in incrusting waters is dissolved by carbonic acid. This view is con-
firmed by the fact that the porous silica is insoluble in weak alkaline
or acid solutions, whilst the stalactiform silica dissolves with the
greatest facility in these reagents.

‘The water carries off the soluble matters, and deposits a reddish
mud; this is attacked by muriatic acid, which removes all the iron ;
the remainder consists of white plastic clay. This mud is com-
posed of —

70 Intelligence and Miscellaneous Articles.

Silicd eA aa eeeeio eee 74:5
Alumina and oxide of iron.... 17°9
Water. sod. chee otenaeeres 75

This composition is nearly identical with that of the deposits -
found in Iceland. Dieffenbach and Hooker found in the interior of
New Zealand a large number of volcanic springs of a high tempera-
ture, which deposited stony substances resembling chalcedony.
These deposits, analysed by Thomson, gave—

NSTC eateries coshenah cheeie) alm cracks 17:35
Alumina suse ae hehe io. a ceebanols oe 9°70
Peroxide of iron .......... 3°72
TUTTE FREE. Phe eS ctates ata aie eae aed 1:54
Waterss. Pettit is moan 7°66

The composition is therefore the same, although the substances
were derived from such different localities. 'The comparison of the
analysis of the mud with that of the rock, shows that the potash and
soda being very soluble, have been carried off by the water; that the
protoxide of iron has been converted into peroxide and accumulated
with the alumina in the deposit, whilst the silica has diminished ;
results whieh confirm Ebelmen’s experiments.

A crust of from 1 to 2 millimetres in thickness, which had been
formed on a rock bathed by the waters of the cascade, and which
was detached with facility, was also examined. It is very white
in the interior, but red on the outside; muriatic acid destroys
this colour; it is very hard, and presents a radiate crystallization.
From its composition it belongs to the class of zeolithes; it con-
sists of—

Caleulated. Found.

Dilicay Jae vsicee eaotee 57°6 57°6

J Nip were scan 641°8 16°3 16°1

srnieres. arte ects 350°0 38 8:6

Water eee 675°0 iva 17°6
3934°0

giving the formula (CaO, Si03 + Al? O°, 358103) + 6HO.

In the clefts of the source of the cascade, and under the arch
through which it issues, abundant white or yellowish efflorescences
are to be seen. Some portions of these are formed of potash alum,
whilst others consist essentially of sulphate of soda. These salts
are nearly always mixed, and it is sufficient to dissolve them to
separate them from the silica. The solution when evaporated and
exposed to the air deposits crystals of alum, and the efflorescent sul-
phate of soda is readily got rid of.

These productions are due evidently to the action of the air upon
the sulphuretted hydrogen which is disengaged from the waters.
The rock exposed to the vapour of the water is much disintegrated ;
it becomes porous, and causes the sulphur to pass to the state of*
sulphuric acid, which assists in its turn in the attack upon the rock

Meteorological Observations. 71

by extracting the alkalies. The author believes that the sulphur
met with also in these and similar localities only makes its appear-
ance when the rock is not porous. The water containing an alka-
line sulphuret, agitated in contact with the air, deposits sulphur.

The comparison of these facts with those observed by C. Deville
on the rocks forming the soufriére of Guadaloupe, will show the
complete concordance which exists between the phznomena pre-
sented in the neighbourhood of volcanos and those produced near
sulphurous thermal springs. In the Pyrenees, where these waters
are so abundant, earthquakes were formerly very frequent, and the
masses of water which pour constantly from the earth serve, so to
speak, as safety-valves for the prevention of greater convulsions.—
Comptes Rendus, August 8, 1853, p. 234.

METEOROLOGICAL OBSERVATIONS FOR NOV. 1853.

Chiswick.—November 1. Cloudy and fine. 2. Very fine. 3. Foggy. 4. Very
fine: overcast. 5. Uniform haze: clear at night. 6. Rain: foggy: uniformly
overcast. 7. Foggy: overcast. 8. Foggy: fine: clear. 9. Clear and fine 10.
Frosty : fine: foggy. 11. Dense fog: clear at night. 12. Overcast. 13. Foggy:
densely overcast. 14. Foggy: overcast. 15. Dense fog: rain at night. 16. Fine.
17. Frosty: fine. 18. Sharp frost: very fine. 19. Frosty: fine: clear and frosty.
20. Overcast : rain: clear and frosty. 21. Frosty: clear. 22. Foggy. 23. Dense
fog. 24. Overcast: rain. 25. Hazy and dull: rain. 26. Overcast. 27. Fine.
28. Overcast throughout. 29. Densely overcast: rain. 30. Hazy: slight rain.

Mean temperature of the Month .....+.cceeessseeesesseeeeeeeces 40°14
Mean temperature of November 1852 .............+4 paceeaese «- 47°38
Mean temperature of Nov. for the last twenty- -seven Uns - 43°18
Average amount of rain in Noy. .......+0++ piissenscscseressestn 2750 WHCHES.

Boston.—Nov. 1—4. Fine. 5. Cloudy. 6. Cloudy: rain a.m. 7. Cloudy.
8—12. Fine. 13. Fine: rain p.m. 14. Fine. 15. Foggy: rainp.m. 16. Rain:
rain A.M. 17—19. Fine. 20. Rain: rain a.m. 21, 22. Fine. 23. Cloudy.
24, 25. Cloudy: rain p.m. 26. Rain: rain A.M. 27, Cloudy. 28. Cloudy:
rainp.m. 29. Cloudy: rain a.m. and p.m. 30. Cloudy: rain a.m.

Sandwick Manse, Orkney): —Novy. 1. Cloudy a.m.: rain p.m. 2. Cloudy a.m. : clear
p.m. 3. Clear,fine A.m.: clear p.m. 4. Damp A.M. and p.M. 5. Cloudy a.m. and P.M.
6. Rain a.m. : clear, fine p.M. 7. Drizzle, shower A.M.: Clear P.M. 8. Rain A.M.
hail-showers, lightning p.m. 9. Cloudy A.m.: damp p.m. 10. Cloudy AM:
showers P.M. 1]. Sleet-showers A.M. : showers p.M. 12. Bright a.m.: clear,
fine p.m. 13. Cloudy am.: clear, fine p.m. 14. Cloudy, frost a.m.: damp p.m.
15. Clear, frost A.m.and p.m. 16, Cloudy, frost a.m.: clear, frost p.m. 17. Clear,
frost a.m. and p.m. 18. Showers a.M.: cloudy p.m. 19. Cloudy A.m.: rain,
cloudy p.m. 20. Clear, fine a.m. : sleet-showers p.M. 21. Clear, fine A.M. : clear
p.m. 22, Bright s.m.: clear, aurora S.p.m. 23. Bright a.m.: clearp.m. 24. Cloudy
A.M. and p.M. 25. Bright A.M.: raine.M. 26. Clear, frost a.m.: clear, aurora
p.m. 27. Clear, frost A.M.: rainp.M. 28. Clear a.m.: clear, aurora p.M. 29. Rain
A.M. : Clear, aurora P.M. 30. Bright a.m. : clear, aurora P.M.

Mean temperature of Noy. for twenty-six previous years ...... 42°59
Mean temperature of this month — ....+.sssseeseeeee baecmanse paene ae Od
Mean temperature of Nov. 1852 — cesssesseseseseeeees sarap AMAA ena 41 °52

Average quantity of rain in Nov. for thirteen previous years. 4°38 inches.

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THE

LONDON, EDINBURGH ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

FEBRUARY 1854,

XII. On the Results of a series of Experiments on the Decom-
position of Water by the Galvanic Battery, with a view to obtain
a constant and brilliant Lime light. By the Rev. N.J.Cauan,
Professor of Natural Philosophy in the Roman Catholic College,
Maynooth*.,

OON after I had discovered the nitric acid cast-iron battery,
and before I had completed the large one which I made

for the College, I began to make experiments on the decompo-
sition of water with a view to obtain a lime light which might
answer for lighthouses. I soon succeeded in obtaining a steady
and brilliant light. In a paper on our new galvanic battery,
dated April 6, 1848, and published in the London Philosophical
Magazine of the following July, I stated that “I got the hme
light by igniting mixed gases as they were produced hy the
decomposition of water and throwing the flame on lime.” I
believe I was the first who obtamed a constant lime light by
means of the galvanic battery. My experiments were frequently
interrupted on account of the state of my health. They were
at one time suspended for more than two years, and several
times for five or six months. The same cause which obliged me
to interrupt them now compels me to bring them to a close
before I could complete all the experiments I intended to make.
These experiments have led to the following results :—First, a
new apparatus for applying with perfect safety the mixed gases,
oxygen and hydrogen, to the production of a flame of the
most intense heat, which, when thrown on lime, produces a
most dazzling light. Secondly, a new voltameter, to which a
common jet may be screwed, and the gases inflamed as they issue

* Communicated by the Author.

Phil. Mag. 8. 4. Vol. 7. No. 48. Feb, 1854. G

74 The Rey. Dr. Callan’s Experiments on the

from it without the smallest risk of injury, and by which the
full decomposing effect of a battery of a hundred or five hundred
pairs, arranged in one series, may be produced without exhaust-
ing the power of the battery more rapidly than if it contained
only three or four cells. Thirdly, a new negative element far
cheaper, far more durable, and one which may be made to act
more powerfully than the platinized silver used in Smee’s hat-
tery. Fourthly, a new mode of protecting iron against the
action of the weather and of various corroding substances, so
that iron thus protected may be used for all the purposes to
which sheet lead and galvanized iron are applied. Fifthly, a
method of producing a brilliant intermittent lime light by means
of a small galvanic battery. Sixthly, a new mode of exhibiting
the dissolving views by means of the lime ight. Lastly, a new
sine galvanometer, which is the only instrument yet made by
which very powerful galvanic currents can be measured.

The first result was a new apparatus for applying with perfect
safety the mixed gases to the production of the oxyhydrogen
flame and lime light. In my first experiments on the decom-
position of water, I made use of a glass vessel containing dilute
sulphuric acid and four parallel plates of platinized platina, each
having a surface of about 14 square inches. The mouth of
the vessel was stopped by a thick piece of wood, through whieh
the wires from the electrodes passed. In this wood was cemented
a tapped brass nut to which a stopcock and Hemming’s jet
might be screwed ; the mouth of the vessel was made air-tight
by cement. I soon found that with a glass vessel the use of
Hemming’s jet was unsafe. On one occasion, when I employed
twenty 6-inch cells of our cast-iron battery, the Hemming’s jet
did not let out all the gases produced in the vessel; for after
breaking the connexion between the battery and electrodes, the
gases continued for some time’to issue from the jet and kept up
the lime light, although the battery had not worked for more
than a minute or two. Had I allowed the battery to work nine
or ten minutes, the gases would have been condensed within,
and would have burst the vessel; I therefore saw that I must
either get the gases separately, or devise some means by which
the mixed gases might be safely inflamed, and might at the same
time pass without much resistance from the glass vessel. I
attempted both. To get the gases separate, I put a plate of
porous earthenware between the electrodes so as to form two
air-tight cells. 1 thus succeeded in obtaining the gases separate ;
but finding so much difficulty in making the cells air-tight, I
gave up the idea of looking for the gases separately. In order
to avoid dangerous explosions in igniting the mixed gases, and at
the same time to allow them to pass freely to the jet, I sent them

Decomposition of Water by the Galvanic Battery. 75

through water contained in an iron vessel, to the top of which
was screwed the jet belonging to our large gas microscope and
polariscope. The first iron vessel which I used was about 54
inches high and 2 inches in diameter; its sides were an inch thick.
This vessel was found to be too small. On two occasions, all, or
nearly all the water was thrown out of the vessel through the
jet; the flame went back and exploded the gases in the bags.
On these two occasions the pressure was very irregular. The
quantity of the gases contained im the bags was too small to be
forced out by weights on the pressure-boards. They were driven
through the jet by a person who pressed frequently and violently
on the bags with his arm. This violent and irregular pressure
forced the water through the jet. Had the pressure been uni-
form, it is probable the explosions would not have occurred.
Dangerous explosions can happen only because the water may
be gradually ejected from the iron vessel through the jet or into
the gas bag; or because, when the gases are made to pass rapidly
through water in large quantities, there is a continuous series of
large bubbles rushing through it; and should the uppermost
bubble be ignited, the flame might possibly descend through the
series of bubbles without being extinguished by the surrounding
water. In the apparatus which I have made, a dangerous ex-
plosion from any of these causes is impossible. The apparatus
consists of two wrought-iron vessels of unequal size. The smaller
is the one already described. The-large one is about 74 inches
high and 4 inches in diameter; its sides are about Zths of an
inch thick. On the top of the vessel is laid a collar of thick vul-
canized India-rubber. An iron plate about 3ths of an inch thick is
then screwed down to it by five iron bolts. The vessel is thus
made air-tight. The top of this vessel is connected by an India-
rubber tube with the bottom of the small one; the bottom of it is
connected by a similar tube with the gas bag, gasometer, or volta-
meter. The two vessels are nearlyfilled with water. The gas is sent
into the bottom of the large one, ascends through the water, passes
through the tube to the bottom of the small one, then through
the water, and issues from the jet screwed to the top of the
small vessel. Since the two vessels are of very unequal size, it
is impossible that all the water should be carried out of both at
the same time by the stream of the gases; and should an ex-
plosion occur after the small vessel became empty, the flame
would be stopped by the water in the large vessel. In each
vessel the gases are made to pass through wire-gauze or perforated
zine, or through small pieces of porous earthenware, in order to
break the bubbles, and thus prevent the gases from ascending
in a continued series of large bubbles. To prevent the water
from being driven into the gas bag or voltameter which may be
G 2

76 The Rev. Dr. Callan’s Experiments on the

used, I have put a strip of vulcanized India-rubber across the
hole through which the gases enter into each of the iron vessels.
The strip of vulcanized India-rubber acts as a valve, which
opens inwards and admits the gases into the vessel ; and when
pressed outwards by the expansive force of the exploded gases,
it closes the hole and prevents the escape of any part of the water
into the gas bag or voltameter. Hence it is evident that in our
apparatus dangerous explosions cannot happen, either because
the water may be gradually ejected from the iron vessel through
the jet or back into the gas bag, or because the flame might
ascend through a continued series of bubbles of the mixed gases.
The size of the iron vessels should be in proportion to the quan-
tities of mixed gases inflamed, and to the length of time the
flame is kept up. Should a person wish to continue the lime
light for a very long time, he would do well to have two pairs of
vessels and change them every hour or half-hour, or examine
occasionally whether the water was carried away by the stream
of the gases. I have several times tried the large vessel alone
without any accident, although the gases above the water occa-
sionally exploded when they were not pressed through the jet
with sufficient force. I believe that this vessel may be used
alone without danger; but I would recommend in all cases the
use of two vessels, one of which should be a good deal larger
than the other, that the small one be about 3 inches in dia-
meter and 6 mches high, and that the experimenter examime
occasionally whether they contain water. I always kept the gas
bag in a place in which, though an explosion should occur, no
injury could be done to any person. On one occasion I filled
the small iron vessel with shot instead of water. The shot pre-
vented the return of the flame for a little time, but after five or
six minutes the gases in the small vessel and in the upper part
of the large one exploded, but the flame did not descend through
the water. The mixed gases which I employed were always
obtained by the decomposition of water. One of the gas bags
commonly used for the gas microscope and polariscope may be
filled in two or three hours by a cast-iron battery of six cells and
as many zine plates, each 6 inches square. I always employed
nitrosulphuric acid which had been previously used. Acid
which had been used before answers very well for producing
decomposition ; because, for this effect, the cells of the battery
must be so arranged that its mtensity will not exceed that of
three, or at most four cells in series. When the gases are ob-
tained by the decomposition of water, they are always mixed in
the proportions in which they answer best for the production of
intense heat and light; hence, when it can be done without
danger, it is better to produce the lime light by the decompo-

Decomposition of Water by the Galvanic Battery. 77

sition of water than by getting the gases into separate vessels,
and then mixing them in the proper proportions. With half a
dozen of cells of the cast-iron battery, a voltameter, a pair of
gas bags, and the apparatus just described, the gas microscope
and polariscope, as well as the dissolving views, may be exhibited.
But the experimenter must, until he acquires experience, proceed
with great caution.

The second result was a new voltameter, to which a common
jet may be screwed, and the mixed gases inflamed as they issue
from it without the slightest risk of injury, aud by which the full
decomposing power of a battery of 100 or 500 cells arranged in
one series may be exerted without exhausting the power of the bat-
tery more rapidly than if it consisted of three or four plates. This
voltameter is new in every respect,—in the material of which it is
made, in the manner in which the electrodes are connected with the
opposite ends of the battery whilst the vessel remains air-tight ;
new in the metallic plates employed as electrodes, and in the ar-
rangement of these plates ; finally, new in the fluid which is used
for the decomposition. After having succeeded in making the ap-
paratus for preventing dangerous explosions, I found that a glass
vessel was totally unfit for a voltameter such as I wanted : first,
because it is extremely difficult to make a glass vessel permanently
air-tight ; secondly, because it is not sufficiently strong to bear
the pressure of the condensed gases; thirdly, because on one
occasion, by unscrewing a bag which I had filled with the mixed
gases, a spark which was produced by accidentally breaking con-
nexion with the battery, or by the contact and separation of the
electrodes, inflamed the gases and caused an explosion which
shattered the vessel. I fortunately escaped unhurt. The vessel
which I have used for nearly the last two years is made of wrought
iron about an inch thick. Its form is cylindrical, its height
about 16 inches, and its inside diameter 6 inches. It is open
at the top, which was turned flat in a lathe; the bottom is laid
on a circular piece of wood, which is placed on an iron plate
about {ths of an inch thick and 8 inches square. On the top
of the vessel is laid a thick collar of vulcanized India-rubber,
and on this an iron plate similar to the one under the bottom.
In the top plate there are two holes, to one of which a stopcock
is adapted ; to the other is fitted, air-tight, a perforated piece of
brass which projects about an inch and a half above the plate.
The hole in this brass is large enough to admit a thick wire.
The upper part of the brass is tapped in order that a brass cap
may be screwed to it, to prevent the escape of the gases through
the hole. When the electrodes are placed in the vessel, one of
them is connected by solder or pressure with the inside; to the
other is soldered or riveted a copper wire, which passes through

78 The Rey. Dr. Callan’s Experiments on the

the hole in the brass screwed into the top iron plate. By means
of four 3-inch bolts of iron, which pass through the top and bot-
tom iron plates, the top plate is screwed down on the India-rubber
collar. The wire is then wedged against the side of the hole in
the piece of brass, and the brass cap is screwed on. The board
between the bottom of the vessel and under iron plate, and the
India-rubber collar between the top and upper iron plate, insu-
late both plates from the iron vessel. The outside of the vessel
is connected with one end of the battery, and the top or bottom
plate with the other. Thus the two electrodes are connected
with opposite ends of the battery; and if acidulated water, or
water containing any of the alkalies, be poured into the vessel,
it will be decomposed by the voltaic current. Ifa stopcock to
which a jet is attached be screwed to the top plate, the gases
will rush through the jet and may be ignited without the small-
est danger, for the explosion of the gases contained within can
never burst a vessel of such strength. I have had frequent
explosions without producing any injurious effect, though the
vessel was sometimes nearly half-filled with the mixed gases.
Before discarding the glass vessel, I began to use sheet iron in-
stead of platina electrodes. I found that when the intensity of
the battery exceeded that of three or four cells, the power of the
battery was soon exhausted; hence in using a battery of eighty
cells, [ was obliged to arrange them in twenty rows, each con-
taining four cells, and to connect all the end zinc plates so as to
form one, and all the iron cells at the other end so as to act as
one. I also found, that, to obtain the full effect of the decom-
posing power of the battery, the acting surface of each electrode
should be as large and a half as the acting surface of the zine
in each circle. Hence about 9 square feet of sheet platina,
which would cost nearly 30/., are necessary for a voltameter
large enough for a battery of eighty 4-inch plates, when they
are properly arranged for decomposition. Platina plates are not
only very expensive, but they are also very easily torn and ren-
dered unfit for use. I used a pair of sheet-iron plates about 4
feet long and 9 inches broad. To one of them I soldered a piece
of thick sheet copper, and to the other a thick copper wire. I
then covered one of them with linen, and rolled the two into a
coil about 4 inches in diameter. I had then two plates of iron,
nearly 3 square feet in surface, separated from each other by the
interposed linen. The coil was put into the iron vessel. The
copper plate soldered to one of the iron plates was connected
with the inside of the vessel, and the copper wire attached to
the other was connected with the perforated brass in the top.
The vessel was then filled with a solution of carbonate of potash.
I employed this solution in order to prevent the oxygen from

Decomposition of Water by the Galvanic Battery. 79

attacking the positive electrode. When the plates were connected
with the opposite ends of a battery, the water was rapidly de-
composed, and a considerable quantity of the mixed gases obtained.
From the intensity of the lime light produced by the gases, it
appeared that the potash effectually prevented the combination
of the oxygen with the positive electrode. The iron plates worked
well for about an hour; the decomposition then began to decline
very rapidly, though the battery was in good order. I then
took up the iron plates, separated them from each other, and
removed the linen cover. One of the plates was coated with a
non-conducting black deposit. This was the first time I found
such a deposit on either of the plates; on all former occasions
they were separated from each other by slips of wood or gutta
percha. I afterwards got a pair of lead plates, which I rolled
up in the same way as the iron plates; they, too, ceased to act
after some time, because one of them became covered with a
black non-conducting substance. I then got four concentric
hollow cylinders made of sheet iron }th of an inch thick, so that
the largest of them fitted in the iron vessel. The first or inner-
most one was connected with the third, and the second with the
fourth ; they were separated from each other by wedges of wood,
and also insulated from the bottom of the vessel. The first and
third were connected with the top plate, and the second and
fourth with the side of the vessel. These acted tolerably well ;
but when I used a pair of lead electrodes with a battery of ten
6-inch plates, the lime light was considerably larger and more
steady than when I employed the iron cylinders. Hence I
resolved, if possible, to give up the use of iron electrodes. I
saw at the same time that lead plates would not answer ; for
when they are placed near each other, a slight pressure, and
sometimes even their own weight, brings them into contact with
each other. It then occurred to me to try strong tin plates
immersed for a few seconds in melted lead, or in a liquid alloy
of lead and tin, in which alloy the quantity of tin would be smail
compared with that of lead. Not having any new tin plates at
hand, I cut up some old tin vessels, and made three plates, each
nearly 4 inches wide and 6 long. I coated one of them, by
means of a soldering iron, with an alloy, containing about seven
parts by weight of lead and one of tin; and another with an
alloy containing about three parts of lead and one of tin. On
the third, after being coated with the alloy, I sprinkled some
powdered sulphur, and held the plate over the fire until the sul-
phur was inflamed: the plate was thus covered with a black
coating of burnt sulphur. I then tried each of the three, and
also a plate of lead about the same size, as the negative element
of a nitric acid battery ; that is, I put each successively, instead

80 The Rev. Dr. Callan’s Haperiments on the

of platina or cast iron, into a porous cell containing nitrosul-
phuric acid. Each of the three acted far more powerfully than
the lead plate. The plate coated with the alloy containing the
largest proportion of lead acted better than the one whose coat-
ing contained least lead, but not so well as the plate on which
sulphur was burnt. This last plate produced a galvanic current
very nearly equal to that of a platina or cast-iron plate. | after-
wards put into concentrated nitric acid a piece of the tin which
was coated with the alloy of lead and tin, and with sulphur, a
piece of one of the alloys of lead and tin and a piece of lead, and
left them in the acid for about twenty hours. On taking them
out of the acid, I found that a good deal of the lead had been
dissolved, but the piece of coated tin and the alloy were merely
blackened on the surface. From the results of these experi-
ments, it is evident that tin plates, coated with an alloy of lead
and tin, in which the proportion of tin is small, are more passive
in nitric acid, less oxidable, and consequently better suited for
the electrodes of a voltameter than lead plates. The tin plates
are stronger and more elastic than leaden ones, and therefore are
not so easily brought into contact with each other. It was in
last March or April that I discovered that tin plates, coated with
an alloy of lead and tin, are less oxidable than lead. Since that
time I have in all my experiments used the coated tin plates as
electrodes. I have arranged these electrodes in two ways; in
one way for a battery of low intensity, and in another for bat-
teries of high intensity, or of a large number of cells all in one
series. In one of the former arrangements there were twenty
plates, each 12 inches by 4; they were all parallel, and separated
from each other by slips of wood about ;,th of an inch thick.
Ten of them were connected with one end of the battery ; these
were of course the alternate plates; the other ten were connected
with the opposite end. The acting surface of each electrode,
including both sides of each plate, was something more than
3 square feet. The electrodes for batteries of high intensity
are also parallel and separated from each other, about one-six-
teenth of an inch, by a non-conductor. But the two outside or
terminal plates only are connected with the battery; one with
the negative, the other with the positive end. The terminal
plate, which is connected with the top iron plate of the volta-
meter, must be covered on the outside by a non-conductor, other-
wise the voltaic current would pass to the side of the iron vessel,
and would not pass through the plates and fluid interposed be-
tween the two outside or terminal plates. The cells between each
pair of plates must be made nearly water-tight, and must be open
only on the top, in order that when the terminal plates are con-
nected with the battery, the voltaic current may have no way of

Decomposition of Water by the Galvanic Battery. 81

passing from one end of the battery to the other but through the
interposed plates and fluid. In each plate there should be a small
hole near the bottom, that the cells may always remain nearly
filled with the fluid. The fluid should never rise above the
upper edge of the electrodes, otherwise a great part of the gal-
vanic current would be transmitted by it from one terminal plate
to the other without passing through the interposed plates or
fluid. The number of cells formed by the interposed plates
should be about one-fourth of the number of cells in the battery.
Thus for a battery of 12 cast-iron cells, there should be 8 cells
or 2 plates between the two terminal plates. For a battery of
100 cast-iron cells in series, there may be 25 decomposing cells
or 24 interposed plates. A battery of 100 cells has twenty-five
times the intensity of a battery of 4 cells, therefore the current
from it will overcome twenty-five times as much resistance as
the current from 4 cells, and will pass through 25 decomposing
cells successively as freely as a current. from a battery of 4 cells
will pass through a single decomposing cell. If the current
from a battery of a hundred well insulated cells be sent through
25 decomposing cells, and afterwards through the coil of a gal-
vanometer, which coil is made of thick copper wire, it will be
found that the deflection of the needle will be equal to that
which will be produced by a current from a battery of 4 cells
passing through one decomposing cell and through the coil of
the same galvanometer. Hence there is as much of the mixed
gases produced in each of the 25 decomposing cells as in the
single cell through which the current from the battery of 4 cells
passed, that is, twenty-five times as much of the mixed gases
as is produced by a battery of four cells. Hence the full decom-
posing power of a battery of a hundred cells is exerted; and
because the intensity of the current is reduced to that of a bat-
tery of four cells, the power of the battery is not exhausted more
rapidly than if it consisted of four cells inseries. If the current
of a battery of a hundred cells in one series were sent through
the electrodes as they are commonly arranged, the power of the
battery would be exhausted about twice as soon as if the current
passed through the electrodes arranged for batteries of high in-
tensity, and the twelfth part of the full decomposing power of the
battery would not be effective. To those who wish to show with
the same battery the deflagrating power of the voltaic current,
the coke light, and the decomposition of water, and the lime
light, an arrangement of the electrodes similar to that which has
been just described will be useful, because a battery arranged for
intensity will answer for all these effects. ~But whena battery is
put up for the sole purpose of decomposing water, it is better to
arrange the cells in such a way that the intensity may not exceed

82 The Rev. Dr. Callan’s Haperiments on the

that of four cells in series; because if a battery of 100 cells be
arranged in series, a single bad porous cell or bad zine plate
will diminish considerably the power of the entire battery; but
if the 100 cells be arranged in twenty-five rows, each con-
taining four cells, and all the terminal zinc plates be connected
so as to act as one plate, and all the end iron cells be connected
so as to act as one, a bad porous cell or zine plate will diminish
the power only of the row to which it belongs, but not of the
other rows.

Some of my experiments led me to believe, that, by means of
the arrangement of the electrodes for a current of high intensity,
the decomposing power of the battery may be considerably in-
creased; from other experiments I was somewhat disposed to
infer that by such arrangement no increase of power can be
gained. Iam at present in doubt, and must remain so till the
state of my health enables me to repeat my experiments.

The fluid which I first used in the voltameter was a solution
of caustic potash. When a current was sent through the solu-
tion, the iron vessel was soon filled with foam, which came out
through the jet with the mixed gas and extinguished the flame.
I then tried a solution of carbonate of soda. The soda prevented
the oxidation of the positive electrode as well as potash, and did
not foam so much. However, even with soda, the quantity of
foam was so great, that the iron voltameter, 16 inches high and
6 inches in diameter, would be very soon filled with it if a bat-
tery of more than about twelve 6-inch cells were employed. I
tried various means of preventing the foam. I first covered the
electrodes all round with a cloth, so that the gases should pass
through it. Many of the bubbles were thus broken ; but when
a powerful battery was used, the voltameter was soon filled with
foam. I then put about a teaspoonful of coal naphtha into the
vessel. This prevented the foam from rising to any considerable
height in the vessel, but it was somewhat injurious to the light.
I also tried turpentine: it diminished the foam, but injured the
light more than the naphtha. I think it increased the vio-
lence of the explosion of the gases. I afterwards tried some
nitre, and also common salt; each of them prevented the foam,
but destroyed the light. After failing in all my efforts to prevent
the foam, I thought there was no alternative but to get an iron
vessel so large that all the foam which could be produced by a
powerful battery would be contained between the top of the elec-
trodes or surface of the fluid, and the top of the vessel without
rushing through the jet. Latterly, I have tried carbonate of am-
monia instead of soda, and have found that it foams much less,
and that it prevents the action of the oxygen on the positive elec-
trode. A solution of the proper strength will be obtained by
dissolving an ounce and a quarter, or an ounce of the carbonate

Decomposition of Water by the Galvanic Battery. 83

of potash, soda, or ammonia in a quart of water. If there be
more than an ounce and a quarter to each quart of water, the
quantity of foam will be very considerable ; if there be less than
an ounce, the conducting power of the solution will not be suffi-
cient, and the quantity of the gases produced will be greatly
diminished,

For either of the two arrangements of the electrodes I have
described, a cylindrical vessel does not answer well. For them
a prismatic vessel having a rectangular bottom is the most con-
venient. The inside of the iron vessel should be coated with an
alloy of lead and tin, or of lead, tin and antimony, in which the
proportion of tin, or of tin and antimony, is small,—first, in order
to preserve it from rust; secondly, to protect it against the
action of sulphuric acid, and thus render it fit for a voltameter,
in which the positive electrode is platina; the negative one, tin
plates coated with an alloy of lead and tin ; and the fluid through
which the voltaic current passes is dilute sulphuric acid. The
coated sides of the vessel may be the negative electrode. With
an iron voltameter such as | have described, the mixed gases
may, without the slightest danger, be inflamed as they are pro-
duced by the decomposition of water, and a constant and bril-
liant lime light may be obtained.

The third result is a new negative element, cheaper, more
durable, and one which may be made to act with greater power
than the platinized silver used in Smee’s battery. It is sheet
tin, coated with an alloy of lead and tin, in which the propor-
tion of tim is not greater than that of lead, or of lead, tin and a
small quantity of antimony. On tin plates thus coated, the
dilute sulphuric acid commonly used in Smee’s battery will
scarcely exert any action. It may be platinized like sheet silver ;
or it may be coated with borax, and will then answer as well, or
very nearly as well, as if it were platinized. It is evident that
tin plates thus prepared are far cheaper and more durable than
platinized silver ; and because they can be brought nearer than
platinized silver to the zine plates without danger of touching
them, they may be made to act with greater power.

The fourth result is a new means of protecting iron against
the action of the weather and of various corroding substances, so
that iron thus protected will answer for all the purposes to which
sheet lead and galvanized iron are applied. Besides the experi-
ments by which I have proved the superiority of tin plates (that
is, of sheet-iron plates), coated with an alloy of lead and tin,
over leaden ones, as the electrodes of a voltameter, I have made
many others, in order to compare the action of concentrated
nitric, sulphuric and muriatic acid, as well as of dilute sulphurie
and muriatic acid on lead and galvanized iron, with their action
on iron coated with an alloy of lead and tin, in which the quan-

84 The Rev. Dr. Callan’s Experiments on the

tity of lead was about equal to that of tin, or from two to seven
or eight times as great as that of tin; and from these experi-
ments I infer that iron, coated with any of the above-mentioned
alloys, is less oxidable and less liable to corrosion than lead or
galvanized iron, the zine coating of which, as every one knows,
is rapidly dissolved by the acids, even when they are greatly
diluted with water. Iron, then, coated with an alloy of lead and
tin, in which the quantity of lead is nearly equal to, or exceeds
that of tin, will answer as well as lead or galvanized iron for
roofing, cisterns, baths, pipes, gutters, window-frames, telegraphic
wires, for marine and various other purposes. A small quantity
of zinc, mixed with the alloy with which the iron is coated,
hardens the coating, but diminishes its power of resisting corro-
sion. But the addition of a little antimony not only hardens
the coating, but also makes it less oxidable and less liable to
corrosive action. Iron, coated with the alloy of lead and tin, or
of lead, tin and antimony, may answer better than lead for
vitriol chambers. It may be sometimes used instead of copper
for the sheathing of ships; and bolts and nails of coated iron
may be sometimes employed instead of copper bolts and nails.
It may also be used for some of the purposes for which enamelled
iron or cast iron is employed, such as the enamelled cast-iron
cisterns and pipes used in water-closets. At the last meeting of
the British Association at Hull, Dr. Gladstone stated that the
owners of iron-built ships object to sugar cargoes, because the
saccharine juices that exude from the casks corrode the metal.
If the casks or the ships were lined with thin sheet iron, coated
with an alloy of lead and tin, containing two or three times as
much lead as tin, it is highly probable that the corrosion of the
ships would be prevented. I have left for a considerable time a
small piece of an alloy of lead and tin, in which the quantity of
lead was four or five times as great as that of tin, in a solution
of sugar and common water; and the alloy came out as bright
as when it was put into the solution.

The fifth result is a new mode of producing, by means of a
small galvanic battery, a brilliant intermittent lime light. By
means of a battery of twelve 4-inch cast-iron cells, or of four
cells each 6 inches by 8, a small voltameter, such as I have
described, and a good Hemming’s jet, a constant lime light, about
a quarter of an inch in diameter, may be produced. If then the
jet be attached to a stopcock, by which the gases are confined
in the iron voltameter for fifty-five seconds in every minute, and
are allowed to issue from the jet only for five seconds in each
minute, twelve times as much of the gases must pass through
the jet in these five seconds as would pass through it in the
same time were the stopcock always open. Hence if the gases
produced by the battery are ignited for five seconds in each

Decomposition of Water by the Galvanic Battery. 85

minute as they issue from the jet, and are confined in the vol-
tameter for the remaining fifty-five seconds, the flame will, when
thrown on lime, give a light twelve times as large as one a quarter
of an inch in diameter, or nearly seven-eighths of an inch in
diameter. If the breadth of the hole in the key of the stopcock
be ,/,th of the circumference of the key, and if the key make a
revolution in every two minutes, the stopcock, because it is
opened twice in each complete revolution of the key, will be
opened once in every minute for five seconds, and will be closed
for fifty-five seconds. Now by clockwork it is very easy to
make the key of the stopcock perform a revolution once in
every two minutes, and consequently to produce a lime light
seven-eighths of an inch in diameter for five seconds in every
minute. It is easy to make the motion of the key and the ratio
of the diameter of the hole to the circumference of the key such
that the stopcock will be opened once in two minutes for ten
seconds, and will be closed for a minute and fifty seconds. In
order to light the gases whenever the stopcock is opened, it is
necessary to have a small flame of gas or of a candle always at
the nozzle of the jet. A lime light of seven-eighths of an inch
in diameter would be seen at a far greater distance, particularly
in foggy weather and in snow-storms, than the light of a lamp ;
and is therefore of the utmost importance in lighthouses. Had
there been such a light in the Bayley Lighthouse, the Victoria
would in all probability not have been lost. The expense or
trouble of such a light would not be very great, and would be
amply compensated by saving the lives of many every year. The
light might be used only in foggy weather or im snow-storms,
when a light capable of penetrating through a dense atmosphere
or a shower of snow would be required. On other occasions the
ordinary lights might be employed. The expense of an inter-
mittent lime light, such as I have described, would be the cost
of working a cast-iron battery containing four zinc plates, each
6 inches by 8, for sixteen or seventeen hours a day, and of a very
minute flame of common coal-gas for the same space of time, as
often as the light might be required. Surely such an expense
could not be very great. Should it be apprehended that the
action of the battery would not be sufficiently constant to give
the light required, then three large gas bags, each of which
would contain as much of the mixed gases as would be sufficient
to maintain a lime light three-fourths or seven-eighths of an
inch in diameter for half an hour, might be filled during the
day with the mixed gases by two or three small batteries. Then,
by means of the apparatus which I have devised for safely ap-
plying the mixed gases to the production of intense heat and
light, of a proper jet, a suitable adjustment of clockwork, and a
very small flame of coal-gas, the intermittent light may be kept

86 The Rey. Dr. Callan’s Eaperiments on the

up for eighteen hours; for the light would last only five seconds
in each minute,.and consequently only five minutes in each hour,
or an hour and a half in eighteen hours. Therefore, since the
three gas bags, filled with the mixed gases, would maintain a
constant light for an hour and a half, they should keep up the
intermittent light for eighteen hours. I believe such an inter-
mittent would answer very well for lighthouses. In the light-
house on the eastern pier at Kingstown, the light is a revolving
one, which completes a revolution in about a minute. The bril-
liant white light, the only one which can be seen at a distance,
shines out only for about five seconds in each minute. Hence
I infer that an intermittent lime light which lasts for five seconds
im-each minute would be sufficient for lighthouse purposes. It
is necessary to observe, that, when gases are gradually cut off
from the jet, the gases in the upper part of the voltameter, or
vessel to which the jet is attached, will explode if a Hemming’s
jet be not used; and this explosion, though perfectly free from
danger, will be attended with inconvenience, for a vacuum will
be produced in the upper part of the voltameter or vessel,
and no gases can pass to the jet till this vacuum is filled.
Hence, in producing an intermittent lime light, a Hemming’s
jet should be employed. Since the discovery of the cast-iron
battery, several persons have obtained patents for apparatuses
for the coke light, or, as it is now called, the electric light. If
they arranged their apparatus so as to produce an imtermittent
coke-light similar to the intermittent lime light I have described,
they would confer a great benefit on society. When the coke
light is constant, the battery is soon exhausted, the coke points
are consumed, and must be frequently renewed ; but were the
light intermittent, a single charge of the battery might last for
an entire night, and it would be sufficient to renew the coke
points two or three times in the course of the night. And if an
intermittent coke light were used in lighthouses only on very
dark and foggy nights and in snow-storms, the expense could not
be considerable. I think the coke light is more intense than
the lime light, and also somewhat less expensive. To produce
a coke light sufficient for all illuminating purposes, forty cast-
iron cells, each containing a zine plate 2 inches by 4, will suffice.
To obtain a lime light of equal illuminating power, a battery
containing at least twice as large a surface of zinc will be required.
A battery with a given charge will scarcely work twice as long
in decomposing water as in igniting a pair of coke points. There-
fore, on the whole, I think the lime light is more expensive, but
much more easily managed than the coke light. The former
requires a battery of only four large plates; the latter depends
on the intensity of the current, and requires a battery of at least
thirty-five or forty cells. The coke points will require to be

Decomposition of Water by the Galvanic Battery. 87

changed more frequently than the lime; and there is more reason
to fear that the coke light will fail on account of the destruction
of the positive coke point, than that the lime light will go out
on account of the-wearing of the lime. For the coke hght, the
zine plates should not contain more than 8 square inches of sur-
face. If they be larger, the positive coke point will be rapidly
destroyed, without a proportional increase of light.

The sixth result is a new mode of exhibiting the dissolving
views by means of the lime light. In the common apparatus for
showing the dissolving views, the apertures of the lanterns are
gradually opened and gradually closed, in order to make the
figures come gradually into view and gradually disappear. By
using the mixed gases, the apertures may be left always open,
and the figure im either lantern may be gradually brought out
on the screen, and may be made to fade away by degrees; for
by opening very slowly the stopcock through which the gases
pass to the jet, the light in the lanterns may be made to increase
very slowly till it has acquired its full intensity, and consequent!
the image thrown on the screen will become gradually brighter
till it attains its full brightness; and by very slowly closing the
stopcock, the light, and consequently the image, will gradually
fade away. By exhibiting the dissolving views in this way, there
is a great saving of the mixed gases; for the light shines out
fully in each lantern only when it is necessary to exhibit the
image in full brightness on the screen. Besides, by diminishing
the quantity of the gases which passes through one jet, the quan-
tity which passes through the other jet, and consequently the
brightness of the full image, is increased.

The last result is a new sine galyanometer, which is the only
instrument yet devised for measuring with accuracy very power-
ful galvanic currents*. Some of my experiments raised doubts
in my mind about some of the generally received theories relating
to the action of the galvanic battery. The galvanometers which
I had were not fit for measuring very powerful currents, such as
I employed. I was therefore obliged to get a new one. After
a good deal of reflection, I resolved to get one which would
answer for a sine instrument, for the common tangent mstru-
ment, and for the new tangent galvanometer, the principle of
which is demonstrated in the Compies Rendus of the 24th of last
January. The galvanometer which I have made consists of a
mahogany circle 2 feet 4 inches in diameter and nearly 2 inches
thick, in the circumference of which is turned a groove half an
inch wide and 33 inches deep ; of seven concentric coils of 3-inch
copper wire in the groove, and well insulated from each other ; of
a strong frame in whieh the circle is moveable on an axis, and

_® The voltameter will not measure powerful currents produced by a
single circle, or by two or three circles,

88 The Rey. Dr. Callan’s Experiments on the

always kept in vertical position; and of a compass-box, which,
by means of a slide 3 feet long and at right angles to the circle
at its centre, may be moved in a direction perpendicular to the
circle to the distance of 3 feet from it, so that the centre of the
needle, which is a bar-needle 54 inches long, will always be in
the axis of the circle and of the coil, and that the line joining
the north and south points of the compass-box will be always
parallel to the horizontal diameter of the mahogany circle and
coil. From this description of the instrument, it is evident that
{no matter where the compass-box is placed on the slide) the
needle is parallel to the mahogany circle and coil, or perpendi-
cular to their axis, whenever it points to 0°. Hence, if a voltaic
current, sent through the coil, deflect the needle, and if the
circle and coil be turned round so as to follow the needle until
it points to 0°, the needle, no matter where it may be placed on
the slide, will then be parallel to the coil and perpendicular to
its axis. The magnetic power of the coil is exerted in the direc-
tion of its axis. The effective part of the earth’s magnetism in
impelling the needle to the magnetic meridian is also exerted in
the direction of a perpendicular to the needle or of the axis of
the coil, but opposite to that in which the magnetic force of the
coil acts. Since the needle is kept at rest by these two forces
acting in opposite directions, they must be equal. But the
effective part of the earth’s magnetism in impelling the needle
to the magnetic meridian, varies as the sine of the angle which
it makes with that meridian. Therefore the magnetic power of
the current flowing through the coil also varies as the sine of the
angle which the needle, when it points to 0°, or the mahogany
circle D, makes with the magnetic meridian. If the connexion
with the battery be broken, the needle will immediately return
to the magnetic meridian. The graduated circle of the compass-
box will give the number of degrees the needle was deflected
from the magnetic meridian. For measuring the angle of
deviation, I have used a large graduated circle about 13 inches
in diameter, which is attached to the upper part of the mahogany
circle, and at right angles to it and to the axis about which it is
moveable. By means of seven brass bolts, each three-eighths of
an inch in diameter, I can send the current from the battery
through one coil, or seven, or through any intermediate number
of coils. I scarcely ever use more than one coil, and that is the
outside one, the diameter of which is about 2 feet 2 inches.
When the current is sent through seven coils, the deflection is
so great that only very feeble currents can be measured on the
sine galvanometer. When the needle is in the centre of the
coil, this galvanometer, used as a sine instrument, large as is its
diameter, is not capable of measurmg the power of a current
produced by a single circle of the cast-iron battery, in which the

Decomposition of Water by the Galvanic Battery. 89

zinc plate is an inch broad and 4 inches long. The coil, when
made to follow the needle, drives it always before it, so that the
needle will never remain parallel to the coil. Hence, in Pouillet’s
sine galvanometer, in which the centre of the needle is in the
centre of the coil, only feeble galvanic currents can be measured.
But by sliding the compass-box and needle to 2 or 3 feet from
the coil, a current of very great power may be measured. A
current which produces a deflection of 75° when the needle is in
the centre of the coil, will produce a deflection of only 3° when
the needle is at a distance of 3 feet from the coil and its centre
in the axis of the coil. Hence, by our galvanometer, in which,
and in which alone, the needle may be moved to a distance from
the mahogany circle or coil whilst its centre is in the axis of the
coil, currents of enormous power may be measured. With this
galvanometer I expect to determine,—first, the smallest number
of circles the currents of which will be fully effective, or at least
as effective as any larger number of. galvanic circles in decom-
posing water, and consequently the number which may be used
with the greatest advantage in decomposition ; secondly, whether
Mr. Faraday’s law, viz. that the quantity of the mixed gases
produced by a voltaic current is proportional to the quantity of
electricity which passes, holds for currents of great power ;
thirdly, the proportion which the surface of the decomposing
plates should bear to the acting surface of zinc in each circle ;
fourthly, whether a battery with a given charge will work longer
in producing the lime light by decomposing water than in pro-
ducing the coke light, and which of the two lights is the more
ceconomical,

To determine the smallest number of cells of the cast-iron
battery which are as effective as any larger number im decom-
posing water, I measured the quantity of the mixed gases pro-
duced in two minutes by 3, 4, 5, 6 and 12 cells, and also the
deflection of the needle produced by the current from each bat-
tery when it passed through a solution of carbonate of soda in
which there was about an ounce and a half of soda to each quart
of water*. From the steadiness of the needle, it was evident that
the current from each battery was perfectly constant durmg the
two minutes it was allowéd to act. The quantity of the gases
produced by 8 cells was less than three-fourths of the quantity
produced by 4, and less than half the quantity produced by 6.

Hence 3 cells are not as effective as 4, 5 or 6, The quantity
of the gases produced by 8 cells was sensibly less in proportion
to the sine of the angle of deviation shown by the sine galvano-

* The quantities of the gases produced by 1 or 2 cells were so small,
compared with that which was produced by 3 or 4, that I did not measure
them.

Phil. Mag. 8. 4. Vol. 7. No, 48, Feb, 1854. H

90 The Rey. Dr, Callan’s Experiments on the

meter, than it was when 4 or 5 cells were employed. Hence it
appears, that, for want of sufficient intensity, a sensible portion
of the electric current produced by 3 cast-iron cells passes through
a solution of carbonate of soda without producing decomposition ;
and therefore in decomposing water, 3 cells cannot be used with
advantage. On one occasion the current was sent from 3, 4 and
6 cells, through a solution of sulphate of soda mixed with some
carbonate of soda, The quantity of the mixed gases was very
nearly in proportion to the number of cells and to the sines of the
angle of deviation shown by the sine galvanometer. The sine of
deviation appeared to be a little less, im proportion to the quan-
tity of the gases produced, with 4 than with 3 or 6 cells. In
this case, the sulphate of soda, as well as the water, was decom-
posed ; for when the flame of the gases was thrown on lime, the
bright white light produced by the oxyhydrogen flame was sur-
rounded by another dim light of a purple hue. With the solu-
tion of carbonate of soda alone, the quantity of the gases pro-
duced by 4, 5, or 6 cells appeared proportional to the number of
cells and to the sines of deviation. Hence, cast-iron batteries
of 4, 5, or 6 cells wall be equally effective in producing decom-
position, But a battery of 4 cells will work as long and a half
with a given charge as one of 6 cells, and as long and a quarter
as one of 5; because in these batteries the quantity of electricity
constantly flowing through each cell is proportional to the num-
ber of cells. Hence in preparing a battery for decomposing
water, all the cells should be arranged in rows of 4each. Four
cells produced more than half the quantity of the gases produced
by 12 cells of the same size. A battery of 60 cells, arranged in
one series, after having worked for some time, produced in one
minute very little more than 4 cells of the same size. I have
not yet tried the decomposing power of a battery of a larger
number acting in one series; but I shall have occasion, in the
month of February, to show to my class a battery of about
250 cells; and I will then measure the quantity of the gases
produced in one minute when all act in one series. Light cells,
arranged in two rows of four each, so that the two end zinc plates
were connected as one, and the two iron cells also acted as one,
produced considerably more of the mixed gases in two minutes
than was produced by 12 cells of the same size acting in one
series. ‘The quantities of the gases produced by the 8 and the
12 cells were in the ratio of 11} to9. But with the 12 cells,
the sine of deviation shown by the sine galvanometer appeared
to be greater in proportion to the quantity of the gases produced
than when the battery of 8 cells in two rows was employed.
Hence it would appear, that when the intensity of the current is
much greater than that of 4 or 6 cells of the cast-iron battery,

ws

Decomposition of Water by the Galvanie Battery. 91

the ratio of the quantity of water decomposed to the quantity of
electricity passing through it is dimimished; and consequently
that Mr. Faraday’s law of definite electro-chemical decomposition
does not hold for powerful currents, which differ much in their
intensity. In my last experiments I perceived a defect in the
magnetic needle employed, and therefore do not feel myself
warranted in drawing a positive conclusion. Besides, I am sure
that my experiments were not made with as much accuracy as
Mr. Faraday’s were; but they incline me-to believe that the
decomposing power of strong currents decreases when their in-
tensity increases. I am inclined to believe that there is a certain
intensity above and below which there is a loss of decomposing
power; and that, in a cast-iron battery, it is the intensity of
4 cells in one series. J am inclined to think that, when the in-
tensity is greater than that, some of the electricity passes through
water without meeting the resistance or reaction necessary for
decomposition ; and that the greater the intensity the greater
the quantity which passes without the required resistance. The
current from a battery of 12 cast-iron cells does not meet with
much resistance in passing through a solution of carbonate of
soda. For when the current was sent, without passing through
the fluid, through the coil of the tangent galvyanometer, it pro-
duced a deflection of 69°; and when sent first through the fluid
and then through the coil, the needle was deflected to 68°.
When a current was sent from 60 cells, first through the fluid
and then through a pair of coke points, the defiection was the
same as when it passed through the coke points without passing
through the fluid. Hence a current from a battery of 60 cells
appears to meet with as little resistance in passing through a
fluid as in passing through a wire. Hence a current of very high
intensity experiences little or no resistance or reaction from the
fluid, and therefore can produce little effect on it.

In comparing the deflection of the needle produced by a cur-
rent from 6 cells through a solution of carbonate of soda with
the deflection produced by the current from the same battery
sent directly through the coil of the galvanometer, it occurred
to me that if 12 cells were arranged in two rows, and the two
end zinc plates connected as one, and the two iron cells con-
nected so as to act as a single cell, the current from these two
rows would, after passing through a fluid, produce a greater
deflection of the needle than they would, if, whilst they acted in
one series, the current were sent directly through the coil of the
galvanometer. Subsequent experiments proved that my con-
jecture was well founded. When 12 cells were arranged in two
rows of six each, and the current from both was sent through a
solution of carbonate of soda and then through the coil, a de-

H 2

92 The Rey. Dr. Callan’s Experiments on the

flection of 67° was produced in the needle of the tangent galva-
nometer. When the current was sent from the same 12 cells
acting in one series through the coil alone, the deflection was
only 64°. Hence more electricity passed from the two rows of
six each through the fluid, than from 12 cells through the wire.
Now it is well known, that when a current of electricity passes
from one end of a battery to the other through a conductor in
which it meets no resistance, the same quantity will pass in a
given time between the ends of the battery, whether it consist of
a single pair, or of a hundred or of a thousand circles, or of any
number whatever. Hence more electricity will pass in any time
through a solution of carbonate of soda from 12 cells arranged
in two rows of six each, than will pass in the same time through
a wire or fluid from a thousand, or any number of cells of the
same size. Therefore whether Mr. Faraday’s law hold for power-
ful currents of great intensity, or whether the conclusion drawn
from my experiments be just, 12 cells, arranged in two rows of
six each, will produce more decomposition in a given time than
will be produced by a thousand, or any number of cells acting
in one series. I have found, in the same way, that 8 cells, in
two rows of four each, will produce as much, or nearly as much,
of the mixed gases in a given time as any number acting in one
series. Hence, with the common voltameter, a battery of 500
cast-iron cells, arranged in rows of four, will produce more than
fifty times as much of the mixed gases as it will produce when
all the cells are arranged in one series. Besides, when the cells
are arranged in rows of four, the battery with a given charge
will act about twice as long as when all act in one series; for in
the latter case about twice as much electricity passes constantly
through each cell as in the former, and consequently the power
of the battery is exhausted about twice as soon. Hence, on the
whole, with the common voltameter, a battery of 500 cast-iron
cells arranged in one series will not produce the hundredth part
of its full decomposing effect; but with the voltameter I have
described, it will, as I have shown, produce its full effect. IZfa
battery of 4 cast-iron cells, and another of 1000 or of any number
of cells of the same size be similarly charged, the former will,
before its power is exhausted, produce as much of the mixed
gases as the latter; because the former will produce in each mi-
nute as [half much as?] the latter, and it will work twice as long.

I will here mention one of the experiments from which I in-
ferred, that in a voltameter for a battery of a large number of
cells arranged in one series, the number of decomposing cells
should be about one-fourth of the number of cells in the battery.
When the current was sent from 12 cells in series, through
4. decomposing cells and through the coil of the galvanometer,

Decomposition of Water by the Galvanic Battery. 93

the deflection was a little less than that which was produced by
the current from 3 cells when it passed through one decom-
posing cell and the coil. The difference arose from the imper-
fect insulation of the cast-iron cells. But when the current was
sent from the same 12 cells through 4 decomposing cells, and
then through the helix of an electro-magnet by which a small
magnetic machine was driven, the speed of the machine was
considerably greater than when the current from 3 cells passed
through one decomposing cell, and then through the coil of the
electro-magnet. The wire coiled on the electro-magnet was
about 50 feet long and one-eighth of an inch thick. The coil of
the galvanometer is about 7 feet long and three-eighths of an
inch in diameter. The resistance in the latter was insensible
compared with the resistance in the former.

The ratio which the acting surface of each electrode should
bear to that of the zine in cach circle may be found by putting
a pair of large plates into a glazed vessel, and connecting them
with the opposite ends of a battery of 4 cast-iron cells in each
of which the zinc plate is small, so that the current will pass
through the coil of a galvanometer. If a solution of carbonate
of soda be then gradually poured into the glazed vessel until the
needle ceases to recede from the magnetic meridian, that is,
until no more electricity is transmitted through the fluid, it will
be found that the acting surface of each of the electrodes, which
is covered by the fluid, is about once and a half as great as the
acting surface of the zinc plate in each circle. By pouring the
fluid to any height whatever into the glazed vessel so as to
increase the acting surface of the electrodes, no increase will be
produced in the deflection of the needle. Hence there is a limit
to the conducting power of fluids for electricity of low intensity.
A solution of carbonate of soda (no matter how thick and short
the column of fluid may be) will not, when interposed between
the opposite ends of a nitric acid battery of 4 cells, conduct
more than about one-half of the electricity which will be con-
ducted by a short, thick wire connected with the opposite ends
of the same battery. In investigating the ratio which the surface
of the electrodes should bear to the surface of each zine plate of
the battery, I used solutions of carbonate of soda of different
degrees of strength, and found that the conducting power of a
solution, which contains an ounce in each quart of water, is very
little inferior to that of the strongest solution, whilst it foams
far less. If a neutral salt could be found, which, when mixed
with carbonate of soda, would prevent its foaming, and, would
not be decomposed by the voltaic current, sheet-iron plates
coated with an alloy of lead and tin would be in every way
preferable to platina electrodes. I have tried nitrate of potash,

94. The Rev. Dr. Callan’s Experiments on the

bisulphate of potash, bichromate of potash, sulphate of soda,
borate of soda, and chloride of sodium mixed with carbonate of
soda. But they were all decomposed by the galvanic current,
as was evident from the light which the gases produced. When
the current was sent from the battery through a solution con-
taining three ounces of bichromate of potash and five of carbonate
of soda in about five quarts of water, there was scarcely any foam,
but the light produced by the gases was tinged with red, and
not so intense as the oxyhydrogen light. The heat of the flame
appeared not inferior to that of the oxyhydrogen flame. When
bisulphate of potash was mixed with carbonate of soda, the light
and heat produced were the same as when bichromate of potash
was used. The light was injured much less by mixing bichromate
of potash, or bisulphate of potash with the carbonate of soda,
than by the mixture of any of the other salts with it.

To estimate the comparative expense of the coke light and the
lime light, it is necessary, first, to determine the size of the
battery which will produce a brilliant coke light, with that of
one, which, by decomposing water, will produce a lime light of
equal illuminating power; and secondly, to determine the time
each battery will work with a given charge. Although I made
a battery of a size which I thought would be most advantageous
for producing the coke light, I have not as yet succeeded in
determining satisfactorily either of these two points. The
battery which I prepared consisted of 60 cast-iron cells in which
each zinc plate was 4 inches by 2. In the battery which
I commonly used, the zinc plates were 4 inches square. I always
found that this battery soon destroyed the coke points. On one
occasion, about five years ago, I got a coke light sufficient for
the gas microscope from a battery of 24 cells, which were
only half-filled with acid. Hence I inferred that zine plates,
2 inches by 4, would be large enough for a brilliant coke light.
When the battery of 60 cells, in which the zinc plates were
2 inches by 4, was prepared, I sent the current, first, from thirty
of them through a pair of coke points. The light was sufficiently ~
brilliant for all illuminating purposes, but did not last very long.
I then changed the connexion that I might try the effect of
40 cells. The light was then both steady and brilliant. I
think that this is the smallest, and therefore the least expensive
battery, by which, with the aid of a good apparatus for at tutitif
the coke points, a continuous light of great illuminating power
can be obtained. If the plates be smaller, the illuminating
power: of the coke points will not be sufficient; and if the
number of cells be less than 40, the electric current will not
have sufficient intensity to pass through the flame between the
coke points. With this battery a pair of coke points lasts a long

Decomposition of Water by the Galvanic Battery. 95

time. I have found that when the battery is not very powerful,
the brilliant light comes only from the positive coke point. For,
if a coke point and a copper poitit be used instead of two coke
points, and if the coke point be connected with the positive end
of the battery, the light is as brilliant as if two coke points were
employed. But if the coke point be connected with the negative,
and the copper point with the positive end, the light will be
worthless. I forgot to make this experiment when I had ocea-
sion to use a very powerful battery. I may mention here that
with 60 cast-iron cells in which the zine plates were 2 inches
by 4, I was able to fuse and deflagrate a round piece of steel
+ inch diameter. Although I made a far greater number of
experiments on the lime light than on the coke light, 1 am not
able to state positively the size of the battery, which, by decom-
posing water, would produce a lime light equal in illuminating
power to that of a pait of coke points ignited by a battery of
40 cast-iron cells in which the zine plates are 2 inches by 4.
I can only say that I think it probable that a battery twice, or
very nearly twice the size, would be required. With regard to
the length of time the two batteries would work with a given
charge, I am equally uncertaim. In decomposing water, all the
cells must be arranged in rows of four each, so that the intensity
of the current may not exceed that of 4 cells. Now, when a
current is sent from 4 cells through a good conducting fluid,
the quantity of electricity which passes through the fluid and
through each cell of the battery is only about one-half of the
quantity which would pass if the ends of the battery were con-
nected by a short, thick wire. This I have found by the galva-
nometer. Hence the battery would work about twice as long in
the former as in the latter case. When the coke points were
ignited by 40 cells, I measured the angle of deviation of the
sine galvanometer, and found it to be 31° when the needle was
in the axis of the coil, and nearly 10 inches from its centre.
When they were ignited by 60 cells, the deviation was 40°.
Unfortunately, I did not measure the angle of deviation which
would be produced by the current passing directly through the
coil of the galvanometer. The experiments were made before
my class, and I intended to measure on the next day the angle
of deviation which would be produced by the current trom 4: cells
of the same size, sent through a fluid. I was prevented from
making the experiment until I had occasion to remagnetize the
needle, and consequently I cannot now depend on its indications
being the same they would have been on the day the battery of
40 and 60 cells was used. I have since tried the effect of
a current from four of the cells on the sine galvanometer after
passing it through a solution of carbonate of soda, and found

96 On the Decomposition of Water by the Galvanic Battery.

that a deflection of 223° was produced in the needle of the sine
galvanometer. But I am inclined to think that had I made the
experiment the day I used the 40 cells, the deflection would
have been considerably less, because the needle was not then so
highly magnetized. The impression made by all my experiments
inclines me to believe that a battery would work nearly twice as
long in decomposing water as in igniting coke poits; that,
therefore, the coke hight and the lime light are nearly equally
expensive, but that the former is somewhat more ceconomical.
I shall soon have occasion to exhibit a battery of about 250 cast-
iron cells, and intend then to compare the quantity of electricity
which will pass between a pair of coke points ignited by 40
cells, with that which will pass through a thick wire connected
with the opposite ends of the same 40 cells. I intended to
investigate the decomposing power of the coil, but I must defer
the investigation till health and leisure permit me to resume
my experiments.

Maynooth College,

January 2, 1854.

P.S. I have got a new iron vessel made of a rectangular form,
for which I am preparing two sets of electrodes ; one for a battery
of low intensity, the other for a battery of high intensity. The
former will consist of 100 iron plates coated with an alloy of lead
and tin; 50 of them (the alternate plates) will be connected with
one end of the battery, and the other 50 with the opposite end.
The 100 plates will be divided into twenty groups, each contain-
ing 5 plates. Hach group will be covered all round with linen,
so that the foam produced by the ascent of the gases in the solu-
tion of soda may be made to pass through the linen, and that
thus the bubbles may be broken. This arrangement of the elec-
trodes will answer for a battery of 60 cast-iron cells arranged in
fifteen rows of four each, and in which each zinc plate is 6 inches
by 4. The quantity of the gases produced by each group of 5
plates will be equal to that which would be produced by 3 cast-
iron cells, or the 4th of 60. Now I have found that a linen
coyer on the electrodes prevents all foam when the battery does
not contain more than 5 or 6 cells, in which each zinc plate is
6 inches by 4. Therefore in the arrangement just described
there can be no foam. The electrodes for a battery of high in-
tensity will consist of 156 coated iron plates, divided into twelve
groups each contaming 13 plates. The 13 plates of each group
will form 12 decomposing cells nearly water-tight, and open only
at the top. The first plate of each group will be connected with
one end of the battery, and the last with the opposite end.
Hence when the cells are nearly filled with a solution of soda,

Mr. J. P. Gassiot on Experiments made with Rubmkorff’s Coil. 97

the voltaic current will pass simultaneously from the first to the
last plate of each group, through the intermediate plates and
fluid, and produce decomposition in each cell. This arrangement
is intended for a battery of 60 cells, in which each zine plate is
6 inches by 4, all acting in one series. The intensity of the
current from this battery will be reduced to that of 5 cells by
passing through the 12 decomposing cells. Each group of 13
plates will be covered with linen, which will prevent all foam,
because in each group the quantity of the gases will be only equal
to that which would be produced by 5 cells, or by ;4,th of 60.
January 25, 1854.

XIII. On some Experiments made with Ruhmkorff’s Induction
Coil. By Joun P. Gassiot, Esq., F.R.S.

To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,

Q* the 7th of January, 1852, Mr. Grove communicated a
paper to the Royal Society (Phil. Trans. 1852, part 1)
entitled ‘On the Polarity of the Gases ;” the experiments de-
scribed in this paper were made by him with a secondary coil appa-
ratus made by M. Ruhmkorff. Mr. Grove, who in his paper fully
describes its construction, kindly procured a similar instrument
for me, and a short time since I obtained another from this
celebrated mechanician of Paris. This last is of the same dia-
meter, but nearly twice the length of the former coil; and there
is a commutator attached to the primary coil by which the direc-
tion of the current can be instantly reversed. Three cells of

Grove’s nitric acid battery are sufficient to excite the action.

With this apparatus the transverse non-luminous or dark
bands first poimted out by Mr. Grove in the above paper, and
more particularly explained by him in a note dated June 9, 1852,
published in the Philosophical Magazine of that year, are obtained
in a very distinct manner. It is impossible to describe the
beauty of this experiment; it must be seen to be appreciated ;
but those experiments I am about to mention will explain the
power of the instrument and the nature of the investigations to
which it is applicable. It opens out a variety of new ideas as to
the extraordinary action or nature of induced currents, and as
such may probably not be uninteresting to the readers of the
Philosophical Magazine.

I may explain that the end or terminals of the secondary coil,
as described by Mr. Grove in his paper, are supported by two
small glass pillars; to these can be attached by binding-screws,
wires of any required length to form the connexion with the
apparatus necessary to be used in the following experiments :—

1. If the ends of the connecting wires are brought within 0°5
of an inch of each other, a discharge takes place through the air.

98 Mr. J.P. Gassiot on Experiments made with Ruhimkorff’s Coil.

2. Through the flame of a spirit-lamp the discharge passes at
a separation of 1 to 2 inches; and if the inner and outer
coatings of a moderate-sized Leyden jar are attached to the ter-
minals of the coil by other wires, this discharge is much height-
ened in its intensity, a long, clear and brilliant white electrical
stream passing through the flame with a sharp rattling noise.

3. If the terminals are of platinum wire, and the ends are
approximated to within 0:1 of an inch, a rapid continued dis-
charge takes place, and in a short time the negative wire becomes
red-hot; the current being reversed, this wire instantly cools,
and the heat appears in the other, which has now become the
negative.

This heating effect of the secondary current has already been
noticed by Masson, but the heat appears in the contrary direc-
tion to that which is produced inthe primary. It is well known
that the disruptive discharge which takes place in a secondary
coil only appears in the form of a spark in breaking contact with
the primary; but if the ends of the terminal wires of a secondary
coil rest on a piece of bibulous paper saturated with a solution
of iodide of potassium, the iodine will be evolved at one terminal
on making, but considerably more at the other on breaking
contact. In describing the terminals as positive or negative, it
must therefore be understood that the positive is that at which
the iodine is evolved at breaking, and remains cool in the dis-
charge throughout while the negative attains a red heat.

I have been thus particular in the description, because the
heating of the positive electrode in the voltaic battery is in itself a
curious phenomenon long since observed (Phil. Mag.1888,p.436),

and the cause of which has not as yet been satisfactorily explained. °

4. Tf the discharge is taken between two metallic or two char-
coal balls in the vacuum of a good aix-pump, the effects are very
marked ; the lower half of the negative ball is surrounded by a
bright, blue glow, while from the positive proceeds a clear,
bright, red stream of light. As the vacuum becomes more per-
fect this increases in brillianey, until the dark space is left
between the red flame and blue glow, as in Mr. Grove’s original
experiment, while the negative wire is surrounded with the
glow, the intensity of each light increasing in proportion to the
vacuum. Where the negative wire is sealed in a glass tube
having only its section exposed, the dark space is no longer per-
ceptible, as also noticed by Mr. Grove.

5. The wires were attached to my double plate gold-leaf electro-
scope, the plates of which are 8 inches in diameter; these were
separated about 04 of an inch, the leaves of the electroscope
attached to the outside terminal of the coil diverged at an angle
of 45°, and the discharge took place with a loud snap, the air
between the plates being charged and discharged as a Leyden jar.

“ .

Mr. J. P. Gassiot on Experiments made with Ruhmkorft’s Coil. 99

6. I coated about two-thirds of the inside of a Berlin glass
beaker of 4 imches depth by 2 inches width with tin-foil, leaving
about 1°5 of an inch of the upper portion uncoated. On the
plate of the air-pump I placed a glass plate, and on it the glass
beaker, covering the whole with an open-mouth glass receiver,
on which was placed a brass plate having a thick wire passing
through collars of leather; the portion of this wire within the
receiver was enclosed in an open glass tube. One end of the
secondary coil was attached to the wire and the other to the
plate of the air-pump. As the vacuum improves, the effect is
truly surprising; at first a faint, clear, blue light appears to
proceed from the lower part of the beaker to the plate ; this gra-
dually becomes brighter, until by slow degrees it rises, increasing
in brilliancy until it arrives at that part which is opposite or on
a line with the inner coating ; the whole being intensely illumi-
nated, a discharge then commences from the inside of the beaker
to the plate of the pump in minute but diffused streams of blue
light ; continuing the exhaustion, at last a discharge takes place
in the form of an undivided continuous stream overlapping the
vessel, as if the electric fluid was itself a material body running
over. When first witnessed, it appears at the moment impossible
to divest the mind of such a conclusion.

7. If the position of the beakers is reversed by placing the
open part on the plate of the air-pump, and the upper wire is
either in contact or within an inch of the outside of the vessel,
streams of blue lambent flame appear to pour down the sides to
the plate, while a continuous discharge takes place from the
inside coating.

8. A thin piece of tale or very thin glass coated on one side with
tin-foil, and the other having a figure as a star, cross letters, &c.,
also of tin-foil, produces a very beautiful experiment. The larger
coating is attached to one end of the coil; the wire of the other
is then by means of a g':7s rod brought into contact with the
figure of the star, cross, &e., which is immediately illuminated in
the most brilliant manner, and the well-known odour of ozone, as
from the electrical machine, is perceptible to an unusual degree.

9. When the air in a glass tube 4 feet 2 inches long and
2 inches in diameter, similar to those used for the aurora expe-
riments, is exhausted, the’ discharge takes place, illuminating
the entire tube.

I will not occupy your valuable space with any further detail
of experiments made by myself with this really beautiful instru-
ment, the construction of which reflects so much credit on the
ingenuity and talent of M. Ruhmkorff.

I am, Gentlemen,
Clapham Common, Yours obediently,
January 11, 1854. Joun P. Gassior,

[ 100 ]

XIV. On the Action of Alkalies on Rocks. By M. DEuEsse*.

De studying the action of alkalies on rocks, I treated the
powder of the specimen under examination in a solution
containing five times its weight of potash ; I then sought what
substances existed in the new solution.
Since many rocks contain water, I dried and weighed the
residue from the potash solution, I then heated it to redness and
weighed again: I thus obtained for the different rocks com-
parable results, as shown in the following table :—

é i x s = ‘
s | Ee atv im =) ‘ 4 See Sa «0 8
2 [Ee laze1€ | 8.| 8:le@ le | 2. lee [BeBe lez! 228
Ss jos Pie, MW 6 mail seca |soc os] E |83 ESSE on] 2m
‘& |ped|ea2s] 5 ~o | £8 | ay g ae |B ag(e 53 ef |Ba|] Se
2 } eo) S| as Be | «es | Fe ace 25 sel eamlas .|3e soe
= BES SE | GS) Sc ).88 (Atl wa) 294] ee 8) Fea] seg/8 $3
Ss BSR aSh) 2a] BS | EH |@e-2] 28) 8h |Setslass| Shalaag Baa
o 1|/ES\SaS| oS S 4s Bog SES S 65 5/2 on en Ss| o8e
5 |}Sa sl S28] Sa | me] SE) ead as jes’ BE so elant | S08
2 | 559/23 =| 2 ss ars est = ad Weare =| 8 |2 2 g| sg s|Soel se F
o |".98/ SHS ~ Odd | aes 5g} a9 BG | ato! See). M|/ Se FESS
-B Sm rl bes| S2| 2] ss (83 | sa] 25 | See Ea sies |Se| ePse
S is a) oF 5) 2& ss SE |ao — out SE ovidn a 8
3 Zreigee| 8 | $2) 2s /38 | 2 | 22/22 |EGEIEE | ge| Fas)
$ 2 BA |e EI 3 So |ao
A |E& BES = a=] = = ° = ya gaa" 56 “3a
Sit ease otach | 2 | 36°00] 17-06 19-40 12-23) 9-50) 19:55] 18:39) 11-45) 7-05) 8:50) 7-68) 4-50
Alumina dis-
solved by the } 3 traces} 2°39) 3°75) 1:16) 1-25] 1:85) 3°78) 1:55; 2:10) 2:20) 2°85) 2-60
potash ....
Total loss of TCTs Gears eee eel en ee ee ae i
ee eae S 4 37-85) 27:27] 30°15) 17-89] 16:55) 26-85, 24-44! 17-20) 18-60) 18-41) 15°35] 8-50] 5:80 |
residue......

Some general conclusions can be drawn from my researches.
When an alkali attacks a rock, it dissolves from it not only
silica, but also alumina, water, potash and soda. Besides a little
lime, magnesia and traces of oxide of iron are taken up by the
alkaline liquor.
The quantity of silica dissolved is always greater than that of
all the other substances. °
Granite may be said to be unaffected by boiling in a solution
of alkali; quartziferous porphyry only loses a few hundredths.
Lava, basalt and melaphyre lose not more than 20 per 100.
Trachyte, retinite, perlite and obsidian are the most attack-
able ; within my experience their loss did not exceed 40 per 100.
A rock containing water is much less easily affected by the
alkalies after it has been calcmed. Thus, in the perlite from the
Cape of Gatis, the action of the alkali before and after caleming
varied in the ratio of 23 to 1.
On the other hand, a rock is much more easily affected when
in a state of decomposition. Thus, argillaceous eurites and

* Communicated by Sir Robert Kane.

(Phil. Mag. S, 4. Vol. 7.—To face page 100.

Canshoric acid, Salskere acid

spec. syrupy. nitric acid.

it ia. Caustic soda,
Aqua regia + spec, gray. 1°340.

—- ——

0 fluid white mass.
0 fibrous yellowish-white
mass.
India nut...... thick 0 orange-white. fibrous white mass.
Pale rapeseed) dirty, 0 dark brown. 0 fibrous yellowish-white
v mass.
Poppy esses d 0 slight yellow.| _ 0 fluid intense rose-
; coloured mass.
French nut -.. Gyn yellow.| dark brown. | _ yellow. fibrous orange mass.
Sesame..-....- c 0 green beco- ditto. fluid orange mass with
ming intense brown liquor beneath.
red.
Castor «..... v 0 brownish-red. 0 fibrous pale rose-

coloured mass.

Hempseed ...|thick green. green beco- green.

fibrous light brown

y ming black. mass.
Linseed.........| fluicwn yellow ditto. greenish-- fluid orange mass.
green. yellow.
Lard ............| pinki 0 brown. 0 fluid pink mass.
Neat’sfoot ...\dirty 0 dark brown. | slight yellow. |fibrous brownish-yellow
Aas, mass.
Sperm ee daark red. dark brown. ditto. fluid orange yellow
- mass.
MORN hasssdatseces « ditto. ditto. ditto. ditto.
Cod liver ...--- ( ditto. ditto. yellow. ditto.

cellular paste,
line quarts,
jaxonys

Ry

hyry, quartziferous,

Po:
reddish-pra
and much.
‘trom

General Table of Reactions.

(Phil. Mag. S. 4,

Vol. 7.—To face page 100.

Oils.

French nut...

Sesame:+-....++

Castor «srs
Hempseed -.-

Linseed.

Lard

Neat’sfoot ...
Sperm «2...

Seal sess

Caustic soda,
spec, gray. 1°340,

slight yellow.
ditto.
thick and white.
dirty yellowish-
white.
ditto.

ditto.

ditto.

white.

thick brownish-
yellow.

fluid yellow.

.| pinkish-white.

dirty yellowish-
* — white.

dark red.

ditto.

Cod liver ......

ditto.

Sulphuric acid,
pec: ray. 1'475)

green tinge,

ditto.

0
brownish.

green tinge.

intense green.
green.
dirty white.
yellow tinge.
light red.

ditto.

purple.

Sulphuric acid,
spec. gray. 1°530,

greenish-white.

gray.

dirty white.
pink.

dirty white.
gray.

greenish dirty
white.

dirty white.
intense green.
dirty green.
dirty white.
brownish dirty
white.

red.

ditto.

purple.

Sulphuric acid,
spec, gray. 1635.

light green.
brown.

light brown.

brown.

brown.

0
intense green.
green.
light brown.
brown.
‘intense brown.)

ditto.

Nitric acid,
spec, gray, 1180.

greenish.

ditto.

0
yellow.

orange-yellow.

light yellow.
slight yellow.

pink.

ditto.

0

Nitric acid,
spec. gray. 1'220,

greenish,

ditto.

yellowish-red.
red.

ditto.

0
greenish dirty;
brown.
yellow.
0
light yellow.

ditto.

light red.

0

Nitric acid,

greenish.

ditto.

red.
dark red.

ditto.

0

brown.

green beeo-
ming brown.

very slight
yellow.

light brown.

red.

ditto,
ditto.

sp. gray, 1'390, + sp, grav. 1°340.|

greenish dirty} fibrous light

Caustic soda, |

fluid white
mass,

fibrous white
mass.

ditto.

fluid white
mass.

light red fluid
mass,

fibrous red
mass.

fluid red mass
with brown li-
quor beneath. |

fibrous white
mass.
brown mass.

fluid yellow
mass.

fluid mass.
fibrous white
mass.

fluid mass.

ditto.

ditto.

Phosphoric acid,
syrupy.

slight green.

ditto.

0

Sulphuric acid

nitric acid.

dark brown.

orange-white.

dark brown.

slight yellow.

brown yellow.| dark brown.

0 green beco-
ming intense
red,
0 brownish-red.
green. green beco-
ming black.
brown yellow ditto.
green.
0 brown.

0 dark brown.
dark red. dark brown,
ditto. ditto.
ditto. ditto.

orange-yellow.|

green.
greenish-
yellow.
0

slight yellow.
ditto.

ditto.

yellow.

Aqua regia. + Caustic soda,

spec, gray, 1340.

fluid white mass.

fibrous yellowish-white
mass.

fibrous white mass.

fibrous yellowish-white
mass.

fluid intense rose-
coloured mass.

fibrous orange mass.

fluid orange mass with
brown liquor beneath.

fibrous pale rose-
coloured mass.

fibrous light brown
mass.

fluid orange mass.
fluid pink mass.
fibrous brownish-yellow

mass.

fluid orange yellow
mass.

ditto.
ditto.

Mr. F. C. Calvert on the Adulteration of Oils. 101

kaolins, which are merely decomposed granitic rocks, undergo in
the alkali losses much greater than those of granitic rocks.

Other conditions being the same, the action of alkalies on
rocks increases with the amount of silica, with the absence of
crystalline structure and of hyaline quartz. On this account,
vitreous rocks which contain little or no quartz, as retinite, obsi-
dian, trachyte, are very strongly affected by alkalies.

When instead of alkalies we use alkaline carbonates, some
rocks, especially the vitreous, are still acted upon, but much less
energetically than by the caustic alkalies.

The readiness with which alkalies, and even alkaline car-
bonates, act upon rocks, shows how cautiously they should be
used for the separation of the free and directly soluble silica that
may be mechanically mixed in a rock, as particularly in the
kaolins and the finer clays.

I may remark, that, for instance, in obsidian the silica dis-
solved is not free, but in the state of soluble silicate; more-
over, in retinite the silica is not im the state of opal, as is sup-
posed, but in that of soluble hydrosilicate. Generally in all
vitreous or porphyritic rocks, hydrous or anhydrous, the silica is
held in a combmation, not definite, forming the paste of these
rocks, and which is attacked by the alkali.

The water penetrating rocks by infiltration always contains,
even near the surface of the earth, small quantities of alkaline
salts; it is easy, then, to conceive that these salts should
aid in decomposing rocks and in producing pseudomorphisms.
But at a greater depth water becomes largely impregnated with
alkaline salts, the temperature and pressure increasing rapidly ;
it then influences greatly the rocks with which it is in contact.
This is the case with the water of mineral springs, of the geysers,
of mud volcanos, and in general of volcanic regions. Conse-
quently the action of the alkalies and of the alkaline salts plays
an important part, not only in the formation of pseudomorphs,
but also in the chemical reactions which take place in the interior
of our planet.

XV. On the Adulteration of Oils.
By F. Cracr Carvert, Esg.*

aN consequence of the large quantities of oils used at the pre-

sent day for machinery, woollen, &c., many varieties are
introduced into the market, and much temptation exists to mix
or adulterate the most expensive ones. Having been at various
times called upon to examine samples of oil, I ascertained that
the processes known to discover adulteration were too general in

* Communicated by the Author.

102 My. F. C, Calvert on the Adulteration of Oils,

their application to enable me to obtain satisfactory results, To
this class belong the delicate process recommended by M. F,
Boudet, principally for the detection of drying oils in olive by
the action of hyponitric acid; and M. Rousseau’s diagometer,
which is based on the very inferior conducting power of olive oil
as compared with that of the others.

For distinguishing one class of oils from another we have
M. Faure’s method, which consists in the brown or black tinge
which fish oils exclusively assume when a stream of chlorine gas
is passed through them ; and M. Maumené’s, by which the drying
oils may be distinguished from the non-drying ones, owing to the
fact that the latter, when mixed with strong sulphuric acid, give
rise to a much higher temperature; but although M. Fehling
has endeayoured lately to give more precision to M, Maumené’s
researches, it is far from being satisfactory,

There are other processes the characters of which are not suf-
ficiently distinct to be employed with any degree of certainty ;
such is M. Faure’s, which consists in adding a given quantity of
caustic ammonia to oils, and noticing after they have been mixed
the peculiar appearance which the white or yellow thick fluids
present, The same may be said of the process proposed by
M. Heidenreich with monohydrated sulphuric acid, or that of
M. Diesel with concentrated nitric acid ; for the chemical actions
are so violent, that the characteristic colorations, which are at
first produced, rapidly disappear in consequence of the destruc-
tion of the oils, .

These facts induced me to examine what would be the action,
on oils, of the above acids when diluted, and the satisfactory
results obtained are described in this paper.

The marked colorations produced may be considered as derived
from two distinct chemical actions ;—first. They appear due to
certain foreign matters which are dissolved im the oils, and which
existed in the substance from which they were extracted;
secondly: The diluted acids have probably an action on the
component parts of the oils themselves; for if caustic soda be
added to oils so acted upon, a different result is obtained than
when no acid has been previously applied ; this fact being clearly
illustrated with French nut oil, as it gives a semi-saponified fluid
mass when caustic soda of spec. grav. 1:340 is alone mixed with
it, and a fibrous mass when treated by dilute nitric acid previous
to the addition of the alkali.

It may betinteresting here to remark, that fish oils have pre-
sented distinet reactions from other animal or vegetable oils;
consequently, in my opinion, not only has cod-liver oil a different
composition to that of other oils, as shown by the researches of
M. Winckler, but also probably sperm and seal oils.

Mr. F. C. Calvert on the Adulteration of Oils. 103

The most difficult part of my researches has been to procure
oils the purity of which I could depend on, and to arrive at this
object I was obliged in many cases to obtain samples from their
sources of production on the Continent; and even then I took
the precaution of ascertaining their degree of purity by applying
to them the various tests which I shall describe further on.

The reason why I employed so many reagents is, that the
adulterations which commercial interests may haye or dictate,
are numerous; and that the reactions presented by organic
substances, and especially oils, are exceedingly delicate. I would
strongly recommend that samples of pure oil be tested compa-
ratively with those suspected of being adulterated, and never to
apply one only of the proposed tests, but all those giving cha-
racteristic reactions with a given oil.

I have great pleasure in acknowledging the intelligence, in-
dustry, and chemical knowledge exhibited in these tedious
researches by my assistant, Mr. Charles Lowe.

As the reactions presented by the various oils depend upon
the special strengths and purity of the reagents, not only great
eare should be taken in their preparation, but also the exact
mode and time required for the chemical action to become appa-
rent should be attended to; these I have taken care to give with
each reagent.

Caustie Soda Solution of spec. grav. 1:°340.—The reactions
given in the following table are obtained by adding one yol. of
the above test-liquor to five vols. of oil, well mixing them, and
then heating the mixture to its point of ebullition :—

Dark colorations. Light colorations.
Fish oils, Vegetable oils. Animal oils. Vegetable oils,
Sp - thick,yell di low Pale d > di
erm. . ck,yellow- irty yellow- € rapesee irty
Seal .. fre Hempseed { ish-brown. Neat’ sfoot { ish-white. Poppy ...... yellow-
Cod liver Linseed.. yellow fluid. 5.04 rae French nut .. ( ish-
via white. Sesame...... rf white.
Castor ......
India nut white
: (thic )
Oliver... 5... }¥ellow.

Caustic soda of spec, grav. 1:340 is principally useful to
distinguish fish from other animal and vegetable oils, owing to
the distinct red colour which the former assume, and which
coloration is so distinct, that 1 per cent. of fish oil ean be de-
tected in any of the others. This table should also he consulted
when the question is, not to discover other adulterations, but to
distinguish some of the oils: for instance, hempseed acquires a
brown yellow colour, and becomes so thick that the vessel whieh
contains it may be inverted without losing any of its contents,

104. Mr. F. C, Calvert on the Adulteration of Oils.

whilst linseed assumes a much brighter yellow colour, and _re-
mains fluid. India nut oil is characterized by giving a white
mass, becoming solid in five minutes after the addition of the
alkali, which is also the case with gallipoli and pale rape, to the
exclusion of the other oils which remain fluid.

Although it is probable that the reason why some of the oils,
on the application of this reagent, acquire a mucilaginous appear-
ance whilst others become stringy or fibrous, is due to the greater
or less facility with which they are saponified, still I regret that
I have not had the time to examine this point carefully.

Action of diluted Sulphuric Acid on Oils.

As different strengths of this acid have distinct reactions on
the oils I had at my disposal, and as they may be employed to
discover some known commercial adulterations, I shall diseuss
separately each series of reactions.

Sulphurie Acid of spec. grav. 1:475.—The mode of applymg
this acid consists in agitating one yol. with five vols. of oil until
complete admixture, and then allowing the whole to stand for fif-
teen minutes, when the appearance is taken as the test reaction.

Not coloured. Coloured.
——_-—_—_ Oh
Animal. Vegetable. Fish, Animal. Vegetable.

SS ata oF oe —

Lard..dirty.} India nut. Sperm.... plea Neat’s- syellow Olive ..-. ) peen

Pale rapeseed. Seal...... red. foot oer Gallipoli . . os :

Poppy. Codliver.. purple. Sesame .. Be.

Castor. Linseed .. green.

intense

Hempseed } cane

French nut. . brownish.

The most striking reactions in this table are those presented
by hempseed and linseed; for the green coloration which they
acquire is such, that if they were used to adulterate any of the
other oils to the amount of 10 per cent., their presence would
be indicated by the distinct green tinge they would communicate
to the others. The red colour assumed by the fish oils with this
test are also sufficiently marked to enable us to detect them im
the proportion of one part in one hundred of any other oil; and
it is at the point of contact of the oil with the acid, on their
being allowed to separate by standing, that the colour is princi-
pally to be noticed.

Sulphuric Acid of spec. grav. 1-530.—Having obtained by the
application of the preceding acid a certain number of charac-
teristic reactions, I was induced to try the influence of a stronger
one, and IJ therefore agitated one vol. of it with five vols. of oil,
and allowed the mixture to stand five minutes.

Mr. F, C. Calvert on the Adulteration of Oils. 105

Light colorations. Dark colorations.
Animal, Vegetable. Fish, Vegetable.
-_ co ee ae =
dirty . greenish- Sperm.... Gallipoli ....
tard... — 4 Olive. ..4..+ { white. Seale’ e.'. }red. French nut ., } BIOs
rownis eenish Cod liver.. purple, intense
Neat foot| dirty Sesame oe { "ass Hempseed .. { green.
white. white. Linseed dirty
India nut.... dirty ~ ae Sn PTeens
Poppy .....- wivte

Pale rapeseed .. pink.

As hempseed, linseed, fish, gallipoli, and French nut are the
only oils that assume with the above reagent decided colorations,
they can be discovered in any of the others.

Sulphuric Acid of spec. grav. 1:635.—This acid was used in a
similar manner to those above, and the coloration noted after
two minutes.

Not coloured. Distinctly coloured.
as ceo _ ——————_—_<—_—
Vegetable. Fish. Animal, Vegetable,
—— _—_—_——S #§——————— Or
Poppy. Sperm.. antenne Neat’sfoot. . brown. Olive (light)........
Sesame. Seal... b Tarek os ss light brown. Hempseed (intense) }green.
Castor. Cod liver ROW Ts imines canoe slate
Gallipoli ..........
Pale rapeseed ......
French nut ........ joe
India nut (light)....

I wish to draw especial attention to this acid, as it gives di-
stinct and widely differing reactions from those of the former
acids. The colorations produced by sulphuric acid, spec. grav.
1635, are so marked that they may be consulted with great
advantage in many cases of adulteration; for example, I have
been able to detect, distinctly, 10 per cent. of rapeseed in olive
yo of lard in poppy, of French nut in olive, of fish oil in neat’s-
oot.

I was much struck by the gradual increase of coloration
assumed by some of the oils when treated by sulphuric acid of
different strengths. Thus I found that gallipoli, which was
white with No. 1 sulphuric acid, becomes brown with No. 3 ;
pale rape, which was white with No. 1 acid, gives a pink colour
with No. 2, and a brown with No. 3; whilst neat’sfoot is of a
light yellow with No. 1, but becomes brown with No.3. These
results therefore clearly show the decomposing action of sulphuric
acid on oils, and that an acid of spec. grav. 1:635 is the maximum
strength that can be used, for nearly all the oils beginning to
carbonize, their distinct colorations are destroyed.

Action of Nitric Acid of different strengths on Oils.

Owing to the reasons given in the first part of this memoir, I
employed diluted acid and obtained a series of reactions, some
of which will, I hope, prove useful in some special cases of adul-

Phil. Mag. 8. 4. Vol. 7. No. 43. Feb, 1854. I

106 Mr. F. C. Calvert on the Adulteration of Oils.

teration, and interesting as showing the influence of gradual
oxidation on oils.

Nitric Acid of spec. grav. 1:180.—One vol. of this acid was
agitated with five vols. of oil, and the appearance, after standing
five minutes, is described in the followmg table :—

Not coloured. Coloured.
—————-qxO«O oO“ oOoIouwue——_}
Fish. Animal. Vegetable. Fish. Animal, Vegetable.

—_—_——s A

i ‘rer |
Cod liver. Lard. India nut. gee f Slight Neat’s- light Olive...... green-
Pale rapeseed. Sperm { yellow. foot } yellow. Gallipoli... } i

Poppy: Seal.... pink, dirty
Castor. Hempseed, . { green.
French nut
Sesame
( orange) yellow.
Linseed

This test is sufficiently delicate to detect, distinctly, 10 per cent.
of hempseed in linseed, as the latter assumes the greenish hue
so characteristic of the former. Although olive acquires also a
green colour, still its shade is such that it is easily distinguished
from that of hempseed.

Nitrie Acid of spec. grav. 1°220.—I employed this stronger
acid with the view of increasing the colorations of certain oils,
so as to render them sufficiently marked to ascertain the pre-
sence of these oils when mixed with others. The proportions
used and the time of contact were the same as above.

Not coloured. Coloured.
te ——
Fish. Animal. Vegetable. Fish. Animal, Vegetable.
Cod liver. Lard. India nut. light Neat’s- | light Poppyyellow)
Pale rapeseed. Sperm { yellow. foot } yellow, French nut .. }red.
Castor, Seal {bent Pca yy ge
< red, lve
Gallipoli } Steenish.
green-
Hempseed err y
brown

Linseed... . yellow.

The chief characters in the above table are those presented by
hempseed, sesame, French nut, poppy, and seal oil; and they
are such that not only may they be employed to distinguish
them from each other, but are sufficiently delicate to detect their
presence when mixed with other oils inthe proportion of 10 per cent.

Nitric Acid of spec. grav. 1°330.—One vol. of this acid was
mixed with five vols. of oil, and remained in contact five minutes.

Not coloured, Coloured.
—_—_—_—_ ve ee eee
Vegetable. Fish, Animal. Vegetable.
Indi § Sa a Ceili Beegdu. tsa
ndia nut. Sperm.. saa slight ODI ie be o nie
Pale rapeseed. Seal.... fred , Lard.. { yellow. French nut (dark) pred
Castor, Cod liver Nenii fot. light brown. Sesame (dark) ..
OUVE Foes sc ics'cs } green-
Gallipoli ,....... ish,
Hempseed ...... { greats dirty
; green becom-
Linseed ...,., a { ing brown.

Mr. F, C. Calvert on the Adulteration of Oils. 107

The colorations here described are very marked, and can be.
employed with advantage to discover several well-known cases of
adulteration ; for instance, if 10 per cent. of sesame, or French
nut, exists in olive; as for poppy with the same oil, the tinge
produced not being so intense as the preceding ones, so small
an adulteration cannot be detected with certainty ; and admitting
any doubt remained in the mind of the operator as to whether
the adulterating oil was sesame, French nut, or poppy, he would
be able to decide by applying the test described in the next table,
where he will find that French nut oil gives a fibrous semi-
saponified mass; sesame a fluid one, with a red liquor beneath ;
and poppy also a fluid mass, but floating in a colourless liquor.

The successive applications of nitric acid of spec. grav. 1°330,
and of caustic soda of spec. grav. 1°340, can also be successfully
applied to detect the following very frequent cases of adultera-
tion :—

Ist. That of gallipoli with fish oils, as gallipoli assumes no
distinct colour with the acid, and gives with soda a mass of
fibrous consistency, whilst fish oils are coloured red and become
mucilaginous with the alkali.

2nd. That of castor with poppy oil, as the former acquires a
reddish tinge, and the mass with the alkali loses much of its
fibrous appearance.

3rd. That of rapeseed with French nut, as nitric acid im-
parts to the former a more or less red tinge, which on addition
of the alkali not only increases, but also renders more fibrous
the semi-saponified mass.

The colorations which divers oils assume under the influence
of the three above nitric acids clearly illustrate the remarks
made at the commencement of this paper, that the reason why
the chemists who preceded me in these tedious researches had
not arrived at satisfactory results in distinguishing oils and their
various adulterations, was owing to the acids they employed
being so concentrated that all the distinctive colorations were
lost, the oils becoming yellow or orange. But there is no doubt
that the above reagents will enhance the value of M. F. Boudet’s
process, as they afford very useful data to specify the special oils
mixed with olive.

Caustic Soda of spec. grav. 1:340.—The following reactions
were obtained on adding ten vols. of this test-liquor to the five
“a of oil which had just been acted upon by one vol. of nitric
acid ;—

12

108 Mr. F. C. Calvert on the Adulteration of Oils.

If a fibrous mass is formed. If a fluid mass is formed.
as | ‘ag 5 yan}
Animal. Vegetable. Fish. Animal. Vegetable.
—_—_ (SSS SS ees
Neat’s-]_)-; Gallipoli... Sperm. Bard) Olive pes. 3 ate. apes .
foot } white. India nut.. >white. Seal. Pale rapeseed . } white.
Castor.... Cod liver. Linseed ..... . yellowish.
French nut... pi. Poppy (light). 5 P
ight brown liquor pred.
Bempecas { brown. Sesame { beneath ..

Having given in a previous paragraph some of the most useful
reactions contained in this table, I shall simply call attention to
the following mixtures :—neat’sfoot with rape, gallipoli with
poppy, castor with poppy, hempseed with linseed, sperm with
French nut, and gallipoli with French nut. It is also necessary
here to mention, that the brown liquor on which the semi-sapo-
nified mass of sesame swims is a very delicate and characteristic
reaction.

Phosphoric Acid.—One vol. of syrupy trihydrated phosphoric
acid was agitated with five vols. of oil and gave the following
results :—

Not coloured. Coloured.
A — Se
Animal. Vegetable. Fish. Vegetable.
Lard. India nut. Sperm.. dani Olive (slight) ........
Neat’sfoot. Pale rapeseed. — Son ia Gallipoli (slight)...... green
Poppy. Cod liver fp PEREDOREGU oi crane sie
Sesame, Linseed (brown yellow)
Castor. Rrench nut. cay. ai brown yellow.

The only reaction to be noticed is the dark red colour rapidly
becoming black, which phosphoric acid imparts exclusively to
the fish oils, as it enables us to detect one part of these oils in
1000 parts of any other animal or vegetable oil; and even at
this great degree of dilution, a distinct coloration is communi-
cated to the mixture.

Mixture of Sulphuric and Nitric Acids.

The results given in the following table are obtained on agi-
tating one vol. ofa mixture of equal volumes of sulphuric acid of
spec. grav. 1°845, and nitric acid of spec. grav. 1330, with
five vols. of oil and allowing the whole to stand two minutes :—

If coloured,
RR. — ay
Fish. Animal. Vegetable.

—_ —y im

Sperm .. | OF i eee GAL 24.5 oie etpine dee a>

Seal.... jaa brown. Neat’sfoot (dark) } brown. Pale rapeseed ..........0. i

Cod liver Brenchinut) 0025.50.00 Wie
Sesame (becoming intense

ROU) sfc mien ft oteeeee eal

Hempseed (becoming black) ( 8°
Linseed (becoming black) ..
Olive (orange) slight ......
Poppy (slight) ..........--. }yellow.
Indian nut (orange) slight .. white.
Canton iceans avisdeniea eric Eegyeah-

My. F. C. Calvert on the Adulteration of Oils. 109

As three oils remain nearly colourless, viz. those of poppy,
olive, and India nut, we are enabled to detect in them the pre-
sence of any of the others; and when olive or poppy are adul-
terated with sesame, the green colour at first produced is
much more persistent than with sesame, consequently it is ne-
cessary that the acid and the oil suspected of containing it should
remain in contact for about ten minutes in order to obtain the
ultimate brownish-red colour of the sesame; in fact it is so
intense, that it may be usefully employed to detect this oil when
mixed with others.

Aqua Regia.—In consequence of the results obtained with
nitric acid I was induced to try the action of aqua regia; but [
found that when it was composed in the ordinary way of three
vols. of hydrochloric and one of nitric acid, the reactions produced
nearly coincided with the last-named acid; I therefore prepared
several aque regi, in which I gradually increased the propor-
tion of hydrochloric acid, and after having tested them, I adopted
one composed of twenty-five volumes of hydrochloric acid of spec.
gray. 1155, and one volume of nitric acid of spec. grav. 1:330,
and allowed them to stand about five hours, The reactions
described in the following table are those which took place when
a mixture of five vols. of oil with one vol. of aqua regiawas agitated
and allowed to stand five minutes :—

Not coloured. Coloured.

-—“ -—_—_ aa ee eee ol

Animal. Vegetable. Fish. Animal. Vegetable.

Ne ll oan) oho

Lard. Olive. Sperm (slight) Neat’s- | slight French nut....

Gallipoli. Seal (slight). . k yellow. foot J yellow. Sesame ...... low.
India nut. Cod liver .... Linseed (green- Enon
Rapeseed. BBD A och eale ys
Poppy- Hempseed.... green.
Castor.

When the facts contained in this table are compared with the
preceding ones, we are struck with their uniformity, and are led
to infer that no marked action had taken place; but this con-
clusion is erroneous, as most of them assume a vivid and distinet
coloration on the addition of an atkali of spec. grav. 1°340, as
seen in the following table :—

If a fibrous mass is formed. If a fluid mass is formed.
—— _ os —
Animal, Vegetable. Fish. Animal. Vegetable.
Neat’s- brownish- Gallipoli (yel- Sperm .+ ) orange- Lard., pink. Olive.. white.
foot yellow. lowish) .... | Seal.... ie P {ner
India nut.... >white. Cod liver} YCOW: OPPY**Y rose.
Pale rapeseed orange with
(yellowish)... Sesame 4 brown liquor
Castor ...... pale rose. beneath.
French nut .. orange. Linseed orange.
Hempseed .. {ght eae

The characters presented in this table are such that we can

110 Mr. F. C. Calvert on the Adulteration of Oils.

discover with facility 10 per cent. of a given oil in many cases of
adulteration ; for example, poppy im rape, olive, gallipoli, and
India nut, as all of them assume a pale rose-colour ; but when
poppy is mixed with olive or castor oils, there is a decrease in
the consistency of the semi-saponified mass.

By the aid of this reagent we can also ascertain the presence
of 10 per cent. of French nut in olive or linseed, as the semi-
saponified mass becomes more fluid; and as to French nut in
pale rape, gallipoli and India nut, it is recognized in consequence
of their white mass acquirimg an orange hue. With respect to
linseed in hempseed, it is detected, as it renders the fibrous mass
of the latter more mucilaginous. Sesame also gives with this
reagent the same characters as those which it afforded with nitric
acid and an alkali; and poppy is distinguished from all other
oils by giving in this case a semi-saponified mass of a beautiful
rose colour.

To give an idea how the tables are to be used, I shall suppose
a sample of rapeseed oil adulterated with one very difficult to
discover. I first apply the caustic alkali test, which in giving a
white mass proves the absence of the fish oils together with those
of hempseed and linseed; and as no distinct reactions are pro-
duced by the oils under examination when mixed with the three
sulphuric and nitric acids above mentioned, poppy and sesame
are thrown out, as they are reddened; neat’sfoot, India nut,
castor, olive, and lard resting only in the scale of probability.
In order to discover which of these is mixed with the suspected
oil, I agitate a portion of it first with mitric acid of spec. grav.
1:330, and then with caustic soda; and their mutual actions
exclude neat’sfoot, India nut and castor, as the sample does not
give a fluid semi-saponified mass. The absence of olive is proved
by no green coloration being obtained on the application of
syrupy phosphoric acid. As to the presence of lard oil in the
rape, it is ascertained on caustic soda bemg added to the oil
which has been previously acted on by aqua regia, as the latter
gives a fibrous yellowish semi-saponified mass, whilst the former
yields a pink fluid one.

In conclusion, I trust that the reagents described in this
paper, and the new method of applying successively two of them
to any particular oil, will prove useful, not only to detect the
numerous admixtures of oils we have noticed, but also to trace
and determine in a given oil the presence of any of the others
which we have examined ; and I give a general table of the pre-
ceding reactions in order to facilitate the research for any adul-
teration.

Royal Institution, Manchester,
January 11, 1854.

ene ny eee

XVI. On the Mechanical Action of Heat. By Wri11aM JouN
Macaquorn Rankine, C.E., F.R.SS. Lond. and Edinb. &€c.

[Continued from p. 21.]

Section I1.—Of Real and Apparent Specific Heat, especially
in the State of Perfect Gas.

(9.) ey lige apparent specific heat of a given substance is found

by adding to the real specific heat (or the heat which
retains its form in producing an elevation of one degree of tem-
perature in unity of weight) that additional heat which disap-
pears in producing changes of volume and of molecular arrange-
ment, and which is represented by Q! in equation 6 of Section I.,
and taking its total differential coefficient with respect to the tem-

perature. Hence, denoting total apparent specific heat by K,
K= dQ dQ’ dQ , dQ dQ! dV

hee? eae a Ee ee

- cay { trea LE -8)-D}- 09

Another mode of expressing this coefficient is the following :-—

Denote the ratio A
a
—_ by N
. BALI Ss yin Wanll ener ewer ka)
and the real specific heat by
at
= CaMN

Then
; dV({1 dU dU
Kae{1+ne—o( Gy — av -=)}. pee

The value of me is to be determined from the conditions of

each particular case ; so that each substance may have a variety
of apparent specific heats, according to the manner in which the
volume varies with the temperature.
dV
If the volume is not permitted to vary, so that eo =0, there
is obtained the following result, being the apparent specific heat
at constant volume :—

feng)
=0(1-No—0)P). - oy, eee

(10.) When the substance under consideration is a perfect

112 Mr. W. J. M. Rankine on the Mechanical Action of Heat,

gas, it has already been stated (equation 7) that
sic pach cc
ar ae ae
and because the volume of unity of weight is directly as the
absolute temperature and inversely as the pressure,
ldV_1_ ap a0)
Vidreptiow2 Gre bk eee
Hence the following are the values of the apparent specific
heats of unity of weight of a theoretically perfect gas under dif-
ferent circumstances.
General value of the total apparent specific heat :—

1 2
= oan W Te) (4 + a) }
1
=omint 9 (4 wt fz) }

Apparent specific heat at constant volume :—

kyon ts -5}
ns(s4x(¢-4))

Apparent specific heat under constant pressure :—
gouty ( apetned a
?=OnM\N =

=1{14N(1—5) }. J

The ratio of the apparent specific heat under constant pressure
to the apparent specific heat at constant volume is the followmg:—

wii a
Kp 1+N(1 ) : T :
seca ed Salis as OREICED)

Ky 1+Nn(£—5) 14N(£-5

The value of « is unknown; and, as yet, no experimental data
exist from which it can be determined. I have found, however,
that practically, results of sufficient accuracy are obtained by

(18)

. : . . K
regarding « as so small in comparison with 7, that -, and a for-
5

2
ric PRt. ;
tiori —3, may be neglected in calculation*.
a

* The mean value of k, as computed from experiments made by Mr. Joule
and Professor William Thomson in 1852, is about 2°1 Centigrade; but

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 1138

Thus are obtained the following approximate results, for per-
fect gases, and gases which may without material error be treated
as perfect.

General value of the total apparent specific heat :—
bopl indi ee AT
K= Galt Far) Pt ge
ee TdP
=m wt! par):
Apparent specific heat at constant volume :—

5; . (20)
Ky =a =t

being equal to the real specific heat.
Apparent specific heat under constant pressure:— |

1 1
Ratio of those two specific heats :—

a SNES Sta yee ee (21)

This ratio is the quantity called by Poisson y¥, in his researches
on the propagation of sound.

(11.) It is unnecessary to do more than to refer to the
researches of Poisson, and to those of Laplace, for the proof that
the effect of the production of heat by the compression of air is
the same as if the elasticity varied in proportion to that power
of the density whose index is the ratio of the two specific heats ;
so that the actual velocity of sound is greater than that which it
would have if there were no such development of heat, in the
proportion of the square root of that ratio*.

The following is the value of the velocity of sound in a gas,
as given by Poisson in the second volume of his Traité de
Mécanique,

mh

aHA/g.y (+ETD=, «= «)(22)

where a denotes the velocity of sound, g the velocity generated
by gravity in unity of time, E the coefficient of increase of elas-
ticity with temperature, at the freezing-point of water, T the

this result is subject to some uncertainty. The details of the calculation
are given in the sixth section of this paper, published in the Transactions
of the Royal Society of Edinburgh, vol. xx. part 4.

* This theorem is proved for all substances whatsoever in a paper on the
Centrifugal Theory of Elasticity, published in the Transactions of the Royal
Society of Edinburgh, vol. xx. part 3.

114 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

temperature measured from that point, m the specific gravity of
mercury, A that of the gas at the temperature of melting ice,
and pressure corresponding to a column of mercury of the
height 4. It follows that the ratio y is given by the formula

a’A
gah ET) (A)

Calculations have been made to determine the ratio y from
the velocity of sound; but as many of them involve erroneous
values of the coefficient of elasticity HE, the experiments have to
be reduced anew.

The following calculation is founded on an experiment quoted
by Poisson on the velocity of sound in atmospheric air, the
values of H, m, and A bemg taken from the experiments of
M. Regnault.

y=1+N nearly =

a=340°'89 metres per second.
g=9™'80896. h=0™-76, T=15°9 Centigrade.

nm

E=0:003665 ;5 — =10513.

A
Consequently, for atmospheric air,
y=1-401.

The results of a reduction, according to correct data, of the
experiments of Dulong upon the velocity of sound in atmospheric
air, oxygen, and hydrogen, are as follows :—

Atmospheric alr. . . .) y= 1410
OMPRe Ries le Ren oe lena MAE
Hydrogen = feceriite este 8 i DPaRG

Thus it appears, that for the simple substances, oxygen and
hydrogen, the ratio N is the same, while for atmospheric air it
is somewhat smaller*.

* The following are some additional determinations of the value of y for
atmospheric air, founded upon experiments on the velocity of sound :—

Observers, Centigrade. Metres per second,
Bravais and Martins: mean of several
experiments at temperatures varying 2 20.6 ,
fon be to 112 Ceneiiratie | 0 332°37 140955
to 0° (Comptes Rendus, xix.)...++++4.
Moll and Van Beek: reduced to . . 0 332°25 1:40853
Stampfer and Myrbach: reduced to 0° 0 332-96 1:41456

(not corrected for moisture) . .
Académie des Sciences, 1738 (not sale 61 337°10 1418

rected for moisture) ... .

A variation of one metre per second in the velocity of sound at U° corre-
sponds to a variation of 0085 in the value of y. See also Phil. Mag.
for June 1853.

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 115

(12.) The ordinary mode of expressing the specific heats of
gases is to state their ratios to that of an equal volume of atmo-
spheric air at the same pressure and temperature.

When < is a very small fraction, specific heats of unity of
volume of a perfect gas are given by the equations

] . . .
ani =o( +!) fi

That is to say, the specific heat of unity of volume at constant
yolume is inversely proportional to the fraction by which the
ratio of the two specific heats exceeds unity ; a conclusion already
deduced from experiment by Dulong.

The following is a comparison of the ratios of the apparent
specific heats under constant pressure, of unity of volume of
oxygen and hydrogen respectively, to that of atmospheric air, as
deduced from equation (24), with those determined experimen-
tally by De la Roche and Bérard.

(24)

, nM Kp (gas)
Rati nM Kp (atmos. air)
Gas. By theory. By experiment.
AIRC Ee anos Sie ured ce 0:9765
Myaropen” Shs.) >) OU O7o 0:9033

This comparison exhibits a much more close agreement between
theory and experiment than has been hitherto supposed to exist,
the errors in the constants employed having had the effect of
making the ratio 1+N seem greater for atmospheric air than
for oxygen and hydrogen, while in fact it is smaller.

To treat the other substances on which both M. Dulong and
MM. De la Roche and Bérard made experiments as perfect gases,
would lead to sensible errors, I have therefore confined my
calculations for the present to oxygen, hydrogen, and atmo-
spheric air*.

(13.) The heat produced by compressing so much of a perfect
gas as would occupy unity of volume under the pressure unity,
at the temperature 0° Centigrade, from its actual volume

aMV,= PC into a volume which is less in a given ratio s (when

« is neglected as compared with 7), is expressed by the following
equation :—
mg=—1 (av. =—nmv, {Pa 2
n =— oy, ean if a, +° (25)
_* For a comparison of the theory with the later and more accurate expe-
riments of M. Regnault, see the Philosophical Magazine for June 1853,

116 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

being, in fact, equal to the mechanical power used in the com-
pression. When the temperature is maintained constant, this

becomes
-

nMQ! O=6 7 log, .= Br wiS* et oe (26)
which is obviously independent of the nature of the gas.

Hence equal volumes of all substances in the state of perfect gas,
at the same pressure and at equal and constant temperatures, being

compressed by the same amount, disengage equal quantities of heat ;
a law already deduced from experiment by Dulong.

(14.) The determination of the fraction N affords the means
of calculating the mechanical or absolute value of specific heat,
as defined by equation 1, Section I. The data for atmospheric
air being taken as follows,

N=0°4, C=274°6 Centigrade,
ats = height of an imaginary column of air of uniform density,
at the temperature 0° Cent., whose pressure by weight on a given
base is equal to its pressure by elasticity,
=7990 metres,
= 26214 feet:
the real specific heat of atmospheric air, or the depth of fall
equivalent to one Centigrade degree of temperature in that gas,
is found to be
k= wine =72°74 metres = 238°66 feet. . . (27)
The ratio of its real specific heat to the apparent specific heat of
water at 0° Centigrade is therefore
k _288°66
Kw 1889-60
Kw being the mechanical value of the apparent specific heat of
liquid water, as determined by Joule.

The apparent specific heat of air under constant pressure, as

compared with that of liquid water, is
Ke =01717 x 1:4=0:2404. . . (28A)
The value of this last quantity, according to the experiment of
De la Roche and Bérard, is
0°2669,
the discrepancy being about one-ninth of the value according to
Joule’s equivalent*.

=0°1717) 9. 88)

* According to the experiments of M. Regnault, = for air =0°2379,
w
differing by about one-hundredth part from the result of theory.

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 117

(15.) Besides the conditions of constant volume and constant
pressure, there is a third condition in which it is of importance
to know the apparent specific heat of an elastic fluid, namely,
the condition of vapour at saturation, or in contact with its
liquid.

The apparent specific heat of a vapour at saturation is the
quantity of heat which unity of weight of that vapour receives
or gives out, while its temperature is increased by one degree,
its volume being at the same time compressed so as to bring it
to the maximum pressure corresponding to the increased tem-
perature.

It has been usually taken for granted, that this quantity is
the same with the variation for one degree of temperature, of
what is called the total heat of evaporation. Such is, indeed,
the case according to the theory of Carnot; but I shall show,
that, according to the mechanical theory of heat, these two
quantities are not only distinct, but in general of contrary signs.

I shall for the present consider such vapours only as may be
treated in practice as perfect gases, so as to make the first of the
equations (20) applicable.

It has been shown that the logarithm of the maximum elas-
ticity of a vapour in contact with its liquid may be represented
by the expression

sag A) dbisy
log P=a eRe Oe

The coefficients «, 8, y being those adapted for calculating
the common logarithm of the pressure, I shall use the accented
letters «', 8', y/ to denote those suited to calculate the hyperbolic
logarithm, beg equal respectively to the former coefficients
x 273025851.

Then for vapour at saturation,

dP pl Yb

Pdr = = + pp . . . . . . (29)
Making this substitution in the general equation (21), we find
the following value for the apparent specific heat of perfectly
gaseous vapour at saturation :—

dv
Ks b+ PD =n(14n. 2 1
=k{1+N(1- ro) ee (80)
! 2+

ni AU eheed B { )
=oulnt}-5- 3):
(16.) For the vapours of which the properties are known, the

118 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

negative terms of this expression exceed the positive at all ordi-
nary temperatures, so that the kind of apparent specific heat
now under consideration is a negative quantity; that is to say,
that if a given weight of vapour at saturation is increased in
temperature, and at the same time maintained by compression
at the maximum elasticity, the heat generated by the compression
is greater than that which is required to produce the elevation:
of temperature, and a surplus of heat is given out; and on the
other hand, if vapour at saturation is allowed to expand, and at
the same time maintained at the temperature of saturation, the
heat which disappears in producing the expansion is greater than
that set free by the fall of temperature, and the deficiency of
heat must be supplied from without, otherwise a portion of the
vapour will be liquefied, in order to supply the heat necessary for
the expansion of the rest*.

This circumstance is obviously of great importance in meteo-
rology, and in the theory of the steam-engine. There is as yet
no experimental proof of it. It is true that, in the working of
non-condensing engines, it has been found that the steam which
escapes is always at the temperature of saturation corresponding
to its pressure, and carries along with it a portion of water in
the liquid state ; but it is impossible to distinguish between the
water which has been liquefied by the expansion of the steam,
and that which has been carried over mechanically from the
boiler+.

The calculation of the proportion of vapour liquefied by a given
expansion, requires the knowledge of the latent heat of evapora-
tion, which forms the subject of the next section.

* This conclusion is applicable only when the mechanical power pro-
duced by the expansion of the vapour is expended in moving another body ;
for example, the piston of an engine. When this power is expended in
producing currents in the vapour itself, the friction of those currents even-
tually reconyerts the whole of the power into heat; so that the vapour,
instead of being partially liquefied, is super-heated, as has been shown theo-
retically by Professor William Thomson, and experimentally by Mr. Charles
W. Siemens. (Civil Engineer and Architect’s Journal, September 1852.)

+ The experiments of Mr, Daniel Kinnear Clark, on the expansive action
of steam in locomotive engines, described in his work “ On Railway Ma-
chinery,” show that a large amount of liquefaction generally takes place
during the expansion of the steam. It appears, however, as Mr. Clark has
pointed out, that a considerable portion of this liquefaction arises from the
transference of heat to the metal of the cylinder, and is followed by re-eva-

oration when the heat is transferred back, upon the pressure of the steam
alling below that due to the temperature of the metal. How much of the
liquefaction is due to this cause, and how much to the expansion of the
steam, it is impossible to determine, in the present imperfect state of our
knowledge of the bulk occupied by a given weight of steam at a given
pressure and temperature.

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 119

Szctron Il].—Of the Latent and Total Heat of Evaporation,
especially for Water.

(17.) The latent heat of evaporation of a given substance ata
given temperature, is the amount of heat which disappears in
transforming unity of weight of the substance from the liquid
. State, to that of vapour of the maximum density for the given
temperature, being consumed in producing an increase of volume,
and an unknown change of molecular arrangement.

It is obvious that if the vapour thus produced is reconverted
into the liquid state at the same temperature, the heat given out
during the liquefaction must be equal to that consumed during
the evaporation ; for as the sum of the expansive and compress-
ive powers, and of those dependent on molecular arrangement
during the whole process, is equal to zero, so must the sum of
the quantities of heat absorbed and evolved.

The heat of liquefaction, at a given temperature, is therefore
equal to that of evaporation, with the sign reversed.

(18.) If to the latent heat of evaporation at a given tempera-
ture is added the quantity of heat necessary to raise unity of
weight of the liquid from a certain fixed temperature (usually
that of melting ice) to the temperature at which the evaporation
takes place, the result is called the total heat of evaporation from
the fixed temperature chosen.

According to the theory of Carnot, this quantity is called the
constituent heat of vapour ; and it is conceived, that if liquid at
the temperature of melting ice be raised to any temperature and
evaporated, and finally brought in the state of vapour to a certain
given temperature, the whole heat expended will be equal to the
constituent heat corresponding to that given temperature, and
will be the same, whatsoever may have been the intermediate
changes of volume, or the temperature of actual evaporation.

According to the mechanical theory of heat, on the other hand,
the quantity of heat expended must vary with the termediate
circumstances ; for otherwise no power could be gained by the
alternate evaporation and liquefaction of a fluid at different
temperatures.

(19.) The law of the latent and total heat of evaporation is
immediately deducible from the principle of the constancy of the
total vis viva in the two forms of heat and expansive power, when
the body has returned to its primitive density and temperature,
as already laid down in article 7.

That principle, when applied to evaporation and liquefaction,
may be stated as follows :—

Let a portion of fluid in the liquid state be raised from a cer-
tain temperature to a higher temperature; let it be evaporated

120 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

at the higher temperature: let the vapour then be allowed to
expand, being maintained always at the temperature of saturation
for its density, until it is restored to the original temperature, at
which temperature let it be liquefied :—then the excess of the heat
absorbed by the fluid above the heat given out, will be equal to
the expansive power generated.

To represent those operations algebraically, let the lower
absolute temperature be 7): the volume of unity of weight of
liquid at that temperature, vp, and that of vapour at saturation, Vo:
let the pressure of that vapour be Py: the latent heat of evapo-
ration of unity of weight, L,: and let the corresponding quan-
tities for the higher absolute temperature 7,, be v,, V,, P,, Ly).
Let K,, represent the mean apparent specific heat of the sub-
stance in the liquid form between the temperatures 7) and 7.
Then,—

First. Unity of weight of liquid being raised from the tempe-
rature T, to the temperature 7,, absorbs the heat

Ky (71;—To),

and produces the expansive power,

Swe “Pi

Secondly. It is evaporated at the temperature 7, absorbing
the heat
L,,

and producing the expansive power,
P,(V,—2)-

Thirdly. The vapour expands, at saturation, until it is restored
to the original temperature Ty. In this process it absorbs the heat

oS Gr . Ks,

and produces the expansive power,
voav.P
v, se

Fourthly. Tt is liquefied at the original temperature, giving
out the heat
Lo
and consuming the compressive power,
Po(Vo—%):
The equation between the heat which has disappeared, and
the expansive power which has been produced, is as follows :—

Mr. W.. J. M. Rankine on the Mechanical Action of Heat. 121
Ty )
Lg Ki (n=) fr Ks

a
1 Vo
=P,(V,—0,)—Po(Vo-v) +f, do.PHy isfy dV.P. |

If the vapour be such that it can be regarded as a perfect gas
without sensible error, the substitution of & + P = for Ks, and
of Cat =kNr for PV, transforms the above to

nM.

L,—1)+ {Ky —&(1 +N) 5 (71-79) }

P,
= Pio +P yr fo. P= =f} a.

In almost all cases which occur in practice, v is so small as

compared with V, that — f dP .v may be considered as sensibly

=0; and therefore (sensibly)

L,+ Kz (7,;—7,) =1p t+ &(1+ N)(7,—7)). - - (88)

Now this quantity is the total heat required to raise unity of
weight of liquid from 7, to 7, of absolute temperature, and to
evaporate it at the latter temperature. Therefore the total heat
of evaporation, where the vapour may be treated as a perfect gas,
increases sensibly at an uniform rate with the temperature of eva-
poration ; and the coefficient of its increase with temperature is
equal to the apparent specific heat of the vapour at constant pres-
sure, &(1+N).

(20.) The experiments of M. Regnault prove that the total
heat of evaporation of water increases uniformly with the tem-
perature from 0° to 200° Centigrade.

The coefficient of increase is equal to

Kw x 0°305.

Its mechanical value is consequently :
129°18 metres =422°83 feet per Centigrade degree, or | * (34)
235°46 feet per degree of Fahrenheit.

Although the principle of the conservation of vis viva has thus
enabled us to ascertain the Jaw of increase of the total heat of
evaporation, it does not enable us to calculate @ priori the con-
stant L, of the formula, being the latent heat of evaporation at
the fixed temperature from which the total heat is measured ; for
the changes of molecular arrangement which constitute evapora-
tion are unknown*.

(31)

(32)

* Other investigations have shown that the latent heat of evaporation is
connected with the increase of volume by the equation

L=(r—xk) - (V—v);
T
but the exact values of V are yet unknown.

Phil. Mag. 8. 4. Vol. 7. No, 43, Feb, 1854: K

122 Prof. Buff on the Electricity of Plants.

When the fixed temperature is that of melting ice, M. Re-
enault’s experiments give 606°5 Centigrade degrees, applied to
liquid water as the value of this constant; so that

L+K,T= Ky (606°5+°305 T°) )

for the Centigrade scale, (35)
= Ky (1091°7 + 305 (T° —32°))

for Fahrenheit’s scale,

is the complete expression for the heat required to raise unity of
weight of water from the temperature of melting ice to T° above
the ordinary zero, and to evaporate it at the latter temperature.

It must be remarked, that the unit of heat in M. Regnault’s
tables is not precisely the specific heat of water at 0° Centigrade,
but its mean specific heat between the initial and final tempera-
tures of the water in the calorimeter. The utmost -error, how-
ever, which can arise from this circumstance, is less than ;755
of the total heat of evaporation, so that it may safely be neglected.

[This section formerly concluded with a computation of the
specifie heats of steam on the supposition of its being sensibly a
perfect gas; but the error of this supposition, though not mate-
rial in calculating the power of steam-engines, is in all proba-
bility sufficiently great to vitiate the computation in question,
which has therefore been cancelled. ]

[To be continued. |

XVII. On the Electricity of Plants. By Professor H. Burr*.

Fr, wept twenty-seven years ago Pouillet (Ann. de Chim. et de
Phys. xxxv. 401) described a number of experiments, from
which he concluded that plants, durmg their germination and
growth, impart positive electricity to the air and negative electri-
city to the soil. The majority of physicists accepted this con-
clusion without further proof, inasmuch as it appeared to render
a satisfactory account of the origin of atmospheric electricity.
A repetition of Pouillet’s experiments, with more delicate appa-
ratus, was undertaken by P. Riess, who however was unable to
obtain the results of the former investigator. Two years ago,
Wartmann (Phil. Mag. [4] 1.578.) and Beequerel (4mm. de Chim.
et de Phys. [8] xxi. 40) communicated observations, according
to which growing plants impart negative electricity to the atmo-
sphere and positive electricity to the soil, the two electricities
thus moving in directions opposite to those inferred from the
observations of Pouillet.

The mode of experiment pursued by the last two physicists
was as follows:—Homogeneous platinum wires were brought

* Communicated by the Author.

Prof. Buff on the Electricity of Plants. 123

into contact with the parts of the plant whose electric deport-
ment was to be ascertained, the wires were connected with a
galvanometer, and the action upon the needle of the instrument
was observed. This procedure has, however, a source of error
connected with it from which the results of the observations
cannot be set free. It is well known, although not sufficiently
attended to by investigators of the electro-chemical school, that
platinum, in contact with different liquids, exhibits different de-
grees of electric excitation. The sum or difference of these
actions must of necessity change the quantity, and perhaps also
the quality of the original action due to the plant alone. The
observations communicated by Wartmann and Becquerel, even
though of themselves perfectly correct, could therefore give no
answer to the question, whether plants, in their natural condi-
tion, and during their free growth, discharge electricity.

To examine the electric deportment of a plant as it occurs in
nature, it is absolutely necessary to bring it into such relation
with the apparatus used in the experiments, that its natural
conditions shall be changed in the least degree possible. Now
the roots of thriving plants generally ramify themselves through
moist earth. The surface of their leaves, though they may not
be wet by rain or dew, are hygroscopically moist. It appeared
to me, therefore, necessary to establish the connexion of the
plants, or parts of plants, with the electrical apparatus, by means
of water alone.

Upon this idea the following arrangement of the apparatus is
founded. Two glass beakers were filled with mercury to a height
of half an inch above the bottom, and then filled nearly to the
rim with water. Platinum wires, smelted into glass tubes, dipped
with their well-amalgamated ends, which projected for some
lines only beyond the glass tubes, into the mercury, their other
ends being connected with the helix of a very delicate multiply-
ing galvanometer. To complete this circuit, it was only necessary
to unite the water of both glasses by a conductor. When the
cireuit was established by means of a strip of moist bibulous
paper, the needle continued motionless. A small addition of
common salt or of the acid sap of a plant to the one or the other
beaker, produced a deflection. By heating the water, or by mix-
ing the contents of both beakers well together, the equilibrium was
again established. A shaking of the fluid, which, when platmum
wires are immersed in it, easily causes electrical excitation, was in
the present case without influence, inasmuch as the wires were pro-
tected by the glass tubes which surrounded them from being un-
equally wetted. When an electric current was conducted through
the cireuit closed by the bibulous paper, the mercury surface be-
came indeed polarized, but much less so than platinum, and the

K 2

124 Prof. Buff on the Electricity of Plants.

equilibrium was soon established again, either of itself, or by
the moderate moving of the liquid metal by a glass rod.

To examine the electric condition of a plant, it was placed
between the two beakers in the place of the bibulous paper. At
the termination of the experiment the circuit was again closed
with the paper, in order to be assured that at the commencement
of a new experiment every foreign influence was effectually re-
moved.

In the first place, plants of the most varied kinds, having
their roots washed in flowing water, were examined. The roots,
including the attached fibres, dipped into one of the beakers; a
portion of the uninjured leaves into the other. Having observed
the direction of the consequent deflection, the experiment was
interrupted, and, when the equilibrium had once more esta-
blished itself, the position of the plant was reversed and the
experiment repeated ; that is to say, the roots were now caused
to dip into the beaker, which in the former experiment con-
tained the leaves; the current, so far as it was dependent on an
electric excitation due to the plant, must therefore in the latter
case be reversed in direction.

The observed deflection sometimes amounted to a few degrees
merely, sometimes it was a large arc. The direction of the de-
flection was however in all cases the same, and announced the
existence of a current which passed through the plant from the
root to the leaves.

As the numerous plants experimented with were not all equally
sappy, nor did they possess equal lengths and thicknesses, they
did not present the same surface of contact to the water; great
differences as to the resistance offered to the passage of the cur-
rent were thus unayoidable. The inequality of the currents was
certainly in a great measure due to this circumstance ; in several
cases the magnitude of the deflection might be increased at
pleasure, when several plants of the same kind were placed, in
the same direction, one above another.

The same mode of experiment enables us to examine, not only
the whole plants, but also any portions of them. The place of
severance from the plant (sometimes after the removal of the
exterior bark) dipped into one glass vessel, the leaves, and fre-
quently only a single leaf, dipped into the other. The current
was in no case absent, and its direction was always from the in-
jured portion, for example, from the place of severance, to the
external surface of the leaves. Severed branches, which had
remained several days in water, or even the fallen and half-
withered leaves, still acted, though with diminished energy, in
the same manner as the freshest.

When the interior of the plant was exposed at any place,

Prof. Buff on the Electricity of Plants. 125

whether on the upper or under portions of the stem or branch,
and when this injured place was brought into contact with the
water of one of the beakers, either immediately or by the inter-
vention of wet bibulous paper, while uninjured leaves dipped
into the other beaker (it bemg a matter of mdifference what
portion of the plant they belonged to), the direction of the cur-
rent was always from the wounded portion of the plant to the
leaves.

Two leaves of the same plant immersed, one into the first
beaker, the other into the second, produced no current, or at
least none whose direction could be predicted beforehand. If,
however, a portion of the surface of one of the leaves was removed
and the place brought into contact with the water, this was suf-
ficient to generate a current towards the uninjured leaf. Even
when the connexion between the liquids was established by one
and the same leaf, the place of severance from the tree being
kept outside, then by scratching the one or the other of the im-
mersed portions, a current could be generated which proceeded
unifarmly from the injured place to the uninjured one.

Exactly the same deportment as that observed in the green
leaves was exhibited by blossoms, flowers and fruits. The fresh
young bark exhibited the deportment of the leaves. Hach un-
injured portion was positively electric compared with the root or
with a wounded portion of the plant, no matter where the wound
was inflicted.

From these observations we obtain the following rule, which
is universally valid :—the roots, and all the interior portions of the
plant filled with sap, are in a permanently negative condition ;
while the moist or moistened surface of the fresh branches, leaves,
flowers and fruits are permanently positively electric.

The external cuticle which embraces the fresh branches and
leaves, the epidermis, is known to contain a substance of the
nature of wax, which possesses the property of interrupting the
transmission of the acid and saline liquids which are contained
within the plant, without losing in the same degree the capa-
bility of being moistened, or of permitting water to permeate it,
and of conducting electricity. Between the moist surface of the
plant, therefore, and the liquids in its interior, a definite limit is
always present, which however does not interrupt the mutual
contact and the connexion necessary for conduction. All the
conditions for a permanent electro-motive activity are therefore
present, an activity, in virtue of which, as experience teaches, the
entire exterior surface assumes positive electricity, while the
interior portions, to the roots, and the latter included, assume a
negative electric state.

It might be expected that an equally strong electric excitation

126 Dr. Percy and Mr. R. Smith on the Detection of Gold

must occur when the plant comes in contact with the water of
the earth. But it may be proved, that in an aqueous solution
composed of successive layers gradually increasing in concentra-
tion, the sum of all the excitations which occur at the places of
contact of the different layers is less than the excitation between
pure water and the most concentrated of the layers; and thus,
no matter what the nature of the solution may be, pure water
will be positively electric at the place of transition to the most
concentrated layer of the solution.

Now this is the exact deportment of plants in the experiments
described above. The epidermis forms a sharp and permanent
limit between the sap in the highest possible state of concen-
tration behind it, and the pure water on its exterior, while by
means of the roots a very gradual transition to water is effected.
In like manner the sap exuding from a wound into the sur-’
rounding water can spread itself with gradually diminishing con-
centration.

The electroscopic actions of the electricity of plants correspond
to the origin of the latter, as explained above; they are very
feeble. Even by means of the condenser and dry-pile electro-
scope, no electric charges of sufficient magnitude can be obtained
to enable us to attribute them in a certain manner to the plant
as source. By forming a compound circuit of plants, I sue-
ceeded in obtaining stronger tension effects. Hach uninjured
leaf, with its severed end, forms as it were a galvanic element. It
was therefore only necessary to arrange suitably a number of
such leaves in a series to obtain a compound galvanic circuit.
Thus, with a battery of twelve sappy leaves, a tension was obtained
which amounted to somewhat more than half of that exhibited
by an element of zine and copper immersed. in water.

XVIII. On the Detection of Gold in Lead and tts Compounds, By
Joun Prurcy, M.D., F.R.S., Lecturer on Metallurgy at the
School of Mines, Jermyn Street ; and Ricuarp Smita, Assist-
ant in the Metallurgical Laboratory*.

i ig) the Philosophical Magazine for April 18538, it was stated

that gold had been detected in numerous samples of lead
and its compounds met with in commerce, and that the experi-
ments upon which the statement was founded should appear on
a future day. Those experiments are now given. The investi-
gation is still in progress, and will embrace the examination of a
variety of ores.

All the experiments have been made by Mr. Smith, and the

* Communicated by the Authors.

in Lead and its Compounds. 127

visible specimen of burnished gold obtained in each experiment
has been preserved in a hermetically sealed tube.

The diffusion of gold, as proved by the experiments in ques-
tion, is at least curious, and may probably suggest chemical
and geological considerations of special interest at the present
time. The fact of gold existing in certain soluble compounds of
lead is remarkable; and it may be that sea-water will one day
be found to contain the precious metal, though in infinitesimally
small proportion.

The quantity of gold obtained in each experiment was far too
minute to be capable of estimation by the most delicate balance.
In order, however, to give an approximate and comparative
notion of the quantities respectively extracted, the following
scale of comparison will be adopted im the description,—trace,
minute trace, very minute trace, and just perceptible trace,

At present it has not been possible to prepare lead free from
a trace of gold,

Method of Examination.

The lead was separated from the compounds of lead examined
by a process of reduction described under each experiment; a
known weight of the lead was then submitted to the process of
cupellation in the usual way, and the button of silver left after
cupellation was carefully detached from the cupel, flattened under
a hammer to free it from adherent matter, transferred to a small
watch-glass, treated first with very dilute nitric acid at a very
gentle heat until all action had ceased, and then with strong
nitric acid, The black residual matter was carefully washed
with distilled water by decantation, transferred to a small piece
of writing-paper, dried at a gentle heat, rubbed with a steel bur-
nisher, gummed to the paper, and preserved in a small glass
tube hermetically sealed. When necessary, this process was per-
formed under a microscope.

Lead.

Exp. 1. A specimen of lead pipe from the Great Exhibition of
1851. Cupelled 2000 grs., the button obtained, treated with
nitric acid, left a trace of gold.

Exp. \1. A specimen of “ Pattinson’s crystallized lead.” Cu-
pelled 2000 grains, treated the remaining button with nitric acid,
and obtained a minute trace of gold.

Exp. Ii1. Specimen of lead from the Nenthead Works near
Alston. Cupelled 2000 grs., the button obtained, parted with
nitric acid, left a very minute trace of gold.

Lap. 1V. Specimen of lead from Tuscany, from the Great
Exhibition of 1851, hard and brittle, with a close-grained ery-

128 Dr. Perey and Mr. R. Smith on the Detection of Gold

stalline fracture, probably due to the presence of antimony.
Cupelled 2000 grs., the residual button, parted with nitric acid,
left avery minute trace of gold.

Exp. V. Specimen of lead from the Austrian collection im
the Great Exhibition of 1851, labelled ‘23, Bleiberger Pro-
bierbiei.” Cupelled 2000 grs., treated the remaining button
with nitric acid, and obtained a minute trace of gold.

Exp. VI. Specimen from ditto, labelled “25, Przibramer
Weichblei.” 2000 grs. cupelled, and the residual button treated
with nitric acid, left a trace of black matter; but the colour of
gold could not be distinctly obtained by burnishing, probably
owing to a small amount of silver left undissolved.

Ezp. Vil. Repeated Exp. VI. upon 2000 grs., and obtained
a very minute trace of gold.

Exp. VIII. Specimen from ditto, labelled “26, Przibramer
Hartblei.” 3340 ers. scorified to a small bulk and then cu-
pelled, left a button weighing ‘1 gr.; treated with nitric acid,
left a minute trace of gold.

Red Lead.

Exp. 1X. Specimen made from Snail-beach lead, Shrop-
shire. Mixed 2 Ibs. troy of red lead with excess of finely-
powdered charcoal, heated the mixture in a Cornish crucible, and
poured out the reduced lead into an ingot mould. Of this lead,
cupelled 2000 grs., parted the residual button with nitric acid,
and obtained a trace of gold.

Exp. X. Specimen made from Derbyshire lead. Weighed
out 5000 grs. of red lead and 300 grs. of powdered charcoal,
heated the mixture in a Cornish crucible, the reduced lead
weighed 3840 grs. Of this lead, cupelled 2000 grs., the button
obtained weighed about ‘1 of a grain; parted with nitric acid,
left a trace of gold.

Litharge.

Exp. XI. Sample purchased at Mr. C. Button’s, Holborn
Bars (in the form of small, thin scales). Mixed 6000 grs. with
300 ers. of powdered charcoal, reduced the mixture in a Cornish
crucible, lead obtained weighed 5460 grs. Of this lead, cupelled
2000 ers., obtained a small button of silver ; parted with nitric
acid, left a very minute trace of gold.

Exp. X11. Sample bought at Mr. G. James’s, 72 Wardour
Street (in powder). 6000 grs. reduced by heating with 800
ers. of powdered charcoal, gave of lead 4910 grs. Of the lead
thus obtained, cupelled 2000 grs., parted the small residual but-
ton of silver with nitric acid, and obtained a very minute trace of
gold.

mm Lead and its Compounds. 129

Lap. XIII. Sample purchased at Mr. Caplin’s, 42 Great Pul-
teney Street (in powder and small lumps). 6000 grs. mixed
with 300 grs. of powdered charcoal and reduced in a Cornish
crucible, gave of lead 5310 grs, Of this lead, cupelled 2000 grs.,
treated the small remaining button of silver with nitric acid, and
obtained a minute trace of gold.

Exp. XIV. Sample brought from Birmingham (im small, thin
seales). Reduced 2880 grs. with 150 grs. of powdered charcoal
in a Cornish crucible ; lead obtained weighed 2270 grs. Of this
lead, cupelled 2000 grs.; the small button of silver obtained,
parted with nitric acid, left a minute trace of gold.

White Lead.

Exp. XV. Specimen purchased at Mr. Button’s, Holborn
Bars, sent as “pure carbonate of lead,” and said to have been
prepared by precipitation from a solution of the nitrate of lead
by carbonate of soda. 6000 grs. mixed with 200 grs. of pow-
dered charcoal and heated in a Cornish crucible, gave of reduced
lead 4190 grs. Of this lead, cupelled 2000 grs., left a very
minute button of silver; parted by nitric acid, a just perceptible
trace of black matter remained undissolved, but no distinct me-
tallic lustre could be obtained by burnishing.

Exp. XVI. Repeated Exp. XV. 2 lbs. troy (11,520 grs.)
reduced by heating in a Cornish crucible with 400 grs. of char-
coal, gave of lead 8550 grs. Of this lead, 4000 grs. cupelled
left a very small button of silver; parted by nitric acid, left a
just perceptible trace of gold.

Exp. XVII. Sample bought at Mr. G. James’s, 72 Wardour
Street. 6000 grs. mixed intimately with 200 grs. of powdered
charcoal and heated in a Cornish crucible, gave of lead 4340 grs.
Of this lead, cupelled 2000 grs., parted the small residual button
of silver with nitric acid, and obtained a very minute trace of gold.

Exp. XVIII. Sample purchased at Mr. Caplin’s, 42 Great
Pulteney Street. Mixed 6000 grs. with 200 grs. of powdered
charcoal, heated the mixture in a Cornish crucible, obtained of
lead 3840 grs. Of this lead, cupelled 2000 grs.; the small
globule of silver obtained, parted by nitric acid, left a very minute
trace of gold.

Oxychloride of Lead.

Exp. XIX. Pattinson’s oxychloride. 1 lb. troy (5760 grs.)
mixed intimately with 4 ozs. (1920 grs.) of dried carbonate of
soda, and } oz. (240 grs.) of powdered charcoal, heated the mix-
ture in a Cornish crucible, lead obtained weighed 4140 grs. Of
this lead, eupelled 4000 grs. (a small portion of the lead was
lost during the operation), no button of silver was obtained (?).
There was not a sufficient quantity of this sample left to repeat
the experiment.

180 = Mr. J. Cockle on the Method of Symmetric Products.

Exp. XX. Sample purchased at Messrs. Blundell, Spence and
Co., 9 Upper Thames Street, as Pattinson’s genuine oxychloride
of lead. Reduced 3 lbs. troy in the same way as Exp, XIX. Of
the lead obtained, cupelled 4000 grs,; the small button of silver
obtained, parted by nitric acid, left a very minute trace of gold.

Exp. XXI. Repeated Exp. XX. on 4000 grs. of lead ; treated
the button of silver left by cupellation with nitric acid, and a
very minute trace of gold was obtained,

Acetate of Lead.

Exp. XXII. Sample purchased at Mr. C. Button’s, Holborn
Bars, slightly coloured with oxide of iron. 2 lbs. troy (11,520
grs.) reduced by projecting it in small quantities at a time into
a hot Cornish crucible, and finally heating until all the lead was
separated ; lead obtained weighed 5700 grs. -2000 grs, of this
lead, eupelled, did not leave any visible trace of silver,

Hap. XXIII. Repeated Exp. XXII. upon 2000 grs,, but no
button of silver was obtained.

Eup, XXIV. Repeated Exp. XXII. Took of acetate of lead
2 lbs. troy (11,520 grs,) and reduced it by heating in a Cornish
crucible; lead obtained weighed 5860 grs. 4000 grs. of this
lead cupelled to about 200 grs. on a large cupel; it was then
transferred to a small cupel and the operation completed ; a very
minute globule of silver remained, which was treated with nitric
acid, and a just perceptible trace of gold was obtained.

Exp. XXV. Sample bought at Mr. H. Barnes’s, 38 Long
Acre (very white and clean). 5760 grs. reduced by heating in
a Cornish crucible, gave of lead 3136 grs, Of this lead, cupelled
2000 grs., obtained a very minute globule of silver, which by
parting with nitric acid left a just perceptible trace of gold.

Exp. XXVI, Repeated Exp. XXV. 5760 grs. reduced as
before, gave of lead 2830 grs. Of this lead, 2000 grs. cupelled
gave a very minute globule of silver, which, after parting with
nitric acid, left a just perceptible trace of gold.

(To be continued. |

XIX. On the Method of Symmetric Products. By JAmus Cock.z,
M.A., of Trinity College, Cambridge ; Barrister-at-Law of the
Middle Temple*.

[Concluded from vol. v. p. 174.]
4A. UADRATICS furnish us with a function which, if not
the strict analogue of those presented by the other
equations, may yet be considered as corresponding to them.

* Communicated by the Author.

Mr. J. Cockle on the Method of Symmetric Products. 181

45, Let
Yi="7+2y Y)'=2y,4 Yo,

and, consequently,

YP+¥,=2.VY=S(e+))(m+y.)=(e+)2-y;
then, if we make

z+1=0,

we have an equation analogous to that which occurs in the higher
degrees, and the result

PP=t'4(Yo) =Y {Y= — Y*)=4y,¥2— (Yi +40)”
shows that Y, may be obtained by the extraction of a square
root, and, = .y being known, the quadratic is solved.

46. It may be well, before addressing ourselves to equations
of the fifth degree, to illustrate the Method of Symmetric Pro-
ducts by an example in which U, does not oceur*. For this
purpose let us take the cubic

a + ax? +be+c=0.
47. Guided by (4) we assume
N=(%—f)-, Yo=(*e—E)', yg=(#s—£)—',
and consequently
Y= (@—8)7" +%(@2—€)“' +B (4s €)-,
Yo= (7, —&)~* + o9(t2—&)-' + Bo(ws— £)-'.
48. The conditions of symmetry are
l=a,a,=8,8,,
E=3.a=5.8=5. &, Bat,
(Ys) =Y,Yo=>.y? + ED. nyo,
and the expressions («,, «), (8,, 85) each involve the roots of
pee Bat Vente t's ee ee eth)
49. From the identity

(4, + 2) (8, + Ba) — (a Bo + 81) — (a)% +B, Bq) =0,

* Systems consisting of two, three, four,., p single equations may be
respectively called dual, ternal, quaternal,. , p-al systems. That which the
discussion of quintics has presented to us for solution is septuagintal and,
in the language of my ‘ Analysis,’ sexdecimary. We have only been able
to solve 60 of the members of this 70-al 16-ary 4-ic system. "The refrac-
tory equations have given rise to the function U, or 3’. For my nomen-
clature of order 1 may cite the authority of Garnier (Anal, Alg. p. 121).

t From this, by excluding nvgatory assumptions, we might obtain

$'(B)=$'(8")={$'(B) }?—2, or $'(8)=2 or —1.
The two relations between the functions ' which are expressed in (42)

figs rise respectively to the two equations which I have, as Question I.
1869) of the ¢ Diary’ for 1854, proposed for simultaneous solution,

182 Mr. J. Cockle on the Method of Symmetric Products.

we, in terms of (48), deduce
K?-—E—2=0,

and find that —1 and 2 are the values of E.
50. The substitution of 2 for E leads to nugatory results, but
that of —1 changes (4) into

2?4+2+1=0,

the roots of which are the unreal cube roots of 1. If we repre-
sent these quantities by « and «, the condition

14+2.4,8,=0
points to the relations

o,=6,=2 anda, P= 0%
51. Denoting the transformed equation in y by

y+ ny? + Joy + 93=9,
we shall find

Y,Yg=9(vy—£)-!=45{ (0°30) + (ab—9e) E+ (02—Bae)},
and, if we determine & so as to make 7,(y;) vanish, the relations
Y, (or Y.)=0, 2-y=qu =.=

will give y and, consequently, #*.
52. The Method of Symmetric Products enables us to confine
the attention to a greatly diminished number of functional

* The reducing equation of (51) was first obtained by Bezout (Par. Mén.
for 1762, p.24). I subsequently (Camb. Math. Journ. for May 1841) was
conducted to it by radically different considerations. Mr. Cayley (Camb.
and Dub. Math. Journ. for May 1851) has, by giving a coefficient to 2%,
generalized my process, and Mr. Rotherham (Eng. Journ. of Ed. for August
1853) has given a solution of a cubic, independently arrived at, but substan-
tially identical with mime. The reducing equation is that which arises
from making 7,(y3) vanish.

The intrinsic interest of Mr. Cayley’s result is enhanced by its connexion
with Dr. Boole’s functions 6 and 6’, and with his own researches on hyper-
determmants, The generalized form of 7, is the function employed by
M. G. Eisensteim (Crelle, for 1844, vol. xxvii.), and adverted to by M. C.
Hermite (Ib. for 1851, vol. xli.) as a “ quadratic form” throwing light on
the structure of cubic equations. .

It is strange that the function 7, should have been so much unnoticed.
Its coefficients were present, and that too in a suggestive form, to Lagrange
(Equations, p. 42) as they had been to La Fontaine (Ib. p. 141). Compare
Waring (Misc. Anal. p. 22, line 7), Garnier (p. 115), Rutherford (Com-
plete Solution, &c. p. 9), and Mech. Mag. li. 229, where for M read —M.

Various direct solutions, including those of Tartaglia, Ivory, Graves,
Waring and Rutherford, and two of my own, are adverted to in my ‘ Notes.’
That of Waring (Med. Alg. p. 98) has been erroneously attributed to Laplace.
Some assumptions suggested, though not for the same purpose, by Newton
(see Fluxions, Lond. 1737, p. 23) may be compared with that of Bezout.
Dr. Rutherford’s solution, characterized by his usual skill, has a general
resemblance to that of Bezout.

Mr. J. Cockle on the Method of Symmetric Products. 1383

values. Thus, for cubics, we employ ¢wo only in place of the
siz which, when approached from first principles, Lagrange’s
process involves (Berl. Mem. for 1770, p. 144; Garnier, Anal.
Alg. 2nd ed., Paris, 1814, p. 174; Young, p. 459). For bi-
quadraties we have three instead of the twenty-four which (Gar-
nier, pp.184,185 ; Young, pp. 464-6) are successively reduced to
twelve and to six, the latter having certain relations one with
another. In the theory of quintics we do not take one hundred
and twenty values as our point of departure, but, startmg from
four, we are conducted to twenty-four as involved in the dis-
cussion.

538. Cardan’s statement of Paciolo’s views as to the impossi-
bility of solving cubics is dealt with by Cossali (Origine, &c.,
vol. 11. pp. 96, 97). Tschirnhausen* seems to have had no doubt
of the possibility of solving equations of any degree. Huler+
did not despair of that of the fifth, notwithstanding obstacles
which Waring t deemed insuperable ; nor did Bezout§. Lagrange
(Berl. Mem. for 1770-71) showed the connexion of a//|| solutions
then known with the permutations of rational functions of the
roots, and pointed out difficulties in the theory of the high equa-
tions. Sir W. R. Hamilton has proved that the relations among
Lagrange’s functions discovered by Badano do not lead toa
solution of equations of the fifth degree. The formule of
Wronski do not, in the opinion of Gergonne and Peacock, differ

* See the first and second pages (204, 205) of Tschirnmhausen’s paper
printed in the Leipsie Acta Eruditorum for 1683, and entitled Methodus
auferendi omnes terminos intermedios ex data equatione.

+ See § 20 (pp. 230-1) of Euler’s essay De formis radicum equationum
cuiusque ordinis coniectatio (Pet. Com. [for 1732-33] vol. vi.); see also § 37
Op. 92, 93) of his essay De resolutione equationum cuiusvis gradus (Pet.
New Com. [for 1762-63] vol. ix.). Garnier (p. 228) points out very clearly
the modification to which Euler subjected his original form of root.

t See Waring’s Miscellanea Analytica, &c. (Camb. 1762), p.47 ; see
also his Meditationes Algebraice (Camb. 1770), pp. 120, 121, 122. The
researches of Bezout, alluded to at p. v. of the Prefatio of the latter work,
appear in the Paris Mémoires for 1762 and 1765 (not 1764). In explana-
tion of the remainder of the paragraph which contains the allusion, Waring’s
paper in the Philosophical Transactions for 1779 (pp. 86-104), not forget-
ting its introductory part, should be referred to, (Et vid. Misc, An. p. 44.)

nge appreciated Waring’s abilities (Berl. Mem, for 1771 [published
in 7731, p- 202).

§ Bezout, Mémoire sur plusieurs classes d’équations de tous les degrés,
ui admettent une Solution algébrique (Paris Mémoires for 1762 [published
in 1764], pp. 17-52), arts. (3.), (6.), and (11.); see also his Mémoire sur la
résolution générale des équations de tous les degrés (Ib. for 1765 [published
in 1768], pp. 533-552), Compare p. 549 with Art. (85.) of Lagrange’s

discussion (Berl. Mem. for 1771, p. 187).

| Lagrange’s omission to notice T. Simpson’s generalization of Ferrari’s
solution of biquadratic is scarcely an exception to this remark,

184 Mr. J. Cockle on the Method of Symmetric Products.

essentially from those of Lagrange. Abel (Cuwvres, vol. ii.
pp. 185-209) never desisted from the efforts commenced by
Ruffini (Ib. p. 186). The jomt argument of Abel and Sir W.
R. Hamilton appears to have been assented to by Murphy (Equa-
tions, p. 77), but grave doubts respecting it have been thrown
out by Dr. Peacock. Professor J. R. Young* inclines to their
conclusion. Im favour of the possibility of the solution we may
cite Ivory (Equations, Encycl. Brit. 7th ed. vol. ix. p. 841),
and Mr. G. B. Jerrard. Mr. Bronwin wavers in opinion. Poinsot
regarded the question as involved in utter uncertainty (Preface
to the 3rd ed. of Lagrange’s Equations, p. xvi.). Vandermonde,
whose theory of equations Lagrange (Hquations, p.272) con-
sidered as being, to some extent, more direct than his own, after
some elaborate investigations, states that he is not in a condition
to offer even a conjecture upon the possibility of the general
solution (Par. Mém. for 1771, pp. 865-416; see Art. XXXIV.
of his paper).

54. In these papers we have been conducted a priori to La-
grange’s functions, as those which seem to fulfill the conditions
of maximum symmetry. Equations of the fifth degree furnish
us, not with a symmetric, but, with what, in the nomenclature of
my Fragment on Multiplicity of Valuest, may be termed an
epimetric product.

55. Thus, « being the root of a general quintic, we have

74(@5) =o(x) +€(2),
where o is symmetric and e epimetric.

56. Let s,, s5,.,8 be the six values of e(v). Then, this
function being Ayposymmetric, it may (Phil. Mag. Dec. 1853,
p. 448, Art. XX.) be expressed in terms of a, and of four quan-
tities ¢,, fg, ts, ¢4 connected with « by the relations

(=a— 85, tg=Xy—t;, t3=Ug—ky t= %4y—45}
or may, in other words, be represented by

€5(2) + $(%5).
57. We have, consequently, six equations of the form (Ibid.)
84 =laty tot ti tal, +b, tg tot lj tig t+ bles) i
and, if by means of five of these ¢ and ¢ be eliminated from the
remaining one, we obtain
(Si Sey» Sg) RO ee we GD
58. Replacing a, 8, y, 8 by 1, 2, 3, 4 respectively, we find
8 =tylofytalhty | + tot! + tgt '+ tyte') + 6(2,).
* Equations, pp. 468, 469; Mechanics’ Magazine, vol. xlviii. pp. 101,

102; On the General Principles of Analysis, pp. 49-51.
+ See Phil. Mag. for December 1853 (S. 4, vol. vi.), pp. 444-8,

Mr. J. Cockle on the Method of Symmetric Products. 185

59. The quantity between the first brackets is a pure epimetric
function, whose structure is

a,(t)=t, e(t)=tz', e()=tr', e(t)=r', e(t)=ts"s
and for which (Ib. p. 446, Art. XI.)
evr(c) =e(e—1) =3 x 256,

a result which confirms our previous determination of the num-
ber of values of e(z). '

60. In the present state of the subject of equations of the fifth
degree, I do not desire to have any remark of mine placed in a
higher category than that of conjecture. I shall be satisfied if
they have a sufficient degree of probability to merit further inves-
tigation. '

61. It would, then, seem that the epimetric (7) is susceptible
of finite algebraic evaluation ; and this for two reasons.

62. First. The six quantities s are not independent, but are
functions of the five quantities z. They do not, therefore, con-
stitute the roots of a general equation of the sixth degree, and,
being subject to the internal relation (/), their determination is
facilitated. (Vide Poinsot, loc. cit. sup.)

63. Second. The product 7,(z;) is one of those ‘critical’
functions which, under their symmetric form, I have defined in (5).

64. We have, in fact,

a(x) =¢,0,+5.3~' (8p,?— 7p, p+ 16p,)*,

and, the unbracketed quantity bemg critical, (b) can only enter
into e(z) through the bracketed expression, which is rational.
Hence the mode in which 4 is involved in s is such as to free
the former quantity from radicality, and to indicate relations
favourable to solution, or rather, perhaps, which account for its
existence, supposing it to exist.

65. Let us now proceed to an equation in y, connected with

* Replacing y by « in (5), it may be well, throughout the whole of this
discussion, to consider the coefficient of pn in Cy as unity, and, conse-
uently, c', C2, Cy, and ¢, as respectively equal to 4, —3, —8 and —5%37!.
e shall then have the result given in (64), from which it appears that the
R of (8) is not equal to U,.
That result may be readily verified, for in Mr. Jerrard’s last notation
(Phil. Mag. for May 1853, p. 355) the relation of (38) becomes

P,=G4—61.3+ 3 (G2%)4G12.2.3 — tr;
and this, by the table at p. 33 of his ‘ Researches,’ is equal to

Pr’ —5pr*po+ bp? + 5pipy—l5p4,

and the substitution of p for B in (41) will afford the means of completing
the verification,

136 Mr. J. Cockle on the Method of Symmetric Products.

that in @ by the relation
Yr=Qy + Quay + Que; + Que, + Queer,

which is substantially the most general transformation that can
be adopted, and let us, in the first instance, make Q, vanish.

The critical nature of 7 justifies us in this course.
66. We shall find

T4(Ys) = Q(z) +€(2)$ + QPQfo'(z) +e(@)}+...+,
there being sia relations of this form.

67. Although a want of hyposymmetry in ¢, é’, &e. will
probably complicate the process by which we arrive at the equa-
tions corresponding to (/), such equations exist in all cases. The
argument of (63) will apply to e, e, &c.

68. The functions ¢ are, all of them, six-valued. The inves-
tigation of their properties will be aided by that of relations like
those which follow, and which seem to indicate that epimetric
and other unsymmetric expressions admit of systematic discussion.

69. Let = be the sign of symmetric and 8S of epimetric s sum-
mation ; so that, in (39), we may make

2. 1? (Yast YsYa) =U=Sy("17°Yo4s)-

70. Change the y’s within the brackets into their correspond-
ing squares, and depress those without to the first power, and
we have

2! W(Yo°¥s +Y3'Ya) = Si (Vi Yo'ys°)-

71. We may take

s,=8,(12)=8, (2) =8,(14) =8,(19) =5,(%)
as giving the law of suffixes*,

72. The following relation, in which a singular case is given
by 6=2a, holds,

S .atababapS .at-barrar?,
73. We also have, omitting identical suffixes,
et IPOS Pie IR TE NEE
DO ag tg > @,2a ere, =,

a result which admits of generalization, and connects epimetries
of various forms+.

+ The product of S, . #°2v3 into 8, . 2,x2°a,37 is the six-valued function
2.2080 +3 .vfefrfo, +? .vpezaeae+
3D). ay '(a x04 + 0,590, +2,50,0,+ 05x52,)+
2S! . a(n eae, +070 yt+ ee ee, + 2m, 729),
in which the sequences occur in known cycles. An outline of the history

Mr. J. Cockle on the Method of Symmetric Products. 137

74. Not to pursue this subject further, let us return to the
theory of quintics, and consider the binomial form, in which all
the roots are given by

Y,= 2",

75. In this case we have
WoO. Noi Noa (Cae
76. For the form of De Moivre, we have

y=ar,+a'r,,
and

77. For the first form of Euler, we haye*

y=ar, +77, or y=aT, + 4°75,
and
re OY =5e VS br) or 0) Yj7=0 or sry:

78. For a form, obtainable by modifying an assumption of
Bezout, we have+
Y=aT, +e77T,+ A575, |
and
Vy Op VY ory) VeSb73) 0 FF.

79. This form is the first suggested by the Method of Sym-
metric Products. Its attainment would reduce the problem to
the following ‘ Given a quintic with a known homogeneous linear
relation (Y=0) existing among its roots, to find those roots {.’

80. Thus far I have traced this symmetric (or epimetric)
method. The discussion of the problem of (79), of the deter-
minability of S(x,27x;), &c., and of the uses to which the dis-
posable members of the series in Q can be put, belong to the
general theory of equations of the fifth degree, under which I
hope at a future time to reconsider them. In dealing with the

of the theory of symmetric functions is given by Lagrange (Equations,
p- 190), and tables of their values, up to the tenth degree inclusive, will be
‘ound at p. 374 of Vandermonde’s Mémoire sur la résolution des équations
referred to in (53), and published in the year 1774. Mr. Jerrard’s ‘ Re-
searches’ and his recent investigations (Phil. Mag. for May and Supp, for
June 1853) have given a great extension to the theory.

* Euler, De resolutione, &c. (§§ 39, 40, 41 and 42, pp. 94-6 of vol. ix.
of the Pet. New Com, published in 1764). The paper De formis, &c. was
published in 1738.

+ By making Bezout’s a (Par. Mém. for 1765, pp. 543, 544) vanish we
should have the form of (78). For each of the forms of (75), (76), (77)
and (78), 74(y5) vanishes.

{ On this part of the subject see my paper On Equations of the Fifth
Degree at pp. 84-6 of the ‘ Diary’ for 1848.

hil, Mag. 8. 4. Vol. 7. No. 48. Feb, 1854. L

138 Prof. Thomson on the Giconomy of the
modified Bezoutian form of (78), the assumption
y=Q\e+ Q,x?
will, the functions ¢ being determinable, suffice for the evanes-

cence of Y,*.

4 Pump Court, Temple,
December 27, 1853.

XX. On the Giconomy of the Heating or Cooling of Buildings
by means of Currents of Air. By Professor W. Tuomsont.

{; it be required to introduce a certain quantity of air at a

stated temperature higher than that of the atmosphere into
a building, it might at first sight appear that the utmost ceconomy
would be attained if all the heat produced by the combustion of
the coals used were communicated to the air; and in fact the
greatest ceconomy that has yet been aimed at in heating air or
any other substance, for any purpose whatever, has had this for
its limit. If an engine be employed to pump in air for heating
and ventilating a building (as is done in Queen’s College, Bel-
fast), all the waste heat of the engine, alongwith the heat of the fire
not used in the engine, may be applied by suitable arrangements
to warm the entering current of air; and even the heat actually
converted into mechanical effect by the engine, will be recon-
verted into heat by the friction of the air in the passages, since
the overcoming of resistance depending on this friction is the
sole work done by the engine. It appears, therefore, that
whether the engine be ceconomical as a converter of heat into
mechanical work or not, there would be perfect ceconomy of the
heat of the fire if all the heat escaping in any way from the engine,
as well as all the residue from the fire, were applied to heating
the air pumped in, and if none of this heat were allowed to

* It will be seen, from my investigation at pp. 45, 46 of the Supple-
mentary Number to vol. iii. of the Mathematician, that the equation

w+aa*+bet+ = =0

admits of finite algebraic solution. I have discussed another solvable form
of quintic at pp. 76, 77 of the ‘ Diary’ for 1851. Euler has devoted §§ 44,
45, and 46 of his paper De resolutione, &c. to the consideration of another
solvable form. Bezout has pointed out others (Par. Mén. for 1765, p. 544).

+ Communicated by the author, having been read before the Glasgow
Philosophical Society, November 15,1852. Mathematical demonstrations
of the results stated in this paper are published in the form of the solution
¢ a Fee ne in the Cambridge and Dublin Mathematical Journal, Novem-

er 1853.

Heating or Cooling of Buildings by means of Currents of Air. 189

escape by conduction through the air passages. It is not my
present object to determine how nearly in practice this degree
of ceconomy may be approximated to; but to point out how the
limit which has hitherto appeared absolute may be surpassed,
and a current of warm air at such a temperature as is convenient
for heating and ventilating a building may be obtained mecha-
nically, either by water power without any consumption of coals,
or by means of a steam-engine driven by a fire burning actually
less coals than are capable of generating by their combustion the
required heat ; and secondly, to show how, with similar mecha-
nical means, currents of cold air, such as might undoubtedly be
used with great advantage to health and comfort for cooling
houses in tropical countries*, may be produced by motive power
requiring (if derived from heat by means of steam-engines) the
consumption of less coals perhaps than are used constantly for
warming houses in this country.

In the mathematical investigation communicated with this
paper, it is shown in the first place, according to the general
principles of the dynamical theory of heat, that any substance
may be heated thirty degrees (Fahr.) above the atmospheric
temperature by means of a properly contrived machine, driven
by an agent spending not more than about 54th of energy of ©
the heat thus communicated ; and that a corresponding machine,
or the same machine worked backwards, may be employed to
produce cooling effects, requirmg about the same expenditure of
energy in working it to cool the same substance through a
similar range of temperature. When a body is heated by such
means, about 33ths of the heat is drawn from surrounding
objects, and =';th is created by the action of the agent; and
when a body is cooled by the corresponding process, the whole
heat abstracted from it, together with a quantity created by the

* The mode of action and apparatus proposed for this purpose differs
from that proposed originally by Professor Piazzi Smyth for the same pur-
pose, only in the use of an egress cylinder, by which the air is made to do
work by its extra pressure and by expansion in passing from the reservoir
to the locality where it is wanted, which not only saves a great proportion
of the motive power that would be required were the air allowed simply to
escape through a passage, regulated by a stopcock or otherwise, but is ab-
solutely essential to the success of the project, as it has been demonstrated
by Mr. Joule and the author of this communication, that the cold of ex-
pansion would be so nearly compensated by the heat generated by friction,
when the air is allowed to rush out without doing work, as to give not a
tenth of a degree of cooling effect in apparatus planned for 30 degrees.
The use of an egress cylinder has (as the meeting was informed by Mr.
Macquorn Rankine) recently been introduced into plans adopted by a com-
mittee of the British Association appointed to consider the practicability of
Professor Piazzi Smyth’s suggestion, with a view to recommending it to
government for public buildings in rio

2

140 Prof. Thomson on the Giconomy of the

agent, equal to about =4th of this amount, is given out to the
surrounding objects.

A very good steam-engine converts about jth of the heat
generated in its furnace into mechanical effect ; and consequently,
if employed to work a machine of the kind described, might
raise a substance thirty degrees above the atmospheric tempera-
ture by the expenditure of only 42ths, or 2ths, that is, less than
one-third of the coal that would be required to produce the same
elevation of temperature with perfect ceconomy in a direct pro-
cess. If a water-wheel were employed, it would produce by
means of the proposed machine the stated elevation of tempera-
ture, with the expenditure of =th of the work, which it would
have to spend to produce the same heating effect by friction.

The machine by which such effects are to be produced must
have the properties of a “ perfect thermo-dynamic engine,” and
in practice would be either like a steam-engine, founded on the
evaporation and recondensation of a liquid (perhaps some liquid
of which the boiling-point is lower than that of water), or an air-
engine of some kind. If the substance is to be heated or cooled by
air, it will be convenient to choose this itself as the medium
operated on in the machine. For carrying out the proposed
* object, including the discharge of the air into the locality where
it is wanted, the following general plan was given as likely to be
found practicable. Two cylinders, each provided with a piston,
ports, valves, and expansion gearing, like a high-pressure double-
acting steam-engine, are used; one of them to pass air from the
atmosphere into a large receiver, and the other to remove air
from this receiver and discharge into the locality where it is
wanted. The first, or ingress cylinder, and the receiver should
be kept with their contents as nearly as possible at the atmo-
spheric temperature, and for this purpose ought to be of good
conducting material, as thin as is consistent with the requisite
strength, and formed so as to expose as much external surface as
possible to the atmosphere, or still better, to a stream of water.
The egress cylinder ought to be protected as much as possible
from thermal communication with the atmosphere or surround-
ing objects. According as the air is to be heated or cooled, the
pistons and valve gearmg must be worked so as to keep the
pressure in the receiver below or above that of the atmosphere.
If the two cylinders be of equal dimensions, the arrangement
when the air is to be heated would be as follows :—The two pistons
working at the same rate, air is to be admitted freely from the
atmosphere into the ingress cylinder, until a certain fraction of
the stroke, depending on the heating effect required, is per-
formed, then the entrance port is to be shut, so that durig the
remainder of the stroke the air may expand down to the pressure

Heating or Cooling of Buildings by means of Currents of Air, 141

of the receiver, into which, by the opening of another valve, it is
to be admitted im the reverse stroke ; while the egress eylinder*
is to draw air freely from the receiver though the whole of each
stroke on one side or the other of its piston; and in the reverse
strokes first to compress this air to the atmospheric pressure (and
so heat it as required), and then discharge it into a pipe leading
to the locality where it is to be used. If it be required to heat
the air from 50° to 80° Fahr., the ratio of expansion to the
whole stroke in the egress cylinder would be ;43,, the pressure
of the air in the receiver would be ;87, of that of the atmosphere
(about 2°7 lbs. on the square inch below the atmospheric pres-
sure), and the ratio of compression to the whole stroke in the
egress cylinder would be 735. If 1 lb. of air (or about 153
cubic feet, at the stated temperature of 80°, and the mean atmo-
spheric pressure) be to be delivered per second, the motive
power required for working the machine would be °283 of a
horse power, were the action perfect, with no loss of effect, by
friction, by luss of expansive power due to cooling in the ingress
cylinder, or otherwise. If each cylinder be 4 feet in stroke,
and 26:3 inches diameter, the pistons would have to be worked
at 30 double strokes per minute.

On the other hand, if it be desired to cool air, either the in-
gress piston must be worked faster than the other, or the stroke
of the other must be diminished, or the ingress cylinder must be
larger, or an auxiliary ingress cylinder must be added. The last
plan appears to be undoubtedly the best, as it will allow the two
principal pistons to be worked stroke for stroke together, and
consequently to be carried by one piston-rod, or connected by a
simple lever, without the necessity of any variable connecting
gearing, whether the machine be used for heating or for cooling
air; all that is necessary to adapt it to the latter purpose, besides
altermg the valve gearing, being to set a small auxilary piston
to work beside the principal ingress cylinder, with which it is to
have free communication at each end. If it were required to
cool air from 80° to 50° Fahr., the auxiliary cylinder would be
required to have its volume '7th of that of each of the principal
cylinders; and if its stroke be the same, its diameter would

* Jn this case the egress cylinder acts merely as an air-pump, to draw
air from the receiver and discharge it into the locality where it is wanted,
and the valves required for this purpose might be ordinary self-acting
pump-valves. A similar remark applies to the action of the ingress cylinder
in the use of the apparatus for producing a cooling effect on the air trans-
mitted, which will then be that of a compressing air-pump to force air
from the atmosphere into the receiver. But in order that the same appa-
ratus may be used for the double purpose of heating or cooling as may be
required at different seasons, it will be convenient to have the valves of
each cylinder worked mechanically, like those of a steam-engine.

142 Royal Society.

therefore be a little less than a quarter of theirs. The valves
would have to be altered to give compression in the ingress
cylinder during the same fraction of the stroke as that required
for expansion when the air is heated through the same range of
temperature, and the valves of the egress ‘cylinder would have to
give the same proportion of expansion as is given of compression
in the other case; and the pressure kept up in the receiver by
the action of the pistons thus arranged would be 148 atmospheres,
or about 3°2 lbs. on the square inch above the atmospheric
pressure. The principal cylinders being of the same dimensions
as those assumed above, and the quantity of air required being
the same (1 lb. per second), the pistons would have to be worked
at only 24°6 double strokes per minute instead of 30, and the
horse power required would be *288, instead of as formerly "283,
when the same machine was used for giving a supply of heated air,

XXI. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from p. 68.]

Dec. 8. 1853.—Colonel Edward Sabine, R.A., V.P. and Treasurer,
in the Chair.
a ea following paper was read:.—‘‘On some of the Products of
the Decomposition of Nitrotoluylic Acid.’””’ By Henry M.
Noad, Ph.D,, Lecturer on Chemistry at St. George’s Hospital.

The author refers to a former memoir in which he described the
mode of preparation and properties of two new organic acids, the
analogues of benzoic and nitrobenzoic acids in the toluyl or im-
mediately succeeding series, and to which the names of toluylic
(C,, H, O4,) and nitrotoluylic (C,; H, (NO,) O,) acids were con-
sequently given.

In the present paper he resumes the study of the action of nitric
acid on cymol (C,,H,,), and describes first some unsuccessful
attempts to procure from that oil the substitution compound

Co { “ae 0 i , from which, by the action of reducing agents, he had

hoped to procure a new organic base homologous with aniline,
toluidine, &c. He then investigates the products of the decompo-
sition of his new nitrogen acid. He describes the preparation and

properties of nitrotoluylamide C,, ‘mo ho, NH,, and haying
4

succeeded, though by a rather tedious process, in obtaining this
substance in some quantity, he studies the action of reducing agents
onit. By the action of hydrosulphate of ammonia upon an aqueous
solution of the amide, a crystalline substance was procured, which
analysis proved to be homologous with the carbamide—carbanilide of
Hofmann, and with the ani/o-urea of Chancel. The study of its
properties showed that it must be considered as the analogue of the

Royal Society. 143

latter, that it is the true urea of the toluyl series, being a well-
defined organic base, forming a series of crystalline salts, of which
the nitrate and oxalate were qualitatively examined. A synoptical
view of these ureas is given, showing their relation with the urea
type.

By the action of a boiling solution of caustic potash on toluyl urea
(C, H,(C,,H,) N,O,), a new acid was procured, the analysis of
which showed that it has three homologues in the benzoyl series,
viz. anthranilic acid, benzamic acid, and carbanilic acid, all of which
are represented by the formula C,,H,NO,, the composition of the
new acid being expressed by the formula (C,,;H, NO,).

The limited quantity of this acid at the author’s disposal, and the
greatdifficulty with whichit wasprocured, did not enable him todecide
positively with which of the above acids it corresponds, though its
mode of formation would render it prebable that it is the true ana-
logue of carbanilic acid. The determination of this question is of
some interest, inasmuch as should it prove to correspond to anthra-
nilic acid, a road might through it be opened for the introduction of
a series of new substances at present entirely wanting, namely, the
proper homologues of salicylic acid and its derivatives. The author
proposes to return to this subject, and he gives, in conclusion, a syn-
optical view of those corresponding members of the benzoyl and toluyl
groups which in the present and former paper he has established.

Dec. 15.—Thomas Bell, Esq., V.P., in the Chair.

1. “On the Acidity, Sweetness, and Strength of Wine, Beer
and Spirits.” By H. Bence Jones, M.D., F.R.S.

(1.) The acidity of the different liquids was determined by means
of a standard solution of caustic soda, The quantity of liquid neu-
tralized was always equal in bulk to 1000 grs. of water at Gili

The acidity in different—

Sherries varied from 1°95 grs. to 2°85 grs. of caustic soda.

Madeira sd DELO “ot lo60 BS
Port +. PO ee ay a5
Claret % 2°55 a3 Berd 3
Burgundy a 2°55 5, § 4°05 gE
Champagne _,, PAO es fr 3: kb a3
Rhine wine 9 Orla. orr toiG0 ss
Moselle pe 2:8by &asacoO. 5
Brandy uu O-L5y! “247 40:60 %
Rum 3 Old sake O780 re
Geneva 3 0°07 ”
Whisky ” 0:07 ”
Bitter ale 2 Or9Dy Yet - 16a ie
Porter 3 13800) 43, 75210 3
Stout i LB5) ings 6 21:25 »
Cider sy [85 v4,;1# 48:90

Hence the order in which these wines may be arranged, beginning
with the least acid, is Sherry, Port, Champagne, Claret, Madeira,
Burgundy, Rhine, Moselle.

(2.) The sugar was determined by means of Soleil’s saccha-

144

Royal Society.

rometer, which: at least gives the lowest limit to the amount of

sugar.

The sweetness in different—
Sherries varied from 4 grs. to 18 grs. in the ounce.
6

Madeira s 3» pO 2
Champagne ,, GB) yin eeae 33
Port > LG) Diy, WSS SS
Malmsy ; HGS; 2G ay
Tokay a 74 3
Samos 88

Paxarette

94 ;

Claret, Burgundy, Rhine, and Moselle contained no sugar.
Hence the order in which these wines may be arranged, beginning

with the driest, is—

Claret

Burgundy

Rhine Moselle
Sherry

Madeira

Champagne

Port

Malmsy

Tokay

Samos

Paxarette.

In a dietetic view, assuming that the sugar becomes acid, then
the mean results as to the acidity of the different fluids examined,
beginning with the least acid, is—

Geneva

Malmsy

Whisky
Rum

Brandy

Claret
Burgundy
Rhine wine
Moselle
Sherry
Madeira
Champagne
Cider

Port

Porter

Stout

Madeira
Ale

Tokay.

(3.) The alcohol was determined by means of the alcoholometer
of M. Geisler of Bonn.
The strength of different samples of —

Port

Sherry He
Madeira fi
Marsala os
Claret "3

Burgundy __,,

varied from 20°7 per cent. to 23°2 per cent. by measure,
15°4 4

”» 24°7 ”
”? 19°7 ”?
ve ps0 ne
» Ul »
» 13°2 ”

Royal Society. 145

Rhinewinevariedfrom 9°5 per cent. to 13°0 per cent. by measure.
Moselle 33 8°7 9-4

> ced

Champagne _,, 14°1 a 14°8 5
Brandy - 50°4 = 53°8 rr}
Rum 5 72:0 Ea 7h pil i,
Geneva Hy 49-4 5
Whisky » 59°38 3
Cider - 54 ep This: at
Bitter ale ‘i 6°6 5 IPE? 5
Porter a 6°5 re 7°0 i
Stout 6°5 7-9

The Burgundy and Claret have less alcohol than was found by
Mr. Brande forty years ago in the wines he examined. The Sherry
is now stronger, the Port is not so strong, the Marsala is weaker,
the Rhine wine is the same strength, the Brandy is as strong
as formerly ; the Rum is nearly half as strong again; the Porter is
stronger, and the Stout rather stronger than formerly.

Lastly, the specific gravity of each liquid was taken. As this
however chiefly depends on the amount of alcohol and sugar present,
and as these were directly determined, the specific gravity may be
taken as a distant control on the amount of sugar present.

Thus, in those wines in which the amount of alcohol was the
same, the specific gravity was found to vary with the amount of
sugar found by the saccharometer.

The results of the analysis of each sample of wine, &c. is given
ina series of tables, which do not admit of any abstract.

2. «On a New Method of propagating Plants.” By E. J. Lowe,
Esq., F.R.A.S., F.G.S. &c.

The author states that the experiment of a new method of propa-
gating plants has been so successful, that he has taken the liberty
of forwarding to the Royal Society this short paper upon the sub-
ject, for the guidance of those who are interested in the advance of
horticulture.

It had occurred to him, that if a cutting of a plant were sealed
at the base, so as to exclude the moisture of the soil from ascending
the stem in injurious quantities, the method of striking cuttings of
most species of plants would not be so precarious a process as at
present; and accordingly some collodion was obtained in order to
make the experiment.

With respect to this new process, he states, that immediately
upon the cutting being severed from the parent stem, the collodion
was applied to the wound, and then left a few seconds to dry, after
which the cuttings were potted in the ordinary manner.

To test the value of this new process more effectually, duplicates
of all the species experimented upon were at the same time similarly
planted, without the collodion being applied to them.

Experiments were carried on in two different ways; one batch of
cuttings being placed on a hot-bed, whilst a second batch was
planted in the open ground, without even the protection of glass.

First Batch.—All of which were placed on a hot-bed ,on the 1st
of September, and examined on the Ist of October ;—

146 Royal Society.
Stove Plants.

Number of Number of
= RE pee cuttings with- aes
: pisut. Which took | OBt the appli-| hich took

collodion ane cation of col- root

applied. lodion,
1 Ixora coccinea ....... pe See peel 1 1 0
1 Tacsonia manicata ......+++ awenandcs 1 1 1
3 Franciscea Hopeana.......-+...s..008 3 3 0
3 Franciscea Pohliana.........-..se0ees 3 3 0
2 Gloxinia Maria van Houtte...... = 0 2 1
2 Begonia incarnata ..........eseenee 2 2 1
8 Achimenes patenS .--.....esersee ie 7 8 6
2 OV a: DEUA cron .c cs iscuses APES 2 2 1
2 Rondeletia speciosa ......seceeseenes 2 2 1
2 Allamanda nerifolia ............. Rekas 2 2 1

Greenhouse Plants.

6 Boronia serrulata .....0..-..sseee xi 5 6 0
3 Polygala dalmaisiana ...,..,..¢ss09+ ] 3 0
6 Polygala grandiflora........ ananseenne 3 6 2
6 WEXDENG JURE ascuaseangeanacsetegeas 6 6 6
1 Chorozema cordata .........+e0+5 4 1 1 0
I Epacris pallida .............0000+ nthe 0 1 0
2 Leschenaultia formosa.........ss0e08 2 2 1
1 Swainsonia astragalifolia......,... Ss 1 1 0
1 Swainsonia galegifolia .......«-.,... ; 0 1 0
2 Abelia rupestris ...... recenegeds Redes 2 2 0
4 Plectranthus concolor, picta ...... 2 4 2

Second Batch.—Planted in the open ground on the Ist of Sep-
tember, and examined on the Ist of October :—

Hardy Plants.

Number of Number of| Number of |number of
uttings 5 W - x
; with Name of plant. epee Si Pout the agai beepers
collodion Bs eh by cation of col- OOF
applied. lodion. 7
12 Garrya elliptica ......cccsecsssesvees 5 12 1
12 FEYICA, VORODSscasaepecyesestearosetnness 7 12 4
18 Bupleurum longifolium ......s+00 6 18 0
12 Laurus TOGGENS oe+.....0enee Seaiiensse 10 12 7
6 Rose, Souvenir de la Malmaison... 4 6 3
12 Taxus baccata, golden-leaved var. 8 12 4

Total number of Total number of
; ‘i Number of : . Number of
eieellction waa | cuttings which | uenesmithowt| cuttings which
applied. took root, Ofcallodion: took root.
aaa
First batch ...,,. 59 46 59 23
Second batch .., 72 40 72 19

The experiment, the author considers, speaks for itself. Not-
withstanding the season being too far advanced for the full benefit
of the process to be thoroughly observed, still twice as many cut-

Royal Society. 147

tings took root treated by the new method as had rooted by the old.
The mortality in the open ground was increased by slugs having
eaten off above the soil some of the cuttings; those thus damaged
were examined after they had been in the ground a month, and it
was found that the collodion was quite as sound as when first ap-
plied. It would therefore appear that the collodion seals the wound
of the cutting, and protects it from the fatal effects of damp, until
roots are prepared to force through the covering of gun-cotton. It
is further stated, that the application of this solution has been found
to be exceedingly beneficial in the pruning of such plants as Huphor-
bia speciosa, Impatiens latifolia, Impatiens latifolia-alba, Hoya bella,
Hoya imperialis, &c., the cut branches being prevented from bleeding.

It is the author’s intention next spring to follow out this experi-
ment, in budding and grafting, as he considers that it will also be
useful in this branch of horticulture.

Gutta-percha, dissolved in wther, was in some instances substi-
tuted to heal the wounds caused by pruning; yet owing to this so-
lution not drying as rapidly as collodion, the first, and sometimes
the second application was not sufficient.

The effect of these solutions upon cut flowers was very marked.
Two branches were gathered as nearly alike as possible; to the
flower-stalks of the one, collodion was applied. These flowers
were placed in vases filled with water; those coated over with
collodion began to fade in thirty-six hours, and many were quite
dead in three days; whilst the flowers merely placed in water in the
ordinary manner remained fresh and healthy. Those that faded
soonest were Reseda odorata and Tropeolum majus, and those which
were least affected were Tagetes erecta and Senecio erubescens.

Dec. 22, 1852.—Thomas Graham, Esq., V.P., in the Chair.

‘*On certain Properties of Square Numbers and other Quadratic
Forms, with a Table by which all the odd numbers up to 9211 may
be resolved into not exceeding four square numbers.” By Sir
Frederick Pollock, F.R.S. &c.

In examining the properties of the triangular numbers 0, 1, 8, 6,
10, &c., the author observed that every triangular number was com-
posed of four triangular numbers, viz. three times a triangular num-
ber plus the one above it or below it; and he found that all the
natural numbers in the interval between anyéwo consecutive triangular
numbers might be composed of four triangular numbers having the
sum of their roots, or rather of the indices of their distances from
the first term of the series constant, viz. the sum of the indices of
the four triangular numbers which compose the first triangular
number of the two.

Not being at that time aware of any law by which the series that
fills up the intervals could be continued, he subsequently turned his
attention to the square numbers as apparently presenting a greater
variety of theorems. He observed that if any four square numbers,
at, b®, c*, d®, have their roots such, that, by making one or more
positive and the rest negative, the sum of the roots may be equal to
1, then if the root or roots of which the sum is 1 less be each of

148 Royal Society.

them increased by 1, and the others or other be each diminished by
1, the sum of the squares of the roots thus increased or diminished
will be at+2+c?+d?4+2. ‘This he found to be only a particular
case of more general theorems.

Theorem A.—If the sum of the roots a, 6, c, d=2n—1, and n be
added to each of the less set, and subtracted from each of the greater,
the increase in the sum of the squares of the new roots will be 2n.

Theorem B.—lIf the sum of the roots =2n+1, and z be added to
each of the less set and subtracted from each of the greater, the
diminution in the sum of the squares of the new roots will be 2z.

By means of these he shows—

Theorem C.—If any four squares be assumed which compose an
odd number, these may be diminished till four squares are attained
the sum of whose roots will equal 1.

By applying the first of these theorems to four roots, the sum of
whose squares is an odd number, the author deduces, in a tabular
form, the squares (four or less) which compose the odd numbers
from 21 to 87; and remarks that there does not appear to be any
limit to this mode of continuing to increase the sum of four squares
by 2 each time. As, however, although this may render it probable
that every odd number is composed of four, three, or two squares, it
falls very short of a mathematical proof, unless it can be shown that
the series can be continued by some inherent property belonging to
it, he proceeds to examine the series, in order to ascertain what
approach can be made to such a proof.

Adopting a method similar to that observed in the triangular num-
bers, the author forms what he terms the series of Gradation, by
means of which the series of squares which compose the odd num-
bers may be advanced by steps or stages which increase regularly
and obey a certain law, and at which this series is, as it were, com-
menced anew from roots of the form n, 2, n,2+1, orn—1,n, n,n;
the form of the sum of the squares of these roots being 4n?+ 2n+1,
and the series of gradation 1, 38, 7, 13, 21, 31, 43, 57, 73, &c. On
this principle a more extended table of the odd numbers resolved
into squares (not exceeding four in number) is constructed. On
this the author remarks that it is complete to the 96th odd number
(191), that is, there are in this table square numbers which will
form the odd numbers in succession, whose roots (some +, some —)
=1; and therefore the expression 422+ 2n+1 up to 4n*+ 2n+191
may be divided into 4 or 3 squares, whatever be the value of n.
The numbers in the table exactly fill up the interval between

472, 472, 472, 48°= 8931,
and 472, 482, 48", 482=9121,
whose difference =190, the difference between the first term and
the last term in the table: it will therefore resolve into square num-
bers any odd number up to 91214+190=9211.

With reference to the mode in which the intervals in the table
may be filled up, the author states the following general theorems re-
lating to the sums of three square numbers, by means of which the

Intelligence and Miscellaneous Articles. . 149

roots may be varied, and yet the sum of the squares remain the
same.

Theorem D.—If any three terms of an arithmetical series, and
emitting the 4th term, the three following terms be arranged thus,
a+b, a+26, a+6b,

a > a+4d, a+56,
the sum of the squares of each set of terms will be the same.
Theorem E,—If four numbers in arithmetical progression be placed
thus, Cae a+ 26,
a+4b, a+66,
and the sum of the 1st and 4th be divided into two parts whose dif-
ference shall be four times the arithmetic ratio, as a+ 7b—(a—),
and the parts be placed with the terms, the greater with the less,
and the less with the greater, thus,
ae a+ 26, a+7b,
a—b, a+4b, a+ 6b,

the sum of the squares will be equal.
Theorem F,—Let two numbers which differ by 2 be placed thus :

a+n, a+n,
a—n, a—n,
then if the sum of the four (2a) be divided so as to have the same

difference (2n), and the parts be placed, the less with the greater,
and the greater with the less, thus,

atn, a+n, 2Qa—n,
a—n, a—n, Qa+n,

the sum of the squares shall be the same.
The author illustrates this part of the subject by deducing six
forms of roots whose squares =197.

XXII. Intelligence and Miscellaneous Articles.

ON THE OCCURRENCE OF NICKEL AND COBALT IN SOME MINERAL
SPRINGS, AND ON A METHOD FOR THEIR ISOLATION. BY
OSSIAN HENRY.

AZADE some time since stated that he had found in the
chalybeate springs of Neyrae and its ochreous deposits,
titanium, glucina, cobalt and nickel. In consequence of this state-
ment, the author has tested several chalybeate waters for nickel
and cobalt, and ascertained the presence of these two metals by
the following process :—
To a large quantity of the water a slight excess of carbonate of
soda is added ; the fluid is then allowed to stand in the air until the

150 Intelligence and Miscellaneous Articles.

iron is completely converted into oxide and deposited. The deposit
of the spring itself may also be taken. These deposits are dissolved
in muriatie acid, and evaporated to a certain degree for the removal
of the glucina, titanium, sand and silica, when the solution generally
contains only alumina, lime, magnesia, iron, manganese, nickel and
cobalt.

To this solution carbonate of soda is again added until a precipi-
tate is obtained, which is agitated in the air with a large quantity of
water. It is then washed; and when it has become oxidized in the
air, it is brought into contact with water which has been saturated
with carbonic acid in an apparatus fitted for the purpose. This
dissolves only the carbonates of nickel and cobalt, upon which sul-
phuretted hydrogen is passed through the solution, or hydrosul-
phuret of sodium added to it. 2

By this means the nickel and cobalt are separated, generally very
slowly, in the form of sulphurets. The sulpburets are dissolved in
nitromuriatic acid, precipitated by carbonate of soda, and treated in
the manner proposed by Laugier for the detection of cobalt and
nickel.— Journ. de Pharm. et de Chim., 3rd ser. xxiv. p. 305.

ON THE INFLUENCE OF PRESSURE UPON THE FORMATION OF
CHEMICAL COMPOUNDS. BY PROF. WOHLER.

Hydrate of chlorine, which is immediately decomposed at ordi-
nary temperatures and at the pressure of the atmosphere, remains
for the most part undecomposed even at a summer heat when en-
closed in hermetically-sealed tubes, under the pressure of the chlo-
rine which is set free from a portion of it which undergoes decom-
position. In such a tube, when plunged into water of a temperature
of 86°-104° F., the hydrate of chlorine is decomposed, but becomes
partially restored on its return to the ordinary temperature.

This decomposition is not prevented by the exclusion of the air
under the pressure of chlorine gas of the tension of the atmosphere ;
under these circumstances the decomposition takes place as usual at
any temperature above 32° F.

‘A tube in which hydrate of chlorine was hermetically sealed was
exposed to the sun fora whole summer’s day. It became fluid, but
did not indicate decomposition of the water by the setting free of
oxygen.

The author had already observed, that during the preparation of
liquid sulphuretted hydrogen from sulphuret of hydrogen in her-
metically-sealed tubes, colourless crystals are sometimes formed,
which immediately disappear on the tube being opened.

In two tubes, in which sulphur, but no liquid sulphuretted hy-
drogen had separated, these crystals were formed in large quantity ;
they did not however make their appearance in a third tube, in
which the persulphuret of hydrogen was enclosed together with con-
centrated muriatic acid. Hence the author concludes, that the ery-

eee

Meteorological Observations. 151

stalline compound, which is no doubt a hydrate of sulphuretted
hydrogen, must be produced when a small quantity of water is en-
closed with hydrate free from acid; the water then combines with
the sulphuretted hydrogen under the pressure of the condensing
sulphuretted hydrogen (17 atmospheres). Under this pressure it is
permanent at ordinary temperatures. If the tube be heated in water
to 86° F., the compound dissolves, and rapidly becomes fluid,
returning to a solid state again on being cooled to the ordinary
temperature.—Ann. der Chem. und Pharm., \xxxv. p. 374.

METEOROLOGICAL OBSERVATIONS FOR DEC. 1853.

Chiswick.—December 1. Overcast: fine: clear and frosty. 2—4. Dense fog.
5. Foggy: slight rain. 6,7. Foggy: overcast. 8. Foggy: fine. 9. Fine: slight
rain. 10,11. Cloudy. 12. Hazy: uniformly overcast. 13. Foggy. 14. Over-
east. 15. Snowing: clear and frosty. 16. Overcast: clear, with bright sun :
severe frost at night. 17. Severe frost: overcast: frosty. 18. Clear: overcast.
19. Uniformly overcast : clear and fine: cloudy. 20. Hazy, 21. Densely clouded :
boisterous at night. 22. Overcast. 23. Cloudy: clear. 24. Clondy: clear and
frosty. 25. Frosty: hazy: clear, with sharp frost at night. 26. Frosty: fine:
frosty. 27. Clear and frosty : hazy: clear and frosty. 28. Clear and frosty : fine:
severe frost at night. 29. Severe frost: clear and fine: frosty. 30. Snow-
shower: frosty. 31. Very clear and frosty: partially overcast: sharp frost at
night.

Mean temperature of the month ............csseesssrecrivetesses G2°49

Mean temperature of Dec. 1852) | oon. ..s.1...0ce.secnsnocerons 46 °56
Mean temperature of Dec. for the last twenty-eight years . 39 -64
Average amount of rain in Dec. .........:se..00e00 spp -grancen LOCH

Boston.—Dec. 1. Cloudy: rain a.m. 2. Fine. 3. Cloudy. 4,5. Foggy. 6.
Cloudy: raina.m. 7. Foggy. 8. Fine. 9. Fine: rainp.m. 10. Fine: rain
early a.m. $11—13. Cloudy. 14. Fine. 15. Snow and rain a.m. and p.m.
16. Cloudy: snow a.m. 17. Cloudy. 18,19. Fine. 20. Cloudy: rain p.m.
21. Cloudy: rain a.M.andp.m. 22, 23. Cloudy: rain a.m. 24. Cloudy. 25.
Foggy. 26. Foggy: rain andsnowr.m. 27. Fine: snow Pm. 28. Snow a.m.
and p.m. 29. Fine. 30. Fine: snowa.m. 31. Fine.

Sandwick Manse, Orkney.—Dec. 1. Hazy a.m.: rain p.m. 2. Damp a.m.:
drops P.M. 3. Bright a.m.: cloudy, aurorarp.m. 4. Clear a.m. andp.m. 5.
Bright a.m.: clear, aurora p.m. 6, Clear a.m.: clear, aurora S. p.m. 7. Bright
A.M.: frost, showers P.M. 8. Showers A.M.andr.m. 9. Showers a.m. : clear p.m.
10. Bright a..: fine p.m. 11. Frost a.m.: damp p.m. 12. Damp a.m.:
showers p.M. 13. Bright a.m.: clear, a.m. lunar halo p.m. 14. Damp
and p.m. 15. Cloudy a.m.: clearp.m. 16. Damp a.m.: clear p.m. 17. Clear,
frost a.m.andp.m. 18. Bright, frost a.m.: clear, frost p.m. 19. Showers a.m.:
clear p.m. 20. Showers a.m.: clear, frost p.m. 21. Clear, frost a.m.: clear,
frost, aurora p.m. 22, Cloudy, frost A-m.: showers P.M. 23. Showers a.M.:
showers, aurora p.m. 24. Cloudy a.m.and p.m. 25. Cloudy a.m. : sleet-showers
p.M. 26. Hail-showers a.m.: snow-showers p.m. 27. Snow drift a.m. and p.m.
28. Snow-showers a.M.: snow, cloudy p.m. 29. Thaw: showers a.m. and p.m.
30,3]. Snow-drift a.m.: snow-showers P.M.

Mean temperature of Dec. for twenty-six previous years ... 41°18
Mean temperature of this month —.......,.+8+.0.5 SPOOL ET «edge tf
Mean temperature Of Dec. 1852 ....,...scsseereeesseerreesensens 40°74
Average quantity of rain in Dec. for thirteen previous years 4°13 inches.

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THE
LONDON, EDINBURGH anno DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

MARCH 1854.

XXIII. Reports on the Progress of the Physical Sciences.
By Dr. Hrrsv.

On the Application of Magnetic Induction to the determination of
the Magnetic Inclination. By Prof. W. Wuser.

[Poggendorff’s Annalen, vol. xc. p. 209.]
[With a Plate. ]

tA is known that by the investigations of Gauss, observations on

terrestrial magnetism have been raised from mere compari-
sons to actual measurements, which in point of precision are
comparable to astronomical ones. The system of measurement
here referred to has, however, been employed hitherto in obser-
vations on the horizontal elements of the earth’s magnetism alone,
the horizontal intensity and declination. It is true that these
horizontal elements form in themselves a complete system, from
which, as Gauss has shown, a complete determination of the
earth’s magnetism may be obtained without the aid of observa-
tions on the inclination. But it is also true that the attainment
of this end would be facilitated by means of observations on the
inclination, and hence the latter must not be disregarded. At
present, however, such observations by no means possess that
classic character which those on the horizontal elements have
attained through the use of the magnetometer. The causes
of their deficiency in this respect are essentially two: First.
The action of the vertical magnetic force is not observed by
itself, but in combination with the action of gravity on our pon-
derable needles. A separation of the effects due to each of the
two forces is certainly possible, by demagnetizing the needle
and thus obtaining several combinations of the two; but the

Phil. Mag. 8. 4. Vol. 7. No, 44, March 1854. M

154 Prof. Weber on the Application of Magnetic Induction

determination of the vertical magnetie force thus obtaimed can
never possess that degree of precision which a determination of
the horizontal magnetic force now enjoys, inasmuch as the latter
is deduced from effects produced by this force alone, and unin-
fluenced by any other forces. Secondly. The magnetometric
arrangements, on which the possibility of accurate observation
depends, cannot be applied to instruments for measuring the
inclination, on account of the influence of friction which is inse-
parable from such instruments; and as long as this exists, the
application of more accurate methods of observation would simply
lead to deceptive results. These defects are so intimately con-
nected with the conditions under which the action of the vertical
component of the earth’s magnetism on the magnetism of other
bodies must be observed, that they cannot possibly be avoided ;
the most ingenious arrangement and combination of observations
may serve to diminish the prejudicial consequences of these de-
fects, but never to remove them.

Soon after Faraday’s discovery of magnetic induction, Gauss
drew attention to the possibility of investigating the earth’s
magnetism by observing its action on the electricity of bodies ;
and, acting on this suggestion, Weber, in 1837, constructed a
new instrument for measuring the magnetic inclination, which he
named the “ Induction-Inclinatorium*.” This instrument was
completely free from the first of the above-mentioned defects,
that is to say, no interference of the force of gravity took place,
and hence no demagnetization was necessary to separate its
effects from those of the vertical magnetic force. The second
defect, however, was not removed; magnetometric arrangements
could not yet be combined with this instrument so as to obtain
accurate results, hence this new method was of no avail.

At length Weber has succeeded in removing this second defect
also, and has discovered an arrangement whereby the electric
action of the vertical as well as the horizontal component of the
earth’s magnetism may be measured, by the unifilar magneto-
meter, with a degree of precision of which hitherto the magneto-
metric determination of the horizontal elements alone could
boast. For the practical solution of the problem, an accurate
and complete investigation of the earth’s magnetism, this ex-
tended application of the magnetometer to measurements of the
inclination is of some importance.

A simple and general notion of Weber’s new instrument may
be obtained by a reference to the well-known construction of the
electro-magnetic telegraphs now in use. These, it will be remem-~
bered, are of two kinds. In one the electric currents made use of

* Resultate aus den Beob. des magn. Vereins im Jahre 1837, 8. 81.

to the determination of the Magnetic Inclination. 155

to give the signs, proceed from a galvanic battery; in the other they
are induced in the electric conductor by means of magnetic force.
Weber has constructed a telegraph of the latter kind, where
the earth’s magnetic force induces electric currents strong enough
to be used for giving signs. For such induction, either the
horizontal or the vertical component of the earth’s magnetism
may be used. Let us suppose the telegraph to be a so-called
needle-telegraph (such as are used in England), in which the
current gives the sign by passing through a helix and de-
flecting a needle suspended in the same from the magnetic
meridian. It is evident that, by an exact comparison of the
deflections, we may determine the ratio of the intensities of the
electric currents respectively induced by the vertical and hori-
zontal component of the earth’s magnetic force; this ratio is
the tangent of the required inclination. In constructing such a
telegraph, therefore, it is necessary to obtain deflections of the
needle which are capable of accurate measurement, and at the
same time to exclude all disturbing influences. For the former
purpose it is clear, that, in place of the common magnetic needle
of the galvanometer, a magnetometer must be used. To exclude
all disturbing influences it is necessary,—1, that no commutation
of the conducting wires be employed in order to increase the
deflection; 2, that the amount of deflection be independent
of the velocity of the inductor’s motion. For, in the first place,
the circuit must remain unchanged if the observed deflections are
to furnish an exact comparison of the forces by which they were
ptoduced; and in the second place, these forces must not be
subject to variation, as would be the case if they were dependent
upon the velocity of the inductor’s motion. It will be shown
that both conditions ave fulfilled when the inductor’s whole
motion is limited to an induction stroke, capable of momentary
execution, and strong enough to produce in the magnetometer
a deflection capable of the finest measurement. Such a simple
induction stroke consists in a semi-rotation of the inductor; no
commutation in the connexion of the inductor wire with that of
the galvanometer is here necessary, because during such a semi-
rotation no change in the direction of the induced current takes
place.

We proceed next, by help of the figures in Plate IL., to give
a description of this new instrument, to which Weber has given
the name induction-magnetometer.

A transverse section of the inductor is shown at A, fig 1. The
circumference of the cylinder on which the wire is coiled is 718°3
millims., its diameter is aa=ala', and its breadth aa’ =120-05
millims. The copper wire around this cylinder is 542296
millims. long, and has a mean sectional area of 4:145 square

M2

156 ~~ Prof. Weber on the Application of Magnetic Induction

millims. It was covered first with wool and then with gutta
percha, and so coiled round the cylinder as to form 605 coils
arranged in eighteen strata. The circumference of the last en-
circling stratum is 1078°6 millims.

This induction coil is surrounded by a strong wooden frame,
6bbb ; at its extremity is a wooden pulley C, with two circular
grooves, in which lie the wires connecting the inductor and gal-
vanometer. To this frame two strong brass pivots, d, d', are fixed.
The two pivots are exactly cylindrical and of equal diameters, and
rest on the Y-formed supports e, e’, fixed to the beam of the
frame B, B!. Fig. 1 shows the induction coil in the position in
which it can rotate around a horizontal axis. To test the hori-
zontality of the axis of rotation, a level, c, is used; its setting is
provided with two Y-formed feet, by means of which it can be
placed on the two pivots d, d' which form the axis of rotation.
At the end of one of the pivots, d’, is a brass ball, in which
a conical-shaped cavity at f is turned. This ball serves to
displace the induction coil, so that from beimg horizontal, its
axis of rotation is brought into a vertical position. For m-
stance, the level c bemg removed, the induction coil A can be
raised by the pivot d when the sphere on the pivot d’ sinks into
a spherical cavity cut at g into the beam B!. When the axis of
rotation is thus brought into a vertical position, as shown by the
dotted lines in the figure, the raised pivot d fits into a Y-formed
support h, fixed to the beam D of the framework, and is held
there by the pressure of a spring ; this pressure can be regulated
by a screw. In this position the point of a screw, passing ver-
tically through the beam B’, fits into the conical-shaped cavity
of the ball on the pivot d'; thus the induction coil can be raised
so as to rotate freely on this pot by merely turning the screw
head at k under the beam. To test the verticality of the axis of
rotation, a level is placed upon the level carrier // which fits on
to the end of the pivot d.

Fig. 2 represents the induction coil in its horizontal position,
as seen from above. The inductor’s axis (¢. e. the axis of
the cylinder on which the wire is coiled) is here perpendicular
to the plane of the figure. Perpendicular to the frame to which
the pivots d, d! are fixed, is a second frame mm, surrounding the
induction coil, which carries two stout brass pins at n,n. On the
rotation of the induction coil these pins strike against screws
fixed into the beam of the framework, and thus at the end of
each induction stroke the inductor’s axis is held vertical. One of
these pins ; which during the rotation moves in the upper semi-
circle, strikes on these screws from above; the other, which
moves in the lower semicircle, from below. These screws can
be somewhat displaced in a vertical direction, and their position

to the determination of the Magnetic Inclination. 157

once found they can be fixed there. This position is determined by
seeking the are through which the induction coil must be moved,
so that the induced currents may annihilate one another. The
position of the induction coil which corresponds to the middle
of this arc is the position of the brass pins at the moment when
they should strike the screws. The two ends of the wire of the
inductor are led to the clamps p, p and there fastened. From
these clamps the connecting wires pass over the pulley C to the
galvanometer.

Fig. 3 is a section of the multiplication coil together with the
magnetic needie. The circumference of the cylindrical surface
around which the wire is coiled is 1027:4 millims., its diameter
is aa=a'a', and its breadth aad =225°6 millims. Around this
cylindrical surface two copper wires, covered first with spun wool
and then with gutta percha, were coiled side by side. Hach wire
is 992656 millims. long, and the mean sectional area of both
wires taken together is 8°1682 square millims. Each of these
wires forms 779 coils, arranged in twenty-five strata. The cir-
cumference of the last stratum is 1528-4 millims.

In the middle of the coil the magnetic needle NS is sus-
pended on a prismatic bar, which can be moved along a eross-
bar 64 and screwed fast to it. Above the coil is another
cross-bar, parallel to the lower one, and suspended from a fine
wire ; the two are connected at their extremities by two thin
vertical connecting rods which pass outside the multiplication
coil. To the upper cross-bar a mirror and torsion circle is affixed.
Lastly, the space enclosed by the coil, in which the needle
oscillates, is closed on both sides by covers, ccce.

Fig. 4 is a vertical section of the galvanometer in the direction
of the magnetic meridian. Here the direction of the upper
cross-bar d, as well as that of the lower cross-bar 0, is perpendi-
cular to the plane of the figure. Both are connected by thin
vertical bars attached to their extremities before and behind the
multiplier. The mirror e is connected with the cross-bar d
by means of a Y-formed hook, and above the mirror, similarly
connected, is the torsion circle hung on a thin wire. The case
which encloses d, e, and f projects a little both before and behind
the multiplier, and on both sides reaches down to the covers
ecce, fig. 3; so that the connected space occupied by d, e, f
and the coil is completely enclosed, with the exception of an
opening through which the thin suspending wire passes. A
parallel plate of glass is placed in the side of this case immedi-
ately before the mirror, so that the image of the scale may be
observed in the mirror by a telescope. Lastly, the frame of the
multiplier has a hexagonal form, and the undermosi side of this
hexagon rests upon a stone pedestal A.

.

158 Prof. Weber on the Application of Magnetic Induction

Fig. 5 is a ground plan of the building, showing the relative
situations of the inductor C, the galvanometer B, and the tele-
scope and scale A. The distance between the galvanometer
and inductor is so great, that the influence of the galvanometer
needle on the inductor vanishes in comparison to that of the
earth’s magnetism. The inductor stands on three foot-screws
a, b, c, which are used to give the axis of the inductor a perfectly
vertical or horizontal position, according as the horizontal or ver-
tical component of the earth’s magnetic force is used for induction.

It was so contrived, that during the observations the person
at the telescope could set the inductor in rotation by means of
his foot ; in the following observations, however, the induction
strokes were made by an assistant. The two wires from the
galvanometer and inductor passed over the telescope-stand close
to the observer, where, by means of a clamp, the galvanometer
wire could be made to return without passing over the inductor,
or a continuous wire made to pass over both the galvanometer
and inductor. As these contrivances, however, can be modified
to suit the conveniences of the observatory and habits of the
observer, a fuller description is unnecessary.

It should be here remarked, that, for inclination measure-
ments alone, a galvanometer with so great a helix as the one
above described is by no means necessary ; it is only because
the mean radius of the coils ought not to be less than 230
millimetres that so great a mass of copper (60 kilogrammes)
was used for this galvanometer. But the great width of the
coil, as well as its circular form, was not chosen on account
of the inclination measurements to be made therewith, but
because it was intended that the instrument should also serve
for fixed standard measurements of the normal resistance in gal-
vanic circuits, similar to the instrument described in the Ab-
handlungen iiber elektrodynamische Maasbestimmungen (Leipzig,
1852), 11., with which, however, such measurements of resistance
could be made but once. Such measurements have actually been
made with the present instrument; but for the results, as well
as for the necessary theoretical elucidations, we must refer the
reader to the original memoir.

For correct and convenient measurements of the inclination,
which at present interests us, Weber remarks that all the dimen-
sions of the galvanometer may without injury be diminished
one-half; so that an eighth part of the wire (about 10 kilo-
grammes) would be sufficient. The accuracy of the inclination
measurements would even be increased by this means, for the de-
flection of the needle would be thereby mcreased in the ratio of
1: 2, and might perhaps be doubled, if, instead of the cir-
cular form, the coil had an appropriate elliptical form, the

to the determination of the Magnetic Inclination. 159

axis of the needle coinciding with the major axis of the ellipse.
Should the deviation of the needle be thus too great to be con-
veniently measured by the scale, only half the amount of wire
(about 10 kilogrammes) need be employed for the inductor.
This diminution of the mass of the inductor would have another
advantage, the rotation of the inductor coil could be made with
greater ease.

In former memoirs* Weber has shown the application of the
induction stroke to delicate measurements, and has developed
the rules according to which the deviations of the magnetic
needle, produced by the induced electric currents, are multiplied
m the galvanometer, as well as subjected the observations
to mathematical calculation. It is not necessary to repeat
these rules here; it will be sufficient to give the observations
made in accordance with them, from which it may be de-
cided whether, in this instrument for the measurement of the
inclination, the necessary delicacy is combined with the intended
simplification of labour, as it should be in order to be an essen-
tial improvement upon the best known inclination instruments.

The magnetometer and galvanometer being prepared, the
position of the inductor was so regulated that,—1, its own axis
(2. e. the axis of the cylindrical surface around which the wire
was coiled) was horizontal, and parallel to the magnetic meridian ;
2, that the axis around which it could be made to revolve 180°
backwards and forwards, was perfectly vertical; this could be
tested within a few seconds by means of the level. The mag-
netometer needle in the galvanometer was at the commencement
in a state of perfect rest in the magnetic meridian. This could
always be secured by the damping force of the galvanometer,
which was increased by connecting the two wires from the gal-
vanometer to the inductor by means of a copper clamp, the gal-
vanometer thus forming a circuit for itself. When the damping
force was thus increased, two succeeding ares of oscillation of the
needle were in the ratio of 100: 71; hence after thirty oscillations,
or, as the time of an oscillation was eighteen seconds, in nine mi-
nutes, the amplitude was diminished 29,000 times by this damping
force ; that is to say, the needle was in a state of rest, no matter
how great the original ares of oscillation might have been. Before
commencing observations, the clamp used to increase the damp-
ing power was removed, and then the first (positive) induction
stroke given with the inductor. The needle being thus set in
motion, left the magnetic meridian, and in nine seconds (half its

* Resultate aus den Beob. des magn. Ver. im Jahre1838 (Leipzig, 1839),
and Abhandlungen iiber elektrodynamische Maasbestimmungen (Leipzig,
Weidmann’sche Buchhandlung,1852), 2° Abhandlung, Beilage C. 8. 341 ff.

160 Prof. Weber on the Application of Magnetic Induction

time of oscillation) attained its maximum deflection to the east
(or west). This was noted by the observer, after having marked
down the needle’s position when at rest. The needle now
returned, and after nine seconds passed through the magnetic
meridian. At this moment followed the second (negative) induc-
tion stroke, caused by turning the inductor back through 180°,
whereby the needle was accelerated in its returning motion.
After nine seconds, the needle, thus accelerated, attained its
maximum western (or eastern) deflection, which was again noted,
and so forth. No. 0 in the following table shows the original
position of rest, Nos. 1 to 16 show the sixteen succeeding elon-
gations observed as above described. These observations lasted
scarcely five mmutes.

Table I.

Gottingen, 1852. Aug. 3, 0b 20™—Oh 25,
0 a ne

Position of the needle in Position of the needle in

No. divisions of the scale at the No. divisions of the scale at the
observed elongation. observed elongation.
0 1236°2 9 1030°8
1 1195-0 10 1450°9
2 1313°8 11 1014-7
3 11311 12 1464-0
4 \ 1367°4 13 1003-1
5 1085°6 14 1473°4
6 1405°3 15 996:9
7 1053°2 16 1479°8
8 1432:0

After the last observation, the clamp for increasing the damp-
ing power of the galvanometer was immediately closed; and
during the damping action the position of the mductor was
changed, so that,—1, its own axis stood vertical; 2, the axis
around which it was revolved 180° backwards and forwards was
exactly horizontal and parallel to the magnetic meridian. This
was effected by means of the level described im fig. 1. After
removing the clamp for damping, the second series of observa-
tions was made in the same manner as the first. This series,
however, was made four times at intervals of ten minutes, or as
soon as the needle had again come to rest. After these four
series of observations, during which the inductor’s position was
unchanged, followed the last series, in which the inductor had
the same position as at first. The following table gives a
summary of the six series of observations, which, including the
time requisite for damping and changing the inductor’s position,
required 14 20™ to complete. The several series are denoted by
the letters A, B, C, D, E and F.

to the determination of the Magnetic Inclination. 161

Table II.
Gottingen, 1852. Aug. 3, 0% 20™—1> 40™.

Position of the needle at the observed elongations.

No. A. B. Cc. D. E, F,
0 1236:2 | 1235-1 | 1234-4 | 1233:8 | 1233-7 | 1283-3
1 1195-0 | 1835-2 | 13384:9 | 138349 | 1333°8 | 1192-2
2 13138 | 1052-7 | 10520 | 1051-0 | 1050-1 | 1310-7
3 1131/1 | 1488-9 | 1488-3 | 1488-0 | 1487-0 | 1128-4
4 1367°4 §22°8 921-9 920°9 920-71 | 1364-4
5 1085°6 | 1596-8 | 1597-5 | 1597-1 | 1595-9 | 1083-0
6 1405°3 830°4 829-7 828-7 827-9 | 1402°8
7 1053°2 | 1674-6 | 1674-6 | 1673-8 | 1672-6 | 1050-9
8 1432-0 764-9 764:0 762°9 762°0 | 1429-8
9 1030'8 | 17288 | 1728-9 | 1728-0 | 1726-9 | 1028-1
10 1450°9 717-9 717-0 715-9 715:2 | 1448-9
11 1014-7 | 1767°8 | 1768-0 | 1767-0 | 1766-1 | 1012-1
12 1464-0 684-3 684-0 683-0 682°1 | 1462-2
13 1003-1 | 1795-4 | 1795-4 | 1794°6 | 1793-9 | 1000-6
14 1473-4 661-0 660°6 659°8 659-0 | 1471°8
15 996-9 | 1815-0 | 18149 | 1814-2 | 1813°6 993-2
16 1479°8 6443 644-2 643-0 642-4 | 1478-2

If in each series of observations the number corresponding to
the position of rest opposite No. 0 be subtracted from the elon-
gations opposite Nos. | to 16, the corresponding distances of
elongation will be obtained, as shown in the following table.
The signs, which are alternately positive and negative, are here
neglected.

Table III.
Gottingen, 1852. Aug. 3, 05 20™—]4 40m,

Distances of elongation.

No. A. B. Cc. D. E. F,
1 41-2 100°1 100°5 101-1 100:1 41-1
2 776 182-4 182-4 1828 183°6 774
3 10571 253'8 253°9 254-2 253°3 104:9
4 131-2 3123 3125 312-9 313-6 131-1
5 | 150°6 861:7 363°1 363°3 362°2 150°3
6 169-1 404°7 404-7 405°1 405°8 169°5
7 183-0 439'5 440-2 440°0 4389 182-4
8 195°8 4702 470°4 470°9 4717 196°5
9 205°4 493-7 494°5 494-2 493°2 205:2
10 2147 5172 5174 517'9 5185 2156
ll 221°5 532-7 533°6 5332 532-4 221-2
12 227°8 550°8 5504 550°8 5516 228-9
13 233°1 5603 561-0 560°8 560-2 232°7

14 237°2 574-1 573°8 574-0 574:°7 238°5
15 239°3 5799 580°5 5804 579-9 240°1
16 | 243°6 590°8 590-2 590°8 591-3 244'9

162 Prof. Weber on the Application of Magnetic Induction

In each of these series it will be seen that the distance of
elongation increases, not uniformly, but according to a known
law; it approaches a certain limit, from which the damping
power, or the decrementum logarithmicum, may be easily caleu-

lated. Let a represent this limit, and log a the decrementum loga-

rithmicum, then the distance of elongation No.n=2#,=a(1—6"),
hence

hcg 2p —Zan
and
10S Dal h le
decrem. log. =log eae log PBF

According to this formula, the decrementum logarithmicum
calculated from the above observations is

log 5 =0:075, nearly ;

and the approximate limit for the’ series of observations A, F
=261:7; for the series of observations B, C, D, E=627.

The following corrections must be applied to the above values
of the distances of elongation :—

1. The correction due to the influence of the oscillation of the
needle at the commencement of the observations.

If +e be the elongation of the needle immediately preceding
the first induction stroke, then to the next following +e? must
be added, to the second +e6?, to the third +e6°. For the
above observations, where e=O, this correction is unnecessary.

2. According to the laws of catoptrics, the observed distances
of elongation are proportional to the tangents of double the
angles of deflection; they must be reduced to values propor-
tional to the sines of half the angles of elongation, 2. e. to the
deflecting forces. For this purpose the horizontal distance from
the mirror to the scale must be known; in the present case this
distance r=3685 divisions of the scale. If x be the observed
distance of an elongation, then its reduced value is

After this reduction, a determination of the tangent of the incli-
nation may be obtained from each observation in the columns
B, C, D, BE by dividing it by the mean of the observations in
the columns A, F. The following table shows the results ;—

to the determination of the Magnetic Inclination. 163

Table IV.

Zz
°
w

Cc. D. E.

° ° i “ ° a“ ° i “
67 40 30 67 45 27 67 52 37 67 40 39
66 57 26 66 57 26 67 0 9 67 5 33
67 29 37 67 30 2 67 31 28 67 27 9
67 10 31 67 11 19 67 12 53 67 15 38
67 25 59 67 26 39 67 22 57

67 14 13 67 14 138 67 15 26 67 17 33
67 20 51 67 22 48 67 22 15 67 19 11
67 15 30 67 16 2 67 17 20 67 19 26
67 18 59 67 20 58 67 20 14 67 17 44
10 67 17 55 67 18 24 67 19 35 67 21 0O
11 67 18 48 67 20 53 67 22 46 67 18 6
12 67 21 28 67 20 34 67 21 28 67 23 15
13 67 17 27 67 19 0 67 18 33 67 17 14
14 67 21 18 67 20 40 67 21 6 67 22 36
15 67 24 15 67 25 31 67 25 19 67 24 15
16 67 23 18 67 22 3 67 23 18 67 24 21

OOND Ore COLD
mr)
aj
bo
=
——
oO

The most correct value of the tangent of the inclination is
obtained from each of the series B, C, D, E by dividing its sum
by the mean of the sums of the two series A, F. For this pur-
pose the corrections already mentioned, instead of being made
on each observation, may be made on their sums; viz.—

_ 916
1. Instead of adding +e6” to each observation, bene

may be added to the sum of the sixteen observations.

eee ht 2 a aD tae 9

2. Instead of deducting 35," — trom each observation, at ee

may be deducted from the sum of all the sixteen observations,
where

— #16 — 432 — #48
= Fe ee ac Wp

16—39 Toe Tae
(16-6

p=

]—616\8
1—@

By this means the calculation will be simplified, masmuch as
the value of p is constant. If we represent the sums of the
series A, B, C, D, E, F by the same letters, then after making
this correction, we obtain

A=2873'05 B=6881°27
F=2877:15 C=6886:10
D=6889°36
E= 6887-98

In this manner the following four determinations of the in-

164 Prof. Weber on the Application of Magnetic Induction

clination I are obtained from the four series of observations

B, C, D, E:—

Tan I. ig
oe 67 19 26
oe 67 20 18
ao 67 20 53
—— 67 20 38

From the 2nd to the 12th of August observations were made
and calculated in a similar manner four times a day, at 14, 74,
134, 194, by Prof. Weber, Dr. vy. Quintus Icilius, M. Hisenlohr
and Mr. Hansen. All these gentlemen were accustomed to
observations with magnetometers, and the agreement in their
several results proved that no other practice is required beyond
that which is necessary for all other magnetometric observations.

The mean inclination deduced from all these observations
was for

Aug. 7, 1852, 67° 19! 43",

For purposes of comparison it was found necessary to apply a
small correction to this result, on account of a slight influence
exerted by the magnetometer upon the inductor; the data for
this correction were easy to determine, and after applying it, the
inclination for

Aug. 7, 1852, was 67° 18! 38".

This result is next compared with others previously made in
Gottingen by Humboldt, Forbes and Gauss. Their results were
the following :—

Dec. 1805 ....'>.0869"29° /0
Sept. 1826. . . 68 29 og, + Humboldt.

July 1; 1837. . . 67 47 6 | Forbes.

t 67 53 80
Oct.8, 1841. . . 67 42 431 4
June 21, 1843 2". 67 89 B96 78"**-

Hence, from Gauss’s observations, the mean annual decrease
of the inclination in Gottingen for the ten years between 1842
and 1852

=2/ gl,

to the determination of the Magnetic Inclination. 165

and from those of Humboldt and Forbes, this mean decrease for
the thirty-six years between 1806 and 1842

=8! 2"-3,

This result agrees with Hansteen’s investigations on the
observations made at other places in Europe, by showing that
the yearly decrease of inclination in Géttingen has become less.
If ¢ be the number of the year, and I the inclination, we may set

I=67° 23! 43!" —122"-29(¢—1850) + 1337 (¢—1850)?,

whence we obtain the following comparison of the observed with

the calculated values :—

Observed. Calculated. Difference.

Dec. 1805 6929 0 693643 —7 43
Sept. 1826 §=68 29 26 68 23 17 +6 9
July 1, 1837 67 47 O 67 52 41 —5 Al
Sed 55 67 53 30 67 52 4) +0 49
Oct. 8, 1841 67 42 43 67 42 O +0 43
June 21,1842 67 389 39 67 40 18 —0 39
Aug. 7, 1852 67 18 38 67 18 34 +0 4

According to this, the annual decrease of inclination at Got-
tingen during twenty-two or twenty-three years has diminished
one minute; in round numbers, therefore, the annual decrease—

in 1828 was 3 minutes
Hee, DSO yeas) 29 cs

-e. 1873 will be 1

Mee NBO5 I sey SSO

Hence, in all probability, the inclination in Géttingen will con-
tinue to decrease until the year 1895, when it will attain a
minimum of

66° 37! 7",
and from that time it will increase.

From this investigation, Weber concludes that the inclina-
tion instruments hitherto employed, being more portable, will
continue to be used on journeys in preference to his own; but
that in fixed observatories, where magnetometers are kept for
other purposes, it will be found advantageous to apply induc-
tion to observations on the inclination with the magnetometer, in-
asmuch as a great simplification of labour and a uniformity in the
treatment of all the three elements of the earth’s magnetism is
thereby attainable.

t Al iieOGand

XXIV. Additional Observations on the Anticlinal Line of the
London and Hampshire Basins. By P.J. Marti, Esq., F.G.S.

(Continued from vol. ii. p. 477.]

To Richard Taylor, Esq.
Dzar Sir,
VERYTHING I have ventured to publish on the geolog
of the Weald denudation having appeared in your Journal,
I am naturally desirous you should give place to some short
observations as an appendix to the series of papers you were so
kind as to print for me two years ago.

In doing this, 1 shall avoid as much as possible all discussion
of a controversial character ; and I leave the appropriation of any
discovery, or the merit of priority of observation, to those who
think such matters worth contending for.

What I have now to say would have been advanced long ago,
but I was given to understand that it was probable a meeting of
the British Association would shortly take place at Brighton.
In that hope I waited, prepared to discuss on the spot some of
the most interesting questions bearing on the subject, and on
the highly illustrative phenomena of that locality.

The workers in the field of inquiry offered by the anticlinal
line of the London and Hampshire basins, and especially of that
part of it which relates to the Weald denudation, seem pretty
well agreed as to structural arrangement. Of the agents that
have been at work in effecting the changes here exhibited, and
of their modus agendi, there is still great difference of opinion ;
and of the phenomena of Drift, now engaging so much public
attention, there exists, and perhaps will coutinue to exist for
some time to come, much contrariety of sentiment. It is to this
point I shall chiefly address myself. But as a preliminary step,
I will first briefly recapitulate the arguments, or rather enume-
rate the natural appearances in favour of the necessary relation
of the various phenomena of denudation, and with which I con-
sider every kind of drift to be most intimately connected.

Let any man look at the left-hand corner of Mr. Greenough’s
map, and consider the surface arrangement of the immense area
comprised in the elevation of this great anticlinal, and the stall
greater area of the countries which must necessarily have been
fashioned by it. No man who does not take this periscopic
view, and who cannot comprehend the phenomena here exhibited
in their ¢oéality, is qualified justly to interpret any part of them.
The key to the whole is in the conception of the contemporaneity
of upheaval and denudation ; not a piecemeal elevation of one
subordinate anticlinal and another subordinate anticlinal, the
excavation of one or of many valleys, or the accumulation of this

On the Anticlinal Line of the London and Hampshire Basins. 167

or that bed of diluvium, to be accounted for by certain local
arrangements. With this key in his mind, let the observer first
consider the phznomena of anticlinal and synclinal contortions,
the flexures and puckerings of strata struggling upwards under
the restraint of lateral pressure, or rather lateral resistance and
incumbency, such foldings and contortions most apparent in the
great argillaceous formation of the Wealden*. Then the system
of cross-fracture, first pointed out by myself and afterwards ma-
thematically accounted for by Mr. Hopkins, as the result of one
great and simultaneous act of upheaval. Thirdly, of the uni-
formity of watershed and drainage, first glanced at by Conybeare
and Phillips, and afterwards enlarged on by myself, and insisted
on as an evidence of the unity and entirety of at least the first
great upburst of the inferior beds. Fourthly, of the uniform and
irrefragable evidence of contemporaneous violent aqueous erosion
to be observed over some hundreds of square miles of country ;
the prominence of stony, and the recession of more friable and
otherwise more destructible surfaces; and especially the down-
cast and laceration of the escarpments of the outcropping second-
ary stony strata. And lastly, in the arrangement and the di-
spersion of drift along the axis of elevation, within the eroded
valleys on either side, and within the basins or great synclinal
depressions, of which the anticlinal forms the line of separation.

Without this key, and this comprehensive view of the general
arrangement of the country from the chalk of the midland coun-
ties to the chalk of the Isle of Wight and the Boulonnais, the
strictly geological features of this area remain a mystery, and all
attempts at forming a just rationale of local phenomena must
fail.

It is with this habit of viewing the south-east of England as
the scene of great disturbance, as I before said, in its ‘totality,
that the phenomena of drift can only be studied with effect. It
has been frequently asserted that the Weald has no drift. Ihave
endeavoured, in my former communications to this Journal, to
bring evidence in contradiction of this assertion. Sir Roderick
Murchison, in his disquisition on “ flint drift,” published in the
Journal of the Geological Society, soon after the promulgation of
my opinions, lays much stress on the bare state of the rocky
Hastings-sand districts; and although he finds some marks of a
local accumulation of detrital matters, and describes with great
accuracy the vicinal remarkable gravel-bed at Hever, he seems
still to think the absence of flint-drift in the centre of the Weald
strong presumptive evidence of an exceptional case. ‘There is no

* It is probably owing to the impressible nature of these beds that they

are made the nucleus of the denudation, and the axis of elevation,—the
point of least resistance, existing thereby.

168 Mr. P. J. Martin on the Anticlinal Line of

drift nor detrital matter, save modern alluvium (I must still retain
the use of that word), that is not, in antiquarian phrase, of the
date “tempore denudationis ;” and it appears to me that the
absence of great accumulations of the relics of the higher strata
on the lofty ridges and well-washed slopes of the “ Forest Ridge”
is just what might be expected. In my cursory description of the
zones of drift as they mantle round the nucleus of the Weald, I
have endeavoured to show, that exactly as we recede from the
vicinity of the higher beds, their relics become correspondingly
rare. The rounded gravel of the eocene, except here and there
a stray pebble, as a general rule, disappears on the thoroughly
denuded chalk downs. Entire flint nodules which abound there
become rare, and are succeeded by angular and fragmentary in
the greensand country. Here, in my subcretaceous zone, we
find large accumulations of flint, mixed up with fragmentary
chert and sandstone, with now and then a chalk pebble or an
eocene pebble, all entangled in deep drifts of disintegrated
sand-rock. Descending the escarpment of the lower greensand,
we find in the place of flint and gravel, a thin sprinkling of the
durable ironstone, and fragments of the chert, of the stratum
next above, with concretional iron-rag or bog-iron of the Weald
clay country, with here and there a small ¢rainée (as Sir Roderick
says) of angular and fuscous flints dyed by the iron imbibed
from the soil. Of these é¢rainées the bed at Hever approaches
hard on the Hastings-sand country and the centre of the de-
nudation; and I had the pleasure of showing another to Sir
Roderick at Shipley, four miles south of Horsham. And since
that time I have discovered another at Slinfold, three miles west
of that town, in the remarkable longitudinal valley which skirts,
if it does not lie in, the exact axis of the great anticlinal of the
Forest Ridge. Here, near the Roman gate on the road between
Stroud and Rudgwick, a bed of diluvium is to be found, with
chert and ironstone, and a fair sprinkling of brown flints.
Agreeably to the foregoimg rule of the gradual disappearance
of the relics of the superior strata, the elevated rocks of Tun-
bridge Wells and the rest of the central districts, as before said,
exhibit only here and there, scattered over the surface or turned
up by the plough, water-worn fragments of sandstone impressed
with Cyprides, fragments of the marble of the Weald clay, and
finally the detritus of the Hastings sands and clays themselves.
To satisfy himself that these are accumulated with all the cha-
racters of diluvium, let the observer take the Ordnance Map, mark
the deep longitudinal valleys of the Rother and its tributaries,
examine particularly the eastern slopes and spurs of the beautiful
and picturesque eminences that there abound, the railway cut-
tings that traverse them, and the more fertile hop-gardens. of

the London and Hampshire Basins. 169

that country, and he will be satisfied that drift of the real diluvial
character is not wanting to this, the barest part of the Wealden.

The presence of these detrital masses, and the absence of the
remains of the higher strata on these clevated ridges, ought to
be received as corroborative proof of the community of character,
and the one and indivisible nature of these drifts of denudation.
It is to be remembered that thousands of feet of greensand,
chalk, and tertiary beds have been cast off from these elevated
ridges, and it is only wonderful that any fragments of their ruins
are still to be found in their vicinity. I venture to reassert,
then, my conviction, that a large and comprehensive view of the
arrangement of drift in concentric zones is agreeable to nature
and fact, from the patches of eocene to be found on the Hamp-
shire chalk down to the lowest beds of Hastings and Winchelsea ;
with such exceptions only as tend to confirm the rule.

Of the absence of the usual mammal bones in the Wealden
zone of drift, I infer but little, but that little is of the affirmative
character. All the upper beds being removed, the greater the
chance that with them would be removed the remains of the
animals which died a natural death on the original surface of the
country, or of the surrounding countries, or which perished in
the catastrophe we contemplate.

Much remains to be said in reference to the local arrange-
ments of drift ; the involved and tumultuous admixture of sands
and clays, the manufacture of brick-earths and loams on the
spot on which they are found, and the quasi stratified beds*
of sand and gravel, and of the boulder clays which have been
swept into the great synclinals on either side; but it is most
convenient to confine our attention at present to the central
and most simple, as well as the most illustrative part of our
subject. Of the fossil or diluvial wood, and trunks of: trees
in situ amongst the gravel beds of Surrey, below the chalk,
spoken of by Sir R. Murchison (on the authority of Mr. Austen)
in attestation of “atrue terrestrial surface” after the commence-
ment of the denuding zra, I cannot say that they do not exist ;
but I have looked into many gravel-pits there, and in the cor-
responding districts under the South Downs, and I have never
seen any wood in drift which was not of the most modern de-

* T believe that many of these diluvial beds contain organic remains
derived from the latest tertiaries, broken up tempore denudationis, Such
remains are supposed to be of pleiocene date, as assimilating to, or even
identical with, existing species.

Specimens of this sort were shown to me by Mr. Mackie from the drift at
Folkstone, and it was from some such semi-stratified deposit near Bognor,
I suspect, that Lady Murchison took the shells spoken of by Sir Roderick.
(Journ. Geol. Soc. vol. vii. p. 371.)

Phil. Mag. 8. 4, Vol. 7. No. 44. March 1854. N

170 On the Anticlinal Line of the London and Hampshire Basins.

scription, such as would till lately have been called mere “ allu-
vium.” Carbonized trunks of trees are to be found in all the
bogs and swamps, especially in the alluvium of the river-courses,
as noticed in my early memoir on Western Sussex. On the
banks of the Mole and the Wey, and of their affluents, I doubt
not such prostrate and uprooted trees may be detected ;—they
are post-diluvial.

It remains that I should say something more of the well-
known raised beach at Brighton, and of the parallel case at
Sangatte, described by Mr. Prestwich. I have treated these,
and I still consider them as belonging to the eocene era, brought
into view at these places by sea-section. I cannot but entertain
the same opinion till similar appearances are pointed out at the
same level below the chalk, and within the areas of denudation on
either side of the channel. At the same time I am not prepared
to insist that there were not intermissions in the operation of
denuding forces; and that during some such lull these beaches
may have been formed. I have not said, as Sir Roderick seems
to think, that the denudation of the Weald was the work of one
transient great act of elevation and flood; but of this I am quite
assured, that the first great upburst gave the character of these
forces, as evinced by the arrangements of anticlinals, the fissures
which determined the disposition of valleys, the watershed and
drainage. I believe also there is evidence to prove a long-con-
tinued season of oscillation, and perhaps of unremitting violent
aqueous erosion contemporaneous therewith. This was succeeded
by a sudden, and not a gradual retirement of these angry waters,
and the season of tranquillity which has continued up to this
time. I hope to be pardoned for insisting thus strongly on the
unity of action, and the grandeur of proportions of these great
changes, when it is considered that Buckland and some other of
our best authorities have held similar sentiments; and that in
working out the details of these and contemporaneous operations
in their entirety, we bring forward the best tests of the bold
generalizations of Elie de Beaumont.

The season seems to be at hand when we skall find less diffi-
culty in readmitting the agency of catastrophic action into the
elements of change. The able expositor of the geological ph-
nomena of Patagonia has said, that any sudden operation which
would account for the spread of the drift materials of that part
of South America would disturb the relations of half a hemi-
sphere. And why not? Are we not on the eve of believing that
at no very remote period we were without any Gulf-stream, and
that its establishment (and how could it be otherwise than sud-
denly established?) put an end to the “glacial, period,” and gave
a temperate climate to western Europe? Are the oser beds of

On the Optical Properties of Chrysammate of Potash. 171

Sweden accounted for on any known principles of slow accu-
mulation ? and can the drift which is so extensively spread over
central and northern Europe be considered solely as the drop-
pings of icebergs? “ Verily,” as it has been wittily said, “ palaces
are not built with a teaspoon, nor hospitals endowed with a pinch
of snuff ! ”

Pulborough, Feb. 13, 1854.

XXV. On the Date of the Discovery of the Optical Properties of
Chrysammateof Potash. In a Letter from Sir Davin BREWSTER
to Professor StoKxs*.

My pear Mr. Stoxzs,
See OuESSOR FISCHER has put into my hands this after-
noon a copy of your interesting paper “On the Metallic
Reflexion exhibited by certain Non-metallic Bodies,” in which I
observe the following passage :—

“Tn mentioning my own observations on safflower-red, Hera-
pathite, &e., nothing is further from my wish than to neglect the
priority of those to whom priority belongs. M. Haidinger had
several years before discovered the phenomenon of the reflexion
of differently coloured oppositely polarized pencils, which Sir
David Brewster shortly afterwards, and independently, discovered
in the case of chrysammate of potash.”

My experiments were made in the end of 1842 and the begin-
ning of 1843, with crystals of chrysammate of potash sent to me
on the 2nd of December 1842 by Mr. Schunck, along with
other seven new substances, aloetinate of potash, &c. Mr.Schunck
directed my attention to the green metallic lustre of the salt, and
to the redness of its solution, which I instantly examined.

I found it very difficult to work with such imperfect crystals,
and I delayed publishing the imperfect results which I had
obtained in the expectation of some time or other getting better
crystals.

On the 1st of March, 1846, I read to the Literary and Philo-
sophical Society of St. Andrew’s all the observations inserted in
my journal of experiments; and not being able to attend the
Southampton meeting of the British Association, I made an
abstract of what I had read at St. Andrew’s, which is the paper
you refer to as published in the Report of the Association.

Tn 1842 and 1843 I examined also various other substances,
but I have not published any of the results which I obtained.

I enclose Mr. Schunck’s letter, which will show you that I

* Communicated by Professor Stokes.
N 2

172 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

had requested him in 1842 to send me for examination some of
those remarkable substances.
Believe me to be,
Ever most truly yours,

St. Leonard’s College, St. Andrew’s, D. Brewster.
January 20, 1854. ,

Note.—In using the expression “discovered” I followed the
common practice of making a discovery date from its publication ;
it would have been more exact to have said “announced the
discovery of.”

Sir David Brewster’s announcement of the discovery was
referred by me to the date of the meeting of the British Associa-
tion at Southampton, because I was not aware of the previous
communication made to the Literary and Philosophical Society
of St. Andrew’s, nor could I well have been. I shall therefore,
I hope, be held excused for not having alluded to the latter.

G. G. Sroxzs.

XXVI. On the Mechanical Action of Heat. By Wr1114M JouHN
Macaquorn Rankine, C.H., F.R.SS. Lond. and Edinb. &c.

[Continued from p. 122.]

Section IV. Of the Mechanical Action of Steam, treated as a
Perfect Gas, and the Power of the Steam-engqine.

(21.) ie the present limited state of our experimental know-

- ledge of the density of steam at pressures differmg much
from that of the atmosphere, it is desirable to ascertain whether any
material error is likely to arise from treating it as a perfect gas.
For this purpose the ratio of the volume of steam at 100° Centi-
grade, under the pressure of one atmosphere, to that of the
water which produces it at 4°:1 Centigrade, as calculated theo-
retically on the supposition of steam being a perfect gas, is to
be compared with the actual ratio*.

The weight of one volume of water at 4°-1 Centigrade being
taken as unity, that of half a volume of oxygen at 0° Centigrade,
under the pressure of one atmosphere, according to the experi-
ments of M. Regnault, is

0-000714900
That of one volume of hydrogen . 0:000089578 . (836)
The sum being. . .. . . . 0:000804478
3746

= 1:364166

The reciprocalof this sum being multiplied by 7A

* The actual ratio is only known approximately.

Mr, W. J. M. Rankine on the Mechanical Action of Heat. 173

(the ratio of dilatation of a perfect gas from 0° to 100° Centi-
grade), the result gives for the volume of steam of saturation at
100° Centigrade as compared with that of water at

4Oshoy eleth tour or 1697S, OO ee. (37)
and for its density } 0:00058972.

The agreement of those results with the known volume and
density of steam is sufficiently close to show, that at pressures
less than one atmosphere it may be regarded as a gas sensibly
perfect ; from which it may be concluded, that in the absence of
more precise data, the errors arising from treating it as a perfect
gas at such higher pressures as occur in practice, will not be of
much importance*.

Representing, then, by v the volume of unity of weight of
water at 4°-1 Centigrade, that of unity of weight of steam at
any pressure and temperature will be given by the formula

ee LS EA cia a hin Pe re
Ces

@ representing the number of units of weight per unit of area

in the pressure of one atmosphere, and (r) the absolute tempe-

yature at which the pressure of saturation is one atmosphere ;

being for the Centigrade scale 374°6, and for Fahrenheit’s

scale 674°:28.

The mechanical action of unity of weight of steam at the
temperature 7 and pressure P, during its entrance into a cylinder,
before it is permitted to expand, is represented by the product
of its pressure and volume, or by

Bape OB a erent neato aul
(7)

— represents a certain depth of fall per

(38)

(39)

The coefficient
degree 4 absolute temperature, and is the same with the coeffi-
CaM
of the factors,
v=0°016 cubic foot per pound avoirdupois,
@=2117 pounds avoirdupois per square foot,
we find this coefficient to be
153:35 feet = 46°74 metres per Centigrade ee (40)
85:19 feet per degree of Fahrenheit ;
this determination may be considered correct to about zy'pq part.

cient

already referred to. By taking the following values

* These remarks are applicable to the calculation of the power of steam-
engines only,

174 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

When French measures are used in the calculation, the following
is the result :—
v=1 cubie centimetre per gramme,
@=1033'3 grammes per square centimetre,
1

GM 46°78 metres per Centigrade degree,
=153°48 feet oon See

or 85:27 feet per degree of Fahrenheit.

The difference, which is of no practical importance in calcu-
lating the power of the steam-engine, arises in the estimation of
the density of liquid water.

(22.) Unit of weight of steam at saturation, of the elasticity
P, and volume V, corresponding to the absolute temperature 7,
being cut off from external sources of heat, it is now to be inves-
tigated what amount of power it will produce in expanding to a
lower pressure P, and temperature 75.

It has already been shown at the end of the second section,
that if vapour at saturation is allowed to expand, it requires a
supply of heat from without to maintain it at the temperature
of saturation, otherwise a portion of it must be liquefied to sup-
ply the heat required to expand the rest. Hence, when unity of
weight of steam at saturation, at the pressure P, and volume V,,
expands to a lower pressure P, being cut off from external sources
of heat, it will not occupy the entire volume V corresponding to
that pressure, according to equation (88), but a less volume

S=mV,
where m represents the weight of water remaining in the gaseous
state, the portion 1—m having been liquefied during the expan-
sion of the remainder. The expansive action of the steam will
therefore be represented by

SJ as.P (42
918 Peery sinha

The law of variation of the fraction m flows from the following
considerations :—

Let dm represent the indefinitely small variation of m corre-
sponding to the indefinitely small change of temperature 5r ;
L, the latent heat of evaporation of unity of weight; Kg, as in
equation (30), the specific heat of vapour at saturation, which is
a negative coefficient varying with the temperature; then we
must have

(41)

—Léim=mKsg 67, or ee =— et ot,

in order that the heat produced by the liquefaction of dm may be

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 175,

equal to the heat required to expand m, Hence making, accord-
ing to equation (30),

Ks brah(Sr +N sv);

and T 1
oT= — vy Vv Bi 2, 9
SB
T a
we obtain
bm _ a 1 \e :
EL OS a
— aoe
cee
and denoting the coefficient of Vv by —y,
dlogm _ dlog8 _j_,, 7
dlog V dlogV
and because
dlogV _
dlog P It @ Qn! ?
te T
dlogm _ (i- 1 (44)
dlog P FETE BI | 2h/' ) |
—+ 3
iene
dlogS _ ( 1 <~y
ee Daehed Cid ae: OO" tee
Pamiet ol i

As the mean temperature of the liquid thus produced more or
less exceeds that of the remaining vapour, a small fraction of it
will be reconverted into vapour if the expansion is carried on
slowly enough ; but its amount is so small, that to take it into
account would needlessly complicate the calculation, without
making it to any material extent more accurate.

(23.) The extreme complexity of the exponent a, considered
as a function of the pressure P, would render a general formula

for the expansive action If PdS yery cumbrous in its application.

For practical purposes, it 1s sufficient to consider the-exponeut o
as constant during the expansion which takes place in any given
engine, assigning it an average value suitable to the part of the
scale of pressures in which the expansion takes place. For
engines in which the steam is introduced at pressures not exceed-
ing four atmospheres, I conceive that it will be sufficiently accu~

rate to make 6
o= 7

176 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

while for engines in which the initial pressure lies between four
and eight atmospheres, the suitable value is

_5
o— ra

The utmost error which can arise from using these exponents
is about ;3, of the whole power of the engine, and that only in

extreme cases.
a, ai
es ce

Making, therefore,
we obtain for the value of the expansive action of unity of weight
of steam,

At P=P,V, 7 s(1-(#) Ss e)
=P,V,7—- (1p ry,

s being used to denote = v, , or the ratio of the volumes occupied

phi (4D)

by steam at the end fie at the beginning of the expansion
respectively.
A table to facilitate the computation is given in the sequel.
The gross mechanical action of unity of weight of steam on
one side of the piston is found by adding to the above quantity
the action of the steam before it begins to expand, or P,V,, and
is therefore

1 Ct GAN:
P,V(;— <= jos v Rae!)
the values of the coefficients and exponent being
1 o ie 1
lo l—o g
for initial pressures between
1 and 4 atmospheres . . 7 6 _ -
4.and 8 atmospheres . . 6 5 i

(24.) The following deductions have to be made from the gross
action, in order to obtain the action effective in overcoming
resistance.

First. For loss of power owimg to a portion of the steam being
employed in filling steam-passages, and the space called the
clearance of the cylinder at one end. Let the bulk of steam so
employed be the fraction cS, of the space filled by steam at the
end of the expansion ; then ‘the loss of power from this cause is

P eS, Ses V0

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 177

Secondly. For the pressure on the opposite side of the piston,
of the steam which escapes into the condenser, or into the atmo-
sphere, as the case may be. Let P, be the pressure of this
steam; the deduction to be made for its action 1s

P.8,(1—c) =P5V,(1—c)s.

These deductions having been made, there is obtained for the
effect of unity of weight of water evaporated,

1 oc i
v, {p,(- = fe es) ~P(1—o)s } _ (47)
(25.) The effect of the engine in unity of time is found by
multiplying the above quantity by the number of units of weight
of water evaporated in unity of time.
_ If this number be denoted by W,

4 WS,(l—c)=WV,(1—c)s=Au. . . . (48)

will represent the cubical space traversed by the piston in unity
of time, A denoting the area of the piston, and wu its mean
velocity.

Now let the whole resistance to be overcome by the engine be
reduced by the principles of statics to a certain equivalent pres-
sure per unit of area of piston, and let this pressure be denoted

by R. Then

RAu=RWV,(l—c)s. . . «+ (49)

expresses the effect of the engine in terms of the gross resistance.

We have now the means of calculating the circumstances
attending the working of a steam-engine according to the prin-
ciple of the conservation of vis viva, or, in other words, of the
equality of power and effect, which regulates the action of all
machines that move with a uniform or periodical velocity.

This principle was first applied to the steam-engine bythe Count
de Pambour ; and accordingly, the formule which I am about to
give only differ from those of his work in the expressions for the
maximum pressure at a given temperature, and for the expansive
action of the steam, which are results peculiar to the theory of
this essay.

In the first place, the effect, as expressed in terms of the pres-
sure, is to be equated to the effect as expressed in terms of the
resistance, as follows :—

1 o age
RAu=RWV,(1 —s=WV (Ta —jfs —cs)
(50)
— P,(1—c) a .

This is the fundamental equation of the action of the steam-

178 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

engine, and corresponds with equation A of M. de Pambour’s
theory.

26) Dividing both sides of equation (50) by the space tra-
versed by the piston in unity of time WV,(1—c)s, and trans-
ferring the pressure of the waste steam, Pg, to the first side, we
obtain this equation :—

1 o 1-2
jG an ae

—
R+P,=P, (I—o)s )

which gives the means of determining the pressure P, at which
the steam must enter the cylinder, in order to overcome a given
resistance and counter-pressure with a given expansion ; or sup-
posing the expansion s to be variable at pleasure, and the initial
pressure P, fixed, the equation gives the means of finding, by
approximation, the expansion best adapted to overcome a given
resistance and counter-pressure.

The next step is to determine, from equations (XV.) of the
Introduction and (38) of this section, the volume V, of unity of
weight of steam corresponding to the maximum pressure P,.
Then equation (48) gives the space traversed by the piston in
unity of time, which, being multiplied by the resistance R per
unit of area of piston, gives the gross effect. of the engine.

(27.) If, on the other hand, the space traversed by the piston
in unity of time is fixed, equation (48) gives the means of deter-
mining, from the evaporating power of the boiler W, either the
volume V, of unity of weight of steam required to work the
engine at the given velocity with a given expansion, or the ex-
pansion s proper to enable steam of a given initial density to
work the engine at the given velocity. The initial pressure P,
being then determined from the volume V,, the resistance which
the engine is capable of overcoming with the given velocity is to
be calculated by means of equation (51).

(28.) This calculation involves the determination of the pres-
sure P, from the volume V, of unity of weight of steam at satu-
ration, which can only be done by approximation. The followimg
formula will be found useful for this purpose :-—

Vo\32
P=0(5 i an a ee

where @ represents the pressure of one atmosphere, V, the
volume of steam of saturation at that pressure (being 1696 times
the volume of water at 4°-1 Cent., or 27°166 cubic feet per pound.
avoirdupois), and V, the volume of steam of saturation at the
pressure P,, This formula is only applicable between the pres-
sures of one and eight atmospheres; that is to say, when the
volume of steam is not greater than 27 cubic feet per pound,

(51)

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 179

nor less than 4, and the temperature not lower than 100° Cen-
tigrade, nor higher than 171° Centigrade (which correspond to
212° and 340° Fahrenheit).

The most convenient and expeditious mode, however, of com-
puting the pressure from the volume, or vice versd, is by inter-
polation from the table given in the sequel.

(29.) The resistance denoted by R may be divided into two
parts; that which arises from the useful work performed, and
that which is independent of it, being, in fact, the resistance of
the engine when unloaded. Now it is evident that the maximum
useful effect of the steam has been attained, as soon as it has
expanded to a pressure which is in equilibrio with the pressure
of the waste steam added to the resistance of the engine when
unloaded ; for any further expansion, though increasing the total
effect, diminishes the useful effect. Therefore if we make

R=R/+ hs
R’ being the resistance arising from the useful work, and f the
resistance of the engine when unloaded, both expressed in the
form of pressure on the piston, the expansion corresponding to
the maximum of useful effect will take place when

Po=Ps+f
the corresponding ratio of expansion being Ln IDG)
(5)
s= .
P3+f,

The maximum useful effect with a given pressure on the
safety-valve has been so fully discussed by M. de Pambour, that
it is unnecessary to do more than to state that it takes place
when the initial pressure in the cylinder is equal to that at the
safety-valve ; that is to say, when it and the useful resistance
are the greatest that the safety-valve will permit.

(30.) Annexed is a table of the values of some of the quan-
tities which enter into the preceding equations in the notation
of the Count de Pambour’s works.

Expression in the Equivalent expression in
notation of this paper. M. de Pambour’s notation,
Lk 58 ak RA nae (L+o)r+f
Au Pt gwen tia av
W S x weight of one cubic
ed he foot of water.
P; “id
l+e
+e
c
c .

180 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

(31.) As an illustration, I shall calculate the maximum useful
effect of one pound, and of one cubic foot of water, in a Cornish
double acting engine, in the circumstances taken by M. de Pam-
bour as an example for that kind of engine; that is to say,—

Clearance one-twentieth of the stroke, or c=,
21’ Per square ft.

Resistance not depending on the useful load, f= 72\bs.
Pressure of condensation, . . . . . . P3=576\bs.
Consequently to give the maximum useful effect,

Po=P3+7 = 648 lbs.

Total pressure of the steam when first admitted, P;=7200 lbs.
Volume of Lb. of steam V,=8'7825 cubic feet.
Therefore P, V, =63234 lbs. raised one foot.

P, _ 7200
P, 648° and consequently
Expansion toproducethemaximum useful effects = ( 5 ys =7°877.
Space traversed by the piston during the action of one pound of
steam, =V,(1—c)s=65°886 cubic feet.
Gross effect of one pound of steam, in pounds raised one foot high,
'
=P,V,(7—65"6 — <) A eh. ya enOA
Deduct for resistance of engine when unloaded = pha
fV,\-—e)s . . . a

Effect of one pound of steam in overcoming re-

sistance depending on useful load ; aft abl
This being multiplied by 623, gives for the effect

of one cubic foot of water evaporated, in pounds 6,703,750

PREM ONE TOObS sync iors At is. a

It is here necessary to observe, that M. de Pambour distin-
euishes the useful resistance into two parts, the resistance of the
useful load independently of the engine, and the increase in the
resistance of the engine, arising from the former resistance, and
found by multiplying it by a constant fraction, which he calls 6.
In calculating the net useful effect, he takes into account the
former portion of the resistance only ; consequently,

Net useful effect as defined by M. de Pambour
_ Gross effect —fV,(1—c)s
% 1+6

The value of 6, for double acting steam-engines generally, is
considered by M. de Pambour to be 7; consequently, to reduce

(54)

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 181

the effect of one cubic foot of water as calculated above to that
which corresponds with his definition, we must deduct 3, which
leaves

5,865,781 lbs. raised one foot.

M. de Pambour’s own calculation gives
6,277,560,
being too large by about one-fifteenth.

Explanation of Tables to be used in calculating the Pressure,
Volume, and Mechanical Action of Steam, treated as a Perfect
Gas.

(32.) The object of the first of the annexed tables is to facili-
tate the calculation of the volume of steam of saturation at a
given pressure, of the pressure of steam of saturation at a given
volume, and of its mechanical action at full pressure.

The pressures are expressed in pounds avoirdupois per square
foot, and the volumes by the number of cubic feet occupied by
one pound avoirdupois of steam, when considered as a perfect
gas; those denominations being the most convenient for mecha-
nical calculations in this country.

The columns to be used in determining the pressure from the
volume, and vice versd, are the third, fourth, sixth and seventh.

The third column contains the common logarithms of the
pressures of steam of saturation for every fifth degree of the
Centigrade thermometer from —30° to + 260°; that is to say,
for every ninth degree of Fahrenheit’s thermometer from —22°
to + 500°.

The fourth column gives the differences of the successive terms
of the third column.

The sixth column contains the common logarithms of the
volume of one pound of steam of saturation corresponding to the
same temperatures.

The seventh column contains the differences of the successive
terms of the sixth column, which are negative ; for the volumes
diminish as the pressures increase.

By the ordinary method of taking proportional parts of the
differences, the logarithms of the volumes corresponding to in-
termediate pressures, or the logarithms of the pressures corre-
sponding to intermediate volumes, can be calculated with great
precision. Thus, let X+A be the logarithm of a pressure not
found in the table, X being the next less logarithm which is
found in the table; let Y be the logarithm of the volume cor-
responding to X, and Y—& the logarithm of the volume corre-
sponding to X+/; let H be the difference between X and the
next greater logarithm in the table, as given in the fourth column,

182 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

and K the corresponding difference in the seventh column ; then
by the proportion
ic I

either Y—/ may be found from ore or X+A/ from Y—&.

In the fifth and eighth columns respectively are given the
actual pressures and volumes corresponding to the logarithms m
the third and sixth columns, to five places of figures.

In the ninth column are given the values of the quantity
denoted by P,V, in the for mule, which represents the mechanical
action of unity of weight of steam at full pressure, or before it
has begun to expand, in raising an equal weight. Those values
are expressed i in feet, being the products of the pressures in the
fifth column by the volumes in the eighth, and have been found
by multiplying the absolute temperature in Centigrade degrees
by 153°48 feet. Intermediate terms in this column, for a given
pressure or a given volume, may be approximated to by the
method of differences, the constant difference for 5° Centigrade
being 767-4 feet ; but it is more accurate to calculate them by
taking the product of the pressure and volume.

When the pressure is given in other denominations, the fol-
lowing logarithms are to he added to its logarithm, in order to
reduce it to pounds avoirdupois per square foot :—

For millimetres of mercury . . . . . . O-44477
For inches of mercury . . we Cat Racha Aen
For atmospheres of 760 millimetres... 3°32559
For atmospheres of 30 inches .« . «fs. (832672

- For kilogrammes on the square centimetre . . 3°311386
For kilogrammes on the circular centimetre . 3°41627
For kilogrammes on the square metre . . . 1°31136 ©
For pounds ayoirdupois on the square inch. = 2°15836
For pounds avoirdupois on the circularinch . 2°26327

To reduce the logarithm of the number of cubic metres occu-
pied by one kilogramme to that of the number of cubic feet
occupied by one pound avoirdupois, add 1+20463.

The logarithms are given to five places of decimals only, as a
greater degree of precision is not attainable in calculations of
this kind.

(33.) The second table is for the purpose of calculating the
_ mechanical action of steam in expansive engines.

The first column contains values of the fraction of the entire
capacity of the cylinder which is filled with steam before the

é ; ‘fel
expansion commences (being the quantity ; of the formule), for

every hundredth part, from 1°00, or the whole cylinder, down
to 0°10, or one-tenth.

Mr. W. J. M. Rankine on the Mechanical Actionof Heat. 183

If / be the entire length of stroke, /' the portion performed at
full pressure, and c the fraction of the entire capacity of the
cylinder allowed for clearance, then

: c
hs ba i
ire and sll) 7 he

The entire capacity of the cylinder is to be understood to m-
clude clearance at one end only.

The second column gives the reciprocals of the quantities in
the first, or the values of the ratio of expansion s.

The third and fourth columns, headed Z, give the values of

1

i
at * of article 23, which represents

the ratio of the entire gross action of the steam to its action at .
full pressure, without allowing for clearance. The third column
is to be used for initial pressures of from one to four atmo-
spheres ; and the fourth for initial pressures of from four to
eight atmospheres.

The deduction to be made from the quantity Z for clearance
is cs, or the product of the fraction of the cylinder allowed for
clearance by the ratio of expansion. Hence, to calculate from
the tables the net mechanical action of unity of weight of steam,
allowing for the counter-pressure of the waste steam P,, as well
as for clearance, we have the formula

P,V,(Z—ces) —P;V,(1—c)s,
being equivalent to the formula (47) of this paper.

the quantity = _

Note.—The third, fourth, and fifth columns of the first of the
following tables may be relied on as showing the pressures of
steam and their logarithms with a degree of accuracy limited
only by that of M. Regnault’s experiments, from which the
formula used in computing them was deduced.

On the other hand, the sixth, seventh, eighth, and ninth
columns of the first table, relating to the volume of one pound
of steam and its action at full pressure, are to be considered as
merely sufficiently accurate, in the absence of more precise data,
for the calculation of the power of steam-engines to an approxi-
mation near enough for practical purposes, and are not to be
relied upon, in theoretical computations, above the temperature
of about 60° Centigrade, or 140° Fahrenheit.

Taser I.—Pressure and Volume of Steam, supposing it to be a
perfect gas, and its Action at Full Pressure.

(1.)

Tempe-| Tempe-

rature
Fahren-
heit.

—23
1g
al
45
4
23
32

rature
Centi-
grade.

(3.)

) | 1:99278

019841
0:39443
058153
0°76017
0:93102
1:09450
125111
1:40123
154527
168363
1:81647
1:94427
2:06724
218566
2-29976
2-40978
251592
2°61839
2°71736
281302
2°90552
2°99505
308163
3°16551
3°24680
8°32559
3°40199
347614
354810
3°61798
3°68586
375183
3°81597
3°878385
3935904
399811
4:05562
411163
416619
421935
4:27122
4:32178
4-37110
441922
446618
| 4°51204
455682
4°60057
464331
4-68507
4°72592
4°76586
4:80492
4°84311
488051
491711
495293
4-98800

4.)

Logarithm
of pressure] Differ-
in Ibs. per| ences.
square foot.

———

0-20563
019602
0-18710
017864
0-17085
0:16348
0°15661
0-15012
014404
0-13836
0-13284
0-12780
0:12297
0:11842
0°11410
0-11002
0-10614
0°10247
0-09897
0:09566
0:09250
008953
0:08658
0-08388
0-08129
0:07879
007640
0-07415
0:07196
0-06988
0:06788
0-06597
0-06414
0-06238
0:06069
005907
0:05751
005601
0:05456
005319
0:05184
0:05056
0-04932
0-04812
004696
004586
0:04478)
0:04375
004274
004176
0-04085
0:03994)
003906)
0:03819
003740
003660
0:03582
003507

(5.)

Pressure in
Ibs. per square
foot.

09835
15791
24799
3°8153
5°7567
85314
12:431
17:828
25-190
35:097
48-265
65°5355
87-957
116°75
153-34
199-42
256-91
325-04
41533
52163
650°16
804-49
988-67
1206°8
1463-9
1765-2
2116°4
2525°4
2993'2
5932'6
41493
48513
5647-2
6545°9
7557-0
8690°4
9956°6
11366
12931
14662
16572
18673
20979
25502
26256
29254
32512
36043
39863
43986
48425
53201
58326
63815
69680
75947
82625
89728
97275

(6.)'
Logarithm
of volume

of one lb. of
steam in
cubic feet.

458173
438489
419748
401883
384847
3°68575
353025
338148
3-23906
310258
297165
284612
272551
260961
2-49815
2-39090
228762
2-18812
2-09219
1-99966
191035
1-82410
1-74074
1-66024
15823

150698
1-43403
1:36339
1-29492
1:22857
1-16423
1-10182
1-04125
0:98244
092533
086985
081592
076350
0:71251
0-66292
061464
056766
052190
0:47733
043391
039160
035034
031011
027087
023258
0:19524
015875
0:12314
008836
005441
002121
1-98877
195707
1:92608

(7)

Differ-
ences.

(8.)

Volume of one

lb. of steam in

cubic feet.

o-196s4eol7t
24260
0°18741
: 15757
017865
F 10443
0°17036 :
f 7054:6
0-16272 ;
4850°1
0:15550| 3°
; 3390-4
0°14877| oe
2407-0
014242) ~3
; 1734-0
0-13648
: 1266-4
0-13093 '
ToRze| 93681
0 12553 4
ae 701-65
0-12061
‘ 531-51
011590
scan A0cot
011146
; 314-88
010725
’ 245-98
010328
193-92
009950 fs
154-21
0-09598 d
naos,| 123°65
009253 ?
; 99-922
008931
$1349
0-08625 ‘5
66-696
0-08336 ;
eee 55-048
0-08050 ‘
45°734
0-07788 ee
38-226
007538
ae 32-135
0:07295
: 27-166
007064
23-088
006847 :
; 19-721
0-06635 Las
Lye 16-927
0-06434
14-596
0-06241
12-642
0-06057
10-996
0-05881 4
99-6037
0-05711 j
$-4204
0-05548
; 7-4105
0-05393 e
Z 65452
0-05242
- 58010
0-05099 be)
51583
0-04959
46017
0-04828 ;
41176
004698
36954
0-04576 ee
3 3-3258
0:04457 30014
0:04342 =)
27159
0-04231
2-4638
0-04126| 6.
22405
0-04023| J.
2-0423
0-08924 }
: 1:8663
0-03829 ;
e 1:7084
003734 ;
a 15676
0-03649 ;
ae 1-4413
0-03561 :
oe 1:3278
0:08478 1:2256
0:08395 1-133
003320 Aor
0-03244 ;
0:97447
0-03170 ‘
0-03099; 0°90588
084349

Action of a given
weight ofsteamin|
raising an equa
weight in feet, at} |
full pressure
=P Vi.

(9.)

|

37541
3839
39076
39843
406\1
Ale)
4214!
42913
43680
44448
45215
45983
46750
47517
48285
49052
49820
50587
51354
52122
52889
53657
54424
55191
55959
56726
57494
58261
59028
59796
60563
61331
62098
62865
63653
64400
65168
65935
66702
67470
68237
69005
69772
70539
71307
72074
72842
73609
74376
79144
75911
76679
77446
78213
78981
79748
80516
81283
82050

Mr. W. J. M. Rankine on the Mechanical Action of Heat.

Tas ie I].—Expansive Action of Steam.

185

(1.) (2.) (3.) (4.) (1.) (2.) (3.) (4.)
Fraction of Coefficient of gross || Fraction of Coefficient of gross
fea. oth Ratio of plea eens sled with Ratio of seen aoe
steam at |expansion| Initial | Initial |!"steam at | expansion | Initial | Initial
full pres- a PTessUre,, | sDECSSUre ll eallipres= =5 pressure | pressure

sure one to four| four to Sth one to four| four to

1 atmo- jeight atmo- 1 atmo- jeight atmo-
a spheres. | spheres. = spheres. spheres.
1:00 1:000 1-000 1-000 “54 1:852 1-586 1-580

99 1:010 1-010 1-010 53 1-887 1-602 1596

98 1:020 1-020 1-020 52 1-923 1-620 1-613

“Yi 1-031 1:030 1-030 3] 1-961 16357 1:630

“96 1-042 1:041 1-041 50 2-000 1-655 1-647

“95 1:053 1-051 1-051 49 2-041 1-673 1-665

94 1-064 1-062 1-062 48 2:083 1-691 1-683

93 1-075 1-072 1-072 47 27128 1-709 1-701

92 1-087 1:083 1-083 46 2174 1-728 1719

“91 1-099 1:094 1-093 45 2:222 1-748 1:738

90 1111 1-104 1104 *A4 2-273 1-767 1-757

“89 1-124 1115 1115 i) 2°326 1-787 1777

88 1136 1-126 1126 “42 2-381 1-808 1-796

87 1-149 1-138 1137 “Al 2-439 1829 1817

“86 1-163 1/149 1149 40 2500 1-850 1:837

“85 1-176 1-160 1-160 39 2564 1-871 1°858

“84 1:190 1-172 1371 38 2:632 1894 1880

83 1-205 1-183 1183 ‘87 2°703 1-916 1-902

*82 1-220 1:195 1-195 36 2-778 1-939 1-924

“81 1-235 1:207 1-206 30 2°857 1-963 1:947

80 1-250 1-219 1:218 34 2-941 1-987 1:970

79 1-266 1-231 1-230 33 3°030 2:012 1-994

78 1-282 1-243 1-242 32 37125 2-038 2-019

Sis 1-299 1-256 1:255 “ol 3°225 2-064 2-044

76 1316 1:268 1:267 “30 3°333 2-091 2:070

75 1333 1:281 1:280 “29 3-448 2-119 2-097

“7A 1-351 1:294 1/292 28 3571 2147 27124

73 1-370 1:307 1:305 27 3°704 2-176 2°152

72 1389 1:320 1318 26 3°846 2:207 27181

71 1-408 1333 1331 “25 4-000 2-238 2-211

70 1-429 1°346 1-344 24 4-167 2:270 2-242

69 1-449 1360 1:358 23 4:348 2°304 2:273

“68 1-471 1-374 1371 22 4:545 2-338 2-306

67 1-493 1:387 1385 “21 4-762 2374 2-341

66 1515 1-401 1-399 20 5000 2-412 2:376

“65 1538 1-416 1-413 19 5°263 2-451 2-413

“64 1-563 1-430 1-427 18 5556 2:492 2-452

63 1587 1-445 1-441 Mid, 5882 2534 2:492

“62 1-613 1-459 1-456 16 6-250 2579 2-534

‘61 1640 1-474 1-471 “15 6°667 2°626 2579

60 1667 1-490 1486 “14 7143 2676 2°626

*b9 1-695 1505 | 1501 13 . 7692 2-730 2°675

58 1-724 152) 1516 “12 8°333 2:786 2-728

57 1-754 1-537 1-532 2 al 9091 2'847 2°784

56 1-786 1553 1547 10 10-000 2°912 2:845

D5 1818 | 1569 1-563

[To be continued. |
Phil. Mag. 8. 4. Vol. 7. No. 44, March 1854, O

[ 186 ]

XXVII. On some Acoustic Phenomena produced by the motion of
Liquids through short Efflua Tubes. By F. Savarr*,

HE memoir, an abstract of which we are about to give, is

a posthumous one, and was presented to the Academy of

Paris by Arago. Of the four paragraphs which the author
intended the memoir to contain, the first only was completed.

When a liquid, such as water, issues through a cylindrical
efflux tube, it produces under certain circumstances musical tones
of great intensity and of a peculiar quality, somewhat analogous
to that of the human voice. The fact that this phenomenon has
not been hitherto observed, arises from the peculiar circumstances
under which alone an efflux tube can occasion such tones ; for it
is necessary, first, that its length should not differ much from its
diameter ; next, that the charges or heights of the issuing liquid
should bear a certain proportion to this diameter; and lastly,
that the diameter of the reservoir should not exceed a certain
magnitude, dependent on the diameter of the efflux tube; ina
word, it is only under particular circumstances that the effect
can exhibit itself in all its beauty.

To obtain a general idea of the phenomenon, conceive one
extremity of a glass tube, from 6 to 8 centimetres in diameter
and 2 metres long, closed by means of a metallic plate, in the
centre of which is a circular aperture whose diameter is equal to
the thickness of the plate. After having fixed the tube in a
vertical position and filling it with water, the orifice is opened,
when it is observed that the efflux takes place periodically, and
is accompanied by a tone which at the commencement is feeble
and confused, but gradually acquires force as the charge dimi-
nishes, until it attains a certain limit, beyond which its intensity
decreases, and in some cases it disappears altogether. But as the
charge continues to sink, the tone soon regains force, becoming
at the same time more grave, until at length it attains another
maximum of intensity, after which it again becomes feebler in
order to increase anew, with a still lower pitch, and so on.
The number of these ventral segments, as they may be called,
depends upon the diameter and height of the tube, as well as
upon the diameter of the orifice.

From the above it evidently follows, that when a liquid issues
through a short efflux tube, its whole mass is periodically subject
to certain modifications, either in the velocity or the direction of
its component threads.

The experimental analysis of these phenomena presents great
difficulties, owing partly to their extremely short duration, par-

* Abridged from the Comptes Rendus for August 1853, and communi-
cated by Dr. Hirst.

On the motion of Liquids through short Efflux Tubes. 187

ticularly when the diameter of the efflux tube is pretty large in
relation to that of the tube which serves as reservoir; then,
again, under like conditions, these phenomena do not rigorously
reproduce themselves in successive experiments ; and lastly, they
are influenced by a number of small and almost imappreciable
circumstances, such as the more or less perfect polish of the
efflux tube, the purity of the liquid, the cleanness of the sides of
the reservoir, &c.

The experiments of M. Savart, so far as recorded, are intended
to illustrate,—

1. The influence of the charge.

2. That of the diameter of the efflux tube.

3. That of its height.

4. That of the diameter of the reservoir, supposing it first to
be cylindrical and concentric with the efflux tube, then cylin-
drical and of small diameter at its inferior part, or seyandned
and of large diameter at its superior part.

1. The influence of the Charge.

The cylindrical efflux tubes consisted each of a simple plate of
brass, in the centre of which was a circular aperture perpendi-
cular to the two parallel faces; or at the centre of such a plate,
a small cylindrical tube was soldered. Every precaution was
taken that the plate in contact with the liquid and the efflux tube
itself were perfectly clean and polished ; that the latter was quite
ene, and exactly perpendicular to the polished face of. the
plate

The tubes which served as reservoirs were of glass, their dia-
meters varied from 30 to 165 millimetres; they were chosen as
cylindrical as possible, and the extremity of each in contact with
the plate was ground so that the plane of the latter was perpen-
dicular to the axis of the cylinder. The plate and glass cylinder ~
were joined by guin-mastic applied hot, care being taken that it
did not penetrate into the interior of the glass tube, and that
the axes of the efflux and glass tubes were coincident.

On experimenting, the glass tube was fixed in a vertical posi-
tion by means of an immoveable support, the efflux tube was
elgsed in order to fill the glass one with water, and after allow-
ing the whole to rest quiet for a quarter of an hour, the efflux
tube was opened, and the observations commenced. In all cases
the experiments were repeated several times, until there was no
longer any uncertainty either as to the tones produced, their
intensity, or their corresponding charges.

The first experiment was made with a glass tube 2°66 metres

O02

188 M. F. Savart on some Acoustic Phenomena produced by

in height and 0-041 metre in diameter, having an efflux tube
whose height and diameter were each 2°15 millims. On observing
the issuing jet during the several phases of the phenomenon, it
was seen to swell out considérably whenever the tone attained its
maximum intensity, and to contract every time this intensity
decreased. In the first case the jet appeared to open, in the
second to close.

As the charge diminished from 2°66 metres to 0°15 metre,
the tone lowered through two octaves; but this fall was not
gradual, it took place by fits, so that the whole series constituted
a number of ventral segments, for each of which the tone was
nearly constant, except when the charge was feeble. These
ventral segments were separated by nodes, where the tone, with-
out disappearing altogether, was much less intense, and reduced
to a kind of rustling noise. At first this appeared to be inca-
pable of analysis by the ear; nevertheless, on closer examination
the noise appeared to be composed of two tones, one being that
of the superior ventral segment, the other that of the inferior; °
from which it is evident that the nodes are the points where the
state of vibration which constitutes a certain ventral segment
becomes modified, in passing to that which constitutes the ven-
tral segment immediately succeeding.

The number of such ventral segments decreases when the
aperture is enlarged. In the above case there were fifteen, and
the vessel was emptied in 315 seconds. In another experiment
with the same glass tube, but with an efflux tube whose height
was 5°456 millims., and diameter 5°4 millims., there were only
four such ventral segments, and the vessel was emptied in
47 seconds. In the former experiment, the tone correspond-
ing to the charge 2°66 metres was more than an octave higher
than in the latter; the lowest audible tone in the latter experi-
ment corresponded to the charge 0°57 millim. When the vessel
emptied itself with great velocity, each ventral segment presented
this peculiarity, that the tone after reaching its maximum in-
tensity always rose a little higher in pitch, sometimes, indeed, a
semitone.

By comparing the numbers of vibrations corresponding to each
pressure with the square roots of the pressures themselves, the
former were found to be in general proportional to the latter, or
to the velocity of efflux. It is clear that this law cannot be
rigorously exact for all pressures, because the tone remains
almost invariable throughout each ventral segment ; nevertheless
its existence was on the whole quite manifest. The degree ot
exactitude may be seen from the following table:—

the motion of Liquids through short Effiux Tubes. 189

Diameter of efflux tube, Diameter of efflux tube,
2°15 millims. 5°5 millims.
Square ite ee ae es
aay eet scat Numbers of vibra- Numbers of vibra-
Bes. tions correspond-| Ratios. | tions correspond-| Ratios.
ing to the tone. ing to the tone.
Centims. |
108 10°4 1:48 3200 1-56 1365 1-48
70 8-4 1-20 2212 1:08 960 1:04
50 ae 1-00 2048 1:00 921 1:00

The general influence of the charge upon the number of vibra-
tions can be easily rendered sensible by inclining the tube during
the efflux of the hquid. In this manner, by a gradual inclina-
tion from a vertical to a nearly horizontal position, the tone fell
rapidly, whereas by raising it more towards the vertical, the
tone rose higher and higher; and, what is worthy of remark,
the differences in intensity were incomparably less now than when
the tube was fixed. The tone could be easily rendered constant
by inclining it gradually towards the vertical, according as the
level of the water fell.

2. Influence of the diameter of Efflux Tube.

In a preceding memoir Savart demonstrated that when a
liquid issues through a circular orifice in a thin plate, pulsations
are produced whose number is proportional to the square root of
the charge, and inversely proportional to the diameter of the
orifice.

It has just been shown that with short efflux tubes the number
of vibrations conforms to the first of these laws, and what follows
will prove that the second law is also fulfilled.

The experiments were made with efflux tubes of various dia-
meters, adapted successively to a tube 1°70 metre in height and
5 centimetres in diameter. From the following table it will be
seen that the numbers of vibrations may be considered inversely
proportional to the diameters of the efflux tubes.

Diameter of efflux tubes ..........00-0000: 2°15 | 4°65 | 5:40 | 9°30
Ratios of these diameters .........+++000: 1°00 | 2°16 | 2°51 | 4°32

metre.
Charge 1-08 | Ratios of the numbers of vibrations...| 4°50 | 2-00 | 1:92 | 1-00
werre0:70 au Bad 4:32 | 2-00 | 188 | 1-00
0°50 wee si 4:27 | 2-13 | 1-94 | 1:00

But here also it is evident that this law can be but an ap-
proximation to the true nature of the phenomenon, inasmuch as
the tone makes sudden changes, and rises always somewhat higher
after each maximum of intensity has been passed.

190 M. F. Savart on some Acoustic Phenomena produced by
3. Influence of the height of Efflux Tube.

The height of the efflux tube has~a far greater influence on
the production of tones than on their nature when produced.
Thus, when the height of the efflux tube exceeds the double of
its diameter, the production of tones may be said to be almost
impossible, slight rustling noises are alone heard, and they, too,
only when the charge is feeble. Similarly, when the height of
the efflux tube is less than half its diameter, the efflux must be
regarded as taking place through a thin plate, and consequently
tones are impossible. Hence it is evident that the necessary
vibratory motion can only occur within very narrow limits.

A series of experiments were made with a reservoir tube 1:70
metre in height and 5 centims. in diameter, to which efflux
tubes, 5°4 millims. in diameter and of different heights, were
successively adapted. One of these had a height of 2°726 mil-
lims., or nearly equal to half the diameter, and the efflux took
place without a tone, as is always the case with thin plates. An-
other had a height of 10°9 millims., or nearly equal to double
its diameter, and with it no tone at all was obtaimed. Between
these extremes the results seemed to indicate, first, that the
number of ventral segments diminishes when the height of the
efflux tube is either greater or less than its diameter; secondly,
that the charges corresponding to the first appearance of tone
are more and more feeble as the height of the efflux tube
becomes greater or less than its diameter; and lastly, that the
tones acquire their greatest intensity when the height is equal to
the diameter.

With regard to the influence of the height of the efflux tube
upon the number of vibrations, although no certain law could be
established, it was evident that the number was greater when
the efflux tube was shorter, and it appeared probable that this
number was inversely proportional to the height of the efflux
tube.

By immersing the tube about 1 centimetre deep in water, and
causing the efflux to take place into this liquid instead of into
air, it was found that extremely short efflux tubes produced very
intense tones, and this continued to be the case until the height
was but one-fourth of the diameter. Indeed, tones continued
to be produced far beyond this limit, even when the height did
not exceed one-tenth of the diameter ; in short, it was only when
the efflux took place through orifices pierced through thin plates
that the production of tones was no longer possible, or rather
no longer perceptible by the ear; for Savart has shown that even
then the efflux takes place with a velocity periodically variable.

With efflux tubes whose height was greater than their dia-

.

the motion of Liquids through short Efflux Tubes. 191

meters, the only effect of causing the efflux to take place in water
seemed to be a slight depression of tone, amounting to about
half a semitone, which circumstance may be easily explained when
we consider the greater resistance of the medium which the jet
has to penetrate.

On repeating the experiments with efflux tubes whose dia-
meters exceeded their heights, it often happened that different
results were obtamed. At such times a depression and elevation
of the tone through an entire octave often occur. Hence it
would appear that the threads of liquid no longer possess that
stability im direction and velocity which was observed with longer
efflux tubes. On this account the only conclusion drawn by
Savart from this series of experiments is, that when the efflux
takes place in the same medium, a state of sonorous vibration
may exist for all orifices, from those in thin plates to those
whose height does not exceed double their diameter.

4. Influence of the diameter of the Reservoir Tube.

In order to study the influence of the reservoir tube, only one
efflux tube was used ; its height and diameter were equal to 2°25
millims., andit was successively adapted to four glass tubesof differ-
ent diameters. The experiments proved that the diameter of the
tube had an influence on the number of ventral segments, which
increased as the diameter of the tube was augmented, or as the
vessel emptied itself more slowly.

Experiments were next made by fixing glass tubes, to which
efflux tubes had been previously adapted, to a vessel of much
larger diameter, in which the level of the liquid could either be
kept constant or not, as required. In doing so, a glass tube was
taken, provided with a certain efflux tube, and the positions of
maximum intensity were determined. The tube was then cut
of such a length, that when it was afterwards adapted perpendi-
cularly to the bottom of a larger vessel, the charge corresponded
to one of those which gave a maximum intensity. It was thus
found that the tone was the same as the one corresponding to a
like charge when a simple tube was employed; it acquired,
however, a remarkable force when the level of the liquid was
kept constant.

he experiments which verified the above remarks were made
with efflux tubes 2°15 millims. and 5:4 millims. in diameter.
With the former, the glass tubes were 62 centims. long, and
varied in diameter from 17 to 63 millims.; these were fixed to
the bottom of a wooden trough whose height was 50 centims.,
a. diameter 46°5 centims., and lower diameter 38 centims.

e efflux tube, whose diameter was 5°4 millims., was adapted
to a glass tube 0°05 metre in diameter and 1°23 metre in

192 Prof. Thomson on the Mechanical Values of

height, which was fixed to the centre of the plane circular base
of a large copper vessel whose height was 0:12 metre and dia-
meter 0°68 metre. In both cases the tones produced were
exactly the same as those corresponding to the same heights
of charge when simple tubes alone were used.

The same experiments were afterwards made with efflux tubes
of larger diameter, the apparatus im other respects being unal-
tered; the agreement in tone between tubes of the same dia-
meter throughout and tubes fixed to a much larger vessel, was
found no longer to exist. This agreement is likewise destroyed
when the height of the glass tube, in relation to that of the vessel
placed above, is less considerable ; which shows that the number
of vibrations does not depend solely upon what takes place at
the orifice itself, but that it depends partially, at least, on the
motion of the liquid in the tube. This motion must be modified
considerably during the passage of a liquid from a vessel of a
large to one of a small capacity ; for at the place of transition a
contraction takes place which must necessarily have ‘some influ-
ence on the velocity of the liquid in the smaller tube, so that the
effect will be the same as a diminution of the charge.

Savart confirmed the above explanation by fixing a glass tube,
with an efilux tube 4°65 millims. in diameter, to the copper vessel
above described. The total charge was 1:06 metre. When the
upper orifice of the glass tube was partially closed by placing a
disc at the bottom of the copper vessel, a depression of tone took
place ; at first this depression was inconsiderable, but it was much
increased when the dise covered half the‘orifice. This depression
was evidently caused by a diminution of the velocity with which
the liquid issued from the efflux tube.

XXVIII. On the Mechanical Values of Distributions of Electricity,
Magnetism and Galvanism. By Professor W. THomson*.

I. Electricty at rest.
ane electrify an insulated conductor (a Leyden phial, for in-

stance, or any mass of metal resting on supports of glass)
in the ordinary way by means of an electrical machine, requires
the expenditure of work in turning the machine. But inasmuch
as part, obviously by far the greater part, of the work done in
this operation goes to generate heat by means of friction, and of
the small residue some, it may be a considerable proportion, is
wasted in generating heat (electrical light bemg included in the

* Communicated by the Author; having been read at a meeting of the
Glasgow Philosophical Society, Jan. 26, 1853.

Distributions of Electricity, Magnetism and Galvanism. 198

term) by the flashes, illuminated points, and sparks which accom-
pany the transmission of the electricity from the glass of the
machine where it is first excited to the conductor which receives
it, the mechanical value of the electrification thus effected would
be enormously over-estimated if it were regarded as equivalent to
the work that has been spent. Notwithstanding, the mecha-
nical value of any electrification of a conductor has a perfectly
definite character, and may be calculated with ease in any par-
ticular case by means of formule demonstrated in this commu-
nication. The simplest case is that of a single conductor insu-
lated at a distance from other conductors, or with only uninsu-
lated conducting matter in its neighbourhood. In this case the
mechanical value of the electrification of the conductor is equal
to half the square of the quantity of electricity multiplied by the
capacity of the conductor*.

In any case whatever, the total mechanical value of all the
distributions of electricity on any number of separate insulated
conductors electrified with any quantities of electricity, is demon-
strated by the author to be equal to half the sum of the products
obtained by multiplying the “ potential; ” in each conductor by
the quantity of electricity by which it is charged. Each term
of this expression does not represent the independent value of
the actual distribution on the conductor to which it corresponds,
imasmuch as the “ potential” in each depends on the presence
of the others when they are near enough to exert any sensible
mutual influence; but independent expressions of these inde-
pendent values are readily obtained, although not im a form con-
venient for statement here; and the author proves that their
sum is equal to the total value, as calculated by the preceding
expression. When a conductor is discharged without other me-
chanically valuable effects being developed, as, for instance, when
the knob of a Leyden phial is put in communication with the
outside coating, or when a flash of lightning takes place, the
heat is equal in mechanical value to the distribution of electricity
lost. Hence, by what precedes, the amount of heat is propor-
tional to the square of the quantities discharged, as was first
demonstrated by Joule, in a communication to the Royal Society
in 1840, although it had been announced by Sir W. Snow Harris

* Electrical capacity is a term introduced by the author to signify the
proportion of the quantity of electricity that the conductor would retain to
that which it would communicate to a conducting ball of unit radius, insu-

lated at a great distance from other conducting matter, if connected with
it by means of a fine wire.

+ Aterm first introduced by Green, which may be defined as the quantity
of mechanical work that would have to be spent to bring a unit of electricity
from a great distance up to the surface of the conductor, supposed to retain
its distribution unaltered.

194 Prof. Thomson on the Mechanical Values of

as an experimental result, to be simply proportional to the quan-
tity. Mr. Joule’s result has been verified by independent expe-
rimenters in France, Italy and Germany. The author pointed
out other applications of his investigation, some of a practical
kind, and others in the Mathematical Theory of Electricity. He
mentioned, that although he had first arrived at the results in
1845, and used them in papers published in that year, the first
explicit publication of the theorem regarding the mechanical
value of the electrification of a conductor appears to be in 1847,
in a paper entitled “Ueber die Erhaltung der Kraft,” by
Helmholtz.

Il. Magnetism.

If a piece of soft iron be allowed to approach a magnet very
slowly from a distant position, and be afterwards drawn away so
rapidly, that, at the instant when it reaches its primitive position,
where it is left at rest, it retains as yet sensibly unimpaired the
magnetization it had acquired at the nearest position, a certain
amount of work must have been finally expanded on the motion
of the iron. For during the approach, the iron has only the
magnetization due to the action of the magnet on it in its actual
position at each instant; but at each instant of the time in which
the iron is bemg drawn away, it has the whole magnetization
due to the action of the magnet on it when it was at the nearest.
Hence it is drawn away against more powerful forces of attrac-
tion by the magnet than those with which the magnet attracts
it during its approach ; from which it follows, that more work
is spent in drawing the iron away than had been gained in letting
it approach the magnet. The sole effect due to this excess of
work is the magnetization which the iron carries away with it;
and consequently, the mechanical value of this magnetization
must be precisely equal to the mechanical value of the balance
of work spent in producing it.

After a very short time has elapsed with the piece of soft iron
at a great distance from the magnet, it will have lost, as is well
known, all or nearly all the magnetization which it had acquired
temporarily in the neighbourhood of the magnet; and in this
short time some energy, equivalent to that of the magnetization
lost, must have been produced. Mr. Joule’s experiments show
that this energy consists of heat, which is generated in the iron
during demagnetization ; and we infer the remarkable conclusion,
that at the end of the process which has been described, or of
any motion of a piece of soft.iron in the neighbourhood of a
magnet, from a certain position and back to the same, the iron
will be as much warmer than it was at the beginning, as it would
have been without any magnetic action, if it had received the

_ Distributions of Electricity, Magnetism and Galvanism. 195

heat that would* be generated by the expenditure of the same
amount of work on mere friction.

The same considerations are applicable to the magnetization
of a piece of steel; with this difference, that, accordmg to the
hardness of the steel, the magnetization which it receives in the
nearest position will be more or less permanent; and if there be
any demagnetization after removal from the magnet, it will be
much less complete than in the case of soft iron, and that heat
will be necessarily generated both during the magnetization
which takes place during the gradual approach, and in the sub-
sequent demagnetization. Further, by putting together a num-
ber of pieces “ot steel, each separately magnetized, a complete
magnet will be formed, of which the mechanical value will be
equal to the sum of the mechanical values of its parts, increased
or diminished by the amount of work spent or gained in bringing
them together.

Upon the principles which have been explained, the author
has investigated the mechanical value of any conceivable distri-
bution of magnetism in any kind of substance. The result,
which cannot be well expressed except in mathematical language,
is as follows :-—

ng?da dy dr + s— Rdx dy dz,
sees SIS

where R denotes the resultant magnetic force at any internal or
external point (v, y, z), q the intensity of magnetization at a
point (#, y, 2) of the magnet, and % a quantity depending on the
nature of the substance at this point.

The integral constituting the first term of this expression in-
eludes the whole of the magnetized substance, and expresses
the sum of the separate mechanical values of the distributions
in all the parts obtained by infinitely minute division along the
lines of magnetization. The second term expresses the amount
of work that would have to be spent to put these parts together,
were they given separately, each with the exact magnetization
that it is to have when in its place in the whole. If the sub-
stance be perfectly free in its susceptibility for magnetization
or demagnetization, X will be such a function of the inductive
capacity, that if a ball of similar substance be placed in a mag-
netic field where ‘!1e force is F, the intensity of the magnetiza-
tion induced in it will be

n+ =

196 Onthe Mechanical Values of Distributions of Electricity, &c.

Ill. Hlectricity in motion.

If an electric current be excited in a conductor, and then left
without electromotive force, it retams energy to produce heat,
light, and other kinds of mechanical effect, and it lasts with
diminishing, or it may be with alternately diminishing and in-
creasing strength, before it finally ceases and electrical equili-
brium is established ; as is amply demonstrated by the experi-
ments of Faraday and Henry, on the spark which takes place
when a galvanic circuit is opened at any point, and by those of
Weber, Helmholtz, and others on the electro-magnetic effects of
varying currents. The object of the present communication is
to show how the mechanical value of all the effects that a current
in a close cireuit can produce after the electromotive force ceases
may be ascertamed, by a determimation founded on the known
laws of electro-dynamic induction, of the mechanical value of the
energy of a current of given strength circulating in a linear
conductor (a bent wire, for instance) of any form. To do this,
in the first place it may be remarked, that a current once
instituted in a conductor, will circulate in it with diminishing
strength after the electromotive force ceases, just as if the
electricity had inertia, and will dimimish in strength according
to the same, or nearly the same, laws as a current of water or
other fluid once set in motion and left without moving force in
a pipe forming a closed cireuit. But according to Faraday, who
found that an electric cireuit consisting of a wire doubled on
itself, with the two parts close together, gives no sensible spark
when suddenly opened compared to that given by an equal
length of wire bent into a coil, it appears that the effects of
ordinary tnertia either do not exist for electricity in motion, or
are but small compared with those which, im a suitable arrange-
ment, are produced by the “induction of the current upon itself.”
In the present state of science it is only these effects that can be
determined by a mathematical investigation ; but the effects of
electrical inertia, should it be found to exist, will be taken into
account by adding a term of determinate form to the fully deter-
mined result of the present investigation, which expresses the
mechanical value of a current in a linear conductor as far as it
depends on the induction of the current on itself.

The general principle of the investigation is this; that if two
conductors, with a current sustained in each by a constant elec-
tromotive force, be slowly moved towards one another, and there
be a certain gain of work on the whole, by electro-dynamic force
operating during the motion, there will be twice as much work
as this spent by the electromotive forces (for instance, twice the

Prof. Faraday on Electric Induction. 197

equivalent of chemical action in the batteries, should the electro-
motive forces be chemical) over and above that which they would
have had to spend in the same time, merely to keep up the cur-
rents, if the conductors had been at rest, because the electro-
dynamic induction produced by the motion will augment the
currents ; while on the other hand, if the motion be such as to
require the expenditure of work against electro-dynamic forces to
produce it, there will be twice as much work saved off the action
of the electromotive forces by currents being diminished during
the motion. Hence the aggregate mechanical value of the cur-
rents in the two conductors when brought to rest will be increased
in the one case by an amount equal to the work done by the
mutual electro-dynamic forces in motion, and will be diminished
by the corresponding amount in the other case. The same consi-
derations are applicable to relative motions of two portions of
the same linear conductor (supposed perfectly flexible). Hence
it is concluded that the mechanical value of a current of given
strength in a linear conductor of any form is determined by cal-
culating the amount of work against electro-dynamic forces
required to double it upon itself, while a current of constant
strength is sustained in it. The mathematical problem thus
presented leads to an expression for the required mechanical
value consisting of two factors, of which one is determined ac-
cording to the form and dimensions of the line of the conductor
in any case, irrespectively of its section, and the other is the
square of the strength of the current. If it be found necessary
to take inertia into account, it will be done by adding to this
expression a term consisting of two factors, of which one is
directly proportional to the length of the conductor, and inversely
proportional to the area of its section, and the other is the square
of the strength of the current.

XXIX. On Electric Induction—Associated cases of Current and
Static Effects. By Professor Farapay, D.C.L., FBS.
[The following important paper is a verbal copy of an abstract

of a lecture given by Professor Faraday at the Royal Institution
on the evening of Friday, Jan. 20, of the present year.—Eps. ]

ERTAIN phenomena that have presented themselves in the
course of the extraordinary expansion which the works of the
Electric Telegraph Company have undergone, appeared to me to
offer remarkable illustrations of some fundamental principles of
electricity, and strong confirmation of the truthfulness of the view
which I put forth sixteen years ago, respecting the mutually

198 Prof. Faraday on Electric Induction—

dependent nature of induction, conduction, and insulation (Ex-
perimental Researches, 1318, &c.). I am deeply mdebted to
the Company, to the Gutta Percha Works, and to Mr. Latimer
Clarke, for the facts; and also for the opportunity both of seeing
and showing them well.

Copper wire is perfectly covered with gutta percha at the
Company’s works, the metal and the covermg being in every
part regular and concentric. The covered wire is usually made
into half-mile lengths, the necessary junctions being effected by
twisting or binding, and ultimately soldering; after which the
place is covered with fine gutta percha, in such a manner as to
make the coating as perfect there as elsewhere: the perfection
of the whole operation is finally tried in the following striking
manner by Mr. Statham, the manager of the works. The half-
mile coils are suspended from the sides of barges floating im a
canal, so that the coils are immersed in the water whilst the two
ends of each coil rise into the air: as many as 200 coils are thus
immersed at once; and when their ends are connected in series,
one great length of 100 miles of submerged wire is produced,
the two extremities of which can be brought into a room for
experiment. An insulated voltaic battery of many pairs of zine
and copper, with dilute sulphuric acid, has one end connected
with the earth, and the other, through a galvanometer, with
either end of the submerged wire. Passing by the first effect,
and continuing the contact, it is evident that the battery current
can take advantage of the whole accumulated conduction or
defective insulation in the 100 miles of gutta percha on the wire,
and that whatever portion of electricity passes through to the
water will be shown by the galvanometer. Now the battery is
made one of intensity, in order to raise the character of the proof,
and the galvanometer employed is of considerable delicacy ; yet
so high is the insulation, that the deflection is not more than
5°. As another test of the perfect state of the wire, when the
two ends of the battery are connected with the two ends of the
wire, there is a powerful current of electricity shown by a much
coarser instrument ; but when any one junction in the course of
the 100 miles is separated, the current is stopped, and the leak
or deficiency of insulation rendered as small as before. The
perfection and condition of the wire may be judged of by these
facts.

The 100 miles, by means of which I saw the phenomena,
were thus good as to insulation. The copper wire was ;;th of
an inch in diameter; the covered wire was ;4,ths; some was a
little less, being #,nds in diameter; the gutta percha on the
metal may therefore be considered as 0-1 of dn inch in thickness.
100 miles of like covered wire in coils were heaped up on the

——

—sT.

<< s) ee

Associated cases of Current and Static Effects. 199

floor of a dry warehouse and connected in one serie’, for com-
parison with that under water.

Consider now an insulated battery of 360 pairs of plates
(4.x 3 inches) having one extremity to the earth ; the water wire
with both its msulated ends in the room, and a good earth dis-
charge wire ready for the requisite communication: when the
free battery end was placed in contact with the water wire and
then removed, and afterwards a person touching the earth dis-
charge touched also the wire, he received a powerful shock. The
shock was rather that of a voltaic than of a Leyden battery; it
occupied ¢ime, and by quick tapping touches could be divided
into numerous small shocks; I obtained as many as forty sen-
sible shocks from one charge of the wire. If tame were allowed
to intervene between the charge and discharge of the wire, the
shock was less; but it was sensible after two, three, or four
minutes, or even a longer period.

When, after the wire had been in contact with the battery, it
was placed in contact with a Statham’s fuse, it ignited the fuse
(or even six fuses in succession) vividly ; it could unite the fuse
three or four seconds after separation from the battery. When,
having been in contact with the battery, it was separated and
placed in contact with a galvanometer, it affected the instrument
very powertully ; it acted on it, though less powerfully, after the
lapse of four or five minutes, and even affected it sensibly twenty
or thirty minutes after it had been separated from the battery.
When the insulated galvanometer was permanently attached to
the end of the water wire, and the battery pole was brought in
contact with the free end of the instrument, it was most mstruct-
ive to see the great rush of electricity into the wire; yet after
that was over, though the contact was continued, the deflection
was not more than 5°, so high was the insulation. Then sepa-
rating the battery from the galvanometer, and touching the latter
with the earth wire, it was just as striking to see the electricity
rush out of the wire, holding for a time the magnet of the instru-
ment in the reverse direction to that due to the ingress or charge.

These effects were produced equally well with either pole of
the battery or with either end of the wire; and whether the
electric condition was conferred and withdrawn at the same end,
or at the opposite ends of the 100 miles, made no difference in
the results. An intensity battery was required, for reasons which
will be very evident in the sequel. That employed was able to
decompose only a very small quantity of water in a given time.
A Grove’s battery of eight or ten pair of plates, which would
have far surpassed it in this respect, would have had scarcely a
sensible power in affecting the wire.

When the 100 miles of wire in the air were experimented

200 Prof. Faraday on Electric Induction—

with in like manner, not the slightest signs of any of these effects
were produced, There is reason, from principle, to believe that
an infinitesimal result is obtainable, but as compared to the water
wire the action was nothing. Yet the wire was equally well and
better imsulated, and as regarded a constant current, it was an
equally good conductor. This point was ascertained by attach-
ing the end of the water wire to one galvanometer, and the
end of the air wire to another like instrument; the two other
ends of the wires were fastened together, and to the earth con-
tact; the two free galvanometet ends were fastened together,
and to the free pole of the battery : in this manner the current
was divided between the air and water wires, but the galvano-
meters were affected to precisely the same amount. ‘To make
the result more certain, these instruments were changed one for
the other, but the deviations were still alike; so that the two
wires conducted with equal facility.

The cause of the first results is, upon consideration, evident
enough. In consequence of the perfection of the workmanship,
a Leyden arrangement is produced upon a large*scale ; the cop-
per wire becomes charged statically with that electricity which
the pole of the battery connected with it can supply*; it acts
by induction through the gutta percha (without which induction
it could not itself become charged, Exp. Res. 1177), producing
the opposite state on the surface of the water touching the gutta
percha, which forms the outer coating of this curious arrange-
ment. The gutta percha across which the induction occurs is
only 01 of an inch thick, and the extent of the coating is enor-
mous. The surface of the copper wire is nearly 8300 square
feet, and the surface of the outer coating of water is four times
that amount, or 33,000 square feet ; hence the striking character
of the results. The intensity of the static charge acquired is
only equal to the intensity at the pole of the battery whence it
is derived ; but its quantity is enormous, because of the immense
extent of the Leyden arrangement ; and hence when the wire is
separated from the battery and the charge employed, it has all
the powers of a considerable voltaic current, and gives results
which the best ordinary electric machines and Leyden arrange-
ments cannot as yet approach.

That the air wire produces none of these effects is simply
because there is no outer coating correspondent to the water, or
only one so far removed as to allow of no sensible induction,
and therefore the inner wire cannot become charged. In the air
wire of the warehouse, the floor, walls, and ceiling of the place
constituted the outer coating, and this was at a considerable
distance ; and in any case could only affect the outside portions

* Davy, Elements of Chemical Philosophy, p. 154.

———

Associated cases of Current and Static Effects. 201

of the coils of wire. I understand that 100 miles of wire,
stretched in a line through the air so as to have its whole extent
opposed to earth, is equally inefficient in showing the effects,
and there it must be the distance of the inductric and inducteous
surfaces (1483.), combined with the lower specific inductive
capacity of air, as compared with gutta percha, which causes the
negative result. The phznomena altogether offer a beautiful
case of the identity of static and dynamic electricity. The whole
power of a considerable battery may in this way be worked off
in separate portions, and measured out in units of static force,
and yet be employed afterwards for any or every purpose of yol-
taic electricity.

I now proceed to further consequences of associated static and
dynamic effects. Wires covered with gutta percha and then
inclosed in tubes of lead or of iron, or buried in the earth, or
sunk in the sea, exhibit the same phenomena as those described,
the like static inductive action being in all these cases permitted
by the conditions. Such subterraneous wires exist between
London and Manchester; and when they are all connected
together so as to make one series, offer above 1500 miles; which,
as the duplications return to London, can be observed by one
experimenter at intervals of about 4.00 miles, by the introduction
of galvanometers at these returns. This wire, or the half or fourth
of it, presented all the phenomena already described ; the only
difference was, that as the insulation was not so perfect, the
charged condition fell more rapidly. Consider 750 miles of the
wire in one length, a galvanometer a being at the beginning of
the wire, a second galvanometer 6 in the middle, and a third ¢
at the end; these three galvanometers being in the room with
the experimenter, and the third c perfectly connected with the
earth. On bringing the pole of the battery into contact with
the wire through the galvanometer a, that instrument was in-
stantly affected ; after a sensible time b was affected, and after a
still longer time ¢: when the whole 1500 miles were included,
it required two seconds for the electric stream to reach the last
instrument. Again; all the instruments being deflected (of
course not equally, because of the electric leakage along the line),
if the battery were cut off at a, that instrument instantly fell to
zero; but 4 did not fall until a little while after; and ¢ only
after a still longer interval,—a current flowing on to the end of
the wire whilst there was none flowing in at the beginning.
Again ; by a short touch of the battery pole against a, it could
be deflected and could fall back into its neutral condition before
the electric power had reached 6; which in its turn would be
for an instant affected, and then left neutral before the power
had reached ¢; a wave of force having been sent into the wire

Phil. Mag, 8. 4. Vol. 7. No. 44. March 1854. P

202 Prof. Faraday on Electric Induction—

which gradually travelled along it, and made itself evident at
successive intervals of time in different parts of the wire. It
was even possible, by adjusted touches of the battery, to have
two simultaneous waves in the wire following each other, so that
at the same moment that ¢ was affected by the first wave, a or b
was affected by the second; and there is no doubt that by the
multiplication of instruments and close attention, four or five
waves might be obtained at once.

If after making and breaking battery contact at a, a be imme-
diately connected with the earth, then additional interesting
effects occur. Part of the electricity which is in the wire will
return, and passing through a will deflect it in the reverse direc-
tion ; so that currents will flow out of both extremities of the
wire in opposite directions, whilst no current is going into it
from any source. Or if a be quickly put to the battery and then
to the earth, it will show a current first entermg into the wire,
and then returning out of the wire at the same place, no sensible
part of it ever travelling on to } or ce.

When an air wire of equal extent is experimented with in lke
manner, no such effects as these are perceived; or if, guided by
principle, the arrangements are such as to be searching, they are
perceived only ina very slight degree, and disappear in com-
parison with the former gross results. The effect at the end of
the very long air wire (or c) is in the smallest degree behind the
effect at galvanometer a; and the accumulation of a charge in
the wire is not sensible.

All these results as to dime, &c. evidently depend upon the
same condition as that which produced the former effect of static
charge, namely, lateral induction ; and are necessary consequences
of the principles of conduction, insulation and induction, three
terms which in their meaning are inseparable from each other
(Exp. Res. 1520, 1826*, 13838, 1561, &c.). If we put a plate

* 1326. All these considerations impress my mind strongly with the
conviction, that insulation and ordinary conduction cannot be properly
separated when we are examining into their nature; that is, into the general
law or laws under which their phenomena are produced. They appear to
me to consist in an action of contiguous particles, dependent on the forces
developed in electrical excitement; these forces bring the particles mto a
state of tension or polarity, which constitutes both ixduction and insulation ;
and being in this state, the contiguous particles have a power or capability
of communicating these forces, one to the other, by which they are lowered
and discharge occurs. Every body appears to discharge (444 987); but
the possession of this capability in a greater or smaller degree in different
bodies makes them better or worse conductors, worse or better insulators :
and both induction and conduction appear to be the same in their principle
and action (1320.), except that in the latter an effect common to both is
raised to the highest degree, whereas in the former it occurs in the best
cases in only an almost msensible quantity.

Associated cases of Current and Static Effects. 208

of shell-lac upon a gold-leaf electrometer and a charged carrier
(an insulated metal ball of two or three inches diameter) upon
it, the electrometer is diverged ; removing the carrier, this diver-
gence instantly falls, this is znsulation and induction: if we replace
the shell-lac by metal, the carrier causes the leaves to diverge as
before; but when removed, though after the shortest possible
contact, the electroscope is left diverged,—this is conduction. If
we employ a plate of spermaceti instead of the metal, and repeat
the experiment, we find the divergence partly falls and partly
remains, because the spermaceti insulates and also conducts,
doing both imperfectly: but the shell-lac also conducts, as 1s
shown if time be allowed; and the metal also obstructs conduc-
tion, and therefore insulates, as is shown by simple arrangements.
For if a copper wire, 74 feet in length and jth of an inch in
diameter, be insulated in the air, having its
end m a metal ball; its ende connected with
the earth, and the parts near m and e brought
within half an inch of each other, as at s;
then an ordinary Leyden jar being charged
sufficiently, its outside connected with e and
its mside with m, will give a charge to the
wire, which imstead of travellmg wholly
through it, though it be so excellent a con-
ductor, will pass in large proportion through
the air at s, as a bright spark ; for with such
a length of wire, the resistance in it is accu-
mulated until it becomes as much, or per-
haps even more, than that of the air, for
electricity of such high intensity.
Admitting that such and similar experiments show that con-
duction through a wire is preceded by the act of induction (1338.),
then all the phenomena presented by the submerged or subter-
ranean wires are explained ; and in their explanation confirm, as
I think, the principles given. After Mr. Wheatstone had, in
1834, measured the velocity of a wave of electricity through a
copper wire, and given it as 288,000 miles in a second, I said,
in 1838, upon the strength of these principles (1333.), “ that
the velocity of discharge through the same wire may be greatly
varied, by attending to the circumstances which cause variations
of discharge through spermaceti or sulphur. Thus, for instance,
it must vary with the tension or intensity of the first urging
force, which tension is charge and induction. So if the two
ends of the wire in Professor Wheatstone’s experiment were
immediately connected with two large insulated metallic surfaces
exposed to the air, so that the primary act of induction, after
making the contact for discharge, might be in part removed
P2

204 Prof, Faraday on Electric Induction—

from the internal portion of the wire at the first instant, and
disposed for the moment on its surface jointly with the air and
surrounding conductors, then I venture to anticipate that the
middle spark would be more retarded than before ; and if these
two plates were the inner and outer coating of a large jar, or a
Leyden battery, then the retardation of that spark would be still
greater.” Now this is precisely the case of the submerged or
subterraneous wires, except that instead of carrying their surfaces
towards the inducteous coatings (1483.), the latter are brought
near the former; in both cases the induction consequent upon
charge, instead of being exerted almost entirely at the moment
within the wire, is to a very large extent determined externally ;
and so the discharge or conduction being caused by a lower ten-
sion, therefore requires a longer time. Hence the reason why,
with 1500 miles of subterraneous wire, the wave was two seconds
in passing from end to end; whilst with the same length of air
wire, the time was almost appreciable.

With these lights it is interesting to look at the measured
velocities of electricity in wires of metal, as given by different

experimenters.
Miles per second.

* Wheatstone, in 1834, with copper wire madeit 288,000

* Walker, in America, with telegraphiron wire . 18,780
* Q’Mitchell, ditto ditto . 28,524
* Fizeau and Gonnelle (copper wire) . . . . 112,680
> Ditto (iron wire) . .. . . +» | 62;600

.+ A.B.G. (copper) London and Brussels Telegraph 2,700
+ Ditto (copper)LondonandEdinburghTelegraph — 7,600

Here the difference in copper is seen by the first and sixth
result to be above a hundred fold. It is further remarked in
Liebig’s report of Fizeau and Gonnelle’s experiments, that the
velocity is not proportional to the conductive capacity, and is
independent of the thickness of the wire. All these circum-
stances and incompatibilities appear rapidly to vanish, as we
recognize and take into consideration the lateral induction of
the wire carrying the current. If the velocity of a brief electric
discharge is to be ascertained in a given length of wire, the
simple circumstances of the latter beg twined round a frame
in small space, or spread through the air through a large space,
or adhering to walls, or lying on the ground, will make a dif-
ference in the results. And in regard to long circuits, such as
those described, their conducting power cannot be understood
whilst no reference is made to their lateral static duction, or

* Liebig and Kopp’s Report, 1850 (translated), p. 168.
+ Atheneum, January 14, 1854, p. 54.

Associated cases of Current and Static Effects. 205

to the conditions of intensity and quantity which then come into
play; especially in the case of short or mtermitting currents,
ic then static and dynamic are continually passing into each
other.

It has already been said, that the conducting power of the air
and water wires are alike for a constant current. This is in
perfect accordance with the principles and with the definite
character of the electric force, whether in the static, or current,
or transition state. When a voltaic current of a certain intensity
is sent into a long water wire, connected at the further extremity
with the earth, part of the force is in the first instance occupied
in raising a lateral induction round the wire, ultimately equal in
intensity at the near end to the intensity of the battery stream,
and decreasing gradually to the earth end, where it becomes
nothing. Whilst this induction is rising, that within the wire
amongst its particles is beneath what it would otherwise be; but
as soon as the first has attained its maximum state, then that in
the wire becomes proportionate to the battery intensity, and
therefore equals that in the air wire, in which the same state is
(because of the absence of lateral induction) almost instantly
attained. Then of course they discharge alike, and therefore
conduct alike.

A striking proof of the variation of the conduction of a wire
by variation of its lateral static induction is given in the experi-
ment proposed sixteen years ago (1333.). If, using a constant
charged jar, the interval s, page 203, be adjusted so that the spark
shall freely pass there (though it would not if a little wider),
whilst the short connecting wires n and 0 are insulated in the
air, the experiment may be repeated twenty times without a
single failure ; but if after that, n and o be connected with the
inside and outside of an insulated Leyden jar, as described, the
spark will never pass across s, but all the charge will go round
the whole of the long wire. Why is this? The quantity of
electricity is the same, the wire is the same, its resistance is the
the same, and that of the air remains unaltered; but because
the intensity is lowered, through the lateral induction momen-
tarily allowed, it is never enough to strike across the air at s;
and it is finally altogether occupied in the wire, which in a little
longer time than before effects the whole discharge. M. Fizeau
has applied the same expedient to the primary voltaic currents
of Ruhmkorff’s beautiful inducting apparatus with great advan-
tage. He thereby reduces the intensity of these currents at the
moment when it would be very disadvantageous, and gives us a
striking instance of the advantage of viewing static anc dynamic
phznomena as the result of the same laws.

Mr, Clarke arranged a Bains’s printing telegraph with three

206 Prof. Faraday on Electric Induction—

pens, so that it gave beautiful illustrations and records of facts
like those stated: the pens are iron wires, under which a band
of paper imbued with ferro-prussiate of potassa passes at a
regular rate by clock-work ; and thus regular lines of prussian
blue are produced whenever a current is transmitted, and the
time of the current is recorded. In the case to be described,
the three lines were side by side, and about 0:1 of an inch apart.
The pen m belonged to a circuit of only a few feet of wire and
a separate battery; it told whenever the contact key was put
down by the finger; the pen n was at the earth end of the long
air wire, and the pen o at the earth end of the long subterraneous
wire ; and by arrangement, the key could be made to throw the
electricity of the chief battery into either of these wires, simul-
taneously with the passage of the short cireuit current through
pen m. When pens m and m were in action, the m record was
a regular line of equal thickness, showing by its length the actual
time during which the electricity flowed into the wires; and the
n record was an equally regular line, parallel to, and of equal
length with the former, but the least degree behind it; thus
indicating that the long air wire conveyed its electric current
almost instantaneously to the further end. But when pens m.
and o were in action, the o line did not begin until some time
after the m line, and it continued after the m line had ceased,
2, e, after the o battery was cut off. Furthermore, it was faint
at first, grew up to a maximum of intensity, continued at that
as long as battery contact was continued, and then gradually
diminished to nothing, Thus the record o showed that the wave
of power took time in the water wire to reach the further extre-
mity; by its first faintness, it showed that power was consumed.
in the exertion of lateral static induction along the wire; by the
attainment of a maximum and the after equality, it showed when
this induction had become proportionate to the intensity of the
battery current ; by its beginning to diminish, it showed when
the battery current was cut off; and its prolongation and gradual
diminution showed the time of the outflow of the static electri-
city laid up in the wire, and the consequent regular falling of
the induction which had been as regularly raised.

With the pens m and 0, the conversion of an intermitting into
a continuous current could be beautifully shown ; the earth wire,
by the static induction which it permitted, acting in a manner
analogous to the fly-wheel of a steam-engine or the air-spring of
apump. Thus, when the contact key was regularly but rapidly
depressed and raised, the pen m made a series of short lines
separated by intervals of equal length. After four or more of
these had passed, then pen 0, belonging to the subterraneous
wire, began to make its mark, weak at first, then rising. to a

Associated cases of Current and Static Effects. 207

maximum, but always continuous. If the action of the contact
key was less rapid, then alternate thickening and attenuations
appeared in the o record; and if the introductions of the electric
current at the one end of the earth wire were at still longer
intervals, the records of action at the other end became entirely
separated from each other. All showing most beautifully how
the individual current or wave, once introduced into the wire,
and never ceasing to go onward in its course, could be affected
in its intensity, its time and other circumstances, by its partial
occupation in static induction.

By other arrangements of the pens n and 0, the near end of
the subterraneous wire could be connected with the earth imme-
diately after separation from the battery; and then the back
flow of the electricity, and the time and manner thereof, were
beautifully recorded ; but I must refram from detailing results
which have already been described in principle.

Many variations of these experiments have been made and
may be devised. Thus the ends of the insulated battery have
been attached to the ends of the long subterraneous wire, and
then the two halves of the wire have given back opposite return _
currents when connected with the earth. In such a case the
wire is positive and negative at the two extremities, being per-
manently sustained by its length and the battery, m the same
condition which is given to the short wire for a moment by the
Leyden discharge (p. 203); or, for an extreme but like case, to a
filament of shell-lac having its extremities charged positive and
negative. Coulomb pointed out the difference of long and short
as to the insulating or conducting power of such filaments, and
like difference occurs with long and short metal wires.

The character of the phenomena described in this report in-
duces me to refer to the terms intensity and quantity as applied
to electricity, terms which I have had such frequent occasion to
employ. ‘These terms, or equivalents for them, cannot be dis-
pensed with by those who study both the static and the dynamic
relations of electricity; every current where there is resistance
has the static element and induction imyolved in it, whilst every
case of insulation has more or less of the dynamic element and
conduction ; and we have seen that with the same voltaic source,
the same current in the same length of the same wire gives a
different result as the intensity is made to vary, with variations of
the induction around the wire. The idea of intensity, or the
power of overcoming resistance, is as necessary to that of elec-
igyl either static or current, as the idea of pressure is to steam
in a boiler, or to air passing through apertures or tubes ; and we
must have language competent to express these conditions and
these ideas. Furthermore, I have never found either of these

208 Mr. A. Cayley on the Homographie Transformation of

terms lead to any mistakes regarding electrical action, or give
rise to any false view of the character of electricity or its unity.
I cannot find other terms of equally useful significance with
these ; or any, which, conveying the same ideas, are not liable to
such misuse as these may be subject to. It would be affectation,
therefore, in me to search about for other words; and besides
that, the present subject has shown me more than ever their
great value and peculiar advantage in electrical language.

Note.—The fuse referred to in page 199 is of the following
nature :—Some copper wire was covered with sulphuretted gutta
percha; after some months it was found that a film of sulphuret
of copper was formed between the metal and the envelope; and
further, that when half the gutta percha was cut away in
any place, and then the copper wire removed for about a quarter
of an inch, so as to remain connected only by the film of sul-
phuret adhering to the remaining gutta percha, an intensity bat-
tery could cause this sulphuret to enter into vivid ignition, and
fire gunpowder with the utmost ease. The experiment was
shown in the lecture-room, of firmg gunpowder at the end of
eight miles of single wire. Mr. Faraday reported that he had
seen it fired through 100 miles of covered wire immersed in the
canal by the use of this fuse.

XXX. On the Homographic Transformation of a Surface of the
Second Order into itself*. By A. Cayiny, Esq.t

PASS to the improper transformation. Sir W. R. Hamilton
has given (in the note, p. 723 of his Lectures on Quarter-
nions) the following theorem :—If there be a polygon of 2m
sides inscribed in a surface of the second order, and (2m—1) of
the sides pass through given points, then will the 2mth side con-
stantly touch two cones cireumscrived about the surface of the
second order. The relation between the extremities of the 2mth
side is that of two points connected by the general improper
transformation ; in other words, if there be on a surface of the
second order two points such that the line joming them touches
two cones circumscribed about the surface of the second order,
then the two points are as regards the transformation in question
a pair of corresponding points, or simply a pair. But the rela-
tion between the two points of a pair may be expressed in a dif-
ferent and much more simple form. For greater clearness call
the surface of the second order U, and the sections along which

* See Phil. Mag. vol. vi. p. 326 (Nov, 1853),
+ Communicated by the Author.

Se ee

a Surface of the Second Order into itself. 209

it is touched by the two cones, 6, @; the cones themselves may,
it is clear, be spoken of as the cones 0, @. And let the two
points be P,Q. The line PQ touches the two cones, it is there-
fore the line of intersection of the tangent plane through P to
the cone 0, and the tangent plane through P tothe cone ¢. Let
one of the generating lines through P meet the section @ in the
point A, and the other of the generating lines through P meet
the section ¢ in the point B. The tangent planes through P to
the cones @, ¢ respectively are nothing else than the tangent
planes to the surface U at the points A, B respectively. We
have therefore at these points two generating lines meeting in
the point P; the other two generating lines at the pomts A, B
meet in like manner in the pomt Q. Or P, Q are opposite
angles of a skew quadrangle formed by four generating lines
(or, what is the same thing, lying upon the surface of the second
order), and having its other two angles, one of them on the sec-
tion @ and the other on the section @; and if we consider the
side PA as belonging determinately to one or the other of the
two systems of generating lines, then when P is given, the corre-
sponding point Q is, it is clear, completely determimed. What
precedes may be recapitulated in the statement, that in the
improper transformation of a surface of the second order into
itself, we have, as corresponding points, the opposite angles of a
skew quadrangle lying upon the surface, and having the other
two opposite angles upon given plane sections of the surface. I
may add, that attending only to the sections through the points
of intersection of 0, ¢, if the pomt P be situate anywhere in one
of these sections, the point Q will be always situate in another
of these sections, 7. e. the sections correspond to each other in
pairs; in particular, the sections 0, ¢ are corresponding sections,
so also are the sections ©, & (each of them two generating lines)
made by tangent planes of the surface. Any three pairs of sec-
tions form an involution ; the two sections which are the sibi-
conjugates of the involution are of course such, that, if the point
P be situate in either of these sections, the corresponding point
Q will be situate in the same section. It may be noticed that
when the two sections 0, ¢ coincide, the line joining the cor-
responding points passes through a fixed point, viz. the pole of
the plane of the coincident sections; in fact the lines PQ and
AB are in every case reciprocal polars, and in the prsent case the
line AB lies in a fixed plane, viz. the plane of the coincident
sections, the line PQ passes therefore through the pole of this
plane. This agrees with the remarks made in the first part of
the present paper.

The analytical investigation in the case where the surface of
the second order is represented under the form 2y—zw=0 is so

210 Mr. A. Cayley on the Homographic Transformation of

simple, that it is, I think, worth while to reproduce it here,
although for several reasons I prefer exhibiting the final result
in relation to the form #?+y?+2*+w?=0 of the equation of the
surface of thesecond order. I considerthen thesurfacexy —zw=0,
and I take («,8,7,8), (a!,6',7',8!) for the coordinates: of the poles
of the two sections 0, &, and (2), 71, 2, W1), (@a; Yar Za) We) as the
coordinates of the points P, Q. We have of course #,y,—z,w,=0,
@oYg—ZoWo=0. The generating lines through P are obtained
by combining the equation ay—zw=O0 of the surface with the
equation 2y,+y2,—zw,;—wz,=0 of the tangent plane at P.
Eliminating x from these equations, and replacing in the result
x, by its value a we have the equation
1

(yz, —2y,) (yw, — wy) = 0.
We may if we please take yz, —zy,=0, wy, + ya, —2w, —wz,=0
as the equations of the line PA; this leads to

2,—2y,=0 } YWa— Wy g=0 }
LY, + ye,—2w, —w2z,=0 Yq + Ylo—2Wy— W2,=0
for the equations of the lines PA, QA respectively ; and we have
therefore the coordinates of the point A, coordinates which must
satisfy the equation Ba+ay—Sz—yw=0 of the plane 0. This
gives rise to the equation
Yo(ay — 921) — Wo V1 — B21) =9-
We have in like manner
yw,—yw=0 Y2_—2Y2=0 }
zy, +ya,—2w, —wz,=0 LYo + YLa— 2ZWy—W2,=0
for the equations of the lines PB, QB respectively ; and we may
thence find the coordinates of the pomt B, coordinates which
must satisfy the equation A'a + a'y—6'z—y'w =0 of the plane ¢.
This gives rise to the equation
yo(aly, —9'w) —22(8'y, — Bm).
It is easy by means of these two equations and the equation
ZYo— ZoW.=0 to form the system
X= (ay, ~ 921) (24, — 9")
Y2= (yy 82) (8'y, — Bu)
= (YY — Ba) (2! —Y'w)
We= (ay, —82,)(S'y, — Pu) 5
or, effecting the multiplications and replacing 2,w, by 2,y,, the
values of 2, Yq) Zg, We contain the common factor y,, which may

be rejected. Also introducing on the left-hand sides the com-
mon factor MM!, where M?@=a8—y8, M'?=a!6!—1/0/, the equa-

a

Vere

a Surface of the Second Order into itself. 211

tions become
MM!2,=7'd2, + aa!y, —a'dz,—ay'w,
MM'y,=f'2, + yy, —Bd'z,—Blyw,
MM'z,= yx, + y2!y, —Balz,— yyw,
MM'w,= 6'd2, + 2b'y, —80'z,—a8'w,,
yalues which give identically x,y,.—z,w .=2\y,—2,- More-
over, by forming the value of the determinant, it is easy to verify
that the transformation is in fact an improper one. We have
thus obtained the equations for the improper transformation of
the surface xy —zw=O0 into itself. By writing 2, +iy,, x,—iy,
for 2, y,, &c., we have the following system of equations, in which
(a, b, c, d), (a', U', c!, d') vepresent, as before, the coordinates of
the poles of the plane sections, and M?=a? +d? +c? + d?,
M?® =a? + 44 ¢?+d?, viz. the system*
MM!z,= (aa! — bb! — cc! — dd!) x, + (ab! +a'b + cd'—c'd)y,
+ (ac! +a'e + db!—d'b)z, + (ad! +a'd+ be! —b'e)w,
MM!'y,= (ab! + ab—cd! + ed) ax, +(—aa! + bb! —ce! —dd')y,
+ (be! + b'e—da! + d'a)z, + (bd! + b'd—ac! + a'c)w
MM'2,= (ac + a'e—db! + d'b)a, + (be! + b'c—ad!' + a'd)y,
+(—aa! —bb! + cc! —da!'\z, + (cd! + bd—ba' + b'a)w,
MM'w,= (ad! + a'd—be! + b'c)x, + (bd' + b'd—ca' + cla)y,
+ (ed! + c'd—ab! + a'b)z, + (—aa! —bb!— ce! + dd! w,,
values which of course satisfy identically 747+ yo? + 297+ w,?
=2rty?+2,°+w,”, and which belong to an improper trans-
formation. We have thus obtained the improper transformation
of the surface of the second order a? + y?+ 2? + w?=0 into itself.
Returning for a moment to the equations which belong to the
surface vy— zw =O, it is easy to see that we may without loss of

generality write 2=@S=a'='=0; the equations take then the
very simple form

MM!2,=y'62,, MM'y,=yd'y,, MM!2.= —yy'w,,
MM'w,= — 882,
where MM'= “ —ydV —/0'; and it thus becomes very easy

to verify the geometrical interpretation of the formule.
It is necessary to remark, that, whenever the coordinates of

* The system is very similar in form to, but is essentially different from,
that which could be obtained from the theory of quaternions by writing
MM (w,+ta.+jy2t kz2)=

(d+ia+jb+ke)(w+ie+jy+kz)(d'+ia'+jb'+ke') ;

the last-mentioned transformation is, in fact, proper, and not improper.

212 On the Transformation of a Surface of the Second Order.

the points Q are connected with the coordinates of the points P
by means of the equations which belong to an improper trans-
formation, the pomts P, Q have to each other the geometrical
relation above mentioned, viz. there exist two plane sections 0, $
such that P, Q are the opposite angles of a skew quadrangle
upon the surface, and having the other two opposite angles in
the sections 0, @ respectively. Hence combining the theory
with that of the proper transformation, we see that if A and B,
BandC...M and N are points corresponding to each other
properly or improperly, then will N and A be points correspond-
ig to each other, viz. properly or improperly, accerding as the
number of the improper pairs in the series A and B, B and
C...M and N is even or odd; 2. e. if all the sides but one of a
polygon satisfy the geometrical conditions im virtue of which
their extremities are pairs of corresponding points, the remain-
ing side will satisfy the geometrical condition in virtue of which
its extremities will be a pair of corresponding points, the pair
being proper or improper according to the rule just explained.

I conclude with the remark, that we may by means of two
plane sections of a surface of the second order obtain a proper
transformation. For if the generating lines through P meet the
sections @, @ in the points A, B respectively, and the remain-
ing generating lines through A, B respectively meet the sec-
tions , 6 respectively in B', A’, and the remaining generating
lines through B', A’ respectively meet in a point P’, then will P, P!
be a pair of corresponding points in a proper transformation. In
fact the generating lines through P meeting the sections 0, ¢ in
the points A, B respectively, and the remaining generating lines
through A, B respectively meeting as before im the poimt Q,
P and Q will correspond to each other improperly, and in like
manner P! and Q will correspond to each other improperly, 7. e.
P and P will correspond to each other properly. The relation
between P, P’ may be expressed by saying that these points are
opposite angles of the skew hexagon PAB! P’A'B lying upon the
surface, and having the opposite angles A, A! in the section 0,
and the opposite angles B, B' in the section ¢. It is, how-
ever, clear from what precedes, that the points P, P’ lie in a
section passing through the points of intersection of 0, ¢, 4. e.
that the proper transformation so obtained is not the general
proper transformation.

2 Stone Buildings, Jan. 11, 1854.

[ 213 ]

| XXXI. On a particular case of Elliptic Integrals whose Para-
meters are Imaginary. By the Rev. James Bootn, LL.D.,
F.R.S. &e*

4 bin are of a spherical parabola may be represented by the
sum of two elliptic integrals of the third order, whose
parameters are tmaginary and reciprocal. The spherical conic
section, whose principal arcs 2a and 28 are connected by the
equation tan? « —tan? 8=1, is called the spherical parabola.
| If we assume the expression given at page 32 of the Theory
of Elliptic Integralst, for an are of the spherical parabola, the
| focus being the pole, and ¢ the augle which the perpendicular
are from the focus, on the tangent are of a great circle to the
curve, makes with the principal transverse arc, y being the modular
angle, or the angle between the focus and the adjacent vertex,

= ————————— i ene 1
) au sin | mses [ V1 —cos?ysin?o+ ()
| Let cosy=i, siny=j. Then differentiating the preceding
equation, it will become, after some reductions,

do _ j[1—? sin? 6 + cos? 6 +7? sin? $] (2)
dp [cos* d — 2? sin? ¢ cos? +7?sin*h] 1 —7 sin?d }
) Now the numerator is equivalent to 2/(1—7* sth? #), and the
) denominator may be written in the form 1 —27* sin? 6+7? sin‘.

But 2?=77(i?+,7"), hence this last expression may be put under
| the form 1—27? sin? 6+74sin* d+7%/? sin*d. This expression
) is the sum of two squares. Resolving this sum into its consti-
) tuent factors, we shal) find
do 2j(1—2? sin? ¢)
ip [1—ifi+j) VW —1)sin?h] [1 —i(i—7 / —1)sin?h] 0/1 —2?sin2h
This product may be resolved into the sum of twoterms. Let
SS eo a SY at oe (4)
1-ii+jV —1)sin’¢] V1 — Paint | [1—i@—j W —1)sin?h | YW 1—sin?’”
or reducing tlicse expressions to a common denominator,
d@_ __(A+B)—(A+B)#sin?¢ + (A—B) VW —1y sin? (5)
Wp [1 —i(i+7 VW —1)sin?] [1—i(i-j VW —1)sin’] 1 — sin?’

(3)

* Communicated by the Author.

Tt The Theory of Elliptic Integrals and the properties of Surfaces of the
second order applied to the investigation of the motion of a body round a
fixed point. 8vo, London, G. Bell. 1851.

: dd ;
o=i fa +j ¥ —l)sin?g] ¥ 1—7*sin?p a

214 On a particular case of Elliptic Integrals. —

Comparing this expression with (3), A+B=2j, A—B=0, or
A=j, B=j. Whence integrating (4), we get

Hence a, the are of a spherical parabola, may be represented by
the sum of two elliptic mtegrals whose parameters are imaginary.

Now if we multiply together the imaginary parameters
(2 +i VY —1) and (#®—¥ / —1), their product is 7’, or the para-
meters are reciprocal.

It is very remarkable, that although the spherical parabola is
a spherical conic, the imaginary parameters satisfy the criterion
of conjugation which belongs to the logarithmic form, and not
that of the circular form. Let m=i(i—j W —1),n=i(i+j7 VW —1).
These values of m and n satisfy the equation of logarithmic con-
jugation m+n—mna=?, and not m—n+mn=?, the condition
of circular conjugation.

The are of a circle may in like manner be represented as the
sum of two imaginary integrals of the logarithmic form, or by
an imaginary arc of a parabola.

Let z= tan@. Then o= f- bal :
1+a?
denominator into its factors, and reducing,

dz dz
29é= SS a er . . «
1+v7%—lz lava (7)

7 4 da i da
—_—-— SS a Se eee aw . . 8
2 SJol+ Faeth, va ®)
Multiply (7) by “—1; then integrating, 3
207-1 11+ v7 —12)—l1— Vv —12),
or . (9)

Hence, resolving the

whence

46 f—1=l1+ V—12)?-lU1— VW —12)2.
Let 2=J, then 0= - whence (9) may be reduced to
7 /—1=log (—1); .
a result we may otherwise obtain. As also = V/V —1=log V=1.

We see, therefore, that the presence of the imaginary symbol
4/—1 indicates a transition from parabolic to circular ares, or
conversely. In a paper published in the Philosophical Transac-
tions for 1852, it has been shown how the transition may be

(ij V—1) sin?) V1 — sim

M. W. Haidinger on the Colours of Mausite. 215

made from the properties of the circle to their analogues in the
parabola.

The difference A between the are of a parabola and its pro-
tangent may be expressed by an imaginary circular are, meaning
by protangent the projection of the radius vector on the tangent

to the curve. As Ry he! let sin O=2z, then A= ae
it, cos @ l-—z
or =f whence ~
ub lily Stilo whys wabowiaggy
Vv —1

This gives a new meaning to the symbol 1/—1. It does not
merely signify a change of angular position through a right
angle; it has a meaning much more extensive. It indicates, as
we have shown*, that a property which is imaginary relatively
to the curve in question, whether it be a circle or a parabola,
becomes real when transferred to the parabola or the circle.
Thus imaginary logarithms represent real circular ares; and
De Moivre’s theorem is an example of a property of imaginary
circular ares, which, when transferred to the parabola, becomes
a real positive geometrical theorem. It would be easy to mul-
tiply examples, the above will suffice.

XXXII. On the Colours of Mausite. By W. Haw1neert.

“PINHE hexagonal saltofiron Fe?0%, SO? + 3(KO)SO? +3H70,

which furnished me such interesting results with respect
to the presence of basic water{, forms crystals which, perpen-
dicular to their axes, allow green light, and parallel to their axes
allow yellow or red-brown light (according to the length of the
six-sided columns or tables) to pass through them. This salt,
however, contains no race of protoxide of iron, but only oxide of
iron, sulphuric acid, potash and water (basic water and water of
crystallization). Under certain circumstances, the same salt
forms a crystalline powder of a beautiful greenfinch colour, a
_tint wherein yellow and green are both distinguishable.”

Thus writes my respected friend Prof. Scheerer of Freiburg,
in a letter addressed to me on the 10th of May, 1853, concern-
ing the crystals whose properties of colour form the subject of
the following remarks.

The above memoi, “Beitrige zur naheren Kenntniss des

* Philosophical Transactions for 1852, part 2. p. 390; also see Cambridge
and Dublin Mathematical Journal for 1853.

+ Translated from Poggendorff’s Annalen, vol. xe. p. 474; having been
communicated to the Academy at Vienna, July 1853.)

ft Poggendorff’s Annalen, vol. xi. p 73.

216 M. W. Haidinger on the Colours of Mausite.

polymeren Isomorphismus,” in Poggendorfi’s Annalen, as well
as Gmelin’s Handbook of Chemistry (vol. im. p. 255), contaim
full descriptions of the above salt, which was first obtamed by
Maus*, and which Scheerer for brevity called Maus’s saltt; a
term which I have here adopted as the root of specific nomen-
clature and transformed into Mausite. The difficulty, almost
impossibility, of forming a systematic chemical nomenclature
will, I think, sufficiently justify the specific name I have pro-
posed in the title.
According to Scheerer, the composition of Mausite is—
Sulphuricacid. . . . 41‘94

Peroxide of iron . . . 20:97
Potash, us: teiemise tk tune
Basic water. . . . .. Q9'4d
Water of crystallization . 7:08

100-00

Analyses were made some time ago by Maus, Anthon and
W. Richter, and since then by R. Richter in Scheerer’s labora-
tory. The latter analysed not only crystals which were obtained
in Scheerer’s laboratory, but other larger ones obtained in
Schweizer’s laboratory at Zurich, by W. Hilgard of Illinois.

According to a later account, crystals of Mausite may be ob- |
tained by simply placing a flat vessel containing a solution of
common alum-iron in a room at the ordinary temperature, and
allowing it there to evaporate. At length Prof. Scheerer sent
me a number of small crystals, which, on an immediate exami-
nation, exhibit properties so unexpected, that I willmgly take
advantage of the last meeting in the academical year to commu-
nicate my observations to the Mathematical and Physical Class ;
even before I have had time, from a process of crystallization
now in progress, to obtain larger specimens upon which, perhaps,
observations may ultimately be made with greater precision.

In agreement with Scheerer’s description, the crystals of
Mausite are regular hexahedral prisms ; those before me measure
about half a line in every direction, though many of equal thick-
ness and in perfectly parallel position group themselves to hexa-
hedral tables which measure as much as three lines. Instead of
the surface at the end, appears a quite flat quartzoid. The
thickness being half a line, I distin-
guish the following tints according to
the usual mineralogical nomenclature.
Colour of the base O hyacinth-red.
Colour of the axis E oliye-green. The
distinction in colour is uncommonly
clear, and increases with the thickness.

* Poggendorff’s Annalen, vol. xi. p. 78. + Ibid. p. 77.

M. W. Haidinger on the Colours of Mausite. 217

It is true the lighter olive-green is sometimes rather more intense,
more yellow, but instead of the red tint a perfectly black one
appears; in the direction of its axis the crystal is opake.
It would be possible to use plates of Mausite, about a line in
thickness, as we use the best tourmaline if they were cut parallel
to the axis, and placed between two polished glass plates. These
small prisms and plates are not so thick, but the tmts may be
best compared through a dichroscopic lens, as shown in the
above figure. When the thickness is less, however, the hyacinth
becomes clearer, it passes into a liver-colour, which exhibits more
and more yellow, and passing through an actual olive-green,
indistinguishable from the colour of the axis in other specimens,
attains a still clearer tint. If a crystal be split with a knife, and
the splinter be magnified sixty times in order to examine it, the
two yellow tints are found almost to coincide, except that the
one is nearly colourless. Microscopes are now often constructed
for polarized light. But when this is not the case, it suffices to
hold’a crystal of Iceland spar between the ocular and the eye.
On the other hand, however, the above-mentioned broader, table-
like groups of crystals are themselves so dark as to have reached
the liver-coloured tint immediately preceding hyacinth-red.
Hence the series of colows for the ordinary and extraordinary
rays are identical,—white, olive-green, liver-colour, hyacinth-red,
black. But the ordinary ray is more absorbed, the darker tints
making their appearance at less thicknesses. At present the
proportion of these thicknesses corresponding to the same tint
for both rays, may be stated as being about 1: 8 or 1: 10, until
future experiments on larger and more complete crystals shall
have furnished numerical data; then, too, it may be decided
whether the more absorbed ray is also most refracted, as required
by the general law which embraces both Babinet’s laws.

The actual object of the present communication, however, is
to direct attention to an indubitable consequence of the above
observations; that is, the proof of the fact that there are
strong dichromatic crystals in which the differences of tint in
different directions do not arise from absolute differences of
colour, but depend upon the greater and less absorption of the
light in passing through such crystals.

Certainly this difference arising from greater and less absorp-
tion could not account for the change of the dark or clear blue
tint of Cordierite into a yellowish-white, or, in darker crystals,
even to a honey-yellow tint ; neither can the blackish-blue (ink-
blue, purple), beautiful violet-blue, and asparagus-green colours
of diaspore arise, one from the other, by greater or less absorption.
Their theoretical consideration, in reference to the position and
form of the colouring bodies, or to the general arrangement of

Phil. Mag. 8. 4. Vol. 7. No. 44. March 1854. Q

218 Royal Society.

the ultimate particles, is consequently much more difficult than
with crystals such as Mausite. Here, notwithstanding the di-
chromatism, one body alone, peroxide of iron, suffices; for it is
sufficient to assume that the particles are so arranged, that when
a ray passes through the hexahedral prism from surface to sur-
face, becoming thereby divided into two polarized perpendicular
to one another, it meets a greater number of material points or
particles with the vibrations of the ordinary ray perpendicular to
the axis, than with those of the extraordinary ray in the direction
of the axis.

Hence the differences of tint, even the olive-green, which in
comparison with hyacinth-red appears still more green, present
no difficulty to this explanation. They depend simply upon
greater or less absorption. On this account, however, the colours
of crystals which contain peroxide of iron in combination with
oxalic acid and alkalies appear all the more enigmatical; for
even when they are dichromatic, the most beautiful grass-green
is coexistent only with quite pale, yellowish-white tints, which
at furthest reach but to olive-green.

XXXII. Proceedings of Learned Societies.
ROYAL SOCIETY.
(Continued from p. 149.]

Dee, 22, 1853.—Thomas Graham, Esq., V.P., in the Chair.

HE following paper was read :—

* An Inquiry into some of the circumstances and principles
which regulate the production of Pictures on the Retina of the Hu-
man Eye, with their measure of endurance, their Colours and
Changes.” By the Rev. W. Scoresby, F.R.S., Corresponding Mem-
ber of the Institute of France, &c,

the case of achromatic pictures; that of coloured pictures of un-
coloured objects, derived simply or mainly from the influence of light
on the eye; and that of the spectra of coloured objects, together
with certain applications of the results obtained to other optical
characteristics, determinations or phenomena.

The general mode of experiment employed in these researches is
described as “‘ the viewing of illuminated objects with a steady fixed
gaze at a special point, and then determining the impression on the
retina by examining the images developed with closed eyes.” The
time of viewing the objects varied from a momentary glance up to
half a minute, more rarely to a minute; and the mode of eliciting
the impression was, primarily, by closing the eyelids into gentlest
contact, whilst the head was kept unmoved, and the eyelids steady

Royal Society. 219

in their original direction. Thus performed, the experiment becomes
yery simple and manageable, and the results, various as they are in
colour or depth of tint, are almost unfailingly elicited and often
curious or beautiful.

Whilst the general result of viewing an illuminated object is the
production of a clearly-defined picture on the retina, appearing in
certain cases instantly, or more commonly, from 3 to 5 seconds after
the eyes are closed,—the nature or quality of the picture, with its
degree of endurance and changes, is found to present, under differ-
ences in the circumstances, an almost endless variety. ‘Thus the
results, it was found, might be varied by differences in the time of
gazing on the object; by differences in the intensity of the external
light, and by the partial or total exclusion of the light of the room
from the eyelids; by alterations in the degree of compression of the
eyelids ; by the movement of the eyeballs during the time of obser-
ving the picture; as also by variations in the normal state of the eyes
on commencing the experiments.

All these influencing circumstances had been made successively,
or sometimes combinedly, the subjects of special investigation by the
author; and ultimately, in most respects, he considered, so far as
his own eyes might be deemed to yield general phenomena, with
satisfactory or conclusive results. Various experiments had heen
made on the spectra derived from light reflected from opake objects
in comparison with those elicited by light transmitted by transparent
substances, both white and coloured; as also on the differences in
the measure of endurance, the variety of their repetitions, and the
phenomena of their changes in colour, of the pictures photographed
within the eye, under curiously modified conditions.

The present communication, however, comprises only a part of
these investigations, the first of the cases referred to at the outset,
viz. inquiries respecting colourless pictures on the retina, derived
from the viewing of objects under low or moderate degrees of light,
or of pictures observed irrespective of chromatic effects.

1, As to the effect of Time in the viewing of an illuminated object,
on the nature and permanency of the picture produced, it was
found that, in fayourable states of the eyes, a mere momentary
glance (such as of a window viewed from the back of a room) was
sufficient for producing a distinct negative picture of the illuminated
aperture, with the cross bars of the window-frame, which, under
certain changes, could be seen ordinarily for about 20 seconds, and
under strong light, sometimes for an interval of a minute or two of
time, if not more. But the impression from a continuous viewing
of a window rather strongly illuminated, for a period of a minute,
was very remarkable, the image remaining on the retina whilst the
experimenter was breakfasting, and also engaged in writing, so as to
be distinctly seen, on slightly closing the eyes, an hour afterwards,
and, in another case which he particularly describes, after a lapse of
80 minutes,

2. Experiments on the effects of quantity or intensity of light, on
the yisual spectra derived from uncoloured objects, showed that

Q 2

220 Royal Society.

such spectra were yielded by extremely low degrees of illumination.
The light, for instance, of the moon or stars thrown on a white
linen blind, produced distinct negative pictures of the slightly illu-
minated aperture. Candlelight gave also negative pictures of white
and black objects. Low illumination from transmitted solar light
gave, in most cases, colourless pictures, appearing sometimes imme-
diately on closing the eyes, as by a flash of light, or otherwise in 3
to 5 seconds in negative tints; these pictures, where the object had
been viewed for some seconds, were found to fade away and subse-
quently reappear in less dark shades, sometimes with several such
changes.

3. The changes in the optical spectra from the partial or entire
exclusion of light from the closed eyelids were found to be very
striking. No matter how this diminution or exclusion of light was
effected,—whether by the thickening of the eyelids by compression,
or turning the face away from the light, or interposing the hand
or other opake substance betwixt the eyes and the light, or covering
the face altogether,-—the spectra assumed a new character as to light
and shadow, ordinarily, but not in all cases, complementary to the
tints originally observed. A total exclusion of the external light
still left the picture clear and distinct, with a continuance, after
occasional changes, little differing from that of other experi-
ments.

4. This measure of fixidity of the spectra impressed on the retina
led the author to some curious results in obtaining duplicate or
multiple pictures of the same object. Thus, by gazing at a window,
successively at different fixed points previously determined on, he
multiplied the cross bars so as to produce a picture of a window with
twice or quadruple the number of panes. A white statuette, viewed
at different points in succession, whilst strongly illuminated, enabled
the author to obtain double pictures in black or gray, associated
according to the relation of the points gazed at, in unlimited variety.
Or viewing the statuette from two positions differing in distance, he
obtained images of different dimensions. Double images, too, were
obtained by using the eyes separately; and also by looking at an
object nearer to the eyes than the statuette, so that the lines of the
axes might diverge at the distance of the statuette, thus beautifully
elucidating one of the chief causes of the indistinctness of vision as
to objects nearer to, or more remote from the eyes than that directly
contemplated.

5. Complete pictures were also obtained by the combination of
parts separately viewed, whilst various impressions, however incon-
gruous, were combined into one picture. Thus parts of the statuette
were viewed, under the adoption of a moveable screen, so as either
to combine the separately-viewed portions rightly, or to transfer one
part, such as the head, to either shoulder, or to adjust two heads in
different positions. Separate impressions, also, of segments of the
statuette were taken on the eyes singly, and these combined, ac-
cordingly as the same or different points of view were selected,
into perfect or distorted pictures. The appearance of the parts of the

Royal Society. 221

resulting spectrum, however, were not always synchronous portions,
sometimes appearing and disappearing by separate or partial changes,
like the effect of the dissolving views of the magic lantern.

6. Pictures, diagrams, printing, &c., were found, under due influ-
ence of light, to yield cognizable and sometimes vivid impressions
on the retina. Diagrams in black and white, or chequered surfaces
like that of a chess-board, gave very distinct pictures, always nega-
tive, the squares coming successively into view, beginning with the
portion gazed at. The succession of changes, when the impression
was strong, in this experiment was not a little curious, the perfect
image of the chess-board after bursting into view, gradually fading
altogether away, and then reviving, in less strung tints, in a series
of repetitions.

Another curious, though anticipated result, the author also de-
scribes under this section,—the determination, by viewing the ocular
spectra, of portions of diagrams or elements in pictorial or typogra-
phical surfaces, which had not been noticed in the act of gazing.
Thus, particularly on viewing a line of printed figures at a particular
point, without noticing those on either side, a considerable series,
right and left, were so plainly depicted on the visual organ as to be
easily known ; whilst, in like manner, a point in a line of a printed
placard being gazed at, the lines above and below came into view on
closing the eyes, and could frequently be read.

Of certain general facts elicited by this first series of investigations,
the author notices, that in viewing impressions on the retina with
closed eyes, all the pictures appear to occupy a position eviernally,
similar to the effect when the objects are directly seen; that the
spectra derived from moderate or strong degrees of transmitted light

‘have prevalently the character of transparency, and those from very
low degrees, most ordinarily, of opacity ; that although many of the
spectral phenomena the author had observed were well known to be
capable of elicitation in the ordinary form of the experiment with
the eyes open, yet the series of phenomena, as a whole, could not
be so elicited, nor was it possible by such form of experiment to
analyse and compare the phenomena whilst in progress of change,
which, in the form he had adopted, were usually exhibited as plainly
as if the spectra were the real and immediate effects of ordinary
direct vision; and that such is the precision and such the cer-
tainty with which the pictures are ordinarily developed, after duly
viewing any illuminated object, that the expected result, so far as the
eliciting of definite pictures is concerned, hardly ever fails.

Jan. 12, 1854,—The Lord Chief Baron, V.P., in the Chair.

A paper was read, entitled ‘‘On some New and Simple Methods
of detecting Manganese in Natural and Artificial Compounds, and
of obtaining its Combinations for ceconomical or other uses.” By
Edmund Davy, Esq., F.R.S., M.R.1.A. &c.

In this paper the growing importance of manganese since its
discovery, and its extensive distribution in Nature are noticed.
Manganese is chiefly found combined with oxygen, but its oxides

222 Royal Society.

are commonly mixed with those of iron, and though different methods
of separating them have been recommended, yet no very simple or
unobjectionable test for manganese seems to be known. ‘Two
methods for detecting manganese are recommended, viz.—

1, The pure hydrated fixed alkalies, potash and soda, and espe-
cially potash. 2. Sulphur. . t

With regard to the first method. Though the compound Cha-
meleon mineral made by strongly heating nitre or potash and
peroxide of manganese together, has long been known, yet it
appears hitherto to have escaped observation, that potash seems
to be a more delicate test of manganese than any other known
substance. The use of potash in this way is simple and easy;
it is employed in solution; equal weights of the alkali and water
form a fluid well-adapted for the purpose; different metals may
be used in the form of slips on which to make the experiments,
but a preference is given to silver foil, as it is less acted on by alka-
lies than platina, and is more readily cleaned. A slip of such foil,
about two or three inches in length and half an inch wide, answers
well. Solids, to be examined for manganese, are finely pulverized ;
fluids require no preparation; the smallest portion of either is mixed
with a drop or part of a drop of the alkali on the foil and heated by
a spirit-lamp (for many experiments a candle affords sufficient heat),
when on boiling the alkali to dryness and raising the heat, the cha-
racteristic green manganate of potash will appear on the foil. The
delicacy of the alkali as a test thus applied, will be obvious on using
the most minute portions of manganese ores in fine powder, and the
author’s son, Dr. E. W. Davy, readily detected manganese in a
single drop of a solution containing one grain of solid sulphate in
ten thousand grains of water. The presence of other oxides do fot
appear to impair the efficacy of this test. A strong solution of
hydrate of soda in water, used in a similar manner, affords an ex-
cellent test for manganese, little inferior in delicacy to potash, but
the latter is shown to be preferable.

Carbonate of soda has long beet regarded as one of the tmost
delicate tests of manganese, especially if aided by a little nitrate or
chlorate of potash, but that carbonate is much inferior as a test for
manganese to potash or soda, requiring a far higher temperature to
form the manganate of soda, and the aid of oxidizing substances,
as nitre and chlorate of potash, which are quite unnecessary with
those alkalies. Borax, too, in point of delicacy is not to be coii-
pared with the fixed alkalies as a test for manganese.

The author is of opinion that the fixed alkalies in solution and
silver foil will form a valuable addition to the agents employed
by the mineralogist and chemist in the examination of minerals,
ores, &c.

2. Sulphur.—If a little flowers of sulphur be mixed with about its
own bulk of the common peroxide of manganese, and exposed on a
slip of platinum foil to a red heat, sesquioxide, sulphuret and sulphate
of manganese will be formed, and by continuing the heat for a short
time, an additional quantity of the sulphate will be produced from

Royal Institution. 228

the sulphuret. On treating the mass with water and filtering the
fluid; a solution of sulphate of manganese will be obtained which
will yield a white precipitate with the ferrocyanide of potassium,
without a trace of iron.

Similar experiments may be made with any manganese ores, or
With substances known or suspected to contain manganese. The
quaitity of materials operated on may be increased or diminished at
pleasure; but if increased, the heat should be continued a little
longer; to decompose any remaining sulphuret, and thus add to the

uantity of sulphate formed. In the same way manganese was

saree in some minerals in which it was known to exist, and in
others in which it had not been previously found; likewise in soils
and subsoils, in the ashes of coal and peat, in a number of pigments,
afid also in the ashes of different fabrics partially dyed brown by
mhangariese.

Sulphate of manganese is formed, with sulphuret, when sulphurous
acid gas is made by heating a mixture of peroxide of manganese and
flowers of sulphur, even in close vessels. The sulphate may also be
more readily obtained, in quantity, by simply boiling a solution of
common green vitriol in water for about a quarter of an hour or
upwards, in contact with an excess of sesquioxide of manganese in
fine powder, till the solution affords a white precipitate with ferro-
cyanide of potassium.

Chloride of manganese inay also be formed in a similar manner by

‘boiling an aqueous solution of protochloride of iron with an excess
of sesquioxide of manganese, or it may be made with greater facility
by dissolving this oxide in the common muriatic acid of commerce,
taking care that the oxide be present in excess.

The brown sesquioxide of manganese may be made, not only by
means of sulphur, but more readily and better by mixing the com-

_ mon peroxide with about one-third of its weight of peat mould, saw-
dust or starch, and exposure to a red heat in an open crucible with
6ecasional stirring for about a quarter of an hour, or until the oxide
acquires a uniform brown colour,

The sulphate and chloride of manganese being extensively used
in dyeing, calico-printing and other arts, and in making the com-
pounds of manganese, the simple means stated of forming those
salts, free from iron (it is presumed), are material improvements on
the circuitous methods hitherto adopted.

ROYAL INSTITUTION OF GREAT BRITAIN.

Jan. 27, 1854.—On the Vibration and Tones produced by the
Contact of Bodies having different Temperatures. By John Tyn-
dall, Esq., Ph.D., F.R.5., Professor of Natural Philosophy, Royal
Institution.

In the year 1805, M. Schwartz, an inspector of one of the smelt

224. Royal Institution.

ing-works of Saxony, placed a cup-shaped mass of hot silver upon a
cold anvil, and was surprised to find that musical tones proceeded
from the mass. Inthe autumn of the same year, Professor Gilbert
of Berlin visited the smelting-works and repeated the experiment.
He observed that the sounds were accompanied by a quivering of
the hot silver; and that when the vibrations ceased, the sound
ceased also. Professcr Gilbert merely stated the facts, and made
no attempt to explain them.

In the year 1829, Mr. Arthur Trevelyan, being engaged in spread-
ing pitch with a hot plastering-iron, and once observing that the
iron was too hot for his purpose, he laid it slantingly against a block
of lead which chanced to be at hand; a shrill note, which he com.
pared to that of the chanter of the small Northumberland pipes,
proceeded from the mass, and on nearer inspection he observed that
the heated iron was in a state of vibration. He was induced by
Dr. Reid of Edinburgh to pursue the subject, and the results of his
numerous experiments were subsequently printed in the Transac-
tions of the Royal Society of Edinburgh.

On. the Ist of April, 1831, these singular sounds and vibrations
formed the subject of a Friday evening lecture by Professor Faraday,
at the Royal Institution. Professor Faraday expanded and further
established the explanation of the sounds given by Mr. Trevelyan
and Sir John Leslie. He referred them to the tapping of the hot
mass against the cold one underneath it, the taps being in many
cases sufficiently quick to produce a high musical note. ‘The alter-
nate expansion and contraction of the cold mass at the points where
the hot rocker descends upon it, he regarded as the sustaining power
of the vibrations. ‘he superiority of lead he ascribed to its great
expansibility, combined with its feeble power of conduction, which
latter prevented the heat from being quickly diffused through the
mass.

Professor J. D. Forbes of Edinburgh was present at this lecture,
and not feeling satisfied with the explanation, undertook the further
examination of the subject; his results are described in a highly
ingenious paper communicated to the Royal Society of Edinburgh
in 1833. He rejects the explanation supported by Professor Faraday,
and refers the vibrations to ‘‘a new species of mechanical agency in
heat ’’—a repulsion exercised by the heat itself on passing from a
good conductor to a bad one. This conclusion is based upon a
number of general laws established by Professor Forbes. If these
laws be correct, then indeed a great step has been taken towards a
knowledge of the intimate nature of heat itself, and this considera-
tion was the lecturer’s principal stimulus in resuming the examina-
tion of the subject.

He had already made some experiments, ignorant that the subject
had been further treated by Seebeck, until informed of the fact by
Professor Magnus of Berlin. On reading Seebeck’s interesting
paper, he found that many of the results which it was his intention
to seek had been already obtained. The portion of the subject

Royal Institution. 225

which remained untouched was, however, of sufficient interest to
induce him to prosecute his original intention.

The general laws of Professor Forbes were submitted in succession
to an experimental examination. The first of these laws affirms
that “‘ the vibrations never take place between substances of the same
nature.’ ‘This the lecturer found to be generally the case when the
hot rocker rested upon a block, or on the edge of a thick plate of the
same metal; but the case was quite altered when a thin plate of
metal was used. ‘Thus, a copper rocker laid upon the edge of a
penny-piece did not vibrate permanently ; but when the coin was
beaten out by a hammer, so as to present a thin, sharp edge, con-
stant vibrations were obtained. A silver rocker resting on the edge
of a half-crown refused to vibrate permanently, but on the edge of
a sixpence continuous vibrations were obtained. ‘An iron rocker on
the edge of a dinner knife gave continuous vibrations. A flat brass
rocker placed upon the points of two common brass pins, and having
its handle suitably supported, gave distinct vibrations. In these
experiments the plates and pins were fixed in a vice, and it was
found that the thinner the plate within its limits of rigidity, the
more certain and striking was the effect. Vibrations were thus
obtained with iron on iron, copper on copper, brass on brass, zine on
zinc, silver on silver, tin on tin. The list might be extended, but
the cases cited are sufficient to show that the proposition above cited
cannot be regarded as expressing a “‘ general law.”

The second general law enunciated by Professor Forbes is, that
“both substances must be metallic.’ ‘This is the law which first
attracted the lecturer’s attention. During the progress of a kindred
inquiry, he had discovered that certain non-metallic bodies are en-
dowed with powers of conduction far higher than has been hitherto
supposed; and the thought occurred to him that such bodies might,
by suitable treatment, be made to supply the place of metals in the
production of vibrations. This anticipation was realized. Rockers
of silver, copper and brass, placed upon the natural edge of a prism
of rock-crystal, gave distinct tones; on the clean edge of a cube of
fluor-spar the tones were still more musical; on a mass of rock-salt
the vibrations were very forcible. ‘There is scarcely a substance,
metallic or non-metallic, on which vibrations can be obtained with
greater ease and certainty than on rock-salt. In most cases a high
temperature is necessary to the production of the tones, but in the
case of rock-salt the temperature need not exceed that of the blood.
A new and singular property is thus found to belong to this already
remarkable substance. It is needless to enter into a full statement
regarding the various minerals submitted to experiment. Upwards
of twenty non-metallic substances had been examined by the lecturer,
and distinct vibrations obtained with every one of them.

‘The number of exceptions here exhibited far exceeds that of the
substances which are mentioned in the paper of Professor Forbes,
and are, it was imagined, sufficient to show that the second general
law is untenable.

The third general law states, that ‘‘ The vibrations take place

226 Royal Institution.

with an intensity proportional (within certain limits) to the difference
of the conducting powers of the metals for heat, the metal having
the least conducting power being necessarily the coldest.” ‘The
evidence adduced against the first law appears to destroy this one
also; for if the intensity of the vibrations be proportional to the
difference of the conducting powers, then where there is no such
difference there ought to be no vibrations. But it has been proved
in half a dozen cases, that vibrations occur between different pieces
of the same metal. The condition stated by Professor Forbes was,
however, reversed. Silver stands at the head of conductors; a strip
of the metal was fixed in a vice, and hot rockers of brass, copper;
and iron were successively laid upon its edge: distinet vibrations
were obtained with all of them. Vibrations were also obtained with
a brass rocker which rested on the edge of a half-sovereign. ‘These
and other experiments show that it is not necessary that the worst
conductor should be the cold metal, as affirmed in the third general
law above quoted. Among the metals, antimony and bismuth were
found perfectly inert by Professor Forbes; the lecturer, however,
had obtained musical tones from both of these substances.

The superiority of lead as a cold block, Professor Faraday, as
already stated, referred to its high expansibility, combined with its
deficient conducting power. Against this notion, which he con-
siders to be “an obvious oversight,” Professor Forbes contends in
an ingenious and apparelitly unanswerable manner. ‘The vibrations,
he urges, depend upon the difference of temperature existing be-
tween the rocker and the block; if the latter be a bad conductor
and retain the heat at its surface, the tendency is to bring both the
surfaces in contact to the same temperature, and thus to stop the
vibration instead of exalting it. Further, the greater the quantity
of heat transmitted from the rock to the block during contact, the
greater must be the expansion ; and hence, if the vibrations be due
to this cause, the effect must be a maximum when the block is the
best conductor possible. But Professor Forbes, in this argument,
seems to have used the term expansion in two different senses. The
expansion which produces the vibration is the sudden upheaval of
the point where the hot rocker comes in contact with the cold mass
underneath; but the expansion due to good conduction would be an
expansion of the general mass. Imagine the conductive power of
the block to be infinite, that is to say, that the heat imparted by the
rocker is instantly diffused equally throughout the block; then,
though the general expansion might be very great, the local expan-
siofi at the point of contact would be wanting, and no vibrations
would be possible. The inevitable consequences of good conduction
is to cause a sudden abstraction of the heat from the point of con-
tact of the rocker with the substance underneath, and this the lec-
turer conceived to be the precise reason why Professor Forbes had
failed to obtain vibrations when the cold metal was a good conductor.
He made use of blocks, and the abstraction of heat from the place of
contact by the circumjacent mass of metal was so sudden as to ex-
tinguish the local elevation on which the vibrations depend. In the

Intelligence and Miscellaneous Articles. 227

experiments desctibed by the lecturer, this abstraction was to a
great extent avoided by redticing the metallic masses to thin lamine ;
and thus the very experiments adduced by Professor Forbes against
_ the theory supported by Professor Faraday appear, when duly con-
sidered, to be converted into strong corroborative proofs of the cor-
rectness of the views of the philosopher last mentioned.

XXXIV. Intelligence and Miscellaneous Articles.

ELECTRO-DEPOSITION OF ALUMINIUM AND SILICIUM.
BY GEORGE GORE, ESQ.

To the Editors of the Philosophical Magazine and Journal.

8 Broad Street, Birmingham,

_ GEenTLeMeEN, February 24, 1854.
aimee are two speciinens of sheet copper, one coated with

metallic aluminium and the other with silicium, by electro-
deposition process; and if the following simple statement of the
manuer in which they were obtained is worthy of a place in your
Magazine, I shall"be happy to have it published.

To obtain the aluminium, I boiled an excess of dry hydrate of
alumina in hydrochloric acid for one hour, then poured off the clear
liquid, and added to it about one-sixth of its volume of water; in
this mixture [ placed an earthen porous vessel contaiuing one mea-
sure of sulphuric acid to twelve measures of water, with a piece of
amalgamated zinc plate in it. In the chloride of aluminium solution I
immersed a piece of copper of the same amount of immersed metallic
surface as that of the zinc, and connected it with the zinc by means
of a copper wire, and set it aside for several hours; when of exami-
ning it, I found it coated with a lead-colour deposit of aluminium,
which when burnished possessed the same degree of whiteness as
platinum, and did not appear to tarnish readily by immersion in
cold water or in the atmosphere, but was acted upon by sulphuric
or nitric acids, either concentrated or dilute.

I found that if the apparatus was kept quite warm, and a cop-
per plate much smaller than the zinc plate was used, the deposit
appeared in a very short time, in several instances in less than half
a minute. Also J found that if the chloride solution was not diluted
with water, the deposit was equally, if not more rapid.

I have also succeeded in obtaining a quick deposit of aluminium
in a less pure state by dissolving ordinary ‘ pipe-clay”’ in boiling
hydrochloric acid, and using the supernatant clear solution undiluted
with water in the place of the before-mentioned liquid. A similar
deposit of aluminium was also obtained from a strong aqueous solu-
tion of acetate of alumina; likewise from a saturated aqueous solu-
tion of ordinary ‘‘ potash alum,” but rather slowly; with each of
the solutions named, the deposit was hastened by putting either one,
two, or three small Smee’s batteries in the circuit.

228 Intelligence and Miscellaneous Articles.

To obtain the deposit of silicium, I dissolved monosilicate of pot-
ash (formed by fusing together 1 part of silica with 21 parts of car-
bonate of potash) in water, in the proportion of 40 grs. to 1 oz.
measure of water, proceeding in like manner as with the alumina
solutions, the process being hastened by interposing one pair of small
Smee’s battery in the circuit. With a very slow and feeble action
of the battery, the colour of the deposited metal was much whiter
than that of the aluminium, closely approximating to that of silver;
its other properties I have not yet had time to examine.

1 I remain,
Yours very truly,
GrorcE Gore.

EXPERIMENTS ON THE ARTIFICIAL PRODUCTION OF POLYCHROISM
IN CRYSTALLIZED SUBSTANCES. BY M. DE SENARMONT.

In some researches upon crystallization which the author has
pursued for several years, he has been led to study the absorption
of light which takes place in coloured crystals, and the polychrojsm
which accompanies it.

This singular property, which is possessed by many minerals and
artificial products, consists essentially in the circumstance that the
two luminous rays resulting from double refraction undergo in
the interior of the crystal an unequal extinction in their colorific
elements, so that a pencil of white natural light is separated on its
emergence from the crystal into two pencils of different colours at
the same time that they are polarized at a right angle.

It may be inquired whether such a phenomenon must be neces-
sarily and exclusively caused by the coloration, either of the crystal
itself, or of some other substance chemically combined with it; and
whether it may not sometimes be the effect of two different and
coexistent causes, as a birefractive power exerted by the crystalline
matter itself, and an absorbent power exercised by some foreign
colouring matter accidentally distributed in the interstices of the
crystal, like the impurities which crystals derive from their mother-
liquors. This question can only be decided by synthesis; it would
be solved if we could succeed in introducing into crystalline salts all
sorts of colouring matters, incapable of forming a chemical union
with them, but capable of incorporating themselves by a sort of
impregnation.

The problem, put in these terms, appears more simple than it
really is. For dichroism, selecting different colours for suppression
in each of the refracted rays, it is impossible that its cause can be
quite independent of that which thus splits the luminous rays in
crystalline refraction. The absorbent agent, whatever it may be,
must, on the contrary, be connected and in some degree subordi-
nated to the crystallization; and if it may reside in coloured non-
crystalline particles, it is at least necessary that their arrangements
should be continuous to a certain point with the crystalline medium,

Intelligence and Miscellaneous Articles. 229

that they should be symmetrically arranged by their interposition
amongst the essential materials of the molecular edifice, and so
adapted to its structure as to participate in its regular arrangement.

The question, therefore, was to find colouring principles of suffi-
cient tenuity to be, as it were, assimilated by the crystals during
their formation, to become distributed almost molecularly in their
interior without forming accumulations in any one portion of their
substance ; and it was necessary to find salts witha molecular tissue
sufficiently loose to form regular and homogeneous crystals in
strongly coloured, and consequently very impure mother-liquors,
whilst nevertheless their formation was not accompanied by a suffi-
ciently energetic eliminatory process for the total expulsion of all
foreign matters; lastly, even when all these conditions were fulfilled,
it still remained doubtful whether the production of polychroism
would take place in this medium; for nothing proves it to be inhe-
rent in every kind of coloration, and its effective conditions are
absolutely unknown.

The author now lays the following facts, the principal result of an
immense number of experiments, before the Academy.

A colouring matter, disseminated continuously in the interior of
a crystal between its laminz of growth, but absolutely foreign to
the substance, and capable of spontaneous elimination by simple
recrystallization from pure water, may nevertheless communicate a
property of polychroism and an energy of absorbent action, equal, if
not superior, to those of natural coloured bodies, in which these pro-
perties are most distinctly manifested.

The author exhibited large crystals of nitrate of strontia formed
in a tincture of logwood which had been rendered purple by a few
drops of ammonia. ‘The crystals thus acquired a colour like that of
chrome-alum, and a sufficiently distinct polychroism to exhibit the
following phenomena : —

1. Natural white light produces by transmission under certain
incidences a red, and under others a blue or violet colour.

2. Observed with a doubly refractive prism, these crystals are
resolved into two images, one red, the other deep violet, according:
to the thickness; and these images change colours by passing
through the intermediate shades in proportion as the crystalline
plate turns in its own plane.

3. Two similar transparent plates superposed in a parallel orien-
tation permit the passage of a portion of the incident white light as
a bundle of purple rays; superposed at right angles, they arrest it
like the tourmalines, or at all events reduce it to a violet tint of such
obscurity that it may be considered as destroyed.

4. Another phenomenon may also serve, if necessary, as a pal-
pable demonstration of the intimate connexion established in this
compound medium, between the absorption thus artificially produced
and the natural birefractive properties.

From these crystals, perfectly homogeneous lamin, slightly in-
clined towards the optical axes, may be separated; when a lamina
of this kind is placed very close to the eye and illuminated by natural

230 Intelligence and Miscellaneous Articles.

white light, there will be seen ultimately, in the direction of each of
these axes, a brilliant orange spot traversed by a hyperbolic branch.
These expand to the right and left of the principal section in the
form of curved pencils, half violet and half dark blue, and divide the
field of the lamina into two regions, in which the purple tints gra-
dually become degraded on either side of their common limit.

The dark tufts interrupted by the luminous spot are also fringed.
towards the point with a little yellow and blue; this coloration is
entirely local, and manifestly arises from the dispersion of the optical
axes corresponding with the different colours. This dispersion is,
in fact, pretty distinct in nitrate of strontia.

These appearances, perfectly characteristic of the polychroism of
crystals with two optical axes, and absolutely identical with those
first observed by Brewster in Cordierite, found by Haidinger in an-
dalusite, and tolerably distinct in some varieties of epidote, are
manifested with much greater splendour in the large laminz which
may readily be prepared with nitrate of strontia, In their natural
state the colourless crystals exhibit nothing similar, and the optical
axes only become visible by means of polarized light. Other suit-
able colouring matters and other crystallized salts produce analogous
effects in various degrees.—Comptes Rendus, Jan. 23, 1854, p. 101.

ON ALUMINIUM AND ITS COMPOUNDS. BY M. DEVILLE.

It is known that Wohler obtained the metal aluminium in the
state of a powder by treating the chloride with potassium. By a
suitable modification of Wohler’s process, the decomposition of the
chloride of aluminium can be regulated so as to produce a tempera-
ture sufficient for the particles of the metal to agglomerate into
globules. If the mass composed of the metal and chloride of
sodium (sodium is preferable to potassium) is exposed to a bright
red heat in a porcelain crucible, the excess of chloride of aluminium
is expelled, and there is left a saline mass with an acid reaction in
which are disseminated more or less large globules of perfectly pure
aluminium.

This metal is as white as silver, and in the highest degree mal-
leable and ductile. When wrought, however, it exhibits greater
resistance, and its tenacity probably approaches that of iron. It is
hardened by hammering, but reacquires its softness on being re-
heated. Its fusing-point differs but slightly from that of silver; its
specific gravity =2°56; it can be smelted and cast without being
perceptibly oxidized; it is a good conductor of heat. It is not in
the least affected by moist or dry air, does not tarnish, but remains
bright by the side of zinc and tin freshly cut, which soon become
dul]. Sulphuretted hydrogen has no action upon it, cold water does
not alter it, boiling water does not tarnish it. It is not acted upon
by nitric acid, weak or strong, or by weak sulphuric acid, employed
cold. Its true solyent is hydrochloric acid, with which it forms

Meteorological Observations. 231

chloride of aluminium, Heated to redness in hydrochloric acid gas
it furnishes dry volatile chloride of aluminium.

It will be readily understood what important uses such a metal,
which is white and unalterable like silver, which does not blacken
in the air, is fusible, malleable, ductile and tenacious, and has in
addition the singular property of being lighter than glass, may be
turned to if it can be obtained readily. This I have every reason
to believe will prove to be the case, for the chloride of aluminium is
decomposed with remarkable ease by the common metals at an ele-
vated temperature ; and a reaction of this kind, which I am attempt-
ing to carry out on a large scale, will solve this question in a prac-
tical point of view.—Comptes Rendus, February 6, 1854.

METEOROLOGICAL OBSERVATIONS FOR JAN. 1854.

Chiswick.—January 1. Clear and frosty: snowing: frosty. 2. Frosty through-
out: severe frost at night. 3. Severe frost, with fog: overcast. 4. Overcast and
cold: snow 7 inches deep. 5. Thick haze: rain and sleet: 2 inches additional
depth of snow. 6. Hazy. 7. Heavy rain. 8. Clear and fine. 9. Rain: foggy:
rain at night. 10,11. Cloudy and cold. 12. Cloudy: slight rain. 13. Slight
haze: clear. 14. Clear: hazy. 15. Foggy: cloudy. 16. Dense fog: overcast.
17. Cloudy. 18. Densely clouded: overcast. 19. Dense fog. 20. Rain: over-
cast. 21. Fine: frosty. 22. Frosty haze: clear and fine: overcast: frosty. 23.
Foggy: very fine. 24. Cloudy and windy: rain: frosty. 25. Frosty: clear and
fine: cloudy. 26. Fine: very clear. 27. Densely overcast: rain. 28, Slight
rain: cloudy: clear. 29. Boisterous, with rain: overcast. 30. Cloudy and mild:
clear. 31. Overcast: cloudy.

Mean temperature of the month ........ Bara ore iesaeesen-peeoe OH
Mean temperature of January 1853 ......... erate stye ssedeuip mien EL
Mean temperature of Jan. for the last twenty-eight years . 36 °68
Average amount of rain in Jan. ....... Setats sah -aevaee ean eee 1°74inch,

Boston.—Jan. 1. Fine. 2. Cloudy: snow aM. and p.m. 3. Cloudy: thermo-
meter at 8 a.m. 5°. 4, Stormy: snow-storm a.m. and p.m. 5.,Cloudy. 6.
Cloudy: snow a.m. 7. Cloudy: raine.m. 8, Cloudy: raina.m. 9—13. Cloudy.
14, Fine. 15. Cloudy: rain early a.m. 16—19. Cloudy. 20. Cloudy: rain p.m.
21. Cloudy. 22,23. Fine. 24. Cloudy: rain a.m. 25. Fine. 26. Fine: rain a.M.
27. Cloudy. 28, 29. Cloudy: raina.m. 30. Fine. 31. Cloudy.

Sandwick Manse, Orkney.—Jan. 1. Snow-drift a.m.: snow-showers P.M. 2,
Bright a.as.: cloudy p.m. 3, Bright a.m.: snow-showers p.m, 4. Bright a.m.:
clearp.m. 5. Bright a.m.: snow-showers p.m. 6. Bright A.m.: clear p.m. 7.
Thaw a.m.: sleet and rain p.m. 8. Sleet-showers a.m. and p.m. 9. Bright,
frost A.M.: cloudy p.m. 10. Bright, frost a.m.: clear p.m. 11. Clear, frost a.m.:
clearp.mM. 12. Snow-showers a.m. snow-drift, showers p.m. 13. Clear, fine 4.m.
cloudy p.m. 14. Cloudy a.m.: clear, frost p.m. 15. Bright a.m. : clear, aurora
p.M. 16. Bright A.m.: rain p.m. 17. Cloudy a.m.: clear, aurora p.m. 18. Bright
AM.: cloudy, aurora p.m. 19. Bright a.m.: cloudy p.m. 20. Bright a.m.:
cloudy, aurora p.m. 21, 22. Cloudy a.m. andp.m. 23. Clear a.m. : cloudy, aurora
p.m. 24. Cloudy a.m.: clear p.M. 25. Cloudy a.m.: sleet-showers, lightning p.m.
26. Hail-showers a.m. : cloudy p.m. 27. Cloudy a.m.: showers P.M. 28. Showers
AM. and p.m. 29. Showers a.M.: showers, aurora p.M. 30. Drizzle a.M.:
drizzle, aurora p.m. 31. Showers a.m.: cloudy P.M.

Mean temperature of Jan. for twenty-seven previous years .., 38°°46
Mean temperature of this month — ....+.++ Sddvenvecssaidetvenseaee 36 *47
Mean temperature of Jan. 1853 — seccsssssssssessccerecseeseenees 38 55

Average quantity of rain in Jan. for thirteen previous years . _4"35 inches.

Pein abel

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e THE
LONDON, EDINBURGH ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

APRIL 1854,

XXXV. On the Composition and Metamorphoses of some Sedi-
mentary Rocks. By 'T. 8S. Hunt, of the Geological Commission
of Canada*.

a the Report of Progress of the Geological Survey of Canada

for 1851-52, I have described a peculiar metamorphosis of
a portion of the Lower Silurian shales at St. Nicolas, on the
south side of the St. Lawrence, near Quebec. The rocks there
exposed have been minutely described by Mr. Logan; they
belong to that division of the formation which is known as the
Hudson River group, and consist of beds of greenish, quartzose
sandstones, from one to three feet in thickness, interstratified
with thin layers of greenish, bluish, or reddish shales. The
colours of these are probably connected with different states of
oxidation of the iron which they contain. The green colour is
sometimes seen in small oblong rounded patches in the red shale,
and when in a mass of the latter a layer of from half an inch to
an inch of somewhat calcareous matter occurs, it is bounded
above and below by a portion of green slate, sometimes no more
than a quarter of an inch in thickness. In one section near
Pointe Lévy, the green colour was seen following down a rift in
the red slates across the stratification, and spreading irregularly
on either side. Such modes of occurrence seem to indicate a
deoxidation of the red slates by imbedded or infiltrating organic
matters.

Mr. Logan had observed that an intrusion of trappean rocks
at St. Nicolas has altered the shales, and converted them into a
material resembling serpentine; and as his researches in the

* Communicated by the Author.

Phil. Mag. S. 4. Vol. 7. No, 45. April 1854. R

234 Mr. T. 8. Hunt on the Composition and Metamorphoses

Eastern Townships have shown that the serpentines of that
metamorphic region belong to Lower Silurian strata, of which
these rocks at St. Nicolas are the stratigraphical equivalent, it
was hoped that a chemical examination of them, and a compa-
rison between the altered and unaltered shales, would throw
some light upon the nature of that widely-spread metamorphism,
and upon the origin of serpentine. The results obtained were
different from what was expected, but are not, however, without
interest.

In the immediate vicinity of the intrusive rock thin layers of
the shale are changed into a greenish translucent material, which
is sometimes an inch in thickness. The surfaces of the sand-
stone in contact with the shale seem to have undergone a similar
change, or at least to be covered with a film of the green trans-
lucent mineral, and they often exhibit a concretionary or mammil-
lated surface. In one instance the thickening of a stratum of
shale forms a mass several inches in diameter, which is earthy
and opake within, but upon the surface next to the overlying
rock assumes the serpentine-like character alluded to; and in a
continuation of the layer, where it becomes thinner, the trans-
formation is complete. In the interstratified sandstones, which
are sometimes conglomerate, masses of the same green mineral
are found ; and it was also observed filling fissures in fragments
of a bright red, and much indurated shale, which had fallen
from a high part of the cliff.

This green mineral is found by chemical analysis to be distinct
from serpentine, and is essentially a hydrous silicate of alumina,
protoxide of iron and potash, with small portions of soda, lime
and magnesia. Its greater density serves also to distinguish it
from serpentine. It occurs in schistose masses with a granular
texture, also botryoidal, with appearance of concentric structure,
and a conchoidal fracture. Hardness 2°5 to 3:0. Density of
the schistose specimens 2°68 to 2°71; of the botryoidal, 2°78.
Lustre waxy, shining ; streak white; powder unctuous; colour
greenish-white, yellowish-green, olive-green, often mottled ;
translucent, subtranslucent. Very fragile, especially when moist-
ened; sectile; the light-coloured portions resemble in appear-
ance some specimens of indurated talc.

To distinguish this material, and to recall its resemblance to
ophite or serpentine, I provisionally gave it the name of par-
ophite, without, however, claiming for an amorphous product of
the alteration of a sedimentary rock the rank of a distinct mineral
species. I give in connexion with some analyses of this sub-
stance, one of the unaltered schist, which passes in a little distance
into parophite. The colour of the schist is dark ash-gray, some-
times marked with red; the lamin are somewhat curyed, their

of some Sedimentary Rocks. 235

surfaces glimmering and slightly unctuous; it is completely
earthy, opake even upon the edges, and very soft, yielding with
ease to the nail; the powder is not at all gritty. ~

The parophite loses water when exposed to heat and turns
gray; it is but imperfectly decomposed by hydrochloric acid.
The following analyses were made by fusion with carbonate of
soda, and the alkalies were determined by decomposing a second
portion with fluor-spar and sulphuric acid. Analyses I. and II.
are of schistose parophite, III. of the botryoidal variety, and IV.
of the earthy schist which passes into I.

I. iT, Il. Iv,
ew . eee OU 48°42 49:13 48°10
BagTINA 4. OY OU 27°60 27°80 28°70
Protoxide of iron. 5°67 4°50 5:90 4°80
oS aerate aera 05% | 2:80 3°80 2°10
Magnesia . . . 2°20 1:80 1:40 1:41
SS a ae 5°30 5:02 : : 4°49
atl genet: CF Oiiakbeiee 5 ane aca Sac aeraiee let
ne. SRR 7°40 6°88 6°30 8°40

100°49 99°80 100:00 99°53

Traces of manganese were found in all of them.

These analyses show that the change consists only in a che-
mical union of the finely divided mixture which makes up the
sedimentary rock. Prof. C. U. Shepard described some time
since by the name of dysyntribite, an aluminous silicate which is
found in St. Lawrence County, New York, and had been mis-
taken for serpentine, which it resembles in colour, lustre, and
general appearance ; it has, according to him, a hardness of 3°5
to 4-0, and a density of 2°76 to 2°81. He gave the following”
analytical results :—silica, 47°68; alumina, 41°50; protoxide of
iron, 5°48; water, 4°83; and traces of lime and magnesia ;
=99°49*. Notwithstanding the resemblance of this to the

arophite of St. Nicolas, the differences in composition, particu-

ly in the large amount of alumina and the absence of alkalies,

according to the analyses of Prof. Shepard, were such that we
supposed the rocks to be distinct.

The recent analyses of dysyntribite by J. Lawrence Smith and
G. Brush have, however, shown that this substance, although of
variable composition, contains a large amount of potash, and in
many specimens approaches the parophite. They obtained from
44°7 to 46°7 per cent. of silica, and from 4°7 to 6:3 of water ;
while the alumina varied from 31 to 35 per cent., and the oxide

* Report of the American Association for the Advancement of Science,
vol, iv. p. 311.
R 2

236 Mr. T. S. Hunt on the Composition and Metamorphoses

of iron from 3 to 4, These specimens also contained, besides
minute quantities of lime and magnesia, from 10°5 to, 11°5 per
cent. of alkalies in which the soda varied from a trace to 3°6 per
cent. Other specimens afforded 8 to 12 per cent. of lime, 7 to
8 of magnesia, and from 4 to 6 per cent. of potash, with traces
of soda; the proportions of silica, water, and oxide of iron being
the same*.

According to Prof. Shepard, this material is often associated
with the deposits of specular iron ore in the crystalline limestones
and felspathic rocks, which in northern New York underlay the
Lower Silurian strata, and are by Dr. Emmons of the New York
Geological Survey, regarded, the limestones and iron included,
as hypogene rocks. he researches of Mr. Logan upon the ex-
tension of these rocks into Canada, where they are very widely
spread, have, however, shown them to be undoubtedly altered
sedimentary deposits, leading us to infer in both cases a similar
origin for these hydrous alkaline silicates.

The large amount of alkalies in the schists of St. Nicolas is
worthy of notice, because the small quantity remaining in kaolin
and some other clays seems to have given rise to an idea that
such sedimentary rocks are generally deficient in alkaline ingre-
dients. Another red slate from the Etchmin river, belonging
to the same strata as the last, afforded the following analytical
results :—

Siena.) ais. 22) 03 keke OED
Alumina and protoxide of iron 24°60
POtaaRS Tip ei ar Sen eae er are
SDA ick wba or alal dae peers
Lime and magnesia. . . . traces
AVater, 7 eo P28 6 awe yar

99°49

Although more siliceous, it resembles that of St. Nicolas in
the large proportion of alkalies and the predominance of potash.
A glance at the first analyses will show that that slate under
igneous action might produce a large amount of a potash felspar
hike orthoclase, together with an alumino-ferruginous augite ; it
is, in fact, the almost unchanged detritus of old felspathic and
pyroxenic rocks, and is converted into similar rocks in the meta-
morphic region further south.

The following analyses were made for the purpose of deter-
mining the chemical composition of good roofing-slates, but are
not without value to the chemical geologist. No. I. is from
Kingsey in the Eastern Townships, and, like those already de-

* American Journal of Science (2), vol. xvi. p. 50.

of some Sedimentary Rocks. 237

scribed, is Lower Silurian ; it is purplish-blue in colour, com-
pletely opake, with a feeble glimmering lustre on its cleavage
planes, which are nearly at right angles to the bedding density
2884. No. II. is an Upper Silurian slate from Westbury,
Eastern Townships ; it is greenish-blue, with a silky surface, and
is translucent on the edges; density 2°711. Both of these are
excellent roofing-slates. No. III. is a Welsh roofing-slate closely
resembling No. I. in appearance, with a density of 2°824; and
No. IV. is from the quarries of Angers in France, very like No. II.,
but more translucent, with a pearly lustre on its cleavage sur-
faces, and somewhat talcose; density 2°882. The analyses were
made by fusion with carbonate of soda, and the alkalies deter-
mined by decomposing a separate portion with a mixture of car-
bonate of lime and sal-ammoniac, after the method of Dr. J.
Lawrence Smith.
ib Il. Ill. Vi.

pica, «rd» .. 5480 65°85 60°50 57:00

BRB 69) 4). ) « BOL 16°65 19°70 20°10

Protoxide of iron. 9°58 5°31 7°83 10:98

BBE Go undithy oa, dO6 39 112 1:23
Magnesia . . . 2°16 2°95 2°20 3°39
BOSD. ve... BST 374 3°18 1:73
BMS bas Jia abs ey eee 131 2°20 1:30
Beet)» lek «ears 0390 3°10 3°30 4-40

100°24 99°50 100°03 10013

It is probable from the colour, that a part of the iron in I.
and III. exists as peroxide ; traces of manganese were detected in
all of them. The last specimen had been exposed to the weather
upon the roof of a house for nearly a century, and this may
account for the smaller quantity of alkalies which it contains.
When finely elutriated, these slates give to the water a distinctly
alkaline reaction, and to such a solvent process is to be ascribed
the deficiency of alkalies in the schist of St. Nicolas compared
with the associated parophite, with which this reaction is much
less distinct. In our Geological Report of last year, from which
these analyses are taken, I have had occasion to point out the
relation between these slates and the alkaline mineral springs
which are so abundant in this region. These waters contain,
besides alkaline chlorides, large portions of alkaline carbonates,
with borates and silicates, the chlorides frequently constituting
the smaller part of the solid contents. Some of these springs
are further remarkable from the large proportion of potash which
they contain, in one instance amounting to one-fourth of the
alkaline salts present, when estimated as chlorides of potassium
and sodium.

238 On theComposition and Metamorphoses of Sedimentary Rocks.

The post-pliocene clays of the St. Lawrence valley also con-
tain a large proportion of alkalies ; they are sometimes calcareous,

and afford, besides carbonates of these bases, a considerable °

amount of lime and magnesia as silicates. The following results
were obtained with a reddish-fawn coloured clay from the Riviere
a la Graisse, Rigaud ; it is impalpable, and remains a long time
suspended in water. It yields to heated hydrochloric acid 12-95
per cent. of alumina and peroxide of iron, 3°97 of lime and 1-92
of magnesia; the amount of carbonic acid evolved isa little more
than is required to form a carbonate with the lime thus obtained.
Its complete analysis gave—

Silica (by difference) . . . 50°81

Aluming? wore she DIA BLO
Peroxide of iron. . . . . 5:60
Lainiesese; dhosely. isn es Op
Miarthesiatrs }it fosnn tx5 outst hea PAGE
CHET scat. eek See aes, ee BSB
SI ve, eer ee
Phosphoric etd .hes) S207 5 "74
Onrbonic acid’ «i ot aN ete EBS
Western NE tke MARS a ep he

100-00

Another clay from the vicinity of Montreal, which was mixed
with 13°5 per cent. of siliceous sand and a little magnetic iron,
and was free from earthy carbonates, afforded (the sand included)
the following results :—

Silica (by difference) . . . . . 65°53
FIL CT MS SD Ae ae aD 13:15
Peraxule of itom~ =i 2). 38) Pee” 1 BO
Ringe eke We PRS ae a
Magnestai! ) ig hele Othe posers
Potash 20970 SOR RRO OH RS
Bade. iF Jo Pitot kh See Ae
Phosphoric atid «ff Le ‘54
Water and some organic matter . 5°30

100-00

The first of these clays, in the proportions of silica, alumina,
lime and alkalies, approaches some of the lime felspars, and its
metamorphosis might yield a mixture of andesite or labradorite,
with hypersthene, constituting a rock similar to one which is
very abundant in our older ante-Silurian strata, and may very
well have been the source of this clay.

Montreal, Canada, Feb. 20, 1854.

eid

[ 239 ]

XXXVI. On the Mechanical Action of Heat. By Wi111aM Joun
Macaquorn Rankine, C.H., F.R.SS. Lond. and Edinb. &c.
[Concluded from p. 185.]

[With a Plate. |
On the Power and Giconomy of Single-acting Expanswe Steam-

engines, being a Supplement to the Fourth Section of a Paper
© On the Mechanical Action of Heat*.’

(34.) Hage objects of this supplementary paper are twofold :

first, to compare the results of the formule and
tables relative to the power of the steam-engine, which have been
deduced from the dynamical theory of heat, with those of expe-
riments on the actual duty of a large Cornish engine at various
rates of expansion; and secondly, to investigate and explain the
method of determining the rate of expansion, and, consequently,
the dimensions and proportions of a Cornish engine, which,
with a given maximum pressure of steam in the cylinder at a
given velocity, shall perform a given amount of work at the least
possible pecuniary cost, taking into account the expense of fuel,
and the interest of the capital required for the construction of
the engine.

This problem is solved with the aid of the tables already
printed, by drawing two straight lines on a diagram annexed to
this paper (Plate IJI.).

The merit of first proposing the question of the ceconomy of
expansive engines in this definite shape belongs, I believe, to the
Artizan Club, who have offered premiums for its solution ; having
done so (to use their own words) “ with a view to enable those
who, from their position, cannot take part in the discussions of the
various scientific societies, to give the profession the benefit of
their studies and experience.” The 5th of April is the latest
day fixed by them for receiving papers ; and as this communica-
tion cannot possibly be read to a meeting before the 7th of April,
nor published until some months afterwards, I trust I may feel
confident that it will not be considered as interfering with their
design.

Formule applicable to the Cornish Engine.

(35.) The equations of motion of the steam-engine in this and
the original paper are the same in their general form with those
of M. de Pambour. The differences consist in the expressions
for the pressure and volume of steam, and for the mechanical
effect of its expansion ; the former of which were deduced from
a formula suggested by peculiar hypothetical views, and the
latter from the dynamical theory of heat.

* Read to the Royal Society of Edinburgh, April 21, 1851.

240 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

Those equations are Nos. (50) and (51) of the original paper.
I shall now express them in a form more convenient for practical
use, the notation being as follows :—

Let A be the area of the piston.

J, the length of stroke.

n, the number of double strokes in unity of time.

c, the fraction of the total bulk of steam above the piston
when down, allowed for clearance and for filling steam-passages ;

so that the total bulk of steam at the end of the effective stroke is_

IA
Pai ot ur evo ode er ketene

I’, the length of the portion of the stroke performed when the
steam is cut off.
s, the ratio of expansion of the steam, so that

1
Y (1-0) $e

1 Marine Kyser Bl
Lis Anais
yrecliese

Let W be the weight of steam expended in unity of time.

P,, the pressure at which it enters the cylinder.

V,, the volume of unity of weight of steam at saturation at
the pressure P|, which may be found from Table I.*

F, the sum of all the resistances not depending on the useful
load reduced to a pressure per unit of area of piston; whether
arising from imperfect vacuum in the condenser, resistance of
the air-pump, feed-pump, and cold water pump, friction, or any
other cause. ;

R, the resistance arising from the useful load, reduced to a
pressure per unit of area of piston.

Z, the ratio of the total action of steam working at the expan-
sion s to its action without expansion. Values of this ratio are
given in Table IT.

Then the following are the two fundamental equations of the
motion of the steam-engine, as comprehended in equation (50)
of the original paper.

First. Equality of power and effect,

RAm=WV,{P,(Z—cs)—F(1—c)s}. . . . (e)
Secondly, Equality of two expressions for the weight of steam
* The volumes thus found (as has been already stated), though near

enough the truth for practical purposes, are only approximately correct,
having been computed on the assumption that steam is a perfect gas.

’

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 241

expended in unity of time,
wa.” (d)
it es ee de
From these two equations is deduced the following, expressing
the ratio of the mean load on the piston to the initial pressure of
the steam :—
R+F Z—es (
AER a HRN aban ee e)
being equivalent to equation (51).
In computing the effect of Cornish engines, these formule
require to be modified, owing to the following circumstances.
The terms depending on the clearance c have been introduced
into equations (c), (d), on the supposition that the steam employed
in filling the space above the piston at the top of its stroke is
lost, being allowed to escape into the condenser, without having
effected any work ; so that a weight of steam Wes is wasted, and
an amount of power WV,(P,—F cs lost, in unity of time. But
in Cornish engines this is not the case; for by closing the equi-
librium-valve at the proper point of the up or out-door stroke,
nearly the whole quantity of steam necessary to fill the clearance
and valve-boxes may be kept imprisoned above the piston so as
to make the loss of power depending on it insensible in practice.
This portion of steam is called a cushion, from its preventing a
shock at the end of the up-stroke ; and as Mr. Pole, in his valu-
able work on the Cornish engine, has observed, its alternate
compression and expansion compensate each other, and have no
effect on the duty of theengine. ‘The proper moment of closing
the equilibriuin-valve is fixed by trial, which is, perhaps, the best
way; but if it is to be fixed by theory, the following is the
proper formula. Let /" be the length of the portion of the up-
stroke remaining to be performed after the equilibrium-valve has
been closed, then y
YS cel
seas! A cananne cee 46CE)

A slight deviation from this adjustment will produce little effect
in practice if the fraction ¢ is small*.

In forming the equations of motion, therefore, of the Cornish
engine, we may, without material error in practice, omit the
terms denoting a waste of steam and loss of power due to clear-
ance and filling of steam-passages, and the results are the fol-
lowing :—

* The same equation will serve to determine the proper moment for
closing the exhaust-port in non-condensing engines, so as nearly to pre-
vent loss of power from clearance.

242 Mr, W. J. M, Rankine on the Mechanical Action of Heat.
Equation of effect and power in unity of time,
Useful effect E=RAmM=WV,{P,Z—F}. . . (57)
Weight of steam expended in unity of time,
Aln
ae
From those two fundamental equations the following are

deduced :—

Ratio of mean load on piston to maximum pressure,

w= (58)

R+F_ Z

ante EE (59)
Duty of unity of weight of steam,

E

W V1 (Pf F)5 cs cawdle sunt (AQ)

which, being multiplied by the number of units of weight of
steam produced by a given weight of fuel, gives the duty of that
weight of fuel,

Weight of steam expended per stroke,

seated) 164 70, 2b eae

In fact, it is clear that if any five quantities out of the follow-
ing seven be given, the other two may be determined by means
of the equations—

R-+F, the mean load on unit of area of piston,

P,, the maximum pressure of steam in the cylinder.

s, the ratio of expansion.

W, the weight of steam produced in unity of time,

A, the area of the piston.

1, the length of stroke.

n, the number of strokes in unity of time.

The other quantities, H, V,, Z, are functions of those seven.

Comparison of the Theory with My. Wicksteed’s Experiments.

(36.) In order to test the practical value of this theory, I
shall compare its results with those of the experiments which
were made by Mr. Wicksteed on the large Cornish pumping-
engine, built under the direction of that eminent engineer by
Messrs. Harvey and West, for the Hast London Water-works at
Old Ford, and which were published in 1841. The dimensions
and structure of the engine, and the details of the experiments,
are stated with such minuteness and precision, that there is
none of that uncertainty respecting the circumstances of par-

Mr. W, J. M. Rankine on the Mechanical Action of Heat. 243

ticular cases, which is the most frequent cause of failure in the
attempt to apply theoretical principles to practice.

The engine was worked under a uniform load at five different
rates of expansion successively. The number of strokes and the
consumption of steam during each trial having been accurately
registered, Mr. Wicksteed gives a table showing the weight of
steam consumed per stroke for each of the five rates of expan-
sion. I shall now compute the weight of steam per stroke
theoretically, and compare the results.

Throughout these calculations I shall uniformly use the foot
as the unit of length, the avoirdupois pound as that of weight,
and the hour as that of time. Pressures are consequently ex-
pressed in pounds per square foot for the purpose of calculation ;
although in the table of experiments I have reduced them to
pounds per square inch, as being the more familiar denomination.

The data respecting the dimensions and load of the engine,
which are constant throughout the experiments, are the fol-
lowing :—

Area of piston . . . . . A==34°854 square feet.
ee tat) ec Bihan’ iapry (ke ae ets

Cubic space traversed by piston | _ ,7_a 40. :
during one down stroke . } = Al=348°54 cubic feet,

Clearance and valve-boxes . . .. 18-00
UMD Usted tio ot coo:

Therefore, c=0°05

R=useful load of piston . =1597> lbs. per square foot.
F=additional resistance . = 266°6 oF
R+F=total mean Breer iin —1868°6 iy

on piston :

The mode of calculation is the following :—
1
Mr. Wicksteed states the fraction : of the stroke performed
at full pressure in each experiment. From this the ratio of ex-
pansion s is computed by equation (4), giving in this case
1
* 30955 +005,
s l
The yalue of Z corresponding to s is then found by means
of the third column of Table I.; that column being selected
because the initial pressures were all below four atmospheres,
This affords the means of determining the initial pressure of the
steam by equation (59), viz.
P\= z (R + F) =18636 5.

Z

244 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

By using Table I. according to the directions prefixed to it,
the volume of one pound of steam at the pressure P, in cubic
feet is calculated, and thence by equation (60) the weight of
steam per stroke, according to theory, which is compared with
the weight as ascertained by experiment.

Further to illustrate the subject, the useful effect or duty of a
pound of steam is computed according to the theory and the
experiments respectively, and the results compared.

The following table exhibits the results :—

Comparison of the Theory with Mr. Wicksteed’s Haperiments on
the Cornish Pumping-engine at Old Ford.

Pressure in| Steam Maximum | Lb. os eas Duty of one lb.
Number! the boiler, |CUt off at) Ratio of| Pressure in} expended per ? of steam,
of expe-| Ib. per y f the| expan- the cylin- stroke, Differ-
riments.| square |7 ° "©! sions, |4er, lb. per|— |__| ence. ence.
inch. stroke. square By |By expe- By |Byexpe-
inch. /theory.| riment. theory.| riment.

ft.-lbs.| ft.-lbs.

30°45 | 0-603/1:605 | 14:27 | 7-781|7-536 |—0-245 |71530) 73860)+-233)
33°20 | 0:-477/ 1-988 | 15:59 | 6-963) 6-463 |—0-500 |79936) 86123/4+6187

41:2 0°352 | 2-605 | 17°89 | 5-905) 5-985 |+-0°085 |94258) 93002 — 1256) :
45:7 0:318 | 2-882 | 18-93 | 5-626) 5-470 |—0-156 |98940/101756)+- 2816

@M} @) | @ |} @ (5) | (6)} @ | (8) | @) | (0) |} GIyy-

B.
C.
D. 39-2 0°397 | 2-342 | 16:9 | 6-236 6-200 |—0-036 89275) 89776)+
E.
F.

This comparison sufficiently proves that the results of the
theory are practically correct.

It is remarkable, that in every instance except one (experi-
ment E) the experimental results show a somewhat less expendi-
ture of steam per stroke, and a greater duty per pound of steam,
than theory indicates. This is to be ascribed to the fact, that
although the action of the steam is computed theoretically, on
the assumption that during the expansion it is cut off from ex-
ternal sources of heat, yet it is not exactly so in practice; for
the cylinder is surrounded with a jacket or casing communicating
with the boiler, in which the temperature is much higher than
the highest temperature in the cylinder, the pressure in the
boiler being more than double the maximum pressure of the
steam when working, as columns (2) and (5) show. There is,
therefore, a portion of steam of whose amount no computation
can be made, which circulates between the boiler and the jacket,
serving to convey heat to the cylinder, and thus augment by a
small quantity the action of the steam expended ; and hence the
formulz almost always err on the safe side*.

* Another, and perhaps a more important cause of the excess of the
actual above the calculated performance of a pound of steam is the follow-
ing. It has been proved experimentally by Messrs. Joule and Thomson
in the case of air and other gases, and by Mr. C. W. Siemens in the case

Mr. W. J. M. Rankine on the Mechanical Actionof Heat. 245

Supposing one pound of the best Welsh coals to be capable
(as found by Mr. Wicksteed) of evaporating 9-493 lbs. of water
at the pressure in the boiler during the experiment IF’, then the
duty of a Cornish bushel, or 94 lbs. of such coals, in the cir-
cumstances of that experiment would be—

By theory . . . . 88,288,000 ft. lbs.
By experiment . . . 90,801,000 ...

Difference . . . + 2,513,000 ...

(Economy of Single-acting Expansive Engines.

(37.) By increasing the ratio of expansion in a Cornish engine,
the quantity of steam required to perform a given duty is dimi-
nished ; and the cost of fuel and of the boilers is lowered. But
at the same time, as the cylinders and every part of the engine
must be made larger to admit of a greater expansion, the cost of
the engine is increased. It thus becomes a problem of maxima
and minima to determime what ratio of expansion ought to be
adopted under given circumstances, in order that the sum of the
annual cost of fuel, and the interest of the capital employed in
construction, may be the least possible as compared with the
work done.

That this problem may admit of a definite solution, the fol-
lowing five quantities must be given :—

P,, the initial pressure in the cylinder.

F, the resistance not depending on the useful load.

In, the amount of the length of the effective strokes made in
unity of time.

h, the annual cost of producing unity of weight of steam in
unity of time, which consists of two parts; the price of fuel, and
the interest of the cost of the boilers.

k, the interest of the cost of the engine, per unit of area of
piston.

Hence the annual expenditure to be taken into consideration,

of steam, that when an elastic fluid expands without performing work, by
rushing through a narrow orifice, so that all the power developed by the
expansion is ex) _nded in agitating the particles of the fluid, and extin-
guished by their friction, then the heat produced by that friction partially
compensates for the heat which disappears during the expansion. Hence
in a Cornish engine, when the steam is wire-drawn so as to be at a lower
ere in the cylinder at the commencement of the stroke than in the
iler, the friction of its particles causes its temperature, and therefore its
volume in the cylinder, to be greater than those corresponding to satura-
tion at the given pressure, upon which the calculations in the text are
founded; and hence a somewhat less weight of steam than that computed
by the formuls suffices to perform a given amount of work.

246 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

reduced to unity of weight of steam, is

A Vis
h+k+ =h+k—-.

And the useful effect of unity of weight of steam being
V,(P,Z—Fs),
the problem is to determine the ratio of expansion s, so that
V,(P,Z—Fs)
Vis

A+k>—

shall be a maximum.

Dividing the numerator of this fraction by V,P,, and the de-
nominator by AS both of which are constants in this problem,
we find that it will be solved by making the ratio

Z— is
1
ae, oi Ve cee ae
RNa ti8
a maximum.

The algebraical solution would be extremely complicated and
tedious. The graphic solution, on the other hand, is very simple
and rapid, and sufficiently accurate for all practical purposes, and
I have therefore adopted it.

In the annexed diagram, Plate ITI. fig. 1, the axis of abscisse,
—X0O+X, is graduated from O towards +X into divisions
representing ratios of expansion, or values of s. The divisions
of the axis of ordinates, OY, represent values of Z. The curve
marked “locus of Z” is laid down from the third column of
Table II. of the Appendix to the original paper, being applicable
to initial pressures not exceeding four atmospheres.

Through the origin O draw a straight line BOA, at such an
inclination to —XO+X that its ordimates are represented by
— Then the ordinates measured from this inclined line to

1

the locus of Z represent the value of the numerator Z— r% of
1

the ratio (62), corresponding to the various values of s.

Take a point at C on the line BOA, whose abscissa, measured

along O—X, represents — ase Then the ordinates, measured
1

from BOA, of any straight line drawn through C, vary propor-

tionally to the denominator a +s of the ratio (62).
1

*

Mr. W.J. M. Rankine on the Mechanical Action of Heat. 247

Through the point C, therefore, draw a straight line CT,
touching the locus of Z; then the ratio (62) is a maximum at
the point of contact T, and the abscissa at that point represents
the ratio of expansion required.

Example.

(38.) To exemplify this method, let us take the followimg data.

Greatest pressure in the cylinder P,;=20 lbs. per square inch,
= 2880 lbs. per square foot.

The corresponding value of V, is 20°248 cubic feet per pound
of steam.

To obtain this initial pressure in the cylinder of a Cornish
engine, it will be necessary to have a pressure of about 50 lbs.
per square inch in the boiler.

F, resistance not depending on the useful load =2 lbs. per
square inch, =288 lbs. per square foot, =+,P).

In, amount of down strokes, =4800 feet per hour ; being the
average speed found to answer best im practice.

To estimate A, the annual cost of producing one pound of
steam per hour, I shall suppose that the engine works 6000
hours per annum ; that the cost of fuel is one penny per 100
Ibs. of steam* ; that the cost of boiler for each pound of steam
per hour is 0-016 ton, at £27, =£0-432; and that the interest
of capital is five per cent. per annum. Hence / is thus made up :—

Fuel for 6000 lbs. of steam at O'0ld. . . £0°2500
Interest on £0°432, at 5 per cent. . . . 0°0216
h=£0°2716

Estimating the cost of the engine at £250 per square foot of
piston, we find =5 per cent. per annum on £250=£12'5, and

h hin
k =0°0217 ; rile 144
The line BOA, then, is to be drawn so that its ordinates are
1
P, }— To Ss.
hin

The point C is taken on this line, at TV. =5:144 divisions of
the axis of abscissz to the left of OY.

The tangent CT being drawn, is found to touch the locus of
Z at 2800 divisions to the right of OY.

Then s=2*800 is the ratio of expansion sought, corresponding

to the greatest ceconomy,

* This estimate is made on the supposition that coals, capable of pro-
ducing nine times their weight of steam, are worth about 16s, 9d. per ton.

248 Mr. W.J. M. Rankine on the Mechanical Action of Heat.

If we make c=0:05, as in Mr. Wicksteed’s engine, then the
fraction of the stroke to be performed at full pressure is

; = 0°323,
being nearly the same as in experiment F.
The mean resistance of the useful load per square foot of
piston is .
R=4P,—F=171866 Ibs.
The duty of one square foot of piston per hour,
Rin= 8,225,300 foot-lbs.

And one horse-power being 1,980,000 foot-lbs. per hour, the
real horse-power of the engine is

4°154 per square foot of piston.
The duty of one pound of steam is
RV,s=97,154 foot-lbs.

To give an example of a special case, let the duty to be per-
formed be 198,000,000 foot-pounds per hour, being equal to
100 real horse-power, for 6000 hours per annum. This being
called KE, we find from the above data that the area of piston
required is

Ae fal =24:072 square feet.

Rin
The consumption of steam per hour is
E
W= RVs = 2038 lbs.,

which requires 2038 x 0:016=32-608 tons of boilers.
The expenditure of steam per annum is

2038 x 6000 = 12,228,000 Ibs.
Hence we have the following estimate :—
Cost of engine, 24072 square feet of piston at £250 £6018-000

Cost of boilers, Oe OUMEONS Hb al. sls) se 880°416
Total capital expended . . . . . . . . . £6898°416
Interest at 5 per cent. per annum. . . £0844°921

Cost of fuel per annum, 12,228,000 lbs. of steam :
at OOld. ae me

Annual cost.for interest and fuel . . . . . . £85442]

I wish it to be understood that the rates I have adopted in
the foregoing calculations, for interest, cost of fuel, and cost of

’

‘Nt tt ymin

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 249

construction, are not intended as estimates of their average
amount, nor of their amount in any particular case, but are
merely assumed in order to illustrate by a numerical example the
rules laid down in the preceding article. It is of course the
business of the engineer to ascertain those data with reference
to the special situation and circumstances of the proposed work ;
and having done so, the method explained in this paper will
enable him to determine the dimensions and ratio of expansion
which ought to be adopted for the engine, in order that it may
effect its duty with the greatest possible ceconomy.

Section V. On the Economy of Heat in Expansive Machines*.

(39.) A machine working by expansive power consists essen-
tially of a portion of some substance to which heat is commu-
nicated, so as to expand it, at a higher temperature, being
abstracted from it, so as to condense it to its original volume at
alower temperature. The quantity of heat given out by the sub-
stance is less than the quantity received; the difference disap-
pearing as heat to appear in the form of expansive power.

The heat originally received by the working body may act in
two ways; to raise its temperature, and to expandit. The heat
given out may also act in two ways; to lower the temperature,
and to contract the body. Now as the conversion of heat into
expansive power arises from changes of volume only, and not
from changes of temperature, it is obvious that the proportion of
the heat received which is converted into expansive power will
be the greatest possible, when the reception of heat, and its
emission, each take place at a constant temperature.

(40.) Carnot was the first to assert the law, that the ratio of
the maximum mechanical effect to the whole heat expended in an
expansive machine is a function solely of the two temperatures at
which the heat is respectively received and emitted, und is inde-
pendent of the nature of the working substance. But his investi-
gations not being based on the principle of the dynamical con-
vertibility of heat, involve the fallacy that power can be produced
out of nothing.

(41.) The merit of combining Carnot’s law, as it is termed,
with that of the convertibility of heat and power, belongs to

_M. Clausius and Professor William Thomson; and in the shape
into which they have brought it, it may be stated thus :—

The maximum proportion of heat converted into expansive power
by any machine is a function solely of the temperatures at which

* Read to the Royal Society of Edinburgh, April 21, 1851.
Phil. Mag. 8. 4. Vol. 7. No. 45. April 1854. S

250 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

heat is received and emitted by the working substance; which
function, for each pair of temperatures, is the same for all sub-
stances in nature.

This law is laid down by M. Clausius, as it originally had
been by Carnot, as an independent axiom; and I had at first
doubts as to the soundness of the reasoning by which he main-
tained it. Having stated those doubts to Professor Thomson, I
am indebted to him for having induced me to investigate the
subject thoroughly ; for although I have not yet seen his paper,
nor become acquainted with the method by which he proves
Carnot’s law, I have received from him a statement of some of
his more important results.

(42.) I have now come to the conclusions,—

First. That Carnot’s law is not an independent principle in the
theory of heat, but is deducible, as a consequence, from the equa-
tions of the mutual conversion of heat and expansive power, as
given in the first Section of this paper.

Secondly. That the function of the temperatures of reception
and emission, which expresses the maximum ratio of the heat con-
verted into power to the total heat received by the working body, is
the ratio of the difference of those temperatures to the absolute
temperature of reception diminished by the constant, which I have
called e=Cnpb, and which must, as I have shown in the Intro-
duction, be the same for all substances, in order that molecular
equilibrium may be possible.

(43.) Let abscisse, parallel to OX in the diagram, PI]. III. fig. 2,
denote the volumes successively assumed by the working body ;
and ordinates, parallel to OY, the corresponding pressures. Let
7, be the constant absolute temperature at which the reception
of heat by the body takes place; 7) the constant absolute tem-
perature at which the emission of heat takes place. Let AB be
a curve such that its ordinates denote the pressures, at the tem-
perature of reception 7,, corresponding to the volumes denoted
by abscisse. Let DC be a similar curve for the temperature of
emission Ty. Let AD and BC be two curves, expressing by

their coordinates how the pressure and volume must vary in ©

order that the body may change its temperature without receiving
or emitting heat; the former corresponding to the most con-
densed, and the latter to the most expanded state of the body
during the working of the machine.

The quantity of heat received or emitted during an operation — ;

on the body, involving indefinitely small variations of volume

and temperature, is expressed by adding to equation (6) of Sec-
tion IV. the heat due to change of temperature only in virtue —

of the real specific heat. We thus obtain the differential equa-
tion

J

+

Mr. W. J. M. Rankine on the Mechanical Action of Heat. 251
aa Neg fae a meee
201+ 00=+ Gar Vy ay) Pree

+kéz,

in which the positive sign denotes absorption, and the negative
emission.

If we now put for — = their values accordmg to equa-
tion (11.), we find

8Q'+8Q= + (7-0). BV

hte io d dP
+{b+ gar(E-S) +O eave 63)

The first term represents the variation of heat due to variation
of volume only ; the second, that due to variation of tempera-
ture. Let us now apply this equation to the cycle of operations
undergone by the working body in an expansive machine, as
denoted by the diagram.

First operation. The body, being at first at the volume V, and
pressure P,, is made to expand by the communication of heat at
the constant temperature 7,, until it reaches the volume Vg
and pressure Py, AB being the locus of the pressures.

Here 5r=0; therefore the total heat received is

Vs dP
H=(,—") fav |

=(71—*){$(Vz, 71) — (Va, 71) }

Second operation. The body, being prevented from receiving

or emitting heat, expands until it falls to the temperature T,

the locus of the pressures being the curve BC. During this
operation the following condition must be fulfilled,

0=6Q'+6Q;

which, attending to the fact that V is now a function of 7, and
transforming the integrals as before, gives the equation

isaer. ke oven
O=+ Olt a) + 0-9 (E+ a ay) ON 9
This equation shows that
$(Vz, 1)—P(Ve, T)=Wlt, 7). - - - (2)
Third operation. The body, by the abstraction of heat, is
made to contract at the constant temperature ty, to the volume
p and pressure Pp, which are such as to satisfy conditions
epending on the fourth operation. CD is the locus of the
$2

(a)

252 Mr. W. J. M. Rankine on the Mechanical Action of Heat.

pressures. The heat emitted is evidently
Ho=(t—«){$(Ve, T)—(Vp, T)}- + + (C)
Fourth operation. The body, being prevented from receiving
or emitting heat, is compressed until it recovers its original
temperature 7,, volume V, and pressure P,; the locus of the

pressures being DA. During this operation, the same condi-
tions must be fulfilled as in the second operation ; therefore

$(Va, 1)—P(Vd, MI=W(7, 7) - + + (A)
vr being the same function as in equation (4).

By comparing equations (d) and (d), we obtain the relation
which must subsist between the four volumes to which the body
is successively brought in order that the maximum effect may
be obtained from the heat. It is expressed by the equation

$(Vs, T1)—P(Va, 71) =h(Vo, 7) — (Vo, 7). - (64)
From this and equations (a) and (c), it appears that
Hy Le=k

Beas a (65)

That is to say, when no heat is employed in producing variations
of temperature, the ratio of the heat received to the heat emitted
by the working body of an expansive machine is equal to that of
the absolute temperatures of reception and emission, each diminished
by the constant x, which is the same for all substances.

Hence let

II=H,—H,

denote the maximum amount of power which can be obtained
out of the total heat H, in an expansive machine working between
the temperatures 7, and 7). Then

Il | 1,—7)

ht ey en ee (66)
being the law which has been enunciated in article 42, and
which is deduced entirely from the principles already laid down
in the Introduction and first Section of this paper.

The value of the constant « is unknown; and the nearest

approximation to accuracy which we can at present make is, to
neglect it in calculation as being very small as compared with 7*.

* Subsequent investigations, founded chiefly on the experiments of
Messrs. Joule and Thomson on the thermic phenomena of currents of
elastic fluids, have shown that the constant «, as anticipated in the text, is
actually very small, if not altogether appreciable. Its approximate values,
computed from these experiments, range from 0° to about 2° Centigrade ;
the discrepancies being too small to affect materially the computation of
the power of engines.

|

Mr. W. J. M. Rankine en the Mechanical Action of Heat. 258

(44.) This approximation having been adopted, I believe it
will be found that the formula (66), although very different in
appearance from that arrived at by Professor Thomson, gives
nearly the same numerical results. For example: let the machine
work between the temperatures 140° and 30° Centigrade; then
7,=414°°6, tT, =304°'6, and

TY ea
sae 0:2653.

Professor Thomson has informed me, that for the same tem-
peratures he finds this ratio to be 0:2713*.

(45.) To make a steam-engine work according to the con-
ditions of maximum effect here laid down, the steam must enter
the cylinder from the boiler without diminishing in pressure,
and must be worked expansively down to the pressure and tem-
perature of condensation. It must then be so far liquefied by
conduction alone, that on the liquefaction being completed by
compression, it may be restored to the temperature of the boiler
by means of that compression alone. These conditions are un-
attainable in steam-engines as at present constructed, and dif-
ferent from those which form the basis of the formule and tables
in the fourth Section of this paper; hence it is found, both by
experiment and by calculation from those formule, that the pro-
portion of the total heat converted into power in any possible
steam-engine is less than that dicated by equation (66).

The annexed table illustrates this :—

- g¢ | 1 T=] U
ge “5 Fae| £58 §
2 52 AS SS Ce || AP
S 3° oo 8 sak 2o
= Sk is) oa 8 ov a>
ate Bae pea Secret). ace
A ae) olla |2es/ESZs| Hs
eo — "3 roePrL =| wes! REO wo
a £5k BSE oT Some] 2s
° oa ees ege|sgoe3) 8.
Sos Sot SaclavVvua| -o
EF-) os BP) EF oi tea
= 2e St eR 50
Ceo so are To —
2m =°9 Se2\ggse a!
ae ce Sesaisee °
Soa ne oS me iS a
a <4 Ee ces

by observation. Ditto. Ditto. Ditto.| 73-23 | 0°1185} Ditto.
(1)

(2) (3) (4) | (5) | (6)

* From information which I have received from Professor Thomson sub-
sequently to the completion of this paper, it appears that his formula
becomes identical with the approximate formula here proposed, on making

the function called by him p=“, J being Joule’s equivalent.
T

Mr. Joule also, some time since, arrived at this approximate formula in
the particular case of a perfect gas.

Maximum proportion
law.

according to Carnot’s

experiment I, }| 135°24274-6=409-8, 30 4+274-6=304-6| 617:7| 71-2 | 0-1153] 0-2567

2)

254 Prof. Grassmann on the Theory of Compound Colours.

The heat transformed into power, as given in the fifth column,
has been reduced to Centigrade degrees in liquid water, by di-
viding the duty of a pound of steam by Mr, Joule’s equivalent,
1389-6 feet per Centigrade degree.

In these examples, founded on the caleulated and observed
duty of Mr. Wicksteed’s engine during experiment F, the actual
ratio is less than half the maximum. ‘This waste of heat is to
be ascribed to the following causes :—

First. The expenditure of heat in raising the feed-water to
the temperature of evaporation.

Secondly. The initial pressure in the cylinder is but 18°93 lbs.
on the square inch, while that in the boiler is 45-7.

Thirdly. The expansive working of the steam, instead of bemg
continued down to 30° Centigrade, the temperature of the con-
denser, stops at a much higher temperature, 74°66. This is
the most important cause of loss of power.

XXXVII. On the Theory of Compound Colours.
By Professor GRassMAann*.

[With a Plate.]
| the 87th volume of this journalt+, Helmholtz published a

series of observations, some of which were new and inge-
nious, and from which he comes to the conclusion, that the
theory of compound colours, universally admitted since the time
of Newton, is erroneous in its most essential points ; and that there
are properly only two prismatic colours, yellow and indigo, which
when mixed give white. It may consequently not be regarded
as superfluous to show that the Newtonian theory of compound
colours is correct to a certain poit, and especially that the
opinion that every colour has its complementary colour, with
which when mixed it gives white, is founded upon mathemati-
cally incontestable facts, so that this opmion must be regarded
as one of the most tenable in physics. I will then show that
the positive observations of Helmholtz, instead of tending to the
subversion of this theory, serve rather partly to prove and partly
to complete it.

For this purpose it will be necessary to analyse the impression
of colour of which the eye is capable into its elements. The
eye first of all distinguishes light as coloured and colourless. In
colourless light (white, gray) it only distinguishes a greater or
less intensity, and this may be mathematically determined.

* From the Annalen der Physik und Chemie, 1853, p. 69.
+ Philosophical Magazine, S. 4. vol. iv. p. 519.

~

Prof. Grassmann on the Theory of Compound Colours. 255

Tn like manner we only distinguish the greater or less intensity
of a homogeneous colour. But even for the difference of the
indiyidual homogeneous colours we have a mathematically deter-
minable standard, which is furnished most perfectly by the
duration of vibration corresponding to each colour; even in
ordinary speech, this difference has been very suitably distin-
guished by the expression tint. Thus, in a homogeneous
colour we can distinguish both its intensity and its tint.
If now a homogeneous colour be mixed with colourless light,
the impression of colour becomes weakened by this inter-
mixture. Ordinary language is rich in terms by which this
difference is characterized ; the expressions, intense, deep, pale,
dull, whitish, which are added to the names of colours, may
serve as instances. The scientific terminology, which must be
substituted for this popular nomenclature, arises spontaneously
from what has been above stated, as every impression of colour
of this kind may be analysed into three mathematically deter-
minable elements,—the tint, the intensity of the colour, and the
intensity of the intermixed white. The various tints form a
continuous series of such a kind, that when we start from one
colour of this series and proceed forward, we finally arrive at
the original colour. One circumstance, however, must not
be left unnoticed here, namely, the difficulty of obtaining homo-
geneous red light, which forms the transition between the violet
and red of the ordinary spectrum, and which can only be pro-
duced by the prism under remarkably favourable circumstances
(on a bright summer’s noon)*. This outermost colour of
the spectrum, which may be equally well regarded as extreme
red or extreme violet, I will call purple. If now we regard any
compounded light, the eye can distinguish in it only the three
elements above mentioned; that is to say, every impression of
light may be imitated by mixing a homogeneous colour of a
certain intensity with colourless light of a certain intensity.
Thus in every sensation of light we have to distinguish three
things,—the intensity of the colour, the tint, and the inten-
sity of the intermixed colourless light. It would be easy to
make an apparatus by means of which we should be enabled
to determine every colour according to these three elements.
In order to give an idea of this, let us suppose two white
screens of similar nature moveable upon a hinge, in such a
manner that the white side of the screens shall be upon the
outside of the angle formed at the hinge; let a divided circle
be also provided to measure this angle. The coloured light to
be examined is now allowed to fall upon one of these screens in

* See Poggendorff’s Annalen, vol. xiii. p. 441.

256 Prof. Grassmaun on the Theory of Compound Colours.

a plane perpendicular to the axis of rotation; on the other
screen, and in the same plane, white light is suffered to fall in
any direction; and in a direction perpendicular to the latter,
homogeneous light; the light bemg so selected that it may
have the same tint as the light to be examined. If now
this latter screen be turned upon the hinge, any desired ratio
of intensity may be given to the colourless and homogeneous
light which is dispersed on all sides from this screen. If the
first screen be then also turned upon the hinge, any degree
of intensity less than that produced by hght falling on it per-
pendicularly may be given to the light diffused from it. In this
manner a position of the screens must necessarily be found, if
the light falling upon the second be not too strong, in which
both will produce the same impression upon an eye observing
them both at the same time. Such an apparatus would there-
fore be sufficient to determine mathematically all the elements
which may come under observation.

The above statement, that the eye can only distinguish these
three elements directly, might indeed be doubted. And truly it
might be difficult to prove it directly, since there always remains
the possibility that one eye, by virtue of its peculiar organization,
might perhaps discover differences invisible to another. How-
ever, for our purpose the fact is perfectly sufficient, that hitherto
no observer has been able to mention another element determi-
ning the impression of colour ; and moreover, in ordinary lan-
guage, we only recognise these three elements in the description
of this phenomenon, so that we may affirm with certainty that
hitherto only these three elements have been observed in the
impression of colour; in the following arguments we shall only
go back to this assertion.

In the second place we assume, “ that if one of two mingling
lights be continuously altered (whilst the other remains un-
changed), the impression of the mixed light also is continuously
changed.”

We say that an impression of light is continuously altered
when the two intensities (that of the colour and that of the in-
termixed colourless light) are continuously changed ; and where
the tint also, supposing that the intensity is not zero, continuously
changes. If the colour have no intensity, the light is colourless ;
and consequently by the continuous diminution of the intensity
to zero, a tint may gradually pass over into another completely
separated from it, if the intensity of the latter crease conti-
nuously from nothing upwards. It scarcely needs to be men-
tioned, that the case in which one or more of the elements deter-
mining the impression remain the same must be regarded as
coming within the idea of continuity. Now as regards the con-

Prof. Grassmann on the Theory of Compound Colours. 257

tinuous change of the tint, this will generally be produced by
the continuous change of the duration of vibration determining
this tint; with this difference, that the impression of colour of
the extreme violet will continuously unite itself to that of the
extreme red. In point of fact, the transition from violet to red
through purple is just as continuous to the eye as that between
any two other colours, although the limit has not yet been fixed
by observation at which the same impression of colour is repro-
duced by a different duration of vibration. I will call the trans-
ition from red through orange, yellow, green, blue, violet, and
purple back to red, the posdtive, and that in the reverse direction
the negative transition. According to this, any coloured light
A may continuously pass into another coloured light B in three
different ways ; namely, by the colour continuously assuming all
the tints which lie between A and B in the positive transition,
or by its passing through all those in the negative transition, or
lastly, by the light becoming colourless once or several times
during its transition. The principle of continuous transition
which we have just developed must be regarded as perfectly
established by experience, as a sudden spring in the phenomena
would be apparent even in the most crude observations, and
such a spring has not as yet been discovered.

From these propositions the following position may be derived
with mathematical certainty :—

“To every colour belongs another homogeneous colour, which,
when mixed with it, gives colourless light.”

Proof. Let a be the tint of the given colour. Let it be
assumed that there is no homogeneous colour, which, when
mixed with this, furnishes colourless light ; let any homogeneous
colour whatever be taken possessing the tint of 2 and the inten-
sity y. If now, whilst z remains constant, y be increased from
nothing upwards until the intensity of the colour a disappears
in comparison, the mixture will continuously change ; and as, ac-
cording to the assumption, it can never give colourless light,
its tint will also change continuously ; thus, as the mixture at
first has the tint a, and finally the tint 2, it has continuously
passed from a to x. This transition may be either positive
or negative; whether it be the one or the other will depend
upon the tint v. If the tint w be supposed to differ infinitesi-
mally from a, but on the side of positive transition, this transition
will also be positive. For if it were negative, all tints besides
those differing infinitesimally from a@ must be produced by the
elevation of the intensity y, and therefore tints which are
quite different from a; let y be an intensity by which a tint
quite different from a is produced. Now it is clear that the
colour, the tint of which is a and its intensity y, when mixed

258 Prof. Grassmann on the Theory af Compound Colours.

with a gives the tint a, whilst the colour which has the tint 2
and the intensity y furnishes quite a different tint ; but these two
colours mixed with a, with the same intensity y, have two in-
finitely close tints; that is to say, these two colours mixed with
a@ pass continuously into one another, so that (according to the
second proposition) the mixture must contmuously change, as
also its tint; but this should be quite different. Thus the sup-
position that the transition from a to # may be negative leads to
a contradiction, that is, it must necessarily be positive. For
the same reason, if a lies at an infinitely small distance from a
towards the negative side, a negative transition from a to # will
take place. If now the tint # be supposed to change continu-
ously from a towards the positive side, so as to pass through the
entire series of colours back to a, the corresponding transition
of the mixture, which in each case is effected by the elevation
of y, as it is at first positive and afterwards negative, must
necessarily change its sign somewhere. Tet a’ be a tint in
which this change occurs, so that before x reaches it the trans-
ition is positive, but as soon as it has passed it becomes negative.
If the tint z passes continuously through the tint a’, the tint of the
mixture must continuously vary with every value of the intensity
y, hence the whole of the tints which result from the increase of
the intensity y he extremely close together in both cases (when
x lies at an infinitesimal distance from a’ on the right or left
side). This, however, is impossible, as some of them he on the
positive and the others on the negative transition from a to al.
Thus the supposition that there is no homogeneous colour, which,
when mixed with a, furnishes white, leads ‘to a contradiction ;
z. e. every colour has another homogeneous colour, which, when
mixed with it, furnishes white. Q. EH. D.

I have chosen the indirect form of proof, because in this
manner the greatest possible exactness is most readily obtained
without digression. Moreover, it is evident that this mdirect
form of proof carries with it the direct assertion that the colour a’,
at which the character of the transition changes, is the same
which, when mixed with a, in any degree of intensity must give
colourless light.

If now we test Helmholtz’s experiments, we obtain from
them, at least approximately, the colour which is capable of
furnishing colourless light with any other given colour. For
yellow, according to Helmholtz, this is indigo, a result which is
by no means so divergent from the Newtonian theory of com-
pound colours as it appears to be at first sight. Helmholtz has
more exactly determmed the two colours, which, according to
him, furnish white ; for the yellow lies between the lines D and
E of Fraunhofer, and about three times as far from Has from D,

Prof. Grassmann on the Theory of Compound Colours. 259

the indigo extends from the middle of the space between the lines
F and G almost to the line G, so that any indigo which lies
between these limits furnishes white with any yellow which lies
near the position above described. Comparison with the New-
tonian theory of compound colours is rendered difficult by the
fact, that the names of the colours as employed by various
observers have not always the same sense, of which one may he
very readily convinced by comparing the descriptions of the
colours lying between the lines of Fraunhofer given in different
handbooks and memoirs. Newton exactly describes the position
of the limits between every two of his colours as they appeared
im the spectrum of his prism; he also determined the mean
refractive and dispersive indices of his prism ; so that all the ele-
ments exist for determining the position of the Newtonian limits
of the colours between Fraunhofer’s lines as exactly as these
determinations of Newton’s will permit. On this principle, by a
comparison of Fraunhofer’s and Newton’s measurements, and
supposing that Newton’s first red and last violet correspond with
Fraunhofer’s lines B and H, I have found that Newton’s first
orange (that is, the limit between red and orange) lies between
the lmes C and D at a proportionate distance of 7: 6; his yellow
commences between D and E, at a distance from the former line
of about ;/th of the interval between D and E; his green com-
mences also between D and H, at about ;4th of the interval
between those two lines from the latter; his blue begins near F,
at a distance of about j,th of the interval FG from F; his
indigo between F and G at a proportionate distance from those
lines of 5:3; his violet commences at G. The assumption
that the boundaries of the Newtonian spectrum coincide with
the lines B and H is certainly somewhat arbitrary, but we arrive
at the same result if we assume that the colours of mean refran-
gibility of Newton and Fraunhofer coincide. If we now construct
Newton’s coloured dise according tothe rules given in his “Optics”
(lib. i. pars 2, prop. vi.), and draw upon it the positions of the
Fraunhofer lines as above given (Plate III. fig. 4), it appears
that, aceording to the Newtonian theory, the yellow determined
by Helmholtz furnishes white with an indigo which lies between
the lines F and G of Fraunhofer, and which is distant from F
and G in the proportion of 15:2. In the figure these colours
are distinguished by the dotted line which unites them. This
indigo therefore falls within the limits of colour, between
which, according to Helmholtz, the complementary colours of
yellow lie. Thus we see that this observation of Helmholtz
agrees essentially with the result of Newton’s investigations. As
regards the other colours, Helmholtz denies the possibility of
obtaining white by the mixture of two of them. But if we test

260 = Prof. Grassmann on the Theory of Compound Colours.

any of his series of researches, as, for instance, that upon the
mixture of ved with the other colours, we shall always readily
obtain the complementary colour. According to him, red gives
with orange, yellow and green, the intermediate tones of colour
which lie in this series, and therefore, according to our denomi-
nation, on the positive side of red. Thus, for example, according
to Helmholtz, red mixed with green gives a pale yellow, which,
when red predominates, passes over through orange into red ;
and when green prevails, passes through yellowish-green to green.
In the same manner, red, with violet, indigo, and sky-blue, fur-
nishes the intermediate tones of colour, which, according to us,
lie on the negative side of red. According to Helmholtz, red
mixed with azure-blue gives a whitish violet, which, when red
predominates, passes into rose-colour and carmine. Thus, from
the propositions proved above, the complementary colour of red
must lie between green and azure-blue, and must therefore be a
tint of bluish-green. Now Helmholtz says that the mixture
of red with the greenish-blue tones produces a flesh-colour, but
nothing is said as to how this flesh-colour passes over into bluish-
green when this tint is in excess, although this must be the case.
- There is consequently a deficiency here. Moreover flesh-colour
is nothing but a red mixed with much white, and it has no other
conceivable transition to bluish-green, except by the gradual
weakening of the red until it entirely disappears before the white,
and the gradual production of bluish-green from this white (or
gray) ; im short, the normal transition through colourless light
takes place in this case. The same applies to the other series of
experments. The table of the complementary colours derived
from them would be as follows :—

Yellow, Yellowish-green, Green, Bluish-green, Azure, Indigo,
Indigo, Violet, Purple, Red, Orange, Yellow,

in which the complementary colours stand one above another.

I have hitherto endeavoured to make as few assumptions as
possible suffice. I will now, in order to introduce the main
principle of compound colours, add a third assumption to the
two preceding ones, namely,—

“That two colours, each of which has a constant tint and a
constant intensity of the intermixed white, also give constant
mixed colours, no matter of what homogeneous colours they may
be composed.”

This proposition also appears to be sufficiently proved by the
preceding observations ; for that coloured powders, when mixed,
furnish results differmg from those obtained when the light
proceeding from them only is mixed, can form no objection,
especially as Helmholtz has disclosed the cause of this difference.

Prof. Grassmann on the Theory of Compound Colours. 261

Let a be a homogeneous colour, and a’ that homogeneous
colour which furnishes white when mixed with a. For the sake
of clearness, let us suppose a and a’ to be represented by two
lines of equal length running from the same point in opposite
directions (fig. 5). Let 65 also be a colour, which, when
mixed with a, furnishes an equal quantity of white to that pro-
duced by its mixture with a’; and in order to express this
equal relation of 6 to a@ and a’, let 5 be represented by an-
other line perpendicular to a and a’. The intensity of the
colour 4 is to be so chosen, that if 6! be the colour which
gives white with 6, the intensity of the light resulting from
this mixture may be equal to that of the light produced by
the mixture of a and a’. This may be represented in the
figure by making the line which expresses the colour 0 as long
as those representing a and a’, whilst the complementary colour
of b may be represented by the line 0’, of equal length with 4,
but running in the opposite direction. We will suppose that,
of the two colours J and J, 6 is that which lies upon the side of
positive transition from a. It is evident that if the colour a
be given, a’, b, and 5! may be found by observation. For
instance, if a be yellow, a’ is indigo; between a and a! on the
side of positive transition lie the various tints of green and
blue; greenish-yellow mixed with yellow (a) gives a very small,
but with indigo (a') a very considerable intermixture of white.
Proceeding from greenish-yellow on the positive side, the inter-
mixture of white will increase by mixture with yellow, and
decrease by mixture with indigo. A tint will consequently
lie on the course of the transition, which will furnish an equal
quantity of white when mixed with yellow, as with idigo.
This must be about green, so that 4 will be green and é! purple.
Now it is evident, that, by the mixture of two of these four
colours, all tints must be obtainable. These tints may be
ascertained by observation for all degrees of intensity of the
homogeneous colours a and b, 6 and a, a! and J/, 6! and a.
Suppose the intensities of the two colours to be mixed to be
signified by the length of the lines representing them, so that
if a colour has the tone a, and its intensity is in the same pro-
portion to that of a as m to 1, then that colour may be repre-
sented by a line having the same direction as a, but m times its
length. Having represented in this manner the two colours
geometrically, let us construct from these lines the geometrical
sum, that is, the diagonal of the parallelogram which has the two
lines for its sides*, and assume that this sum or diagonal shall

* The idea of this geometrical sum was first developed by Mobius in his
Mechanik des Himmels (1843), and by myself in my Ausdehnungslehre
(1844).

262 = Prof. Grassmann on the Theory of Compound Colours.

represent the colour of the mixture, its direction showing the
tint, and its length the intensity of the colour.

This done, the tint and intensity of any mixture of colours
may be found by mere construction. Thus it is only necessaty
to determine the lines which represent the tint and mtensity of
the mixed colours, and then to add these geometrically, that is,
to compound them as ‘forces, and the geometrical sum (the
resultants of these forces) represents the tint and intensity of
the mixture. This follows immediately, because the order in
which the geometrical addition (or compounding of the forces)
is effected is without influence upon the result. Thus the colours
represented in conformity with the above determination by the
lines a, 0, a', b' may be taken as a basis ; then let aa, when @ is
positive, represent a colour which has the tint a, and the inten-
sity of which is in the same relation to that of a as ato 1; or
if « be negative, a colour which possesses the tint of the com-
plementary colour a’, and the intensity of which is in the same
relation to that of a! as @ to 1. The same applies to the second
colour 6, and its complementary colour J!. Of the two colours
e and ée/, the component colours of which are to be ascertained,
let the first be represented by the mixture of the colours aa and
8b, and the other by the mixture of the colours aa and 6'b, then
(leaving the intermixture of white out of the question) the mix-
ture of c and ¢’ may be represented by the combination of the
four colours aa, 8b, a'a, Bb. But aa mixed with ala gives
(#+2')a, and 8b mixed with 6’b gives (8+ ')b. Consequently
the mixture of c and c! may also be represented by the mixture
of the two colours (#+«!)a and (8+ ')b. As, however, these
latter have the original tints a, 6 or a’, U', their mixture is re-
presented by the geometrical sum of the lines, and consequentl
by the lines (a +«')a+ (84 6')b, i. e. by (aa+ Bb) +(a'a+'d),
i. e. by the geometrical sum of two lines, which, taken separately,
represent the colours to be mixed.

This law, which follows of necessity from the three original
assumptions, and which only requires a simple but complete
series of observations for the determination of the series of
colours, may also be expressed in another manner. Thus, if 4
circle be drawn round the origin of the lines, having @ for
its radius, and substituting for each line the point at which
it strikes the periphery provided with a weight proportional
to the length of the line, the mixed colour produced by two
given colours may be ascertained in the following manner.
Each of the colours is represented by a loaded point on the peri-
phery, in such a manner that the radius belonging to it shows
its tint, whilst the weight expresses the intensity, and deter-
mines the centre of gravity. A line drawn from the centre to

Prof. Grassmann on the Theory of Compound Colours. 268

the centre of gravity then represents the tint ; and when mul-
tiplied by the sum of the weights, the intensity also. The
identity of this determination with the preceding one is readily
seen from the following construction of the centre of gravity
pointed out in my Ausdehnungslehre. The centre of gravity of
the points A, B, C..., to which are respectively attached the
weights a, 8, y..., 1s ascertamed by drawing from any point
O the lines OA, OB, OC ; these are multiplied respectively by
a, 8, y-.., and changed in the proportion of L:a, 1:8, Ll: se.
without altering their directions; from the lines thus obtained
the geometrical sum is formed, and this divided by a+8+y¥ «.. 5
the terminal point of the line thus obtained is the desired centre
of gravity.

Lastly, with regard to the intermixture of colourless light,
another assumption is still necessary. The simplest method is
to assume—

“That the total intensity of the mixture is the sum of the
intensities of the lights mixed.”

I understand under the term total intensity of light, the
sum of the intensity of the colour, expressed as above, and
the intensity of the imtermixed white. The intensity of the
white, as also of every single colour, is assumed proportional,
not to the square of the amplitude, but to the amplitude itself ;
so that by the mixture of two white, or similarly coloured lights,
the intensity of the mixture is the sum of the intensity of the
mixed hghts.

This fourth assumption is not to be regarded as so well
founded as the three preceding, although on theoretical grounds
it appears to be the most probable. In order to draw the con-
clusions from this hypothesis, we will suppose the intensity of
the colour represented by the line a to be equal to 1, and assume
that the various homogeneous colours, the intensity of which is
1, are represented by points on the periphery of a circle, so that,
in conformity with what has been stated above, the weight of
these points must also be supposed equal to 1. Now let A and
B (fig. 6) be two points on the periphery, which consequently
represent homogeneous colours of an intensity =1. Let the
colours aA and SB be mixed, i. e. two homogeneous colours,
whose intensities are a and,and their tintsA and B, then the sum
of the intensities is «+. In order now to determine the colour
of the mixture, we have, as above described, to find the centre of
gravity of the points A and B, furnished with the weights «
and 8. Let this be C, the centre of the circle O; then if the
radius of the circle be supposed =1, the intensity of the colour
is =(2+)OC. Let the point at which OC, if produced, strikes

264 Prof. Grassmann on the Theory of Compound Colours.

the periphery be D, then the total intensity is «+, or, as the
radius is supposed to be 1, (2+ )OD. The total imtensity,
according to the supposition, will be equal to the intensity of
the colour plus the intensity of the intermixed white ; the latter
is consequently («+ 8)OD—(a+8)OC=(e+8)CD. The in-
tensity of the intermixed white is therefore equal to the distance
of the centre of gravity from the periphery, multiplied by the
sum of the weights. rom this it follows, further, that if the
total mass be regarded as united in the centre of gravity, in
which case, when furnished with such a weight, it is called the
geometrical sum* of the individual points with their attached
weights, then every impression of light, according to its three
elements, is accurately represented by a point with a certain
weight attached to it. The direction in which this point lies
with regard to the centre, or the point at which this direction,
if followed, strikes the periphery, represents the tint; the
weight of the point, the total intensity of the light; and the
distance from the periphery multiplied by this weight, the inten-
sity of the intermixed white. If by the depth of the colour
of a light we understand the intensity of its colour, divided by
the total intensity of the light, the depth of colour is repre-
sented by the simple recession of the point from the centre. . If,
then, two or more colours be represented in this manner, their
mixture is completely represented by the geometrical sum of
the loaded points denoting the individual colours. It will be
seen that this rule, derived by a purely mathematical method
from four sufficiently well-founded assumptions, agrees in its
essential features with Newton’s empirical rule. Nevertheless,
the manner in which Newton distributes the homogeneous colours
on the circumference of his discs requires a thorough revision,
towards which only the first steps are made by the researches of
Helmholtz. Not until sufficient light has been thrown upon
this subject can we attempt the solution of the imteresting ques-
tion with regard to the law by which the vibrations belonging
to the various colours combine to produce simple impressions of
colour upon the nerves of the sensorium, a question upon the
solution of which the idea of the various colours and of colour-
less light essentially depends.

* See my Ausdehnungslehre and Mobius’ Barycentrischen Calcul.

XXXVIII. On Electro-dynamic Induction in Liquids.
By Professor Farapay, F.R.S,. &¢.*

To Prof. Aug. de la Rive, For. Mem. R.S. &c.
Royal Institution,
My pear Frienp, March 7, 1854.

1 ue question, “ whether I have ever succeeded in produ-
cing induction currents in other liquids than mercury or
melted metals, as, for instance, in acid or saline solutions?” has
led me to make a few experiments on the subject; for though I
believed in the possibility of such currents, I had never obtained
affirmative results: I have now procured them, and send you a
description of the method pursued. A powerful electro-magnet
of the horse-shoe form was associated with a Grove’s battery of
twenty pairs of plates. The poles of the magnet were upwards,
their flat end faces being in the same horizontal plane; they are
3°5 inches square and above 6 inches apart. A cylindrical bar
of soft iron, 8 inches long and 1:7 in diameter, was employed
as a keeper or submagnet: the cylindrical form was adopted,
first, because it best allowed of the formation of a fluid helix
around it; and next, because when placed on the poles of the
magnet, and the battery connexions made and broken, the mag-
net and also the keeper rises and falls through much larger
variations of power, and far more rapidly than when a square or
flat-faced keeper is employed; for the latter, if massive, has, as
you know, the power of sustaining the magnetic conditions of
the magnet in a very great degree when the battery connexion
is broken. A fluid helix was formed round this keeper, having
12 conyolutions and a total length of 7 feet; the fluid was only
0°25 of an inch in diameter, the object being to obtain a certain
amount of intensity in the current by making the inductive
excitement extend to all parts of that great length, rather than
to produce a quantity current by largeness of diameter, 7. e. by
' a shorter mass of fluid. This helix was easily constructed by
the use of 8:5 feet of vulcanized caoutchouc tube, having an
internal diameter of 0:25, and an external diameter of 0°5 of an
inch: such a tube is sufficiently strong not to collapse when
placed round the iron cylinder. The twelve convolutions occu-
pied the interval of 6 inches, and two lengths of 9 inches each
constituted the ends. This helix was easily and perfectly filled
by holding it with its axes perpendicular, dipping the lower end
into the fluid to be used, and withdrawing the air at the upper;
then two long, clean, copper wires, 0°25 of an inch in diameter,
were introduced at the ends, and being thrust forward until they
reached the helix, were made secure by ligaments, and thus

* From the Bibliotheque Universelle de Geneve.
Phil. Mag. 8. 4, Vol. 7. No. 45. April 1854. T

266 Prof. Faraday on Electro-dynamie Induction in Liquids.

formed conductors between the fluid helix and the galvanometer :
the whole was attached to a wooden frame so as to protect the
helix from pressure or derangement when moved to and fro.
The quantity of fluid contained in the helix was about 3 cubic
inches in the length of 7 feet. The galvanometer was of copper
wire, =4,th of an inch in diameter and 164 feet in length, occu-
pying 310 convolutions; it was 18 feet from the magnet, and
connected with the helix by thick wires dipping into cups of
mercury. It was in the same horizontal plane with the magnetic
poles, and very little affected by direct action from the latter.

A solution formed by mixing onevolume of strong sulphuric acid
and three of water was introduced into the helix tube, the iron
keeper placed on the helix, and the whole adjusted on the magnetic
poles in such a position, that the ends of the copper connectors in
the tube were above the iron cylinder or keeper, and were advanced
so far over it as to reach the perpendicular plane passing through
its axis: in this position the lines of magnetic force had no ten-
dency to excite an induced current through the metallic parts of
the communication. The outer ends of the copper terminals
were well connected together and the whole left for a time, so
that any voltaic tendency due to the contact of the acid and
copper might be diminished or exhausted: after that, the copper
ends were separated, and the connexions with the galvanometer
so adjusted, that they could be in an instant either interrupted,
or completed, or crossed at the mercury cups. Being interrupted,
the magnet was excited by the full force of the battery, and then
the direct magnetic effect on the galvanometer was observed:
the helix had been so arranged that any current induced in it
should give a deflection in the contrary direction to that thus
caused directly by the magnet, that the two effects might be the
better separated. The battery was then disconnected, and when
the reverse action was over, the galvanometer connexions were
completed with the helix; this caused a deflection of only 2°, .
due to a voltaic current generated by the action of the acid in
the helix on the copper ends: it showed that the connexion
throughout was good; and being constant im power, caused a
steady deflection, and was thus easily distinguished from the final
result. Lastly, the battery was thrown into action upon the mag-
net, and immediately the galvanometer was deflected in one direc-
tion, and upon breaking battery contact it was deflected in the
other direction, so that by a few alternations considerable swing
could be imparted to the needles. They moved also in that par-
ticular manner often observed with induced currents, as if urged
by an impact or push at the moment when the magnet was
excited or lowered in force; and the motion was in the reverse
direction to that produced by the mere direct action of the mag-

Prof. Faraday on Electro-dynamic Induction in Liquids. 267

net. The effects were constant ; when the communicating wires
were crossed they again occurred, giving reverse actions at the
galvanometer. Further proof that they were due to currents
mduced in the fluid helix was obtained by arranging one turn of
a copper wire round the iron core or keeper in the same direction
as that of the fluid helix, and using one pair of plates to excite
the magnet ; the induced current caused in the copper wire was
much stronger than that obtained with the fluid, but it was
always in the same direction.

After these experiments with the highly conducting solution,
the helix was removed, the dilute acid poured out, a stream of
water sent through the helix for some time, distilled water then
introduced and allowed to remain in it a while, which being
replaced by fresh distilled water, all things were restored to
their places as before, and thus a helix of pure water submitted
to experiment. The direct action of the magnet was the same
as in the first instance, but there was no appearance of a voltaic
current when the galvanometer communications were completed ;
nor were there any signs of an induced current upon throwing
the magnet into and out of action. Pure water is too bad a
conductor to give any sensible effects with a galvanometer and
magnet of this sensibility and power.

I then dismissed the helix, but, placing the keeper on the
magnetic poles, arranged a glass dish under it and filled the
dish with the same acid solution as before; so that the liquid
formed a horizontal fluid disc 6 mches in diameter nearly, an
inch deep, and within 0°25 of an inch of the keeper; two long,
clean, platina plates dipped into this acid on each side of the
keeper and parallel to it, and were at least 5 inches apart from
each other; these were first connected together for a time that
any voltaic tendency might subside, and then arranged so as to
be united with the galvanometer when requisite, as before. Here
the induced currents were obtained as in the first instance, but
not with the same degree of strength. Their direction was
compared with that of the current mduced in a single copper
wire passed between the fluid and the keeper, the magnet bemg
then excited by one cell, and was found to be the same. How-
ever, here the possibility exists of the current being in part or
altogether excited upon the portions of the wire conductors con-
nected with the platinum plates; for as their ends tend to go
beneath the keeper, and so into the circuit of magnetic power
formed by it and the magnet, they are subject to the lines of
force in such a position as to have the induced current formed in
them ; and the induced current can obtain power enough to go
through liquid, as I showed in 1831. But as the helix experi-
ment is free from this objection, I do not doubt that a weak
induced current occurred in the fluid in the dish also,

T2

268 Mr. T. Dobson on the Storm-tracks of

So I consider the excitement of induction currents im liquids
not metallic as proved; and as far as I can judge, they are pro-
portionate in strength to the conducting power of the body in
which they are generated. In the dilute sulphuric acid they
were of course stronger than they appeared by the deflection to
be, because they had first to overcome the contrary deflection
which the direct action of the magnet was able to produce; the
sum of the two deflections, in fact, expressed the force of the
induced current. Whether the conduction by virtue of which
they occur is electrolytic in character or conduction proper I can-
not say. The present phenomena do not aid to settle that ques-
tion, because the induced current may exist by either the one
or the other process. I believe that conduction proper exists,
and that a very weak induction current may pass altogether by
it, exerting for the time only a tendency to electrolysis, whilst a
stronger current may pass, partly by it and partly by full elec-
trolytic action.

I am, my dear friend,
Ever most truly yours,
M. Farapay.

XXXIX. On the Storm-tracks of the South Pacific Ocean. By
Tuomas Doxsson, B.A., Head Master of the High School of
Hobart Town, Van Diemen’s Land.

| With a Plate. ]

HE law of the westerly progressive motion of tropical cy-
clones has now been well established in all the regions
sufficiently frequented by large ships to afford several trust-
worthy observations of the same storm; as in the West Indian
Seas, the South Indian Qcean, the Bay of Bengal, and the
China Sea. For the South Pacific Ocean not a single storm-
track is given in any work on cyclonology. The results of the
researches that I have undertaken with a view to supply this
deficiency have induced me to doubt the generality of the law of
westerly progression, and to suspect the existence of an import-
ant anomaly in the region referred to; for while they do not
present one exception to the law of rotation in the order N.E.8.W.,
they all tend to show that in the South Pacific Ocean cyclones
travel at first to the eastward, and then towards the south-east
and south, moving off finally towards the south-west. The mean
storm-track of the South Pacific Ocean is therefore exactly the
reverse of that of the South Indian Ocean, instead of being
similar to it in position, as is always supposed by writers on
cyclonology.» The followmg is an abstract of the facts from
which this conclusion has been deduced.

the South Pacific Ocean. 269
The Rev. W. Day of Hobart Town, in a journal kept by him

at Upolu, one of the Navigators’ Islands, describes a hurricane
which occurred there on the 15th of December 1842. The wind
set in from N.E., and got round to 8.E. by 8S. This order of
veering implies progression to the south of east. At 8 P.M. on
the 16th of December, the hurricane reached H.M.S. Favourite
in 21° S. 204° E., and lasted during the 17th and 18th. When
off Mangaia on the 17th, the Favourite lost sails, boats, and one
man. The wind shifted from N.E. to E.N.H. and to 8. by W.,
so that the cyclone was now moving towards the south-east. In
the Nautical Magazine, p. 425, volume for 1845, is given an
extract from the log of the Favourite ; and Captain Stokes has
added many particu- Upolu.

lars of this hurricane | |
in yol. il. p. 44, of'the
Voyage of the Beagle;
where, however, he
erroneously supposes
the progressive mo-
tion to be towards the
south-west. (Track A in the chart, Plate III. fig. 3.)

The Sydney Morning Herald states that there was a hurricane
at Upolu on the 16th of March, 1846. H.M.S. Juno, &c. were
in the harbour. It blew hardest from N.W. A great many
whalers came in to repair after the storm. The northern qua-
drant passed over Upolu.

The Rev. A. Buzzacott has given me the particulars of what
is called “the great hurricane” at Raratonga. On the 16th of
March there was a furious gale from the
eastward. At 1 a.m. of the 17th there was |
a dead calm for a few minutes, and then the Sw.
wind shifted suddenly to the south-west. /K \

This implies the passage of the central space
towards the south-eastward. At Mangaia, )
forty miles 8.E. of Raratonga, the change % \

of wind occurred at 10 a.m. of the 17th. At :
Raratonga the actual violence lasted from 9 p.m. of the 16th
to 3 a.m. of the 17th. On board a vessel between Raratonga
and Mangaia the barometer was lowest at 5 a.m. of the 17th.
The barometrical fluctuations at Raratonga were—

March 16,10 a.m. 29°50 March 17,1 a.m. 27°70

Mangaia,

7PM. 29°00 2a.mM. 28:00
10 p.m. 28°50 4am. 29:00
12 p.m. 28:00 6'a.m. 29°50

The track of this cyclone is marked B on the chart.

270 Mr. T. Dobson on the Storm-tracks of

In the log of the missionary brig ‘John
Williams, I find a notice of a hurricane
which veered from N. to W. and then to
S.W. in Jan. 1845, the vessel being thirty
miles E.N.E. of Raratonga. The motion is
still to the south-eastward. (Track C.)

In Wilkes’s Narrative of the American
Explormg Expedition, vol. v. p. 19, is an
account of a violent hurricane at Upolu on the 16th of December,
1840, in which the wind shifted from N.H. to 8S.W., and the
motion wasconsequently
to the 8.E. The storm
reached the Island of
Tutuilah, S.E. of Upolu,
on the next day (17th),
the wind changing from

_N.W. to S.W. On the
1st of December a ty-
phoonhad raged near the Laughlin Islands in 9° 8. and 154° E.,
but I possess no #écount of the changes of wind. (Track Don
chart.)

The Raratonga hurricane, described by Williams in his ‘ Mis-
sionary Enterprize,’. which also devastated the Navigators’
Islands, was undoubtedly one of the class of which the track
has just been determined. At Raratonga the wind veered from
eastward towards the west, and was therefore moving towards.
the south.

Lieut. Wilkes describes a hurricane at the Feejee Islands
which lasted from the 22nd to the 25th of
February 1840. It came on from N.E. and
veered to N. and then to N.W., gradually
hauling to the southward. The motion was
therefore to the south-eastward.

At midnight, on the 28th, the missionary
brig ‘Camden,’ Captain Morgan, was in 3198.
174° 7' E., sailing eastward. During the
29th the hurricane passed over her, veering
from S.E. to S.W. The centre therefore lay
to the eastward of the ship, and was moving
towards the south.

Lieut. Wilkes, at p. 381, vol. ii. of his
‘Narrative,’ has shown that the calm central
area of a hurricane passed across the Bay of
Islands, New Zealand, on the 1st of March, and that the cyclone
was moving in a south-west direction. This is likewise confirmed
by Mr. Piddington, Horn Book, p. 61. All the accounts coin-

the South Pacific Ocean. 271

cide in showing that this was a hurricane of very unusual vio-
lence. (Track E.)

On the 10th of February, 1849, the barque
Nimrod, from Sydney for China, was in
17° 38! S. and 161° 26! E., sailing N.W. SEW,

On the 13th, the centre of a hurricane,
_ beginning at N.E. and ending at S.S.W.,
passed over the vessel, during which she lost
her masts, &e. The progressive motion is
towards the south-east. .

On the 15th of February, in 23° 38’ S. |
and 167° 40! E.,about fifty-eight miles S8.8.E.
of the Isle of Pines, the hurricane struck the
brig Scamander, veering from EH. to 8S. At
10 p.m. the brig was wrecked on the south
reef of New Caledonia, and all hands except
two drowned. (Track F.)

From the 18th to the 23rd of February,

NE

1852, a cyclone was raging at New Caledonia
and Amatam, the schooner Deborah was .
wrecked.—(Sydney Morning Herald.) On *

the 5th and 6th of March, the barque Lady
Franklin was seventy miles 8.E. of Norfolk
Island. The calm passed her at 2 a.m. of
the 6th. The wind veered from E.S.H. to
W.N.W., indicating progression to the W.
of 8.

At Auckland, New Zealand, on the 6th of March, there was
a furious storm, for the most part from E.N.E. The brig Mau-
kin was wrecked, and H.M. surveying schooner parted both her
anchors and drove on shore. (Track G.)

In Hunter’s ‘ New South Wales’ is de-
scribed, by Governor King, a furious hurri-
eane which devastated Norfolk Island in
February, 1789. The wind began at N,E.,
veering round to E.S.E., and then to 8. and
moderating. Wind S.W. during the re-
mainder of the month.

The motion is south-eastward, the central
area passing to the eastward of the Island. (‘Track H.)

On comparing the curvature of the tracks thus determined
with that of the celebrated Rodriguez hurricane (Track K), the
nature of the anomaly will be apparent.

[t is remarkable that the track marked EB, which may be
regarded as a mean of all the tracts determined, coincides with
the Australian yoleanic series, which, commencing about New

272 Prof. Magnus on an Apparatus for the illustration

Guinea, passes between New Caledonia and the Navigators’
Islands, and extends to the voleanoes of New Zealand.

It is obvious that the curvature of: the storm-tracks of the
South Pacific Ocean is of the same kind as that of the east coast
of Australia; and the storm-tracks of the South Indian Ocean
have likewise the same kind of curvature as the west coast of
Australia. This relation holds equally in the case of the West
Indian cyclones, and the coasts which they traverse. These
observations may probably contain the germ of a law of pro-
gressive motion of cyclones more general than that of their mitial
westerly progression.

Hobart Town, April 25, 1853.

XL. Improved construction of an Apparatus for the illustration of
various phenomena of Rotating Bodies. By Professor Macnus*.

[With a Plate. |

if a paper of mine on the deviation of projectiles, I have

drawn attention to a remarkable phenomenon which is ex-
hibited during a body’s rotation, and described an apparatus in-
tended for the purpose of illustrating the motion of cylindro-
conical projectiles, and of showing that the axis of a rotating body
is fixed only under the condition that it is perfectly free, being,
on the contrary, quite mobile when it is prevented from moving
in one direction.

I have had this apparatus constructed in a modified form,
which renders it more convenient for experiment, and at the
same time alterations are introduced which render it possible to
observe with this instrument the various remarkable phenomena
exhibited by rotating bodies more completely than has hitherto
been attainable.

The new construction is represented in figs. 1 and 2, Plate IV.
AB and CD are two brass discs with thick edges, 3°8 inches in
diameter, which having their axes ab and cd placed between points
in the stirrups abfg and cdhk, areeasily moveable. The stirrups
are attached to the bar mn, which is held fast in the collar os by
the screw e, and with this collar is free to move round the hon-
zontal axis gr between two points, gand7, attached to the forked
piece pgr. The forked piece is carried by the axis vw, which
is pointed underneath. The entire apparatus, therefore, rests
upon the point at w, and hence is free to move round a vertical,
as also round a horizontal axis.

In order to check the one or the other of these motions, the
piece of brass pu is so attached at p to the forked piece pgr, that

* From Poggendorfft’s Annalen for February, 1854.

of various phenomena of Rotating Bodies. 278

by means of the screw z it can be readily elevated, and pressed
against the semicircular piece wy attached to the collar os. In
this way it is possible to fix mn at any inclination to the horizon.
When the screw z is loosened, the piece pu sinks by its own
weight, and the motion is once more free.

In order to control the motion round the vertical axis, and
besides this to accelerate it or to retard it, a wire ¢u is screwed
into the piece pu at wu.

Fromm and n depend the wires ml and ni, on which different
weights, P, furnished with hooks, may be suspended.

A wooden handle EF, to which two strings of equal lengths
are fastened at E and F, serves to set the discs AB and CD in
rotation. By winding these strings round the axes of the discs
either in the same or in opposite ways, it is possible to cause the
discs to rotate either in the same or in opposite directions, and
to impart to them velocities which are very nearly equal.

When both are caused to rotate in the same direction, so that
they move as a single mass, and when the axis mn is perfectly
free to move, the axis retains its direction either without weights,
or when equal weights are placed at 7 and <.. When on the one
side a greater weight is placed than on the other, the apparatus
moves round a vertical axis; and if the overweight be placed at
m, the direction of rotation is opposed to what follows when the
greater weight is placed at n. It is also evident that the direc-
tion of the motion is different according as the discs rotate in
the one or the other direction. When, in respect to an observer
situated in the production of mn, the motion is that of the hand
of a clock, the weight being attached to that side of the appa-
ratus which is nearest to the observer, then this side moves
from the right of the observer to his left.

During this motion round a vertical axis, the inclination
towards the horizon is scarcely sensibly changed, even when
the one side sustains 2 lbs. or 1000 grms. more than the other.
Accelerating the rotation round the vertical axis by carrying the
rod tu round with the hand, the side on which the greater weight
rests is elevated ; whereas when the angular velocity of the ap-
paratus is retarded, the same side sinks. Checking this com-
pletely, by holding fast the rod to u, the overweighted side falls
as low as possible.

Permitting the apparatus weighted on one side, for example
atm, to rotate freely round the vertical axis, and clamping it
during its motion with the screw z in the exact inclination which
it has assumed towards the horizon, the rotation round the ver-
tical axis ceases, but begins again immediately, provided the
dises AB and CD persist in their rotation, when the screw z is
loosened. Care must, however, be taken in loosening the screw

274: On various phenomena of Rotating Bodies.

that the incipient rotation round the vertical axis be not checked,
otherwise the weighted side of the apparatus falls immediately.

When this side falls as low as it can, that is, until one of the
protuberances w or y strikes against the piece pu, the rotation
round the vertical axis ceases, because the rotation round the
horizontal axis is checked. If, however, the weighted side be
raised with the hand, the rotation commences again round the
vertical axis. In this case a peculiar motion generally sets in.
While the apparatus rotates round the vertical axis, the weighted
side moves up and down like a pendulum.

If instead of lifting this side the rod ¢w be carried round with
the hand, and the entire apparatus thus turned round its vertical
axis with a somewhat greater velocity than it would have turned
of itself if the motion round the horizontal axis had not been
checked, then the weighted side rises of itself, and the rotation
round the vertical axis continues of itself, provided that the discs
AB and CD rotate with sufficient velocity.

When the two discs AB and CD are impressed with equal
velocities but in opposite directions, then the apparatus, although
its motions are perfectly unhindered, is easily moveable, and the
smallest surplus weight at m or causes the overweighted side
to sink immediately. If one dise only rotated, the entire appa-
ratus would turn round the vertical axis vw in an opposite direc-
tion to that of the motion when both the dises rotate. Hence it
is solicited in two opposite directions round this axis, and as the
rotating forces are equal, they neutralize each other. In this
way the two rotations round the vertical axis are checked. Hence
the same consequence follows as if only a single disc rotated, or
as if both moved in the same direction, the rod tw being held
fast by the hand.

The whole of these experiments may be made without the use
of weights. When the screw e is loosened, the rod mn may be
moved back and forward in the collar os, so that the apparatus
may assume the position given to it in fig 1. The weight of
the dise CD acts then at the end of a longer arm than that of
the other, AB, and in this way the same effect is obtained as if
weights had been placed at n. The greater the difference of the
two arms of the lever, the more quickly does the apparatus
rotate.

By moving mn in the collar os, it is possible to make another
experiment. If the distances of the rotating dises from the
vertical axis ow be unequal, and the two dises be set in rotation
with as nearly the same velocity as possible in opposite directions,
then the apparatus is perfectly mobile. In like manner, when
the shorter arm is so weighted as to establish an equilibrium,
then the slightest weight, which while the dises are at rest is

Mr. A. H. Church on the Spheroidal State of Bodies. 275

sufficient to destroy the equilibrium, destroys it also when the
dises are in motion. From this it follows, which might also be
inferred from other grounds, that the distance of the rotating
mass from the vertical axis has no effect, or at least a remarkably
small one, on the rotation of the apparatus.

As it appears convenient to distinguish this apparatus by a
name, and inasmuch as it may be used for a great number of
experiments on rotation, I would propose for it the name of
polytropium or polytrope.

XI. On the Spheroidal State of Bodies.
By Antuur H. Cuurcu, Esq.

To Dr. Tyndall, F.R.S. &c.
Royal College of Chemistry,
Dear Sir, March 18, 1854.

jo he successful method by which, in your last lecture, the
existence of a space between water in the spheroidal state
and the containing vessel was proved by the complete interrup-
tion that space offered to the passage of a galvanic current, has

induced me to devise a few experiments on the subject.

I have to describe in the present communication, in the first
place, some experiments I have just performed for the purpose
of obtaining decisive evidence of the isolation of all bodies in
the spheroidal state from the surfaces on which they roll; and
in the second place, to offer a few suggestions as to the probable
causes of the phenomena under consideration.

It was found by Boutigny, that if into a clean, red-hot pla-
tinum capsule acids and alkalies be placed, the acid and alkaline
liguids will roll about, repelling one another violently. This,
though an interesting example of the suspension of chemical
affinity, does not prove the existence of a space between the pla-
tinum vessel and the spheroids.

The first experiment I have to mention was this:—I took a
copper basin, three inches in diameter and rather more than half
an inch deep, polished its concave surface, and covered it with a
thin film of silver by the galvanic process. The plated basin
was now brought to a very high temperature, and while thus
heated, a few drops of a slightly alkaline solution of sulphide of
sodium were poured into it. These drops instantly assumed the
spheroidal form and rolled about, making, however, no mark or
track upon the silver. The source of heat was now withdrawn:
the temperature was soon so far reduced that the liquid exhibited
its normal properties, the space between it and the silver no
a existed, and a black stain of sulphide of silver covered the

ish.

276 Mr. A. H. Church on the Spheroidal State of Bodies.

Another instance of the assumption of the spheroidal state
has been often noticed. It occurs when ether is placed on the
surface of boiling water. Now, if a fixed inorganic acid be dis-
solved in the ether, and the water be coloured with litmus, no
reddening of the latter will take place as long as the «ther
remains in the spheroidal state. The acidulated ether and the
tinted water cannot, therefore, be in communication; they are
separated by a film of air or of vapour.

I pass on to notice in as few words as possible the remainder
of my experiments. I have remarked that in certain cireum-
stances spheroidal globules form upon the surface of hquids
during the processes of filtration and distillation. The pheno-
menon to which I refer is exhibited by many liquids, more fre-
quently and conspicuously perhaps by those that are the more
volatile. I have observed it with alcohol, water, aqueous and
aleoholic solutions, syrup, with essential oils and many other
organic substances. I have sometimes, however, found consi-
derable difficulty in its reproduction, and will therefore describe
in detail a method which is applicable in most cases for obtaining
in this manner an example of the spheroidal state. We will
employ a particular imstance. If we take cymole, a hydrocarbon
belonging to the benzole series, and half fill a bottle two or more
inches in diameter with it, placing in the neck of the bottlea
perforated cork through which passes a funnel-tube filled with
cymole, and having a piece of sheet Indian-rubber stretched
over its mouth, we shall find that on adjusting the funnel-tube
till its lower extremity is rather less than half an inch from the
surface of the liquid in the bottle, and on letting fall a drop of
cymole from it, beautiful spheroidal globules will be formed and
roll about for some time, scarcely diminishing in size. This
experiment may be performed with great advantage if the cymole
be warmed first. An ordmary funnel with a filter may be sub-
stituted for the funnel-tube, and will answer well if the lower
aperture of the funnel has a diameter of about °13 of an inch.
The experiment may be repeated with other materials with
similar effects. That the spheroids ave not in contact with the
surfaces on which they roll, may be proved by saturating the
liquid in the tube with something that shall have a visible effect
upon a substance dissolved in the liquid in the bottle. A beau-
tiful illustration of this occurs when, under conditions similar to
those before mentioned, we employ in the funnel-tube a solution
of sugar contaiming sulphocyanide of potassium, and in the bottle a
solution of sugar containing sesquichlorideof iron; noredcoloration
takes place until the coalescence of the spheroids with the liquid
beneath them. Many other chemical reactions may be made
use of with similar results. It is very curious to see a solution

Mr. A. H. Church on the Spheroidal State of Bodies. 277

of ferrocyanide of potassium floating upon a solution of sesqui-
chloride of iron, while not a trace of Prussian blue is formed.
These experiments must of course be recommenced whenever
any union of the liquids employed has taken place. The cork
spoken of above should have two perforations, one to admit the
funnel-tube, and the other to allow the escape of air.

Is the employment of a volatile substance essential to the pro-
duction of these phenomena? I imagined that this question
might be answered by the following experiment. A dish of pla-
tinum might be heated strongly, and a drop of melted lead then
placed upon it; now if the production of vapour from the sub-
stances employed were essential to the formation of the sphe-
roidal state, the lead should at once dissolve and perforate the
platinum ; if, however, the spheroidal state occurs when two
non-volatile substances are employed, the platinum vessel should
not be perforated until its temperature has been considerably
reduced. The experiment was tried with every precaution to
prevent the oxidation of the lead and ensure an accurate result ;
a perforation of the platinum ensued the moment of placing the
melted lead upon it. ‘This proves that the production of vapour
is essential to the occurrence of the spheroidal state; for it can-
not be urged that that condition is never manifested when metals
only are employed; for a drop of a volatile metal, mercury
(melted mercury, we may say, in order to render its relationship
to melted lead the more apparent), placed on an intensely heated
surface of platinum instantly assumes the spheroidal form, and
evaporating slowly, dances about in the vessel with peculiar
movements. Upon thin, sonorous vessels of copper, &c., this
movement takes place with such rapidity as to produce a musical
tone of high pitch. I have sometimes seen globules of mercury
and water rise to the height of six inches from the capsules in
which they had been formed.

A word or two in conclusion, as an attempt at an explanation
of the phenomena observed may not be out out of place.

Since a space always exists between the lower body and that
in the spheroidal state, and since that state is not manifested. by
non-volatile substances, it seems reasonable to conclude that the
vapour proceeding from those parts of the liquids nearest to the
contaiming vessel or subjacent fluid tends to assist the internal
molecular cohesive force of the drops in assuming and maintain-
ing their spheroidal form. Other forces originated by the tem-
perature may also be in operation.

I should premise that the solution of sulphide of sodium
employed in my first experiment made a dark stain upon silver
even in the cold. This renders the nullity of its action at a high
temperature the more remarkable. It will be scarecly necessary

278 Prof. Challis on two new Theorems —

to mention, that, for the successful performance of most of these
experiments, considerable manipulative care is required.
If, in the further prosecution of my inquiries in this direction,
I should discover anything worthy of notice, I hope to have the
pleasure of communicating it to you.
I remain, dear Sir,
Truly yours,
Arruur H. Cuurcu.

XLII. Proofs of two new Theorems relating to the Moon’s Orbit.
By Professor CHatuis*.

8 oe theorems which I propose to demonstrate are con-

tained in a paper recently communicated to the Cam-
bridge Philosophical Society. As I have reason to think that
they are new, and of considerable importance in the lunar theory,
I am desirous of giving them immediate publicity in the pages
of the Philosophical Magazine. They may be enunciated as
follows.

Theorem 1. All small quantities of the second order being
taken into account, the relation between the radius-vector and
the time in the moon’s orbit is the same as that in an orbit
deseribed by a body acted upon by a force tending to a fixed
centre.

Theorem I. The eccentricity of the moon’s orbit is a function
of the ratio of her periodic time to the earth’s periodic time, and
the first approximation to its value is that ratio divided by the
square root of 2.

Let the moon’s place be referred to the plane of the ecliptic
by rectangular coordinates, the origin being the earth’s centre at
rest, and the axis of 2 passing through the first point of Aries:
let w= the sum of the attractions of the sun and moon at the
unit of distance, m!= the sun’s attraction at the unit of distance,
and let 7, r! be the radius-vectors of the moon and sun, and 6,
their true longitudes, at the time ¢ reckoned from a given epoch.
The following equations, including small quantities of the third
order, may be readily obtained :—

d?x z ma 3m!
oe = — (4s) + geeos 0-20)

a:
d% py my\ 38n'p.

= aye (4- =) — 3,15 sin (0—26')
dz (a mz 3m!z

qe =~ 55 38) — Be

* Communicated by the Author.

relating to the Moon’s Orbit. 279

p being the projection of the moon’s radius-veetor on the plane

of the ecliptic. Multiplying the equations by 2da, 2dy and 2dz

respectively, adding, and putting V for the moon’s velocity, we

have

2dr mde) 3m

d.V?=— 72 7 To, 5,18
rep 2d6' sin 20—6' +

d .p?cos20 — 6—@

It is proposed to integrate this equation so as to include all
small quantities of the second order. That the approximation
may apply to the case of the moon’s motion, it will be assumed,
in accordance with what is known by observation, that the true
longitudes @ and 6! always differ from mean longitudes nt-+a

de! .
and n/¢+«! by small quantities. Hence 76 is a small quantity
of the first order. Omitting, therefore, the terms in ,the above
equation which involve dé! and zdz, and putting for 7’ the sun’s
mean distance a’, all small quantities of the second order are
still retained, and we i by integration,
V?+C=

my? 3m'p?

9q18 + _/5 cos20—6'. . . (A)

Again, small siete of the second order being included,

d? dx 37
er fe da 5) F sin 20—6@'
de, | a*2 d*z _d*y

The first of these equations is equivalent to
sin 20— 6! dt

p-dd *d0 dt
“dt do

fe _ Bio?
m 9q!3

!
= — $4 sin 20-0). dt
and
sin 26— pay ed 7 dp Be = sin (2n—nlt + 2a—a!)dt nearly.

Hence by integrating, and neglecting all small quantities of a
higher order than the second,

Also we have
dz dx dz dy

re wigs =Cy er eat =C3.

280 Prof. Challis on two new Theorems

Hence, if df be the small angle described by the radius-vector
7, corresponding to the increment d@ of longitude in the time df,
and if ¢,?+¢°+¢,?=h%, and pn be put for ¢, in the small term,
we have to the same approximation,
227] f2 2 [Aa =
eR IES PEE his Ob Be kes. Va)

dt? 7?" 2a'8

But

dy? f® Qn a'r?
This is the equation that would be obtained if a body were sup-

posed to be acted upon by the central force 5 Hence this

ae
equation proves Theorem I.

It may be remarked, that in the foregoing reasoning the incli-
nation of the orbit to the plane of the ecliptic is taken into
account, and that there is no limitation of the value of 7 except-
ing that its ratio to a' is a small quantity of the second order,
the approximation in other respects proceeding solely on the
hypothesis that the true longitudes of the sun and moon differ
by small quantities from mean longitudes.

But it is evident from theoretical considerations, that on that
hypothesis the moon’s orbit cannot differ much from a circle,
and it is known from common observation of her apparent dia-
meter that this must be the case. Our approximation will con-
sequently conform to the moon’s motion, if the radius-vector be
supposed to differ by a small quantity of the first order from a
mean value a. If, therefore, a be put for 7 in the small term of
the equation (C), it would seem that all small quantities of the
second order are taken into account, and that we have to inte-.
grate the equation

This integral would give the same relation between 7 and ¢ as
that in an orbit described by the central force s the constant h

being twice the area described by the radius-vector in the
unit of time. And the equation (B) shows that / is also the
mean value of twice the area described by the moon’s radius-
vector in the unit of time. Hence we must conclude that the
mean distance and mean periodic time in this approximation to

relating to the Moon’s Orit. 281
the moon’s orbit are the same as those in an elliptic orbit de-
seribed by the action of the central force = Now as the first

power of the disturbing force has been fully taken into account,
it is impossible that this result can be true. Some step in the
reasoning inconsistent with the hypothesis of the approximation
must have been taken, which it is necessary to correct before we
advance further.

After various fruitless attempts I discovered at length the
following solution of this difficulty. Let it be supposed that the
equation (C) contains the disturbing force as a factor. In that
case, putting the equation under the form

—rdr

di
io, 4 iL! mle?
—Cr?+2ur—h + 978

and substituting a+r—a for 7, it is necessary to expand to the
second power of r—a in the small term, in order to embrace
small quantities of the second order. This proceeding is legiti-
mate, because it is only required that the value of r should be
consistent with the hypothesis that the true longitude of the
moon differs by a small quantity from a mean longitude. The
approximation being conducted in this manner, the two equations
(B) and (C) readily give by integration the following results,
which include all small quantities of the second order :—

r=a+aecosw

3 5m 2 4
OF (1 gps C+ Da tesingy

a(l—eé 8m! p?

ee 2 bpm
_ Ke, mp ey WC, alp
ies pe society “ae + 2a
ae )i= the moon’s periodic time (p)
a®C3 J ~ the earth’s periodic time (P) °
We have now to satisfy, by means of the arbitrary constants,

the condition on which alone the above results can be obtained,
viz. that the disturbing force is a factor of the equation (C).

By substituting in that equation the values of 7 and _ given by

the first and second of the above equations, it will appear that
the condition is satisfied if the arbitrary constants / and C are

Phil. Mag. 8. 4. Vol. 7. No. 45. April 1854. U

282 On two new Theorems relating to the Moon’s Orbit.

such that A?C=y?. Hence it follows that
e= —2_
V2P°
which proves Theorem II.

The third of the foregoing equations gives by a direct process
the known value of the motion of the apse to the first approxi-
mation. The periodic time is found to.be the same as that in
an elliptic orbit whose mean distance is a, the force tending to

2
the focus being a — = at the unit of distance, which is
otherwise known to be true.

The numerical value of aan for the moon is 0:0529, and the
known eccentricity of her orbit is 0°0548. The difference 0:0019
is not more than might be expected from the degree of approxi-
mation embraced by the analysis. For Jupiter’s four satellites

the values of ap are 0:00029, 0:00058, 0°001168, and0°002724,
Respecting the eccentricities of their orbits, observation shows
that those of the first and second are too small to be sensible,
and that those of the third and fourth are only just sensible.
The eccentricities of the orbits of the other satellites of the solar
system are known with too little precision to admit of compa-
rison with the theory, excepting that of Titan’s orbit, which is
stated to be 0°0293. But in this instance the large inclination
of the orbit to the plane of Saturn’s orbit forbids making a com-
parison.

The following considerations appear to me sufficient to prove
that the eccentricity of the moon’s orbit must be a function of
the disturbing force. A straight lme being drawn from the
earth’s centre m any direction in the plane of the moon’s orbit,
the radius-vector at the imstants the moon passes this line in
successive revolutions has different values. The fluctuations of
value, which, as is known, do not exist in the elliptic theory,
depend on the disturbing force in such a manner that the func-
tion by which they are expressed would vanish if the disturbing
force were indefinitely small. The total fluctuations, in the case
of a uniform apsidal motion, are the same in all directions, and
take place about the same mean distance; and the difference
between the extreme values of the radius-vector in any given
direction is equal to the difference of the two apsidal distances,
and therefore proportional to the eccentricity. Hence as the
fluctuations of the radius-vector in a given direction depend on
the disturbing force, it follows that the eccentricity is also a
function of the disturbing force.

On the Spheroidal State of Water in Steam-boilers. 288

In opposition to these views, it will perhaps be urged that a
satellite might be projected in such a manner that the eccentri-
city of the orbit it begins to describe would be different from
that given by the above theorem. But without mathematical
proof, which is altogether wanting, it cannot be asserted that
the orbit would retain that eccentricity under the influence of a
disturbing force, or that there would be a mean motion either
of the radius-vector or of the apse. If such were the case, there
would seem to be no reason for the failure of the method of inte-
gration which was applied in the first instance to the equation (C).
In all probability, the motion in the case supposed would not
settle down to a permanent state till the eccentricity of the orbit
had reached the value which accords with the theorem.

If any hesitation to admit the truth of the theorem be felt,
because none of the many eminent mathematicians who have
treated of the lunar theory have arrived at the same conclusion,
I may urge that by no previous method of investigation has the
motion of the moon’s apse been found in a direct manner. The
indirect methods hitherto adopted to determine the motion of
the apse precluded the possibility of arriving at any determina-
tion of the value of the eccentricity. It appears to me that I
have indicated the initial steps of a new solution of the problem
of the moon’s motion, which it might be worth the while of
those who have time for such researches to trace to its conse-
quences.

Cambridge Observatory,
March 20, 1854.

XLIII. On the Spheroidal State of Water in. Steam-boilers.
By A. Normanpy, Esq.

To Dr. Tyndall, F.R.S. &c.

67 Judd Street, Brunswick Square,
Dear Sir, March 20, 1854.

GJONVINCED as I am that water frequently assumes the

spheroidal state in boilers, in consequence of which these
most important vessels, on which the very existence of the steam-
engine, that is, of most of the comforts of civilized life, depend, are
too often converted by mismanagement or ignorance into frighful
engines of death and destruction, I venture now to trouble you
with a few observations in addition to those which you were
kind enough to listen to the other day, in the hope that, should
the facts which I am about to relate appear to you as conclusive
as they do to me, you may be induced, in your lectures on heat,
to call once more the attention of the audience, should you deem
fit to do so, to this, I believe, fruitful but almost unsuspected,
or at any rate scarcely credited source of explosion.

9

~

284. Mr. A. Normandy on the Spheroidal State

I have already had the honour to relate to you that I had seen
the plates of a Cornish boiler, a quarter of an inch thick, become
red-hot in the flue, although at the time the boiler contained its
due quantity of water. It was a new boiler, about 18 feet long ;
and that the water had assumed therein the spheroidal state 1s
proved by the fact, that a lead rivet, 1 mch in diameter, put in
for safety was actually melted. It is, in fact, this rivet which
led to the detection of the cause of the occurrence, and an inves-
tigation of the subject brought out the following details. The
fireman or stoker was an ignorant mulatto, who having noticed
the lead rivet im the boiler, had given it as his opinion that it
would soon be melted by the fire; the possibility of such an
accident having been denied by one of his fellow-workmen, a bet
had taken place between them. The wager having thus been
laid, the fireman set to keeping up a brisk, bright fire; in con-
sequence of which, steam being generated exceedingly fast, pri-
ming, that is, a production of steam under the supermcumbent
water, took place, and, as a matter of course, the water, or a por-
tion thereof, not being any longer in contact with the surface of
the iron plate, the latter in a very short time became red-hot,
and the rivet melted; for some time afterwards, however, the
water being in the spheroidal state, the boiler remained appa-
rently sound, that is, it did not leak, although it had an opening
of an inch diameter left in consequence of the melting of the
rivet; it is only shortly afterwards I was told, that the heat
having diminished, torrents of water poured through the hole
with almost explosive violence, emitting volumes of scalding
steam as it came in contact with the fire on the grate.

This took place at the Wenlock Timber Saw-mills; and I can
bear testimony to the above fact, and likewise to this cireum-
stance, that when filled as usual with its normal quantity of
water, the bottom of the boiler over the fire could, in the course
of five or six minutes, be made red-hot at pleasure by brisk
firmg. In fact, having called at the above works, according
to appointment, to meet the engineer there, my inquiry as to
the then state of the boiler was answered by the foreman, in
presence of his master, in these words :—‘“ The boiler is not red-
hot now, but if you will step this way it will be made so immedi-
ately ;” and in spite of all remonstrance as to the danger of such
an experiment, he came shortly afterwards to announce that the
boiler was red-hot, and J saw if in that state in presence of the
engineer, the master, his nephew, the foreman, and the fireman
or stoker. The production of steam had been thereby sponta-
neously reduced, the bolt or lead rivet eventually melted, but
not in my presence; for seeing the state of things, I speedily
retreated with the engineer and the master, but almost reluct-

of Water in Steam-boilers. 285

antly followed by the foreman, in whose somewhat jeering looks
I could plainly read that he entertained but a poor idea of our
pluck.

In addition to this, I may say that in “ waggon boilers,” a
shape than which none can be more unsafe, but which is now for-
tunately much less in use than in former years, bulgg bumps
are very often observed, which are certainly due to the pressure
of the steam in the boiler upon the iron plates of the bottom,
when by extravagant or incautious firing they have been made
red-hot. Frequently, however, instead of bulgings or bumps
being thus produced, a disruption of the bouer takes place,
attended with more or less fatal consequences. Many such
accidents have thus happened at Manchester, and particularly
on Monday mornings.

The following occurrence, related to me by my friend Mr. A.
M. Perkins as having taken place in his presence in a boiler of a
peculiar construction in which steam was generated by means of
his hot-water pipes, is also well worth mentioning, as I think
we may gather from it a correct explanation of the facts under
consideration; and the rough sketch below, which represents a
cross section of the boiler, will perhaps explain the matter better
than I could do by writing.

The boiler had the dimen-
sions indicated, and was 8
feet in length; it was filled
with water to about A as
usual, the safety-valve had an rf
area of 4 inches. From such
a boiler the whole of the water
was completely driven off
through the valve by vio-
lent priming ; that is to say,
steam was generated so fast
by a hot water pipe in the
limb B, that it completely
lifted up the water and vio-
lently squirted it out of the
boiler, as just related. In
such a case, the water being
heated by pipes, and not by
contact with the heated sur-
faces of the boiler, no other
mischief could result than
that of priming: but sup-
pose, on the contrary, such a
boiler to have been heated in

286 On the Spheroidal State of Water in Steam-boilers.

the usual manner; there is no doubt that the steam generated
in the limb B would, by lifting the superincumbent water,
have soon permitted that part of the boiler to become red-hot,
and thus have produced the curious phenomenon revived and
studied by Boutigny d’Evyreux, and named by him a fourth or
spheroidal condition of matter, but to which, so far as refers to
water, the late Jacob Perkins had, to my certain knowledge,
called the attention of engineers and of savants more than
twenty-five years ago (in fact, as far back as 1824).

Allow me to relate also the curious experiment of a distin-
guished civil engineer, Mr. Alexander Gordon, made several years
ago, as related to me by Mr. A. M. Perkins.

AB is a cylinder provided with four try-cocks, A

1, 2, 3,4; water beimg introduced into the 1
cylinder and heated therein, the cocks on being
successively turned gave the following results ;
namely, steam issuing from 1, 2, 3, and water
from 4; but after urging the fire, the above
order was found to be completely reversed ;
that is to say, cock No. 1 emitted water, and 3
cocks Nos. 2, 3, 4 steam.

These facts, in my humble judgement, ap- 4
pear to me to prove in a decided manner,—

1. That the heating of surfaces previous to B
the introduction of water is not necessary to
produce the spheroidal state.

. 2. That many boiler explosions may be referable to that con-
ition.

3. That all boilers which offer an extensive surface to the heat,
that is to say, all boilers with internal flues, are pre-eminently
liable to explosions from this cause.

Earthy deposits in all kinds of boilers are favourable to the
production of this dangerous phenomenon.

I cannot terminate this informal letter without apologising for
having so long trespassed on your valuable time and patience ;
but if a collection of facts be essential to the progress of science,
I hope that you will indulgently receive this communication, and
believe me,

Yours very faithfully,
A. NorMANnpDy.

[ 287 ]

~ XLIV. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from p. 223.]

Jan. 12, 1854.—The Lord Chief Baron, V.P., in the Chair.

THE following was read :—

Supplement to a paper ‘‘ On certain Properties of Square Num-
bers and other Quadratic Forms, with a Table, &c.” By Sir Fre-
derick Pollock, F.R.S. &c.

In the original draft of this paper there was a suggestion that all
the terms of the series 1, 3, 7, 13, &c. [there called the Gradation-
Series] possessed the property that was exhibited as belonging to
the odd number 197. This was omitted in the copy from some
doubt whether it was universally true. Since the paper was read
that doubt has been removed, and it turns out that the property
belongs not only to all the terms of the series 1, 3, 7, 13, &c., but
to all odd numbers whatsoever. I am desirous to add to the paper
this statement by way of supplement. ‘he property referred to
may be thus enunciated :—

Every odd number may be divided into square numbers (not ex-
ceeding 4) whose roots (positive or negative) will by their sum or
difference [in some form of the roots] give every odd number from
1 to the greatest sum of the roots, which (of course) must always be
an odd number.

Or the theorem may be stated in a purely algebraical form,
thus :—If there be two equations

C4+0+C4+07=2n+4+1
a+b+e +d=2r+1,
a, b, c, d being each integral or zero, n and r being positive, and r
a maximum; then if any positive integer r’ (not greater than r) be
assumed, it will always be possible to satisfy the pair of equations
w+ertyt+2=—2n +1
w+tet+y +2=2r41
by integral values (positive, negative or zero) of w, «, y, 2.

I hope shortly to communicate a proof of the above theorem, in-
dependent of any of the usual modes of proving that every odd
number is composed of (not exceeding) four square numbers.

Note.—The differences of the roots of 197 were not fully stated
in the paper, I add them here :—

197
has 7 forms of roots :—
1A; 1,.0,.0
tO LG By 0.1: > Biss} ¥ sed eceyscenisesa te LF seeis 21
BPO Gy) dtd. D vsriss 9, 11, 13, 19, 21, 23,
Mh LAG Beil: B: cass 9, 13, 21, 25,
B | 10)95.4,0 |) 9.8; By sssatssscasaans.s ABs ddtieisvals ih 23
By: 1Oy Gy OpBb 18s 5, 7 sasines...00 sis LGA Tye cave scticnas events 27
i By By Cp 4hdy 8) 5,00 By 15, 19; 9 iase. bdsbLs 27.

288 Royal Society.

Jan. 19.—Charles Wheatstone, Esq., V.P., in the Chair.

A paper was read, entitled ‘‘On the Geometrical Repxesentation
of the Expansive Action of Heat, and the Theory of Thermo-dynamic
Engines.” By W. J. Macquorn Rankine, F.R.5.S.L. & E. &e.

The author remarks, that if abscissee be measured from an origin
of rectangular coordinates, representing the volumes assumed by an
elastic substance, and if ordinates, at right angles to those abscisse,
be taken to denote the corresponding expansive pressures exerted by
the substance, then any succession of changes of pressure and volume
may be represented geometrically by the coordinates of a curve. If
such a curve have two extremities, the area included between the curve
and the ordinates let fall from its extremities will represent (when
positive) the expansive power given out by the substance during the
process represented by the curve. Should the curve be closed, return-
ing into itself, so as to denote a cycle of periodical changes of pressure
and volume, then will the area, enclosed within the curve, represent
(when positive) the expansive power given out during one cycle of
changes. This area is positive when increase of volume takes place
on the whole at greater pressures than diminution of volume. ‘The
area of such a closed curve represents also (when positive) the me-
chanical equivalent of the heat which permanently disappears, or is
converted into expansive power, during a cycle of changes, for were
it not so, the sum of energy in the universe would be changed,
which is impossible.

As the principles of the expansive action of heat are capable of
being presented to the mind more clearly by the aid of diagrams of
energy than by means of words and symbols alone, such diagrams
are applied, in the present paper, partly to the illustration and de-
monstration of propositions previously proved by other means, but
chiefly to the solution of new questions, especially those relating to
the theory of thermo-dynamic engines.

Throughout the whole of this paper, quantities of heat are ex-
pressed, not by units of temperature in an unit of weight of water,
but by equivalent quantities of mechanical power, stated in foot-
pounds according to the ratio established by Mr. Joule’s experiments
on friction (Phil. Trans. 1850), that is to say, 772 foot-pounds per
degree of Fahrenheit, or 1389-6 foot-pounds per Centigrade degree,
applied to one pound of liquid water at atmospheric temperatures.

A curve described on a diagram of energy, such that its ordinates
represent the pressures of a homogeneous substance corresponding
to various volumes of an unit of weight, while the total sensible or
actual heat (Q) present in an unit of weight of the substance, is
maintained at a constant value (Q,), may be called the Jsothermal
Curve of Q, for the given substance. Its equation is

Q=Q,.

If an unit of weight of a substance be allowed to expand, under a
pressure equal to its own elasticity, without receiving or emitting
heat, its actual heat will diminish during the expansion, and its
pressure will diminish more rapidly than it would do if the actual
heat were maintained constant. A curve whose coordinates repre-
sent this mode of variation of pressure and volume may be called a

Royal Society. 289

Curve of no Transmission of Heat. For every such curve a certain
function of pressure, volume and actual heat, called a Thermo-dy-
namic Function (F), has a constant value (F,) proper to the parti-
cular curve under consideration; whose equation is therefore

B=) <

A curve whose coordinates represent the relation between pressure
and volume when the substance is absolutely destitute of heat, may
be called the Curve of Absolute Cold. It is at once an isothermal
curve and a curve of no transmission, and is an asymptote to all the
other curves of both those kinds, which approach it indefinitely as
the substance expands without limit.

The whole theory of the expansive action of heat is comprehended
in the geometrical properties and mutual relations of those two
classes of curves ; and all those properties and relations are the con-
sequences of and are virtually expressed by the two following theo-
rems :—

Turorem I.—The mechanical equivalent of the heat absorbed or
given out by a substance in passing from one given state as to pressure
and volume to another given state, through a series of states repre-
sented by the coordinates of a given curve on a diagram of energy,
is represented by the area included between the given curve and two
curves of no transmission drawn from its extremities, and indefinitely
prolonged in the direction representing increase of volume.

Tuerorem II.—IJf across any pair of curves of no transmission on a
diagram of energy there be drawn any series of isothermal curves at
intervals corresponding to equal differences of actual heat, the series
of quadrilateral areas thus cut off from the space between the curves of
no transmission will be all equal to each other.

These two propositions are the geometrical representation of the
application, to the particular case of heat and expansive power, of
two axioms respecting Energy in the abstract, viz.—

Axiom I.—The sum of energy in the Universe is unalterable.

Axiom II.—The effect, in causing transformation of energy, of the
whole quantity of actual energy present in a substance, is the sum of
the effects of all its parts.

The application of these axioms to heat and expansive power in-
volves the following

Derinition.—Lapansive Heat is a species of actual Energy, the
presence of which in a substance affects, and in general increases, its
tendency to expand ;—
and this definition, arrived at by induction from experience, is the
foundation of the theory of the expansive action of heat.

The first section of the paper is occupied chiefly with the demon-
stration of the first of the theorems quoted and its immediate con-
sequences, which are applicable to all substances, homogeneous and
heterogeneous.

The second section relates to the theory of the expansive action
of heat in homogeneous substances.

From the second theorem above quoted, it is deduced, that the
area of any quadrilateral bounded above and below by any two iso-
thermal curves, and laterally by two curves of no transmission, is

290 Royal Society.

the product of the difference between the two quantities of actual
heat proper to the isothermal curves, by the difference between the
two thermo-dynamic functions proper to the curves of no transmis-
sion, being represented by an expression of this form,
(Q,—@,). (F,—F,).

While the area of a figure bounded above by the isothermal curve
of Q,, and laterally by the indefinitely-extended curves of no trans-
mission corresponding to the thermo-dynamic functions F,, F,, is
represented by Q,(F,—F,).

The area of a diagram of energy of any figure is calculated by
conceiving it to be divided, by a network of isothermal curves and
curves of no transmission, into an indefinite number of stripes or
quadrilaterals, finding the area of each and adding them by summa-
tion or integration. By the aid of these principles various problems
are solved.

In the third section the same principles are applied to determine
the efficiency of thermo-dynamic engines worked by the expansion
and contraction of permanent gases without and with the aid of
economisers or regenerators. The efficiency of a thermo-dynamic
engine is the proportion of the whole heat communicated to the
working substance which is converted into motive power.

The maximum theoretical efficiency of a thermo-dynamic engine
working between the limits of actual heat Q, and Q,, whether with-
out a regenerator or with a perfect regenerator, is expressed by the
fraction Q,=—Q,

ll

A theoretically perfect regenerator does not increase the maxi-
mum efficiency between given limits of actual heat, but merely
enables that efficiency to be attained with a smaller extent of expan-
sion, and consequently with a smaller engine.

The fourth section treats of the relation between actual heat and
temperature, which must be known before the propositions of the
preceding sections can be applied to actual substances. Existing
experimental data are not yet adequate to the ewact determination of
this relation; but it is considered they are sufficient to show that a
relation deduced by the author from the Hypothesis of Molecular
Vortices (see Philosophical Magazine for December 1851, p. 510), is
at least near enough to the truth for all purposes connected with the
computation of the efficiency of thermo-dynamic engines. This re-
lation is expressed by the formula

Q=k(T+T)),

where T is temperature, measured from the melting-point of ice ;
T,, the height of the melting-point of ice above the point of total
privation of heat; and k, the mechanical value of the real specific
heat of the substance. According to computations made in 1852
by the author from experiments by Messrs. Thomson and Joule,
T,=2722° Centigrade=4903° Fahrenheit, a value which may be
considered sufficiently correct for practical purposes.

The maximum theoretical efficiency of every conceivable thermo-
dynamic engine receiving heat at the temperature T,, and giving out

Royal Institution. 291

heat at the temperature T,, is
Q,-Q,_T, —T,
Q, = 1T,4+T

The fourth section concludes with a system of formule, illustrated
by numerical examples, for computing the power and efficiency of
air-engines.

In the fifth section, the principles of the preceding sections are
applied to aggregates consisting of heterogeneous substances, or of
the same substance in different conditions, especially the aggregate
of a liquid and its vapour ; and the results are applied to the nume-
rical computation of the theoretical efficiency of steam-engines.

Jan. 26.—The Rev- Baden Powell, V.P., in the Chair.

A paper was read, entitled ‘‘ On the Vibrations and Tones pro-
duced by the contact of bodies having different Temperatures.” By
J. Tyndall, Esq., F.R.S. [An abstract of this paper was given in
our last Number. ]

ROYAL INSTITUTION OF GREAT BRITAIN.

March 3, 1854.-——On certain Phenomena of Retatory Motion.
By the Rev. Baden Powell, M.A., V.P.R.S., F.R.A.S., F.G.S.,
Savilian Professor of Geometry, Oxford.

The mechanical principle of ‘‘the composition of Rotatory
Motion,” originally discovered by Frisi about 1750 (see Frisius de
Rotatione, Op. ii. 134, 157, and Cosmographia, ii. 24), is equally
simple in its nature, important and fertile in its consequences and
applications, and susceptible of the easiest explanation and experi-
mental illustration; yet it has been singularly lost sight of in the
common elementary treatises. It is, indeed, discussed and applied
in a mathematical form in Mr. Airy’s Tract on Precession (Math.
Tracts, p. 192, 2nd ed.); and the theorem is stated by Professor
Playfair in his Outlines of Natural Philosophy (vol. i. p. 144), and
its application explained (ib. vol. ii. p. 308). These, however, are
not books of a popular kind, and the author is not aware of any
mention of it in other English works. In a more abstract analytical
form it has been discussed by several foreign mathematicians, espe-
cially by Poinsot, in a memoir read to the Academy of Sciences,
May 19, 1834, but of which only an abstract was published; as
well as by Poisson, in a paper in the Journal de l’ Ecole Polytechnique
(vol. xvi. p. 247).

The principle is involved in the explanation of several important
phenomena, some of which are, in fact, mere direct instances of it ;
so that a simple experimental mode of exhibiting it would be emi-
nently desirable; and several such have accordingly been devised
which yet seem to have been but little generally known.

An ingenious instrument of the kind was contrived some years
ago by Mr. H. Atkinson, a very brief account of which is given in
the Astronomical Society’s Notices, vol. i. p. 43, though so brief
that it is difficult to collect what the precise mode of its action was,
—but it seems somewhat complex.

A far more complete and instructive apparatus was invented by
Bohnenberger, hd described in Gilbert's Annalen (vol. lx. p. 60). It

292 Royal Institution.

is also explained in some German elementary works. Attention has
been more recently drawn to the subject by a highly interesting
paper of Professor Magnus of Berlin (Verhandlungen der Kénigl.
Preuss. Akad. 1852, translated in Taylor’s Foreign Scientific Me-
moirs, N.S. part 3, p. 210), in which some remarkable applications
of this apparatus are given; he also describes it (with a figure), and
observes that the execution of it requires great delicacy and correct-
ness of workmanship. Copies of this instrument have indeed been
made in this country (one of which was exhibited through the kind-
ness of Professor Wheatstone) ; but of these the author believes no
description has ever appeared in English works, and they are cer-
tainly very little known, notwithstanding their manifest value to
every lecturer: the essential parts are a sphere capable of rotating
about an axis whose extremities rest in opposite points of a hoop
which can turn on pivots horizontally, within another hoop turning
on pivots about a vertical line.

In fact, the author of the present communication has long felt the
want of such an apparatus for lecture illustration; and before he
was aware of the existence of any of those just alluded to, had con-
structed one in a different form, and which is found to answer fully
the purposes of illustration for which it is designed, without any nice
workmanship or complex machinery. (See Astronomical Society’s
Notices, vol. xiii. pp. 221-248.)

Its object, like that of the instrument last mentioned, is to exhibit
experimentally the actual composition of rotations about two different
axes impressed at once on the same body.

The essential parts are merely a bar capable of rotating freely
about one end of an axis (and loaded at its extremities to keep up
the rotation), while the axis itself can turn about a point in its length
near the end carrying the bar, upon a horizontal axis, capable of
moving freely round a vertical pillar. At the lower end of the first
axis is a weight which more than counterpoises the upper part.

If, then, there be no rotation in the bar about the first axis, the
effect of the weight is to produce a rotation about the second alone,
bringing down the first axis into a vertical position.

If now the first axis be held horizontally or obliquely, and a rota-
tory motion be given to the bar about it, on letting the axis go we
compound both rotations; and the resulting effect is, that the weight
will no longer bring the axis down, or alter its inclination at all, but
will cause it to take a new position, or make the whole to turn
round the vertical, in a direction opposite to that of the rotation.

Thus, although confessedly not new in principle, to make public
an experimental illustration in so simple a form may not be without
its use for a great majority of students.

Even the theoretical principle is capable of being stated in a way
quite intelligible to those acquainted only with the very first rudi-
ments of theoretical mechanics, presenting itself in close analogy to
that well-known first principle, the composition of rectilinear motion.

As in this last case, if a body be in motion in one direction, and
any cause tend to make it move in another, it will move in neither,
but in an intermediate direction,—so we have the strictly analogous

Royal Institution. 293

case in rotatory motion ; when a body is rotating about an axis, and
any cause tends to make it rotate about another axis, it will not rotate
about either, but about a new axis intermediate to the two. Thus the
result of compounding the two rotations will be, that the axis (car-
rying with it the rotating body) will simply take a new position, or will
move ina direction determined by the nature of the impressed motions.

Professor Magnus, in the very able but rather prolix and obscurely
written memoir before referred to, speaks (p. 223) of the conse-
quences of such a law as evinced in the resulting rotations, but
without any distinct or explicit statement of the essential theorem of
the composition of rotatory motion. He gives, however, some sin-
gular and even paradoxical exemplifications of it. We may allude
to one of these, which is capable of being put into a form at once
more simple, and at the same time more paradovical, than that in
which he describes it. It consists in this: a wheel at one end of
an axis and a weight at the other are suspended in equilibrio, which
is of course unaltered, whether the wheel be at rest or in rotation;
the weight is then slid so that the balance is destroyed; now if the
wheel be set in rapid rotation, the equilibrium is restored. This is
nothing but a simple case of the principle just stated, as shown
by the author’s apparatus.

Besides certain other cases traceable to a different cause, Professor
Magnus’s immediate object is to explan a curious observed anomaly
in the motion of projectiles of an elongated form shot from rifled
guns, and which consequently rotate about their axis while passing
through the air in the direction of that axis.

He mentions the fact, that artillery experiments in different coun-
tries with rifled cannon and missiles of a cylindrical form with a
conical apex, always show a deviation of the pojnt of the missile to the
right, the rifle-spiral being right-handed.

To explain the nature of this deviation was the object of special
experiments on the part of the Prussian Artillery Commission, in
which Professor Magnus assisted. The missiles were fired with low
charges, so as to allow the motion to be accurately observed, and
it was found that the axis remained sensibly in the direction of the
tangent to the curved path, while the deviation to the right was
always clearly marked. He observes that left-handed rifles have
never been tried.

Professor Magnus, after some fruitless conjectures as to the cause,
at length sought it in the principle of the composition of rotatory
motion. He tried experimentally the effect of a current of air on a
projectile of the form employed, by inserting such a body instead of
the rotating sphere in Bohnenberger’s apparatus, and observing the
effect on it, first at rest and then in rotation, when the strong cur-
rent of a blowing-machine was directed against the conical apex.
When at rest, the current elevated the apex; owing to the form of
the missile, the resistance acting not through the centre of gravity,
but above it; when in rotation no elevation took place, but a devia-
lion in the direction of the axis, ina direction opposite to that of
rotation. ‘To show the application of the principle in this case, he
observes that the axis of the elongated projectile, which for an instant

294 Royal Institution.

coincides with the tangent to its curved path, momentarily changes
_ its'direction, so that the front extremity or apex falls below its former
position. Or, for a single instant it may be regarded as if locally at
rest, but turning about its centre of gravity so as to depress the apex.

If the motion were simply in the direction of the axis, the resist-
ance of the air would operate-directly against it; but when the apex
is continually tending to turn downwards from that line, the resist-
ance acts against it partially upwards, and thus tends to raise the apex.
_ Thus, at a given instant, the elongated projectile may be repre-

sented by the rotating part of the apparatus just described.

When there is no rotation, the resistance of the air tending to
raise the apex is represented by the weight at the lower end, which
produces the same effect.

When a rapid rotation is communicated (suppose from left to right
of the gunner), the result will be no elevation of the apex, but a
lateral movement, or commencement of a rotation round the vertical
—ain astronomical language retrograde, if the former rotation be
direct; but which, beginning from the opposite part of the circle, is,
relative to the operator, towards the right.

The form of the projectile used in these experiments differs from
that in the Minié rifle, in that the latter is hollow at its broader end,
and thus the centre of gravity is thrown forward towards the apex.
Hence, according to the same theory, the effect would probably here
be to depress the apex, and therefore to give an opposite deviation ;
but it does not appear whether any such observations have been
made; and in practice the effect would probably be quite insensible.

It occurred to the author that a very simple illustration of this
deviation of rifle projectiles might be made by merely forming a sort
of small arrow, whose head was composed of a cork, like a shuttle-
cock, but instead of the feathers, small card vanes inclined in the
same direction round it, with a tail to balance it, and which thus in
the mere act of throwing acquires a rotatory motion from the reac-
tion of the air, to the right or left according as the vanes are in-
clined ; and on trying this, there was always observed a deviation
in the direction of the axis or point of the missile to the right or left
accordingly, relative to the experimenter. It is, in fact, nearly im-
possible to throw such a body in a direction perfectly in one plane.
The true deviation is, however, peculiarly liable to be disguised by
the general resistance of the air on so light a missile, as well as by
currents, &c. which it is not easy to guard against.

The well-known case of the Boomerang exhibits effects closely
similar ; for it is found that if so projected that its rotation is from
left to right, its deviation will be in the same direction, and vice versd ;
that is, supposing (as is the usual case) that its plane is inclined
upwards from the operator :—if it be inclined downwards, the devia-
tion is in the direction opposite to that of the rotation.

In the former case the reaction of the air against the flat surface
of the missile would tend to increase its inclination upwards, in the
latter downwards, with respect to the operator; and this in each
case respectively would give the motion stated ; as is easily seen on
the principle, and by means of the apparatus, before described.

Royal Institution. 295

Thus it would follow, that this extraordinary instance of savage
invention, which long ago puzzled inquirers, is simply a case (like
the last) of ‘the composition of rotatory motion.”

{t should, however, be mentioned, that some experimentalists have
entertained a different view of the cause of deviation in this instance.

Besides the results above stated, Professor Magnus (in the same
memoir) mentions several other highly curious cases produced by
certain modifications of the apparatus, but all referable to the same
principles.

M. Fessel has also invented an apparatus (since called the gyro-
scope), an account of which is given with some remarks by Professor
Plicker, and the editor in Poggendorff’s Annalen (18538, Nos. 9 and
10), which, though apparently invented without any knowledge of
Bohnenberger’s apparatus, is a modification of it, referring to phe-
nomena of the same kind as those of the equilibrium experiment
mentioned at first.

This apparatus has been greatly improved upon by Professor
Wheatstone, who has introduced other movements to include the
conditions of rotation in different planes. One of these instruments
was exhibited.

From these singular applications of a very simple mechanical
truth, we may now turn to what is but another exemplification of
the same thing, however apparently remote from those we have con-
sidered, and upon a far grander scale.

The phenomenon of the precession of equinoxes was known to
Hipparchus, but no explanation of the fact was for ages imagined.
Eyen Kepler, in the multiplicity of his hypothetical resources, could
not succeed in devising anything plausible. The axis of the earth
is slowly shifting its position, so that its pole points continually to a
new part of the heavens-—a new pole star—at the rate of about 50!
a year, and of course carries with it the point of intersection of the
earth’s equator with the ecliptic or plane of its orbit, at the same
rate and in a direction opposite to that of its motion, or the order of
the signs. .

These phenomena remained wholly without explanation till
Newton, led by the analogy of those disturbing forces on the orbit
of a planet which cause its nodes to regress, showed that the same
would occur in a satellite to the earth—in a ring of such satellites—
in such a ring adhering to the equator, or the protuberant part of
the terrestrial sphere, and thus that the equinoctial points would
slowly regress, (See Principia, vol. i. p. 66, corr. 11-22.)

The more exact determination of quantitative results was reserved
for Newton’s successors, when a more powerful analysis had been
applied by Euler, D’Alembert and others, to the full exposition of
the theory, founded on general equations of motion; as since given
in the writings of Laplace (Méc. Cél. liv. xiv. ch. 1), and Pontécou-
lant (Théorie du Systéme du Monde, liv. iv. ch. 5), which are neces-
sary for including all the minuter variations detected by Bradley,
and subsequent observers, showing the nutation of the axis, and the
inequalities of precession due to the varying configurations of the
attracting luminaries.

296 Royal Institution.

These higher mathematical views, though of course the most
complete and systematic, are not the most direct or easy mode of
explaining the subject to the student. Greater simplicity certainly
characterizes the method adopted by Mr. Airy (in the tract before
cited) of applying directly the theorem of the composition of rotatory
motion, as doubtless Newton would have done had it been known to
him. But here, as in so many other instances, the first explanation
presented itself mixed up with more complex considerations ; and
as has been well observed, ‘‘ simplicity is not always a fruit of the
first growth.”

To those not versed in the mathematical theory of all points in
physical astronomy, the ‘‘ modus operandi’ of the precession, per-
haps, usually seems the most paradoxical; and the explanations
given in some of the best popular treatises are seldom found satis-
factory, following as they do the letter of Newton’s illustration, and
omitting the direct introduction of the principle of composition,
which, if only from what has been here offered, is at once seen to be
easily capable of the most elementary explanation. Indeed it was
from this consideration forcing itself on the mind of the author, in
several courses of popular lectures on astronomy, that he was led to
seek the means of experimental illustration above described; and
which would more palpably imitate the phenomena to the eye, if,
instead of the rotating bar a terrestrial globe be substituted (as in
Bohnenberger’s instrument)—for better illustration made protuberant
at the equator—where the weight at the south pole acts the part of
the sun’s and moon’s attraction, to pull down the protuberant matter
of the spheroid at the equator if at rest, but when combined with
the earth’s rotation results in a transference of the position of its
axis, or slow revolution of its pole round the pole of the ecliptic in
a direction opposite to its rotation, carrying with it the equinoctial
points, and causing the sigvs of the zodiac to shift backwards from
their respective constellations.

It always affords a sort of intellectual surprise to perceive for the
first time the application of some simple and familiar mechanical
principle to the grand phenomena of astronomy ; to see that it is
but one and the same set of laws which governs the motions of
matter on the earth and in the most distant regions of the heavens ;
to find the revolution of the apsides in a pendulum vibrating in
ellipses, or the conservation of areas in a ball whirled round by a
string suddenly shortened; or (as in the present case) to perceive a
celestial phenomenon, vast in its relations both to time and space,
and complex in its conditions, identified, as to its mechanical cause,
with the rotatory movement of a little apparatus on the table before
us, or to discover the precession of equinoxes in the deviation of a
rifle or a boomerang. And the simple experimental elucidation of
such phenomena and their laws will not be useless, as it tends to
confirm in the mind of the student the great characteristic of the
modern physical philosophy first asserted by Galileo, the identity of the
causes of the celestial and terrestrial motions, and to aid and elevate
our conception of those grand and simple principles according to
which the whole machinery of the universe is so profoundly adjusted.

XLV. Intelligence and Miscellaneous Articles.

ON THE HEAT PRODUCED BY AN ELECTRIC DISCHARGE.
BY R, CLAUSIUS.
To the Editors of the Philosophical Magazine and Journal.

GENTLEMEN,
- a paper by Prof. W. Thomson, in the March Number of the
Philosophical Magazine, p. 198, the following statement occurs
on the discovery of the important law, that the heat capable of being
produced by an electric discharge is not simply proportional to the
quantity of electricity employed, but to the square of the same,
“as was first demonstrated by Joule in a communication to the
Royal Society in 1840, although it had been announced by Sir W.
Snow Harris as an experimental result, to be simply proportional to
the quantity. Mr. Joule’s result has been verified by independent
observers in France, Italy and Germany.” I may be allowed to
observe on this subject, that the investigations of Riess, mentioned
by me in my paper on the mechanical equivalent of an electric dis-
charge, are of a much older date. The memoir in which Riess
refuted the statement of Snow Harris, and proved to a certainty by
numerous experiments that the heat which is produced by the dis-
charge of a Leyden battery in any part of the connecting wire is
represented by the formula Gredust
s
in which g denotes the quantity of electricity used, and s the surface
of the inner coating, is printed in Poggendorff’s Annalen for March,
1837.
I am, Gentlemen,
Yours faithfully,
Berlin, March 19, 1854. R. Crausivs.

ON SOME PECULIAR REDUCTIONS OF METALS IN THE HUMID
WAY. BY PROF. WOHLER.

The following experiments were made for Prof. Wéhler by Hiller.
The observation first made by Bucholz, that long crystals of metallic
tin ave formed when a rod of that metal is inserted in a solution of
protochloride of tin, and the latter carefully overlaid with water, was
first of all further tested. It appeared that, for the production of
large crystals, the solution of chloride of tin must be acid. Of the
tin immersed in the solution there was always more dissolved than
was made up by that which crystallized. In one experiment the
proportions were as 7:6. ‘

These crystals are formed at the point of contact between the two
fluids. If the solution be neutral, they appear below this in the
solution of the protochloride, and remain bright.

Copper, inserted into a neutral solution of nitrate of copper, covers
itself entirely with brownish-red crystals of protoxide of copper, and
afterwards with sharp crystals of metallic copper. The copper is
dissolved, especially at the point of contact of the fluids. The same
phenomenon is produced, but in a less degree, with sulphate of
copper. In solution of perchloride of copper, the copper is covered
with crystals of the protochloride.

Phil. Mag. 8. 4, Vol. 7. No. 45. April 1854, ».¢

298 Intelligence and Miscellaneous Articles.

A rod of zine, under similar circumstances, covers itself with gray
granules of metallic zine, especially at its lower end. In this case
also the zinc is dissolved at the point of contact of the fluids.

Cadmium behaves in a similar manner in the solution of its
nitrate; the reduced metal is more pulverulent, and therefore much
more readily oxidized in the air than the reduced zinc.

Lead, in a solution of neutral nitrate or acetate of lead, furnishes
small shining crystals of lead.

Bismuth precipitates the metal from a solution of protochloride of
bismuth, if the latter has been overlaid first with muriatic acid, and
afterwards with water.

On silver, immersed in a concentrated solution of nitrate of silver
overlaid with water, metallic silver is deposited in a dendritic form,
always originating from a few scattered points Be oe surface of the
silver.—Ann. der Chem. und Pharm., \xxxv. p. 253

ON THE DECOMPOSITION OF WATER BY THE PILE. BY J. JAMIN,

M. Foucault has just published a note in which he shows that two
voltameters traversed by the same current disengage different quan-
tities of gas, if one contain acidulated water, with electrodes of pla-
tinum wire, and the other only pure water, with plates of a certain
size for electrodes.

M. Foucault explains this phenomenon by supposing that fluids
transmit electricity in two ways: by physical conductibility, which
is effected without decomposition ; and by chemical conductibility,
which causes a separation of their elements. M. Foucault collected
the gases in the same receiver, and did not endeavour to ascertain
whether the passage of the current gave rise to any new chemical
compound, The author has been occupied for several months in
similar researches, and had ascertained the fact which M. Foucault
has published.. He now confirms it, but adds some experiments
which prevent his admitting the theoretical consequences of M.
Foucault.

In attentively studying the decomposition of water, it is evident
the separation of its elements does not take place with the simplicity
hitherto supposed. The double volume of hydrogen is scarcely ever
obtained, and predominating quantities of either gas may be produced
by alteration of circumstances, and especially by changing the extent
of one of the electrodes.

Employing as a positive electrode a Wollaston wire, and as a ne-
gative a plate of 15 square centimetres, the author obtained five cubic
centimetres of hydrogen and nine of oxygen, being in a proportion
of 0°55 instead of 2to 1. By changing the direction of the current
so as to reverse the electrodes, and waiting for some hours to avoid
errors of polarization, the volume of hydrogen collected was to that
of oxygen as 9°3 to 10 instead of 2. ‘These experiments, frequently
repeated, did not always furnish equally decisive results, but they
had always the same tendency; showing that electrodes with a
large surface, whether positive or negative, disengage less gas than
fine slender wires employed as the opposite electrodes in the same
voltameters.

_ Intelligence and Miscellaneous Articles. _ 299

The experiment is more striking when two voltameters, arranged
as in the first and second case, are placed in the same circuit. In
one case there were—

Py aik 929 1204
ZO Tiss 544

H

a ae 1°60 4°42
O

If the two plates be put into one voltameter and the two wires
into the other, without any change in the other arrangements,
similar results will be obtained; the two plates produce but little
gas, whilst the two wires furnish a large quantity. A voltameter
may be formed with a permanent Wollaston wire, and with a plate of
platinum or of some other metal which may be changed at pleasure ;
each plate will disengage (the intensity of the current being the
same) very variable quantities of gas, whilst the wire produces aconstant
action; there is consequently complete independence between the
two electrodes. These inequalities may be increased or diminished by
very different circumstances ; they become very remarkable in employ-
ing the platinum plates of a Grove’s battery. The author thus formed
two dissymmetrical voltameters, which only produced a disengage-
ment of gas at the wires, but none from the plates; the first furnished
nothing but hydrogen, the second only oxygen; by putting the two
plates in the first vessel and the two wires in the second, and passing
the current through them, the former allowed it to pass without de-
composition, whilst the second produced a great disengagement of
gas. This, therefore, has nothing to do with conductibility, but
depends on a property peculiar to each electrode.

As one only of the elements of water is obtained by a dis-
symmetrical voltameter, it must be admitted that the one which is
not disengaged must combine with the liquid, or become condensed
on the plates. These two effects take place simultaneously.

To show that oxygenated water is produced when hydrogen alone
is evolved, all that is necessary is to carry on the decomposition in a
cold platinum crucible communicating with the positive pole, immer-
sing the negative wire in the fluid which it contains. The author
has found that the hydrogenated liquid produced by the evolution of
oxygen from water possesses new properties.

The decomposition of water never takes place without an altera-
tion of the electrodes, which is slow, but continuous. The positive
electrode becomes yellow, and passes to orange; the negative
acquires a violetcolour. These tints gradually increase and blacken,
so that it is evident that something is deposited upon the platinum.
These deposits disappear in the air, especially when the electrodes
are heated. The negative plate becomes clean in nitric acid, and
absorbs gaseous oxygen ; the positive plate is cleaned by deoxidizing
liquids, and absorbs hydrogen. Lastly, if the two electrodes be im-
mersed in acidulated water and united by a galvanometer, they give
rise to a current of reaction which lasts several days. These pro-
perties acquired by the plates deserve particular attention, and the
author thinks they are to be attributed to condensation of the two
gases on their surfaces. This opinion is confirmed by the fact, that

X 2

300 Intelligence and Miscellaneous Articles.

when the coloration has become very intense, the plates continue to
disengage gas for a long time after the passage of the current has
ceased.

To resume, the author thinks that the decomposition of water is
not a simple phenomenon,—that electricity first of all produces the
pure and simple separation of the elements of water, and afterwards
physical or chemical actions, which, although difficult to observe,
certainly exist. These are weak in ordinary cases, but are no longer
to be neglected where electrodes of large dimensions are employed,
and it is to these actions that the anomalies observed in the decom-
position must be attributed.—Comptes Rendus, February 27, 1854,
p. 390.

LITHOLOGIC STUDIES. BY C. SAINTE-CLAIRE DEVILLE.

What are the elements that should guide us in the natural classifi-
cation of igneous rocks? Such is the problem which I have set before
me in this first memoir. The very nature of the question, as it was
put forward by M. Cordier in the important memoir which he pub-
lished in 1815, led me necessarily to re-examine minerals from a
particular point of view, that of the part which they take in the for-
mation of rocks. In this study I must particularly dwell upon an
important notion, first introduced into science by M. Elie de Beau-
mont*, the distinction which that geologist has established between
matters formed by igneous fusion, or eruptive matters in the manner
of lava, and matters volatilized or carried up in the molecular state,
eruptive matters in the manner of sulphur, sal-ammoniac, &c. The
natural divisions which may thus be established in minerals are
based, as I show, at once on the characteristic properties of the
minerals of each group, on their stratification, and on the labora-
tory experiments by which they have been reproduced.

In the latter part of my memoir I endeavour to indicate what
advantage may be derived from the characteristic properties of mine-
rals, in establishing the natural relations between rocks which are
only aggregates of these various minerals.

The conditions of stratification which every good classification
should indicate, lead me to inquire what ought to be understood by
the words—the age of an igneous rock. I close this question, by
which lithology enters into relation with stratigraphy, by showing
that in each family of rocks the age is in immediate relation with
the nature and abundance of the minerals formed in the manner of
sulphur ; so that we may say, that this kind of minerals plays in some
sort, in the igneous rocks, the part of characteristic fossils.

The certainty or the probability of these conclusions resting entirely
upon the facts brought together in my memoir, some of which are
known, whilst others appear to me to be new, it will be readily
understood, that, both from its nature and extent, the work which I
lay before the Academy is scarcely susceptible of an analysis. I
shall therefore confine myself, in concluding this note, to calling
attention to some of the prominent points of my work, and which I

* Des Emanations Voleaniques et Meétalliféres, Bull. Soc. Géol. Fr.
2nd ser. vol. iv.

Intelligence and Miscellaneous Articles. 301

hope will possess some interest, as they settle the chemical formula
of several substances on which the opinions of scientific men do not
ee.

To establish the normal composition of the minerals formed in the
manner of sulphur, 1 suppose that wherever a certain proportion of
fluorine or chlorine is met with in these minerals, these bodies only
exist there still because the reaction which should have converted the
chlorides and fluorides into oxides has only been imperfectly effected.
But if we complete, by calculation, the substitution of oxygen for
the chlorine and fluorine, converting the whole into oxides, we arrive
at a simple formula.

For the topaz, these suppositions, already sufficiently justified by
the discussion of the analyses of this mineral due to M. Forch-
hammer, have just been confirmed by some. unpublished researchs
of my brother and M. Fouqué. The topaz would thus be as-
similated to a silicate of alumina, in which the oxygen of the base
would be in relation to that of the acid in the proportion of 4 to 3.

When the mineral contains, together with fluorine, a body which,
like silicium, and especially boron, is capable of being sublimed with
it during calcination, we may, by taking the most probable hypo-
thesis, restore to the mineral its primitive composition. I find an
example of this in the tourmaline. It is well known that mineralo-
gists are far from being agreed as to the formula which should be
attributed to this substance. In his last supplement, M. Rammels-
berg proposes three different formulz, which have scarcely anything
in common, to represent the different varieties of a mineral so homo-
geneous in its crystalline form andinits properties. I have no space
_ here to discuss the numerous analyses of tourmaline contained in the
same volume; but if we suppose that the loss by calcination, which
varies from 1°8 to 3°8 per cent., is owing to a disengagement of
fluoride of boron, and calculate from this datum and from the boron
determined, the corresponding quantity of boracic acid, we obtain the
following numbers for the oxygen of the four constituent elements
of the mineral :—

Protoxides. Boracic acid. Sesquioxides. Silex.
Calculated . . 4°33 6°50 16°24 19°48
Found , . . 4°56 6°43 16°77 19°48

A remarkable concordance, which, I think, justifies us in attributing
a single formula to all the varieties of tourmaline, according to
which the oxygen would be distributed amongst the four elements
in the following proportions :—

4:6:15:18.

This formula would certainly not apply to the last group of tour-
malines of M. Rammelsberg, the tourmalines containing lithia.
But the presence of this base may throw a light upon the causes of
this anomaly ; the lithia must in great part be carried off by the
fluorine, and this supposition is confirmed by the researches of
MM. H. Sainte-Claire Deville and Fouqué. Moreover, when the
same hypothesis is applied to analyses of tourmalines which doubt-

302 Intelligence and Miscellaneous Articles.

less had not been previously exposed to a white heat, such as those
mentioned in M. Dufrénoy’s Traité de Minéralogie, although the
oxygen of the protoxides always presents a slight deficiency, we
obtain results very similar to the preceding*. Certain groups of
minerals, although belonging to the class of those which are formed
in the manner of lavas, are nevertheless capable of containing in a
state of mixture quantities, sometimes considerable, of minerals
formed in the manner of sulphur. It is thus that we may explain
the presence of fluorine, boron, titanium, &c. in pyroxene, and espe-
cially in hornblende.

The following is an immediate consequence of this remark. The
efforts which have been made by mineralogists to reduce to a simple
formula the analyses of hornblende, in which the alumina mayamount
to 20:0, or be entirely wanting, are well known. ‘The opinion gene-
rally adopted for want of a better is that of M. Bonsdorff, who, sup-
posing that alumina is isomorphous with silica, represents the mineral
pretty well by a silicate of protoxides, in which the proportions of
the oxygen in the acid and in the base would be 9:4, instead of
8:4 as in pyroxene. But everything is explained and simplified if
we suppose that the alumina is foreign to the normal composition of
the mineral, and that it only exists there as an integral portion of a
substance formed essentially in the manner of sulphur; a spinedlide,
that is to say, a body of the form R2 O3 RO, like the spinels of iron
or magnesia, protoxide of iron, &c., which are found mechanically
mixed with hornblende, and consequently never alter its crystalline
form.

In applying this hypothesis to a great number of analyses taken
at random from amongst those contained in M. Rammelsberg’s work,
we find, after previously deducting the intermixed aluminate, that
the oxygen of the silica is nearly equal to double that of the prot-
oxides. The analyses which present a noticeable discrepancy are
those of the hornblendes, which contain much magnesia, and this fact
bears a relation to the difficulty which is experienced in determining
this base exactly.

I wished my idea to be checked by analyses made in the laboratory
of the Ecole Normale with the precision afforded by the methods
recently introduced there. The following are the results furnished :—

* I do not mean to say that the boron is necessarily in the form of
boracic acid in the tourmaline, nor that fluorme may not be normally con-
tained in it. This is a point that can only be settled by analyses in which
these bodies shall have been very exactly determined. My hypothesis consists
simply in considering fluorine as capable of substituting itself atomically
for oxygen.

I have as yet arrived at nothing so clear as regards mica, but I have no
doubt that the application of the same principle to complete analyses of
this singular body will explain its anomalous composition ; and it may be
that the optical anomalies which M. de Sénarmont has simplified and de-
fined so remarkably in his memoir, are only due to the variable proportions
in which the mutual substitution of fluorme and oxygen takes place in it ;
it is a question which I propose, with my brother’s assistance, to examine
in a separate memoir.

Meteorological Observations. 303

Contents per cent. Proportion of the oxygen

of the protoxides to that
of the silica after the

Alumina. Magnesia. _|removal of the spinellide.
White amphibole (Fremolite) : si ae
from St. Gothard ............ eS a Te a-02
Green amphibole (actinote) : = als
from St. Gothard ............ Sey 1§'52 oe ahegs
Black amphibole (hornblende) } 15-48 14:37 1: 2-00
from Guadaloupe ............ A
Average 1: 1:95

Ss ee ee ee eS Se ee.

I think, therefore, that the chemical formula of hornblende is
exactly the same as that of pyroxene, and that we must consequently
return to an opinion formerly maintained by M. G. Rose, but which
he has since abandoned, attributing, I think, to the presence of the
sesquioxide an influence which it should not have upon the normal
constitution of the mineral. The secondary dimorphism of pyroxene
and hornblende would also be sufficiently explained by the very pecu-
liar gaseous medium in which the latter mineral appears to have
been formed, and the curious facts noticed by M. G. Rose in ura-
lite would favour this explanation.—Comptes Rendus, February 27,
1854, p. 390.

METEOROLOGICAL OBSERVATIONS FOR FEB. 1854.

Chiswick.—February 1. Cloudy: rain. 2. Overcast: clear, with bright sun:
frosty. 3. Frosty: dense fog. 4. Frosty: very fine: overcast. 5. Clear: cloudy.
6. Fine. 7. Cloudy: clear at night. 8. Clear: cold and dry: overcast. 9.
Cloudy: rain. 10. Clear and frosty: cloudy and cold: clear. “11. Cloudy and
fine: hazy. 12. Foggy: clear and fine. 13. Frosty: cold and dry: clear, with
sharp frost at night. 14. Sharp frost: fine. 15. Overcast. 16. Cloudy : clear:
overcast. 17. Cloudy. 18. Drifting snow: clear and cold: boisterous at night.
19. Clearand cold. 20. Overcast. 21. Clear and fine. 22. Fine: cloudy. 23.
Clear. 24. Cloudy. 25, 26. Very clear. 27. Uniformly overcast: clear: over-
cast. 28. Fine.

Mean temperature of the month ..... SWodaGevs eee steed eecseeees 3707
Mean temperature of February 1853 ........ Saecneameeensecee «- 32 53
Mean temperature of Feb. for the last twenty-eight years... 39 -13
Average amount of rain in Feb. ..............ssssscesesssceooece 1°57 inch.

Boston.—Feb. 1. Cloudy. 2—4. Fine. 5—9. Cloudy. 10. Fine: snow a.m.
11. Cloudy. 12. Fine. 13. Cloudy. 14. Fine. 15, 16. Cloudy. 17. Cloudy :
rain P.M. 18. Cloudy: stormy. 19. Fine. 20. Cloudy: rain a.m. and p.m.
21. Fine. 22. Fine: rain p.m. 23—26. Fine. 27, 28. Cloudy.

Sandwick Manse, Orkney.—Feb. 1. Showers a.m.: clear p.m. 2. Showers a.m.
and p.m. 3. Cloudy a.m.: cloudy, aurora p.m. 4, Cloudy a.M. and v.m. 5,
Sleet-showers a.m.: showers p.m. 6. Showers A.M.and p.m. 7. Sleet-showers
A.M. : hail-showers p.m. 8. Hail-showers a.m.andp.m. 9. Snow-showers A.M.:
clear p.M. 10. Cloudy a.m.andp.m. 11. Drizzle a.m.: cloudy p.m. 12. Cloudy
AM. and p.m. 13,14. Drizzle a.m. and p.m. 15. Hail-showers A.M. and p.m.
16. Drizzle a.m. and p.m. 17. Snow-showers A.M.andp.m. 18. Snow-showers
A.M. : hail-showers p.m. 19. Cloudy a.m.and p.m. 20. Showers A.M. : clear P.M.
21. Bright a.m.: cloudy p.m. 22. Drizzle a.m.: showers p.m. 23. Snow-showers
A™M.: hail-showers p.m. 24. Showers a.m.: showers, aurora p.m. 25, Showers

A.M.: aurora P.M. 26. Cloudy a.M.and p.m. 27. Rain a.m.andp.M. 28, Sleet-
showers A.M.: showers P.M.

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THE
LONDON, EDINBURGH anno DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

MAY 1854.

XLVI. Theory of the Electric Residue in the Leyden Jar.
By R. Koutrauscn*.

[With a Plate. ]

HE solution of an important electrical problem rendered it
necessary for me to seek the law of the formation of the elec-
tric residue in the Leyden jar. The sine-electrometer described in
Poggendorff’s Annalen, vol. lxxxviil. p. 497, was constructed for
this purpose; and having, by means of it and the multiplier
described in the present memoir, subjected the facts of the case
to a more strict investigation ($ 1 to § 8), it soon appeared
(§ 9) that the explanations of the phenomenon hitherto given
could lay little claim to accuracy. Another cause for the pro-
duction of the residue was therefore sought (§ 10), and the con-
sequence was, that a numerical law was discovered (§ 11) which
was applicable to practical purposes (§ 12).

The new hypothesis ought, indeed, to be subjected to strict
criticism, for such hypotheses, on account of their wide appli-
cability, have something attractive in them, and are therefore to
be received with due caution. If, however, the explanation
given in § 10 should be rejected, still the facts cited, and the
correctness of the calculations, will not be questioned.

§1.

When a Leyden jar is charged, a constant diminution of the
tension upon its knob is observed. If, in observing this, suitable
electrometers be made use of, it will appear that the decrease
shortly after charging is much more considerable than after some
time has elapsed, and the conjecture arises that the phenomenon

* From Poggendorff’s Annalen, vol. xci. p. 56,

Phil, Mag, 8. 4, Vol. 7, No. 46, May 1854. b

306 M. R. Kohlrausch’s Theory of the

must be due to a cause different from the mere loss of the elec-
tricity in the surrounding air.

For the decision of this question, it is in the first place neces-
sary to determine accurately the curve according to which the
tension diminishes, more especially as this curve is to form the
basis of conjectures regarding the existence of causes different
from those hitherto assigned. Hence our first step is to make
the observations necessary for the construction of such a curve.

If the observations are to be made with purity, care must be
taken that the charging of the jar is of momentary duration, and
not gradual, so that no uncertainty shall exist as to what occurs
during the gradual augmentation of the electricity ; an electro-
meter is also necessary, by means of which the tension may be
observed from the moment of charging onwards. The first con-
dition is secured by connecting a jar with another, or with a
battery of jars, already charged; and the second is secured by
the use of the sine- electrometer, applying the method described
in vol. Ixxxviii. p. 508 6. of Poggendorff’s Annalen.

In order to interrupt the pursuit of the real question as little
as possible, I have deferred to Appendix I> the full description
of the mode of observation for such a curve, and moreover for
the one marked a in the table which follows, and state here the
results merely; these were obtained with three different kinds
of apparatus, a, ), c.

a, An ordinary Leyden jar with tinfoil coatings of about five-
sixths of a square foot, and in the form of a sugar-glass.

b. A thick bottle with a narrow, short neck, usually applied
to the holding of reagents. The neck was heated, and coated
within and without with sealing-wax; the bottle was then filled
up to the sealing-wax with mercury, and was surrounded outside
by a layer of the same metal, 1 inch thick. To prevent the
vessel from floating, it was held fast by means of screws in a
cylindrical wooden trough.

ce. A thick rectangular piece of a looking-glass had its metallic
coating removed for 2 inches from the edge, and was coated
on the other side with tinfoil; the glass rim on both sides was
coated with sealing-wax. During the experiments the plate was
laid with the tinfoil upon a sheet of metal, and to the other
side, which was connected with the electrometer, electricity was
communicated.

In all three cases, both of the bottles a, 5, and the plate c, one
of the coatings was carefully connected by a wire with the moist
earth of a garden. In the columns marked 4, J, ¢, the results of
the observations are stated. In the column headed i, the time
after charging is expressed in seconds. ‘The column is contains
the magnitude of the charge as given by the sine-electrometer.

Electric Residue in the Leyden Jar. 307

Table a. Table b. Table c.
ts Lip t. Li. t. Ly

0 04742 0 1:4968 0 0:5559
18 00-4133 5 1:4120 6 05266
50 0:3896 24 13221 43 0-4918
110 03692 | 59 1:2640 71 0:4843
160 0°3516 91 1:2256 133 0:4677
215 0°3461 114 1:2060 193 0:4566
265 03373 | 144 1/1826 256 04446
830 03290 188 11552 328 0:4368
382 0:3223 | 230 1:1326 423 0°4268
450 0:3141 282 1:1093 53] 0:4166
§23 0:3080 | LL 1:0854 620 0:4097
577 0:3029 406 10608 715 0-4027
680 0:2951 485 1:0354 864 03918

573 1:0093

683 0:9823

804 09543

935 09254

1105 0-8954

1285 0°8643

1505 0-8317

1770 07977

2070 0°7622

2430 0:7247

2870 0-6851

3420 0:6429

4110 0:5977

| 4980 | 0:5486

| | 5370 05266

The series of observations contained under b is represented
graphically in fig. 2, Plate VI., by the line L;. The curves of the
two other series of observations are not drawn.

On the whole these curves present a similarity to parabolas,
but they satisfy a constant parameter for a short distance only.
It is seen, however, at first sight that they cannot be due to the
mere loss of electricity in the air, as they are much too curved
to be accounted for in this manner. Adhering to the results
stated in b, and assuming that the loss of electricity is solely due
to its dispersion in the air, the charge, which at first amounted to
1-4968 according to the arbitrary unit of the sine-electrometer,
being reduced in 5370 seconds to 0°5266, the corresponding
curve would be shown by the dotted line N, in which the stronger
points are calculated *.

* This is proved as follows :—Let Ly be the charge of an insulated con-
ductor at the commencement, then we have

where # is a constant dependent on the state of the air.
Integrating from t=0 to tt, we have
» tae

~

308 M. R. Kohlrausch’s Theory of the
§ 2.

The question, to what other source than the loss of electricity
in the air is the quick diminution of the tension of the knob of
the Leyden jar at the commencement to be ascribed, finds a
kind of answer in the fact, that after complete discharge has
taken place, a short time having elapsed, a charge more or less
considerable, of the same kind of electricity as that with which the
jar was originally charged, makes its appearance. From this we
may conclude that a portion of the electricity first communicated
has concealed itself somewhere, so as not to contribute to the
tension of the knob, and was prevented at the same time from
being a sharer in the discharge; to this circumstance we might
be inclined to refer the more speedy diminution of the tension
than that which could be referred to the loss in the air.

Besides this, the following effect is observed. If a charge
has remained in the jar for a considerable time, and a consider-
able portion of the electricity be taken from the jar, so that the
tension becomes feebler by sudden springs, then immediately
afterwards this tension is observed to sink very slowly, or some-
times to stand for a time and then sink, or, which is mostly the
case, first rise for a time, then stand, and then sink finally.

Combining the facts of the last two paragraphs, we are com-
pelled to divide the entire quantity of electricity, Q, in the jar
into two portions, one of which, L, can be discharged, and which
on this account may be called the disposable charge, and the
other 7, which is prevented from sharing in the discharge, and
first makes its appearance after the removal or diminution of the

log hyp —at.
If by observation we have ;
L,=1°4968 and Li=0°5266,
then
2=0°0001945 ;
and as, on the other hand,
at=a,e—*t,
we can readily calculate the value of the charges for every ¢ between the
beginning and the end, and lay down the curve represented by the dotted
Ime. In this way we learn that for the times ¢ the curve must possess the
following ordinates 0.

t | 0 | t 0.
59 | 14797 | 2070 10071
14 | 14640 || 3420 0-7696
573 1:3389 | 4110 0-6714
1105 1:2073 || 5370 0:5266

Electric Residue in the Leyden Jar. 309

disposable charge, that is to say, becomes changed into a dispo-
sable charge.

This second portion, 7, has been named the residue, and we
will retain the term; and by the term concealed residue, we will
denote the said portion while it remains inefficient in the jar,
calling that portion which makes its appearance after the dis-
charge the restored residue.

The observation of the restored residue is best accomplished
by means of the sine-electrometer, by connecting the knob of
the jar with the instrument immediately after the jar has been
discharged. It is at once seen that the needle commences to
diverge from the magnetic meridian ; and by following the needle
and reading off the deflections, we obtain a series of points suffi-
ciently near to each other to permit of a curve being constructed
which shall represent the augmentation of the charge. The
ordinates of this curve increase most speedily at the commence-
ment, so that in this case also the curve is not unlike a parabola:
but the greater the loss of electricity in the air, the sooner does
a point arrive where this increase passes over into a diminution ;
this point represents the moment when the exhibition of the
residue is exactly balanced by the loss in the air. When the
latter, on account of the nature of the jar, is very small, the
augmentation continues for several hours; and for hours the
charge appears to remain perfectly unchanged, the discharge
requiring a number of days to effect it completely. When, how-
ever, the quantity lost in the air, or on account of imperfect in-
sulation, is considerable as compared with the size of the jar, the
curve, which ascends for a short time abruptly, is suddenly bent
downwards. Drawings of such curves are given in fig. 2 p.

When the first residue has been discharged, a second small
residual curve is observed, which proves that a concealed residue
was still remaining ; this can be repeated several times.

This repetition of the discharge is the only means of learning
how much of a charge has changed itself into a concealed residue 7.
To reduce the loss of electricity during the process to a mimimum,
a magnetic needle of very small magnetic moment is necessary ;
and the observations must be made with small angles between
the needle and the repelling arm. We first permit as much
of the residue to return as can be observed with certainty, then
discharge*, read off the angle, and repeat the process as long
as a measurable residue remains. Although this process fre-
quently continues for several hours, still, in comparison with the
total residue, the loss of electricity is very small. The greater por-
tion of the residue appears very quickly at the commencement of

* It is essential here that the outer coating is perfectly discharged, for
otherwise the deflection is illusory.

310 M. R. Kohlrausch’s Theory of the

the operation, so that using small angles, several discharges are
sometimes effected during the first minute. Whenwe subsequently
reduce the results obtaimed by making use of the small magnet
and small deflections a, to the deflection of the strong ueedle and
large deflections «, made use of in the observation of the original
charge, and the sinking of the same, that is, in the construction
of the tables a, 6, and c, we obtain the residue (which, however,
js still to be set free from the influence of the loss of electricity)
equal to the sum p+p'+p"+.... of the single residual dis-
charges,

To the tables a, b and c, § 1, belong the corresponding ones
a', L', c, in order to form the basis of a calculation. At the
time when the last observation recorded in each of the first men-
tioned tables was made, the apparatus was completely discharged
by connecting the inner coating of the jar for about half a second
with the moist earth of the garden. At the same time the con-
necting wire was removed from between the jar and the electro-
meter, the new magnetic needle was suspended, and the new
angle # arranged. The connexion between the jar and the in-
strument being again established, a second observer noted the
times of the single discharges. These are set down in the
columns ¢, and are reckoned in seconds, commencing from the
moment of the first discharge. The numbers under p’ denote
the residues which again appeared.

Table a’. Table 5'. Table cl.
t p! t p’. t p’

65 00443 255 0:1131 34 0:0265
153 0:0166 990 0:0763 169 0:0101
270 0:0158 2250 0:0565 288 0:0101
535 0:0138 5040 0:0538 479 0:0101
835 0:0109 8760 0:0375 794 0-:0101

1615 0:0109 13740 00301 1234 0:0080
3895 0:0109 | 37140 0:0207 12034 0:0109
5935 0:0075 73140 0:0107
Sum 0:1307 Sum 0:3987 Sum 0:0858
§ 3.

The question now presents itself, what is it that we have
actually measured by the sme-electrometer? According to my
conviction, most certainly the same as we should have measured
if at the same moments we had tested the same point of the
knob, The electrometer in connexion with the interior coating
of the jar is, indeed, nothing else than a continuation of the
knob.

We have seen, however, in § 1, that the results obtained by

Electric Residue in the Leyden Jar. 3ll

the electrometer are by no means proportional to the quantity of
electricity which was certainly present, but that, on the contrary,
a portion of this electricity became in some measure latent, that
is, was lost as far as the tension of the knob was concerned, and
we referred the effect to the concealed residue which was formed.
It might appear rash to assume without further consideration,
that the portion which we saw returning as residue, 7, after the
discharge of the jar, was, during the charging of the jar, altogether
without influence upon the tension of the electricity upon the
knob. If the residue, as is usual, be referred to the gradual
penetration of the glass to a certain depth by the electricity,
then it would seem most natural to regard the total quantity of
electricity in a jar in which a residue is formed neither as pro-
portional to the tension on the knob of the jar, nor to the dis-
posable charge, but to something made up of both, At all
events we must, in the first place, ascertain how the matter
really stands.

To decide this question, it is necessary to compare the same
tension, measured electroscopically, first of a battery where the
concealed residue is as small as possible, and secondly when it
contains a large residue, with the disposable charge,—the latter,
however, being measured in some other than an electroscopic
way. In such a case we may make use either of the thermic or
magnetic action of the current. The latter was the action
chosen.

In the Appendix II. the small multiplyig galvanometer is
described which served for this purpose, its magnetic needle,
furnished with a mirror and scale, being observed through a
telescope like a magnetometer; and in the same place also the
arrangement is described by which the inner and outer coatings
of the battery, at the suitable moment determined by the sine-
electrometer, are connected with the galvanometer wire for a
time sufficient to allow the disposable charge to pass, but not
sufficient to permit any measurable portion of the residue to
make its appearance.

When the current of a Leyden jar or battery, retarded by the
introduction of a liquid into the circuit, is sent through such a
galvanometer, and when the discharge, as in the case before us,
is accomplished in a small portion of a second, consequently in
a very small fraction of the time of oscillation of the needle, the
action of the current may be regarded as an instantaneous shock,
which imparts suddenly to the needle a certain velocity of rota-
tion, C. This velocity is proportional to the strength of the
shock, and hence, in the present case, to the disposable charge
sent through the galvanometer. Now W. Weber, in his Electro-
dynamic Measurements, page 316, has given a formula, accord-

312 M. R. Kohlrausch’s Theory of the

ing to which, in the case of a galvanometer furnished with a
damper, the velocity C may be determined from the first elon-
gation 2 of the needle. The formula is

ri
x are tan —

T
C=2.—.e7 X
.

For the same galvanometer the time of oscillation T of the
needle and the logarithmic decrement X are constant, and hence
also the magnitude of the disposable charge of the battery is
proportional to the first elongation a of the needle ; which elon-
gation, on account of its smallness, may be regarded as propor-
tional to the number of parts of the scale read off by the tele-
scope. The observations were as follows.

A battery having about three square feet of coating, in which
no residue existed, was charged, the sine-electrometer was intro-
duced, and at the moment when the latter gave the charge 2°673
according to its own arbitrary unit, the discharge through the
galvanometer was effected. The first elongation amounted to
44:0 parts of the scale. Between the charging and discharging
a minute and a half intervened, and the concealed residue col-
lected afterwards amounted to 0°14. The repetition of this
experiment gave for the first elongation, in a case where the
needle was not completely at rest, 43°8, and in a subsequent
case 44°] parts of the scale. In both of these last-mentioned
cases the residue was not determined.

The highly charged battery now remained for fifty minutes
without being discharged, at the end of which time the sine-
electrometer showed the charge 2°673, and was then discharged.

Three such experiments gave for the first elongation of the
needle 44:0, 44°1, and 44:1 parts of the scale.

Thirdly, a strong charge was permitted to remain standing in
the battery for 210 minutes, was then considerably weakened in
order to bring the charge down to 2°673, and afterwards gave
44-0 parts of the scale for the first elongation. In a short time
a concealed residue of 0°754 made its appearance, and the mea-
surement of the remaining portion of the residue, which, accord-
ing to estimation, would have given about twice the quantity,
was interrupted, inasmuch as the experiment was sufficiently
decisive. As therefore the concealed residue appeared to exert
no influence whatever, it was not at all taken into account in the
following experiments. Another battery was taken, and the
action of its discharge under different circumstances ascertained.
In the first column of the following little table are contained the
deflections ¢ of the needle of the sine-electrometer; in the
second the square root of the sine of this angle, which from the
nature of the instrument is proportional to the charge, but in

Electric Residue in the Leyden Jar. 313

this case not reduced to the ordinary unit of the instrument ; in
the third and fourth columns, stands the observed first elongation
E of the galvanometer needle in parts of the scale; in the fifth
the number of parts of the scale calculated from the strong-
est charge, as they must have been if the results given by both
instruments had completely coincided ; and in the sixth column
the difference d, given in parts of the charge.

¢- V sin ¢. E. Mean. ___| Calculated. d.
i18* | 0-1505 108 108 10°85 | —0-0046
8 45 03900 | 28

| | 27-9 ' ,
ong 27-92 2812 | —0-0071
28
<i ge agmaregl air 485 4853 | —0-0006
79 15 09911 73 C7 I eas
| 725 72°75 | 72°75 0

These experiments leave no doubt of the fact, that the dispo-
sable charge of the battery is truly given by the sine-electrometer,
and hence that the disposable charge of the battery is proportional
to the tension of the electricity on the knob of the jar. These
experiments were made with Franklin’s plate with the same
result.

§ 4.

Having thus assured ourselves that the sine-electrometer en-
ables us accurately to compare the disposable charges of the same
jar with each other, the mstrument may be applied to the mea-
surement of these discharges if we assume one of them as unit ;
the electrometer has its own unit of measure. As stated in
Poggendorff’s Annalen, vol. Ixxxviii. p. 502, it is the quantity of
electricity which, when the repulsion of the magnetic needle by
the repelling arm amounts to a certain small angle a, causes the
needle to stand at right angles to the magnetic meridian; and
to this unit all results of the instrument, when different needles
and different angles of observation are made use of, are reduced.
Let us choose, then, as unit, according to which the disposable
charge of any jar is to be measured, the quantity of electricity
which must be present in order to cause the electrometer to
exhibit its own unit; then the numerical results of the latter
serve immediately as the measure of the disposable charges for
this particular jart.

* This charge consisted of a residue which had again made its appear-
ance.
+ It is here manifest that an absolute measure is not attained; for,

314. M. R. Kohlrauseh’s Theory of the

The curves obtained from the observations in the tables a, 8, ¢,
§ 1, are therefore the actual representants of the disposable
charges L; present at the different times ¢ in the apparatus, and
the residues p! sought in the tables a’, b!, c', § 2, denote also
quantities of electricity so circumstanced that @ and a’, 6 and U,
and ¢ and ¢, are referred to the same unit respectively *.

The first question which comes under our consideration is,
whether means are at hand which will enable us to obtain from
the observations a clear view as to the comparative quantities
of the residues formed in the charged jar. For the smking
of the charge has, as we have observed, two causes; the loss of
electricity in the air, and the formation of the residue. If the
quantity of electricity Q, be imparted to the interior coating of
the jar, which at the first moment shows the charge Lp>=Qo,
then at the end of the time ¢ the quantity v is lost m the art,
and a concealed residue 7; is formed, so that the disposable
charge at present is only

L,=Q)—0,-7;5
while the quantity of electricity Q, in the jar at the end of the
time ¢ is expressed by the equation

Q= L,+7,=Q)-?;-
The observations gave us Q, and L; directly, the latter at least
for the times ¢ at which the disposable charge was observed ; and

the question now is, whether we can determine 2% so that the
residue for all observed times ¢ may be given by the equation

7,=Qo—(L,+%).

This leads us to the construction of a residue-curve, the nature
of which we shall be enabled to recognize ; and thus the hope is

according to what has been said, every distinct jar will have its own peculiar
unit. If, therefore, the sine-electrometer is to be made use of to compare
the charges of different jars, not the tensions on the knobs, but the quan-
tities of electricity actually present, it is in the first place necessary to ascer-
tain the ratio of the quantities assumed as units in the two jars. This can
be found with certainty by first causing the electrometer to show the same
divergence in both cases, and then discharging the jars through the multi-
plying galvanometer.

* More was not necessary for our present purpose. The three different
units referred to in the tables a, 6, c might indeed be reduced to each other.
Two other tables besides those to be used subsequently must for this pur-
pose be calculated, and the advantage did not appear to be worth this
trouble.

+ We intentionally avoid taking into account the loss of electricity by
the imperfect insulation of the edge of the jar, because otherwise we could
not set the loss as proportional to the charge Lz. The charge Q, should
therefore be not taken greater than the validity of this assumption would
permit of.

Electric Residue in the Leyden Jar. 315

generated of our being able to arrive at a strict law, the coinci-
dence of which with the observations will render probable the
hypotheses on which the said law is founded.

Let us in the first place determine »,.

Tn fig. 3 let ab represent the quantity of electricity Q,=L,
communicated at the beginning; 64'6'b"...c¢ the curves of
the disposable charges L, observed at numerous points, lying
near each other, and referred to the abscissa ad, which is the
representant of the time. This is reckoned from the moment
when the jar was charged, and we have therefore after the times
t}, ta, tz, the disposable charges L,, L, L;. After the time T,
which is expressed by the length ad in the figure, the jar will be
discharged, consequently a quantity of electricity Ly correspond-
ing to the line de will have been removed.

At the end of the times ¢!=da', t"=dd", t"=dd", &c., the
quantities p', p"’, p!, &c., as concealed residues, make their ap-
pearance, the sum of which is .

pl+p!+pl4+ ... =p.

We know that we have recovered the quantity L,+p from
the jar, and hence conclude that what is wanting to make up
the origimal charge Qo, has been lost in the air during the time
of operation ; calling this last portion V, we haye

V=Q)—(Lr+p).

If in the figure ef=p, we have fe=V.

This total loss must now be distributed over the times in which
it has taken place ; more especially for the determination of r,, it
is necessary to inquire what portion v; has been lost up to the
particular times ¢, at which the disposable charge of the jar has
been measured.

This charge is constantly proportional to the loss of electricity,

consequently
dv, =aldt ;

and the integration of the expression to the right between the
limits ¢=0 and ¢=¢ would, if we could perform it, and knew
the value of « and the law of the curve L,, at once give us the
magnitude of v,.

Now, in the first place, it is manifest that the constant «
which has reference to the loss of electricity in the case of a
Leyden jar, cannot be directly determined; secondly, that we
have no hope of finding the law of the curve expressing the
disposable charges, before we know the law of the residue in
the jar. Inasmuch as v, L, and 7, are all dependent on each
other, the solution of the problem appears only possible by find-

316 M. R. Kohlrausch’s Theory of the

ing at once the laws of all three curves. But assuming even
that we possessed this gift of divination, we should nevertheless
find the differential equation so complicated that its integration
is scarcely to be thought of.

Under such circumstances we must make a virtue of necessity,
and in seeking to determine v, we must take, instead of the
actual law of the curve of the disposable electricity, the curve
itself. :

The expression ( L,dt
v0

is nothing else than the superficial area bounded by the curve,
the abscissa, and the ordinates at the begining and end of the
time ¢, and we see immediately that the loss of electricity durmg
the respective times

t\—ty to—t, ts—te &e.,
which latter are represented in the figure by the portions aa’,
da", ala", &c. of the abscissa, are proportional to the spaces

t, ty
ab Bal = ( Lat=f;; dota ={ Ldt=fo, &c.
: 20 4
Denoting by F the total surface abb'b"...cd, so that
Pa (Latah hth ee

then we have aF as the loss of electricity up to the first discharge
of the battery. In lke manner, the loss in the second operation
is proportional to the surfaces

djd=f'; dg'd'=f", &e.
Denoting the entire sum of these spaces f’+f"+f""+ ... by

¢, then the total loss of electricity during the second operation
will be expressed by ad.

Hence as
V=aF +ad,
we obtain immediately
Vv
a= Fi¢

V is given to us by observation, and thus our knowledge of
depends solely on our knowledge of F and f.

If the measurements made at the times ¢,, f,, ts, &c. lie so
nearly together that the portion of curve which they limit may
be regarded as a straight line, the surfaces f,, f;, &c. become
trapeziums, and we have

—L L,—-L
Az a 5} 2 (ty —to) ; f= = 5) 1(t2—t,), &e.,

Electric Residue in the Leyden Jar. 317
the sum F of which may be found, and will differ very little from

T
{ Lt.
0

The surfaces f’, f", f!..., which are bounded by the curves
of the residues, may be regarded as triangles, so that we have

p= 5 UO) + plete) +..].

In this we obtain, instead of

the equation

where

B(A=Athth:-» A:

which contains no unknown quantity, when for ¢ is substituted
the actual time of observation.

We can thus calculate for all observed disposable charges L,,
the loss v, incurred up to the time of discharge, and have at the
same time, according to the former equations, the corresponding
concealed residues 7, and the total quantities Q, which exist in
the jar at the respective times. In the three following tables,
a", b" and ¢', the quantities so calculated are placed side by side
with the former ones.

Table a’.
t L, Of. Q: bs
0 0°4742 0 0°4742 0
18 04133 0:0013 0°:4729 0-:0596
50 0°3896 0:00338 04709 0-:0813
110 0°3692 0:0069 04673 0:0981

160 0°3516 0:0097 0°4645 0:1084

318 M. R. Kohlrausch’s Theory of the

Table 5".
if Le CPs Q. Ts
0 14968 0 14968 0
5 1-4120 0-0009 14959 0:0839
24 1-3221 0-0040 1:4982 0:1707
59 1:2640 0:0094 14874 02234
91 1:2256 0-0141 14827 0:2571
114 1:2060 00175 1:4793 -|- 0:2727
144 1/1826 0:0218 14750 0:2924
188 1/1552 0:0279 1:4689 0°3137
230 11326 0:0337 146381 0:3305
282 11093 0:0406 1-4562 0:3469
341 1-0854 0:0484 14484 03630
406 1:0608 | 0:0567 14401 03793
485 1:0354 0:0666 1:-4302 0°3948
573 1:0093 0:0774 14194 0:4101 -
683 0-9823 0:0905 14063 0:4240
804 0°95438 01045 1:3923 0:4380
935 0:9254 01192 13776 0:4522
1105 0°8954 01377 1:359L 0:4637
1285 0°8643 0-1566 1-3402 0°4759
1505 08317 | 01789 1°3179 0-4862
1770 =|) =—(0°9977 0-2047 1-292] 0:4943
2070 0°7622 0:2327 12641 05019
2430 0:7247 0:2647 12321 0:5074
2870 06851 0:3018 1/1950 0:5099
3420 0-6429 0°3455 11513 0:5094
4110 0:5977 03967 1:1001 0:5024
4980 05486 | 0:4563 10405 04919
5370 0:5266 0:4814 10154 0:4888
Table ec”.
t. Oye v. Q). Ti
0 0:5559 0 0°5559 0
6 0-5266 0-0005 0:5554 0:0288
43 04918 0:0034 0:5525 0:0607
71 0-4843 0:0055 0:5504 0:0661
133 0:4677 0-0101 0:5458 0:0781
193 0:4566 00144 0-5415 0:0849
256 04446 0-0188 0°5371 0:0925
328 0:4368 0:0237 0:5322 0:0954
423 0-4268 0:0301 0:5258 00990
531 04166 0:0372 05187 0:1021
620 0-4097 0-0429 0:5130 0:1033
715 0-4027 0-0489 0:5070 01043
864 03918 0-0581 0-4978 0:1060

To make these comparative quantities evident to the eye, the
table 4! is represented graphically in fig. 2. Setting, for in-
stance, by the observed L, the corresponding v,, then the points
thus obtained determine the residue-curve denoted by 7, the

Electric Residue in the Leyden Jar. 319

ordinates of which, however, have the line de as abscissa. Set-
ting, on the contrary, by the observed L, the corresponding 7,
we obtain a series of points, which, on being united, constitute
the line Q, or v,, which is almost straight. The ordinates of
this line, referred to ad as abscissa, represent the quantity Q; of
electricity present in the jar at the time ¢; and, when they are
referred to be, they represent loss of electricity v,.

§ 5.

The question now naturally presents itself, in what relation
does the concealed residue of the same jar stand with respect to
the magnitude of the charge first communicated ; for it is soon
evident that a stronger charge produces a greater residue.
Whether the residue produced in equal times, but with different
charges, be proportional to the strength of these charges, may
be solved by ascertaining whether the sinking of the disposable
charge follows the law of proportionality ; for the air, retaining
its quality, the electric loss from this source has this property.
On this point a single decisive experiment may be cited.

The method described in Appendix I. of communicating to a
jar instantaneously a known charge, may be easily so applied
that the charge in one case is exactly ten times what it is in
another case. This was done on two successive serene days,
during which the warmed air of the room remained in a constant
condition as regards the loss of electricity, a jar being chosen
with which the loss was inconsiderable. The results are stated
in the following small tables d and e. In table a! the results
given in d are reduced to the times of table e.

Table d. Table e. Table d’.
t. iZ t. Lg Liz
0 | 01406 0 | 1:4062 0-1406
20 | 01368 | | 60 | 1:3586 0°1352
65 | 01349 | 120 | 1:3374 0:1334
135 | 0:1329 | 180 | 13220 0-1322
270 =| 01808 300 | 1:3087 0°1805
390 | 01296 | 420 | 1:2962 01293
600 | 0-1274 540 | 1-2858 0:1280
720 | 01268 720 | 1:2737 0:1268
900 | 01255 900 | 1:2583 0°1255

The same experiment has been repeated several times with the
same degree of coincidence.

We have thus arrived at the conclusion, that with the sameyjar,
the residues formed in the same time are proportional to the charge
imparted at the commencement. It must be left undecided whether

320 Mr. S. V. Wood on some Tubular Cavities in

the conclusion is strictly true for the strongest charges, as on
account of the loss through imperfect insulation these cannot be
examined in the manner which we have pursued.

Before we make the attempt to discover a formula for the
calculation of the residue-curve, a few facts must be introduced
which may be useful to enable us to form a clear and correct
conception with regard to the residue, and thus prepare the way
for the hypothesis upon which the formula is to be based.

[To be continued. ]

XLVII. On some Tubular Cavities in the Coralline Crag at Sud-
bourn and Gedgrave near Orford. By Snartes V. Woop, Esq.*
[With a Plate.]

T has been long observed that the surface of the chalk is more
or less perforated with funnel-shaped depressions or “ sand-
pipes,” as they are called in England, while they are known in
France under the name of “ puits naturels;”’ and in the year
1839, Sir Charles Lyell published a paper in the Philosophical
Magazine, in which was brought under notice these sand-pipes,
with an account of the manner of their supposed production.
These pipes are therein described as varying in magnitude as
well as in depth, and are also of various forms and inclina-
tions, but are all of an angular or funnel shape, being larger at
the upper part and generally terminating in a point: the mode
by which it is therein supposed these excavations have been
effected is by the operation of a chemical action upon the calea-
reous material of the mass of the chalk, the eroding action of
acidulated waters, produced by the decomposition of vegetable
matter, abstracting the carbonate of lime which had passed off
into the atmosphere in the form of carbonic acid gas, and the
depression or opening thus produced to have been gradually
filled in by the weight of the superincumbent gravel. This
hypothesis has been called in question by Mr. Trimmer, who in
a paper read before the Geological Society in 1842, and published
in their Proceedings, vol. iv. part 1. p. 6, and part 3. p. 482,
1844, has assigned the production of these depressions to the
action of running waters which had eroded in furrows the sur-
face of the chalk, and he considers their funnel-shaped appear-
ance to be simply a transverse section of these gullies. It is,
however, most probable that the surface of the calcareous rocks
beneath the superficial gravel has been in various places acted
upon both by a chemical agent as well as by mechanical action ;

* Communicated by the Author; having been read before the Geological
Section of the British Association, at Ipswich, 185].

the Coralline Crag at Sudbourn and Gedgrave near Orford. 321

and that the hypothesis proposed by Sir Charles Lyell is the
true one for the funnel-shaped depressions, while there is also
no doubt that the surface of the chalk has in some places been
eroded as described by Mr. Trimmer.

The cavities immediately below the superficial soil on the
eastern side of England might, I think, be classed under three
distinct heads, as they are not only the presumed productions
of different agents, but also the result of actions very dissimilar
in their operations. The first are the well-known “puts natu-
rels,’ which from their peculiar forms may for mere distinction
be called funnel pipes; the second may be termed gully pipes ;
these, however, are not, strictly speaking, pipes at all, as they
all terminate in a closed point; and the third more correctly
chimney pipes.

The first or funnel pipes are more or less of an angular form,
irregular in outline, and where it is possible to ascertain their
full extent, they invariably terminate in a point. These are not
only common on the surface of the chalk, but are very nume-
rous, though generally small in size, upon the coralline crag ;
and in the parishes of Sudbourn and Gedgrave, wherever a
section of this formation is visible, the whole surface is more
or less excavated in this manner, and none that I could see
exceeded in depth 3 or 4 feet, while 12 or 18 inches was the
diameter of the upper part. The larger and deeper pipes of the
chalk may be due to the erosive action having been prolonged
through a much greater period; and in examining the contents
of two or three of these excavations, which were filled with the
superincumbent gravel, not a single fragment of shell could be
observed, or any trace of carbonate of lime, which might have
been the case had they resulted simply from the action of run-
ning waters ; moreover, the edges of these depressions were too
sharp in a material so loose and incoherent as is the coralline
crag, and their positions too proximate for the probable action
of any other agent than the slow and gradual process of a che-
mical abstraction acting from above.

The second class, or gully pipes, are described by Mr. Trim-
mer as having been formed by the action of running waters
draining the surface of the chalk previous to its elevation above
the sea, and the angular depressions visible in that rock, and
now filled with gravel, are merely the transverse sections of these
gullies; and he further states his having removed for a consi-
derable space the superincumbent material and exposed the con-
tinuance of these depressions. Another form of excavation may
also here be mentioned as being more in connexion with this
last mechanical mode of operation, and is spoken of by Lieut.
Newbold as occurring in southern India, wherein he describes

Phil. Mag. 8. 4, Vol. 7. No. 46. May 1854. Z

322 Mr. 8. V. Wood on some Tubular Cavities in

the surface of the rock as eroded into cup-shaped cavities pro-
duced by the action of running waters, whose eddies or gyrations
have by the trituration of sandy particles worn them into a sub-
globular form. These poteria or cup-shaped cavities are spoken
of by Mr. Trimmer (p. 498) as having been observed by him on
the surface of the chalk at Thorpe and Rackheath in Norfolk, as
also in Kent: these he considers as incipient pipes, and they are
presumed to be identical with those rock basins described by Lieut.
Newbold in the Proceedings of the Geological Society, vol. iu.
p- 702. Mr. Jukes also, in his account of Newfoundland, vol. ii.
p- 138, mentions similar excavations close to Buchan’s Island m
the river Exploits, and particularizes two holes worn in the rock
of a form somewhat singular, being perfectly perpendicular to
the depth of 8 feet, with a diameter of about 2 feet; he says
they were exactly circular, nearly full of water, and each con-
tained a large stone and a quantity of sand at the bottom, and
these were so produced by the whirling round of the stone from
the rapidity of the current of water rushing over them.

The third class are what I propose to call chimney pipes,
and are more especially the subject of the present notice; their
form, as well as the mode by which it is presumed they were
produced, being wholly different from the before-mentioned ex-
cavations, they appear to be deserving of a particular designation.

In a quarry of the coralline crag at Sudbourn near Orford,
close to the gate which leads to the mansion of the Marquis of
Hertford, are a number of these “pipes;” not less than nine
were visible within the space of twenty yards when I visited the
pit, all nearly of the same size, and excavated perpendicularly or
nearly so, one only appearing to decline a little from that direc-
tion: the general dimensions of these pipes were about 18
or 20 inches in diameter. And in another pit in the parish
of Gedgrave, at the distance of about a mile due south of this,
may be seen also eleven more of these perforations, one of which
is much larger than the others, with a somewhat different form
(Plate V.)*.

The coralline crag in this locality consists of a sort of low
table-land, bounded or rather cut off on the N.E. by the river
Alde, and extending to the S.W. about five miles, where it is
again cut out by the small river that runs up to Butley, having
a transverse direction of about two miles and a half with a vari-
able thickness; and a depth of 50 feet is reported to have been
pierced through without coming to the clay. Wherever a sec-
tion of this is visible, it appears to have formed on the upper
part a complete coral bank, beneath which, as seen in the valleys

* The Plate is from a sketch of some years date, and the pit at that part
has sinee been worked, by which a copsiderable alteration is made.

the Coralline Crag at Sudbourn and Gedgrave near Orford. 323

where it has been denuded, is a deposit composed almost entirely
of shells and their débris; while in the upper portion shells are
rarely to be obtained, and only in the valleys corresponding
with the present watersheds can this lower stratum be seen.
The upper or coralline portion has here become somewhat indu-
rated, and on some occasions has been employed as a building
stone, the tower of Chillesford Church having been constructed
principally of that material.

These chimney pipes appear to have perforated the entire
thickness of the coralline crag deposit, at least it is‘so presumed,
although I was unable to trace them to a greater depth than
12 or 14 feet from the surface, or immediately beneath the gravel
to where they are lost in the talus at the bottom of the pit;
. but the crag at these localities has not probably more than
20 feet of thickness, as the water stands in the pit at that
depth, indicating the presence of the clay beneath.

The most perfect of these tubes now remaining is one that
presents rather more than a semicylindrical shape, but is emptied
of its contents by the loss of the lateral supports: a small por-
tion of another, the walls of which are as flat and nearly as
smooth as the walls of a room, has been undermined so as to be
visible from beneath; and through this aperture, which has a dia-
meter of about 18 or 20 inches, a boy might readily pass. The
large masses of Fascicularia and Theonoa, which in the ordinary
surface of the crag stand out in prominent relief, were in these
chimney pipes literally cut in halves, as if they had been pro-
duced by the mechanical operation of a boring implement.

From the cylindrical form of most of these tubes and their
vertical position it is presumed they cannot be ranged in the
second class, as it is quite impossible they can have been produced
by running water ; and their perfect regularity precludes any inti-
mate connexion with the funnel-shaped pipes from the downward
action of acidulated waters so removing the carbonate of lime,
as in that case they must necessarily have an irregular outline,
So large a number of them within so small an area militates
against the probability of their having been produced by human
agency, which the sight of a solitary one might have led to the
belief ; their great proximity would have rendered the repetition
of such an operation useless, or at least very improbable, and
the form of one of them being somewhat elliptical is an evidence
against the probability of such a production.

That the erosion is effected by chemical action, and not by
mechanical means, there is every reason to believe from the regu-
larity of form and perfect smoothness of the sides of these cylin-
ders; for in a mass of deposit composed of a homogeneous
material, or nearly so, as regards its chemical components,

Z2

324 Mr. S. V. Wood on some Tubular Cavities in

though not all in the same state of compactness or density, the
acid would act alike upon the more indurated as upon the less
solid material, whereas a mechanical agent would be directed to
the place of least resistance; and had the looser fragments
then been removed the nodules of compact corals would have
projected from the sides of the tubes. The whole aperture has
a lining or coating upon its walls such as might be expected as
the residuum adhering to the sides deposited by the evaporation
of the carbonic acid gas: this covering or lining of the sides of
the chimney is of an ochreous colour and of an aluminous com-
position, and may perhaps have been thicker than what now
remains, as exposure to the rain and weather would leave only a
small portion adhering to the crag.

One cause to which Sir Charles Lyell alludes regarding the
possibility of his funnel-shaped tubes having been formed by the
large tap roots of trees that had decayed away, and the aperture
so left afterwards filled up by the falling in of the supermeum-
bent gravel, could not be applicable asa cause for the production
of these chimney pipes, which are much too regular in form to
have been so produced.

In some parts of the coralline crag at Ramsholt I have met
with several caves or openings, such as might have been produced
by the subsidence or contraction of the clay beneath. One
of these was so small as to be not more than a foot or 18
inches in height, such as would scarcely admit a man to crawl
in, with a width only of a few feet: another somewhat larger,
near the same locality, has been in former times used by smug-
glers as a place of retreat. These fractures seem to have been
near the bottom of the crag, which at this place has a thickness
of not more than 6 or 8 feet; the upper or more coralline por-
tion has been washed off and the red crag is superimposed,
while the London clay is visible immediately beneath, showmg
portions of all three deposits above the level of the river Deben.
These cavities of a distant locality in the coralline crag are here
mentioned as indicating the probability that similar fractures
and openings exist in various other parts.

- There is every reason to believe that these gravel-filled cavities
were not eroded from above, either chemically or mechanically,
but that the openings under notice were formed by the evolution
and upward issue of acidulated gases. To produce this effect, it
is necessary to suppose these tubes to have been connected with
cavities or fissures in or through the clay beneath where the car-
bonic acid or other gases might have been elaborated. The
regular and tranquil deposits of these older tertiary clay beds, as
seen in England, give no indication whatever of any proximity
to volcanic action even in its most subdued form; and the pro-

the Coralline Crag at Sudbourn and Gedgrave near Orford. 325

duction of these gases must be accounted for, either by the sup-
position of their having risen from regions of considerable depth
through the clay out of rocks of an igneous character beneath,
or that some acid gas may have been formed in the clay itself by
the decomposition of pyrites which is found in great abundance
in that deposit; in either case it would be necessary, I should
imagine, for cavities to have existed in the clay either for the
passage of the gas or for its elaboration; and although no ap-
pearance exists of anything like disturbance in this neighbour-
hood, it may be remembered that the sea now approaches within
a mile of the locus in quo, and all traces of such action may have
been removed.

In speaking of the “sand-pipes”’ of the chalk, Sir Charles Lyell
says, “If some of the largest pipes, of which the bottom has not
been yet reached, be prolonged indefinitely downwards and con-
nected with deep fissures, we may suppose that springs charged
with carbonic acid rose up at some former period through the
chalk and crag while these were still submerged. In proportion as
the chalk was corroded, the incumbent substances would subside
into the hollows thus formed, and the water would freely perco-
late, the matter thus intruding itself dissolving any calcareous
ingredients which may be associated with it, and still continuing
to widen the tube by corroding its walls.”

Our chimney pipes were probably formed, as above stated,
while the crag was beneath the sea, although I was unable to
ascertain what were the true contents of these openimgs when
first broken into. The form of one of these being of a funnel
shape and opening outwards, would seem rather to imply a dif-
ferent mode of action from the other more perfectly formed
cylinders in close proximity, bearing in that character a resem-
blance to the funnel-pipes of the general surface. I am inclined,
however, to believe this tube is continued downwards, of a
cylindrical form, and produced in the same manner, the enlarge-
ment of the upper part having been caused by some impediment
to the ready and regular escape of the gas, retaining it near the
surface, where it has in consequence exerted a more destructive
force, the erosive power diminishing downwards, causing the
angular inclination of the sides.

These pipes seem to differ from those of the Geysers in Iceland,
or others that have been formed by water in various parts of the
world in the immediate neighbourhood of volcanoes, inasmuch as
from the fragile nature of the crag rock, the narrow partition
between these pipes would have been ruptured by the upward
action of water impelled through them with any degree of vio-
lence; and the more probable solution appears to be the quiet
action of carbonic acid gas evolved in an upward direction ; and

826 The Rev. J. B. Reade on some early

the gas thus produced had its origin deep seated beneath the
London clay, showing that volcanic force, although in a moderate
degree, has exerted an influence in this locality since the depo-
sition of the coralline crag bed. Whether these fumeroles or
mofettes were formed only at the period immediately antecedent
to the present epoch, is, perhaps, difficult to determime; they
might have existed during the latter portion of the time when
this bank was under formation, before it was ever elevated above
the sea: I am inclined to attribute them to the time when the
gravelly and sandy deposit of the red crag overlaid this coral
bank before the face of the country was modified into its present
form. They are, however, here brought forward to show the
great probability that these calcareous rocks have been acted
upon by gases rising from below as well as by acids in a down-
ward direction ; and although the surface of the chalk, as well as
the crag, is corroded in most places, denoted by the funnel-
shaped depressions beneath the superficial soil, there have not
been recorded, that I am aware of, such marked evidences of
upward action in any other rock in this country from the cre-
taceous period to the present time.

XLVIII. On some early Experiments in Photography, being the
substance of a Letter addressed to Ropprt Hunt, Esq. By
the Rev. J. B. Reapz, M.A., F.R.S.

Stone Vicarage, Aylesbury,

My pear Sir, Yobruate La, {s54. >
giving you the information you require respecting my
early researches in photography in 1836 and following
years, | may assume that you are already aware, from my letter
to Mr. Brayley of March 9, 1839, and published in the British

Review for August, 1847, that the principal agents 1 employed,

before Mr. Talbot’s processes were known, were infusion of galls

as an accelerator, and hyposulphite of soda as a fixer.

I have no doubt, though I have not a distinct recollection of
the fact, that I was led to use the infusion of galls from my
knowledge of the early experiments by Wedgwood. 1 was aware
that he found leather more sensitive than paper ; and it is highly
probable that the tanning process, which might cause the silver
solution to be more readily acted upon when applied to the
leather, suggested my application of the tanning solution to
paper.

In your own history of the photographic process, you say
“the discovery of the extraordinary property of the gallic acid
in increasing the sensibility of the iodide of silver was the most
valuable of the numerous contributions which Mr, Talbot has

Experiments in Photography. - 327

made to the photographic art.” It is nevertheless true, as stated
by Sir David Brewster, that “the first public use of the infusion
of nut-galls, which is an essential element in Mr. Talbot’s patented
process, is due to Mr. Reade,” and in my letter to Mr. Brayley I
attribute the sensitiveness of my process to the formation of a gal-
late or tannate of silver. I need scarcely say, that among various
experiments I tried gallic and tannic acid in their pure state, both
separately and mixed ; but the colour of the pictures thus ob-
tained with the solar microscope was at that time less pleasing
to my eye, than the rich warm tone which the same acids pro-
duced when in their natural connexion with solutions of vege-
table matter in the gall-nut. This organic combination, however,
was more effective with the solar microscope than with the camera,
though the lenses of my camera were five inches jn diameter. It
is probable enough that the richer tone was due to the greater
energy of direct solar rays. In using the solar microscope, I
employed a combination of lenses which produced a convergence
of the luminous and photogenic rays, together with a dispersion
of the calorific rays, and the consequent absence of all sensible
heat enabled me to use Ross’s cemented powers, and to make
drawings of objects inclosed in Canada balsam, and of living
animalcules in single drops of water. The method I employed
was communicated to the Royal Society in December 1836, and
a notice of it is contained in the ‘Abstracts.’

You inform me that some persons doubt whether | really
obtain gallate of silver when using an infusion of gall-nuts, and
that one of Mr. Talbot’s friends raises the question. It is suffi-
cient to reply, that though gallic acid is largely formed by a
long exposure of an infusion of gall-nuts to the atmosphere, as
first proposed by Scheele, yet this acid does exist in the gall-nut
in its natural state, and in a sufficient quantity to form gallate
of silver as a photogenic agent ; for M. Deyeux observes, that
“when heat is very slowly applied to powdered gall-nuts, gallic
acid sublimes from them, a part of which, when the process is
conducted with great care, appears in the form of small white
erystals.” M. Fiedler also obtained gallic acid by mixing together
a solution of gall-nuts and pure alumina, which latter combines
with the tannin and leaves the gallic acid free in the solution ;
and this solution is found, on experiment, to produce very admi-
rable pictures. But what is more to the point, Mr. Brayley, in
explaining my process in his lectures, showed experimentally how
gallate of silver was formed, and confirmed my view of the sen-
sitiveness of the preparation. It is therefore certain that the
use of gallate of silver as a photogenic agent had been made
public in two lectures by Mr. Brayley at least two years before
Mr. Talbot’s patent was sealed,

328 The Rev. J. B. Reade on some early

I employed hyposulphite of soda asa fixer. Mr. Hodgson, an
able practical chemist at Apothecaries’ Hall, assisted me in the
preparation of this salt, which at that time was probably not to
be found, as an article of sale, in any chemist’s shop in London.
Sir John Herschel had previously announced the peculiar action
of this preparation of soda on salts of silver, but I believe that I
was the first to use it in the processes of photography. I also
used iodide of potassium, as appears from my letter, as a fixer,
and I employed it as well to form iodide of lead on glazed cards
as an accelerator. lLodide of lead has of itself, as I form it, con-
siderable photographic properties, and receives very fair impres-
sions of plants, lace, and drawings when placed upon it, but with
the addition of nitrate of silver and the infusion of galls the
operation is perfect and instantaneous. Pictures thus taken
were exhibited at the Royal Society before Mr. Talbot proposed
his iodized paper. The microscopic photographs exhibited at
Lord Northampton’s in 1839 remained in his lordship’s posses-
sion. I subsequently made drawings of sections of teeth; and
one of them, a longitudinal section of a tooth of the Lamna, was
copied on zine by Mr. Lens Aldous for Owen’s ‘ Odontography.’
I may say this much as to my own approximation to an art,
which has deservedly and by universal consent obtained the name
of Talbotype.

Sir David Brewster, in his ‘ History of Photography,’ passes
immediately from the experiments of Wedgwood to those of
Talbot ; but the Transactions of the Royal Society, to which my
friend Mr. Gravatt has directed my attention, will enable us to
insert, if not a chapter, at least a very pregnant parenthesis.
The Bakerian Lecture, in 1803, by Dr. Young, who never
touched a subject without leaving his mark upon it, contains a
highly interesting and original experiment on the photographic
representation of the invisible chemical rays beyond the blue end
of the spectrum. This experiment does not happen to be recorded
in the first edition of your ‘ Researches on Light ;’? but no one
will refer to it with greater pleasure than yourself, not only
because it is the first photographic analysis of the spectrum, but
also because it has the higher merit, even as it stands alone, of
being the one sufficient fact which establishes the consummation
so devoutly looked for, at the conclusion of your work, from the
perservering accumulation of facts only; for it is in itself a
simple and demonstrative proof, to use the words of Dr. Young,
of the general law of interference, and, in your own words,
“reconciles the chemical action of the photographic force, energia,
with the undulatory theory of light.’ Dr. Young’s experiment
forms the conclusion of his lecture, and is given in the following
terms :—“ The existence of solar rays accompanying light more

Haperiments in Photography. 329

refrangible than the violet rays, and cognisable by their chemical
effects, was first ascertained by Mr. Ritter; but Dr. Wollaston
made the same experiments a very short time afterwards, without
having been informed what had been done on the Continent.
These rays appear to extend beyond the violet rays of the pris-
matic spectrum, through a space nearly equal to that which is
occupied by the violet. In order to complete the comparison of
their properties with those of visible light, I was desirous of
examining the effect of their reflexion from a thin plate of air
capable of producing the well-known rings of colours. For this
purpose I formed an image of the rings, by means of the solar
microscope, with the apparatus which I have described in the
Journals of the Royal Institution, and I threw this image on
paper dipped in a solution of nitrate of silver, placed at a distance
of about nine inches from the microscope. In the course of an
hour, portions of three dark rings were very distinctly visible,
much smaller than the brightest rings of the coloured image,
and coinciding very nearly in their dimensions with the rings of
violet light that appeared upon the interposition of violet glass,
I thought the dark rings were a little smaller than the violet
rings, but the difference was not sufficiently great to be accu-
rately ascertained ; it might be as much as =,th or th of the
diameters, but not greater. It is the less surprising that the
ditference should be so small, as the dimensions of the coloured
rings do not by any means vary at the violet end of the spectrum
so rapidly as at the red end. For performing this experiment
with very great accuracy a heliostate would be necessary, since
the motion of the sun causes a slight change in the place of the
image, and leather impregnated with the muriate of silver would
indicate the effect with greater delicacy. The experiment, how-
ever, in its present state is sufficient to complete the analogy of
the invisible with the visible rays, and to show that they are
equally liable to the general law (of interference), which is the
principal subject of this paper.”

It detracts nothing from the greatness of Dr. Young to say,
that although, the philosophy of this experiment is permanent
truth, yet the spectral image of it soon faded away. Photo-
graphy was not then, at the beginning of the century, an art as
permanent as it is elegant and useful. Little was wanted to
make it so, but it hung fire for nearly fifty years, till Talbot
supplied that little.

I have just learnt from Admiral Smyth, that his friend
Dr. Peacock, the Dean of Ely, has for the last seven years been
engaged on a life of Dr. Young; and when the work appears, we
shall have a more accurate knowledge of the man who was un-
questionably the Newton of his day. Like his illustrious pre-

330 On some early Experiments in Photography.

decessor, he was a pioneer in the philosophy of light; and, as
we have seen, by a single photographie experiment, overlooked
hitherto by us all, has shown a perfect analogy between the un-
dulations of the visible and invisible rays. Had he happened
to head his chapter, as Wedgwood does, ‘‘ On a method of taking
Pictures by the agency of Light on Nitrate of Silver,” his name
and place would have been duly marked; but because theory,
and not experiment, was the great point before him, the philo-
sophical photographer is overlooked by the practical one.

Dr. Young’s propositions are, that radiant light consists in
undulations of the luminiferous ether, that light differs from
heat only in the frequency of its undulations, that undulations
less frequent than those of light produce heat, and that undula-
tions more frequent than those of light produce chemical and
photographic action,—all proved by experiments.

You close your own ‘ Researches on Light’ by proposing the
following questions as of the greatest importance for future inves-
tigation :—“Is energia absorbed by material bodies? Does it
influence their internal constitution? Is it radiated from bodies
in the dark, or at all concerned in the production of any of those
changes which have been attributed to dark rays?”

Dr. Young’s hypothesis seems to anticipate your questions,
and almost to answer them in their order. He says, “ All mate-
rial bodies have an attraction for the etherial medium,—by means
of which it is accumulated within their substance,—and for a
small space around them—in a state of greater density, but not
of greater elasticity.”’ (Bakerian Lecture, 1801.) Hence he con-
siders material bodies to have within them latent light, latent
heat, and latent chemical force, or “energia” (which is, in his
opinion, a particular condition of the ztherial medium) ; that the
luminous, calorific, and chemical phenomena are exhibited under
two modifications,—the vibratory or permanent, and the undula-
tory or transient state; and that the forces which produce these
several effects differ from each other only in the frequency of
their undulations or vibrations.

Such are the conclusions at which the all-inquiryyg Dr. Young
arrived in 1801, on a subject which in 1850 is proposed for our
investigation. Well may Admiral Smyth say, ‘ How strange it
is that we are still but half acquainted with the results of his
powerful mind!”

Of course I shall not quarrel with you if you do not accept
his conelusions, totidem verbis, because, as | am aware, you see
reasons for believing that light, or that agent which affects the
organs of sight, is broadly distinguished from those rays which
bring heat from its solar source, and both of these classes from
those which produce, in the constitution of bodies, those smgular

On the Contacts of Lines and Surfaces of the Second Order. 331

changes which are more particularly the objects of your study.
But Sir John Herschel has shown that, by certain artifices, even
the extreme rays may be rendered visible ; and Dr. Young, by
an experiment most ingenious, and to his own mind, at least,
most conclusive, has demonstrated the analogy of the invisible
with the visible rays. I feel sure, therefore, that while adducing
and discussing the proofs of your own theory, you will be glad
to take the opportunity afforded by your second edition of placing
Dr. Young’s name in the niche which Fame has left empty.
Believe me to be, my dear Sir,
Very truly yours,
To Robert Hunt, Esq. J. B. Reape,

XLIX. Note on the “ Enumeration of the Contacts of Lines and
Surfaces of the Second Order.” By J.J. Sytvuster, M.4A.,
F.R.S.*

* the month of February, 1851, I gave in this Magazine an

a@ priori and exhaustive process, founded upon the method
of determinants, for determining every different kind of simple
or collective contact capable of happening between lines and
surfaces, and in general between all loci (whether intraspatial or
extraspatial) of the second order. The question was shown to
resolve itself into that of determining the number of singular
relations capable of existing between two quadratic homogeneous
functions of any given degree. My object in the paper referred
to was actually to calculate the geometrical and analytical cha-
racters of these contents and singularities for intraspatial loci,
i. e. loci representable by homogeneous quadratics of two, three,
and four variables; but I incidentally appended a statement of
the number of such for loci of five, six, seven, and eight variables,
without, however, dwelling upon the means of representing the
general law. This statement is, however, affected with certain
inaccuracies of computation which will be presently pointed out.

It will be at once apparent, from an inspection of the prin-
ciple of my method, that it remains equally applicable (mu-
tatis mutandis) to the more general question of determining
the relative singularities (in character and amount) of two
functions, each linear in respect of two systems of variables
By Taps +yHn3 H'), a'g,... 2,5 Which species of functions dege-
nerate into quadratic forms, when the two systems of variables
become identical so as to coalesce into a single system. Some
researches of Mr. Cayley into the autometamorphic substitutions
of quadratic forms (meaning thereby the linear substitutions

* Communicated by the Author.

382 Mr. J. J. Sylvester on the Enumeration of the Contacts

which leave the form unaltered) required him to consider the
nature of the singular relations capable of existing between two
linear substitutions, which is precisely the question, differently
stated, of the singular relations connecting two lineo-linear func-
tions above adverted to; accordingly, I am indebted to Mr. Cay-
ley for making an observation on the effect of my rule for finding
such singularities, which leads to a most elegant formulization
of the number of singularities in question, and which I proceed
to introduce to the notice of my readers.

If U and V be two quadratic functions, each of n variables,
and if we call D the discriminant of U+-AV=D(a), D(A) will
be a function of Xof the nth degree. Now, first, I have observed
that if any of these n roots be repeated any number of times,
there will be a corresponding degree of singularity about one of the
points of intersection of the loci represented by U=0, V=0% so
that if the x roots of D(A) be made up of 7, roots a), 7g roots da,
rz roots as, &e., there will be an inclusive singularity r, at one
point, 7, at another, r, at a third, and so on—by nclusive sin-
gularity meaning a number one unit greater than the index of
singularity properly so termed; the inclusive-singularity at an
ordinary intersection being called, 1, at a poimt of simple singu-
larity, 2, of double singularity 3, and in general at a pomt of the
(r—1)th degree of singularity, 7.

Hence the total-inclusive singularity (which is an unit greater
than the total-singularity, properly so called) may be broken
up into as many partial heaps of inclusive-smgularity as there
are modes of decomposing 7 into integers. We may now con-
fine our attention exclusively to the different modes in which
a given amount of inclusive-singularity at a single pomt admits
of subdivision into distinct species of singularity, for which I have
given in my paper referred to the followmg rule:—The minor
systems of determinants corresponding to the matrix of U+AV
are to be considered in succession ; and if (a) be any root of the
complete determinant of the matrix occurring 7 times, every
hypothesis is to be exhausted as regards the number of times in
which (\—a) may be conceived to enter as a factor into each of
the system of 1st minors, into each minor of the system of 2nd
minors, into each minor of the system of 3rd minors, and so on ;
the number of such hypotheses being limited by the condition
that,if guoad the root a,(—a)", (A— a)", (s—a)" be the greatest
common factors respectively to three consecutive systems of
minor determinants, s; must be not less than 2k,—A,. Here
steps in the beautiful observation of Mr. Cayley, that the ques-
tion of assigning the different species of singularities respondent
to the factor (a) supposed to occur (r) times, is, by virtue of the
above condition, tantamount precisely to that of assigning the

of Lines and Surfaces of the Second Order. 333

total number of decreasing* series of positive integers, com-
mencing with a given number (7), subject to the condition that
the second differences shall be all positive ; which (he adds) call-
ing the successive second differences 6, 6/, 6", &c., is tantamount
to finding the number of ways that the equation r=6 + 26! + 36"
+ &c. admits of being solved by positive integers, which is
obviously the same as the number of modes in which 7 admits
of being decomposed into positive integer parts. Thus the idea
of partition, which arises naturally in the first part of the pro-
cess (that, namely, of the decomposition of the collective inclu-
sive-singularity in every possible way into modes of distributive
inclusive-singularity), reappears quite unexpectedly (it may almost
be said miraculously), and as the result of an analytical trans-
formation in the second part of the same.

It should be observed that the case of complete coincidence
between U and V, which, supposing them to be functions of (7)
variables, corresponds to the supposition of the same factor oc-
curring respectively n times, (n—1) times, (n—2) times, &c.
2 times and | time in the complete determinant, the 1st minor
system, the 2nd minor system, &c., the (n—2)th minor system
and the (n—1)th minor system respectively, is here taken as the
highest case of singularity ; this and the case of non-singularity,
which also adds a unit to the index of singularity, properly so
called, will together make a difference of 2 units in the numbers
given by me in the paper referred to, which numbers will accord-
ingly be 3, 6, 14, &c., in lieu of 1, 2, 12+, &. We are now
enabled to give the following simple statement of the law for
determining the total number of singularities which can exist
between two quadratic forms of n variables (or if we like so to
say, more generally between two linear substitution-systems of
the nth order, viz. the number of the singularities (including abso-
lute unrelatedness and entire coincidence within the purview of
the term) is the index of double decomposition into parts of the
number n. To raise up in the mind a clear conception of the
idea of double decomposition, we may proceed as follows :—
First. Suppose a state of things in which a body is supposed to
be determined completely, provided that the number of mole-
cules which it contains, and the different number of atoms in
each molecule are given, the index of simple decomposition, 2. e.
of ordinary partitionment of the number of n, will be the number
of different bodies which are capable of being formed out of n
atoms. Now imagine that, for the complete determination of a

* Such a series must, from its very nature, be always decreasing or
increasing in the same direction.

+ These numbers refer to quadratic homogeneous functions, containing
respectively 2, 3, 4, &c. variables. For the case of functions containing
but one variable there is no distinction between coincidence and unrelated-
ness, and the number of modes of relation is a single unit.

334 On the Contacts of Lines and Surfaces of the Second Order.

body, another step in the hierarchy of aggregation is to be taken
into account, and that we must know for this purpose not only
the number of molecules in the body and the number of atoms
in each molecule, but also the number of monads in each atom ;
the number of bodies (differing by definition) capable of being
formed out of x monads will then represent what I mean by the
index of double decomposition of (or if we like so to say) to the
modulus x. Anditis obvious that this idea admits of indefinite
extension, and that we may speak of the index of decomposition
of any order of multiplicity (single, double, treble, &c.) of or to
the modulus 2.

For single decomposition it is well known and immediately
obvious, that the imdices to the successive moduli given by the
rational numbers in regular progression will be the coefficients
of z, x®, a°, &e. in the continued product,

(l—2z)~*. (1—2?)7?. (1—a8)7!, &e. ad inf. ;
calling these 7,, mg, 73, &c., it is of course obvious, as Mr. Cayley
has observed, that the indices of double decomposition to the
same successive moduli will be the coefficients of the same argu-
ments x, 2”, #3, &c. in the continued product

(l—#)"". (l—a®)*. (l—a?)~”, &e. ad inf.;
and by aid of this formula he has calculated (with extreme faci-
lity) the indices in question up to the modulus 11, and found
that they form the series 1, 3, 6, 14, 27, 58, 111, 223, 424, 817,
1527, which accordingly is the series representing the number
of singularities capable of existing between quadratic loci com-
mencing with 1 and ending with 11 variables.

The values of 7,, 7, M3,-+.+,,, &e. themselves are given in
Euler’s introduction, and are respectively

1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, &c.,

which numbers will accordingly represent to their respectively
corresponding moduli the number of classes of singularity,
whether these classes be defined with reference to the different
modes of distribution of the total collective singularity about
different points, or with reference to the degree of the lowest
system of minor determinants of the matrix to the determinant
to U+AV haying one or more factors in common, which latter
is the mode of forming the classes adopted by me in the “ Enu-
meration.”

Let me be permitted to express the satisfaction which I have
felt in finding this theory, which appeared to be doomed to hope-
less oblivion, thus unexpectedly, after three years of interment,
coming back to life, and at once filling a desired place in ana-
lytical researches pursued with apparently a totally different aim,

26 Lincoln’s Inn Fields,
March 10, 1854,

[ 335 ]

L. On the Chemical Composition of Recent and Fossil Lingule,
and some other Shells. By W. E. Locan, F.R.S., and T.S.
Hounr*,

> he the Report of Progress of the Geological Survey of Canada
for 1851-52, we have mentioned the existence of small
masses containing phosphate of lime, and having the characters
of coprolites, which occur in several parts of the Lower Silurian
rocks. In a bed of siliceous conglomerate towards the top of
the calciferous sandstone, at the Lac des Allumettes, on the .
Ottawa, they are abundant in cylindrical and imitative shapes,
sometimes an inch in diameter. The same material forms casts
of the interior of a species of Holopea or Pleurotomaria, and
often fills or completely encases the separated valves of a large
species of Lingula, which Salter has referred to L. parallela of
Phillips. The phosphatic matter is porous, friable, and of a
chocolate-brown colour ; it contains intermixed a large quantity
of sand, and small pebbles of quartz are sometimes partly im-
bedded in it. The analysis of one specimen gave 36 per cent. of
phosphate of lime, with 5 per cent. of carbonate and fluoride,
besides some magnesia and oxide of iron, and 50 per cent. of
siliceous sand.

Similar masses occur in the same formation at Grenville, and
in the lower part of the Chazy limestone at Hawkesbury, in both
cases containing fragments of Lingula. Those from the latter
place are rounded in shape, and from one-fourth to one-half of
an inch in diameter, blackish without, but yellowish-brown
within, and having an earthy fracture ; the analysis of one of
them gave :—

Phosphate of lime (PO®, be . . . 44°70
Carbonate of lime . . eR 9G :EO
Carbonate of magnesia . . MN ale a
Peroxide of iron and a trace of ‘ftuaiin oe S60
Insoluble siliceous residue . . . . . 27:90
Welatile matter OR 8s .2ergougp OO

97°56

From the colour it is probable that the iron exists as a car-
bonate. When heated in a tube, a strong odour like burning
horn is perceived, accompanied by ammonia which reddens tur-
meric paper and gives white fumes with acetic acid, showing
that a part at least of the volatile matter is of an animal nature.
The specimens from Lac des Allumettes lose 1:7 per cent. by
gentle ignition, with a like production of ammonia, and an odour

* From Silliman’s American Journal, vol, xvii. p, 235.

336 Messrs. W. E. Logan and T. 8. Hunt on the

of animal matter: the same thing was observed with those from
Grenville.

The existence in Lower Silurian rocks, of these masses, whose
characters leave no doubt that they are coprolites, and whose
chemical composition is like that of the execrements of creatures
feeding upon vertebrate animals, led us to examine the shells of
the Lingule always associated with these phosphatic bodies. The
result has been that all the specimens yet examined consist
chiefly of phosphate of lime; they dissolve readily with slight
. effervescence in hydrochloric acid, and the solution gives with »
ammonia a copious precipitate readily soluble in acetic acid, from
which oxalic acid throws down lime. With a solution of molyb-
date of ammonia there is obtained a quantity of the characteristic
yellow molybdo-phosphate, many times greater than the bulk of
the shell.

We have thus examined Lingula prima and L. antiqua from
the Potsdam sandstone, L. parallela from the calciferous, and a
species somewhat resembling L. quadrata from the Trenton
limestone. It was desirable to compare with these the shell of
a recent species, and for this purpose fine specimens of the Lin-
guia ovalis, of Reeve, from the Sandwich Islands, were furnished
us by J. H. Redfield, Esq., of New York. The shell of this
species had the same composition as the fossil ones; and the
thick, green epidermis, which swelled up like horn when heated,
gave a bulky white ash of phosphate of lime.

For a further analysis, the shell was boiled in water to remove
all soluble matters, the soft parts still adherent were carefully
detached, and the shell with its epidermis weighing ‘186 grm.,
was calcined over a spirit-lamp. ‘The brownish residue, weigh-
ing ‘114 grm., readily dissolved with slight effervescence in
dilute hydrochloric acid, leaving but a few light flakes of car-
bonaceous matter. Acetate of soda and perchloride of iron were
added to the solution, which was boiled, and the precipitated
basic salt separated by filtration and decomposed by hydrosul-
phuret of ammonia. The filtrate from the sulphuret of iron
having been concentrated, the phosphoric acid was thrown down
by ammonia with a magnesian salt; there was obtamed ‘070
grm. of pyrophosphate of magnesia, equal to ‘044 of phosphoric
acid, or ‘0978 of phosphate of lime, PO®, 3CaO.

The lime was separated from the acetic filtrate as an oxalate,
and gave ‘108 of carbonate, equal to ‘0605 of lime, being an
excess of (0075 over the amount required to form the phosphate,
and corresponding to ‘0134 of carbonate; the small amount of
material did not permit us to determine whether a portion of the
lime exists as fluoride. There was also obtained ‘0082 of mag-
nesia; the results from the calcined shell of Lingula ovalis are

Chemical Composition of Recent and Fossil Lingule. 337
then as follows :—

Phosphate of lime . . ‘0978= 85-79 per cent.

Carbonate of lime . . °01384= 11:75...

Marnesia =.) 1s)! yaiXG: 0082 = ha BONT 54
*1144= 100°34

The proportion of phosphate of lime is that contained in
human bones after their organic matter has been removed.

The texture of the ancient Lingule was observed to be unlike
that of most other fossil shells, being more or less dark brown in
colour, brilliant, almost opake, and not at all crystalline. These
characters are also found in the allied genus Orbicula, and we
therefore examined an undescribed species of it from the Trenton
limestone, beautifully marked in a manner resembling Conwlaria
granulata, and another large species, also undescribed, from the
Upper Silurian; both of these consist chiefly of phosphate of
lime ; and the shell of a recent species, O. /amedlosa, from Callao
was found to be similar in composition. We have not yet been
able to examine a specimen of the genus Obolus. The same dark
colour and brillancy were also remarked in the genus Conularia,
and the shell of C. trentonensis proved on examination to be
composed in like manner of phosphate.

The similarity of composition in these genera 1s in accordance
with the acute observations of Mr. Hall, who finds that Conu-
laria is almost always associated with Lingula and Orbicula, and
remarks that “these shells, so unlike im structure and habit,
appear to have flourished under similar circumstances, and to
have required the same kind of ocean bed or sediment ” (Pale-
ontology, vol. i. p. LO1).

For the sake of comparison we have examined the following
fossil shells ; they have a common character, distinct from those
already described, being lighter coloured, more translucent and
granular in texture : Atrypa extans, Leptena alternata, and Orthis
pectenella from the Trenton limestone; O. erratica from the
Hudson River group, and Chonetes lata? from the Upper Silu-
rian, besides Jsotelus gigas, and a species of Cythere from the
Trenton. All of these consist of carbonate of lime, with only
such traces of phosphate as are generally found in calcareous
shells.

In the Report already quoted we have given a description of
some phosphatic bodies which resemble the coprolites of the
calciferous sandstone, and are found at Riviere Ouelle in thin
layers of a conglomerate limestone, which is interstratitied with
red and green shales, and belongs to the top of the Hudson
River group, or the base of the Oneida conglomerates. The -
phosphatic masses are very abundant, and rounded, flattened, or

Phil, Mag. 8. 4. Vol. 7. No. 46. May 1854. 2A

338 On the Chemical Composition of Recent and Fossil Lingule.

cylindrical in shape, and from one-eighth of an inch to an inch
in diameter; they sometimes make up the larger part of the
conglomerate. Iron pyrites m small globular masses occurs
abundantly with them, often filling their interstices, but is not
found elsewhere in the rock. These coprolites are finer grained
and more compact than those from the Ottawa, and have a con-
choidal fracture; their colour is bluish or brownish-black ; the
powder is ash-gray, becoming reddish after ignition. They have
the hardness of calcite, and a density of 3:15. When heated
they evolve ammonia with an animal odour, and with sulphuric
acid give the reactions of fluorine. The quantitative analysis of
one gave—

Phosphate of lime, PO®,3CaO° . . 40:34 per cent.
Carbonate of lime, with fluoride. . S14 «.

Carbonate of magnesia . . . « DVO oo
Peroxide of iron with a littlealumina 12°62 ...
Oxide of manganese . . . . . trace han
Insoluble siliceous residue . . . 25°44 ...
WVolatilermatler casts tek eke Noone acre Manone
95°37

The iron exists, in part at least, as carbonate, and its introduc-
tion in so large a quantity, giving colour and density to the
coprolites, is doubtless connected with the formation of iron
pyrites by the deoxidizing action of organic matters. The
production of an equivalent of bisulphuret of iron from a neutral
protosulphate of iron, which alone could exist im contact with
limestone, must be attended with the elimination of an equivalent
of protoxide of iron, for 2(SO*®. FeO) —O7= Fe S* + FeO.

It is remarkable that no traces of Lingule or any other shells
have been detected with these coprolites. Thin sections of
them are translucent, and under the microscope are seen to con-
sist of a fine granular base, in which are imbedded numerous
grains of quartz, and small siliceous spicule, like those of some
sponges. Ina bed of sandstone, associated with these conglo-
merates and slates at Riviére Ouelle, were found several hollow
cylindrical bodies, resembling bones in appearance. The longest
one is an.inch and a half long, and one-fourth of an inch in dia-
meter. It is hollow throughout, and had been entirely filled
with the calcareous sandstone, in which it is imbedded, and
whose disintegration has left the larger end exposed. The
smaller extremity is cylindrical and thin, but it gradually en-
larges from a thickening of the walls, and at the other end
becomes externally somewhat triangulariform ; the cavity remains
nearly cylindrical, but the exposed surfaces are rough and irre-
gular within.

On the Porism of the In-and-circumscribed Polygon. 339

The texture of these tubes is compact, their colour brownish-
black, with a yellowish-brown translucency in tlin layers. Ana-
lysis shows them to consist, like the coprolites, principally of
phosphate of lime. One hundred parts gave—

Phosphate of lime. . . . . . 67°53
Carbonate oflime . . . . . . 4°85
Migcmegia . te ell eles hts «kel oe Be AD
Protoxide Of gnatiicss cad, 2.06 eae
Insoluble siliceous sand . . . . 21°10
Volatile animal matter . . . . 9 2°15

99°73

The microscopic examination of a section shows that the walls
of the tube are homogeneous, unlike the coprolites, and that the
siliceous sand in the analysis came from the sandstone which
incrusted the rough interior of the fossil. The phosphate is
finely granular, and retains no vestige of organic structure. The
chemical composition and the remarkable shape of the specimens,
however, leave little doubt of their osseous nature, unless we
suppose them to be the remains of some hitherto unknown in-
vertebrate animal, whose skeleton, like those of Lingula, Orbicula
and Conularia, consisted of phosphate of lime, a composition
hitherto supposed to be peculiar to vertebrate skeletons.

Montreal, Jan. 5, 1854.

LI. Developments on the Porism of the In-and-circumscribed
Polygon. By A. Cayury, Esq.*

us PROPOSE to develope some particular cases of the theo-

rems given in my paper, “Correction of two Theorems rela-
ting to the Porism of the in-and-circumscribed Polygon” (Phil.
Mag. Nov. 1853). The two theorems are as follows.

Theorem. The condition that there may be inscribed in the
conic U=0 an infinity of n-gons circumscribed about the conic
V=O, depends upon the development in ascending powers of &
of the square root of the discriminant of [U+V>; viz. if this
square root be

A+BE+C24D&+ EE + FE 4 GE+4 He 4+ ..,
then for n=3, 5, 7, &c. respectively, the conditions are

| C | =0, C, DpA=0, C, D, E| =0, &e.;
D,E D, E, F
E, F, G

* Communicated by the Author.
2A2

340 Mr. A. Cayley on the Porism of

and for n=4, 6, 8, &c. respectively, the conditions are

[D|=0," |D,E|=0, 1D, EF | =0, &e.
E, F E, F,G
F, G, H|

Theorem. In the case where the conics are replaced by the
two circles 2? +y?—R?=0, (w—a)?+y°—7*?=0, then the discri-
minant, the square root of which gives the series

A+BE4+C#24D&+4 Ee + &e.,
=A + £){r2 + E(r? + R222) +2R?}.
Write for a moment

A+ Bé+C£4 D+ BE+4+ &e.= V(1+a€) (1468) (1+ c€),
then

1s

A=]
2B=a+b+e
—8C=a? +b? +4 c? —2be—2ca—2ab
16D=a?4+ 4? +4+ 3—a*(b+ce)— 265 (¢-peys Allein Bae
—128E=5at+54*+4+ 5c4
—4a3(b +c) —4b3(c+ a) —4c3(a + b)

4+ 4a?be + 4b2ca + 4c2ab
— 262¢? — 22a? — 2a7b?
&e.

To adapt these to the case of the two circles, we have to write

r2(1 +a£)(1-+08)(1-+c£) = (148) (72+ E02 + R2—a) + PRY}.
and therefore

es
r?(a +b) =r? + R?—a?
r2ab= R? ;
values which after some reductions give
ee |

722B = 27? + R?—a?
—7*8C = (R?—a*)?—4R?*?
7®16D = (R? —a?) { (R? —a*)? —2r?(R? + a?) }
—7°128E=5(R*—a?)*
—8(R?— a®\?(R2 + 272)?
+ 16a*r4.

the In-and-circumscribed Polygon. 341

Whence, also,
r'2]024(CE—D?) =
{5(R2—a?)*—8(R2—a?)?(R2 +: 27?)r? + 1604} { (R?—a?)?—-4R*r*) }
= Af (R?—a?)? —2(R?—a?) (R? + ig va
which after all reductions is
(R2—a2)6

—12R?(R?—a?)*r?

+ 16R?(R? + 2a?) (R?—a?)*r4

—64R2a*r®.

Hence the condition that there may be inscribed in the circle
z+ y?—R?=0, and circumscribed about the circle (7 —a)?+y?
—r?=0, an infinity of n-gons is for n=3, 4, 5 respectively,
i. e. in the case of a triangle, a quadrangle and a pentagon, is as

follows.
I. For the triangle, the relation is
(R? —a?)?—4R*?=0,
which is the completely rationalized form (the simple power of a
radius being of course analytically a radical) of the well-known
equation
a? = R?—2Rr,

which expresses the relation between the radii R, 7 of the cir-
cumscribed and inscribed circles, and the distance a between

their centres.
II. For the quadrangle, the relation is

(R?—a?)?—2r?(R? + a?) =0,
which may also be written
(R+7r+a)(R4+r—a)(R—r+a)(R—r—a)—1*=0.
(Steiner, Credle, vol. ii. p. 289.)
III. For the pentagon, the relation is
(R?—a?)®—12R°(R?—a?)4r? + 16R%R? + 2a”) (R? —a?)*r4
— 64R?a47°=0,
which may also be written
(R2—a2)2{ (R2—a?)?— 4R2r?}?— 4 R424 (R2—a?)?—4a°r?}? =O.
The equation may therefore be considered as the completely
rationalized form of
(R2—a?)? + 2R(R?— a2)? —4R2(R? —a?)r? —8Ra*v?=0.
This is, in fact, the form given by Fuss in his memoir “ De
Polygonis Symmetrice irregularibus circulo simul inscriptis et
cireumseriptis,’ Nova Acta Petrop. vol. xiii. pp. 166-189 (1 quote

342 Mr. A. Cayley on the Porism of :

from Jacobi’s memoir, to be presently referred to). Fuss puts
R+a=p, R—a=gq, and he finds the equation
Pera (pte) _ 1. /q—r

Pe@—plr+g) — a
which, he remarks, is satisfied by r= —p andr= = , and that

consequently the rationalized equation will divide by p+r and
pq—r(p+q); and he finds, after the division,

PYEt+P E(t gr—Pa p+ 9)? —(p+q)(p—9g)7?=9,
which, restoring for p, q their values R+a, R—a, is the very
equation above found.

The form given by Steiner (Crelle, vol. u. p. 289) is

r(R—a)=(R+a) V (R—r+a)(R—r—a) + (R+a) V (R—r—a)2K,
which, putting p, q instead of R+a, R—a, is

qr=p V (p—r)(q—r) +p V (G—") (9 +P):

And Jacobi has shown in his memoir, “ Anwendung der ellip-
tischen Transcendenten,” &c., Crelle, vol. iii. p. 376, that the
rationalized equation divides (like that of Fuss) by the factor
pg—(p+q)r, and becomes by that means identical with the
rational equation given by Fuss.

In the case of two concentric circles a=0, and putting for
2

greater simplicity = =M, we have

A+BE+C2+ D4 EH +4 &. =(14 €) V1+ ME:
This is, in fact, the very formula which corresponds to the
general case of two conics having double contact. For suppose
that the polygon is inscribed in the conic U=0, and circum-
scribed about the conic U + P?=0, we have then to find the dis-
criminant of £U+U+P?, 2. e. of (1+£)U+P?. Let K be the
discriminant of U, and let F be what the polar reciprocal of U
becomes when the variables are replaced by the coefficients of P,
or, what is the same thing, let —F be the determinant obtained
by bordering K (considered as a matrix) with the coefficients of P.
The discriminant of (14 £)U + P? is (14 €)8K +4 (1+ &)?F, 2. e.

(1+8) {KI +£)+F}=(K+F)(1+é) + M6),
where M= a or, what is the same thing, M is the dis-

criminant of U divided by the discriminant of U+P?.. And M
having this meaning, the condition of there being inscribed in
the conic U=0 an infinity of n-gons circumscribed about the
eonic U + P?=0, is found by means of the series

A+ BE+C&+4 D4 HE + &e. =(14+ &) “14+ ME.

the In-and-circumscribed Polygon. 343

We have, therefore,

Ai
2B=M+2
—8C=M?—4M
16) = M°— 2M?
—128E=5M*—8M3
&e.
1024(CE — D?) = M4(M?—12M + 16)
&e

Hence for the triangle, quadrangle and pentagon, the condi-
tions are—
I. For the triangle,

M+2=0.
II. For the quadrangle,
M—4=0.

III, For the pentagon,
M?—12M+16=0.
And so on.

It is worth noticing, that, in the case of two conics having a
4-point contact, we have F=0, and consequently M=1. The
discriminant is therefore (1+ £)%, and as this does not contain
any variable parameter, the conics cannot be determined so that
there may be for a given value of m (nor, indeed, for any value
whatever of n) an infinity of n-gons inscribed in the one conic,
and circumscribed about the other conic.

The geometrical properties of a triangle, &c. imscribed in a
conic and circumscribed about another conic, these two conics
having double contact with each other, are at once obtained from
those of the system in which the two conics are replaced by con-
centric circles. Thus, in the case of a triangle, if ABC be the

triangle, and «Sy be the points of contact of the sides with the

B44 Mr. A. Cayley on the Porism of

imscribed conic, then the tangents to the circumscribed conic at
ABC meet the opposite sides BC, CA, AB in points lying in the
chord of contact, the lines A#, BB, Cy meet in the pole of con-
tact, and so on.

In the case of a quadrangle, if ACEG be the quadrangle, and
b, d, f, h the poimts of contact with the imscribed conic, then

the tangents to the circumscribed conic at the pair of opposite
angles A, E and the corresponding diagonal CG, and in hke
manner the tangents at the pair of opposite angles C, G and the
corresponding diagonal AE, meet in the chord of contact. Again,
the pairs of opposite sides AC, EG, and the line dh joiming the
points of contact of the other two sides with the inscribed conic, ”
and the pairs of opposite sides AG, CE, and the line df joming
the pairs of contact of the other two sides with the mscribed
conic, mect in the chord of contact. The diagonals AE, CG,
and the lines bf, dh through the points of contact of pairs of
opposite sides with the inscribed conic, meet in the pole of con-
tact, &c.

The beautiful systems of ‘ focal relations ’ for regular polygons
(in particular for the pentagon and the hexagon), given in Sir W.
R. Hamilton’s Lectures on Quaternions, Nos. 379-393, belong,
it is clear, to polygons which are inscribed in and circumscribed
about two conics having double contact with each other. In
fact, the focus of a conic is a point such that the lines joining
such point with the circular points at infinity (7. e. the points in
which a circle is intersected by the line infinity) are tangents to
the conic. In the case of two concentric circles, these are to be

the In-and-circumscribed Polygon. 345

considered as touching in the circular points at infinity; and
consequently, when the concentric circles are replaced by two
conics haying double contact, the circular points at infinity are
replaced by the points of contact of the two conics.

Thus, in the figure (which is simply Sir W. R. Hamilton’s

figure 81 put into perspective), the system of relations

F, G(-- )ABCI
G, H(..)BCDK
H, 1( .- )CDBE
I, K(--)DEAG
K, F( .- )EABH

will mean, F, G( --)ABCI, that there is a conic inscribed in the
quadrilateral ABCT such that the tangents to this conic through
the points F and G pass two and two through the points of con-
tact of the circumscribed and the inscribed conics, and simi-
larly for the other relations of the system. As the figure is
drawn, the tangents in question are of course (as the tangents
through the foci in the case of the two concentric circles) ima-

ginary.

2 Stone Buildings,
March 7, 1854.

[ 346 ]

LIT. Note on the Penetration of the Spermatozoon into the Inte-
rior of the Ovum. By Manrin Barry, M.D., F.RS.*

Ss fact that the spermatozoon penetrates into the interior

of the ovum was published by myself in the Philosophical
Transactions of the Royal Society of London for 1840. Further
observations enabled me to record the same as established, in the
Philosophical Transactions for 1843. And in the Edinburgh
New Philosophical Journal for October 1843, will be found a
drawing I gave of an ovum of the Rabbit containing spermatozoa
—nine in number, with the statement that I once counted more
_ than twenty in an ovum of this animal.

These observations were held by physiologists to have been a
mistake, an opinion which lasted up to the year 1852, when
Nelson confirmed them in ova of an Entozoon, Keber in ova of
the freshwater Mussels Unio and Anodonta, and Newport in ova
of the Frog. And the present note contains, I believe, the first
announcement in this country of their having been confirmed in
the Mammalia themselves. I have just received a letter from a
friend in Germany informing me of a paper published by Prof.
Bischoff, dated March 15, 1854+, in which it is stated that
spermatozoa have at length been seen within the zona, not only
by R. Wagner, Henle, Baum, and Meissner, but even by Bischoff
himself, who up to 1852 had considered my observations as
“born of the imagination,” but now candidly acknowledges that
he had done me injustice, the mistake having been his own.
And he remarks, that “ Barry was certainly the first to see sper-
matozoa in the interior, not only of the mammiferous ovum, but of
any ova.” Professor Bischoff might have added, that for a dozen
years Barry had a melancholy and not very enviable monopoly
of the said observations. And it may now be mentioned that in
this respect they resembled certain others, for confirmation of
which I have always felt that I could afford to “bide my time.”
Thus I have at length received notice from a physiologist on the
Continent of a work he is about to publish, containing a confir-
mation of my fact announced in Miiller’s Archiv for 1850, that
cilia are composed of spirals.

* Communicated by the Author.

+ Entitled, “ Bestatigung des von Dr. Newport bei den Batrachiern und
Dr. Barry bei den Kaninchen behaupteten Eindringens der Spermatozoiden
in das Ei.”

[ 347 ]

LIII. On the Heat produced by an Electric Discharge.
By Professor W. Tuomson.

To the Editors of the Philosophical Magazine and Journal.
2 College, Glasgow,
GENTLEMEN, April 19, 1854.
if has been pointed out by M. Clausius, in a letter addressed
to you and published in the last Number of your Magazine,
that the first discovery of the true relation between the genera-
tion of heat in the discharge of a Leyden phial and the quantity
of the previous charge is not, as I had stated it to be, due to
Joule, but that it had been given in a paper published about
three years earlier by Riess. I may be allowed to explain, that,
in making the statement in question, I considered the law of that
relation as an evident corollary from the great principle, that
the whole heat generated in any discharge of electricity is exactly
the equivalent in thermal energy for the mechanical value of the
electrical charge which is lost*. There is no doubt who is the
discoverer of ¢his, and the originator, in your most valuable
Magazine, of the theory of mechanical equivalence among the
electric, chemical, magnetic, frictional, and pneumatic develop-
ments of energy, which has within the last two or three years
attracted so many investigators.

The mere law, that the heat generated by the discharge of a
Leyden phial or battery is proportional to the square of the quan-
tity of electricity in the previous charge, is not, as I inadvertently
stated, due to Joule; neither is it, as M. Clausius seems to sup-
pose, due to Riess. Becquerel, I find, in his Traité de I’ Electricité
(vol. il. p. 150, published in 1835, or two years earlier than the
paper referred to by M. Clausius), enunciates it quite explicitly
as having been established by “Cuthbertson and others, who
had used electrometers in measuring the calorific action of the
discharge of a battery.” Mr. Joule, too, although in his first
publication he only referred to the researches of Snow Harris
which had recently appeared in the Philosophical Transactions,
remarks in a subsequent paper (On the Heat disengaged in che-
mical Combinations, Phil. Mag. June 1852), “that Brooke and

* The application of this principle to the discharge of a Leyden phial

shows that the whole heat generated must be equal to y iQ? =, if J de-
note the mechanical equivalent of the thermal unit, Q the amount of the
charge, r the thickness of the glass, I its specific inductive capacity, and S

the area of either side of the coated surface; a conclusion which wants no
other experimental verification than such as may be considered desirable

for verifying that I = is the true expression for the capacity of a Leyden
TT
phial.

348 M. P. Riess on the Generation of Heat by Electricity.

Cuthbertson found that the length of wire melted by an electrical
battery varied nearly with the square of its charge ;” and at the
same time he refers to the researches of Riess on the calorific
effects of frictional electricity, acknowledging their priority to
his own researches on the heat generated by continuous electric
currents.
I remain, Gentlemen,,.
Yours very faithfully,
Wituiam THomson.

LIV. On the Generation of Heat by Electricity. By P. Riess.
To the Editors of the Philosophical Magazine and Journal.

GENTLEMEN,

R. WILLIAM THOMSON has stated, in the Philoso-
phical Magazine for March 1854, p. 193, that the quan-
tity of heat generated by the discharge of a Leyden jar is pro-
portional to the square of the quantity of electricity, which was
first proved in 1840 by Mr. Joule, in opposition to the results
derived previously from the experiments of Sir W. Snow Harris.
This statement is in all respects incorrect. Mr. Joule never
proved the law above stated ; but in a remark attached to his
investigation on the heat of the voltaic current he gave utterance
to the presumption, that under the necessary limitations the heat
generated is proportional to the square of the charge of a given
battery. (Phil. Mag. Oct. 1841, p. 265.) When this vague con-
jecture was first hazarded, a memoir of mine had been published
for four years in which the conclusions of Harris were refuted
and the law of the square of the current was proved (Pogg. Ann.
March 1837, p. 341); and in two extensive inquiries I had
already given the complete formula for the heat generated by the
battery discharge, after having discovered the remarkable rela-
tion subsisting between the quantity of heat generated in a wire
and the resistance of the said wire.

Such reclamations, which cannot be more painful to those
who cause them than to those who find themselves compelled to
make them, might be avoided if the reasonable demand were
everywhere recognized, that an assertion of such a general cha-
racter as that ventured by Mr. Thomson ought to be the conse-
quence of a careful examimation, not only of what has been done
at home, but also of what has been published in other countries

on the subject in question.
P. Rress.
Berlin, April 13, 1854.

[ 349 ]

LV. On a Method for preserving the Sensitiveness of Collodion
Plates for a considerable time. By Joun Spitter and Wi1-
LIAM CROOKES*.

HE extreme sensitiveness of collodion as compared with paper
and other photographic surfaces renders this material in-
valuable in all cases where rapidity of action is desirable, but up
to the present time its use has been greatly restricted by the
necessity for preparing the plate and completing the whole of
the manipulatory details within a comparatively short space of
time, thus rendering this beautiful process practically imap-
plicable in all cases where the conveniences of a photographic
laboratory are not at hand.

For some time past we have been investigating the causes
which operate to prevent the excited plate retaining its efficiency
for more than a few hours. It seemed highly probable that the
permanent sensitiveness of the film was principally dependent
on the retention of a moist surface; and if by any artificial
means this end could be secured, the original sensitiveness of the
film would be, for at least a reasonable time, preserved unim-
paired.

The only attempts up to the present time to effect this object
are, we believe, that of M. Girod+, who proposes to enclose the
‘sensitive collodion film between two plates of glass, with only so
much of the exciting silver solution as might be retained by
capillary attraction; and thus by retarding the evaporation of
the water, to keep the surface moist, and consequently sensitive,
for a longer period; and secondly, that of M. Gaudint{, who
suggests the use of perfectly air-tight dark frames or boxes, in
which a number of the wet plates could be arranged in a hori-
zontal position and there kept until required. Besides these
two methods, it is well known that the plate will remain excited
for a considerable time if kept immersed in a solution of nitrate
of silver; in fact, a glass bath in the camera has been often used
in cases where the length of exposure was likely to be too pro-
longed to admit of the plate being placed in the ordinary slide.

Instead, however, of having recourse to a mechanical means
for preventing the evaporation from the surface, we have endea-
youred to avail ourselves of a chemical process, by the employ-
ment in the bath of substances having a powerful affinity for
water ; in the choice of these, however, we are necessarily limited
to such as are neutral in constitution, and do not form insoluble
compounds with silver. The nitrates and acetates, especially

’ * Communicated by the Authors.
+ Jown. Phot. Soc. No. 9. + Ibid. No. 10.

350 Messrs. J. Spiller and W. Crookes on a Method for

the former, seemed most convenient for our purpose on account
of their general deliquescent nature, and for our first experiments
we selected the nitrates of lime, magnesia, and zinc, as most pro-
mising of success. ‘These agents were at first tried in the above-
mentioned order; but from a few preliminary trials we were
inclined to give the preference to the zine salt, and having ob-
tained such satisfactory results with its use, are induced to com-
municate them at once rather than withhold them until our inves-
tigation of the other compounds shall have been completed. At
first we endeavoured to add the nitrate of zine direct to the
exciting bath, but the quantity required to prevent so large an
amount of nitrate of silver from crystallizing out on the plate
rendered the solution too dense to work with.

The following process can be recommended as having proved
perfectly successful in our hands; we do not doubt that with
more general use it may be considerably modified and improved,
but at present we have rather contented ourselves with establish-
ing the broad principle with such detail only as will suffice to
ensure good results, and to leave to a future period the consi-
deration of those minor points which only a long experience can
develope.

The plate, coated with collodion (that which we employ con-
tains iodide, bromide, and chloride of ammonium, in about equal
proportions), is made sensitive by immersion in the ordinary
solution of nitrate of silver (30 grains to the ounce), and after
remaining there for the usual time, is transferred to a second so-
lution of the following composition :—

Nitrate of zie (fused) . . . 2 ounces.
Nitrate’of silver "2072/9... >. BS! araime,
ON A ce eek sft bus oat neon, OOo

The plate must be left in this bath until the zine solution has
thoroughly penetrated the film (we have found five minutes
amply sufficient for this purpose, although a much longer time
is of no consequence) ; it should then be taken out, allowed to
drain upright on blotting-paper until all the surface moisture
has been absorbed (about half an hour), and then put by until
required. The nitrate of zinc, which is still retained on the plate,
is sufficient to keep it moist for any length of time, and we see
no theoretical or practical reason why its sensitiveness should not
be retained as long: experiments on this point are im progress ;
at present, however, we have only subjected them to the trial of
about a week, although at the end of that period they were hardly
deteriorated in any appreciable degree. It is not necessary that
the exposure in the camera should be immediately followed by
the development, as this latter process can be deferred to any

preserving the Sensitiveness of Collodion Plates. 351

convenient opportunity provided it be within the week. Pre-
vious to development, the plate should be allowed to remain for
a few seconds in the original 30-grain silver-bath, then removed
and developed with either pyrogallic acid or a protosalt of iron,
and afterwards fixed, &c. in the usual manner.

The advantages of this process can scarcely be overrated.
Besides the facility it affords of working in the open air without
any cumbrous apparatus, photography may now be applied in
cases where it would have been hitherto impracticable, owing to
the feebleness of the light, e. g. badly illuminated interiors,
natural caverns, &c.; if necessary, the exposure could be pro-
tracted for a week, or possibly much longer, and the deficiency
of daylight compensated for by the employment of the electric or
other artificial light. It will also be found useful where the plate
must be kept ready excited, but the exact moment of exposure
may. depend upon possible contingencies rather than on the will
of the operator, or in cases where it would be impracticable to
prepare the plate just before exposure ; for these reasons it might
prove a valuable adjunct on the eve of a naval or military engage-
ment, for accurately recording the positions of the forces.

A small proportion of nitrate of zinc added to the ordinary
nitrate of silver bath in no way interferes with its action, and
might obviate the inconvenience sometimes felt durmg hot
weather in photographic rooms, of the film becoming partially
dry before exposure. If added im a still smaller proportion to
the silver solution used for exciting the ordmary Talbotype
paper* (without the employment of gallic acid), it is very pro-
bable that its sensitiveness may be preserved during a much
longer period than is generally possible. As far as our experi-
ments have gone, they tend to confirm this supposition ; but at
present we can hardly speak more confidently on this point, as
it is still under investigation.

There are, no doubt, many other substances which might
equally well answer the purpose of nitrate of zinc; besides those
already mentioned, the nitrates of cadmium, manganese, and
perhaps also those of copper, nickel, and cobalt might be found
serviceable. Glycerine at first seemed to promise very good
results, but the principal difficulty was the necessary impurity of
the commercial product, in consequence of its being obtained
from the exhausted leys of the soap boilers.

* This addition of nitrate of zinc to the silver solution in the Talbotype
a was suggested, we have been informed, some time back by the

rench, but not with reference to its keeping properties—only as an acce-
lerator.

P3527

LVI. Additional Directions and Improvements in the Process. for
the Manufacture of Artificial. Tourmalines, By Witi1aM
Birp Heraparu, Hsqg., M.D. Lond.*

Ha the last November Number of this Journal the author gave
a formula for the production of these crystals of large size,
so as to be available for optical purposes. .

That formula sueceeds very well when the temperature of the
atmosphere in the apartment is 65°, and likely to be maintained
at this point for three or four hours, falling gradually to 45°
Fahr. in the course of the night. Under these circumstances
it is rarely the case that some large plates are not discovered in
the morning. These should be at once secured or they will
re-dissolve or sink, and thus be lost.

When the temperature does not fall below 50° or 55° Fahr.
a different formula is necessary. Less spirit must then be
employed, in order to render the compound less soluble in the
menstruum.

Formula No. 2 may now be used most successfully.

(2) Take of disulphate of quinine 100 grains,

.. acetic acid (1042) 4 fluid ounces,
.. rectified spirit (0°837) 1 fluid ounce,
.-. spirituous solution of iodine | fluid drachm.

The crystals are produced more quickly by this formula than
by the previous one; and in three or four hours must be re-
moved, or the mother-liquid will quickly redissolve them.
Many of the larger crystals become too heavy to float any longer,
and fall to the bottom of the flask, from whence they are: not
easily removed ; still by the exercise of patience and some in-,
genuity they may be recovered, and fully repay for the trouble
of cutting off the top of the flask, &c., by producing: a, field:
wholly devoid of violet light upon crossing two plates, especially
when examined by daylight. )

Formula No. 3.—I have recently succeeded in making, these,
crystals of large size, by replacing the spirit of wine in, No, 2
formula, by an equal quantity of hyponitric «ther (sweet nitre).
There is some advantage in using this solvent, as the crystals
remain even for a week floating on the surface, without showing
the least appearance of disintegration.

It is frequently the case in this experiment, that the) free
iodine disappears very readily; the solution becoming ,nearly
colourless—under these circumstances, the compound does not
form. If the temperature employed be too elevated, this is
almost certain to occur; of course it is only necessary to add a

* Communicated by the Author.

On the Manufacture of Artificial Tourmalines. 353

second quantity of iodine solution, so that the liquid may retain
its dark sherry colour during the cooling.

After making the addition of the tincture of iodine in either
of the previous formule, it is necessary to continue the heat of
the spirit lamp for a short time, to dissolve all the cinnamon-
brown iodide of quinine first deposited, so that the solution shall
become perfectly clear dark-sherry wine colour, and then to
filter the solution rapidly through white porous paper into a
perfectly clean wide-mouthed Florence flask, matrass, or beaker,
and to attend to the following conditions :—

1st. It is well to have at least six flasks half-filled with solu-
tions made by the above formule, so as to ensure the production
of foliaceous plates in some one or more of them; according to
the state of the atmospheric temperature, as previously explained.

2ndly. It is more convenient to set these at work as nearly
simultaneously as possible, and to watch them well during the
next three or four hours, especially if formula No. 2 be employed,
so that the produce may be caught at the most favourable
moment. If any foreign bodies, as hair, dust, or filaments of
paper, are floating in the solutions, the broad plates do not form,
as those particles act as nidi for the crystals, and fatally hasten
the process of deposition, so that the produce is small and con-
fused.

3rdly. It rarely or never happens that we obtain these large
plates at the first attempt; it 1s often necessary to redissolve
and crystallize two, three or four times before we find any large
enough for optical purposes; the reason is that the process of
erystallization is at first much too confused and rapid to allow of
the requisite arrangement of the particles or prisms, so as to
constitute the broad compound optical leaflets.

4thly. It is always desirable not to raise the temperature to
the boiling-point when redissolving, as spirit and iodine are both
then lost, and the formative power of the mother-liquid becomes
impaired and at length completely lost, in consequence of the
relative proportions of acid and spirit being so altered by con-
tinued distillation of the latter.

5thly. It is always better to add four or five drops of the
tincture of iodine after redissolving, in order to produce an
atmosphere of iodine vapour above the liquid ; this in condensing
_ Starts an early surface crystallization, whiist the mother-liquid
is sufficiently charged with the compound.

6thly. These compound foliaceous plates having “ crenated
edges” consist of prisms arranged side by side in various forms,
but frequently producing discs of considerable size, the com-
ponent atoms of which are all arranged in the same optical
direction ; but at other times crystallization appears to start from

Phil. Mag. 8. 4. Vol. 7. No. 46, May 1854. 2B

354 Dr, Herapath on the Process for

a central point, and then the foliaceous lamine (still consisting
of adherent component prisms or sections of rhombic plates)
vadiate like the petals of a flower; under these circumstances
the corolla-shaped disc would be useless; but either petal, if
large enough, would be serviceable, as in the latter all the atoms
would be in the same relative plane with regard to polarized
light ; consequently it is necessary to select for mounting the
most uniform plates, and not always the largest clusters, for
these would have a “ macled” appearance, and produce a beam
of light polarized in more than one plane, and therefore creating
confused results in the polariscope,

Having obtained these crystals by one of the above formule,
and caught one upon the glass circle as before described, it is
better to submit it to a process of washing (before drying) so as
to remove the mother-liquid and get rid of the interference of
crystals of sulphate of quinine deposited either beneath or upon
the plate ; in my last paper, “cold distilled water imbued with
iodine ” was recommended for this purpose.

However, as the effect I then ascribed to iodine is by no
means certain, and as it sometimes also injures the plate by de-
positing the brown iodide of quinine upon its surface, it is far
better to employ a saucer or evaporating basin full of a saturated
solution of Herapathite in a mixture of distilled water, and one-
eighth of its bulk of acetic acid for this purpose. The acetic
acid greatly hinders the tangential flying off of the crystalline
plates from the glass dises upon our slowly and very cautiously
immersing them in a horizontal position beneath the surface of the
water; and if this should occur, the plate is frequently broken ;
should it float off, it must be recaught upon the glass disc as
before, and then be cautiously dried by absorbing all moisture
by bibulous paper as before, and drying it as rapidly as may be
consistent with safety by exposure to air at 50° or 60°.

If it be considered desirable, it may be exposed for a short
time to the vapour of iodine; this is best accomplished by means
of solid iodine—the tincture was once recommended, but the
alcoholic vapour renders it brittle, a defect which is not found
with the solid substance.

I have been recently oceupied, in conjunction with my friend
Mr. Thwaites, in making some experiments upon different media
for mounting these crystals. ‘Those principally employed have
been iodized almond oil and pure elaine, also slightly charged
with iodine, as well as glycerine similarly iodized. The mode of
using these is to prepare a saturated solution of iodine in either
medium, then dilute it with four times the quantity of pure
medium for use. Having placed the cireular disc on the table,
with a yery minute drop of either substance on its centre, mvert

.

the Manufacture of Artificial Tourmalines. 355

the plate carrying the crystal (this being downwards) upon the
oil, elaine, &c., press together slightly, and then if too much
medium has not been used, the plates are just kept apart by the
interposed fluid. The edges are then surrounded or painted
with a solution of gum-arabic, slightly toughened by the addition
of a little isinglass or gelatine. This is a very rapid mode of
mounting, but not certain or safe; sometimes the edging of gum
cracks, air is admitted, the definition of the plate is lost, and its
brillianey for the polariscope much damaged. Oil and elaine
appear to dissolve and disintegrate the crystals.

I therefore infinitely prefer the etherial and iodized Canada
balsam.

Crystals thus mounted keep without change or disintegration ;
some of the author’s plates have been so prepared for months
and are still perfect, whilst others mounted very recently in
iodized oil, or elaine, or glycerine, have shown symptoms of de-
struction in as many weeks or days even, I have some which
are quite as good as ever after three years’ wear, these were
mounted in fluid Canada balsam. When disintegration occurs,
it appears to be greatly influenced by imperfection in the wash-
ing process, for those plates which have been mounted with ery-
stals of sulphate of quinine beneath them certainly break up and
dissect themselves with great rapidity ; it appears to be produced
by some unknown molecular action going on, and a rearrange-
ment of the atomic constituents. The plates appear to become
henpecked by minute parallelogrammatic holes; these begin at
the edges and go onwards through the disc, rendering the plate
useless.

The etherialized Canada balsam has no action on the plates ;
however, it is perfect as a mounting fluid; it dries very readily
too, a few days’ exposure to air of 60° or 70° being alone suffi-
cient for this purpose.

As turpentine has no solvent power over Herapathite, even at a
boiling temperature, fluid Canada balssm may be employed ;
I therefore was in error in ascribing the disintegration to that
medium, I have since found that the crystals must be washed to
render them secure for mounting in it; the only objection to
this medium is, that it dries so slowly.

The object of using the iodized compound is to give a black
tone to the field; this it certamly accomplishes ; the periodized
erystals, when examined by daylight, are black as midnight,
even if the plates are no thicker than gold-leaf, but an intense
lamp or gaslight appears to pass through them with a violet
hue, perhaps more inclining to brown-red ; this is an unpolarized
ray, and it cannot be obstructed by tourmaline or Nichol’s prism ;
it requires four thicknesses of Herapathite (all parallel) to stop

2

356 Dr. Herapath on the Process for

this last portion of the beam; it is doubtful whether the effect
of periodizing the plate is lasting—I think not.

When it is absolutely necessary to obtain a perfectly black
field with a total stoppage of all the incident rays (upon “‘cross-
ing” the two crystals), it is much the better plan to employ a
thicker plate of this substance: such a erystal will be generally
found in the flask at the bottom of the mother-fluid. There is
more trouble requisite in obtaining perfect plates, free from all
intervening crystals, but the experimenter is generally repaid in
the end by the perfection of the polarizing medium.

When the selenite stage is employed, the thinner and violet-
coloured crystals are far preferable to those which give a black
tone to the field; as the colours are more brilliant, and the flood
of transmitted light much greater, so that we are enabled to use
a less illuminating power. I am not in the habit of using an
achromatic condenser with my polarizing apparatus, which pro-
bably accounts for some discrepancies in the results of observa-
tions made by different experimenters upon the same crystalline
plates: those crystals which will transmit the violet rays, when
strongly illuminated by gas or lamp light, will not do so when
the instrument is used in daylight, or with a plane instead of a
concave mirror, and without the achromatic condenser.

If it be necessary to obtain a most decidedly black field, the
violet rays may be readily absorbed by interposing a thin plate
of sulphate of copper beneath the polarizing plate of Herapathite
and the source of illuminating power.

I have recently employed a plate of this substance, one-twen-
tieth of an inch thick, cut on a hone, polished and mounted
between two plates of thin glass in Canada balsam, as a means
of correcting the defects of the thinner plates of these new tour-
malines*—this substance possessing the power of absorbing the
violet rays of the spectrum in a pre-eminent degree. In order
to succeed in this experiment, it is necessary that the sulphate
of copper should be inclined at a certain angle to the plane of
primitive polarization, as it is a substance possessing two neutral
axes, or planes of no-depolarizing power, the position of which
may be easily found, and their direction marked upon the sup-
port, so that the intervening plate may be always inserted at the
angle of its greatest activity. Professor Stokes has lately, in a
letter to me, suggested the employment of a glass laden with
the oxide of copper as a means of attainmg the same end.
Having, therefore, prepared a boracic glass, coloured by the
black oxide of copper, I have used it effectually as an absorbent
medium for counteracting the violet-red colour of the polarized

* A solution of the sulphate or nitrate of copper in water will equally
succeed in producing a black field.

the Manufacture of Artificial Tourmalines. 357

beam. But although it offers great and manifest advantages
when the new tourmalines are crossed at right angles, yet, upon
revolving the superior crystal, and therefore bringing the two
plates into a parallel position, we have a blue colour in the field,
which must assuredly alter the colours of depolarizing media : it
is, however, a very agreeable light to work by, as the intense
yellow of gaslight is much mellowed down and counteracted by
it. This corrective medium would be inadmissible when the
selenite stage is employed, as the tints would be materially
changed by its absorptive agency.

The mode of making this glass is simply to dry powdered
biborate of soda in a crucible by the heat of an ordinary fire ;
again reduce the effloresced mass to powder, and mix it with a
small quantity of the oxide of copper, such as is generally used
m organic analysis; then introduce the mixture into a platinum
crucible, and with a steady, long-continued heat, thoroughl
vitrify it, pour it out upon a flat slate, clear metallic or Wedge-
wood-ware surface, and press it while still soft into a flattened
plate. Upon cooling, a portion must be quickly ground down
upon a hone, polished, and then mounted in Canada balsam
between glass; the unmounted boracic glass may be kept for
any length of time in turpentine without change, but in the air
it effloresces, and becomes opake and useless.

I have been asked for a process by which the quinine may be
recovered from the mother-solutions and from Herapathite itself.
The following will be found very successful.

It is merely necessary to boil the mother-liquids with the
Herapathite crystals, add a little solution of some soluble sul-
phuret, say potassium or ammonium, to convert the iodine into
hydriodic acid, evaporate to dryness so as to expel the spirit,
acetic acid, by a water-bath; redissolve the remaming salt in
just sufficient boiling distilled water, filter, and set aside to cry-
stallize ; filter when cold, and dry the crystals by expression, and
by a gentle heat.

The mother-liquid contains acetate and some sulphate of
quinine; add to it, when cold, an alkali in solution, potassa,
soda, or ammonia, or the carbonates of these; collect the sepa-
rated alkaloid on a filter, and dissolve it in boiling water acidu-
lated with sulphuric acid; if this be not in excess, the disulphate
of quinine crystallizes on cooling, and the loss is very slight*.

32 Old Market Street, Bristol.

* This disulphate may be again employed for the manufacture of the
i gy ; so may the neutral sulphate of quinine obtained by the first part
of the process.

[ 358 J

LVII. Notice on Barometrical, Thermometrical, and Hygrometrical
Clocks. By Si Davin Brewster, K.H., D.C.L., F.R.S.,
V.P.R.S. Edin., and Associate of the Institute of France*.

ie the Number of this Journal for December 1853, Mr-

Macquorn Rankine has described a Barometric Pendulum,
and has referred to the history of this class of instruments.

About the year 1810 or 1811, I proposed, in the articles ‘Atmo-
spherical Clock and Barometer,’ published in the Edinburgh
Encyclopedia+, the construction of barometrical, thermometrical,
and hygrometrical pendulums for registering the indications of
such instruments. As I was prevented by more interesting
pursuits from constructing any of these clocks, I should not
have thought of claiming any priority in proposing them ; but
I owe it to Mr. Babbage to state, that about 1820, without know-
ing of my suggestions, he actually constructed a barometrical
clock and sent to me a paper on the subject, which he declined
to have published, in consequence, I believe, of my having anti-
cipated him in the idea. If I recollect rightly, Mr. Babbage
not only made observations with his barometrical clock, but it
was proposed by some of the influential members of the Royal
Society to erect one of them in their apartments.

LVIIL. Poceedings of Learned Societies.

ROYAL SOCIETY.
[Continued from p. 291.]
Feb. 23, 1854.—The Rev. Baden Powell, V.P., in the Chair.

teen following communications were read :—

1. A paper entitled, ‘‘ Continuation of the subject of a paper
read Dec. 22, 1853, the supplement to which was read Jan. 12, 1854,
by Sir Frederick Pollock, &c.; with a proof of Fermat’s first and
second Theorems of the Polygonal Numbers, viz. that every odd
number is composed of four square numbers or less, and of three trian-
gular numbers or less.’”’ By Sir Frederick Pollock, M.A., F.R.S. &c.

The object of this paper is in the first instance to prove the
truth of a theorem stated in the supplement to a former paper, viz.
“‘ that every odd number can be divided into four squares (zero being
considered an even square) the algebraic sum of whose roots (in
some form or other) will equal 1, 3, 5, 7, &c. up to the greatest
possible sum of the roots.”” The paper also contains a proof, that if
every odd number 2n+1 can be divided into four square numbers,
the algebraic sum of whose roots is equal to 1, then any number 2
is composed of not exceeding three triangular numbers,

* Communicated by the Author.
+ Vol. iii. pp. 57 and 294.

Royal Society. 359

The general statement of the method of proof may be made thus:
two theorems are introduced which connect every odd number with
the gradation series, 1, 3, 7, 13, &c., of which the general term is
n+n*+1 or 4p*+ 2p+1 (that is, the double of a triangular number
+1), each term of which series can be resolved into four squares, the
algebraic sum of the roots of which, p, p,p, p+1, or p—l, p,p, p
may manifestly be =1. By these theorems it is shown that every
odd number is divisible into four squares, having roots capable of
forming as the sum of the roots 1, 3, 5, 7, &c. up to the greatest
possible sum of the roots.

As the four square numbers which compose an odd number must
obviously be three of them even and one odd, or three odd and one
even, the differences of the roots among themselves must be the first
odd and the third even, or vice versd; and therefore these roots must
have the sum of the first and third differences an odd number; the
middle difference may be either odd or even.

The first of the theorems referred to, called by the author ‘‘ Theo-
rem P,” is insubstance this :—

Let r, s, t, v be the roots the squares of which compose any odd
number N, such that r-+s+¢+v=1, and let each of these roots be
increased by m; then r+m, s+m, t-+m, v+m will be the roots of
the odd number N+2m(2m+1); and m—r, m—s, m—t, m—v the
roots of the odd number N+2m(2m—1); the sum of the roots in
the first case being 4m+1, and-in the second 4m—1. So that
giving to m successively the values 0, 1, 2, 3, &c. in the general form
N+2m(2m+1), a series will be formed in which the sums of the
roots will be 1, 3, 5, 7, 9, &c., and the sums of their squares N,
N+2.1.1, N4+2.1.3, N4+2.2.3, N4+2.2.5,N42.3.5,
N+2.3.7,N+2.4.7, &c.; or N, N4+1.2, N+2.3, N+8.4,
N+4.5, N+5.6, N+6.7, N+7.8, &c. So that if p be the
distance of any odd number in this series from N, the number will be
N+p(p+1), and the sum of its roots will be 2p+1.

The conclusions to be drawn from this theorem are then stated :—

1. The greatest sum of the roots of the squares into which any
odd number can be divided may be obtained: for let 2n+1 be any
odd number, and 2p+ 1 the odd number to which the algebraic sum
of its roots is required to be equal; then if p is such that p(p+1)
is less than 2n+1, the number 2n+1 can be resolved into squares
the sum of whose roots is 29+1; otherwise it cannot.

2. The form of the roots of 2n+1 may be found of which the
algebraic sum is any possible odd number 2+ 1 except 1, provided
all the odd numbers less than 2n+1 possess the property of having
the algebraic sum of their roots =1. For if from 2n+1, p(p+1)
be taken, there will remain an odd number (N in Theorem P) such
that, according to the condition stated, the algebraic sum of its
roots =1; and in the series of roots and odd numbers formed from
these roots according to theorem P, p terms from N will be found
the number 22+ 1 composed of squares the algebraic sum of whose
roots is 2p+1.

It thus appears that any odd number 2n+1 can be divided into

360 Royal Society.

squares thesum of whose roots will equal 8, 5, 7, &c. (any possible
odd number except 1) if the odd numbers below it can be divided
into squares the sum of whose roots =1; and if it can be shown
that its roots in some form will equal 1, then the theorem M will be
true for that number and for every number below it.

This is illustrated by an example, and then another theorem,
called “Theorem Q,” is stated. In this a series of roots and odd
numbers is formed by making the Ist and 3rd differences of the
reots constant, but reversed every alternate term, and increasing or
diminishing the middle difference by 1 each term ;—or the middle
difference is made constant and the lst and 3rd vary. The sums of
the roots thus become constant in every term of the series, but the
sums of the squares of the roots increase, as in theorem P, by the
even numbers 2, 4, 6, 8, &c., so that the increase at any number of
terms p is p(p+1), or the double of a triangular number.

By the application of these theorems to a variety of examples, it
is shown how any odd number may be composed of four squares,
such that the algebraic sum of their roots may equal 1.

The theorems P and Q, it is considered, connect every odd num-
ber with every other odd number, so as to make it impossible if one
odd number be composed of four squares, but that every other odd
number should likewise be so. It is pointed out in what manner
every possible combination of numbers which can furnish the differ-
ences of the roots of any squares, not exceeding four, which can
make an odd number, and the sum of which roots = 1, can be derived
from the gradation series, that is from 4p*+2p+1. The combined
effect of the theorems P and Q is therefore to prove that every odd
number must be composed of not exceeding four square numbers.

The author goes on to show that every number is composed of
not exceeding three triangular numbers, by proving that if every
odd number 2x+1 can be divided into four square numbers the sum
of whose roots = 1, then z will be composed of not exceeding three
triangular numbers. This is done by taking the differences of the
roots of 2n+), the algebraic sum of which roots is one, and dimi-
nishing the middle difference by theorem Q until it reaches a number
nearest to half the sum of the first and third differences. The
difference between 22+ 1 and the number thus obtained will be the
double of a triangular number =2T. By the next step, the extreme
differences are reduced until they are of the form m, m+1; and the
difference between 2n-+1—2T and the number thus obtained will
again be the double of a triangular number =2T'. The differences
last obtained give the double of a triangular number +1=2T"+1.
So that we find 22+1=2T+2T’+2T"+1. Consequently n= the
sum of three triangular numbers, if all the three operations be
necessary; if not, to two or one triangular number only.

2. The first part of a paper ‘“‘Ona class of Differential Equa-
tions, including those which occur in Dynamical Problems.” By
W. F. Donkin, M.A., F.R.S., F.R.A.S., Savilian Professor of Astro-
nomy in the University of Oxford.

This paper is intended to contain a discussion of some properties

Royal Society. 361

of aclass of simultaneous differential equations of the first order,
including as a particular case the form (which again includes the
dynamical equations),
pL sips ide
a; ay Tom ae? (I.)
where 2, ...2,, ¥, ... Y, ave two sets of nm variables each, and accents
denote total differentiation with respect to the independent variable ¢ ;
Z being any function of 2, &e., y, &c., which may also contain ¢ ex-
plicitly. ‘The part now laid before the Society is limited to the
consideration of the above form.
After deducing from known properties of functional determinants
a general theorem to be used afterwards, the author establishes the
following propositions.
If z, ...z, be m variables connected with z other variables y, ...y,

by 2 equations of the form y,= = (X being a given function of

2,...%,); then the equations obtained by solving these algebrai-
cally, so as to express v, ... 2, in terms of y, ... y,, will also be of the

form 7j;= os where Y is a function of y,...y,,; which may be de-

fined by the equation
Y=—(X)+(@)y,+ ... + (@,)Y ns

in which the brackets indicate that the terms within them are to be
expressed as functions of y,...y,- Moreover, if p be any other
quantity contained explicitly in X (besides the variables yh caeg)}
the following relation will subsist; namely,

aXaor you.

dp * dp
the differentiation in each case being performed only so far as p
appears explicitly in the function.

It is then shown that if X contain explicitly, besides 2, ... x, the

n constants dj, d,,...a@,, and the variable ¢, and if the 2n variables
Ly wee Vas Y «+ Y» De determined as functions of t¢ by the system of
2n equations,

>

ga ote mab} Pi tooviiod copoly
where 6, ... 5, are n other ccnstants, the elimination of the 2n con-
stants from these equations and their differentials with respect to ¢,
leads to the system of differential equations (I.), if for Z be put the

result of substituting in Ta the values of the 2n constants in

terms of the variables. ‘The equations expressing the 2z constants
in terms of the variables may be considered as the 2n integrals of
the system (I.).

The author employs the symbol [p, g] in a sense similar to that
in which Poisson and others have employed (p, q), namely, as an

abbreviation for 3, i Bs — a zz): and he shows that if p, g

362 Royal Society.

represent any two of the 2” constants a, &c., 6, &c., then [p, 9] is
either =1 or =0, according as p, g are a conjugate pair a;, 6;, or not.
Next it is shown that if a,, @,...a, represent any functions of 2nn

— n(n— 1)

variables a, ... 2»; Y, «+ Yq» Satisfying identically the con-

ditions [a;, a,)=0, then if by means of the x given sence ex-
pressing a,, &c. in terms of the variables, the set hy; Petey Al

4 unr— .
expressed as functions of @ ... ®, @ ...@,, the places 2 relations

7 = we will be identically satisfied ; in other std the expres-
sion for Y, ++. Y, Will be the partial differential coefficients of a func-
tion, Of aiesi@,.

Hence it easily follows, that if any z integrals a, ... a, of the
system (I.) be given, which satisfy the conditions [a,, a;|=0, a
* Principal Function ” X can always be found, from which the re-
maining integrals of the system may be deduced by means of the
second set of equations (II.).

The relation in which these investigations stand to the discovery
of Sir W. R. Hamilton (as improved and coinpleted by Jacobi) is
pointed out. And it isshown that the system of differential equa-
tions of the second order
c= ; ae WwW.

(to which Lagrange had moiinod the ee equations, and which
Sir W. Hamilton had transformed into the system (I.) by a process
depending upon the circumstance that, in dynamical problems, W
contains 2’,, 2',, ... 2’, only in the form of a homogeneous function)
may, by means of the theorems established at the beginning of the
paper, be reduced to the form (I.) without assuming anything as to
the form of W, which may be any function whatever of 2, ... x,
a, ... z',, and ¢.

The 2n integrals of the system (I.), obtained in the way above
explained, being shown to satisfy the conditions

[a b,)=1, [a;, a;|)= [a;, b\= [b;, 6 ;) =0,
it is proposed to call them ‘‘ normal integrals,’’ and the constants
a, &c., 6, &c. “normal elements,” any pair a;, 6; being called con-
Jjugate.

In the second section, the author gives a simplified demonstration
of Poisson’s theorem (extended to the general system (I.)), that if
Ff, g be any two integrals, [f, g] is constant. ‘The preceding prin-
ciples are then exemplified by application to the problems of the
motion of a material point under the action of a central force, and
the rotation of a solid body abouta fixed point.

In each case three integrals, ¢,, c,, c,, are taken, satisfying the
three conditions [es ¢,|=0, (es, ¢,]=0, (¢,, ¢,)=0; the first teine
the integral of vis viva, and the other two being derived from the
integrals expressing the conservation of areas. In the former pro-
blem the “ principal function” is then found with great ease, and the

Royal Society. 363

remaining integrals deduced. The set of ‘“ normal elements ” thus
obtained coincide with those given by Jacobi (in a memoir in Crelle’s
Journal, vol.xvii.). In the problem of rotation, the algebraical solution
of the three assumed integrals for y,, y, y; depends upon that of an
equation of the fourth degree. It is therefore impracticable to
exhibit the principal function in an explicit form. In this respect
the result arrived at resembles that obtained by Mr. Cayley in a
totally different way ; Mr. Cayley having shown that the solution of
the problem is reducible to quadratures, assuming the algebraical
solution of a certain system of equations of the same form as those
to which the author of the present investigation is conducted. (Camb.
and Dub. Math. Journ. vol. i. p. 172.)

Methods are then indicated by which, when one system of ‘‘normal
elements” is given, other systems may be found.

‘The practical value of “normal solutions”’ of the system (I.) de-
pends chiefly upon the simplicity of the corresponding formule for
the variation of elements, the theory of which is intended to form
part of the subject of the following sections.

March 2.—Professor Graham, V.P., in the Chair.

The following Papers were read :—

1. “On the Growth of Land Shells.” By E. J. Lowe, Esgq.,
F.G.S., F.R.A.S. &c.

Perhaps the following observations on the growth of land shells
may contain sufficient information to prove interesting to the Royal
Society. Before describing them, however, a few introductory re-
marks will be necessary. Every individual experimented upon has
been kept in confinement since the day it was hatched. Each
species has been placed in a separate box (filled with soil to the
depth of three inches), and care has been taken to feed the Mollusca
every other day, the food chiefly consisting of the leaves of the
lettuce and cabbage. In very dry weather the soil has been moistened
with rain-water about once a week; in the box containing Helix
pomatia small lumps of chalk have been mixed with the soil.

The species experimented upon were :-—

Helix aspersa Zonites cellarius

— caperata | — lucidus

— hispida | — nitidulus
— nemoralis — radiatulus
— pu.natia | Bulimus obscurus
— rotundata Clausilia nigricans
— virgata | Pupa umbilicata

The facts arrived at are,—

lst. The shells of Helicide increase but little for a considerable
period, never arriving at maturity before the animal has once become
dormant.

2nd, Shells do not grow whilst the animal itself remains dor-
mant.

3rd. The growth of shells is very rapid when it does take place.

364 Royal Society.

4th. Most species bury themselves in the ground to increase the
dimensions of their shells.

First Experiment with Helix pomatia.

A specimen of this species having deposited thirteen eggs which
were hatched during the first week of August 1852, six of the
young ones were deposited in a box (having a lace cover) placed
in the shade. The young Helices were regularly fed every other
day until the beginning of December, when they buried themselves
in the soil for winter; up to this period they had gradually increased
in dimensions to the size of Helix hispida. From December until
April the soil was kept dry, the box being placed in the cellar. On
the Ist of April they were replaced in the garden, the soil having
previously been copiously watered. On the 3rd of April the young
ones appeared on the surface, being zo larger in size than they were
in December, and although regularly fed up to the 20th of June
they scarcely increased, not being perceptibly larger in size than
they were in December. However, on the 20th of June five of
them disappeared, having buried themselves (with the mouth of the
shell downwards) in the soil; on the 30th of June they reappeared,
having in ten days grown so rapidly as at this time to become equal
in size to Helix pisana. They again buried themselves on the 15th
of July and reappeared on the Ist of August, having again in-
creased in size. From this date they did not apparently become any
larger, and on the 2nd of November food was withheld for the
winter, and at the present time (February 14th) they are in a dor-
mant state. Probably they will arrive at maturity by July or August
next. The sixth specimen did not bury itself until the 15th of
August.

Second Experiment with Helix aspersa.

A pair of Helix aspersa having been procured in the act of copu-
lation on the 19th of May 1852, they were placed in confinement,
Each individual deposited about 70 eggs, which began to hatch on
the 20th of June: these young ones grew but little during the
summer. They buried themselves in the soil on the 10th of October,
coming again to the surface on the 5th of April, not having grown
during the winter. In May they buried themselves (with their heads
downwards as with Helix pomatia, in winter they and other species
buried themselves with the head upwards), appearing again in a
week double the size ; this process was carried on at about fortnightly
intervals until July the 18th, when they were almost fully grown.
It is worthy of remark that this species, as well as Helix pomatia
and Helix nemoralis, and probably other of the Helicz, form an oper-
culum at the aperture, after which they retire considerably within
the shell, and form a second (much thinner), behind which they
rest during the winter.

It would be swelling this paper too much to describe all the obser-
vations in full; it will perhaps therefore be considered sufficient to
remark that the process of growth within the ground takes place

Royal Society. 365

with Helix nemoralis, Helix virgata, Helix caperata, and Helix hispida.
Helix rotundata burrows into decayed wood to increase the size
of its shell. Zomites radiutulus appears to remain on decaying blades
of grass; whilst Pupa umbilicata, Clausilia nigricans and Bulimus
obscurus bury their heads only to increase their shells. With respect
to Zonites cellarius, Zonites lucidus, and Zonites nitidulus, it was
not satisfactorily ascertained whether their heads were buried du-
ring the process of growth.

Observatory, Beeston, E. J. Lowe.

1854, February 14th.

2. ‘Note on the Decomposition of Sulphuric Acid by Penta-
chloride of Phosphorus.” By Alexander Williamson, Ph.D., F.C.S.,
Professor of Practical Chemistry in University College.

Chemists have long been aware of the fact that some acids unite
with bases in one proportion only, others in two or more proportions.
Thus a given quantity of nitric acid forms with what is termed its
equivalent of potash, a definite nitrate of potash; if less than this
equivalent quantity of potash were added to the nitric acid, the
product would be a mechanical mixture of the same nitrate of potash
with uncombined nitric acid; if more than the equivalent of potash
were added, the excess of alkali would remain uncombined. Sul-
phuric acid, on the other hand, is capable of forming two compounds
with potash, and it depends upon the proportions in which the two
substances are brought together whether the neutral or acid sulphate
is formed.

The number of compounds which an acid forms with one base is
now considered as indicating its atomic weight. The weights of
sulphuric and nitric acids which are respectively susceptible of neu-
tralizing the same quantity of potash are termed equivalent, but
these are by no means the same as their atomic weights. Sixty-
three parts of nitric acid (nitrate of water) contains the same quantity
of hydrogen as forty-five parts of sulphuric acid, and when they are
neutralized by potash the whole of this hydrogen is removed and
replaced by potassium; and if neither of the acids could combine in
any other proportion with potash, their atomic weights would be the
same as their equivalent weights. But sulphuric acid also forms a
potash compound in which half of its hydrogen is replaced by potas-
sium, the other half remaining in the compound, whereas the smallest
particles of nitric acid either exchange the whole or none of their
hydrogen for potassium.

This fact is expressed in the simplest possible manner by the
statement that the smallest indivisible particles of sulphuric acid
contain two atoms of hydrogen, whilst those of nitric acid only
contain one. Thus it is, that whereas the equivalent weights of the
two acids are the quantities which contain the same amount of basic
hydrogen, their atomic weights must be in the proportion of two
equivalents of sulphuric to one of nitric acid. ‘The simplest expres-
sion for an atom of nitric acid being empirically NO, H, we shall
accordingly represent an atom of sulphuric acid by the formula
§$O,H,. In like manner, an atom of common phosphoric acid,

366 Royal Society.

being tribasic, is expressed empirically by the formula PO, H,. The
labours of Messrs. Laurent and Gerhardt greatly contributed to the
establishment of these results, which are uncontroverted.

We have hitherto been accustomed to resort very freely to ima-
ginary distinctions of form and arrangement of matter to explain the
differences of properties ; but of late years an opposite tendency has
arisen, and chemists have felt the necessity of reducing their language
and ideas to simpler and more consistent forms, This necessity was
first felt in the most complex, 7. e. the so-called organic part of che-
mistry. But the simplifications thus introduced have proved to be
equally applicable to the inorganic part of the science; and their
introduction is calculated to disengage, for the consideration of sub-
stantial differences of composition, the attention which has hitherto
been absorbed by imaginary distinctions of form. Being unable to
express the constitution of compounds without some formal artifice,
we shall be able to see and compare their substantial differences
most easily when all unnecessary variations of those formal artifices
are eliminated. The success of this operation of course depends on
our finding one form sufficiently general to replace the special and
limited forms now employed.

In some papers published in the Journal of the Chemical Society
two or three years ago, I endeavoured to show that the constitution
of salts may be reduced to the type of water; that acids and bases
being, truly, acid salts and basic salts, are perfectly conformable to
the same principle ; and that, amongst other things, the difference
between monobasic and bibasic acids, &c. admits of a simple and easy
explanation by it. The leading propositions in those papers have been
adopted by several eminent chemists in this country and in France;
and M. Gerhardt speedily enriched science with a series of brilliant
and striking illustrations of their truth. As regards the constitution
of bibasic acids, M. Gerhardt’s results were, however, at variance
with that theory; and he was led to represent them by formule
equally inconsistent with his own previous views on the subject. I
believe that this discrepancy is satisfactorily removed by the facts I
have the honour of submitting to the consideration of the Society,

An atom of nitric acid, being eminently monobasic, is, as we have

already shown, represented in the monobasic type yO by the
formula (NO)o, in which peroxide of nitrogen (NO,) replaces one

atom of hydrogen. In like manner, hydrate of potash (0) is ob-
tained by replacing one atom of hydrogen in the type by its equiva-
lent of potassium; and nitrate of potash CNG) by a simultane-

ous substitution of one atom of hydrogen by peroxide of nitrogen,

the other by potassium. Sulphuric acid is formed from two atoms of
Ho ;

water f! ; one of hydrogen from each is removed, and the two
H

Royal Society. 367

replaced by the indivisible radical SO,. The series
Sulphuric acid. Acid sulphate of potash. Neutral sulphate of potash.

H Ho Ko
so,? 7 sO, _, sO,
HO KO KO

explains itself.

Chemists have long known how to remove the basylous consti-
tuents H, K, &c. of these salts, and to replace them by others. But
it is only recently that they have learnt to remove the chlorous
radicals SO,, NO,, &c. in a similar manner. To obtain the chloride
of potassium from its sulphate, it is sufficient to bring the latter into
liquid contact with chloride of barium; but the same reagent would
be powerless for the preparation of the chlorides of the radicals SO,
or NO,.

M. Cahours has shown us a reagent (the pentachloride of phos-
phorus) which is capable of forming from a great number of mono-
basic acids the chlorides of the acid radicals. Whilst extending our
knowledge of the action of the body on monobasic and organic acids,
and preparing numerous compounds of their radicals with one atom
of chlorine, M. Gerhardt examined also the nature of its action upon
bibasic acids and their compounds; and states that it consists of two
successive phases, first, the liberation of the anhydrous acid, secondly,
the substitution of two atoms of chlorine for one of oxygen in that
anhydrous acid. These facts, if correct, would be unfavourable to
the above view of the constitution of sulphuric and the other bibasic
acids; and M. Gerhardt adopted accordingly the old formulz, repre-
senting in their composition an atom of water ready-formed, SO,H,O,

Confining my remarks for the present to the case of sulphuric
acid, whose decomposition is doubtless typical of that of other bibasic
acids, I may state as the result of numerous experiments with the
most varied proportions of pentachloride and acid, performed on a
scale of considerable magnitude, that the first action of the penta-
chloride consists in removing one atom of hydrogen and one of
oxygen (empirically peroxide of hydrogen) from the acid, putting in

an atom of chlorine in their place and forming the compound s0,? -
Cl

which is strictly intermediate between the hydrated acid and the
final product SO, Cl, formed by a repetition of the same process of
substitution of chlorine for peroxide of hydrogen. The existence
and formation of this body, which we may call chloro-hydrated sul-
phuric acid, furnishes the most direct evidence of the truth of the
notion, that the bibasic character of sulphuric acid is owing to the
fact of one atom of its radical SO, replacing or (to use the customary
expression) being equivalent to two atoms of hydrogen. Had this
radical been divisible like an equivalent quantity of a monobasic
acid, we should have obtained a mixture, not a compound of the
chloride with the hydrate,—or, at least, the products of decomposi-
tion of that mixture,

Chloro-hydrated sulphuric acid boils at 145° Cent., distilling

368 Royal Society.

without decomposition. The intensity of its action upon water
varies according to the manner in which the two bodies are brought
together. When poured rapidly into a large quantity of cold water,
a portion of it sinks to the bottom, and only gradually dissolves as
a mixture of hydrochloric and sulphuric acids. When a small
quantity of water is added to the compound, the same decomposition
takes place with explosive violence. The acid dissolves chloride of
sodium on the application of a gentle heat with evolution of hydro-
Na
chloric acid, giving rise to a compound of the formula s0,0 . When
Cl
poured upon pieces of melted nitre at the atmospheric temperature,
an effervescence takes place with evolution of a colourless vapour
which possesses in a striking degree the odour of aqua regia. This
vapour may be dissolved in various liquids, and when decomposed
by water, yields nitric and hydrochloric acids. It is doubtless
chloro-nitric acid, NO,Cl. In like manner the chlorides of other
inorganic acid radicals may be obtained, as from chlorates, perchlo-
rates, sulphites, &c., but of these and other reactions I beg leave to
defer any further account until the experiments now in hand are
more advanced.

From the general resemblance of properties and identity of boiling-
point of the chloro-hydrate with a compound discovered by Rose,
and described by that eminent chemist as possessing empirically the
composition 8, O,Cl,, I was led to suspect that the two might in
reality be identical, which of course would require the addition of
the elements of water to Rose’s formula, and several experiments I
have performed afford strong confirmation of that identity. The
same compound is obtained by the action of dry hydrochloric acid
on anhydrous sulphuric acid; and finally, I may mention that
Mr. Railton obtained a small quantity of the same substance some
weeks ago in my laboratory by the action of platinum-black at a
high temperature on an imperfectly dried mixture of chlorine and
sulphurous acid.

As regards the successive transformations effected in the penta-
chloride, I have observed the formation of Wurtz’s oxychloride (the
tribasic chloro-phosphoric acid (PO Cl,)), and also of a compound
boiling above 145°, probably PO, Cl. Hydrated phosphoric acid is
always found unless the amount of pentachloride added is very
great.

March 9.—-Thomas Bell, Esq., V.P., in the Chair.

The following paper was read :—

**On a new and more correct method of determining the Angle
of Aperture of Microscopic Object-Glasses.”” By William S. Gillett,
Esq., M.A.

The very large apertures assigned to the more recent microscopic
object-glasses drew the author’s attention some time since to the im-
portance of testing the accuracy of the method employed to deter-
mine their amount.

Royal Society. 369

With this object in view he began with the consideration that
the central pencil was alone to be regarded, and that the marginal
rays of this were the true limits of the angle of aperture, and that
consequently the rays of all oblique pencils were to. be excluded, as
these might cross at a point not coincident with the principal focus,
and being measured separately might form an angle (apparently of
aperture) not coinciding of course with the true one, although per-
haps not differing from it in amount. A short description of the
usual method of measuring these angles will suffice to show what
claim it has to confidence in these respects.

The microscope, with the object-glass to be examined and an or-
dinary eye-piece, is used as a telescope, and a light placed at some
distance is commonly made an object to define the limit of the field
of view, the image of which is formed near the back surface of the
posterior combination, and the diffused light of this image, as seen
through the eye-piece, is the indication that a pencil of light is ad-
mitted, whether central or oblique. Sometimes by an additional
glass the eye-piece is made an erecting one capable of bringing the
image into focus. This adds much to the convenience, but not to
the correctness of the method. Thus the conditions of the micro-
scopic object-glass are reversed, the principal focus being transferred
from the front to the back, and the rays estimated are those of the ex-
treme oblique pencils, which may or may not pass through the point
of the principal focus of the glass when used for the microscope.

The importance of this in the illumination of objects immediately
suggested itself; and the author obtained a further proof by another
experiment bearing directly upon this point. A blackened wire was
placed under a microscope at the focal point, with an object-glass
of considerable power and aperture, the wire covering the field with
the eye-piece used. The field was then illuminated with an achro-
matic condenser, the field of illumination exceeding, as it usually
does, that of the microscope. As was expected, the oblique rays
which passed on both sides of the wire prevented its biackness from
being seen (this becoming of a milky-grey), until the field of illumi-
nation was reduced to the extent of that of the microscope, when it
immediately assumed to the eye its natural blackness. This re-
minded the author of a beautiful illustration given by Professor Fara-
day some years since at the Royal Institution, of the effect of glare
produced by placing white muslin blackened in parts before a white
paper printed in large letters; with the white muslin in front, the
letters were scarcely visible, while through the blackened parts they
resumed their natural appearance. ‘These experiments suggested
the new method adopted, which may be briefly stated as follows :—

The microscope of which the object-glass is to be examined is
placed horizontally and centred by an object placed in the focus.
Next, there is substituted in place of the eye-piece, a hollow cone
with an aperture at its summit. Light passing through this aper-
ture is made to form an image of it in the principal focus of the ob-
ject-glass, in the place of the original object. On this image a
horizontally placed examining microscope is then directed, which

Phil. Mag. 8. 4, Vol. 7. No. 46. May 1854. 2C

370 Royal Society.

traverses as the radius of a graduated circle, having its centre corre-
sponding with the place of the original object, and therefore with
the image to be viewed; and the angle of aperture is measured by
the arc passed through between two extreme positions, in the usual
manner. The method is further explained in the paper by a figure
and description of the apparatus, which was itself exhibited in the
Library after the meeting.

March 16.—Charles Wheatstone, Esq., V.P., in the Chair.

The following paper was read:—‘‘On some new Compounds of
Phenyle.” By A. Williamson, Ph.D., F.C.S., Professor of Practical
Chemistry in University College.

This communication contains a notice of some of the results ob-
tained in an investigation of Carbolic Acid or Hydrated Oxide of
Phenyle, conducted, under the author’s superintendence, by Mr.
Scrugham in the Analytical Laboratory of University College.

Referring to the substitution products obtained by Laurent from
hydrate of phenyle by the action of chlorine and bromine, as well as
to its combination with acids prepared by that chemist in conjunc-
tion with Gerhardt, the author states that the substance which they
conceived to be chloride of phenyle has been found by Mr. Scrugham
to be a mixture of two compounds.

As regards the preparation of hydrate of phenyle from the creosote
of coal-tar, it is observed that the numerous fractional distillations
by which it is usually isolated may be abridged by crystallization ;
for if creosote, having the boiling-point between 186° and 188° Cent.,
be left for some time in contact with a few crystals of the pure hy-
drate, it deposits a considerable quantity of beautiful colourless
needles, which, when separated from the mother-liquid, distil at
184° Cent., and condense in the neck of the retort into a solid mass
of pure hydrate of phenyle.

When pentachloride of phosphorus is added to hydrate of phenyle,
the action is at first very energetic, hydrochloric acid being evolved,
and the mixture becoming hot; but after a time the addition of fresh
portions of pentachloride produces no perceptible action, unless the
mixture be heated. Oxychloride of phosphorus is formed, as well as
a neutral oily body, which is insoluble in aqueous potash at the
common temperature, but soluble with decomposition in boiling pot-
ash. This oily compound would, from its mode of formation, be
naturally supposed to be the chloride of phenyle, and it has been so
considered by some distinguished chemists. It may, however, be sepa-
rated by distillation into two perfectly definite and distinct bodies, one
of which boils at 136° Cent., the other at a temperature above the
range of mercurial thermometers. The former of these is a colour-
less mobile liquid, possessing a fragrant smell, not unlike that of
bitter almonds. The latter is a more consistent inodorous liquid,
which solidifies at a low temperature into a mass of colourless cry-
stals. The liquid having the boiling-point of 136° is nothing else
than the chloride of phenyle. The crystalline body is the phosphate of
phenyle, one of the most beautiful products in organic chemistry. In
the liquid state it is slightly yellow by transmitted light, and it re-

Royal Society. 371

flects the more refrangible rays with a fine opalescent appearance,
due no doubt to the so-called epipolic refraction. The epipolic rays
visible by ordinary daylight on and at some depth below its sur-
face, are of a fine violet tint, differing decidedly from the blue colour
exhibited by disulphate of quinine in like circumstances. The flame
of sulphur does not bring out this effect more strongly than the
diffused light of the sun.

Phosphate of phenyle dissolves in strong nitric acid with evolution
of considerable heat, and the solution gives out nitrous fumes on
ebullition. A heavy yellow oil is precipitated by water from this
solution, and collects in drops which ultimately solidify, and their
solidification is, singularly enough, accelerated by hot water, by
reason of its more quickly dissolving out the nitric acid which at first
holds the‘solid body in solution. Nitrophosphate of phenyle is an acid,
and forms with potash a beautiful crystalline salt.

An alcoholic solution of phosphate of phenyle decomposes acetate
of potash on ebullition. After the alcoliol is distilled off, the tempe-
rature of the mixture rises rapidly on the application of further heat,
and a limpid oleaginous substance, having a very peculiar odour,
distils over, which possesses the composition of acetate of phenyle.
This compound boils at 190° Cent.; it is heavier than water, and
very slightly soluble in that liquid. It dissolves with decomposition
in boiling potash.

Cyanide of phenyle is obtained by the action of the phosphate on
cyanide of potassium. It is decomposed by boiling potash with
evolution of ammonia.

Terchloride of phosphorus, when distilled with hydrate of phenyle,
seems to act at first similarly to the pentachloride, but the phosphite
of phenyle formed is decomposed by heat ; and among the products of
distillation is found a body boiling at 80° Cent., and possessing all
the properties of benzine, i. e. hydruret of phenyle.

The formation of the iodide of phenyle is necessarily attended with
some difficulty, owing to the circumstance of phosphorus not com-
bining with more than three equivalents of iodine. Its boiling-
point is 190° Cent.

Mr. Scrugham has had reason to confirm the statements of Lau-
rent and Gerhardt respecting the benzoate of phenyle, and has pre-
pared that compound in considerable quantities by the action of
chloride of benzoyle on phenylate of potash. Chloride and phos-
phate of phenyle could not be made to react on benzoate of potash.

Chloride of cuminyle reacts with violence on phenylate of potash,
with formation of cuminate of phenyle, a compound analogous to the
benzoate.

Chloride of phenyle was heated with phenylate of sodium, with a
view to the formation of oxide of phenyle, and there is no doubt that
this compound was formed by the reaction, as the correlative pro-
duct, chloride of sodium, was detected. But a further account of
this and other reactions is deferred until the experimental investiga-
tion is more advanced.

Specimens of most of the compounds mentioned were exhibited.

2C2

372 Royal Institution.

ROYAL INSTITUTION OF GREAT BRITAIN.

March 31, 1854.—On Chemical Affinity among Substances in
Solution. By John Hall Gladstone, Esq., Ph.D., F.R.S.

An historical sketch of the development of the ideas of chemists
concerning “ affinity” was first given. ‘The dogma of Hippocrates
that “like combines only with like,” was shown to be superseded
by the view of Glauber and others, that unlike substances combine
most readily; and that where two bodies have an affinity for one
another, it is a sign that they have zo affinity with one another.
The views of Newton and Boyle in reference to the different degrees
of strength of affinity were then considered, and particular attention
was directed to the doctrine of Bergmann, that when a decompo-
sition takes place by means of the greater elective attraction of a
third body, that decomposition is complete. In opposition to this,
Berthollet contended that in all such cases of composition or decom-
position there takes place a partition of the base, or subject of the
combination, between the two bodies whose actions are opposed ;
and that the proportions of this partition are determined, not solely
by the difference of energy in the affinities, but also by the differ-
ence of the quantities of the bodies—by their physical condition,—
and by that of the combinations capable of being generated. These
views did not meet with a favourable reception at the time of their
promulgation; and the attention of chemists had been drawn away
from the subject until within these last few years, when Malaguti,
Bunsen, Debus, and Williamson have published investigations bear-
ing upon the point. The lecturer then stated, that before any of
these papers had appeared, he had been thinking of and performing
some experiments upon the subject in question, and that he was still
continuing them.

After a few experiments illustrative of ‘‘ chemical combination ”
and of ‘elective affinity,” others were introduced to show how
easily this latter phenomenon was affected by circumstances. Thus
ammonia will displace alumina from a solution of the sulphate, but
on the other hand, alumina will displace ammonia when heated with
the solid sulphate of that volatile base; whilst if solutions of chloride
of aluminium and sulphate of ammonia be mixed and evaporated,
crystals of the double sulphate, ammonia-alum, will appear. There
were on the table two white salts; the one had been carbonate of
baryta, but by boiling with excess of sulphate of potash, it had been
converted into the sulphate; the other had been sulphate of baryta,
but by long-continued boiling with much carbonate of potash, it had
suffered the opposite change into the carbonate. ‘The lecturer then
stated that so great is the influence exerted by these various circum-
stances, that some have doubted whether there be a true “ elective
affinity ;”’ he however believed that after making every allowance for
known causes there is still a residuary phenomenon to which that
name is the most appropriate. Allowing then, with Bergmann,
that relative degrees of affinity exist, the question arises :— Is
Berthollet’s law also correct? It is very difficult to arrive at a
satisfactory answer, since it is almost impossible to eliminate

Royal Institution. 373

other influences. Several reactions, however, were mentioned
as tending to show that there is some truth in the law :—for
instance, the solution of gold in hydrochloric acid upon the addition
of nitrate of potash. The experiments of Bunsen on mixtures of
carbonic oxide and hydrogen, exploded with a quantity of oxygen
insufficient for complete combustion; and those of Debus on the
precipitation of mixed hydrates of lime and baryta by carbonic acid
were explained; as also the remarkable fact noticed by both, that
the resulting products were always in certain atomic proportions to
one another. But in both these cases the first products of the
chemical action are removed at once from the field: it is quite
another case when they remain free to act and react on one another.
Supposing they all remain in solution, the requisite is fulfilled ; but
how are we to know what has then taken place? Malaguti thought
to obtain an indication of this by mixing the aqueous solutions of
two salts, one of which is soluble in alcohol, and the other is
insoluble, and then pouring them into very strong alcohol, and
analyzing the salts immediately thrown down. His results are
tabulated; they are valuable, but to some extent open to objection,
on account of the disturbing influence of the alcohol. Some
observations of Professor Graham, and others of Professor William-
son, as yet unpublished, were then spoken of, and the Lecturer
proceeded to describe his own endeavours to arrive at a knowledge
of the intimate constitution of a mixture of salts in solution by
observing their physical properties, especially colour.

If solutions of one equivalent of nitrate of iron, and a triple equi-
valent of sulphocyanide of potassium be mixed, a blood-red colour
results owing to the formation of sulphocyanide of the sesquioxide
of iron; the question arises—Has all the iron left the nitric acid
to unite itself with the sulphocyanogen? It has not; for on the
addition of equivalent after equivalent of sulphocyanide of potassium,
a deeper red is constantly obtained. The arrangement by which
this deepening of colour was quantitatively determined was explained,
and imitated on the lecture table. The result was that even up to
375 equivalents, a regular increase was observed to take place, more
rapidly at first than afterwards, which was exhibited to the eye by
the results being projected as a curve. Again, as in the mixture of
equal equivalents of the two salts, some iron still remains in combina-
tion with the nitric acid, a portion of the potassium must still remain
united to the sulphocyanogen. Accordingly the addition of more iron
salt also gives a deeper colour. The curve expressing the results of
this experiment was a regular continuation of the curve formerly
mentioned ; and neither of them exhibited any of those sudden trans-
itions which the experiments of Bunsen and Debus present. Dia-
grams exhibiting curves of the gallate and meconate of iron were
also exhibited. Various experiments were then performed, showing
the alteration in the resulting colour upon any change of any of the
elements in the primary experiment ; for instance, the substitution of
other acids for the nitric acid. or of other bases for the potash. On
the addition of a colourless salt to a coloured one, there results a

374 Royal Institution.

diminution of the colour greater than the mere dilution would have
produced, as was exemplified in the cases of the red sulphocyanide
of iron mixed with sulphate of potash, and of the scarlet bromide
of gold mixed with chloride of potassium. The lecturer accord-~
ingly drew the conclusion that when two salts mix without preci-
pitation or volatilization, the acids and bases frequently, if not uni-
versally, arrange themselves according to some definite proportion ;
and that this depends on the relative quantity of the two salts, as
well as upon the proper affinities of the substances composing them.
He was unable then to enter upon the influence of heat, or of dilu-
tion in certain cases, or to add any remarks connected with double
salts, or with other metals, or upon certain practical applications of
these views in chemical and physiological science.

The fact that we very frequently find the double decomposition of
a salt to be complete, the whole of one of its constituents being pre-
cipitated, was shown to be easily explained on the principles of
Berthollet. Thus, for instance, when chromate of potash and
nitrate of silver are mixed, at the first moment a division will take
place producing four salts, but one of these—the chromate of
silver—is thrown down at once as a precipitate, and thus put out of
the field of action. Another division of the acids with the bases
must take place, producing of course more of the insoluble chromate,
and so on, till at length the whole of the silver is removed. And
that this is really what does take place is rendered almost certain by
the fact that wherever by an interchange of acids and bases a pre-
cipitate can be produced, that precipitate does form; and, if the
substance be perfectly insoluble, the whole is thrown down; this
occurring in opposition to all rules of “‘ affinity,” and to all tables
that Bergmann, or any other chemist, ever did or could construct.
The volatility of one of the products acts in the same manner as in-
solubility, as is exemplified in the decomposition of carbonates by
any other acid. Crystallization also is but another phase of the same
phenomenon. An experiment was exhibited in illustration of this.
Dilute solutions of nitrate of lime, and sulphate of soda, were mixed
at the ordinary temperature without producing any separation of
solid matter; but they were so proportioned that upon heating the
mixture, the crystallization of some sulphate of lime was determined,
and when once this had commenced, it progressed rapidly; re-
sembling in that respect the ordinary phenomena of precipitation.
If in a double decomposition a far larger quantity of a sparingly
soluble salt be produced at the first moment than the water can dis-
solve, the crystals will be formed rapidly and will accordingly be
very small in size; but should there be formed at once only just
sufficient to determine a separation in the solid form, the crystals
will grow gradually, and will often attain a large size. This was
exemplified on the mixture of nitrate of silver with the sulphates of
copper and of potash respectively.

It is possible that the law of Berthollet may not be universally
applicable ; yet the present advanced state of science shows that not
only is there, as Bergmann insisted, a true chemical affinity, that is,

Royal Institution. 375

a preference of one substance to combine with a certain other sub-
stance instead of a third, but, in a great number of instances at
least, this substance will combine with both according to certain
proportions, whenever the whole of the affinities can be brought into
play at the same time.

April 7.—On Silica and some of its applications to the Arts.
By the Rev. J. Barlow, M.A., F.R.S., Vice-President, and Sec. R.I.

Silica is one of the most abundant substances known. Quartz,
common sand, &c., flint, chalcedony, opal, &c,, and a variety of sand
described by Mr. J. T. Way*, may respectively be taken as examples
of crystallized and uncrystallized silica. Under all these forms
silica is capable of combining with bases as an acid. Heat is how-
ever essentially necessary to effect this combination, a combination
of which all the well-known silicates, whether natural, as felspar,
mica, clay, &c., or artificial, as glass, slags, &c., are the results. The
common forms of insoluble glass are produced by the union of
silica with more than one base. But, when combined with an
alkaline base only, silica forms a soluble glass, the degree of solu-
bility of which depends on the proportion which the silicic acid
bears to this alkaline base . . . . This soluble silicated alkali (or
water-glass) may be prepared by various processes. If sand be
used, 15 parts of fine sand, thoroughly incorporated with 8 parts of
carbonate of soda, or with ten of carbonate of potash, and one of
charcoal fused in a furnace, will produce a silicated alkali which is
soluble in boiling water. Messrs. Ransomes obtained this silicated
alkali by dissolving broken flints in a solution of caustic alkali at
a temperature of 300° Fahr. And more recently, Mr. Way has ob-
served that the sand which he has described will combine with
caustic alkali at boiling heat, also producing a water-glass.

This water-glass has been applied to several important purposes,
three of which were specially noticed.

I. To protect Building-stones from decay.—The stone surfaces
of buildings, by being exposed to the action of the atmosphere, be-
come liable to disintegration from various causes. Moisture is
absorbed into their pores. The tendency of their particles to sepa-
rate, in consequence of expansion and contraction, produced by
alternation of temperature, is thus increased. Sulphurous acid is
always present in the atmosphere of coal-burning cities, and cannot
but corrode the calcareous and magnesian ingredients of oolites and
dolomites. It is true that good stone resists these sources of injury
for an indefinite time, but such a material is rarely obtained. Asa
preventive of destruction, whether arising from physical or chemical
causes, it has been proposed to saturate the surfaces of the stones
with a solution of the water-glass.

It is well known that the affinity of silica for alkali is so feeble
that it may be separated from this base by the weakest acids, even
by carbonic acid. According to the expectation of those who
recommend the silification of stone, the carbonic acid of the atmo-

* Quarterly Journal of Chemical Society, July 1, 1853, and Journal of
Royal Agricultural Society, vol. xiv. part 1.

376 Royal Institution.

sphere will set the silica free from the water-glass, and the silica,
thus separated, will be deposited within the pores and around the
particles of the stone. The points of contact of these particles will
thus be enlarged, and a sort of glazing of insoluble silica will be
formed, sufficient to protect the stone against the effects of moisture,
&c. This cause of protection applies chiefly to sand-stones. But
wherever carbonate of lime or carbonate of magnesia enters notably
into the composition of the building-stone, then an additional
chemical action, also protective of the stone, is expected to take
place hetween these carbonates and the water-glass. Kuhlmann
remarks, ‘‘ Toutes les fois que l’on met en contact un sel insoluble
avec la dissolution d’un sel dont l’acide peut former avec la base du
sel insoluble un sel plus insoluble encore, il ya échange ; mais le
plus souvent cet échange n’est que partiel*.’” In consequence of
this “‘ partial exchange” an insoluble salt of lime may be looked for
whenever a solution of water-glass is made to act on the carbonate
of lime or carbonate of magnesia existing in oolitic or dolomitic
building-stones.

This expectation, however, has not been altogether sanctioned by
experiment. A gentleman, eminently conversant with building
materialst, immersed a piece of Caen-stone in a solution of silicate
of potash in the month of January 1849. This fragment, together
with a portion of the block from which it had been separated, was
placed on the roof of a building in order that it might be fully
exposed to the action of atmosphere and climate. After five years
the silicated and the unsilicated specimens were found to be both
in the same condition, both being equally corroded. ‘These specimens
were exhibited in the Theatre of the Institution. But whatever
ultimate results may ensue from this process, the immediate effects
on the stone are remarkable. ‘Two portions of Caen-stone were
exhibited, one of which had been soaked in a solution of water-
glass two months before. The surface of the unsilicated specimen
was soft, readily abraded when brushed with water, and its calca-
reous ingredients dissolved in a weak solution of sulphurous acid.
The silicated surface, on the other hand, was perceptibly hard, and
resisted the action of water and of dilute acid when similarly appliedt.

II. Another proposed use of the water-glass is that of hardening
cements, mortar, &c., so 2s to render them impermeable by water.

Fourteen years since Anthon§ of Prague proposed several applica-
tions of the water-glass. Among others he suggested the rendering
mortars water-proof. He also suggests that this substance might

* Expériences Chimiques et Agronomiques, p. 120.

+ Charles H. Smith, Esq., one of the authors of the ‘ Report on the Se-
lection of Stone for the Building of the New Houses of Parliament.’

t Silliman’s American Journal, January, 1854, contains a notice of the
application of the water-glass to the decaying surfaces in the Cathedral of
Notre Dame in Paris.

Neuere Mittheilungen iiber die Nutzanwendung des Wasser-Glases,
1840. This subject has also been fully treated by Kuhlmann in his ‘ Mé-
moire sur ]’Intervention de la potasse ou de la soude dans la formation des
chaux hydrauliques,’ &e., 1841.—Eapériences Chimiques et Agronomiques.

Royal Institution. 877

be beneficially employed as a substitute for size in white- washing
and staining walls. It was demonstrated by several experiments
that carbonate of lime, mixed up with a weak solution of water-glass,
and applied as a whitewash to surfaces, was not washed off by
sponging with water, and that common whitewash, laid on in the
usual manner with size, was rendered equally adhesive when washed
over with water- glass.

III. The Stereochrome of Fuchs.—The formation of an insoluble
cement by means of the water-glass, whenever the carbonic acid. of
the atmosphere acts on this substance, or whenever it is brought in
contact with a lime-salt, has been applied by Fuchs to a most im-
portant purpose. The stereochrome is essentially the process of
fresco secco* invested with the capability of receiving and perpe-
tuating works of the highest artistic character, and which may be
executed on a vast scale. Fuchs’s method is as followst:—

“Clean and washed quartz-sand is mixed with the smallest quan-
tity of lime which will enable the plasterer to place it on the wall.
The surface is then taken off with an iron scraper, in order to re-
move the layer formed in contact with the atmosphere; the wall
being still moist during this operation. The wall is then allowed
to dry ; after drying it is just in the state in which it could be rubbed
off by the finger. The wall has now to be fized, i.e. moistened with
water-glasst. [An important point is not to use too much water-
glass in moistening the wall.] This operation is usually performed
with a brush. The wall must be left in such a condition as to be
capable of receiving colours when afterwards painted on. If, as
frequently happens, the wall has been too strongly fixed, the surface
has to be removed with pumice and to be fixed again. Being fixed
in this manner the wall is suffered to dry. Before the painter
begins, he moistens the part on which he purposes to work with
distilled water, squirted on by a syringe. He then paints: if he
wishes to repaint any part, he moistens again. As soon as the
picture is finished, it is syringed over with water-glass. After the
wall is dry, the syringing is continued as long as a wet sponge can
remove any of the colour. An efflorescence of carbonate of soda
sometimes appears on the picture soon after its completion. This
may either be removed by syringing with water, or may be left to
the action of the atmosphere.” Not to dwell on the obvious ad-
vantages possessed by the stereochrome over the real fresco, (such
as its admitting of being retouched and its dispensing with joinings),
it appears that damp and atmospheric influences, notoriously de-
structive of real fresco, do not injure pictures executed by this process.

* Vide Eastlake’s Materials for a History of Oil Painting, p. 142.

+ These particulars were obtained by Dr. Hofmann from Mr. Echter. A
stereochromic picture by Echter and a sample of the water-glass as pre-
pared in Munich were also exhibited by Dr. Hofmann.

} The composition of the specimen was—

per cent.
PUM sieeve ssvspacstordeacarares seve Wtrare 23°21
BOOS cress ecinceseattssesasep wparhexcneactt «nes 8:90
OTEReisaer ciara secs ctit;tectesps ots sacce 2°52

[The specific gravity of the solution 3'81.]

378 Intelligence and Miscellaneous Articles.

The following crucial experiment was made on one of these pic-
tures. It was suspended for twelve months in the open air, under
the principal chimney of the New Museum at Berlin; ‘ during that
time it was exposed to sunshine, mist, snow, and rain,” and never-
theless ‘‘ retained its full brilliancy of colour.”

The stereochrome has been adopted on a grand scale by Kaulbach
in decorating the interior of the great national edifice at Berlin
already alluded to. These decorations are now in progress, and
will consist of historical pictures (the dimensions of which are
21 feet in height and 243 in width), single colossal figures, friezes,
arabesques, chiaro scuro, &c. On the effect of the three finished
pictures, it has been remarked by one whose opinion is entitled to
respect, that they have all the brilliancy and vigour of oil paintings,
while there is the absence of that dazzling confusion which new oil
paintings are apt to present, unless they are viewed in one direction,
which the spectator has to seek for.

Mr. A. Church has suggested that if the surface of oolitic stones
(such as Caen-stone) is found to be protected by the process already
described, it might be used, as a natural intonaco, to receive coloured
designs, &c. for exterior decorations; the painting would then ve
cemented to the stone by the action of the water-glass.

Mr. Church has also executed designs of leaves on a sort of terra
cotta, prepared from a variety of Way’s silica rock, consisting of 75
parts clay and 25 of soluble silica. This surface, after being hard-
ened by heat, is very well adapted for receiving colours in the first
instance, and for retaining them after silication.

LIX. Intelligence and Miscellaneous Articles.

ON A NEW METEORITE FROM NEW MEXICO.
BY DR. F. A. GENTH.

I AM indebted to Prof. Joseph Henry, Secretary of the Smith-
sonian Institution, for a small piece of an interesting meteorite
from New Mexico. It was labelled ‘‘ native iron,” and is said to occur
there in large quantities. Fortunately it was just sufficient for an
examination, the results of which I here give. There is no doubt

that the mineral is of meteoric, and not of telluric origin.

It is very crytalline, and shows a distinct octahedral cleavage. Its
colour is iron-gray, its lustre metallic. Quite ductile. Spec. grav.
(at 18° Cels.) =8°130.

Dissolves readily in diluted nitric acid, leaving a small quantity
of insoluble residue, which, however, was also slowly dissolved by
strong nitric acid or aqua regia, but still more easily by fusion with
bisulphate of potash.

The methods used for its analysis were the following :—In ana-
lysis I. the meteorite was dissolved in strong nitric acid; nickel and
cobalt were separated from iron by carbonate of baryta; nickel and
cobalt were separated by hydrocyanic acid, potash, and oxide of
mercury.

In analysis II. the meteorite was dissolved in diluted nitric acid
and the residue filtered off on a weighed filter. In the filtrate, iron

Intelligence and Miscellaneous Articles. 379

was separated from cobalt and nickel by addition of a sufficient
quantity of acetate of potash, in order to convert the nitrates into
acetates, and evaporation to dryness ina water-bath. The dry mass
was boiled with water and filtered. From the filtrate, which con-
tained the whole quantity of oxides of cobalt and nickel, these were
precipitated by caustic potash. The precipitate of sesquioxide of
iron was redissolved in hydrochloric acid and precipitated by am-
monia. ‘This method gives excellent results if used with care; the
only objection might be, that the sesquioxide of iron thus separated
is difficult to filter.

The insoluble residue was ignited and fused with bisulphate of
potash. On treating the fused mass with water, a white substance
of the appearance of titanic acid remained, which hydrochloric acid
slowly dissolved. This substance and sesquioxide of iron were pre-
cipitated by ammonia, and from the filtrate, oxide of nickel separated
as usual. The precipitate was weighed, dissolved in hydrochloric
acid, and the iron precipitated by sulphide of ammonium after the
addition of tartaric acid and ammonia. From the sulphide of iron the
iron was determined as usual. From the filtrate, the other substance
remained after the tartaric acid was destroyed by heat. It was,
however, a very small quantity, and only sufficient for one blowpipe
reaction. The borax bead gave in the inner flame an enamel of a
bluish colour. I therefore believe that it is titanic acid, though the
reactions somewhat differ.

The insoluble residue seems to be a combination of iron, nickel,
and titanium. Itcontains zo cobalt. Neither part of the meteorite
contained carbon, sulphur, phosphorus or tin.

I

F II.
TRG 3A). tile oh 2 =96'17 95:92
Nickel ........ = 30 j
Covaltia.f5% 22ne = 0°42 3°57
Insoluble ...... — wee 0°57
99°66 100-00

The insoluble part consisted of a steel-coloured powder in micro-
scopic crystals, which showed three-sided planes. Its composition is—

INOW pe efor te as: =55:07 per cent.
Mickelr; at%5.03. 35 =28°78
? Pitanitim 2% 4: =16:15
100°00
It is remarkable that the elements in the insoluble part are in the
following ratio :— Fe : Ni:? Ti=6: 3: 2.

—Silliman’s American Journal, March 1854, p. 239.

ON M. FOUCAULT’S PENDULUM EXPERIMENTS*.
Your Committee having undertaken to make this experiment with
as much care as possible, have the honour to submit the following
report on the results obtained by them.

* Extracted from the Second Report of the Special Committee of the
Literary and Historical Society of Canada.

380 Intelligence and Miscellaneous Articles.

A carefully turned spherical ball of lead, 5°2 inches in diameter
and weighing about 17 lbs., was employed as the weight, and sus-
pended in the passage of the Quebec Music Hall, where a height of
60 feet was obtained. This weight was suspended by a fine steel
wire, on one end of which a fine screw was turned, by means of
which the wire was fastened to the ball from which the pendulum
was suspended.

The following were the arrangements adopted by your Committee
at the point of suspension. A small spherical ball of brass was
ground into a hemisphere in a plate of the same metal. A hole was
drilled through the centre of the hemisphere for the wire, and suffi-
ciently large to allow the pendulum to vibrate in the required arc
without coming into contact with the plate. The wire was screwed
into the ball of suspension.

In order to start the pendulum for the experiments, a cotton
thread was passed round the ball and tied over two pins in a heavy
moveable block. When the weight secured in this manner had
been brought to a state of rest, the thread was fired with a taper,
and the pendulum commenced vibrating, the thread falling to the
ground. A circle, 10 feet in diameter, was described on the floor
from a centre under the point of suspension, and graduated into
degrees, by which the progress of the plane of vibration was mea-
sured.

The first series of observations recorded in the tables were made
on the 14th, 15th and 16th; and the second series on the 19th and
20th of May, 1853.

The first series of observations gives the angle actually moved
through in 475 18™ (after applying the correction for the progression
of the apse due to elliptic motion) only 1° 56’ less than that calcu-
lated. The second series gives an error of 2° 2! in 23 10™. These
errors may be represented in time by about 10 and 12 minutes; and
your Committee consider that these experiments agree so nearly with
calculation as to be strong corroborative evidence of the correctness
of the theory, that the time taken by: the plane of vibration to per-
form a complete revolution varies approximately as the time of the
latitude.

It may not here be out of place to give an explanation of the
accompanying tables. Columns (1) and (2) refer to the times of
observation; (3) denotes the nature of the ellipse described by the
pendulum, showing, if there be no elliptic motion, or if elliptic
motion, whether it is progressing or retarding; (4) shows the azi-
muthal angle observed; (5) the angle moved through, and (6) the
time between the observations; (9) is the angle calculated; (7) is
the difference between (5) and (9); (8) is the angle corrected for
elliptic motion; and (10) is the difference between (8) and (9).

Your Committee have great satisfaction in submitting the results
of the different experiments. In some instances they have varied
considerably from the calculated angles; but in all these the fact
that the pendulum had acquired an elliptic motion, would seem to
point to that circumstance as the chief cause of disturbance, while
in most of the experiments in which there was no elliptic motion,

381

the angles, as nearly as could be measured, were equal to thcse cal-
culated by theory. ‘The whole respectfully submitted.
(Signed) A. Nosts, Lieut. R.A. and V.P.
W. Dariine CaMpBELL.

Intelligence and Miscellaneous Articles.

| oo
@
(ray
=
2

Remarks.

Ellipse.
Azimuthal
angle
observed.
Angle
moved
through.
Difference
of time
Corrected
Calculated
angle
Difference
between
8 and 9

=
oO
Ot Bm bO bO OD BD BO bO SO DO GO OUD et tS ee

~
ou

+0 30 |started N.
—0O 28:5 peds.mr
povgeies ae
: iy a measured,
+0 21
—0 89
—0 8
—1 50
—0 30
42 4
41 46
—0 8
—0 3
—0 59:8
—2 53°6
—0 26:2

ZpRRAAZs

No elliptic
motion re-
corded.

Ellipse
slightly re-
tarding.

—0O 25:8 |21 52:8
~2 0 |20 56
—3 56:4 |21 35
—1 21:2|41 25
—0 15°8|21 55°8|21 55°8
+1 0 |23 1 j21 55:8
—1 21-643 51:6 |43 51-6

21
21
24 28°6
41 51:2

+0 45

ZeU PPR RR ZAZA:

40 425

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—1 56:8

30 49-5 |32 53
22 51:3|21 1

30 44
53 14

62 12)
86 35)

8 58
24 44
15 29

8 57
25 2
16 24

100 50,
129 0
151 30
172 20
P.|209 40
P.\248 0

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23 29:2 |27 24
21 32°8|21 55
36 52:8 |34 30
37 40°5 132 53

BRR RR APA

j eo to bo to GO NS Oe CO

to
oe

ON THE SUPPOSED CONVERSION OF AMMONIA INTO NITRIC ACID
IN THE ANIMAL ORGANISM. BY CHRISTIAN JAFFE.

A series of experiments have recently been published by Dr.

Bence Jones, from which it is inferred, that after introducing into

382 Intelligence and Miscellaneous Articles.

the stomach a large quantity of ammoniacal compounds, nitric acid
appears in the urine as a product of their oxidation.

From the extreme apparent improbability that such an oxidation
could be effected in the animal organism, and at the instigation of
Prof. Lehmann, the author has repeated the experiments upon which
this inference is founded; and has come to the conclusion, that the
method which Dr. Bence Jones adopted for detecting the presence
of nitric acid in the urine is altogether inapplicable, and consequently
that the inference that ammonia is oxidized within the organism is
perfectly unfounded.

The method consists in distilling the somewhat concentrated urine
with concentrated sulphuric acid until about one-half or two-thirds
have passed over, treating the distillate with carbonate of potash,
evaporating and testing the residue for nitric acid by means of starch,
iodide of potassium and dilute hydrochloric acid, or with indigo.

The author believes that this process is inapplicable, because,
even admitting the presence of nitric acid, it would appear impos-
sible to distil over this acid in the presence of urea, or indeed any
other organic substance. In order to decide this point, the author
added a few drops of nitric acid to normal urine, concentrated by
evaporation, and then distilled with sulphuric acid. The distillate,
treated with starch and iodide of potassium, gave a reaction, which,
although readily accounted for by subsequent experiments, at first
led the author to form the erroneous opinion that a distillation of
undecomposed nitric acid from urine actually took place. Normal
urine, distilled with concentrated sulphuric acid, gave a liquid which
became intensely blue when treated with starch and iodide of
potassium, while at the same time it gave no indication of nitric
acid with protosulphate of iron. It soon became evident that this
reaction was altogether owing to the presence of sulphurous acid,
formed by the action of the sulphuric acid upon the organic sub-
stances, and which, as is well known, causes a separation of iodine.
It thus becomes easily intelligible why Dr. Bence Jones so seldom
obtained this reaction in normal urine, as he saturated the distillate
with carbonate of potash, and evaporated.

The presenee of sulphurous acid in the distillate, and thedependence
of the reaction upon it, was demonstrated in the following manner :—

In the first instance, normal urine was distilled without any addi-
tion of acid; and, as was to be expected, the distillate gave no re-
action. Normal urine was then distilled with sulphuric acid; the
distillate gave a reaction with starch and iodide of potassium; when
tested with protochloride of tin for sulphurous acid, it acquired a
yellow colour, but even on boiling no precipitate was formed, a
result which might fairly be attributed to the small quantity of sul-
phurous acid. In order to prove more decisively that the reaction
was owing to this small quantity of sulphurous acid, normal urine
was distilled with phosphoric instead of sulphuric acid; and the
distillate when tested did not give the slightest trace of a reaction.
Lastly, when a distillate which at first gave the reaction was allowed
to stand twenty-four fours, it no longer gave it, but the presence of
sulphuric acid could be distinctly ascertained.

Meteorological Observations. 383

Thus then it appears that an oxidation of ammonia to nitric acid
in the animal organism has not by any means been proved by
Dr. Bence Jones's experiments. It remained, therefore, necessary
to ascertain by some other means whether such a formation of nitric
acid really took place. For this purpose, concentrated urine, mixed
with a few drops of nitric acid, was distilled with phosphoric acid ;
and the distillate did not give the slightest reaction either with
starch and iodide of potassium or with protosulphate of iron.

After these results, the author considers it unnecessary to enter
more fully upon the consideration of the various deductions from
Dr. Bence Jones’s experiments; such, for instance, as the assumed
formation of nitric acid from urea introduced into the stomach, espe-
cially as Frerich has already proved that this is always attended
by an increase in the quantity of urea in the urine.—Jowrn. fiir
Prakt. Chem., June1853.

METEOROLOGICAL OBSERVATIONS FOR MARCH 1854,

Chiswick.—March 1. Frosty: very fine: clear, with sharp frost at night. 2.
Frosty : very fine: hazy. 3. Very dense fog: foggy: partially overcast: frosty.
- Frosty, with slight fog: overcast. 5. Overcast: clear: dense fog. 6. Dense
fog : foggy throughout. 7. Foggy: fine: overcast. 8. Cloudy: overcast: clear.
9. Overcast: very fine: overcast. 10. Cloudy: slight rain. 11. Fine: clear.
12. Slight fog: very fine. 13. Clear and fine. 14. Cloudy: slight rain. 15.
Foggy: cloudy. 16. Cloudy and fine. 17. Clear throughout: frosty at night.
18. Slight haze: rain. 19. Rain: overcast. 20. Clear and cold. 21, 22. Fine.
23. Cloudy and cold. 24, 25. Overcast. 26. Cloudy. 27. Overcast : very fine.

28. Cloudy: very fine. 29. Clear: very fine. 30. Overcast: fine. 31. Clear
throughout.

Mean temperature of the month .......... srecesretrtese seeseeese 42°54
Mean temperature of March 1853 ......... Reanes eee sesseseeevee OF “41
Mean temperature of March for the last twenty-eight years. 42 -23
Average amount of rain in March .............+5 eanvedes seoseee 1°36 inch.

Boston.—March 1—3. Fine. 4,5. Cloudy. 6,7. Foggy. 8,9. Cloudy. 10.
Fine. 11. Cloudy. 12,13. Fine. 14. Cloudy: rain a.m. 15. Fine. 16. Cloudy :
rain a.M. 17. Fine: rain a.m.andp.m. 18. Cloudy. 19. Fine. 20—26, Cloudy.
27. Fine: rain a.m. 28. Cloudy. 29. Fine. 30. Cloudy. 31. Fine.

Sandwick Manse, Orkney.—March 1. Cloudy a.m. and p.m. 2. Bright a.m. :
cloudy p.m. 3. Clear, fine A.m.: clear, aurora p.m. 4. Clear, fine A.M.:
clearp.M. 5. Bright a.m.: drizzle p.m. 6,7. Cloudy a.M.andp.m. 8. Bright
A.M.: clearp.M. 9. Rain a.m.: cloudy p.m. 10. Bright a.m.: showers P.M.
11. Rain a.m.: cloudy p.m. 12. Bright a.m.: cleare.m. 13. Bright a.m. :
cloudy p.m. 14. Cloudy a.m.: fine p.m. 15. Clear a.m: cloudy p.m. 16.
Cloudy a.m.: clear p.m. 17. Cloudy a.m.: drops p.m. 18. Cloudy a.m. :
showers p.M. 19, 20. Cloudy a.m.: clear, aurora p.m. 21. Bright a.m. : cloudy,
aurora P.M. 22. Cloudy a.M.andp.m. 23. Cloudy a.m.: clear p.m. 24, Cloudy
A.M.andp.M. 25. Cloudy a.m.: clear, aurora p.m. 26. Bright a.m.: clear,
aurora P.M. 27. Showers a.m.: cloudy p.m. 28. Clear a.m.: cloudy, hazy p.m.
29. Cloudy a.m.: cloudy, drizzle p.m. 30. Clear a.m.and p.m. 31. Clear A.M. :
cloudy p.m.

Mean temperature of March for twenty-seven previous years . 40°37
Mean temperature of this month ........seesesesseeeees Specsecees! 40 714
Mean temperature of March 1853 ...........0..00.- wighedmees saunas 38 *24
Average quantity of rain in March for thirteen previous years 2°59 inches.

The mean temperature of this month is higher than that of any March for the
last twenty-seven years, and the barometer on the 4th was as high as on any day
during the same period except on two, viz. 27th December 1840, when it was
30°72, and on Ist February 1841, when it was 30°76.

On the 30th, about 8 o’clock p.m., a comet with a long tail was seen N.W.
about 7° above the horizon, and remained visible to the naked eye, and attracting
attention for an hour and a half, but has not been seen since then, as the sky was
too cloudy for several evenings.

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THE
LONDON, EDINBURGH ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

JUNE 1854,

LX. On a new and simple Method of determining the amount of
Urea in the Urinary Secretion. By Epmunp W. Davy, A.B.,
M.B.T.C.D., Lecturer on Chemistry in the Carmichael School
of Medicine, &c., Dublin*.

REA has long been regarded with much interest by scien-
tific men, on account of its physiological and chemical
relations. It represents one of the last stages of a series of me-
tamorphoses or changes which nitrogenous matter undergoes in
the animal ceconomy, and is the form under which the detritus
of pre-existing nitrogenous tissues which have become effete,
principally pass from the system. This interesting organic base,
urea, is not only formed during the exercise of the vital functions
in man and some of the higher animals, but is also produced
during the chemical decomposition of a number of substances
containing nitrogen ; and the chemist can now obtain it in any
quantity by artificial means, and thus imitate one of the most
important results of the chemistry of life.

In reference to medicine, urea is not without some practical
interest, as it is well known that during various diseased condi-
tions of the system the quantity of urea eliminated from the
blood by the action of the kidneys and excreted in the urine is
occasionally subject to great variation, and some ready means of
ascertaining its quantity in that secretion might frequently aid
the physician in forming his diagnosis of certain diseases.

Different means of effecting this object have from time to time
been proposed; but all the methods hitherto recommended, with
the exception, perhaps, of Baron Liebig’s recent one, require for

* Communicated by the Author.
Phil. Mag. 8. 4. Vol. 7. No. 47. June 1854. 2D

386 Dr. E. W. Davy on a new and simple Method of

their execution much time and trouble, and in some cases com-
plicated and expensive apparatus; and though capable in ex-
perienced hands of yielding tolerably accurate results, would in
the case of those not much practised in chemical manipulation,
and perhaps unaware of the many sources of error to be guarded
against, give anything but correct results, and are therefore in-
applicable to the greater number of those desirous of a quick
and easy method of determining the quantity of urea in urine.

The method I propose is one of extreme simplicity, and can
be performed by almost any one in a very few minutes, and is
capable of yielding results sufficiently accurate for all practical
purposes. It is founded on the fact I have recently observed,
that urea is very readily decomposed by the chlorides, or rather
hypochlorites of soda, potash or lime; and its constituent
nitrogen is evolved in the gaseous state, and from the quantity
of gas evolved I estimate the amount of urea present.

After trying different means of carrying out that fact with a
view of making it available to determine the quantity of urea in
urine, I found that the following very simple one seemed to
answer the purpose completely. I take a strong glass tube,
about 12 or 14 inches long, closed at one end, and its open
extremity ground smooth, and having the bore not larger than
the thumb can conyeniently cover. This I fill more than a third
full of mercury, and afterwards pour in carefully a measured
quantity of urine to be examined, which may be from a quarter
of a drachm to a drachm or upwards, according to the capacity
of the tube; then holding the tube in one hand near its open ex-
tremity, and having the thumb in readiness to cover the aperture,
I quickly fill it completely full with a solution of the hypochlorite
of soda (taking care not to overflow the tube), and then instantly
cover the opening tightly with the thumb, and having rapidly
inverted the tube once or twice to mix the urine with the hypo-
chlorite, I finally open the tube under a saturated solution of
common salt in water, contained in a steady cup or small mortar.
The mercury then flows out and the solution of salt takes its
place, and the mixture of urine and hypochlorite being lighter
than the solution of salt, will remain in the upper part of the
tube, and will therefore be prevented from descending and mixing
with the fluid in the cup. A rapid disengagement of minute
globules of gas soon takes place in the mixture in the upper part
of the tube, and the gas is there retained and collected. The
tube is then left in the upright position till there is no further
appearance of minute globules of gas being formed, the time
being dependent on the strength of the hypochlorite and the
quantity of urea present; but the decomposition is generally
completed in from three to four hours; it may, however, be left

determining the amount of Urea in the Urinary Secretion. 387

much longer, even for a day if convenient, and having set the
experiment gomg, it requires no further attention; and when
the decomposition is completed, it is only necessary to measure
the quantity of gas produced by transferring it into a graduated
tube or measure.

I have generally used a graduated tube in the first instance,
as it saves the trouble of transferring the gas and incurring the
risk of losmg some of it in the process. That which I would
recommend as being convenient for this purpose is a stout tube
having a bore of half an inch in diameter, and capable of hold-
ing from 2 to 3 cubic inches. A tube having this bore and
about 14 inches in length, will hold 22 cubic inches, which will
be quite large enough. Each cubic inch of it should be divided
into tenths and hundredths of a part of a cubic inch.

It is scarcely necessary to remark, that im cases where great
accuracy is required, due attention must be paid to the tempera-
ture and atmospheric pressure, and certain corrections made if
these should deviate from the usual standards of comparison at
the time of reading off the volume of the gas; but in most cases
sufficiently near approximations to accuracy may be obtained
without reference to those particulars. From a number of expe-
riments, I have ascertained that the quantity of gas evolved from
different amounts of urea, treated in the way I have just de-
scribed, very closely approximates to the quantity of nitrogen
gas which should be furnished from the urea by calculation.
This will be seen from the following, taken from many experi-
ments.

The fifth part of a grain of urea should furnish by calculation
0°3098 parts of a cubic inch of nitrogen gas at 60° F. and 30!
bar. ; the same quantity of urea treated as described furnished in
one experiment 0°3001, and in another 0°3069 parts of a cubic
inch of gas at the same temperature and pressure ; which shows
that the calculated quantity of nitrogen differs from the amount
of nitrogen gas obtained by only a few thousandths of a part of
a cubic inch. I may observe that I was obliged to operate on
such small quantities of urea, on account of the graduated tube
I had at the time being only of one cubic inch capacity.

Seeing, then, that the quantity of gas evolved agrees so very
closely with the calculated amount of nitrogen present in a cer-
tain quantity of urea, I take the calculated amount as being the
more correct; and knowing the relation that exists between a
certain quantity of urea and nitrogen, I can from the quantity
of gas evolved in any case easily calculate the amount of urea
present by the simple process of rule of three. Thus the fifth
part of a grain, or 0-2 of a grain of urea, gives by calculation
03098 parts of a cubic inch of nitrogen gas. Then 0°3098 : the

2D2

388 Dr. E. W. Davy on a new and simple Method of

volume of gas found :: 0-2: to the required quantity of urea;
or multiplying the first and third terms by 5, we have 1-549
cubic inch of gas representing one grain of urea, which is a
simpler proportion. Using these data, I made several compara-
tive experiments on different samples of urine with my method
and that of Baron Liebig’s, which I believe is considered one of
the most accurate of the methods of determining urea in urine
at present known. The following are the results of three com-
parative experiments on different samples of urine, using the
same with each method.

Amount of urea in grains and parts of a grain in one fluid ounce

of urine.

Liebig’s. New method.
lst experiment . . 3°680 3°712
2nd experiment . . 5°328 5472
3rd experiment . . 4°976 4976

In the first and second experiments the quantity of common
salt present in the urine was taken into account, as it is found
to increase to a slight degree the apparent quantity of urea in
the urine by Liebig’s method. In the third this was not taken
into consideration, and the quantity of urea was compared with
the mean of two results obtained by my method. These experi-
ments show how very closely the results obtained by the new
method agree with those by Baron Liebig’s, and therefore show
the correctness of the former method.

I prefer the hypochlorite of soda to that of potash as a decom-
posing agent, because the soda salt is an article of our pharma-
copoeia under the name “ Sodz chlorinatz liquor,” and therefore
can be so easily procured ; whereas the potash salt, not being
used in medicine, would require to be specially made for the
purpose. As to the hypochlorite of lime, I do not think it so
effectual, and it has the disadvantage of soiling the sides of the
graduated tube by the carbonate of lime formed in the reaction.

In reference to the quantity of hypochlorite of soda to be
employed, it should always be used in excess ; and I think that
about five or six times the volume of the urine employed would
be found generally to be quite sufficient, and ensure there being
an excess of the hypochlorite. The amount required may be
easily determined also by direct experiment, by adding to a cer-
tain quantity of urine to be examined in a glass a measured
quantity of the hypochlorite, and leaving it for a short time till
the evolution of gas is nearly over; then if, on the addition of
more of the hypochlorite, the effervescence is renewed, it shows
that there was not enough of the decomposing liquor first em-
ployed, and more must be added from time to time till no further

determining the amount of Urea in the Urinary Secretion. 389

evolution of gas is produced; and the quantity of hypochlorite
used to arrive at this point indicates the amount necessary. I
found by experiment that one grain of urea requires somewhere
about half a fluid ounce of the ordinary sode chlorinatz liquor
for its complete decomposition. The amount of mercury em-
ployed requires some little attention. It should, as a general
rule, be never less than the volume of gas produced; for if the
volume of gas evolved is more than that of the mercury used, it
will be more than that of the solution of salt, and therefore some
of the mixture of urine and hypochlorite will be forced out of
the tube before it is completely decomposed, and consequently
some of the gas will be lost; so that if this occurs, we must
repeat the experiment, using either a larger quantity of mercury
if our tube will allow, or diminishing the quantity of urine em-
ployed.

It might be supposed on first sight that this method would be
liable to the following source of error, viz. that some of the gas
would be evolved and lost during the pouring in of the hypo-
chlorite ; but this is not the case, as several seconds elapse before
there is any apparent reaction or evolution of gas on mixing the
hypochlorite with the urine, and there is therefore full time to
perform the experiment without any loss of the gas. I have
also ascertained that the acid reaction of the urme does not
affect my method. I should observe that this new method, like
all the others known, is not perfectly free from some slight
sources of error ; the principal one being, that ammonia, if it
exists in the urine, gives rise to nitrogen gas, and therefore
increases the apparent amount of urea; but the same objection
holds equally in Liebig’s and Ragsky’s methods, which are per-
haps the two most accurate at present known. Uric acid also is
similarly affected by the hypochlorite ; but it and ammonia ordi-
narily occur in such small proportion in urine, that the error
produced from these substances would be but trifling, and is
partly corrected by taking the calculated quantity of nitrogen,
which is, as I have shown, something more than that obtamed
from a certain quantity of urea by direct experiment.

In cases where ammonia or uric acid occurs in more than ordi-
nary quantity, these substances must be separated by the usual
means employed before having recourse to my method.

I should think that gently heating the urine with a certain
quantity of baryta water as long as the odour of ammonia is
disengaged, and then filtering the solution, as recommended by
Liebig, for the separation of ammonia before applying his method
(see the Quarterly Journal of the Chemical Society, vol. vi. p. 30),
would effect the object very easily, and separate not only the am-
monia, but also the greater part, if not all of the uric acid present.

390 =The Rev. 8. Haughton’s Account of Experiments to

There is one other source of error which may arise, and which
can be easily avoided. It is the following: that if a solution of
the hypochlorite of soda alone, or standing over mercury, be
exposed to the light for several days, it will very gradually evolve
a minute quantity of oxygen, which shows that in determming
urea we should not allow the experiment to go on for too long a
time; but if left for a day, or even two, it will scarcely make any
appreciable effect on the quantity of gas evolved in testing for
urea.

The reaction which appears to take place in the process seems
to be the following. The hypochlorite of soda acting on the
urea gives rise to the formation of carbonic acid, water, and
chloride of sodium, together with the evolution of nitrogen gas.
Thus

Urea. 3 Hypochlorite soda.
C2. H4. N2. 02. + 8(Cl, O . NaO) =2C0?+ 4HO +8C1.Na.+ N*.

The nitrogen is evolved and the carbonic acid is absorbed by
some of the hypochlorite of soda in excess, for I find that this
salt absorbs carbonic acid very quickly without evolving any
other gas; and I failed in several experiments to detect the
smallest portion of carbonic acid in the gas produced by acting
on urea, though I have always noticed the presence of a very
minute quantity of oxygen in the nitrogen gas. These appear
from my experiments to be the changes produced ; but this part
of the subject [have not as yet minutely examined, and my expe-
riments have hitherto been made on healthy urine; I have, how-
ever, ascertained that several of the substances found in urine
during disease, as for example, sugar, albumen, bile, and excess
of urinary colouring matter, produce scarcely any effect on the
results obtained by this new method of determining the quan-
tity of urea in the urinary secretion.

LXI. Account of Experiments to determine the Velocities of the
Rifle Bullets commonly used. By the Rev. Samu, Haveuton*.

fy Betge following experiments were made for the purpose of
ascertaining the reason of the alleged inferiority of the

belted spherical bullet, used with the two-grooved rifle, as com-
pared with elongated bullets of different kinds. The guns com-
pared are the following :—

1. A two-grooved rifle; length 31°50 inches; diameter 0°66
inch; one turn in 4 feet.

2. The regulation Minié rifle; length 39 inches; diameter
0°69 inch.

* Communicated by the Author.

determine the Velocities of the Rifle Bullets commonly used. 391

3. Police carbine ; length 28°75 inches; diameter 0°66 inch.
With these guns were used the following bullets :—
Two-groove rifle—1. A Minié bullet, provided with two pro-
jections corresponding to the grooves of the rifle, without ‘ culot ;’
weight 697 grs. 2. A sugarloaf bullet, fired point foremost ;
weight 669°75 grs. 3. A belted, spherical bullet; weight 482
rs.
i Minié rifle—The regulation Minié bullet, with ‘culot ;’
weight 744 grs.

Carbine.—Spherical bullet ; weight 391 grs.

The method employed to determine the velocity of the bullets
was Robins’ ballistic pendulum; and the same quantity of the
best gunpowder (40 grs.) was employed with each gun and bullet.

For the erection of the pendulum, and most efficient assistance
afforded in the conduct of the experiments, I am indebted to
Mr. Joseph Harris, of the firm of Truloch and Son, Dawson
Street, Dublin, without whose aid I should have been unable to
bring these experiments to a successful issue.

I shall first give the details of the experiments, and then men-
tion the principal deductions which may be obtamed from them.

The formula used in calculating the velocity is the following*:

gla

oer afe comet: fhe? deen)
where v = velocity of bullet in feet per second.
T = time of oscillation of pendulum.
a = distance of centre of gravity from axis of suspension.
a = ratio of circumference of a circle to its diameter.
f = distance from axis of gun attached to pendulum to
axis of suspension.
c = distance from axis of suspension to point of attach-

ment of tape, by which the recoil is measured.
n = ratio of weight of pendulum to weight of bullet.
b = chord of arc of recoil, measured by tape.

The two-groove rifle barrel being firmly strapped with iron
plates to the pendulum, the constants of the pendulum were
carefully determined, and were as follows :—
g=32'195 feet. @=3:14159 Weight of pend. =36°75 lbs.
T=1°29 sec. f=75°25 in.
a=57°39 in. c= 78°25 in.

From these data we obtain from (1)

v=0'12894xnb. 2 2 2... (2)

~

The following tables contain the results of the experiments

* Poisson, Trailé de Mécanique, vol. ii. p. 119.

392 The Rev. 8S. Haughten’s Account of Experiments to

made on the recoil of the two-groove rifle with the three bullets
already described.

Table I.—Minié Bullet.

No. n. b. v.

in. ft.
r. 369 17°50 833
2. bares 18-25 869
sc wool ec anecds 17°25 821
es Poae ee ces 18-50 881
PER ey. tee gs 18-00 857
[eegey wy] ROP re one 6 17:25 $21

Mean velocity = 847 feet per second.
Mean quantity of motion measured in avoirdupois pounds
moving through 1 foot per second = 84:33 lbs.

Table I1.—Sugarloaf Bullet.

Mean velocity = 863°7 feet.
Mean quantity of motion = 82°63 lbs.

Table IIJ.—Belted Bullet.

in. ft.
1 533 14:75 1013°3
Bilt Nah has aceee 15°37 1055-9
SHUR ene SERRE 14:75 1013-3
Real lit Seeees 15°12 1038-7
Deter tats eae 14:37 987-2

Mean velocity = 1021-68.
Mean quantity of motion = 70°39 lbs.

The Minié regulation-rifle barrel having been attached to the ~
pendulum, formula (1) was calculated with the following con-
stants, and the results are given in Table IV.

The carbine barrel was then attached to the pendulum and
the recoil observed. The results are contained in Table V.

determine the Velocities of the Rifle Bullets commonly used. 393

g=32'195 feet. Weight of pend. and Minié barrel =56-50\bs.

a= 1°29 sec. Weight of pend. and carbine barrel = 55°25 lbs.
a=61°75 in.

a= 3'14159.
f= TAGs.
c=77 in.
From these constants we find

$=0TABI6 ee

Table [V.—Minié Regulation Rifle.

No. n. b. v.
in. ft.
1 531 12-25 931-90
Da raaale hy wees 11°50 874-85
A pS i 12°12 922-39
ee nee wsteons 12°12 922'39
Ste TLD) Ce ke 11°75 893°86

Mean velocity =909°08 feet.
Mean quantity of motion =96°63 lbs.

Table V.—Carbine.

No. Ne b. ve
in. ft.
| 989 9-00 1275-21
ge i Wheeere 9°12 1292:92
Sia We A ccees 8-75 1239-78
ree ee ere 8-62 1222-07

Mean velocity = 1257-49 feet.
Mean quantity of motion = 70:24 lbs.

If we assume that the force developed by the explosion of the
powder, diminished by the friction of the barrel, is constant, it
is easy to deduce the following expression for the velocity

v=Oxa/S, a De CREE cer (A)

in which Q denotes a constant depending on the quantity of
powder and diameter of the rifle, s the length of the barrel, and
m the weight of the bullet.

Taking the velocity of the belted bullet, 1021-7 feet, as our

datum, and calculating the velocities of the others from (4), we
find

394 The Rey. S. Haughton’s Account of Experiments to

Table VI.—Theoretical and observed Velocities.

Calculated. Observed. Differenee.

ft. ft. ft.
Minié bullet in two-groove rifle...) 849-0 847-0 + 20
Sugarloaf........-.ss.secssceseseessees 866-8 863°7 + 31
Regulation Minié .........se0see00+ 915-0 909:08 | + 5:92

Carbine bullet.........ssesesescsseeee 1083-7 1257-49 | —173°79

The agreement of these results is very striking in the case of
the rifles, and proves the truth of equation (4) ; and the disagree-
ment in the case of the carbine proves, as might be expected,
that the force of the powder is greater in the smooth bore than
in the rifle. From the preceding results we may assert with
confidence, that the velocity with which a bullet is propelled from
arifle by a given charge of powder depends mainly on the weight
of the bullet and the length of the barrel, varying inversely as the
square root of the former, and directly as the square root of the
latter*.

The following experiments were made to ascertain the resist-
ance of the air to bullets of different figures and weights. The
bullets were fired at 80 feet distance, from the two-groove rifle
into the pendulum, and the velocities calculated from formula (1).

The constants of the pendulum were—

g=82°195 feet. @=3'14159.
T=1-29 sec. c=77 in.
a=60 in. Weight of pend. after Exprs. = 51-20 lbs.

Table VII.—Minié Bullet at 80 feet.

No. Ne b. dé v

in. in. ft.
1. 501 11-75 72:50 836°42
2. 502 11°87 71:00 864-54
3. 503 11-12 72:00 80025
4, 504 11:00 69:00 827-68
5. 505 11:25 71:00 824-28
6. 507 11°37 69:00 860°61

Mean velocity = 835-62 feet.
Mean quantity of motion = 83°22 lbs.

* The former of these laws was proved by Mr. Hutton to hold for smooth
bore guns of large size, but the latter did not hold true for his experiments.
I suppose the reason it is nearer the truth in rifles is on account of the
increased friction in the latter.

determine the Velocities of the Rifle Bullets commonly used. 395
Table VIII.—Sugarloaf Bullet at 80 feet.

No. | n. b. Ps v.

in. in. ft.
1. 516 11:50 71-00 860-95
2. 517 11:37 71-00 852°87
3. 518 11-25 71-00 845:50
4, 519 10-62 67°75 838-05
5. 520 11:12 69-00 863-27

Mean velocity = 852°13 feet.
Mean quantity of motion = 81°53 lbs.

Table IX.—Belted Bullet at 80 feet.

No. nN. b. fe v.
in. in. ft.
1 731 8-62 71:00 912-13
2. 732 $25 69:00 901-58
3. 734 8-62 69-00 944-59
4, 735 7°62 66-00 874-15
5 736 7:75 67:00 876-99

Mean velocity = 901°88 feet.
Mean quantity of motion = 62°23 lbs.

Collecting the preceding results into one table, we obtam—

Table X.
4 peed - Quantity of | Quantity of
Velocity at | Velocity at | “motion at | motion at
muzzle. 80 feet.
on ft. ft. Ibs. Ibs.
Minié bullet (two-grooye).) 847 835-62 84-33 83-22
Minié bullet (regulation)... 909-08 | ......... 96°63
Sugarloaf bullet ............) 863-7 852-13 82°63 81:53
Belted bullet. ............++«| 1021-68 901°88 70:39 62°23

Carbine bullet............... 1257-49 [\, seapenere 70°24

From this table it appears—

Ist. That the quantity of motion communicated by a given
quantity of powder to the Minié bullet, discharged from the regu-
lation rifle, is greater than the quantity of motion possessed by
any of the other bullets; this result being due partly to the
greater weight of the bullet, and partly to the greater length of
the rifle.

2nd. That the quantity of motion communicated to the belted
bullet, discharged from the two-groove or Brunswick rifle, is less
than that possessed by the other rifle bullets, this result being
due to the lesser weight of the belted bullet.

396 Prof. Faraday on Subterraneous Electro-telegraph Wires.

3rd. That the quantity of motion communicated to the carbine
bullet is equal to that possessed by the belted rifle bullet, although
the carbine is shorter and its bullet lighter; this result bemg
due to the greater friction of the bullet in the rifle barrel.

4th. That in traversing 80 feet of still air, the quantity of
motion of the Minié bullet is diminished by ,,th; of the sugar-
loaf bullet, by 7;th; and of the belted bullet, by aig th; the
remarkable inferiority of the belted bullet being principally due
to its shape, which appears to have been contrived so as to cause
the maximum amount of resistance to its passage through the air.

5th. That the large stock of Brunswick two-groove rifles con-
structed for the use of the British rifle service, might be made as
useful as the regulation Minié rifles, by adapting to them a bul-
let of the proper weight, shaped like the Minié bullet, provided
with two projections at the side to fit the grooves of the rifle,
and used with or without the iron ‘culot’ of the French bullets.

The length of barrel of the Brunswick rifle is 30 inches, and
the size of bore is 0°704 inch. Calculating from these data the
weight of the ball which should be used with this rifle in order
to produce the same quantity of motion as in the Minié regulation
rifle, I find it to be 967 grs., or 71 balls to the pound. If Minié
balls of this weight were constructed to suit the bore of the
Brunswick rifle, and provided with projections or wings to fit the
grooves, they would be as efficient as the regulation rifles of 39
inches in length.

Trinity College, Dublin,

May 12, 1854.

LXII. On Subterraneous Electro-telegraph Wires.
By Professor Farapvay, F.R.S. &e.

To the Editors of the Philosophical Magazine and Journal.

Royal Institution,
GENTLEMEN, April 28, 1854.

A COMMUNICATION has been just brought to my notice
on some remarkable phenomena presented by subter-
raneous electro-telegraph wires observed and described by M.
Werner Siemens of Berlin, in a communication bearing date
April 15, 1850. They are the same phenomena as those shown
to me by Mr. Latimer Clarke, and used in my communication
(inserted in your Magazine for March 1854, p. 197) as: illustra-
tions of the truth of my ancient views of the nature of insulation,
induction and conduction. It is only justice that I should refer
to them; and I think they are so interesting, that you will be
willing to reprint the account, very slightly abbreviated, which I

Prof. Faraday on Subterraneous Electro-telegraph Wires. 397

send you; the effects are produced with wires covered with gutta
percha and laid in the earth.

« A very remarkable phenomenon is constantly observed on
long, well-insulated telegraphic lines. Suppose one extremity,
B, of the wire be insulated, and the other, A, be connected
with one pole of a battery of which the other touches the earth ;
at the instant of communication a brief current is observed in
the near parts of the wire in the same direction as the instanta-
neous current which would exist if the extremity B were con-
nected with the earth; on lines of perfect insulation no trace of
this current remains. Suddenly replacing, through the action
of a commutator, the battery by an earth conductor, a second
instantaneous current is obtamed of an intensity nearly equal to
the first, but in the inverse direction. Finally, breaking the
communication of A with the battery and also the earth, so as
to insulate this extremity, and uniting the end B at the same
instant with the ground, an instantaneous current is observed
nearly equal in intensity to the former, and this time in the
same direction as the first, 7. e. as the continuous current of the
battery. This last experiment can only be made on a double
subterranean line having the two extremities A and B at the
same station. One might at first sight suppose these phzno-
mena to be due to secondary polarities developed on the wire,
but many facts oppose such a conclusion. 1. The phenomena
are more striking as the wire is better msulated. 2. The cur-
rents are much more brief than those due to secondary polarities.
3. Their intensity is proportional to the force of the battery, and
independent of the intensity of any derived current that may
occur in consequence of imperfect insulation ; it follows that the
intensity of the instantaneous currents can greatly surpass the
maximum intensity which secondary currents in the same cir-
euit could acquire. 4. Finally, the intensity of the mstanta-
neous currents is proportional to the length of the wire, whilst
an inverse relation ought to occur if the currents were due to
secondary polarities.

“The phenomena are easily comprehended if we recall the
beautiful experiment by which Volta furnished the most striking
proof of the identity of galvanism and electricity. He showed
that on communicating one of the ends of his pile with the earth,
and the other with the interior of a non-insulated Leyden bat-
tery, the battery was charged in an instant of time to a degree
proportional to the force of the pile. At the same time an instan-
taneous current was observed in the conductor between the pile
and the battery, which, according to Ritter, had all the proper-
ties of an ordinary current. Now it is evident that the subter-
raneous wire with its insulating covering may be assimilated

398 The Rev. B. Powell on some Experiments

exactly to an immense Leyden battery: the glass of the jars
represents the gutta percha; the internal coating is the surface
of the copper wire; the external surface is the moistened earth.
To form an idea of the capacity of this new kind of battery, we
have only to remember that the surface of the wire is equal to
7 square metres per kilometre. Making such a wire communicate
by one of its ends with a pile, of which the other extremity is in
contact with the earth, whilst the other extremity of the wire is
insulated, must cause the wire to take a charge, of the same
character and tension as that of the pole of the pile touched by
it :—that is what came to pass in the first of the mstantaneous
currents described. In Volta’s experiment, on breaking the
communication between the pole and the battery and connecting
the two coatings of the latter by a conductor, an ordinary dis-
charge was obtained:—to this discharge correspond the two
instantaneous currents which are observed in opposite directions
at the two extremities of the charged wire, on communicating
their extremities with the earth, to the exclusion of the pile. It
will be understood, also, that the first instantaneous current,
namely, that which is connected with the charge of the wire,
ought to be equally produced, though of a lower intensity, even
when the other extremity of the wire is in communication with
the earth. The instantaneous current then precedes the conti-
nuous current, or, if the statement be preferred, is added to it at
the first moment. This instantaneous current has an intensity
much greater than that of the continuous current ; doubtless
because in the act of charging the wire, the electricity in going
to the different points of the wire passes through paths so much
the shorter as the points to be charged are nearer to the pile.”
The above is from the Annales de Chimie, 1850, vol. xxix.
p. 398, &e.
I am, Gentlemen,
Your very faithful Servant,
M. Farapay.

LXIII. Note on some Experiments on Rotatory Motion,
By the Rev. Baven Powe 11, M.d., V.P.R.S. &c.

To the Editors of the Philosophical Magazine and Journal.

GENTLEMEN,
BSERVING in a late Number some account of Professor
Magnus’s experiments, I conceive it may not be uninter-
esting to your readers to give the few following particulars rela-
tive to the closely-allied experiments of M. Fessel, and the dis-
cussions which have taken place respecting them, more especially

on Rotatory Motion. 399

as they will form an appropriate introduction to the beautiful
researches on the subject which Professor Wheatstone has very
recently brought before the Royal Society.

In Poggendorff’s Annalen, Sept. 1853, No. 9, Prof. Pliicker
has given some account of the rotatory machine of M. Fessel.
Notwithstanding the luminous theoretical researches on the sub-
ject in the papers of MM. Poinsot and Poisson, he observes that
experimental illustration of it is still desirable, and mentions
that M. Fessel, “formerly teacher in the provincial school of
industry, now by the kindness or unkindness of circumstances
led to exercise his art as a mechanician,” has constructed an ap-
paratus, which, from the way in which it presents the phzno-
mena to the eye, excites surprise even in those who are acquainted
with the principle.

The instrument will be understood at once from the sketch
annexed.

The dise A, loaded
round its circumfer-
ence, can be spun
rapidly on the axis B,
whose ends rest in the
ring CG, itself jomed by
a hinge at D to the
axis bent at a night
angle at E, the ver-
tical part of which
turns freely in the «
tube F, supported on
the stand G.

The observed phenomenon is this. When the disc is set in
rapid rotation about B, the whole begins also to revolve bodily
round the vertical axis E, and this is easily seen to be due to
the action of gravitation tending to bring down the ring C
about D.

M. Fessel adds, in a note, an account of the way in which he
accidentally discovered the principle, by rotating a heavy wheel
on one end of an axis. And M. Pliicker proposed to him to
modify the construction by attaching the ring C to one end of a
bar carrying a sliding counterpoise, and capable of revolving
about a pivot; and this, he says, answered admirably.

“The apparatus thus improved,” Prof. Pliicker continues,
“gave the previous phenomena, but at the same time others
immediately appeared.

“Tf the dise rotated in a vertical plane, then the axis moved
itself round towards the opposite direction in the horizontal
plane. If the first rotatory motion gradually lost, the second

400 Note on some Experiments on Rotatory Motion.

gained. If the second’ motion was quickened by an extraneous
force, then the ring with the disc appeared to become Lighter,
since it rose up; on the contrary, by a retardation of the hori-
zontal movement, it seemed to become heavier, or sank. With
the same rotatory velocity of the disc, the horizontal rotation
increased or diminished according as the force of gravitation was
increased or diminished ; as, for example, if the rotating dise be
made of soft iron, it rises or sinks if we precede or follow it with
a magnet, thereby accelerating or retarding the horizontal revo-
lution.”

He also points out the analogy of this apparatus to that of
Bonenberger. In the Annalen, No. 10 (Oct. 1853), the editor
adds “one more word on the Fessel rotatory machine,” in which
he confirms the account of its inventor by his own experience of
its use, and adds an explanation of its principle, as he observes,
for the sake of those who may wish to understand it without
going into calculation.

The general nature of this explanation may be stated thus:
the disc being supposed to rotate in a vertical plane, or the axis
B horizontal; then at any point in its circumference the motion
in the direction of the tangent may be conceived resolved into a
horizontal and a vertical component, the direction of motion’in™
each being of course opposed at opposite parts of the ecirele. —

Now if the ring C be free to be acted on by gravitation, or
the axis B tend to become inclined, or the rotation to take place
in an oblique plane, the horizontal components will not change
their direction, but the vertical components will; and will no:,
longer have their direction in the plane of the disc: they will
consequently cause it to change its plane, or exert a lateral force,
and thus give the whole a motion of revolution round the vertical
axis E. But while this takes place, the tendency to inclination
of the axis B is counteracted, and the opposing lateral effects of
the horizontal components result in the rotation of the dise
round its horizontal axis in a vertical plane. .

M. Fessel has added a small slider below D, which, when)
pushed out, supports the ring C against gravitation ; and in this
case there is no revolution round the vertical. M. Poggendorff,
also observes, that if the rotatory part of the instrument, be
balanced about a point near D, either on a pivot, or suspended
by a string with a counterpoise, the same results are more satis-
factorily exhibited.

He observes that the same principles apply to the explanation
of Prof. Magnus’s remarkable experiment with two discs rotating
at opposite ends of a suspended axis. (See his paper translated
in Taylor’s Foreign Scientific Memoirs, Part III. May 1853,
p- 229.)

The Attraction of Ellipsoids considered geometrically. 401

Finally, the author observes with regard to the application of
the Bonenberger apparatus which he had first pointed out (Az-
nalen, June 1851, p. 308), “ M. Person has lately made the just
remark (Comptes Rendus, 1852, Sept. 27 and Oct. 18), that in
order to withdraw it completely from the influence of the rota-
tion of the earth, the apparatus must be placed with its principal
axis parallel to the earth’s axis; since (in strictness) the motion
of the whole apparatus round an axis, which does not coincide
with one of the three axes contained in it, must alter the rotation
of the ball.”

And he suggests, that in the experiment the whole should be
furnished with the means of rapid rotation about a vertical axis,
and so that the rotatory axis of the ball might have any required
position given to it with respect to the new axis.

LXIV. The Attraction of Ellipsoids considered geometrically. By
Marruew Couns, B.A., Senior Moderator in Mathematics
and Physics, and Bishop Law’s Mathematical Prizeman, Trin.
Coll. Dublin; Professor of Mathematics in the Mechanics’
Institute, Liverpool*.

tice attraction of an ellipsoid A on a point P on its surface,

or within it in a direction perpendicular to one of its
principal planes B, is proportional to the distance of the attracted
point P from that principal plane.

1. When P is on the surface. Draw PP! a chord of A perpen-
dicular to B, and through P and P’ draw planes parallel to B
cutting the principal axis CC’ perpendicularly in p and p'; then
describe through p and p! an ellipsoid a, concentric, similar, and
similarly placed to A, and its attraction on p will be equal to the
attraction of A on P in a direction perpendicular to B.

For through PP! draw two planes E, F containing a very small
angle, and through pp! draw two planes e, f parallel to the former ;
then let a cone of revolution, whose axis is PP’ and vertex P cut
E, F along the straight lines PE, PE’, PF, PF’, and let another
such cone very close to the former, and having the same axis
and vertex, also cut EH, F along PE, PE’, PF, PE’, and through
p draw, in the planes e, f, the straight lines pe pe! pf pf' and
pe, pe, Pf, pf, respectively parallel to the foregomg ; then as the
sections of the two similar ellipsoids A and a by the parallel
planes E, ¢ are necessarily similar ellipses, and as the chord PP!

arallel to an axis (CC’) of the greater ellipse is = to the homo-
Seserie axis pp! of the less, .*. by Airy’s Tract on the Figure of the
Earth, Props. 2 and 3, PE + PE! =pe+pe'; and .*. by Airy’s 4th

* Communicated by the Author.
Phil. Mag, 8. 4, Vol. 7. No, 47, June 1854. . 2E

402 Prof. Collins on the Aitraction of Ellipsoids

proposition, the sum of the attractions exerted on P along PP’
by the two small pyramids PEFE,F,, PE'E’E!F’, is equal to the
sum of the attractions exerted on p along pp! by the two corre-
sponding small pyramids pefe,f,, pe'f'e',f',, since the solid angles
of the four pyramids are all equal to each other: and since there
are obviously as many pairs of pyramids in the double wedge PP’E
FE'F’ as there are corresponding pairs of pyramids (whose solid <s
are also equal to those of the former) in the double wedge pp'efelf',
and as, moreover, each double wedge of A has a corresponding
double wedge of a, .*. the whole attraction of a on p is equal to
the attraction of A on P along PP’; but since a is similar to A,
the attraction of a on p: attraction of A on C : : pp!(=PP’) : CC!
(Principia, Prop, 87, Cor. 1, Book 1); and so the attraction of

A on P perpendicular to B, which was proved equal to attraction
ipp!

of a on p, is ... = 2,5, attraction of A on C, which, since A

2CC
and CC! are constant, oc 1 PP’, which is the distance of P from B.

2. The general equation of surfaces of the second order being

deb herpey Be+Cy+Dz+ Ez?+ &c. =0, the equation of the

jametral plane bisecting all chords parallel to the straight line
xz=mz and y=nz is known to be md,6+nd,p+d,.p=0, which,
on account of not containing the absolute constant term A, indi-
eates that if any straight lime ABBA! cuts two surfaces of the
second order whose equations differ only in the constant terms,
the intercepts AB, A'B! will be equal, smce the chords AA’, BB!
are bisected in the same point by the diametral plane conjugate
to it, which plane is the same for both surfaces. Now the equa-
tions of two ellipsoids which are concentric, similar, and simi-
larly placed, differ only in the absolute constant terms, and
.. the intercepts AB, A'B! of any straight line ABB'A! cutting
two such ellipsoids are equal; and hence it follows that a shell
or couch bounded by two concentric, similar, and similary placed
ellipsoidal surfaces, exerts no attraction on a point P situated
anywhere within it, or on its terior surface. See Airy’s Tract
on the Figure of the Karth, Prop. 12, or the Principia, Prop. 70,
and Prop. 91, Cor. 3, Book 1.

8. When P is within the ellipsoid A, we have then only to
describe through P another ellipsoid A’, concentric, similar, and
similarly situated to A; and since the shell between A and A!
exerts no attraction on P, as was just proved, .*. the whole attrac-
tion of A on P is the same as that of A! on P: then, as in 1,
draw PP’ a chord of A! perpendicular to B, and through P and
P’ draw planes parallel to B cutting the principal axis CC’ per-
pendicularly in p and p', and then describe through p and p!
another ellipsoid a, concentric, similar, and similarly placed to
A or A’; and by 1, the attraction of A (or A’) on P perpendi-

considered geometrically. 403

cularly to B is equal to the whole attraction of a on p, and
1

—— 700) ™ attraction of A on C, which, as already observed,

octPP’, which is the distance of P (now supposed within A)

from B.

4, The preceding proposition shows that the attraction of an
ellipsoid on any point on its surface, or within it, can be got at
once from the attraction of the same ellipsoid on a point placed
at the extremity-of an axis; and this latter attraction is found
and reduced to elliptic functions as follows.

Let O be the centre, and OA=a, OB=b, OC =c the semiaxes,
and let the attracted point C be the vertex, and CO the axis of a
cone of revolution D whose semiangle is 0, and let 0+d6 be the
semiangle of another such cone E very close to D, and having
the same vertex and axis, and let O be the common vertex of two
other cones D! and E! parallel to D-and E. Conceive the por-
tion of the ellipsoid between D and E to be divided into elemen-
tary pyramids by planes passing through CO; let f be the length
of a side of one of these little pyramids, which is a chord of the
ellipsoid and a side of D; and let g be the parallel side of D',
which is a radius of the ellipsoid; and let f' and g! be the pro-
jections of f and g upon ce, and let » be the small angle between
two consecutive f§ (or g*); then the attraction of the little
pyramid whose side is f on its vertex C is =fw.d6 (see Airy’s
Tract on the Figure of the Earth, Prop. 4), and .-. its component

12
along CO is =f'w.d0, .*. =2c x Lona; but 5 =% said

4
component = = g’o.d0,". = he 2 g? cos? Ow .d@; now 39°w

is the area on D! included between the two consecutive g’, and
the sum of all such elements is the entire surface of D! which we
shall still name D!; .:. the attraction of the slice of the ellipsoid
4D! cos? 6. d6
c
the projection of D! on the plane of ab is obviously an ellipse
whose area D" is =D! sin 8; let 7 and 7’ be the sides of D! (radii
of the ellipsoid) lying in the planes of ca and cb, then the semi-
axes of I)" are plainly the projections of r and ", or 7 sin @ and

between D and E upon C along CO is = Now

7 sin @; and .*. D! =r’ sin? 0, and so D=>, “. =orr'sin 6;
and so the attraction of the slice on C along CO is
= cos? O sin 8. dé.

Now i e08e. 2. xin® q.. a 1 cos?@~ sin?é .
id = ce ae gl? pew c ¢ b2 F |

2E2

404 Prof. Collins on the Attraction of Ellipsoids
and .*. the differential of the required attraction on C is

4crabe cos? 6 sin. 6 . dO :
(c? sin? 6 + a? cos? 6)3(c? sin? 6 + 5? cos? 6)?”

by putting cos@=u, or tan?@=v, this expression, given by
Poisson (Mécanique, vol. i. p. 190), becomes transformed into

4crabcu*du

(2+e—2. uv) (e&+P—e. ue)
or
2ac. dv

(1 +v)A/ (1+1)(14+5») (1450)

5. Now supposing a> b>c, let OA! and OB! portions of OA
and OB be the semiaxes of the focal ellipse whose plane is perpen-
dicular to OC, then OA? =a?—c? and OB? =b?—c’; let OQ be
perpendicular to the tangent PTQ, which touches this ellipse in
T and meets OA! at the point P; let < OPT=¢, and

p?=c? + (b?—c*)u?=c? + OB” cos? 8
and

p?=c? + (a®@—c*)u?=c* + OA” cos? 0;
OP
OA!

OA!

and if the point P be taken such that £ or OP = cored

then the equation
OA? cos ?A'OQ + OB” cos? BOQ=0Q?;
.. =OP? sin? d gives

2
(a? —c*) sin*h + (b?—c?)cos* = -

fae ——
: 2 (c? + 6?—c? . cos @) sin®¢,

which gives
(a?—c?) cos? 0= cos? $(c? + a?—c? . cos? 6),
t
i, e. OA’? cos? O=p? cos* g, and .*. cos p= “ cos; and since

! !
OP= ae pie = (c?+ OB? cos? @)*,

OA! -} : :
°. Pp=d,OP= = (c?-+ OB” cos? 6) * x OB’? cos 6 sin 8. dé

' ore
oa. cos @ sin 6.d0.

considered geometrically, 405

Let PP’ be perpendicular to the consecutive tangent from p,

then pP!=Pp cos nd :

OF ae

C

cos? @sin@.dé:

but the attraction of the slice of the ellipsoid between D and E
on C along CO was found above
__ 4arabe cos? 6 sin 0. dO
Satin CHRP,
And, moreover, as P'p is obviously =d. B/TP,
. =d(B/TP— const BTA),
i. e, =d(TP—are TA’); .*. the attraction of the slice on C is

Arrabc* Atrabe*
= 0A?.OB? MPETH Sees et EP are TA);
and .*. the attraction of the whole ellipsoid on C is
bs ne j
where P, and T, mene the pedtvaGte positions of P and T corre-
sponding to @=0; and since by construction

!
OP ea eat (c? +22, cos? 0)*,

.“. when 9=0, op,=< OA’, and
a(b?—c2) a2(b?—c?)
die ere) Suehe abe
6. Hence, also, the differential of the ellipsoid’s attraction on B,
i. e. the attraction on B along BO of a slice of the ellipsoid com-

prised between two cones of revolution whose vertex is B and
axis BO, and semiangles are 0 and 0+ 4d0, is

@: Arrabe cos? 6 sin@ . dO

~ (8? sin? 0+ c2 cos? 6)3(b? sin? 6 + a® cos? 6)4
eth Arrabcu* . du i

~ (PB? u2)4(b2 + a2 —B u2)h?

‘ i

406 Prof. Collins on the Attraction of Ellipsoids

where, as before, w= cos @. Now to represent this geometrically,
let OA” and OC’ portions of OA, OC be the semiaxes of the focal
hyperbola whose plane is perpendicular to OB, then OA!?= a?— 6?
and OC?=c?—t?= —(?—c?)=—OB”. And putting now
p?=b?— (b?—c?) cos? @ and p’”=b?+ (a?—4”) cos* @, and taking
the point P on the primary semiaxis OA", so that aon f. So
that as p<, P will lie between O and A"; then drawing PT
touching the hyperbola in T, we find, as before, mutatis mutandis,
the whole attraction of the ellipsoid on B

Arrab?c
— (@—P)(P—e) > 4 (T,P,—are TA”) >

P, and T, being now, as before, the ultimate positions of P and
T corresponding to 2=0. So that, as before, OP,=;0A", and

ab?—ce2
ee PT= ee

The whole attraction on A cannot be similarly represented,
because there is no real focal conic perpendicular to OA; but

exactly the same as before.

the equation = + a + = =Arrp, discovered by the late ingenious

Professor MacCullagh, will then serve to find A; where p denotes
the density, and A, B, C denote the whole attractions of the ellip-
soid on the points A, B, C.

7. Let a, 6, e be the semiaxes of a homogeneous fluid ellipsoid,
and A, B, C the attractions on points at the ends of a, 3, ¢,
caused partly by the eliipsoid’s own attractions on its parts, and
partly by the centrifugal force of revolution about an axis (2c),
or by the action of an extraneous force directed towards its centre,
and oc distance from the centre, then the ellipsoid will preserve
its shape if Aa=Bb=Ce.

For then the whole forces acting on any point ayz of the mass

a4

in directions parallel to a, 6, ¢ will obviously be ca 4, an

and dividing these by Aa=Bdb=Ce, they are as , and ai

2) iy
but when the point yz is on the surface, these last are as the
cosines of the angles that the normal at the point #yz makes

; ray 2 fat yy ez!
with the axes, as is evident from the equation ( atRetse 1)
c

of the tangent plane. Thus the components of the force acting
on the point wyz at the surface are as the cosines of the angles
that the normal at this point makes with the axis, .*, the direc-
tion of the resultant foree coincides with the normal or perpen-

considered geometrically. 407

dicular to the surface itself, which is the condition necessary for
equilibrium.

The general formula dy=p(Xdx+ Ydy + Zdz) obyiously be-
comes in this case

Az B C. adz ydy zdz
pap (Paes Hays Siz) =—pha Se +S),

b
2,2 42
and .°. pao (4 + _ ae a at the surface p= 0, and
Bh a: 8
0 ad Be By pe and .*. the pressure at any point

2 2
ayz of the mass is = P “(1 _ - — . —- 2) ,whichatthe centre,

where z=y=z=0, becomes ene ; and shows, moreover, that the

surface of any ellipsoid concentric, similar, and similarly placed
to the given one, is a surface de niveau, on every part of which
the pressure is the same; and since A, B, C are obviously op,
. the pressure at any given point of the mass ocp*. See the
Principia, Prop. 20, Book 3; M¢Laurin’s De Causa Phys. flux
et reflux Maris, Prop. 1; Airy’s Tract on the Figure of the
Earth, Props. 14, 15 and 16.

8. Let R andr be the radii of two homogeneous concentric
globes, A and a the attractions of each on a point on the surface

of the other, then ee = a whatever be the law of attraction as

a function of the distance.

For let O be their common centre, OrR a radius meeting
them at r and R, be a chord of the less parallel to OR; pro-
duce Ob, Oc to meet the large globe’s surface at B,C, then
BC will be parallel to be or to OR; and if 6 describe any
little figure 0! on the surface of 7, it is evident B will describe a
similar figure B! on the surface of R; and the areas 8, s of the
normal sections of the cylinders C and ¢ simultaneously described
by BC, be will obviously be to each other as B!: d!; .*. as R*:7?.
Now by Euclid (Prop. 4, Book 1) Br=0R and Cr=cR; .*. by
Airy’s Tract on the Figure of the Earth, Prop. 18 (generalized),
attraction of cylinder C on the point r along 7O : attraction of
cylinder ¢ on point R along RO::S:s::R*:7?; and as this
fixed proportion holds true for each corresponding pair of cylin-
ders, .*. by taking their sums we shall still have A: a@:: R*:7°.
See Poisson’s Mécanique, vol. 1. p. 201.

Mechanics’ Institute, Liverpool,
April 19, 1854.

[408 J
LXV. On the Theory of Groups, as depending on the Symbolic
Equation @°=1.—Part I.* By A. Cayury, Esq.t

| Bxecaahony the symbols
LL Sie 2 3,

such that L being any symbol of the system,
L“'L, L7'M, L'N,..

d, a, B, Sa

Then, in the first place, M being any other symbol of the
system, M~'L, M~'M, M“'N, . . will be the same group 1, a, 8..
In fact, the system L, M, N .. may be written L, Le, L@..; and
if e.g. M=La, N=LA, then

M7'N=(La)7*L8=e7'LL8=a7'B,

which belongs to the group 1, 4, B..

Next it may be shown that

|) a hac ys

is a group, although not in general the same group as 1, a, B..
In fact, writing M=La, N=LA, &c., the symbols just written
down are

is the group

Thos Lalee, at, ok

and we have e.g. LeL7’. L@L7'=LeSL-'=LyL"", where y
belongs to the group 1, a, 8.

The system L, M, N .. may be termed a group-holding system,
or simply a holder; and with reference to the two groups to
which it gives rise, may be said to hold on the nearer side
the group L7'L,L7'M, L7’N .., and to hold on the further
side the group LL™'’, LM~’, LN~’.. Suppose that these
groups are one and the same group 1, a, @.., the system
L, M, N.. is in this case termed a symmetrical holder, and in
reference to the last-mentioned group is said to hold such group
symmetrically. It is evident that the symmetrical holder
L, M,N... may be expressed indifferently and at pleasure in
either of the two forms L, La, L@.. and L, aL, BL; i. e. we
may say that the group is convertible with any symbol L of the
holder, and that the group operating upon, or operated upon, by
a symbol 1. of the holder produces the holder. We may also

* See January Number, p. 40.
+ Communicated by the Author.

Mr. A, Cayley on the Theory of Groups. 409

say that the holder operated upon by, or operating upon, a sym-
bol « of the group reproduces the holder.
Suppose now that the group

I, a, B, Y é, €, oe .
can be divided into a series of symmetrical holders of the smaller
eroup
1; a, B aS.*

The former group is said to be a multiple of the latter group,
and the latter group to be a submultiple of the former group.
Thus considering the two different forms of a group of six, and
first the form

iF a, a, Yo Y% yo? (a =1, y=1, ay=ryx),

the group of six is a-multiple of the group of three, 1, «, «? (in
fact, 1, a, a and y, ya, ya® are each of them a symmetrical
holder of the group 1, a, #*) ; and so in like manner the group
of six is a multiple of the group of two, 1, y (in fact, 1, y and
a, ary, and a, ay are each a symmetrical holder of the group 1, +).
There would not, in a case such as the one in question, be any
harm in speaking of the group of six as the product of the two
groups 1, a, a? and 1, y, but upon the whole it is, I think,
better to dispense with the expression.
Considering, secondly, the other form of a group of six, viz.

1, @, a, y, ye, ye? (a=, V=l1, ay=ye*).

Here the group of six is a multiple of the group of three, 1, «, «2
(in fact, as before, 1, a, a and y, ya, ya* are each a symmetrical
holder of the group 1, a, a, since, as regards y, ye, yx, we have
(7, ye*)=¥(2, «, «)=(1, a, a)y). But the group of six is
not a multiple of any group of two whatever; in fact, besides
the group 1, y itself, there is not any symmetrical holder of this
group 1, y; and so, in like manner, with respect to the other
groups of two, 1, ye and 1, ya*. The group of three, 1, a, «2, is
therefore, in the present case, the only submultiple of the group
of six.

It may be remarked, that if there be any number of symme-
trical holders of the same group, 1, «, 8, . . then any one of these
holders bears to the aggregate of the holders a relation such as
the submultiple of a group bears to such group: it is proper to
notice that the aggregate of the holders is not of necessity itself
a holder.

[ 410 ]

LXVI. On the Cartesian Barometer.
By Wrt11am Roxsuren, M.D.*

OON after the discovery of the variations in height of the
barometer, Descartes proposed the following mode of ren-
dering them more conspicuous, almost as much so as they are
in one filled with water alone. He suggested that two tubes
should be joined to the opposite ends of a short wide cylinder so
as to form one straight tube, which, being closed at one end,
was to be filled with pure water and mercury in such proportions
as to allow of the two fluids at all pressures meetmg im the
cylinder. In this, the Cartesian barometer, the pressure of the
atmosphere is balanced by the water and mercury conjoitly, but
the variations of pressure are indicated chiefly by movements of
the water, as the level of the mercury varies little im consequence
of the large area of the cylinder. The movements of the water
and mercury are to each other inversely as the areas of the tube
and cylinder. The scale is that of the common barometer en-
larged as in the wheel barometer; when, therefore, the move-
ments are said to amount to so many hundredths of an inch, it
is to be understood as meaning that they are equal in value to
that height of mercury. The scale can be enlarged so as to
render movements of ;,dth of an inch visible to the unassisted
eye.

"The only records of this instrument that I have seen, state
that the air contained in the water is given off when the pressure
is removed, and so renders its indications incorrect ; also that
this imperfection is irremediable. This depression, amounting
in one year, in my first experiment, to only ‘02 of an inch, has
led me to suppose that the depression which caused the plan to
be set aside was owing to the force of vapour, which was not so
well understood at that time as at present ; and as many varia-
tions of pressure are easily seen in this barometer, which would
escape notice in the mercurial one, and if not attended to give
rise to error, I think it will prove a valuable addition to a stand-
ard barometer, though never a substitute for one.

In hopes of getting rid of the air, and of lessening the cor-
rection required for the force of vapour, I tried several fluids
in place of pure water. Among these was oil of turpentine ;
this caused a rapid evolution of gas and blackening of the mer-
cury, and depressing the column several inches in a few minutes.
A saturated solution of muriate of soda seemed at first more suc-
cessful, but in a short time the column became depressed, and
this depression continuing to increase at a regular rate, the tube

* Communicated by the Author.

Dr. Roxburgh on the Cartesian Barometer. 411

was emptied, when it was found that the salt having crystallized
between the mercury and the glass, had so allowed the air to
enter.

A solution of muriate of lime, not being crystallizable, was
next tried; and this seems to stand best, as yet having sunk in
21 years only 03 of an inch, the greater part of this depression
having occurred in the first few months, giving rise to the sur-
mise that the air which has caused it was left in at the time of
filling, and has not crept in since. The addition of the salt to
the water, besides removing to a great extent the air, has the
effect of diminishing the correction required for the force of
vapour; the last named solution has its boiling-point at 234° F.,
and, as has been shown by experiments, the tension of vapour
from water and watery solutions of salts is the same at an equal
number of degrees below their boiling-points, the correction to
be applied is lessened to that of pure water 22° lower than the
observed temperature. This correction, which is to be added,
and that for the expansion of the fluids, which is to be subtracted,
thus nearly neutralizing each other at low temperatures, I have
applied by means of a moveable scale, in the same way as is used
in the sympiesometer. Among the slighter variations shown by
this barometer, may be mentioned the oscillations during a gale
of wind; these are quite as conspicuous in this barometer as they
were observed by Professor Daniell in the water barometer,
amounting frequently to 0°03, and once to 0-4 of an inch ;
they vary in duration from 5 to 7 seconds; they begin with a
short, quick rise, followed by a slower and much greater descent,
and then a return to the point of rest, which is much nearer the
top than the bottom of the oscillation. Previously to a gale of
wind, the column descends by jerks and with irregular rapidity ;
but on one occasion, on which no wind followed for two days,
the column fell without the slightest jerk more than half an inch ;
there was, however, a heavy and long-continued fall of rain.
During heavy and sudden showers the column rises, and falls
again on the cessation of the shower; on one occasion the rise
was ‘02 of an inch. In a room with a fire, with door and win-
dow shut, the column is lower than when the window is open ;
the difference is usually ‘005, but with a good fire ‘01 of an inch.
The last two cases are very likely to give rise to error, and the
better the barometer the greater will be the error.

38 Gloucester Place, Portman Square.

Paley

LXVII. Theory of the Electric Residue in the Leyden Jar.
By R. Koutravscu.

[Continued from p. 320.]

§ 6.

ig is clear the question may arise, whether the cause of the

residue does not reside in the uncoated part of the jar or
rim, inasmuch as a part of the electricity may move about be-
tween the glass and the varnish.

It appears plausible, that if such a movement occurred, it
would do so gradually and in tolerable quantity, for the electri-
city pushed on to the rim on the insulated side would cause the
opposite electricity to follow it up the other side, and condensa-
tion might take place as well on the insulator as under the
coatings. At any rate the decision of this question does not
appear superfluous.

If the rim of the jar actually influences the residue, then this
influence ought to be more considerable, in proportion to the
total charge, not only when the rim is broader (for it might be
assumed that the movement was never very extensive), but parti-
cularly when the periphery of the coating is greater in compari-
son to its superficial area. Hence if, with an equal area of
coating, the rim be reduced to a minimum, the residue ought to
be reduced also.

The neck of the bottle which was described in § 1, under 4,
and to which the tables 4, b', 6" belong, had a circumference of
5:7 centims., and an interior surface of 11-4 square centims.,
whilst the part of the interior surface of the same bottle which
was covered with mercury contained 275 square centims.

The metallic coating of the Franklin’s plate, which was de-
scribed under ¢ in § 1, and to which the tables c, c', and c”
belong, formed a rectangle whose sides measured 15 and 25
centims., whose periphery therefore was 80 centims., and area
375 square centims., whilst the surface of the uncoated rim
amounted to 296 square centims.

If now we compare the tables 5" and c" of § 4, we shall find
that in 864 seconds, and with a primitive charge of 0°5559, the
Franklin’s plate had concealed the residue 0°1060; whilst the
bottle 4 in 935 seconds, and with a primitive charge of 1:4968,
produced the residue 04522, which is equivalent to a residue of
about 0°4445 in 864 seconds, i.e. in the same time as the
Franklin’s plate. Hence, notwithstanding the unequal propor-
tions of rim, the residue amounted to 0°297 of the original
charge in the bottle, and 0°190, in the Franklin’s plate. The
proportion will be about the same if we compare these residues

On the Theory of the Electric Residue in the Leyden Jar. 413

with the quantities of electricity Q; which were present in both
cases after 864 seconds. The bottle had a residue equal to 0°321
of this quantity, the plate 0:213. The whole hypothesis, how-
ever, is destroyed the moment we consider that according to the
above almost half as much electricity ought at this time to be
collected on the neck of the bottle, whose area is 114 square
centims., as on the 275 square centims. of the whole interior
coating ; a proportion which will be still more unreasonable if
we consider the state of the bottle at its final discharge after the
lapse of 5370 seconds.

So much is clear, therefore,—the rim, if not entirely without,
has at any rate a very small influence on the residue.

§ 7.

In reference to this production of a residue, an influence has
also been ascribed to the cement with which the coating of tin-
foil is usually attached to the glass. Without entering into
theoretical considerations as to whether this influence must not
in every case be a very secondary one, we shall here mention a
few facts merely.

In the Franklin’s plate c, the sine-electrometer was connected
with the metallic coating, which rests immediately on the glass
without the interposition of any cement. If we consider the
tables a", b", and ce’, and reduce the numbers of the two last to
the time 680, 7. e. when the jar a, coated internally and exter-
nally with tinfoil, was discharged, the metallic coating certainly
appears to possess an advantage over this jar a, as well as over
the bottle 4, filled with mercury ; for in 680 seconds the propor-
tion of the concealed residue to the charge imparted at the com-
mencement is

a. b. c.
0:297, 0:281, 0:187,
and the proportion of the same to the total quantity Q,, which
was still present after 680 seconds, is

a. b. Cc.
0°324, 0:299, 0:204.

According to this, the jar a, with the cement, furnished the
greatest residue, and that with the metallic coating the least.

Apart from the fact that this difference may be attributed to
the kinds of glass and to their thicknesses, the following experi-
ment is particularly worthy of notice.

Before the bottle 4, filled with mereury, was used for the
examination of the residue, it had been already filled with acidu-
lated water and examined, after having previously been washed
out with a solution of caustic potash, in order that the surface

414 M. R. Kohlrausch’s Theory of the

might be completely moistened. If analogous to the influence
of cements, one would expect that in this case the proportions of
the residues would be different from those when, between the
surfaces of the mercury and the glass, a thin and dry stratum of
air must have been interposed; for it may be here remarked,
that before pouring in the well-dried mercury, the glass had
been washed with distilled water, heated, and sucked dry by
means of a glass tube. No difference however was observable in
these two cases; the residues formed in the same time had just
the same magnitude, as may be seen from the following num-
bers, which refer to a case where, at both times, the charge at
first imparted had been allowed to stand for 606 seconds :—

is Los Collected residue.
Water . . 1:49 1:03 0:30
Mercury. . ‘1°49 1°05 0:29

Here, indeed, the mercury appears to have the advantage,
though the circumstance may probably be attributed to the
areat difficulty of constructing two Leyden jars with exactly
equal magnitudes of coating, the one with an adhering, and the
other with a non-adhering liquid.

The question as to the influence of the cement would be
answered most decidedly by coating a glass plate on both sides
with amalgam, and after examination replacing it by tinfoil. It
will, we think, be difficult to find any measurable difference.

§ 8.

The magnitude of the residue appears to depend most essen-
tially upon the thickness of the glass, the thicker glass pro-
ducing the greater residue. The experiment about to be cited
on this point is not quite decisive, for the amount of residue, of
course, depends very much upon the kind of glass; and the two
bottles which were compared should, on this account, have been
blown from the same mass of glass, and cooled in exactly the
same manner. Although this was not the case, yet the interesting
result which was obtained may here be mentioned.

The mean thickness of glass of the bottle 4, so often referred
to, was 2°7 millims. This was found from the absolute and spe-
cific gravities, as well as from direct measurements. The imterior
surface, so far as it can be considered as coating, has been
already stated to contain 230 square centims.

Another bottle, e, of thin glass had a mean thickness of 0:82
millims., and an imterior surface of 230 square centims.

Both bottles were converted into Leyden jars by filling, and
surrounding them with acidulated water; and by the methods
described in Appendix I. and II., it was found that the quan-

Electric Residue in the Leyden Jar. 415

tities of electricity in these bottles b and e, at equal tensions on
their knobs, had the proportion 508 : 1303.

To both jars a charge was momentarily imparted, which was
immediately indicated by the sine-electrometer as 1'4941; and
on discharging the jars after an interval of 9 minutes, the
residues 0°3052 and 6:1180 were collected.

The proportion of the mean densities of electricity in the two
bottles b and e, if they possess equal tensions at their knobs, is

508 | 1303

275 230’

The proportion of the quantities of electricity concealed as
residues in 6 and e is

508 x 0°3052 : 1303 x 0°1180, or 1:0°991.

We see, therefore, that the jar, whieh, compared with a second,
has three times the thickness of glass, produces the same quantity
of electricity as residue, although the mean density is three times
less.

Exactly similar phenomena were observed with two Franklin’s
plates of unequal thicknesses.

§ 9.

For a moment let us subject the usual explanation of the
electric residue to a stricter examination.

According to it, the pressure of the electricity imparted to the
one coating, and the strong attraction of the opposite electricity
on the other coating, gradually force a part of the same into the
glass. Either the whole of the electricity which thus penetrates
the glass, or only the part which lies deepest, is prevented from
sharing in the discharge, and gradually makes its appearance
afterwards; for although the mutual attraction between the
electricities in the glass has not ceased, the reappearance of the
same may be accounted for, without attributing a repulsive force
to the substance of the glass, by the changed conditions of equi-
librium after the discharge, and particularly by the cessation of
the pressure of the imparted electricity on the corresponding
coating.

This explanation, however, necessarily involves the assump-
tion, that the potential of the electricity which remains in the
glass after discharging is zero for every point within the insu-
lated coating. This results from the following conclusions :—

Let us suppose the insulated coating to have received a posi-
tive charge: then, according to hypothesis, there will be a stra-
tum of positive electricity in the glass under it, and a stratum of
negative electricity on the other side, The whole or a part of

or 1:38:07.

416 M..\R. Kohlrausch’s Theory of the

the electricities which have thus penetrated the glass have not
been able to participate in the discharge; and. their motion
within the insulator 1s so slow, that for the short duration ofa
discharge they may be considered as motionless. Notwith-
standing the quickness of the discharge, however, a state of
equilibrium must establish itself, because, during the same, both
coatings have been connected by conductors with the earth. If,
therefore, the potential of the electricity which has remained in
the glass be not zero for a point on the coating formerly charged
with positive electricity, 2. e. should the actions of these electrical.
masses on the said point not annul one another, then electricity,
from some source or other, must have accumulated on the con-
ducting parts of the system, in this instance on the coatings, in
order to have produced equilibrium with that in the glass, As
to the nature of this latent electricity, as it is called, it is evident,
in Franklin’s plate for instance, that negative electricity will now
be present on the side of the coating which is turned towards
the glass, 7. e. which is next to the positive stratum in the glass,
and which had a positive charge imparted to it at the commences:
ment. For masmuch as a so-called excess of electricity was at
first present on this coating, it cannot be assumed that the elec-
tricity which has here penetrated the glass is less than that on
the other side, and consequently the conclusion is forced upon
us, that the action of this positive stratum on its adjacent coating
will be greater than that exerted on it by the more distant nega-
tive stratum. This unequal action can only be met by assuming
a suitable quantity of negative electricity on the inner side of one
of the two coatings, As it would be without meaning, however,
to place this quantity, a greater in this case, on the side of the
glass which is occupied by negative electricity, it must. be con-
ceived as being present on the other side, i. e. under the coating
which was formerly positive.

On the other hand, however, it is evident, if this state of things
had actually existed, that the residue capable of being collected
on the remsulated side would but be equal to the difference of
the positive electricity within the glass and the latent, negative
electricity under the coating. But experiment shows that’ the
collected residue approaches more to an equality with the loss of
disposable charge, the less the electricity which is lost in the air,
that is to say, the shorter the time during which the plate is
allowed to remain charged ; so that there can be no doubt that
these two quantities would be exactly equal could all loss of
electricity be avoided.

Thus it appears to be proved that the potential of the elec-
tricity, which during the discharge remained in the glass, must
be assumed as zero in reference to the interior of the coating

Electric Residue in the Leyden Jar. 417

under examination ; an assumption which, from the ecommence-
ment, appears requisite on account of the proportionality existing
Oe the disposable charge and the tension on the knob of
the jar.

Further, the following facts ought to be considered :—

1. If after discharging the Franklin’s plate it be turned up-
side down, the sine-electrometer being connected with the coating
formerly in connexion with the earth, whilst the side which be-
fore was positive is now connected with the earth, a residue of
negative electricity will be obtained.

2. If a Franklin’s plate, with exactly equal sides, had equal
and opposite charges imparted to them, then the quantities
which penetrate the glass would certainly be exactly equal, in
reference to arrangement and magnitude. In such a case, how-
ever, the potential before referred to would certainly not be zero.
But how little this state must differ from that which ensues
when, with a thin plate, the one coating remains connected with
the earth! And, bearing fact 1 in mind, is it not probable that
the residue would be obtained with exactly equal and oppositely
charged sides ?

3. Why, with equal charge of coating, does the thicker Frank-
lin’s plate give the greater residue ?

4, Why does not the residue continually increase the longer
the jar remains charged, or why does it approach a definite
maximum dependent upon the magnitude of the charge?

These are points which after some consideration cause legiti-
mate doubts concerning the truth of the whole hypothesis which
regards the electricity as penetrating the glass; and in any case
they authorize the attempt here made to substitute another hy-
pothesis which will solve all these problems. Departing, there-
fore, from the usual method of representation, let us seek some-
thing new.

§ 10.

In this investigation it will be best, for the present, entirely to
neglect the electricity lost in the air, which although unavoidable
is still accidental, and to deduce the phenomena of the residue,
in their purity, from the facts already recorded, so as to arrive
at certain conclusions about them. The phznomenon presents
itself in the following manner :—

A quantity Q of electricity is imparted to the insulated coating
of the Franklin’s plate, whereby a certain state of equilibrium is
established. This state of equilibrium next gradually changes,
so that a part r of Q enters into a new state, in which it can no
longer act on the electroscopic tension ; and this part 7 increases,
at first quickly, but afterwards more and more slowly, towards a

Phil. Mag. 8. 4. Vol. 7, No, 47, June 1854. 2F

418 M. R. Kohlrausch’s Theory of the

certain limit R, which it only reaches asymptotically. For the
same jar this R is a definite part of Q, so that we have R=pQ.
Exactly the same part 7, too, is prevented from sharing in the
discharge ; but as soon as Q—r has been discharged, it imme-
diately begins to convert itself into disposable charge, and the
conversion, becoming slower and slower, advances towards a cer-
tain limit, where we have again a certain part 7’ =pr, which has
no electroscopic action, and cannot be discharged.

Instead of considering the part r of the charge (which we have
called the concealed residue) as, according to the old hypothesis,
placed in a kind of prison which it cannot leave, either person-
ally or with respect to its action, we are still free to assume
that it is placed underneath the coating, or, in other words, on
the surface of the glass, though subject to an influence formed
after, and indeed by the charge imparted to the plate. In order
to correspond to the phenomena, the magnitude of this new in-
fluence must be a function not only of Q, but also of the time;
for after imparting the charge to the jar, it must gradually
come into existence, increase to a limit dependent upon Q, and
finally, after withdrawing the disposable charge, gradually de-
crease.

To the inquiry, what this something may be which can exert
an influence on the electricity, the only answer compatible with
the present state of science is, that this something must again be
electricity. As to where it resides, the fact that it continues
when both coatings are in connexion with the earth, suggests the
assumption that its residence is in the insulator, 7. e. the glass
itself. Lastly, it may be asked, how is it possible that this some-
thing, this electricity within the glass, can detain positive elec-
tricity under the one coating, and negative under the other?
We may reply, that the fact of opposite sides having opposite
actions shows that the glass has assumed a polarity ; and finally,
if, for the sake of greater clearness, we regard similar conditions,
e. g. the magnetic moment, as represented by Gauss in his Inten-
sitas, &c., the indefinite notion will be immediately converted into
a definite one.

The definition of magnetic moment, as given by Gauss on the
13th page of his celebrated memoir under the hypothesis of a
magnetic fluid, can be applied verbatim to the electric fluid of
every body, so that the explanations of most electrical phzno-
mena might be based upon the electric moment thus defined.
Clearly, however, a new expression would be thus unnecessarily
introduced for that which, under the terms electromotive force
and potential, has already received its name in science. This
expression would be particularly inappropriate for conductors, in
which the electric moment will be changed by every external in-

Electric Residue in the Leyden Jar. 419

fluence, whereas under the magnetic moment of a magnet the
idea of stability is associated, or at any rate the idea that within
pretty large limits the magnetic moment is essentially indepen-
dent of external influences. Nevertheless, for the condition and
mode of action of a body in whose interior the electric fluids are
unequally distributed, and are only capable of extremely slow
motion or of none at all, we have no better term, inasmuch as the
condition itself is hypothetical, and hence it may not be deemed
inappropriate to introduce the expression “ electric moment.”

Let us conceive the possibility of the neutral electricity within
an insulator being by some cause or other so separated, that

a. under the surface on the one side a stratum of positive,
and on the opposite side a stratum of negative electricity formed
itself; or that

b. a series of such alternate parallel strata were arranged be-
hind each other; or that

c. in every ultimate particle the separation took place in the
same direction, but that the electricity could not pass from one
particle to another; and if we now further assume that such a
state can exist after the cause which produced this separation of
the electricities has ceased to act, then such an insulator could
exercise an action, 7. e. an electromotive force, on an external
point.

d. A fourth condition is also conceivable; for instance, in
every particle of the glass the electricities may be naturally sepa-
rated, but in general without external action (for exactly the same
reason as the molecular currents in soft iron are so, that is, be-
cause their own condition of equilibrium does not permit it) ; but,
through some influence or other, the several particles, together
with the fixed electricities clinging to them, may be so turned
more or less in the same direction, that in this case also the sum
of the distances of all positive particies from any plane may be
different from the sum of the distances of all negative particles
from the same. In reference to some one plane, the difference
of these sums may, under certain circumstances, be greatest ;
and in reference to this plane, or to a normal erected on it, the
electric moment of the body will be a maximum, and the normal
may be called an electric axis.

By way of example, let us suppose a glass plate with its prin-
cipal faces y and A symmetrically placed between two parallel
surfaces, ¢. gy. metallic plates, which we will call G and H, and
which we will suppose to be charged with opposite electricities,
then one of the four states a, b, c, or d may be conceived gra-
dually to take place in the glass. Through the electromotive
force of these metallic plates on the interior of the glass, the
natural electricities might there be separated, so that, if G be

2F2

420 M. R. Kohlrausch’s Theory of the

positive, the negative particles in the glass will now lie nearer
to G than the positive ones. We will, for the present, assume
that no electricity has passed over immediately from the plates
to the glass surfaces ; let them now be withdrawn, then the glass
will possess an electric moment, whose axis, if we thus call the
direction of greatest action, is normal to the surfaces g and h of
the glass, and it will therefore exert an independent electro-
motive force on any point without these surfaces; so that if a
positively electric particle be now presented to the side g, where
the positive plate G formerly stood, it will be attracted, if a nega~
tive it will be repelled: on the other side, 4, the opposite of this
will take place. Ifwe replace the plate G, which has in the
mean time been discharged, the potential of the electricities
within the glass cannot be zero in reference to a point within
the metallic plate ; on the contrary, the electricities in the latter
will be separated, so that to restore equilibrium positive elec-
tricity will continue to pass towards the side turned to the glass,
and negative to flow away (supposing the plate not to be insu-
lated), until the potential of the total electricity in reference to
the interior of the metallic plate has become zero. Thus on the
plate G a quantity of positive electricity, distributed in a deter-
minate manner, is now rendered latent. If, instead of the above,
we had replaced the plate H after discharging it and connecting
it with the earth, then an exactly opposite condition would have
been produced, #. e. negative electricity would have been rendered
latent on H. If G, however, be first placed in the manner above
explained, so that on it the distribution necessary to produce
equilibrium can establish itself, then this equilibrium will no
longer exist if H be placed in its old position ; for to the action
of the glass plate g is now added the similar action of the nega-
tive electricity collected on H; hence it is clear, that, if G and
H are connected with the earth, more electricity must be now
present on the sides turned towards the glass than when each
plate singly stood near the glass, in order that the potential of
the whole electricity, in reference to every point within the me-
tallic plates, may be zero.

On the whole, it is clear that nothing will be altered if the
plates are brought into contact with the glass; but if so, then
we have a Franklin’s plate which is charged and incapable of
being discharged. ‘The attraction of the electric moment in the
glass is at the same time substituted for the pressure of the
free electricity on the exterior surface of the coating m a com-
monly charged jar, which free electricity determines the discharge.
Although it is not here asserted that the distribution of the elec-
tricities on the coatings of a plate charged by an electric moment
of the glass is the same as that on the coatings of a plate charged

Electric Residue in the Leyden Jar. 421

in the usual manner, it is nevertheless evident that some such
distribution causing equilibrium is possible.

If we now insulate one of the coatings, and impart to it a fresh
quantity of the same kind of electricity as it already possesses, so
that on the other side a corresponding quantity of the opposite
kind of electricity will be rendered latent, then these new elec-
tricities will distribute themselves as if the plate had not been
charged. The principle of statics is here applicable, according
to which, if a system of forces are in equilibrium, they will still
remain so when another system, itself in equilibrium, is added
to the former. Hence the tension, at any point of the insulated
coating, will be proportional to the quantity of electricity newly
imparted, and the latter only will constitute the disposable
charge.

It is only necessary to invert the process of reasoning here
given, in order to see that the phenomena of the electric residue
are contained in what has been said.

At the commencement, let everything about the Franklin’s
plate be non-electric. Next, let a quantity Q of positive elec-
tricity be imparted to the insulated coating, whereby a certain
distribution on both coatings will ensue. An electric moment
will now gradually establish itself in the glass, which, by its
reaction, will produce a new distribution in such a manner that
Q will be divided into two parts, belonging to two different sy-
stems of equilibrium, and consequently superposed upon one
another. The quantity 7 which must be present underneath the
insulated coating, in order that the newly created action of the
electric moment in the glass may be held in equilibrium, is so
withdrawn from Q that only the quantity Q—r=L can distri-
bute itself over the coating in the form of disposable charge as
at the commencement, and only this quantity can be discharged.

Before long we shall assume a cause for the slow production
of the electric moment, and why it can but reach a certain maxi-
mum, 7=pQ, dependent upon the quantity of electricity Q. At
present thus much is clear: in our representation of the phzeno-
menon we must be prepared to admit, not only that the dis-
posable part L of the charge, but also that the electromotive
force of the whole quantity Q or L+r of electricity on the sur-
faces of the glass has an influence on the formation of the elec-
tric moment, for there is no reason why im this respect one
part should be inactive. We attribute the same cause to the
slow disappearance of the electric moment as to its slow forma-
tion.

In this manner we may easily explain why, after discharging
the plate, the concealed residue 7 continues to convert itself again
into disposable charge until the part 7! of it which still remains

422 M. R. Kohlrausch’s Theory of the

has attamed its maximum pr. In a similar manner it may be
shown why, when a part of the charge is suddenly withdrawn,
the disposable charge either sinks more slowly than before, or
stands, or increases according to the proportion which the residue
already formed bears to the quantity of electricity which still
remains.

Hitherto we have neglected all loss of electricity. In prac-
tice, where such a loss always occurs, the residue cannot, of
course, attain any fixed maximum, and the condition of the plate
at the time ¢ will depend upon the proportion existing between
the velocity with which the residue is formed and that of the loss
of electricity in the air. From this point of view all the pha-
nomena may be explained, although, it is true, such explanations
will first acquire the requisite amount of certamty when the law
of the residue-curve in § 11 shall have been deduced.

We have yet to discuss the cause which generates in the glass
a kind of resistance to the influence of the external electricity, or,
in other words, to the formation of the electric residue. For
this purpose we must dive still deeper into the sea of hypothesis;
and although this may appear hazardous when we reflect that
we know nothing either of the essential nature of electricity or
of the law of molecular forces, yet such an attempt may be per-
missible provided we confine ourselves to perfectly definite ideas,
and obtain a result from our speculations.

Two essentially different suppositions may be made as to the
slow formation of the residue, or rather of the electric moment
which causes it :—

1. Electricity actually passes from one particle of glass to
another, without, however, being able to break through the sur-
faces of the giass in order to combine with the opposite electri-
cities there situated; so that a condition will ensue exactly the
opposite of that before assumed for the penetration of the glass
by the external electricities. After the discharge, the electricities
in the glass combine in the same manner in which they were
separated. Then the slowness of the formation of a residue may
be attributed to the great difficulty of motion for the electricity
in the interior of a bad conductor ; the limit of the moment, how-
ever, to the circumstance, that within the glass, and on the coat-
ings, such a distribution has at length taken place, that the
potential of the whole electricity, in reference to every point
within the glass, has become constant. The question, whether
the possibility of such a distribution can be proved or not, must
remain an open one. Although in this hypothesis the assump-
tion of a quite peculiar force opposed to the electricity in the
surface appears strange, it might still be admitted if everything
else fitted well, for the surface is quite different from the interior,

Electric Residue in the Leyden Jar. 423

Tt would be difficult, however, by this method of representation,
to show why the thicker plate should furnish the greater residue.
Let us therefore consider the second.

2. Electricity does not pass from one particle of glass to
another, but either separates itself on each particle, as in the
case of magnets, or was already separated on these particles, and
the latter, together with the electricities clinging to them, are
turned. In the first hypothesis, a force must be attributed to
the several particles of glass, which only permits the separation,
and the corresponding motion, to take place gradually, and which
resists it the more the longer it is prolonged, so that the limit of
the residue has herein its cause. Although in this case the
molecular forces might play the part of resistance, inasmuch as
with the separation of the electricities a simultaneous displace-
ment of the atoms might be connected, yet it is clear that a more
natural explanation of the slow change of condition, and of the
maximum results from the last hypothesis, 7. e. that the atoms
are turned, and that the molecular forces, as in bends, torsions,
&e., resist this turning. And if we consider the phenomena of
elasticity as a whole, we shall soon find a circumstance which
has great similarity with the one here mentioned, and which in
its way stands single. This is the so-called elastic secondary
action, which has been made known to us by W. Weber*, through
his researches on silken threads (the only complete research
which exists on this subject).

Probably all bodies possess this elastic secondary action ; at
least glass certainly does sot. The phenomenon may be thus
characterized :—

When the form of a body is changed through the influence of
some external force, without however surpassing the limits of
perfect elasticity, the new state of equilibrium within the body,
and hence also the change of form, will require time to establish
itself; will, in fact, establish itself asymptotically after an inde-
finitely long period. At first the form changes quickly, after-
wards very slowly. The subsequent slow change has been de-
signated the “elastic secondary action,” although the latter, as
W. Weber remarks, is separated by no natural limit from the
quicker change, for the velocity of the change of form does not
anywhere decrease discontinuously. If the external action which
produced the change of form cease, the body will assume the
same series of forms, only in inverse order and with an opposite
velocity ; only after a long time (indefinitely long) will it per-
fectly recover its original form, In these wonderful phenomena,
where the velocity of the moved mass bears no proportion to the

* De fili bombycini vi elastica. Gottinge, 1841.
+ Poggendorti’s Annalen, vol. lx. p. 393.

424. M. R.. Kohlrausch’s Theory of the

moving force, it is, to use an image, as if, whilst. the resistance
to the attack increased each moment, it. became tired out by the
duration, of the same, so that gradually it became actually ex-
hausted.

In a graphic representation, if we take the time calculated
from the moment when the external influence commenced as
abscissa, and the magnitudes of the changes of form as ordinates,
then to different bodies differently shaped curves will correspond.
Whilst with steel the curve, rising at first almost perpendicularly,
will then appear bent almost at right angles and have a pretty
sharp corner, we find that Weber’s curve for the silken thread rises
much more slowly, and approaches its asymptote at a greater
inclination ; and lastly, if we bear in mind the properties of a
spiral coil of wax, the tapers cut from which, when placed on
our Christmas trees, grew always crooked again, there can be no
longer a doubt that the curve in question possesses but a gradual
curvature, and rises quickly but for a very short period of time.

According to this, if no loss of electricity took place, there is
nothing in the form of the residue curve (R, Plate VI. fig. 2),
which was produced in the bottle 4, that is contradictory to the
hypothesis which regards the molecular forces of the glass as the
cause of the slow formation of the residue and of its limit; in-
asmuch as they, in this case as well as in that of elasticity, per-
mit but a slow realization of any changes in the state of equili-
brium.

Although, it must be confessed, this explanation by means of
a mechanical, resisting force rests ultimately on only one analo-
gous action, we nevertheless abide by this manner of representa-
tion, on account of the difficulty there is to find a parallel case
for the peculiar pheenomenon of so slow a motion in comparison
to the acting forces.

By this manner of representing the electric moment of the
glass, where throughout the interior of the same the electricity
on every particle is brought into a different position, we can now
explain why the thicker plate furnishes a greater residue. In
order to see this, however, we must again make a small digression.

The question is virtually this. We have two thin, insulated,
metallic plates, which, being charged equally with opposite elec-
tricities, are placed parallel and at a very small distance from
one another in comparison to their own dimensions. Will the
action of these plates on a point between them decrease very
much when tie distance between them is increased, e. g. doubled,
but still remains very small in comparison to their dimensions ?

Here, where a strict calculation appears inadmissible, a few
indications may serve to decide the question.

Let a plane, circular surface with the radius R be conceived,

Electric Residue in the Leyden Jar. 425

charged everywhere with electricity of the same density, ‘so that
the unit of surface contains the quantity e. At a distance a from
the plane, and in the normal erected in the centre of the circle,
conceive the quantity e! of electricity to be placed; required the
action, 2. e. the electromotive force exerted on this point, in the
direction of the normal, by the whole electricity on the circular
surface.

An element of surface, which is at the distance r from the
centre, and makes an angle ¢ with any radius assumed as fixed,
can be expressed by rdrd¢ ; and, neglecting the sign, the action
of the same on e! in the direction of the normal is

edardrdd

(@+7")3°
Integrating this, first between the limits 6=0 and 6=27, and
then between the limits 7=0 and r=R, it becomes

2eela ( fer ea Saat )
pay earn” + R27"

If we here set R = , we obtain the following theorem :—
An indefinite plane, charged uniformly with electricity, attracts
or repels an electric particle e' with the same force, 2zree', what-
ever may be its finite distance from the same.

If R be not infinite, and a=mR, the formula becomes

Ym+1—m

Ym+1 —
In order to see then what influence the distance of the point
from the plane of the circle has, we select for m the numerical

values 0'l and 0:01. Then for the electric action we have the
numbers

2ee ar

2ee'mr . 0°9046 and eer .0°9901.

We see, therefore, that so long as the distance is small in
comparison to the radius, the electric action is almost indepen-
dent of the distance ; for stance, when the distance is increased
ten times, the action is only one-tenth of what it was before.

On the other hand, we may conclude that the action exerted
on e! is principally due to the parts of the plane which lie nearest
it. For example, if a remains the same, whilst for R we set at
one time 10a, and then 100a, we obtain for the second action
searcely one-tenth more than for the first.

These numbers show, that if the electricities were uniformly
distributed over the coatings of a Franklin’s plate, and if, whilst
their quantity remained the same, the thickness of the glass
were increased, the electric moment would also be augmented,
because more particles of glass would now be acted upon. But

426 Prof. Connell on the Voltaic Decomposition of Water.

the electricity actually is distributed almost uniformly over a
great portion of the Franklin’s plate ; and near the rim, where
this is not the case, the principal action on the poimts in the
glass must be ascribed to the neighbouring parts of the coatings,
so that the conclusions before made will be approximately true*.
Herefrom we learn, not only that with the same quantity of
charge a greater electric moment is produced with the thicker
glass, but also that at different places the action on the glass will
be different ; so that the manner in which the concealed residue
produced by the electric moment disposes itself, cannot be very
different from the distribution of the electricity which is pro-
duced underneath the coating by the disposable charge.

What has here been said of the Franklin’s plate may, with
modifications suited to their forms, be on the whole repeated of
the common Leyden jar; hence it would appear that the phe-
nomena of the electric residue may be completely explained by
the electric moment, particularly under the hypothesis that the
change in the glass affects its individual particles only.

[To be continued. |

LXVIII. On the Voltaic Decomposition of Water. By A. Con-
NELL, F.R.S.E., Professor of Chemistry in the University of
St. Andrewst.

iT HAVE learned during the last few months, from that excel-

lent French periodical the Cosmos, that some experiments
lately made by M. Leon Foucault and others, showing a differ-
ence in the amount of hydrogen evolved from two negative poles
placed in water by the same galvanic current under certain
varieties of circumstances, particularly where the current passed
through acidulated water and distilled water, have been attract-
ing a good deal of attention, and that the appearances have
been thought by M. Foucault and some others to lead to some

* The above must not be confounded with the fact, that the thinner the
glass is, the stronger the charge which the same constant source of elec-
tricity will impart to the Franklin’s plate. Here, as in the condenser, the
theorem holds, that if the distances between the plates are very small in
comparison to their magnitude, their charges are almost inversely propor-
tional to their distances asunder; a result which agrees very beautifully
with the calculations of Clausius in his able memoir “ On the distribution
of electricity on a single, very thin plate, and on the two coatings of a
Franklin’s plate” (Poggendorff’s Annalen, vol. Ixxxvi. p. 198, x.). What
we have considered above is a quite different question to the one, how
much electricity must be present on plates, at different distances asunder,
in order that its potential, in reference to their interior, may everywhere
be exactly the same.

+ Communicated by the Author,

Prof. Connell on the Voltaic Decomposition of Water. 427

restriction of Mr. Faraday’s beautiful law of the detinite de-
composing agency of the galvanic current. It may not per-
haps be altogether superfluous to state, that it is now nearly
fourteen years since I read to the Chemical Section of the
British Scientific Association at Glasgow a notice of experi-
ments to precisely the same effect, although from which assu-
redly no inference was drawn affecting Mr. Faraday’s law ; and
which notice was afterwards inserted, in January 1841, in the
18th volume of this Journal, page 49%. My object at that time
was to illustrate the voltaic decomposition of alcohol, by showing
that the quantity of hydrogen liberated from the negative pole
in acidulated water was the same as that liberated from the
negative pole in alcohol, having its conducting power improved
by the solution in it of minute quantities of potash or of potas-
sium; my inference from the whole experiments on the subject
being, that it was the water of the alcohol, considered as a hydrate
which suffered voltaic decomposition. To obtain this compara-
tive illustration of that view, it was shown that certain parti-
culars required to be attended to, and that two circumstances
seemed to modify the result: first, the absorption of hydrogen
by the fluid, which hydrogen entered into the constitution of the
secondary products of oxidation formed at the positive pole; and
secondly, that when the conducting power of the liquid dimi-
nished, the galvanic action diminished also, “a result,” I added,
“which may be imitated by passing the same current through
distilled water, and water acidulated with sulphuric acid, when the
hydrogen liberated from the pure water will be found to be notably
less than that from the well-conducting fluid.” Here, then, we
have precisely the same experiment made and published about
fourteen years ago, which is now brought forward as new by
M. L. Foucault +.

On looking back to my notes of the experiment here referred
to, I find more than one taken down, and all to the same effect.
The following I find amongst them. Two tubes with platinum
wires terminated by platinum foils, sealed hermetically in their
closed extremities, were filled with distilled water and inverted
in a small evaporating basin also containing distilled water, and
secured in that position. Two other similar tubes were filled
with distilled water acidulated with th of sulphuric acid, and
inverted in another evaporating basin containing acidulated water.
Connexion was then made by a wire between the wires of two
of the tubes, one in each basin; and the wires of the other two
tubes were connected respectively with the poles of a Cruk-

* In the eighth line of that page for rigorous read vigorous.
+ M. Foucault’s notice was read to the Academy of Sciences, Feb. 20,
1854. Cosmos, vol. iv. p. 249.

428 M.P. Riess on the Generation of Heat by Electricity.

shank’s battery of 36 pairs of 4-inch plates, charged with water
containing =4rd of a mixture of two measures sulphuric acid and
one measure nitric acid. Fyrom the bad conducting power of the
distilled water which formed a part of the circwt, the action was
slight. During the first half-hour similar minute quantities of
hydrogen were collected at the two negative poles. After 8%
hours’ action, a decided difference in the quantities had become
apparent, there having been evolved from the negative pole in
the distilled water 0°04 cubic inch, and from the negative pole
in the acidulated water 0°07 cubic inch. After 24 hours, the
amounts were respectively 0°105 cubic inch and 0-2 cubic inch,
i. e. twice as much from the acidulated water as from the distilled
water.

The only inference which I attempted to draw from such ex-
periments was, that the bad conducting power of the distilled
water interfered with the full electrolytic action. I confess that it
never once occurred to me that any inference could be drawn from
them, trenching upon the law of definite voltaic chemical agency ;
nor does it yet appear to me that there is any foundation for
such an inference*. If M. Foucault’s views be well founded, that
it follows from this and other experiments to which he refers,
that liquids have a conducting power independently of suffering
decomposition, and that im experiments such as the above, a
part of the current passes by this proper conduction, how is it
to be expected that the full decomposing effect should be pro-
duced? It would be a violation of the law of definite agency if
the same amount of electrolytic action ensued, when a part of
the current passed by proper conduction, as when the whole
current passed in virtue of decomposing agency. There is
scarcely any law in science which does not present exceptions
and limitations, till we come to be able to ascertain the true
causes of such restrictions, when they by degrees return within
the limits of the general proposition. The histories of the rela-
tion between atomic weights and specific heats, of isomorphism,
and even of gravitation itself, afford illustrations of this principle.

St. Andrews, May 8, 1854.

LXIX. On the Generation of Heat by Electricity. By P. Rixss.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
if REGRET exceedingly to find that Mr. Thomson, in the
Philosophical Magazine for May, page 347, while admitting
one error, has fallen into a new and more serious one, which I

[* On reconsidering the subject our correspondent may, perhaps, find
reason to change his opinion.— Ep. |

On certain Questions relating to the Moon’s Orbit. 429

cannot allow to pass unnoticed. Mr. Thomson no longer ascribes
the discovery of the law, that the quantity of heat generated by
the Leyden jar is proportional to the square of the quantity of
electricity, to Mr. Joule, but claims it for Cuthbertson, from
whose experiments, he asserts, M. Becquerel had “ quite ex-
plicitly enunciated” the law in 1835. I regret that the re-
mark of M. Becquerel has not been given completely, for if
this had been done I should have been spared the present
communication. The place in the original reads as follows :—
“Cuthbertson et autres physiciens qui ont mesuré avec des
électrométres action calorifique produite par la décharge d’une
batterie, ont trouvé qu’elle croissait 4 peu pres comme la carré
des charges des batteries pour certaines longueurs des fils. Cette
loi varie en outre suivant |’épaisseur des jarres qui composent la
batterie. Celles qui sont épaisses ont une puissance de fusion
moins grande.” It is not necessary to be acquaimted with the
experiments of Cuthbertson to see, from the tenour of the above,
that M. Becquerel speaks of fusion, and of fusion only. That,
however, by the well-known fusion experiments of Cuthbertson
and others, which I myself have discussed in a memoir upon the
same subject (Poggendorff’s Annalen, vol. lxv. p. 497, translated
in the Scientific Memoirs), the law in question has been proved,
will scarcely be asserted by any man, even though he should not
be acquainted with the fact that in the case of fusion, besides
the heating, another electric action comes into play.
I have the honour to be,
Your obedient Servant,
Berlin, May 11, 1854. P. Rizss.

LXX. On certain questions relating to the Moon’s Orbit.
By Professor CHaxtis.

To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,

| BEG of you the favour to make public the following state-
ment on a matter which nearly concerns my scientific credit.
In the communication which I made to the April Number of
the Philosophical Magazine on two new Theorems relating to
the Moon’s Orbit, I stated that a paper containing the proofs of
these theorems had been read before the Cambridge Philosophical
Society. Having become aware that hesitation was felt on the
part of the Council of the Society to order the printing of the
aper, on account of an adverse opinion formed of it by one or
both of the gentlemen to whom it was referred, I at once with-
drew it, with the view of relieving the Council from the necessity
of coming to a decision, and because i considered that my com-
munication to the Philosophical Magazine sufficiently secured

430 My. J. J. Sylvester on Multiplications, &e.

my priority in the discovery of the remarkable theorems which
I had succeeded in demonstrating. After I had signified my
withdrawal, one of the reporters submitted to me of his own
accord the reasons which induced him to form an unfavourable
opinion of the paper, in perfect confidence that these reasons
would convince me of my errors. The arguments are mainly
directed against the truth of the new equation

dr? h? Qp m'r?

date 208 tae
(see Phil. Mag. for April, p. 280), which is the principal feature
of my paper, and with which the theorems stand or fall. Now
what distinctly marks the character of these arguments is, that
they contain not the slightest allusion to the reasoning by which the
equation is established. They are all drawn from extraneous con-
siderations, or from swpposed consequences of the equation, and are
all such as I would readily answer if they were advanced publicly.

In fact, the proof of the equation is too simple and straight-
forward to admit of any question. In support of this assertion,
I appeal to the reasoning given in my communication to the Phi-
losophical Magazine ; and I may add, that in an examimation
for the award of Dr. Smith’s prizes held in January last, I pro-
posed this equation for the candidates to investigate, when it
was impossible they could have known of its existence till the
examination paper was placed before them, and I received a com-
plete proof of it. This circumstance suffices to show that it
requires for its demonstration nothing but mathematical prin-
ciples and processes commonly received and taught.

I now invite the reporter on my paper to discuss with me in
this Journal (anonymously if he pleases), the important and in-
teresting questions in the Lunar Theory raised by my communi-
cation to the April Number.

I am, Gentlemen,
Your obedient Servant,

Cambridge Observatory, J. CHALLIS.

May 22, 1854.

LXXI. Note on a Formula by aid of which and of a table of
single entry the continued product of any set of numbers (or at
least a given constant multiple thereof) may be effected by addi-
tions and subtractions only without the use of Logarithms. By
J.J. Sytvester, M.A., F.RS.*

Introduction.
eos remark to which this note refers is not new; it has
been well observed somewhere in Gergonne’s Annales
(Mr. Cayley being my informant), that by aid of the formula

* Communicated by the Author.

by a Table of Single Entry. 431

4ab=(a+6)?—(a—b)? the question of finding the product of
two numbers is virtually reduced to a process of addition and
subtraction, and of finding the values of two squares out of a
table of squares. If the two factors a and 6 are both even or
both odd, the formula ought to be changed into

nate Hl
Ce SOM) ai ae dg

if one of them is odd and the other even, we may employ the

formula
a soa (oy
ab= ( 5) 3 +a.

So, again, for the product of three numbers, there exists the
analogous formula

6abe= (a+b +c)?— (a+ b—c)?—(b + e—a)8— (e+a—b).

Object of the Paper.

The object of this brief note is to exhibit and demonstrate the
generalization of the above formule, 7. e. to express the product
of any ” quantities a, a5, 5,... a, under the form of the sum of
powers of simple linear functions of @,, a,,...4@,. This may be

done as follows.

General Formula.

Let 05 Oa; Basie. Py
be disjunctively equal to
5 gt Se: ae 7
then

(2.456...) 2n)(a, Fag. a.)
=(a9,+49,+49,+ ... +49,)"—2(—a9,+49,+ --. +49,)”
+2(—dg,—ag,+49,+ ... +49,)"+&e.
+(—)"(—a9,—a,— -.. —a9,)",

which I call the principal equation.

Demonstration of the principal Equation.

Tet 1 pa ba ++ Pai

be disjunctively equal to
A pep BiresBly side os dates 1),

432 Mr. J. J. Sylvester on Multiplications, &c.
then it is easily seen that
(ag, +49, + +++ +49,)"= (dg, + 4g, + oes dy a)"
2(—a, +49, + «+. +49,)"=U (dy, +g,+ ++. +4 —4,)"
+2(—ady, Fdg.t +++ +g +4,)"
>(— 49, ag oF ag,)"==(—ay, era maine ag any
+2(—ay,—a4, + cee t G41 ri a,)"
&e. = &e.
2(— 49, G9. Ag +49,)"=2(— Ag, Age ag, ty Oy)”
+ (—4a4,— 4, Ty “1 @,)”
(—ag,—a,.--—adg_,—49,)"=(—ay — ay, . + —dy —a,yn,
Hence it is apparent that when a,= 0, the right-hand side. of
the so-called principal equation spontaneously vanishes ; it will
therefore always contain a, as a factor, and by parity of reason-
ing it will contain every one of the quantities a,,d9,...a,
as a factor, and will consequently be equal to the product

@, My... dy multiplied by a numerical factor, which by making
@;, Qo,-.+ Gy each equal to unity, is readily seen to be

a"x (1.2.3...n)

(2” being the sum of the numbers of terms in the (n+ 1) groups) ;
or if we please so to say, to 2.4.6...(2n). Q. HE. D.

Conclusion.
If n is odd and be called 2m+1, we have
4.6.8... (Qn)a,;. dg... An
= (ap, +a9,+ -+. +49,)"—2(—a9, +49, + «.. +49,)”
+2(—ay —ag,+%,,+ +++ +49,)" + &e.
+ (=)™(= 49, = 49, 06+ = Mn+ A, pt + Op,§
and if n be even and be called 2m, we have
4.6.8... (2m) (a). dq »@,)
= (ap, +49,+ .-. +49,)"—>(—ao, +49, + ... +4a9,)"
+2(—ap,—ag,+49,+ «+. + 4,)"+ &e.
+3(—)"2(— 49, 49, +? Gm +0, FO yg Hes TH On)"5,

where, it should be observed, that the last term is made up’ of im-
teger parts, notwithstanding the presence of the factor }, which
factor may be construed as only serving to denote that, of any’
pair of complementary linear functions of those which enter into

m+

by a Table of Single Entry. ~ 433

this term, such as

one ate a, ee

iret = +45,
and

ot gt hake ates 4, + Ag, + Ag. + ae + gy

one only is to be retained. The entire term is of course made
up exclusively of such pairs.

Corollary.
If R(a,, a.,...a,) denote any symmetrical algebraic function
whatever of a, dg,...4,,
0.0
p> 2’ (—)'R(—a, — 4» see = 49, ma: ’ a9.) eee a%,,)

t
will contain a, . a,.d3...d, as a factor. In this formula y; de-
notes the number of combinations of m things taken i and 7
together.

26 Lincoln’s Inn Fields,
March 8, 1854.

Postscript.

In constructing a table of single entry for appplying the

formula

4ab = (a+ b)?—(a—b)?,
i. e.

1 1

ab= 4 (a+b)?— Z (a—b)?,
it is only necessary to retain the integer part of the quarters of
the squares of all the numbers from 2 to the sum of the highest
of the values of a and ) to which the application of the table is

b 2
proposed to be restricted, because the fractional parts of ote)
—p\2
and ad) will always destroy one another. A table for the

multiplication of a ternary set of factors by means of the formula

1 1 1
abo= = (a+b+eP~—s (a+b—e)?— 5 (a—b+ e)8

1
— 94 (ato +e),

will imply the registration of the values of the 24th parts of all
numbers up to the highest value of (a+4-+¢), and it becomes a
question of some practical interest to determine in what way the
fractional remainders of these 24th parts are to be dealt with.
The formula last written may give rise to either of the two

Phil, Mag. 8. 4, Vol. 7. No. 47. June 1854, 2G

$<
434: My. J. J. Sylvester on Multiplications, &c.

subjoined cases, according as the numbers a, 6, ¢ correspond or
not to the lengths of a possible triangle, viz.

(1)dn Cases NA eg eee,

Da, Te A, 24. 24.
or

1 1 1 Ne 1
2 = N24. N 8 SN So NS
@) abe= 5 NP +5, NS— 55 Ne’ gg NS

the quantities N,, N,, Ns, N, being all supposed to represent
positive integers.

A very little consideration will show, that if we neglect frac-
tions in the table there may be entailed an error of 2, 1, 0, or
—1. Whether the error is, on the one hand, an error of an even
order (viz. 0 or 2), or, on the other hand, of an odd order (viz.
1 or —1), would be at once obvious by looking to see whether the
formula, after neglecting the fractions, gave an odd result when
the result ought to be odd, and an even result when the result
ought to be even, or vice versd. And the nature of the result
as to whether it owght to be odd or even could be immediately
inferred from observing whether a, 6, c were or were not all of
them odd numbers. But there would still remain an ambiguity
in the correction to be applied in either case, arising from the
doubt whether it should be zero or 2 in the one case, or whether
it should be +1 or —1 in the other case.

This ambiguity might of course be removed by inserting in

3

the table employed the first decimal place of 3 and increasing
the decimal part in the final result to unity, or lowering it to
zero, according as its value might be greater or less than };
and it would be easy to ascertain the limits within which the
decimal digit in the result must lie, and the range of values (of
which 5 is one) from which it is excluded. The same end may,
however, be gamed much more elegantly and expeditiously, and
by a method more closely analogous to that employed for the
evolution of binary products, by the intervention of a very simple
expedient.

The cubic residues in respect to the modulus 24 are easily
verified to be as follows: 0, 1, 3, 5, 7, 8, 9, 11, 13, 15, 16, 17,

3

3
19, 21, 23. Let the tabular value of x be made ey + Ky,
; d
where [oa means the integer part of the quantity within the

brackets, and Ky may have any one of the three values 0, 3,11,
viz.
Ky =0 when the remainder of N® to the divisor 24 is 0, 1,
3, or 5;

by a Table of Single Entry. 435

ao = when the said remainder is 7, 8, 9, 11, 18, 15, 16 or 17;
an
Ky =1 when the remainder is 19, 21 or 28;

3
and let he | + Ky be called the cubic respondent to N, and be
denoted by R(N) ;
3
and let the exact value of = be called R!(N).

Let
R/(a+b+c)—R’/(a+b—c) —R'(a—b +c) —RB!(—a+b+e)
=R (a+b+c)—R(a+b—c) —R(a—b + ce) —R(—a+b+4+e)+A.,

If in general we write R!(n) —R(n)=E(n), A must be of one
or the other of the two forms

E(7,) —E(n.) — E(n;) —E(m,),
K(n,) +E (nm) —E(n3) — E(m4),

where 7, g, 23, 24 are supposed to beall positive integers. Now

or

5
2A?
that is to say, it may reach up to a4 down to ay but can
never transgress these values in either direction. Hence it is
obvious that A, which is made up of four terms, each of the form
E(n), can never be so great as +1 or so small as —1, and con-
sequently A can only have one of the three values +3, 0, —2.

Hence, then, we may work with the tabular cubic respondents
in lieu of the exact cubic respondents ; if the result is an integer,
it is good without any correction; if it is a fraction, } must be
added to, or taken away from it. And to ascertain which of
these processes is to be applied, it is only necessary to consider
whether the three factors to be multiplied are or not all of them
odd.

In practically constructing a table of cubic respondents, it
would not be necessary actually to insert the fraction } in any
case; a dot over, or a stroke through the last integer, would
serve to denote that this fraction was to be understood.

A table of quadratic respondents (7. e. of the integer parts of
the fourths of the square numbers) up to the base 20,000, has
been actually constructed and published by a M. Antoine Voisin,
under the title ‘Tables des Multiplications ou Logarithmes de
Nombres entiers depuis 1 jusqu’da 20,000, au moyen desquelles
on peut multiplier tous les nombres qui n’excéedent pas 20,000
par 20,000,” &c. 12mo. a Paris, Firmin Didot, 1817. A copy

2G2

it is easily seen that E(n) always lies within the limits +—

436 On Multiplications, &c. by a Table of Single Entry.

of this is in Mr. J. T. Graves’s valuable mathematical library at
Cheltenham.

By logarithms the author intends the same quantities as I
term respondents, certainly a less objectionable and safer term
to employ. There appears to be an error in the title in affirming
that any two numbers, not separately exceeding 20,000, may be
multiplied by aid of these tables, as the sum of the two factors
ought not to exceed 20,000. Mr. Peter Gray, so favourably
known to an important section of the public as the author of
many useful tables, has informed me that Major Shortredd, now in
India, has computed a table of quadratic respondents extending to
the argument 200,000, which he is taking measures to have pub-
lished. Such tables would be very useful to computers, as they
would serve for the multiplication of any two numbers whatever
not containing more than five figures each. I should like to
see a table of cubic respondents up to 30,000 appended to this
work *,

26 Lincoln’s Inn Fields,
May 12, 1854.

* The best practical mode of using and arranging such a table I find, after
much thought and consideration, would be as follows. It is easy to add two
quantities and subtract their sum from a third by a single operation, _ If,
then, a, b, c are the three numbers whose product it is required to find,
they should be written under one another ; and against (a) should be set
the value of a—b—c ; against (b), that of b—a—c; and against (c), that of
c—a—b; under these three last results should be written the value of
a+b-+c; of the three former, two at least must be, all may be negative;
their values arithmetically expressed will be of the form K(10,000) + N,
where K is 0, 1] or 2. In order that the final process of combining the 4
cubes may be made purely additive, the tables should show the values of
(10,000)* less the respondent to K(10,000)—N, when K is 1 or 2 for all
values of N from 1 to 9999. These complements to the respondents of the
simple or augmented complements of N may be termed respectively the
simply and doubly affected respondents of N, but in using the tables no
distinction need be drawn between the respondents and the affected re-
spondents. The arrangement of the tables will be as follows. In each
page there will be a column for the arguments, which will extend from 1 to
9999, and five other columns containing respondents and bearmg respect-
ively for their headings the numbers 2, 1, 0, 1, 2. The four quantities
formed by addition, or by addition and subtraction, from a, 6, c, will all be
of the form K 7; vg vg vg (v4 v2 v3 v4 denoting respectively some one or other
of the digits from 0 to 9), and K being one of the five symbols 2, 1, 0, 1, 2,
the value corresponding to 7, vz vz v, will then be sought for in its proper
column (according to the value of the guiding figure K), and the sum of
the four values so found will be taken (the last figure to the left, which
will be 2 or 3, being rejected). This result, affected, if necessary, with the
proper correction of +3, will express the value of ax xc.

[ 437 ]
LXXII. Proceedings of Learned Societies.

ROYAL SOCIETY.
[Continued from p. 371.]
March 23, 1854.—Colonel Sabine, R.A. and V.P., in the Chair.

T HE following paper was read :—“ Note on an indication of depth
of Primeval Seas, afforded by the remains of colour in Fossil
Testacea.” By Edward Forbes, F.R.S., Pres. G.S. &c.

When engaged in the investigation of the bathymetrical distribu-
tion of existing mollusks, the author found that not only did the
colour of their shells cease to be strongly marked at considerable
depths, but also that well-defined patterns were, with very few and
slight exceptions, presented only by testacea inhabiting the littoral,
circumlittoral and median zones. In the Mediterranean only one in
eighteen of the shells taken from below 100 fathoms exhibited any
markings of colour, and even the few that did so, were questionable
inhabitants of those depths. Between 35 and 55 fathoms, the pro-
portion of marked to plain shells was rather less than one in three,
and between the sea-margin and 2 fathoms the striped or mottled
species exceeded one-half of the total number.

In our own seas the author observes that testacea taken from below
100 fathoms, even when they were individuals of species vividly
striped or banded in shallower zones, are quite white or colourless.
Between 60 and 80 fathoms, striping and banding are rarely
presented by our shells, especially in the northern provinces ;
and from 50 fathoms shallow-wards, colours and patterns are well
marked.

The relation of these arrangements of colour to the degrees of
light penetrating the different zones of depth, is a subject well worthy
of minute inquiry, and has not yet been investigated by natural phi-
losophers.

The purpose in this brief notice is not, however, to pursue this
kind of research, but to put on record an application of our know-
ledge of the fact that vivid patterns are not presented by testacea
living below certain depths, to the indication of the depth, within
certain limits, of paleozoic seas, through an examination of the
traces of colour afforded by fossil remains of testacea.

Although their original colour is very rarely exhibited by fossil
shells, occasionally we meet with specimens in which, owing proba-
bly to organic differences in the minute structure of the coloured
and colourless portions of the shell, the pattern of the original paint-
ing is clearly distinguished from the ground tint. Nota few exam-
ples are found in Mesozoic as well as in Tertiary strata, but in all
the instances on record, the association of species, mostly closely allied
to existing types, and the habits of the animals of the genera to
which they belong, are such as to prevent our having much difficulty
about ascertaining the probable bathymetrical zone of the sea in
which they lived.

438 Royal Society.

But in paleozoic strata the general assemblage of articulate, mol-
luscan and radiate forms is so different from any now existing with
which we can compare it, and so few species of generic types
still remaining are presented for our guidance, that in many in-
stances we can scarcely venture to infer with safety the original
bathymetrical zone of a deposit from its fossil contents. Con-
sequently any fact that will help us in elucidating this point be-
comes of considerable importance.

Traces of colouring are rarely presented by palzeozoic fossils, and
the author knows of few examples in which they have been noticed.
Professor Phillips, in his ‘ Geology of Yorkshire,’ represents the car-
boniferous species, Pleurotomaria flammigera (i. e. carinata) and co-
nica, as marked with colour, and Sowerby has figured such mark-
ings in P. carinatd and P. rotundata. In the excellent monograph
of the carboniferous fossils of Belgium, by Professor De Koninck of
Liége, indications of pattern-colouring are faintly shown in the
figures of Solarium pentangulatum, and distinctly in those of Pleu-
rotomaria carinata and Patella solaris.

In the cabinets of the Geological Survey of Great Britain are
some finely-preserved fossils from the carboniferous limestone of
Parkhill, near Longnor in Derbyshire. Among these are several
that present unmistakeable pattern-markings, evidently derived from
the original colouring. They are—

Pleurotomaria carinata and conica, showing wavy blotches, resem-
bling the colouring of many recent Trochide.

An undescribed Trochus, showing a spiral band of colour.

Metoptoma pileus, and

Patella ? retrorsa, both with radiating stripes, such as are pre-
sented by numerous existing Patellide.

Natica plicistria, with broad mottled bands.

Aviculo-pecten, a large unnamed species, with spotty markings on
the ribs in the manner of many existing Pectines.

Aviculo-pecten sublobatus, Ph.? Beautifully marked with radiating,
well-defined stripes, varying in each individual, and resembling the
patterns presented by those recent Avicule that inhabit shallows
and moderate depths.

Aviculo-pecten intercostatus and elongatus also exhibit markings.

Spirifer decorus and Orthis resupinata, show fine radiating white
lines.

Terebratula hastata, with radiating stripes.

The analogy of any existing forms that can be compared with
those enumerated, would lead to the conclusion that the markings
in these instances are characteristic of mollusks living in a less
depth of water than 50 fathoms. In the case of the Terebratula,
which belongs to a genus the majority of whose living representa-
tives inhabit deep water, it may be noticed that all the living spe-
cies exhibiting striped shells are exceptions to the rule, and come
from shallow water.

There are many circumstances which warrant us to suspect that
the carboniferous mountain limestone of most regions was a deposit

Royal Society. 439

in shallow water. The facts now adduced materially strengthen
this inference.

In the British Museum there is a beautifully spotted example of a
Devonian Terebratula, brought by Sir John Richardson from Boreal
America.

Specimens of the Turbo rupestris, from the Lower Silurian Lime-
stone of the Chair of Kildare near Dublin, exhibit appearances that
seem to indicate spiral bands of colour.

March 30.—Thomas Bell, Esq., V.P., in the Chair.

The following paper was read :—Note on the Melting-point and
Transformations of Sulphur.” By B. C. Brodie, Esq., F.R.S.

In the treatises of chemistry where the results of different ob-
servers are collected, various statements will be found as to the
melting-point of sulphur. The numbers given in Gmelin’s Che-
mistry vary from 104°5 C. to 112°'2C., but of five chemists cited, no
two agree as to this apparently simple fact. There is evidently
some peculiarity about this melting-point which is the cause of these
anomalous results. In some experiments on allotropic substances,
in which I have been engaged, I had occasion to submit this ques-
tion to a more searching inquiry than it had hitherto received, in
which I have discovered the cause of these discrepancies. In the
present note I will briefly give the results at which I have arrived,
reserving the details for a further and more full communication.

The melting-point of sulphur varies according to its allotropic
condition. This condition is readily altered by heat, and invariably,
without peculiar precautions, by melting. Hence the temperature
at which sulphur melts is different from that at which it will solidify,
or at which, having been melted, it will melt again.

The melting-pvint of the octohedral sulphur, as crystallized from
the bisulphide of carbon, is 114°°5 C. But from the facility with
which this sulphur, when heated even below its melting-point,
passes into the sulphur of the oblique system, this fact may readily
be overlooked. When this sulphur, in the state of fine powder, is
heated eyen for the shortest time between 100° and 114°°5, this
change cannot be avoided. For the transformation of large crystals
a longer time is required. Ata certain point the crystal becomes
opake, and is often broken in pieces at the moment of the change.
When in such a crystal this change has either entirely or par-
tially taken place, the melting-point will be above 114°5. The
minute crystals of sulphur from alcohol, which are so extremely thin
that their angles cannot be measured, have this melting-point of
114°-5, which fixes the system to which the crystals belong. The
erystals of sulphur from benzole (rectified coal naphtha) melt also at
114°5. ‘The crystals from alcohol are very minute, consequently
so readily transformed, that they presented anomalies which led me
to doubt whether sulphur of both forms did not exist among them.
I answered this question by dividing a certain number of carefully
selected crystals, and taking the melting-point of the two halves of
the same crystal. I found that these melting-points in many cases

440 Royal Society.

did not correspond, which would have been the case if the anomalies
had arisen from the different nature of the crystals. Sulphur which
has been melted at 114°°5, and of which the temperature has not
been raised above 115°, remains, on solidification, perfectly transpa-
rent for any length of time. Heated beyond this point, it becomes,
on cooling, more or less opake.

When sulphur has been converted by heating for a sufficient
length of time, in the manner above mentioned, between 100° and
114°:5, it acquires a fixed melting-point of 120° C. This is the melt-
ing-point of the oblique prismatic sulphur. If sulphur thus converted
be carefully melted so as to raise the temperature as little as possible
above the melting-point, no sensible difference will be observed be-
tween the point of melting and of solidification. To obtain this fixed
melting-point of 120°, care must be taken that the transformation of
the sulphur has been thoroughly effected. If this be not done, it may
melt at any point between 114°5 and 120°. If, however, the tempera-
ture of the melted sulphur be raised above its melting-point of 120°,
the point of solidification will be altered, and may lie even below the
first melting-point of 114°°5*. The point of solidification is in this
case not fixed, but depends upon the temperature to which the sul-
phur is raised and upon the mode in which it is cooled. It has varied
in my experiments from 118° to as Jow as 111°. When the melting-
point of the sulphur, thus solidified, is taken, it will begin to melt
at about the temperature of solidification. The cause of this ano-
maly is evident. When the temperature of sulphur is raised above
120°, a transformation into the viscid form instantly commences, so
that the sulphur is a mixture of the two varieties, and the melting-
point varies according to the proportion in which these two varieties
are mixed. It varies inversely with the temperature to which the
sulphur is raised, so that the presence of the viscid sulphur lowers
the point of solidification. There is, however, a limit beyond which
the melting-point is not affected by this admixture. I made the
experiment of pouring sulphur, heated to its boiling-point, into
water of different temperatures, and of taking the melting-point of
the sulphur when it had become hard. Five different preparations,
which, when extracted with bisulphide of carbon, gave each a differ-
ent quantity of insoluble sulphur, coincided in the melting-point of
about 112°. This sulphur, before melting, becomes transparent, and
passes again into the viscid or elastic condition.

The sulphur which is insoluble in bisulphide of carbon, and which
is prepared by extracting the hardened viscid sulphur with that re-
agent, has a melting-point considerably above 120°, but which I
have not been able to determine with precision.

I had placed in a water-bath, at 100°, tubes containing fragments
of the three definite varieties of sulphur. After a short time, on
examining the tubes, I found the insoluble sulphur, which I have

* This has been observed by Person, who states that if sulphur be heated above
150° its melting-point is lowered to about 112° or 110°. He says, that when heated
with care, the thermometer will remain constant during crystallization, at 115°.
I have not found this correct.—Ann. de Chemie, vol. xxi. p. 323.

Royal Society. 44)

stated to have such a high melting-point, distinctly melted... The
octohedral sulphur had become opake and rounded at the edges, the
other was unaltered in appearance. Further inquiry convinced me
that the cause of the melting of the insoluble sulphur was, that it
had passed into another modification, and that this conversion was
attended with evolution of heat sufficient to melt the sulphur.» The
insoluble sulphur thus converted remains transparent, and is per-
fectly soluble in bisulphide of carbon.

It is stated in chemical treatises that the opacity which on solidi-
fication comes over the melted sulphur, is due to the transformation
of the oblique prismatic into the octohedral sulphur, and the con-
sequent disruption of the crystal. ‘To this cause also is attributed the
evolution of heat which has been observed in solid Sulphur imme-
diately after cooling. ‘There are, however, no sufficient grounds for
this view, and some of the observations which I have given are de-
cidedly adverse to it. 1. ‘The change readily takes place, even at tem-
peratures at which sulphur becomes opake, in the opposite direction,
namely, from the octohedron to the oblique prism, 2. The melting-
point of the opake sulphur coincides too nearly with its point of soli-
dification for it to be supposed that this change in it has taken place.
On extracting melted sulphur which had become opake with bisul-
phide of carbon, I have constantly found present traces of insoluble
matter, even where the greatest precaution had been taken to avoid
elevation of temperature ; and this opacity appears to me to be due
to the hardening of the viscid sulphur, and the consequent deposition
of opake matter in the pores of the crystals, which is quite sufficient
to account for it. It remains to ascertain the cause of the evolution
of the heat. On this point also I will offer a suggestion. It is well
known that the appearance of opacity is delayed by pouring the sul-
phur into cold water, and that the sulphur thus formed is at first
viscid and transparent, and only after a time becomes solid and opake.
The received view, I believe, is that the hard sulphur thus formed
is the solid form of the viscid sulphur, in the same sense as ice is the
solid form of water. It appears to me more probable that these two
sulphurs stand in a different relation, and that the change which
takes place on solidification is an allotropic transformation of the
viscid sulphur into the insoluble sulphur and one of the other modi-
fications. In the case of sulphur gradually cooled this change takes
place with rapidity, and, like other similar transformations, is attended
with a sensible evolution of heat. Where the sulphur is tempered
the change takes place very slowly, and the heat evolved is not per-
ceived. ‘This view is confirmed by a fact which I have discovered,
namely, that the viscid sulphur possesses another solid form. I
have found that when sulphur, melted at a high temperature, is sud-
denly exposed to intense cold—the cold of solid carbonic acid and
wther—the sulphur formed is not viscid, but solid, hard, and perfectly
transparent. When the temperature is allowed to rise to that of the
air, the sulphur becomes soft and elastic. It is probable that this is
the true solid form of the viscid sulphur.

4.42 Cambridge Philosophical Society.

CAMBRIDGE PHILOSOPHICAL SOCIETY.
{Continued from vol. vi. p. 73.]

Noy. 14, 1853.—A paper was read by Mr. Dobson on the Theory
of Cyclones. See Philosophical Magazine, vol. vi. p. 438.

Also, on the Storm-tracks of the South Pacific Ocean. See Phi-
losophical Magazine, vol. vil. p. 268.

A communication was made by Mr. C. C. Babington on the use
that has been made of the mode of growth to distinguish nearly
allied Species.

Noy. 28.—A paper was read by Mr. Wedgwood on the Geometry
of the first thsee books of Euclid, synthetically demonstrated from
premises consisting exclusively of definitions.

In a treatise* published by the author a few years ago, definitions
founded on relations of direction were indicated as exhibiting the
ultimate analysis of the conceptions of straightness and parallelism
in lines, and of planeness in surface ; and in proof of the adequacy of
these definitions as the basis of a complete system of geometry
without the aid of axioms or any other assumption whatever, they
were employed in demonstrating the principal propositions necessary
to place.the student on the ground occupied by the definitions and
axioms of the ordinary system. If the basis thus built in underneath
the old foundations of the science had been complete in every nook
and corner, nothing more would have been required in order to rest
the entire demonstration on the single principle of definitions. So
long, however, as any step in the process, however subordinate, was
left to be supplied by others, there always would be room for sus-
picion that the assumption in reasoning which was speciously plas-
tered over in one place might be secretly undermining the system in
another. The reform, moreover, of the premises in geometry is a
problem on which such an infinity of thought has been spent, and
to which so many answers, more or less plausible, have been offered,
that nothing short of a complete exposition of a consistent scheme
of demonstration can be expected to carry conviction in the validity
of a fresh solution. The object of the present paper is accordingly
to complete the task undertaken in the foregoing publication by a
formal statement of the other definitions required in connexion with
those of straight and parallel lines and plane surface, and by a rigid
demonstration from these premises of the steps intervening between
those and the premises of the ordinary system; and in additional
proof of the fundamental character of the proposed analysis, the de-
monstration is carried on through the geometry of the three first
books of Euclid by direct reasoning, without resort to the compara-
tively unsatisfactory method of ew absurdo proof, which, although
equally conclusive as to the necessity of the result, yet always leaves
a hankering in the mind for an answer why the case must be as the
demonstration. shows that it cannot avoid being.

* The Principles of Geometrical Demonstration deduced from the ori-
ginal conception of Space and Form. Taylor and Walton. 1844.

Cambridge Philosophical Society. 443

In the execution of the foregoing plan, the whole of the problems
cof Euclid are omitted as irrelevant to the demonstration of the other
propositions. The grounds on which they were adopted in the
system of Euclid appear to be these. It frequently happens that it
is necessary in the course of demonstration to make some new con-
struction not included in the figure which forms the original] subject
of the proposition, and it was evidently thought that the geometer
would not in strictness be entitled to take such a step until he had
demonstrated the means of executing it with exactitude. ‘The stu-
dent was accordingly in the postulates put in possession of a ruler
and a pair of compasses; and wherever any additional construction
was required in the proof of a proposition, a problem was premised,
showing the means by which the construction might be made by the
aid of those implements.

But it should be recollected that the figure by which the demon-
stration is commonly accompanied is not the actual subject of the
reasoning, but a mere illustration to aid the imagination and the
memory, the exactitude of which is matter of comparative indiffer-
ence. Moreover, the principle on which the problems are introduced
is not consistently carried out to its legitimate conclusion even in
Euclid. There is no difference in the reasoning between the figure
which forms the original subject of the proposition, and the addi-
tional construction which is made in the course of demonstration;
and therefore if it were necessary for the validity of the conclusion
to demonstrate the means of executing the latter figure, it would be
equally necessary in the case of the former. The student would not
be entitled to move a step in the demonstration of the equality of
two triangles having two sides and the included angle equal, until
he had been taught how to construct two such triangles, and con-
sequently how to describe an angle equal to a given angle. The
demonstration in Euclid begins with perfect legitimacy. ‘‘ Let ABC,
DEF be two triangles in such and such conditions,” without the
necessity of indicating the means by which those conditions may be
mechanically executed, or indeed of their possibility of actual exist-
ence; and it may with equal legitimacy proceed to exemplify in
like manner any further construction which may be found necessary
in the course of demonstration.

The question of motion has commonly been considered so essen-
tially distinct from that of position, that all reference to the former
subject has rigorously been excluded from the field of geometrical
inquiry. But the position of every point must ultimately be deter-
mined by motion from points antecedently known, and to the inci-
dents of motion we should accordingly look for the original source
of the relations of position. Now motion (in as far as it influences
position) admits of variation in two ways; viz. in the direction of
the motion at each indivisible instant of time, and in the length of
the track accomplished in a finite period; whence it has been.said
by Sir John Herschel that space (which is primarily known as the
receptacle of motion) is reducible in ultimate analysis to distance
and direction.

The relations of extent are simply those of equal, greater, and less,

444 Cambridge Philosophical Society.

with respect to which it will be necessary only to define the test by
which they are respectively to be demonstrated in concrete figure.
The relations of direction are of a much more complicated nature.
The different phases of this elementary attribute of motion are di-
stinguished, not, like those of colour, by a permanent character inde-
pendently cognizable in each individual, but more like musical notes,
by their relative position on a peculiar scale which may be made to
rest on any individual as an arbitrary basis.

The scale by which directions are compared is founded on the
elementary relations of opposition and transverseness. In whatever
direction we suppose ourselves to be traversing space, we recognize
the possibility of returning to the same position from whence we set
out by motion in a different direction, the relation of which to the
original is that of opposition ; or the two may be classed together as
the positive and negative modifications of a common direction.

Again, if we fix our thoughts upon any given direction, we find a
series of others in each of which it is possible to traverse space with-
out advance in the original direction or in the one opposed to it.
The directions so marked out by negation of progress in a certain
direction are said to be transverse to the normal or direction in which
no progress js made by the observer while advancing in the direction
of any of the transverse series. If now we start afresh from any of
the individuals of the latter series, it will be found that the series
includes the opposite direction, as well as one direction and its
opposite transverse to the former two. Every other individual of
the series will be recognized as partaking in different proportions of
the nature of these coordinates, or transverse directions, adopted as
the basis of the scale. In other words, it will be found that distance
in any intermediate direction is essentially composed of distance in
the direction of each of the coordinates in different proportions, vary-
ing from all of the one and none of the other, to all of the latter and
none of the former, with every modification arising from taking each
of the coordinates in both a positive and a negative sense.

In like manner, as each intermediate direction is transverse to
the original normal, a secondary series of directions with a differ-
ent normal will arise from the combination of these coordinates
in every proportion, and the whole expanse of space around the
observer will be recognized as consisting of distance in every pos-
sible combination of proportions in the direction of three coordinates,
of which the first may be taken at pleasure in space, the second may
be identified with any of the series transverse to the first coordinate,
and the third will be the single direction transverse to each of the
former two. Within the sphere of three directions so related to each
other we are entirely shut in. Whatever may be the particular
direction in which the coordinates be laid, we can conceive no fourth
direction essentially differing in nature from the former three,
and therefore can conceive no possible direction which cannot be
derived from some combination of three coordinates, or in which
a given distance cannot be resolved into equivalent distances in the
direction of the three coordinates.

We have thus in the relations of transverseness and opposition,

Cambridge Philosophical Society. 445

and in the conception of intermediate directions arising from the
combination of transverse coordinates in different proportions, a
uniform scale by which, when applied to known directions in space,
the position of any other direction may be accurately defined inde-
pendent (it must be observed) of any reference to the notion of
angular magnitude, of which as yet no mention has been made.

When two directions only are known in a system, they must be
considered as members of the series transverse to a common normal ;
and one of the two being identified with the first coordinate of the
seale, the position of the second will be completely determimed by
the proportion in which it partakes of the nature of the secohd co-
ordinate or transverse direction of the series.

The directions commonly adopted as the basis of the scale, are the
up and down, fore and aft, and right and left lines marked out (in
any given position of the observer in a system) by the constitution
of his bodily frame; and thus (in any given position of our bodies)
a particular direction is defined in our thoughts by the proportion in
which it partakes of the nature of those coordinates, that is to say,
by the proportion in which distance in the direction in question is
essentially composed of distance up or down, distance to the front
or rear, and of distance to the right or left.

For the sake of simplifying the question, we will now confine our
thoughts to motion in a plane surface, or to directions having refer-
ence to two transverse coordinates. Now although, in the actual
apprehension of a figured system, the observer must be supposed to
traverse the entire outline, and thus continually to change his place,
yet he must be capable of doing so without rotation on his own axis,
as he would otherwise acquire no notion of the configuration of his
track in the external system. He will accordingly carry with him
throughout the fundamental conceptions of front and back, right and
left, and by reference to these coordinates will be able to compare
and to identify directions in any part of the system.

It is in virtue of this complex scheme of relation between direc-
tions, that we are enabled to conceive the possibility of reaching the
same point by different tracks from a common starting-point. We
are indeed so much in the habit of thinking of points as marked out
by physical phenomena (as by the letters in a geometrical illustra-
tion), that it is by no means obvious where the difficulty of the con-
ception lies. But it must be remembered that points in geometry
are distinguished solely by position, while the position of a given
point is determined by the nature of the track by which it is reached
from a point antecedently known. It is plain, therefore, that there
would be no means of identifying points attained by tracks differing
in any respect from each other, if the precise combination of distance
and direction by which they were respectively attained were the
ultimate test of their position. But now the knowledge of the fun-
damental scheme of relationship above explained makes us regard
the space traversed in each successive instant of time in the track
by which the position of a point is determined (and consequently
the whole space traversed in the entire track), as equivalent toa

446 Cambridge Philosophical Society.

certain distance in the direction of each of the two coordinates of
the scale. The aggregate character (in respect of distance and
direction) of the space traversed in different tracks (by which the
position of the terminal points is governed) will thus be made to
depend on the aggregate distance advanced in the direction of the
two coordinates, a question to be tried by simple superposition.
When the distance advanced in the direction of each coordinate is
the same, the positions finally attained will be recognized as iden-
tical, and the points will coincide whatever may be the amount of
intermediate divergence in the tracks by which they have actually
been reached.

From the same principle it may be showm, that a straight line may
be drawn from a given point to any other point in space. Because
the space traversed in the track by which the second point must be
supposed to have been determined, will be equivalent in distance and
direction to a certain distance in each of the two standard directions of
the system. Now inasmuch as the series of directions intermediate
between any pairof transverse directions includes individuals partaking
in every conceivable proportion of the nature of both the transverse
directions between which they lie, it will always be possible to select
one of the series a certain distance in which will be equivalent to
given distances in each of the two transverse directions, and there-
fore the distances in the direction of the coordinates of the system
under consideration, into which the space traversed in the original
track has been resolved, may again be exchanged for an equivalent
distance in a single direction duly related to each of the coordinates ;
in other words, the same position may be attained by motion ina
single continucus direction as by a track of any other description, or
what amounts to the same thing, a straight line may be drawn from
a given point to a point determined by a track of any other de-
scription.

As soon as a straight line is known as lying in a single continuous
direction, it becomes the most obyious means of marking the direc-
tion so exhibited throughout a finite extent of line. The series of
directions transverse to a given normal may then be represented by
two straight lines crossing each other at right angles, and an inde-
finite number of other straight lines diverging from the point of
intersection, and dividing the plane surface round that point into as
many parts as there are diverging lines. If now we take two of
these lines, like the hands of a clock, and suppose one to remain
fixed while the other revolves from left to right, it will pass suecess-
ively through all the directions intermediate between left and front,
while the quantity of plane surface intercepted between the hands
abutting on the point of intersection will continually increase as the
difference in their direction becomes greater, or in proportion as
distance in the direction of the moveable hand contains a greater
proportion of distance in the direction transverse to that of the fixed
one. Thus we are taught a new mode of estimating the relation
between the direction of straight lines diverging from a common
point; not by a proportion which addresses itself to the understand-

Cambridge Philosophical Society. 447

ing merely, but by a quantity admitting of measurement by bodily
comparison, viz. by the quantity of plane surface intercepted between
the diverging lines and abutting on the point of intersection, or by
the magnitude of the included angle.

Professor Challis gave an account of a luminous appearance ob-
served at the time of the perihelion passage of Klinkerfue’s comet.

Professor Stokes read a paper on the Optical properties of Light
reflected from Crystals of Permanganate of Potash. The substance
of this paper is embodied in a paper on the Metallic Reflexion exhi-
bited by certain Non-metallic Bodies, published in the Philosophical
Magazine, vol. vi. p. 393.

Dec. 12.—Professor Fisher read the first part of a paper, entitled
*« Researches, Physiological and Pathological, on the Development
of the Vertebral System.”

After having explained what he meant by the term vertebral
system, he stated (and he illustrated what he described by drawings)
that the spinal marrow, at a particular stage of growth of the human
embryon, exhibits indications of segmental development correspond-
ing to that of the spinal column; that is to say, that each of its
halves offers on its external surface a series of symmetrical spaces
defined by transverse lines, each of which spaces corresponds to the
roots of a single spinal nerve; and again, that each half presents in
its internal structure, a double series, one anterior, the other poste-
rior, of symmetrical areas, two of which appeared to equal in extent
one of the external spaces just spoken of. Professor Fisher also
stated that the spinal marrow offers, at the period of development in
question, several other peculiarities, some of them bearing likewise
a segmental character; but he reserved a detailed description of
them for a future communication.

Feb. 27, 1854.—A paper was read by Professor Challis, entitled
** A direct Method of obtaining by Analysis the mean motions of the
apse and node of the Moon’s Orbit.” See Philosophical Magazine,
vol, vii. p. 278.

Also a paper by Mr. J. B. Phear on some parts of the Geology
of Suffolk, particularly with reference to the Valley of the Gipping.

The deposits which constitute what is often termed the glacial
formation, but which the present state of our knowledge hardly
allows us to designate by a name significant of a common origin,
present so much confusion to the inquirer, and impose upon him so
much laborious research by the extent and the unconnected character
of their distribution, that they have hitherto met with less attention
than their importance deserves.

The county of Suffolk seems to be a district where a portion of
these deposits is manifested with more than usual distinctness, and
is capable of being studied with comparative facility. The county
is separated from Norfolk on the north by the well-marked valleys of
the Ouse and the Waveney, is bounded on the east and south by the
sea and valley of the Stour, and is bordered by chalk uplands on the
north-west; the whole central portion is thickly covered with a mass

448 Cambridge Philosophical Society.

of blue drift-clay, cut into abrupt undulations bya network of val-
leys. This clay is totally without any symptom of stratification, and
is full of fragments of ‘all rocks. of ‘the secondary period, including
specimens of granite and other igneous rocks. Sate

Wells sunk in different parts of the county. show. this drift-clay to
have a*thickness varying from 200 feet to a few inches; it seems to
thin off from the northern and western parts of the county towards
the coast, and only exists in the shape of outliers. beyond a. line
passing through Sudbury, Hadleigh, Bramford, Woodbridge, and
Saxmundham ; a line, it may be remarked, nearly coinciding with
the edge both of the London clay and of the crag, and approximately
passing through the heads of the tidal estuaries of the Orwell, Deben,
Ore and Alde. The clay is almost universally underlaid by an un-
fossiliferous sand; and there is reason to conjecture that this sand,
of a prevailing red colour, passes out beyond the just-mentioned line,
and covers in many places the surface of the strip of land between
it and the sea.

A detailed examination of the Gipping valley reveals a well-
marked and connected line of sand cliffs fringing it, and its Codden-
ham tributary in particular, at a high level on both sides; the sand
is generally pure white, though often red, horizontally stratified and
capped with an unrolled gravel, which evidently owed its existence
to the quiet washing away of the drift-clay from its insoluble con...
tents. Above Needham Market the valley is channelled in. drift-..
clay, but between Needham and Bramford it is cut through chalk;
and it should be remarked, that the line of sand-hills does not extend »
up the valley with any great distinctness beyond the chalk. The ..
phznomena seen at Creeting are not consistent with this sand lying »
beneath the drift-clay ; and the inference is, that it constitutes the .
remains of an estuary deposit formed in the valley subsequent to its.
excavation in the drift clay.

All the other streams west of the Gipping have chalk for their
floor during the middle part of their course, thus manifesting the
existence of a ridge of chalk running beneath the drift accumu-,,
lations nearly due west and east from Sudbury to Bramford. . Di-.,.
sturbances evidenced in this ridge, and perhape due to its elevation,
are partaken of by the London clay and crag deposits which overlie.
it on the east and south. ae

In Norfolk the drift-clay attains a greater thickness than in Suf-.
folk, and towards the north of the county is overlaid by a sand and
gravel formation which may be appropriately termed upper drift. .
The gradual disappearance of this towards the south, together with
the thinning away and final extinction of the drift-clay in the same
direction, point to a region of greater denuding activity ; it may be
an interesting question whether such denudation be in any degree
connected with the upheaval of the before-mentioned chalk ridge,
or again, whether the sands of the Gipping valley bear any relation
to the upper drift of Norfolk.

March 13.—A paper was read by Prof. Challis on the Eccentricity
of the Moon’s Orbit ; supplement to a former communication on the

Cambridge. Philosophical: Society, 449

mean motions of the Apse and Node. See the former, paper, Phil.
Mag. vol. vii. p. 278.

Also a paper by Mr. J. Clerk Maxwell on the Transformation: of
Surfaces by Bending.

The kind of transformation here considered is that in-which’a
surface changes its form without extension or contraction of any of
its parts. Such a process may be called bending or development.
The most obvious case is that in which the surface is originally a
plane, and becomes, by bending, one of the class called ‘‘ developable
surfaces.” Surfaces generated by straight lines, which do not ulti-
mately intersect, may also be bent about these straight lines as axes.
In this way they may be transformed into surfaces whose generating
lines are parallel to a given plane, just as the former class are trans-
formed into planes.

In both these cases, the bending round one straight line of the
system is quite independent of that round any other; but in those
which follow, the bending at one point influences that at every other
point. The case of a surface of revolution bent symmetrically with
respect to the axis is taken as an example.

The remainder of the paper contains an elementary investigation
of the conditions of bending of a surface of any form.

The surface is considered as the limit of the inscribed polyhedron
when the number of the sides is increased and their size diminished
indefinitely.

A method is then given by which a polyhedron with triangular
facets may be inscribed in any surface; and it is shown, that when
a certain condition is fulfilled, the triangles unite in pairs so as to
form a polyhedron with quadrilateral facets. The edges of this
polyhedron form two intersecting systems of polygons, which become
in the limit curves of double curvature; and when the condition
referred to is satisfied, the two systems of curves are said to be
conjugate ” to one another.

The solid angle formed by four facets which meet in a point is
then considered, and in this way a “‘ measure of curvature” of the
surface at that point is obtained.

It is then shown that if there be two surfaces, one of which has
been developed from the other, one, and only one, pair of systems of
corresponding lines can be drawn on the two surfaces so as to be
conjugate to each other on both surfaees. This pair of systems
completely determines the nature of the transformation, and is called
a double system of “lines of bending.” By means of these lines
the most general cases are reduced to that of the quadrilateral poly-
hedron. ‘The condition to be fulfilled at every point of the surface
during bending is deduced from the consideration of one solid angle
of the polyhedron. It is found that the product of the principal
radii of curvature is constant.

By considering the angles of the four edges which meet in a point,
we obtain certain conditions, which must be satisfied by the lines of
bending in order that any bending may be possible. If one of these
conditions be satisfied, an infinitesimal amount of bending may take

Phil, Mag. 8, 4, Vol, 7, No, 47, June 1854, 2H

450 Cambridge Philosophical Society.

place, after which the system of lines must be altered that the bend-
ing may continue. Such lines of bending are in continual motion
over the surface during bending, and may be called “instantaneous
lines of bending.” When a second condition is satisfied, a finite
amount of bending may take place about the same system of lines.
Such a system may be called a ‘‘permanent system of lines of
bending.”

Every conception required by the problem is thus rendered per-
fectly definite and intelligible, and the difficulties of further investi-
gation are entirely analytical. No attempt has been made to over-
come these, as the elementary considerations previously employed
would soon become too complicated to be of any use.

For the analytical treatment of the subject the reader is referred
to the following memoirs :—

1. ‘Disquisitiones generales circa superficies curvas,” by M, C.
F. Gauss (1827).—Comm. Recentiores Gott. vol. vi.; andin Monge’s
«« Application de l’Analyse a la Géométrie,” edit. 1850.

2. “Sur un Théoréme de M. Gauss, &c.,” par J. Liouville.—
Liouville’s Journal, 1847.

3. “‘ Démonstration d’un Théoréme de M. Gauss,” par M. J. Ber--
trand.—Liouville’s Journal, 1848.

4. ‘‘Démonstration d’un Théoréme,” Note de M. Diguet.—Liou-
ville’s Journal, 1848.

5. “Sur le méme Théoréme,” par M. Puiseux.—Liouville’s Jour-
nal, 1848,

And two notes appended by M. Liouville to his edition of Monge.

March 28.—Prof. Miller gave an account of the relation between
the physical characters and form of crystals of the oblique system as
established by the observations of Mitscherlich, Neumann, De Se-

°
narmont, Wiedemann and Angstrom.

A paper was read by Prof. De Morgan on some Points in the
theory of differential equations.

1. The words primordinal, biordinal, &c. are used in abbreviation
of the phrases ‘ of the first order,’ ‘ of the second order,’ &c.

The symbol for a differential coefficient, U, for © , &c., long used
A

by the author, is thus extended. By Us|», is meant dU: dz with
reference to z as contained in p and q, as well as explicitly. Thus
Unip,q means U,+U,p,+U,q,; and Ur|y means U,+U,y'.

Differentiations are sometimes expressed thus: d,U =U, dz,
dz, yU=U,de+U,dy.

When it is only requisite to express functional relation, without
specification of form, (z, y,z)=0 or z=(#,y) may signify an equa-
tion between 2, y, and z. A letter may be used as its own functional
symbol: thus w=w(2, y,z) may signify that w is a function of a, y, z.
And in ‘for u write u(z,y, 2)’ there is a convenient abbreviation of
‘for w substitute its value in terms of 2, y, z.’

2. When, as so often happens, a variable enters under relations

Cambridge Philosophical Society. 45]

which destroy the effect of its variation upon the form of differential
coefficients, it is called self-compensating. Thus ¢(a, y, a) =0,
@, (2, y, @)=0, contain the self-compensating variable a. Similarly,
when ¢(z,y, a4, b)=0 is accompanied by ¢,da+¢4,db=0, a and 6 are
mutually compensative, and primordinally. The addition of —

ga(wiy) 44+ Pyx|y) d6=0
makes a and 0 biordinally compensative.

3. When a finite change in « makes an infinite change in y, it
makes an infinite change in y’:y, iny”:y', &c. When either or
both P and Q become infinite, P: Q and P,: Q, are both nothing,
both finite and equal, or both infinite; provided that the infinite
form is produced by substitution for x. If u=(v,w, ...), any rela-
tion which makes wu, infinite either makes w,, infinite, or is indepen-
dent of w. And if u,= be produced by a relation containing v,
then u,dv+u,dw+...=0 and u,,dv+u,,dv+...=0 are relations of
identical meaning.

4. From the last it follows that U=const. is solved by making
any factor of dU either0 oro. In dU=M(Pdr+ Qdy), singular
solutions are obtained, as is known, from M=o: it ought to be
asked whether M=0 does not give singular exceptions, that is, cases
in which U=const. arises otherwise than from P+Qy'=0. It is
found more convenient to treat these cases without actual separation
of the factor; that is, from dU=U,dr+U,dy.

5. In a former paper, the author insisted on the arbitrary func-
tions which enter the intermediate primitives: maintaining, for ex-
ample, that the primordinal of y’=0 is ¢(y', cy'—y)=0, for any
form of g. Lagrange, he has since found, notices this extension,
and rejects it, because it leads to y'=a, «y!—y=6, as necessary
consequences of its ordinary solution. Mr. De Morgan maintains
his opinion, and observes that Lagrange’s reason would make it
imperative to reject one of the two, y!=a, zy!—y=8, since either is
the necessary consequence of the other.

6. In order to avoid the ambiguous use of the word singular, a
singular solution is defined as any one which, by the mode of obtain-
ing it, cannot have the ordinal number of constants: it is further
styled intraneous or extraneous, according as it is or is not a case of
the general solution. If y=y(a, a) or a=A(z, y) give y'= x(a, y),
then dA=A,(y'— x)dx and y=—A,: A, are identical equations.
Every relation which satisfies Ay= isa solution, and a singular
solution ; except possibly, relations of the form «= const., which
must always be examined apart. Also, Ay=o is identical with
w=0. ‘There can exist no solutions whatsoever except those which
are contained in A=const., A,=, and (possibly) e=const.

Again, x,=(log ),),- Of this equation the author has found
neither notice nor use: supposing it to have ever been given, he
holds it most remarkable that it has not become common as the mode
of connecting the two well-known and widely used tests of singular
solution. It easily shows that y,== contains all extrancous solu-
tions, and all intraneous solutions which (as often happens) can be

2H2

452 Cambridge Philosophical Society.

also obtained by making @ a function of z. It also easily gives a
conclusion arrived at by the author in his last paper, namely, that
when x,=© is satisfied and not y'=x, it follows that x,+x,x is
infinite.

7. The author gives his own version of the demonstration of a
theorem of M. Cauchy, for distinguishing extraneous and intraneous
solutions. If y=P, P being a given function of 2, satisfy y’= (z, y),
that is, if P’ and x(a, P) be identical, then y=P is an extraneous or
intraneous solution of y’= (a, y), according as

1 dy

P x(%y)—x(@, P)

(x being constant) is finite or infinite for small values of 3. This
theorem has attracted little notice in this country: the author
believes it to be fully demonstrated, and considers it one of the most
remarkable accessions of this century to the theory of differential
equations.

8. It is observed that the validity of the extraneous solution may
depend upon the interpretation of the sign of equality by which A=B
is held satisfied when both sides are O, or both infinite, even though
A: B=1 is not satisfied. Thus y’=2”/y or y=(a+a)2, has the
extraneous solution y=0, which, however, is not a solution if by
y'=2 Vy we understand in all cases y!: /y=2.

9, The common mode of obtaining the singular solution of a bior-
dinal (by combining ¢(z, y, a, 6)=0, da, 1¢=0, da, b$x|y=0) though
sufficiently general, is never shown to be so.

Let y= (2, a, b), combined with y'=W,, give a=A(a, y, y'),
b=B(z, y,y'), from either of which follows y= (a, y,y'). The
most general primordinal is f(A, B)=0, f being arbitrary. Any
given curve, y=wa, may be made to solve this for some form of /;
but, generally speaking, this solution will be evtraneous. For A and
B are so related that every intraneous solution makes A and B con-
stant. And any primordinal equation whatever may in an infinite
number of ways be thrown into the form f(A, B)=0, so that the
intraneous solutions shall make A and B constant.

(Given y=aza, required a key to all the primordinals of which it
is a singular solution. Take any equation y=i(z, a, b), eliminate x
between a=A(a, wx, a'x) and b=B(a, wx, a'x), and write A(z, y, y')
and B(a, y, y') for a and 6 in the result.)

The equations dA=A,)(y”—)dz, dB=B,(y’—x)dz are identi-
cally true. And Ay =o, or any relation which satisfies it, is a
singular primordinal of y’=y, whenever it is a primordinal at all;
that is, when y' appears in it. When A, =o is satisfied by a rela-
tion void of y', that relation is not necessarily a solution. The
ordinary solutions of Ay, =o are solutions of y!!=y ; but not (neces-
sarily) the singular solutions. The singular solutions of a relation
which makes A, =o may make A,’ finite.

Comparing A and B with y, we have

fese be = Ya
Ay=— ——___ , Te) Ee
; WaWou “% bpWax By Wa Wow aed La bae

Xy! ” {log Chabon Peban ) } Po

Cambridge Philosophical Society. 453

From these are obtained results in complete analogy with those
for primordinal equations. But when WaWy:.—Wyw.2=0, the usual
criterion of singular solution, is made valid by Ja=0, ,=0, a sin-
gular primitive of the singular primordinal may be obtained, which
does not necessarily satisfy y”=y.

10. Similar forms are given for triordinal equations. In noticing
the manner in which the equations of the general theory may be
easily expressed by what are called determinants, Mr. De Morgan
expresses his admiration of the system, and his sense of the important
services rendered by those who have laid its foundations. But he
refuses to employ the word determinant in the sense proposed, on
account of its not expressing any distinctive property of these func-
tions. Until those who have a better right to give a name provide
themselves with a distinctive one, he intends to call them eliminants.

The forms connected with y=i(a, a,b) may be easily translated
into others derived from $(«,y,a,b)=0. But the formula which
connects y,' with @ is as follows :—

= Slog (dabiev— mya ne 4 Gabry dobay
a= {eal vy Gabtoly—Vobary

where by Uz, is meant mae , even when U is a function of y’,
Thus (zy'!—y)zjy , as here used, is 0.

11. The following idea of reciprocal polarity has been presented
by M. Druckenmiiller (as cited from Crelle’s Journal by Mr. Boole),
and, independently, by Professor Boole: it occurred to the author of
this paper before he had seen the researches of either. If there be
equations involving m+ 2 variables, and if, determining a point by
fixing m of the variables, a curve be determined by giving all possible
values to the remaining z (point and curve being here merely names
of objects determined), we may say that the (m)-point is the pole of
the ()-curve. Similarly, we may make each (7)-point the pole of
an (m)-curve. And all the points of any curve have polar curves
which contain the pole of that curve. If the two sets of variables
be severally made primordinally compensative, the general properties
which arise are easy extensions of the well-known theory of reci-
procal polars. Let (z, y) and (a,d) be two points: the polar pro-
perty of 22+y*=ax-+ by contains the direct and converse property
of the angle in a semicircle. If ¢(z, y, a,b) be the modular equation,
and if x, y and a,b be compensative, any element (2, y, y') of any
(x, y)-curve to the pole (a, b) determines an element (a, 8, 6’) of an
(a, b)-curve to the pole (v,y). These curves are reciprocal polars.
{n the common system, the modular equation is linear with respect
to both pairs of coordinates, and the locus of those poles which lie
in their polar straight lines is a conic section, to which the polars
are tangents.

12. The method of transforming differential equations, given by
the author in his last paper, is precisely the reference of the curves
sought to their reciprocal polars, the modular equation being taken
at pleasure. Mr, De Morgan now proposes to call it the method of
polar transformation. Let ¢(a,y, a,b)=0 be the modular equation,

454 Cambridge Philosophical Society,

and let ¢,+9,y'=0, ¢,+,0'=0, b' being db: da. Hence

a=A(a,y,y'), 6=B(a,y,y'); c=X(a, 6, b'), y=Y(a, 6, b')

b'=B, +Ay y=Yu Xp; fF

the biordinal factors, y”— y(z,y, y'), b” —a(a, b, O'), disappearing
from 6' and y'. Hence i! depends on @, YY Similarly, b” depends
z,y,y',y’, &c., and similarly for y',y”,&c. “If i inf(@,y,y',y",&c.) 0
we substitute for 2, y, y!, &c. in terms of a, , b’, &c., the two equa-
tions belong to polar reciprocals. If either can be integrated, the
integration of the other depends on elimination: thus if the equa-
tion in a, 5, &c. can be integrated, the solution of the equation in
x, y is obtained by eliminating a and 4 between the integral obtained
and =X, y=Y

13. There are two reciprocal biordinal equations belonging to the
modular equation ¢(2, y, a,6)=0; y"=y when a and 6 are constant,
b"=a@ when x and y are constant. The two have the same condition
of singular solution; for Ay'g@,=Xy@y. Let this be o(2, y, a, 6)=0,
when cleared of y' or 4'. The following table exhibits the relations
of the double system :—

STRESS pr a Pn me rece
a(z,y,a,b)=0 | pat pyy'=0 ; pat pob'=0 o(#,y,a,b)=0
ante a a dig 9
y'=aley) a= A(a,y.y') O=B(a,y,y') w=X(a,b,b') y=Y¥(a,b,b') b'=X(a,6)
bat ee esd. AS)
ui ake
y=I(a, C) y"=x(a,y,y') b"=a(a,b,b') b=A(a,Z).

Eliminate a and 6 between ¢=0, c=0, gay =0, and we have
y'=@, y=Il, the singular primordinal and primitive of y’=y; those
of 6’=a are obtained by eliminating x and y from =O, a=0,
$xly =O. There is a relation involved between C and Z, the con-
stants of integration. For each value of C, y=II is the zy-curve
which touches all in ¢(a,y,a, A)=0, for the corresponding value
of Z and all values ofa. The same of Z, b=A, and ¢(2, II, a, b)=0.
The contacts are of the second order, and y=II, b=A, are polar
reciprocals for corresponding values of Cand Z, But the singular
primitives of y'=a@ and b'=) are not necessarily reciprocals: when
this does happen, their contacts with primitives are of the third
order,

14, When a surface is described by one set of curves, as in the
surface obtained by eliminating a from ¢(a,y,z,a)=0, (a,y,z,a)=0,
it is proposed to call it a shaded surface, and the curves lines of sha-
ding, The equation f(a, y, z, y',2')=0, y and z being functions of
x, cannot, generally, belong to any family of surfaces in an unre-
stricted sense; that is, it cannot be always true of a point moving
in any way upon a surface. Such a supposition would be equivalent
to imagining a surface every point of which has the primordinal
character of the vertex of a cone. But it may belong to any surface,
properly shaded, or to any mode of shading, if the proper surface be
chosen.

15, Two equations of the form y=®(z, a, b,c) z=¥(a, a, b, c),
give one, and only one, primordinal of the form f(a, y, 2, y',2')=

Cambridge Philosophical Society. 455

Assume any surface w(2, y, z)=0; by this, and compensative rela-
tions between a, 4, c, another pair of primitives may befound. But
the primitives obtained from w=0 do not shade this surface, except
in cases determined by two relations between the constants. Again,
making a, 6, ¢ compensative, without any assumed surface, we find
one equation of the form (a, 4, c, a’, 6')=0, any primitives of which
lead to other primitive forms for f=0. Each of the second primi-
tives has contact of the first order with one family of curves from
among the original primitives ; and all ordinary primitives are found,
in an infinite number of ways, among the connecting curves of others.
There is a singular solution, a curve of contact to all primitives, when
®,=0, ¥,=0, &c. can all be satisfied at once.

Since y=, z=¥, give a primordinal equation independent of
constants, the polar reciprocal properties of curves in space are of a
restricted form. Every surface dictates another surface, and a mode
of shading both, so that each line of shading on either surface is the
polar reciprocal of a line on the other.

16. The conversion of constants into compensative variables may
give restricted solutions, as in the ordinary case of two variables, and
every other in which the constants are converted into separately
self-compensating variables. When these variables are made collect-
ively compensating, and the equations permit elimination of the
original variables, ordinary differential equations may be produced,
the integration of which may, after substitution, give primitives of
the same form as those from which they came. But when the ori-
ginal variables cannot be eliminated, arbitrary relations may be
required, in number enough to eliminate the differentials of the new
variables: in this case arbitrary functions enter the primitives finally
deduced, Of this last case one instance is Lagrange’s transition
from a primitive of a primordinal partial equation having two con-
stants to the complete primitive of that equation.

17. A biordinal partial equation may be produced from

U(a, y, z, a, b, ¢, e, h)=0

by eliminating the five constants between U=0 and the five results
of primordinal and biordinal differentiation. But it is not true that
every form of U=O leads to one biordinal equation only : many
forms lead to an infinite number. Two attempts to procure other
primitives by making a, b, &c. compensative variables, end in two
different forms of result. First, when all the resulting equations
are required to be integrable, by introduction of a proper factor, the
success of the process requires the integral of two partial equations,
one primordinal and one biordinal, between four variables. Secondly,
when no such condition is required, the result is another form in-
volving five constants.

18. A primordinal partial equation belongs to a family of surfaces
of which one is determined by any given curve through which it is
to be drawn. A biordinal equation belongs to an infinite number of
families ; and a distinct conception of the conditions which select
an individual surface is best formed by an extension of the following
kind. A curve on a surface is analogous to a point on a curve: two
curves being drawn on a surface, the analogue of the chord joining

456 Cambridge Philosophical Society.

two points on a curve is the developable surface (or surfaces) drawn
through the two curves. The developable surface which touches
the given surface in a curve (and not the tangent plane) is the ana-
logue of the line which touches a curve in a point. A biordinal
equation being given, one surface satisfying it is selected by a curve
through which that surface is to pass, and a developable surface
passing through that curve which the surface is to touch.

19, 20. The restrictions under which two arbitrary forms must
enter, in order that a biordinal partial equation may exist indepen-
dent of these functions, are wholly unknown. The case which is
fully analogous to a biordinal of two variables, is of the most limited
character. Ampére has noticed this: Mr. De Morgan was led to
it by an examination of the polar properties of 9(a, y, z, a,b, c)=0.
This equation leads to a=A, 6=B, c=C, where A, B, C are func-
tions of x, y, z, p,q. The primordinal AA, B, C)=0 is satisfied by
o=0, subject to ¢(a, b, c)=0, and leads to a biordinal, independent
of f, of the form

Q+Rr+Ss+Ti+ U(s?—rt)=0,

in which Q, R, &c. are not wholly independent of each other.

If the pole (a, 6, c) move along a certain curve, the polar surface
must touch a certain surface in one of the lines of a certain shading.
That is, every abc-curve has a shaded surface, which is its polar
reciprocal: and every line of shading of that surface has another
surface for its polar reciprocal, shaded by lines of which the original
abe-curve is one. And every surface has a reciprocal surface such
that for each point on one there is a point on the other; and the
point on one surface being taken, the polar surface of that point
touches the other surface in the other point.

The singular solutions of the two biordinals derived from

o(x,y, 2, a, b, c)=0
by means of z, y, z and of a, b, c, are connected by relations analo-
gous to those already seen in the case of two variables. In fact,
there is perfect coincidence and coextension between the properties
of the general equation y”= (a, y, y') and a particular species of the
equation Q+Rr+Ss+Tt+U(s?—rt)=0. It is proposed to call
this species the polar biordinal.

21. The general method of transforming partial equations, given
in the last paper, is the investigation of the class of surfaces con-
tained under a given equation by reference of them to their polar
reciprocals, any convenient modular equation ¢(z, y, z, a, 6, c) being
made the means of transformation.

22. The following notation is proposed for eliminants. The com-
ponents being A,, A, &c., B,, &e., the eliminants are ( A,y, (AB one
(ABC, ,r), &c. ; the ‘components being A, A’, &c. B, &c., the elimi-
nants are (A°), (AB°'), (ABC°!'”), &c. Thus

(Ap =A,

(ABpq)=Ap (By) —Bp (Ag)

(ABC) =Ap (BC gry + Bp (CAgr) + Cp (ABgr)

(ABCD pq7)=Ap(BCD ys) — Bp(CDAqs) +Cp(DABgrs) —Dp(ABC yrs),

Cambridge Philosophical Society. 457

andso on. Some slight investigation of properties is made, to ex-
hibit the notation.

The following rule is suggested to determine, in any complicated
case, whether the number of contiguous interchanges by which one
arrangement of letters is converted into another shall be odd or even.
This is an important matter in the theory of eliminants, though very
complicated instances may seldom occur in practice. Write down
one arrangement under the other, and, beginning at one letter in one
line, mark the companion letter in the other line, pass on to that
companion in the first line, mark its companion, and so on, until we
arrive at a letter already marked. Call this sequence a chain, each
mark being one /ink. Having formed one chain, begin at a letter
not yet used, and form another; and so on until every letter has
been used. Then, according as the number of chains with even
links is odd or even, the number of interchanges of contiguous letters
required is odd or even, For example, the two arrangements being

ABCDEFGHIJKLMNOPQ
HMOGQBKLJPFCINADE
12123221222 1°24 1°2°3.

Under A is H, under H is L, under L is C, under C is O, under
O is A, already taken: the first chain has five links, the second is
found to have nine, the third two, the fourth one. The number
having even links is one, an odd number; hence an odd number of
contiguous interchanges converts the first arrangement into the
second.

23. The following is the method of ascertaining whether the bior-
dinal equation

Q+Rr+Ss+Ti+U(st—rt)=0 . 2. (1)

possesses a primordinal of the form f(a, y, z, p, ¢)=0, containing
an arbitrary function. Considering 2, y, z, p, g as five independent
variables, integrate, by common methods, the equations

dv dv dv k dv
rai = T—— Sia
u( +p z) ih re 0

dx 14k” dg
;{dv , dv dv 1 dv

Se = R————S— =0,
u(z +92) us dq 1+k dp

k being one of the roots of AS¢=(1+4)?(RT+QU). Ifa common
solution v=A can be found, then A=const. is a primordinal of (1).

If two common solutions, A and B, can be found, then B=@A is
a primordinal, @ being arbitrary. But though in this case A=const.
and B=const. are solutions, they cannot coexist, unless the values of
k be equal, or unless S°=4(RL+QU). This last equation is one
condition of polarity; and if, when satisfied, we find ¢hree (and there
cannot be more) common solutions, A, B, C, inexpressible in terms
of each other, then f(A, B, C)=0 is the most general primordinal,
any two forms of it may coexist, or even any three, which amount
to A=const., B=const., C=const. Elimination of p and g between
these last equations gives (2, y, z, a, b, c)=0, the modular equa-

458 Cambridge Philosophical Society.

tion. And the general solution of (1) is found by assuming } and
c in terms of a, and then making a a self-compensating variable.
24. The paper is concluded by some remarks on notation.

In an appendix to the preceding paper, read to the Society on the
lst of May, 1854, Mr. De Morgan points out an error committed
by M. Cauchy in a very remarkable theorem, of which his enuncia-
tion is as follows.

Let gx be a function which can be developed in integer powers
of x. Let r(cos@+sin@. “—1), 7 being positive, be any one of
the roots of ¢r= or of g'v=a. Then the development of gz is
convergent from «=O up to x = the least value of r.

M. Cauchy stipulates that the function shall be continuous; but
he defines a function to be continuous so long as it remains finite,
and receives only infinitely small increments from infinitely small
accessions to the variable. It is then obviously impossible that the
above theorem should be universally true. Were it so, it would

follow that the development of (1+z)? is convergent for all finite
values of x, whereas it is well known that this development becomes
divergent when @ is greater than unity. The error of M. Cauchy’s
demonstration (which contains a valuable method for establishing a
large class of definite integrals) is the assumption that if an infinite
number of convergent series of the form a+6r+czr*?+..., all with
one value of 2 but different values of a, 6, c,..., be added together,
the sum divided by the number of series is also a convergent series,
This assumption is not universally true.

Mr. De Morgan takes a totally different line of demonstration,
and establishes the following theorems.

If r(cos0+sin 0. ./—1), r being positive, represent a root of
any one of the equations dr=o, glta=~n, ¢!xv=o0,.... then the
development of gz in powers of x is always convergent from r=0
up to =the least value of 7, and divergent for all greater values of 2.

If the development have all its coefficients positive, or if all beyond
an assignable coefficient be positive, the least value of r is obtained
from a real and positive root.

If the signs of the development be, or finally become, recurring
cycles, with 7 in each cycle, the least value of r is obtained from a
root in which cos @+sin@. “—1 is one of the /th roots of unity.
If no such cycle be finally established, cos 4+sin 0. /—1 may have
a value of @ which is incommensurable with the right angle.

M. Cauchy has established from his own theorem (the want of
sufficient statement of conditions not affecting this particular case)
the necessity of the observed fact, that the developments produced
by Lagrange’s theorem for the development of implied functions
always give, when convergent, the least of the real values which are
implied.

[ 459 ]

LXXIII. Intelligence and Miscellaneous Articles.

ON THE PRODUCTION OF OZONE BY THE DECOMPOSITION OF
WATER AT LOW TEMPERATURES. BY M. GORET.

~ some experiments in which I employed a voltameter cooled ina
mixture of ice and common salt, I observed that the gas evolved,
which was to be carried through drying tubes, attacked and quickly
ate through the caoutchouc tubes uniting the different pieces of the
apparatus. When the voltameter was not cooled, the caoutchouc
completely retained the gas. It appeared to me that this corrosive
action must be due to the presence of a larger quantity of ozone
when the decomposition of water is effected at a low temperature.

I endeavoured to ascertain this quantity in the following manner.
Ozone, like chlorine, possesses the property of converting arsenious
acid into arsenic acid. If, then, we employ a standard solution of
arsenious acid, of such a strength that it requires 1 litre of chlorine
to convert the whole of the arsenious acid in 1 litre of the solution
into arsenic acid, by passing the gas evolved by the pile through 50
cubic centimetres of this solution, the ozone contained in the gas
will effect the conversion of a certain portion of the arsenious acid.
For the determination of the quantity which bas undergone this
change, it is sufficient to compare the quantity of hypochlorite of
lime required to complete the oxidation of the arsenious acid into

which the gas has been passed, with the quantity necessary to con-
yert the whole of the arsenious acid contained in 50 cubic centi-
- metres of the normal solution into arsenic acid.
Let N be the number of cubic centimetres of a certain solution of
» hypochlorite of lime required for the conversion of 50 cubic centi-
metres of the normal fluid into arsenic acid, a change which is indi-
_ cated by the decoloration of a drop of indigo.
Let N! be the number of cubic centimetres of the same solution
of hypochlorite of lime required to produce the decoloration of a
drop of indigo in 50 cubic centimetres of the solution of arsenious
acid previously partially oxidized by the action of the ozone.

Then the quantity of ozone which has been absorbed will have

produced the same effect as « cubic centimetres of chlorine,

N: N—N’:: 50 cubic centims. : 7;
and if we suppose that 1 cubic centimetre of ozone is equivalent to
2 cubic centimetres of chlorine, = will express the number of cubic

centimetres of ozone.

But in order to ascertain the proportion of the quantity of ozone
to the quantity of oxygen evolved, the volume of detonating gas
produced must be measured. With this view I employed two vol-
tameters traversed by the same electrical current. One was furnished
with a conducting tube, which conveyed the gas to a gauged receiver
placed on the water-trough. As the two voltameters disengage, at
all events, very nearly the same quantity of gas, the proportion of ,
oxygen produced by the other apparatus may be very well ascer-

460 Intelligence and Miscellaneous Articles.

tained. The gas evolved by the second yoltameter was conveyed by a
glass tube to the bottom of a test-tube containing the 50 cubic centi-
metres of the solution of arsenious acid; this glass tube was recurved
at its extremity, and the bubbles of gas escaping from it were received
in a funnel immersed in the fluid. ‘The narrow portion of this fun-
nel was also recurved, so as to compel the gas to pass twice through
the arsenious acid.

Notwithstanding the adoption of this method to effect a more
complete absorption, the gas which had passed still possessed an
odour of ozone, and there is reason to believe that a considerable
portion escaped the action of the arsenious acid. The results here
given are consequently by no means maximum determinations.

The liquid placed in the voltameters was pure ‘sulphuric acid
diluted with six times its volume of water, except in two experi-
ments, when chromic acid was employed. In the first experiments
the voltameter was composed of a rather small bottle, so that it
rapidly became heated by the passage of the current, and it was dif-
ficult to keep it at a low temperature. 1t was afterwards replaced
by a larger vessel.

One or two experiments were made without cooling the volta-
meter, in the rest it was surrounded by a mixture of ice and common
salt. The results are given in the following table :—

Sulphuric Acid diluted with Water.

Size of Duration Volume of | Proportion
voltameter. |0fevolu-| N. N’. oxygen of ozone to Temperature,
tion. evolved. oxygen.
Ki hm D D ce

1\Small ......... 1 52 | 127-5 | 127:0| 666 about.|insensible| Without cooling.

2)Small ...+s-. 2 45 | 1285 | 128°8)1500 .. os ”

3\Small ......... 1 O | 128-0 | 1261] 731°64 0:00082 |But little cooled.

4)Small ......... 3 55 | 128-1 | 121-2 |1461-16 0-00092 |Little cooled.

5lA littlelarger.| ,, | $40 74-0|126816 | o-o0236|{ Cris’ mith ee and

6A little larger.| _,, 84:0 | 72-0 |1166-89 0:00351 ”
The temperature was

7\Small ........ 2 5 |102-1 | 84:3 |1488-471 000293 { still above 32°F, at

the end of exp.

S\Large sss. 0.50 [1025 | 87-7) 737-47 | 0-00489 |{ *Xherimonte
Without cooling ;

OlLarge’J...tes. 215 | 1028 | 95-1 |1445-5 0:00129 { temperature atcom-
mencement 43° F,
Temperatureat com-

LOj\Large ....04..: 255 | 202-25) 157-3 |1451-48 0:00383 { Petre, 7° F;
1° at close.

Chromic Acid diluted with Water.

1462-37 nese Cooled.

Without cooling.

415
3 35

LU[Small povcses sc
TRIS eeseseces

—Comptes Rendus, March 6, 1854, p, 445.

101°8 | 99:0 |1444°43 0:000306

1013 | 97-0

Intelligence and Miscellaneous Articles. 461

ON THE SEPARATION OF NICKEL FROM COBALT.
BY PROF. LIEBIG.

The mixture of the two oxides is dissolved in hydrocyanic acid
and potash; the solution is then heated for half an hour on the
water-bath in an open dish, or, what is better, boiled in a flask.
Cyanide of cobalt and potassium and protocyanide of nickel and
potassium are produced, Mercury added to the solution, throws
down all the nickel in the form of oxide, forming cyanide of mer-
cury, whilst the cobalt compound remains unchanged.

Or it may be treated as just described, but instead of adding mer-
cury, the fluid may be allowed to cool, and supersaturated when
cold with chlorine; caustic potash or soda is then added in such
proportion, that as the protocyanide of nickel separates, it may be
again dissolved. At last the nickel is completely separated in the
form of black peroxide; but the cobalt compound is not altered by
the chlorine, and the nickel thus separated is free of cobalt.—Ann.
der Chem. und Pharm., \xxxvii. p. 128.

ON THE PREPARATION OF HYDROFERROCYANIC ACID.
BY PROF. LIEBIG.

If equal volumes of a cold saturated solution of cyanide of potas-
sium and fuming muriatic acid free from iron be mixed (the latter
being gradually added to the former), pure snow-white hydrofer-
rocyanic acid is precipitated. When dried upon a tile, it dissolves
readily in alcohol, and may be obtained in crystals, free from mu-
riatic acid, by treatment with ether and allowing it to stand.— Ann.
der Chem. und Pharm,, \xxxvii. p. 127.

OBSERVATIONS ON THE NOMENCLATURE OF THE METALS CON-
TAINED IN COLUMBITE AND TANTALITE. BY PROF, A, CON-
NELL.

In 1801 Mr. Hatchett announced the discovery of a new metallic
substance, contained as an oxygen acid combined with oxide of iron
in an undescribed heavy black mineral from Massachussetts. To
this new metal Mr. Hatchett gave the name of columbium, and the ore
in which he found it has usually in this country been called colum-
bite. A year afterwards Ekeberg announced a new metal which he
called tantalum, in two Swedish minerals, which he distinguished by
the names of tantalite and yttrotantalite.

A few years afterwards, Dr. Wollaston conceived that he had suc-
ceeded in establishing that columbium and tantalum are identical ;
and this view was tacitly acquiesced in by the greater portion of the
chemical public for many years, the metal and its ores usually obtain-
ing in this country the names of columbium and columbite, and on
the Continent the names of tantalum, and tantalite and yttrotantalite.
A mineral was also discovered at Bodenmais, which was held to con-
tain this same metal.

This state of things continued till about 1846, when M, H, Rose

462 Intelligence and Miscellaneous Articles.

of Berlin published a series of researches on the ores from these
different localities, from which, so far as I can understand the matter,
he drew the following conclusions: first, that the metal in the
Swedish tantalite is a distinct metal, with its peculiar oxygen acidand ©
other combinations, and for this metal the name of tantalum may be
with great propriety reserved, being the metal discovered by Eke-
berg, and by him called tantalum; secondly, that in the Bodenmais
and American minerals two metals are contained, which M. Rose
proposed to distinguish by the names of Niobium and Pelopium, the
latter being supposed to be nearly allied to tantalum, but the former
quite distinct in its characters*.

This view of Rose has more or less prevailed for the last eight
years ; although I confess it had always occurred to me, and occa-
sionally I spoke out the view, that Mr. Hatchett’s memory had been
rather hardly dealt with, since M. Rose had left him entirely out of
view, although truly the first discoverer of the first known of these
metals and minerals.

When cerium was ascertained not to be a pure metal, but to con-
tain lanthanium and didymium mixed with it, no one thought of
dropping entirely the name of cerium. It still belongs to an ac-
knowledged metal, and the rights of its discoverers are unimpaired.

Precisely the same observation applies in regard to yttria and the
new oxides of erbium and terbium.

Other examples of the same kind might be quoted.

Now, on the authority of such precedents, when it was thought
to be ascertained that the American columbite and the analogous
Bodenmais mineral did not contain one new metal only, but at least
two, justice seems to have required that the name of columbium
should have been reserved for the more abundant of these two, just
as the names of cerium and of yttrium have been preserved.

But how much more strongly does such a view hold good now, when
it has. been announced by M. Rose that the American and Boden-
mais mineral contain only one metal, and for this metal he actually
proposes the name of niobium*? Does it not follow very clearly
that this metal ought to have the name of columbium? M. Rose has
now come to the same conclusion at which Mr. Hatchett arrived
fifty years ago, when he announced that one new metal, to which he
gave the name of columbium, existed.in the American mineral colum-
bite. If the countrymen of the latter most distinguished analytical
chemist have any sense of justice or regard for the memory of an
eminent man—one with whom I am proud to say I had a slight
acquaintance, and from whom I received some kindness—they will
now unite for the future in support of his just right not to be for-
gotten and entirely laid aside in this matter. There cannot bea
better opportunity than the present for taking this step.

I am very far from wishing to overlook the important researches
of M. Rose on this, as on so very many other interesting topics, and
we shall always feel grateful for his further investigations regarding

* See Chemical Gazette, vol. iv, p. 349.
+ See Chemical Gazette, vol. xii. p. 149.

Meteorological Observations. . 463

columbium and its various oxides and other combinations. But we
ought not to overlook what was done before him.

The matter is now reduced to a very simple issue.

We have columbium in the American and Bodenmais columbites,
and probably now in some other minerals.

We have tantalum in Swedish tantalite and yttrotantalite, and
probably in some other minerals,

Of all courses, one of the most ill-advised seems that followed by
some English chemists, of giving occasionally the name of columbium
to tantalum, which, as I understand the matter, is now quite ascer-
tained to be different from any of the other metals. This course
can only lead to confusion. Tantalum is not columbium.

METEOROLOGICAL OBSERVATIONS FOR APRIL 1854.

Chiswick.—April 1, 2. Very fine. 3. Fine: clear: frosty. 4. Slight haze:
cloudless: very clear. 5. Very fine. 6. Foggy: very fine. 7—9. Very fine.
10. Foggy: cold haze. 11. Hazy: fine: clear. 12. Cold haze: very dry air:
partially overcast. 13. Dry haze: fine: clear. 14,15. Very fine. 16. Quite
clear : very fine: overcast. 17. Light clouds: fine: clear. 18. Slight haze: fine :
very clear. 19. Slight haze: cloudless. 20. Very fine. 21. Cloudy. 22. Uni-
formly overcast: drizzling rain. 23. Cloudy and cold, with dry air: boisterous :
very clear. 24. Cloudless : masses of white clouds formed in the forenoon: ex-
cessively dry air: very clear: severe and destructive black frost at night. 25. Light
clouds : very dry air: clear. 26. Overcast. 27. Showery. 28. Cloudy and cold:
very clear. 29. Rain: cloudy: clear. 30. Rain: cloudy: overcast.—The frost
on the 24th was more severe than in any April for at least thirty previous years.

Mean temperature of the month ..... goebs Cevensceseycecsee bocttim Vee tip
Mean temperature of April 1853 .........ceescceeessececeeteenees 45 44
Mean temperature of April for the last twenty-eight years . 47 °16
Average amount of rain in April ....... DAY ORR EEE a estes oy L-O4:INChy

Boston.—April 1—7. Fine. 8. Cloudy. 9—14. Fine. 15. Cloudy. 16—20.
Fine. 21. Rain a.m. 22. Rain a.m.andr.m. 23—26, Cloudy. 27. Rain a.m.
and p.m., with thunder and lightning. 28. Rain a.m. 29. Cloudy: rain a.m.
30. Cloudy : rain P.M.

Sandwick Manse, Orkney. mie sey 1. Rain a.M.: rain, clear P.M. 2, Clears A.M.:
showers p.m. 3. Showers a.M.: rain P.M. Z Bright a.M.: Cloudy p.m. 5,
Showers a.m.: cloudy p.m. 6. Drizzle a.w.: clear p.m. 7. Bright A.M. : cloudy
p.M. 8. Bright a.M.: showersp.m. 9. Bright a.m.: cloudy p.m. 10. Bright a.m.:
showers p.m. 11. Bright a.m.: clear, aurora p.m. 12. Clear a.m.and p.m. 13,
Fine a.m.: clear p.m. 14, Hing, clear A.M.: clear, aurora P.M. 15. Fog a.m.:
damp p.m. 16, Cloudy a.m.: clearp.m. 17. Clear, fine A.M. and p.m. 18,
19. Clear A.m.: clear, aurora p.m. 20. Clear, fine a.m.: clear, fine, aurora P.M.
21. Clear, fine A.m.: cloudy p.m. 22. Cloudy a.m.and p.m. 23. Snow-showers
AM.: cloudy p.m. 24. Cloudy a.m.: cloudy, solar halo p.m. 25. Bright a.m. :
clear p.m. 26. Damp a.M.: rainp.M. 27. Showers a.m. and p.m. 28, Snow-
showers A.M. andp.M. 29. Clear A.m.: rain p.m. 30. Showers a.m.: showers,
clear P.M.

Mean temperature of April for twenty-seven previous years . 43°43
Mean temperature of April 1853 ............scsssssscerseeeees we 44°49
Mean temperature of this month — .........+60.065 yep age ivan Teds 44 +68
Average quantity of rain in April for thirteen previous years 1°86 inch,

cas of.0 10.£7 |gf.gb| z.LblEg.E€ |Ez.19] Lzo.of 6£0.08 gl.6z gfo.0£ 1Sr.0f | -uvay
of. Lo. | to. |-mss| -m | ms | fob | +h] gb! ob | 2S £g.gz 63.37 40,62 $6z.6z gzS.6z ‘of
Lo. gl. Fo. “s U are LE | g10 | Ch) 6c | €S zZ£.6% 11.67 9£.6z Lf9.6z 669.62 she
fo. | zh jeer] oo) um | em | $46} 68 | obi ze | €S VL.6z 96.62 $$.6z ovg.6z £16.62 “gz
gf. | zo, | Er. |emuu| maf ema| rm] $b] 61S] of | +5 $6.62 9L.6z £$.6z 703.62 z00,0£ L7@®
Lacdsgpessl Sxestos “mw | cu | can | ob | 6%] of] SE | of 63.62 Ez.0f 90.0£ Zo£,0£ 166.06 | «gz
setesnee sseceseteleneneetee] aay aa a | sbb| gh! ¢.6£| 6F 1S zv.0£ gt.o£ or.of PLE.O£ Lzt.of Sz
ies ae eee Ce eee ae fv| gt 1S 6£.0€ 6£.0£ 00.0£ 66z.0£ gtt.of “bz
to. So. rou | LE | Slt by) rf | Ly LE,0£ 1z.0£ $9.6z 98.62 II1,0£ “£z
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THE
LONDON, EDINBURGH anv DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE,

SUPPLEMENT To VOL. VII. FOURTH SERIES.

-LXXIV. On the Theory of Chances developed in Professor Boole’s

“ Laws of Thought.” By Henry Witerauam, M.A., Fellow
of Trinity College, Cambridge*.
OME communications having already within the last few
months appeared in the Philosophical Magazine, by Mr.
Cayley and Professor Boole, relating to the subjects treated in

» the work lately published by the latter on the Laws of Thought,
| it may be considered not out of place to publish in the pages of

the same Magazine the following observations on the theory of
chances developed in that work.

The object of this paper is to show that Professor Boole does in
the greater number of questions relating to chances solvable by his
method (or at least in those which are most difficult to treat by

_| other methods), tacitly assume certain conditions expressible by
_ algebraical equations, over and above the conditions expressed by

the data of the problem, and to show how these assumed con-

ditions may be algebraically expressed.

When no condition among the chances of the simple events,

but only the absolute chances of those several simple events
are given, the reasoning of Chapter XVII. of Prof. Boole’s
book shows that it is assumed that the events are independent,

i,.¢. that the event A is as likely to happen in one state of cir-
cumstances, as regards the remaining events as in another ; for
instanee, that A is as likely to happen if B happen and C do not,
as if is if B and C both happen or both fail; and this assump-
tion is implicitly introduced in the logical method of working

. the problem. | It is an assumption easily expressed by an alge-

1

braical equation or system of equations. For instance, take the
most simple case,—there are two events A and B, the chance of
A happening is a, of B, b: what is the chance of A and B both
happening? There are four possible cases; viz. (1) both hap-
pening, (2) B happening without A, (3) A without B, (4) both

* Communicated by the Author,
Phil, Mag. 8. 4. No, 48, Suppl. Vol. 7.

~

I

466 Mr. H. Wilbraham on the Theory of Chances

failing. Let the chances of these four contingencies be respect-
ively 0, , uw, b. To determine these we have the equations

O4+A+p+Go=1, O+p=a, 04+2r=5.

Another equation is given in Professor Boole’s assumption that
A is as likely to happen if B happen as it is if B fail, viz.
ae on OX

(O4N wth eG
The same equation is given by the condition that B is as likely
to happen if A happen as if it fail. These four equations deter-
mine the values of 0,2, uw, d. Again, suppose three simple
events A, B, C, the chances of which are a, b,c. There are here
eight possible cases, (@) A, B, C all happening, (A) B and C but
not A, (w) A and C not B, (v) A and B not C, (p) A not Bor C,
(c) B not A or C, (r) C not A or B, (¢) all failing. Denoting
the chances of these several contingencies by the Greek letters
prefixed to them, we have the equations

O4+rA+pm+v+pto+T+g=1
6+p+v+p=a
O6+rX+v+a=b
04+A+p4+T=c.

Professor Boole’s assumption of the independence of the simple
events completes the system of equations necessary to determine
the unknown quantities. It gives the equations

Og wolpioO Not Loe Ws ame

Xr oP por p @ va p ®
which comprise, in fact, four independent equations, from which,
together with the first four, the unknown quantities may be de-
termined algebraically.

That Professor Boole’s method doés in such cases as the two
just mentioned tacitly make the assumptions stated, is evident
as well a posteriori as @ priori. For, in the first case, if we seek
to find by the Professor’s logical equations the chance of A and
B both occurring, we find it to be ad, that of B and not A (1—a)d,
and so on, which necessarily imply the condition I have stated
to be assumed. So in the second case, we should find the chance
of A, B, C all happening to be abe, that of B and C but not A
(1—a)be, and so on, which imply the four additional assumed
conditions. ri

Now let us pass to the cases where certain conditions among
the chances of the several events are given. In the first question
which I have stated, where there are only two simple events A
and B, suppose there to be another given relation among the

developed in Professor Boole’s “ Laws of Thought.’ 467

chances besides the absolute chances of the simple events A
and B. The new given condition appears now to supersede and
take the place of the previously asswmed condition ; and with this
new condition combined with the three former equations among
8, r, #, $, the problem is easily solvable by algebra. In the
second question, where there are three simple events A, B and C,
suppose there to be one other given relation among the chances.
This new condition certainly does to some extent supersede those
previously assumed ; and it appears to me that Professor Boole’s
reasoning would lead one to suppose that the former assumptions
are entirely banished from the problem, and no others except the
said newly given condition assumed in their stead. The fact,
however, is that in this case certain additional assumptions are
made, otherwise the problem would be indeterminate. The
nature of these assumptions, which are different from the assump-
tions made when no condition besides the absolute chances of
the simple events is given, will perhaps be better seen from the
following discussion of an example than from any general rea-
soning. I shall adopt in it the same assumptions as are made
in Professor Boole’s method, but work it out without the aid of
his logical equations. Any question which can be solved by the
logical method may also be treated in this manner.

The chances of three events A, B, and C are a, b, ¢ respect-
ively, and the chance of all three happening together is m; what
is the chance of A occurring without B?

Suppose A, B and C, and a further event S, to be four simple
events mutually independent, the absolute chances of which are
respectively x, y, z ands. We suppose for the present no con-
nexion to exist between the original simple events A, B and C,
and the subsidiary event S. There will be altogether sixteen
possible mutually exclusive compound events, the chances of
which (since the simple events are independent) are as follows :—

(6) ayzs, (a) #(1—y)(1—2)s,
(e-) (l—a)yzs, (p) #(1—y)z(1—s),
(9) x(1—y)zs, (t) «y(1—z)(1—s),
(1) ay(1—z}s, (v) a(1—y)(1—z)(1—s),
(x) ayz(1—s), (6) (1—#)y(1—z)(1—s),

(A) (l—2)(l—y)zs = (x) (1-2) (1—y)a(1—-8),

(4) (L—a)y(1—z)s, (¥) (1—a)(1—y)(1—2)s,

(vy) (1—a)yz(l—s), (@) (1—a)(1—y)(1—2)(1—s).

Let us now make an assumption with respect to the subsidiary
event 8, viz. that it is never observed except in conjunction with

the three other events, and is always observed to happen if they
212

468 Mr. H. Wilbraham on the Theory of Chances

concur. Consequently those of the above sixteen compound
events which represent S occurring while any one or more of the
other three events do not occur, and which represent A, B, C all
to occur without S occurring, must be considered as beyond the
range of our observation. This does not contradict the former
assumption of the mutual independence of the four simple events ;
for we do not by this last supposition say that such compound
events are impossible, nor do we make any new assumption as
to the probability of their occurrence, but only that, as they are
beyond the limits of our observation, we have nothing to do with
them. The events, therefore, which come within our circle of
observation are those marked respectively 6, v, p, 7, vu, $, x, @3
and the absolute chance that any event which may occur is an
event within the range of our observation is

xyzs + (1—2x)yz(1—s) + a(1—y)z2(1—s) + ay(1—z)(1—s)

+a(1—y)(1—z)(1—s) + (l—2)y(1 —z)(1—s)

+(1—2)(1—y)e(1—s) + (1—#)(1-y)(1—2) (1s),
which is similar to the quantity called V in Professor Boole’s
book.

I must here observe that z, y, and z are not the same as the
given quantities a, b and c; for the latter represent the chances
of A, B, and C respectively occurring, provided that the event
is one which comes within our range of observation, whereas
x, y, and z represent the absolute chances of the same events
whether the event be or be not within that range.

Of the eight events 6, v, p, T, v, 6, x, @ which compose V,
four, viz. 5, p, T, and v, imply the occurrence of A. Consequently
the chance that if the event be within our range of observation
A will occur, is the sum of the chances of these last four events
divided by the sum of the chances of the eight. This will be
equal to the given chance a. Hence

ayzs + {(l—y)ze+y(l—2) + (l—y)(1—2) ja(1—s) _
V

So also
LYz8 + {(l—a#)2+ a(1 es +(1—z)(1—z) ty —s) i

wyzs+{(1 —y)e+y(l—z) + (1—y)(1—z) fe(1 —s) a
V

Also as the event S always in cases within our range of observa-
tion occurs conjointly with A, B and C, the chance of S occur-
ring and that of A, B, and C all occurring are the same, and
equal tom. Therefore

xryzs

V

=m.

developed in Professor Beole’s “ Laws of Thought.’ 469

Out of the events represented by V there are two, @ and v,
which imply that A occurs but not B; consequently the chance
of A occurring but not B, which is the required chance and may

be called u, = en . From these five equations 2,y,z,s
may be eliminated, and there remains an equation which gives w.
Or the values of x, y, z, and s may be found from the first four
equations, and thence the value of any function of them is known.

This method of solution is almost identical with Professor
Boole’s. The assumptions are the same in both, and they differ
only in my examining as above the import of each step taken
separately. Representing the chances of the sixteen separate
compound events by the Greek letters prefixed to them, the
condition that the four events A, B, C, and § are mutually inde-
pendent is equivalent to the following relations among 6, e, &c.

Ce thes Fen ei 2B ah we Bs

eA fo vo xX bo

ee ee ene

Ox os pb x vo

Gen 5 Osh pey eyDicn Heverp 06

Ch ae tT bf hb vw

Desa! ee ley th lhe pl

KeviaSb vase cult Pak 8! clk Oi
These are reducible to eleven independent equations, viz. the
seven in the first line and 5 =~ Ser tay and =~. Thestate-

O@ wa pv 5 7

ment that the four simple events are independent is only a con-
cise way of stating that these eleven equations are assumed to
hold good. The assumption of these eleven is equivalent to
saying that 6, e, &c. are proportional to zyzs, (l—a)yzs, &e.

We have taken S to represent a simple event of which the
absolute chance is s, not to represent the concurrence of A, B
and C; and when eight out of the sixteen compound events were
struck out as implying the concurrence of the events which we
know to be incompatible, we did not make S identical with A,
B, and C concurring, but we only say that the cases in which S
is accompanied with the absence of A, B and C, or of any of them,
are beyond our universe of observation. The truth of the eleven
assumed equations is supposed throughout the problem; for if
at any point we were to discard or deny them, all conclusions
based on them would fall to the ground.

It may naturally be asked, how comes it that when there were
given only the chances of the events A, B and C, we assumed

470 Mr. H. Wilbraham on the Theory of Chances

the independence of only ¢hree events, which is equivalent to
assuming four equations ; and when an additional datum was
given, viz. the chance m of the concurrence of A, B and C, we
assumed the independence of four events A, B, C and S, which
implies eleven equations, whereas we might have expected that
one assumed equation less than before would have been requi-
site? The answer is, that though all the eleven equations have
been stated to be assumed, only some of them are in the actual
working of the problem necessary assumptions. It is sufficient
that the eleven equations should be true so far as they affect the
relations among the eight contingencies in the compound event
represented by V. It will be found that three only out of the
eleven give such relations; and upon the assumptions comprised
in these last three equations rests the truth of the solution. The
three equations are —= T=? ond ae The other eight
equations, though not contradictory to the data, are not essential
to the solution, and need not have been assumed. If these three
conditions had been inserted in the data of the problem, it might
have been solved by a simple algebraical process without imtro-
ducing the subsidiary event S.

This assumption of the independence of the simple events
made directly in the solution I have given of the last question,
is, as I have said, tacitly made in the logical solutions of the
questions given in Professor Boole’s book. In Proposition I.
of Chapter XVII. the events represented by 2, y, &c. are by
hypothesis independent. In other words, the equations of
condition implied by that independence (in number, 1 if there
be 2 events w, y, 4 if there be 3 events, 2"—n—1 if there be n
events) are assumed to subsist among the compound events,
which are combinations of the simple events 2, y, &c. The
theorem is proved and proveable only on this assumption. This
proposition is assumed in Prop. II., and forms the basis of the
application of the logical equations to questions of chances. In
Prop. II. p. 261, the question is of this nature; given that,
whenever it be known that the event which will happen will
belong toa certain group of events represented by V, the chance
of x happening is p, of y, g, &c. ; required the absolute probabi-
lities of 2, y,... when we have no such previous knowledge.
As in the solution in the book, Prop. I. is in the outset assumed
with regard to w, y,..., the conditions of Prop. I. are assumed,
and one of these is that z, y,... are “simple unconditioned
events,’ which (page 258) implies that they are independent.
Consequently z, y,... are in Prop. I. assumed to be mdepen-
dent. How this can be reconciled with Professor Boole’s state-
ment with regard to a particular example of the proposition that

developed in Professor Boole’s “ Laws of Thought.” 471

his reasoning “does not require that the drawings of a white and
marble ball should be independent in virtue of the physical con-
stitution of the balls ; that the assumption of their independence
is indeed involved in the solution, but does not rest upon any
prior assumption as to the nature of the balls, and their relations
or freedom from relations, of form, colour, structure, &e.”
(page 262), I am at a loss to understand. It would appear
that its being involved in the solution proves that it must rest
on a prior assumption, and that the prior assumption in this case
is that the simple events are subject to the results of Prop. I.

When additional conditions, that the chance of a combination
of events $,(z,y,...) is m, that of ¢,(z,y,...) 1s m, and so on,
are given, and consequently subsidiary events s, ¢ are introduced,
the question becomes this :—given that 2, y,...5,¢,... are in-
dependent events, and that if it be known that the event which
will happen will belong to a certain group of events selected out of
the whole number of possible combinations, in which s does not
happen except in conjunction with $,(a,y,..-), nor (2, y,+++)
except in conjunction with s, and so on with respect to ¢ an
(2, y,-..), &e., the chances of w,y,... are p,g,... and of
s,t,...are m,n, ...; required the absolute probabilities of 2, y,...
when we have no such previous knowledge; or more usually,
required the probability that out of the same group of events as
before the event will be some definite combination of 2, y,...

The independence of the events #,y,...8, t,... 18, as before,
assumed in the assumption of the results of Prop. I. Never-
theless Professor Boole says (page 264) that the events denoted
by s, ¢, &c., whose probabilities are given, have such probabilities
not as independent events, but as events subject to a certain con-
dition V. He seems throughout to consider V as a condition
which does always obtain, and consequently that the chance of
any event inconsistent with it is 0, and therefore he ignores the
previously assumed independence of the simple events which is
inconsistent with such a supposition, instead of considering V as
a condition which, if it obtain, the chances of 2, y,... are as
given in the data of the problem.

I will now take the first problem of Chap. XX. p. 321, which
is the question treated of by Mr. Cayley in a paper in the Philo-
sophical Magazine of last October, which elicited an answer from
Professor Boole in a succeeding Number of the same Magazine,
and work it out in the same manner as I have done a former
question on Professor Boole’s assumptions. The question is,—
the probabilities of two causes A, and A, are c, and ¢, respect-
ively ; the probability that if A, happen E will happen is p,, that
if A, happen E will happen is p.. E cannot happen if neither
A, nor A, happen. Required the probability of E.

‘

472 Mr. H. Wilbraham on the Theory of Chances

I will first, however, examine what result can be arrived at
without making any assumption. Let € be the chance of A, and
A, both happening and being followed by H, &' that of their both
happening but not fallawed: by E, » and ¥ the chances of A,
happening without A,, according as it is followed and not fol-
lowed by E, € and ¢' those of A, happening without A, accord-
ing as it is followed or not by E, and o! the chance of neither A,
nor A, happening, and E of course not happening. The data of
the problem give the equations

E+E +nt+y+ot+etc=1

E+24+64+0'=c,
E+E +n+1=¢,
&+f=c,p,
E+=CoPo3

the chance (w) of E happening = £+ » + €=c, p, + copo— &,where&é
is necessarily less than either ¢,p, or cypa. We can get no further
in the solution without further assumptions or data, having only
six equations from which to eliminate seven unknown quantities.
Without such the question is indeterminate.

Now, to adopt Professor Boole’s assumptions, let z, y, z be
the chances of A,, Ag, and E respectively, and s, ¢ those of two
subsidiary events; 2, y, s, é are assumed to be mutually inde-
pendent events ; consequently the chances of the sixteen mu-
tually exclusive contingencies formed by combinations of these
four simple events will be

(6) zyst, (a) 2(1l—y)(1—s)t,
(ec) (L—a)yst, (p) a(1—y)s(1—4),
(0) 2(1—y)st, (tr) ay(1—s)(1—2),

(.) ay(1—s)t, (vy) #(1—y)(1—s)(1—4,
(x) axys(1—z?), ( (l—z)y(1—s)(1—4),
(A) (1—2)(1—y)st, (x) (1-2) (1—y)s(1—d)
(u) (L—a)y(l—s)t, (w) (1-2)(1—y)1—s)t,
() (L—a)ys(l—d), (@) (l—2)(1—y)(1—s)(1—d.
The relations among these sixteen events implied by the inde-
pendence of the four simple events are, as before, eleven in
number. As the events represented by s and ¢ in all cases
within our range of observation are concomitant with the con-
currence of A, and E, and of A, and E respectively, the events
represented by €, 0, t, K, A, V, X> re must be struck out, being
inconsistent with such concomitance, and consequently the ag-
gregate event V comprises only the events 6, p, p, T, v, p, @.

3

developed in Professor Boole’s “ Laws of Thought.” 473

Of the eleven equations given by the independence of the simple
events, only two involve merely terms comprised in V, and con-
sequently those two are the only necessary assumptions. The
truth of the remaining nine is immaterial to the question. The
two which affect the terms in V only are
E cate ae

= 5 =

@ U

As the events represented by s and «z are concomitant, and also
those represented by ¢ and yz, the event 5 is equivalent to A,,
A, and E all happening, » to A, and Ei not Aj, p to A, E not A,,
7tto A, A, not E, v to A, not A, or HE, ¢ to A, not A, or E,
to neither A, A, nor E. Consequently the two equations
assumed by Professor Boole in virtue of the method he employs
are

Prob. of A,,A,,and Eallhappening__——~Prob. A,, not A,, E

Prob. not A,, A,, E ~ Prob. not Aj, not Aj, not EK’
and
Prob A,, A,, not E Prob. A,, not A, not E

Prob. not A,, Aj, not E~ Prob. not A,, not A,, not KE”

These two conditions being assumed, it is easy by common
algebra to determine the question ; for, besides the six equations
given, as I said before, in the data, we have the two

iy

!
==, and a5.
From the first five and these last two it is easy to eliminate
2, n, 7, & C', aud o’, leaving a quadratic in £; and in this the
value c,p,+¢,p,—u must be substituted for &, giving a qua-
dratic to determine wu similar to that found by Professor Boole.
The second of these two assumed equations, though perfectly
arbitrary, is perhaps not an unreasonable one. It asserts that
in those cases in which FE does not occur, the relation of inde-
pendence subsists between A, and A,; that is, that provided E
do not occur, A, is as likely to happen if A, happen as if A, fail.
I do not see, however, that it is a more reasonable or probable
hypothesis than others that might be framed ; for instance, than
those assumed by Mr. Cayley in his memoir in this Magazine.
But the first of these equations appears to me not only arbitrary
but eminently anomalous. In the form in which it stands as a
relation among the chances of A,, A, and H, no one, I should
think, can contend that it is either deduced from the data of the
problem, or that the mind by the operation of any law of thought
recognizes it as a necessary or most reasonable assumption.
Neither can it be said that the mutual independence of the events

474 Mr. H. Wilbraham on the Theory of Chances

A,, Ao, and the other two represented by s and ¢ (from which
assumed independence the two equations are derived), is either a
datum of the problem or a condition necessarily recognized by
the mind; the absurdity of this is shown enough by the fact,
that the latter two are purely imaginary events.
Mr. Cayley’s solution is, in fact, as follows: he introduces the
subsidiary quantities \,, X, determined by the equations
Py=y + (L—Ay) Agee
Pa=Nqt (L—Ag)Aye1,
and finds u by the equation
In the preceding notation, and according to the meaning which
Mr. Cayley attaches to the subsidiary quantities 4,A,, we have
E=€Cq(Ny + Ag—Ajrq)
E!=c409(1 —,) (1—Ag)

N= C1 —C))Aq
nf =0,(1—c,) (1—Ae)
f=c,(1—c,)r,

€!=¢,(1 —¢,)(1 — Yj)

o! =(1—e)(1~ea) 5
values which, combined with the equations for the determination
of X4, Ao, Satisfy, as they should do, the fundamental system of

relations between &, &', n, 7, € €', o'. But the equations last
written down give also

oat!
A(E+E)=(n4+7')(64+ 8);

or, as they may also be written,

tia)
Tee
AE echo
achat vice abi

Prob. A,, Ay, not E Prob. A,, not A, not E

Prob. not A,,A,, not E = Prob. not Aj, not A, not E
and

Prob. A,, A, Prob. Aj, not Ag |
Prob. not A,, A, Prob. not A,, not A,’

which are the assumptions made in Mr. Cayley’s solution ; it is
clear that they amount to this, viz. that the events A,, Ag are

developed in Professor Boole’s “ Laws of Thought.’ 4.75

treated as independent ; first, in the case in which E does not
happen; secondly, in the case where it is not observed whether
E does or does not happen.

Though the data of the problem, together with the equations
derived from the assumed independence of the simple events, are
always enough to determine the unknown quantities z, y, &c.,
and consequently to determine the chances of the compound
events represented above by the Greek letters 5, ¢, &c., there are
cases in which the required chance cannot be exactly expressed
in a series of the terms 8, e, &c.- In these cases the problem
remains indeterminate, notwithstanding the assumptions. Of
this nature are Examples 1, 4, 7 of Chapter XVIII. In Ex. 1,
for instance, the absolute chances of the four events there repre-
sented by wax, u(l—zx), (l—u)a, (l—u)(1—z) may be found,
but the chance of the required event cannot be expressed in a
series of these chances, for it’ comprises all cases which come
under the event wz, but only part, an unknown part, of those
which come under (1 —z)(1—z).

What, now, is the practical value of Professor Boole’s logical
method as applied to the theory of chances? In cases determi-
nable by ordinary algebraical processes, his book gives a system-
atic and uniform method of solving the questions, though very
commonly a longer one than we should otherwise use ; at least
it appears to me that the really determinate problems solved in
the book, as 2 and 3 of Chap. XVIII., might be more shortly
solved without the logical equations. In these cases the ori-
ginally assumed independence of the simple events is unneces-
sary, none of the equations implied thereby consisting wholly of
terms comprised in V. The disadvantage of Professor Boole’s
method in such cases is, that it does not show us whether the
problem is really determinate or requires further assumptions,—
whether, in fact, the assumptions made are necessary or not.
On the other hand, in eases not determinable by ordinary algebra,
his system is this; he takes a general indeterminate problem,
applies to it particular assumptions not definitely stated in his
book, but which may be shown, as I have done, to be implied
in his method, and with these assumptions solves it; that is to
say, he solves a particular determinate case of an indeterminate
problem, while his book may mislead the reader by making him
suppose that it is the general problem which is being treated of.
The question arises, Is the particular case thus solved a pecu-
liarly valuable one, or one more worthy than any other of being
solved? It is clearly not an assumption which must in all cases
be true ; nor is it one which, without knowing the connexion
among the simple events, we can suppose more likely than any
other to represent that connexion ; for if we examined the assump-

476 M. R. Kohlrausch’s Theory of the

tions as applied to any particular problem (as has been done with
reference to the problem last discussed), we should find them to
be such as do not strike us as particularly applicable, as was the
case with that problem. If, beimg in ignorance what system of
assumptions ought to be made to render the problem determi-
nate, we were to wish to give a definite answer to the problem,
it might be in the following form: ascertain the chance of the
required event happening on any one system of assumptions,
and the chance of that system representing the true connexion
among the simple events, and multiply the values of these
chances together ; the sum of a series of these products compri-
sing every possible system of assumptions would be the true
chance of the event. But Professor Boole’s method evidently
does not attempt to solve any question of this nature. It would
seem that though Professor Boole gives a uniform and emi-
nently elegant method of solving a class of cases of such in-
determinate problems, that class is not one of much practical
application.

LXXV. Theory of the Electric Residue in the Leyden Jar.
By R. Koniravscu.

[Concluded from p. 426. ]
§ 11.

\ \" 7¥ willnow endeavour to obtain an equation for the residue-
curve by help of the principles stated in the foregoing
paragraph.

The charge Q, being suddenly imparted to the jar, generates
an electric moment m, which increases with the time, and, in order
to re-establish an equilibrium between the action of the charge
Q, and a contrary action which has been elicited in the glass,
approaches a certain limit M, proportional to Q). In order to
bring this electric moment into calculation, we must select some
unit by which to measure it. Let the unit of moment be that
which can detain a residue equal to unity; the latter unit bemg
- a certain quantity of electricity, indeed the same quantity ac-
cording to which Q, is measured. As the moment, however,
may be assumed proportional to the residue, instead of the former
we shall substitute the latter, which is its effect, and say the
primitive charge Q, has produced the residue 7, in the time ¢,
which, in order to restore the equilibrium, must increase to R,

so that then
: R =pQo,
where p is a constant.

If, however, the primitive charge Q, continually suffers a loss

Electric Residue in the Leyden Jar. 477

through the air, so that at the time ¢ it amounts only to Q,, then
the ideal state of equilibrium towards which the glass strives at
the time ¢ will no longer necessitate the residue pQ,, but merely
pQ,. If an actual concealed residue r, has been formed during
this time, then the distance from the state of equilibrium is
PQ,—";. .

Now this distance will continually decrease; whence its dif-
ferential must be made negative, and the velocity of its change,

or
d( pQ,—7,)
are

is evidently greater the greater the distance which still exists ;
hence it might be set proportional to some function of the same.
If, by way of trial, we write

d —?r
we find by integration that the constants, among which p (as
may easily be seen from the observations) has not a very exten-
sive field of variation, cannot be determined so as sufficiently to
satisfy the observations.

The velocity in the change of the distance from the state of
equilibrium, however, is not in reality merely a function of this
distance, as may be seen from the following fact, the mention of
which has been hitherto purposely postponed.

If the residue r be generated by a strong charge in a very
short time, and afterwards the same residue r be generated by a
weak charge in a longer time, the distances from the state of
equilibrium on discharging the jar will still in both cases be
equal. Notwithstanding this, the former residue sooner converts
itself into disposable charge than the latter. Thus we see that
the said velocity in the change does not depend solely upon the
magnitude of the distance from the state of equilibrium, but
also upon the time during which the strain has continued. Owing
to the secondary action, similar phenomena would probably be
observed in elasticity if suitable bodies could be investigated. If
a piece of wood were considerably bent for a short time, or only
bent a little but for a long time, it may easily be conceived that,
when released, an equal departure from the original form might
be manifested in both cases, whilst the times which would be
required completely to regain that form might be very different*.

* Tt should here be mentioned, that W. Weber, in his research on the
elastic force of a silken thread, has obtained an equation for the curve of
elastic secondary action which is exactly analogous to the above, and does
not contain a particular function of the time. That which we have called

478 M. R. Kohlrausch’s Theory of the -

On the right-hand side of the differential equation, therefore,
we place a power ¢” of the time, and as, by trial, it was found that
the exponent n on this side must necessarily be unity*, we have

d(pQ,—7)) _ _ j9m( nQ —
1. SPST) = —0"(pQ—r))

Integrating between the limits =0 and ¢=¢, and bearing in
mind that when ¢=0, 7,=0 and Q,=0, we have

FTEs tc Sie peep s erar se

and

I. r4=p(Q—Qeaa””),

Provided the principles from which this equation has been
deduced are correct, and proper values be given to the con-
stants p, m and b, we may calculate residues which ought to
agree pretty well with the observed ones as recorded in § 4,
Tables a", 6" and e'.

It is not difficult to find approximate values for these con-
stants. In the first place let us determine p. When the expe-
riment has already continued for a considerable time, the state
of equilibrium will be nearly reached, that is to say, the residue
will not differ much from the limit which it is possible for it to
reach with the charge then present. Thus approximately we
shall have

" =pQ,

wali

Q,

and p will not be much greater than For example, the last

determination in the Table 4! gives
7, _ 04888
Q,~ T0154

and we may assure ourselves that the value p=O0°5 is not far

pPQA.—r, in the above, he has represented by #, and hence, according to him,

dx=— ba" dt.
An attempt to construct the curve from the equation
dx=— bat™ dt

gave me less correct results. This attempt, however, might possibly have
been more successful had the constants been otherwise determined.
Without repeating the calculation I will not venture to decide the point.

* Tt would lead us too far to explain this, nor is it necessary, seeing that
it does not interest us to know what equations are inapplicable.

Electric Residue in the Leyden Jar. 479

from being correct. Again, if /’ and ¢! be two of the times of
observation, and the corresponding Q, and 7, be written with the
same accents, we deduce from equation II.

log ¢’—log ¢"

b=— pe log nat ee
Po
so that from two observations, properly chosen, approximate
values for these magnitudes may be immediately found.

With these approximate values for the constants p, b and m,
those of the several 7, may be calculated, which even now will be
found to agree pretty well with the observed values; the cor-
rection of the constants may then be determined according to
the method of minimum squares.

The values which we obtain in this manner from the Table a’
are,—

and

p=0°4289 ; b=0:0397 ; m=—0'5744.

If we examine the values of these constants for the Tables 6"
and ¢’, we soon notice that the constant m, and hence also the
function of the time which was introduced into the equation,
differs so little for the three observed curves, which have
reference respectively to a common cylindrical jar with tinfoil
coatings, to a narrow-necked bottle filled with mercury, and to
a Franklin’s plate, that it is evidently a number common to each
of these pieces of apparatus. If, therefore, from the above value
of m we determine the two other constants which belong to the
observations in the Tables 5" and ce", we obtain the three follow-
ing equations for the calculation of the residues, as they are
given in the three Tables a", b" and ec” :—

070397 . 42'4255
r,=0°4289 La aye Dae |
_ 0702237 ; 0°4255
1,=0'5794 [9 —are os |

r,=0°2562 [a —Oe Raa

Herein the values of Q,, corresponding to the times ¢, are to be
taken from the tables. In the following Tables a!", 6" and el",

0°0446 aio

480 M. R. Kohlrausch’s Theory of the

the values of 7,, thus calculated, may be compared with the ob-
served values :—

Table a’. Table b!". Table o!!".
ve | Un "t ug: "t re
t. | caleu- ob- t. | caleu- ob- t. | caleu- ob-
lated. | served. lated. | served. |: lated. | served.
0/0 0 0) 0 0 0|90 0
18 | 0:0556| 0-0596 5} 0:0872) 00839 6 | 0:0285) 0-0288
50 | 00782) 0:08138 24/ 01619] 0:1707 43 | 0:0567| 0:0607
110] 0:0988} 0-098) 59} 0:2180} 0:2234 71 | 0-:0661| 0:0661
160 | 0:1090} 0-1084 91) 02544) 0-2571 133 | 0:0783) 0:0781
215 | 0:1169) 0-11538 114| 0:2738) 0:2727 193 | 0:0855) 0-0849
265 | 01224) 0-1214 144) 0-2949| 0:2924 256 | 0:0907) 0:0925
330 | 0:1278} 0-1263 188] 0°3199| 0:3137 328 | 0:0971) 0:0954
382 | 0-1313} 0°1303 230) 0:3379) 0°3305 423 | 0-:0990) 0:0990)
450 | 01349} 0-1351 282) 0:3592! 0°3469 531 | 0:1016| 0:1021
528 | 0:1880) 0:1896 341) 0°3782) 0°3630 620 | 0-10382) 0:1033
577 | 0:1898) 0:1401 406) 0:3947| 0°3793 715 | 0:1045| 0:1043
680 | 0°1426) 0:1421 485) 0-4119} 0-3948 864 | 01052) 0:1060
573) 0:4273) 0-4101
683} 0:4432| 0-4240
804! 0:4569} 0-4380
935) 0°4688) 0-4522
1105) 0-4809| 0:-4637
1285} 0:4902| 0°4759
1505} 0°4983} 0°4862)
1770} 0°5051} 0:49438
2070} 05091) 05019
2430) 0:5108) 05074
2870) 0:5099) 0-5099
3420) 0:5053) 0-5094
4110} 0-4961| 0:-5024
4980} 0°4839) 0:4919
5370) 0-4749 0°4888)

mW

and c' are sometimes

Whilst the calculated values in a
greater and sometimes less than the observed ones, a more regu-
lar deviation is observed in 6’; on the whole the calculated
curve is a little more curved than the observed one. As the cor-)
respondence would not be improved by basing the calculation of
these curves on values of the constants deducible, by the method
of minimum squares, from all three, we must conclude that the
observed curve contains errors. In fact, it was not immediately
deduced from observation, but was obtained in § 4, by bringing
the loss of electricity into calculation ; and it is evident that this
method will be the more uncertain the longer the observation
lasted. In the present case, however, the first charge of the
bottle was observed for an hour and a half, and the collection of
the residue lasted twenty minutes; so that a correspondence be-
tween calculation and observation, so great as is here manifested,
is rather to be wondered at, and places the certainty of the
method in a clear light.

Electric Residue in the Leyden Jar. 481

§ 12.

With respect to the meaning of the three constants p, b and
m, 6 is found to be connected with the resistance which the
glass opposes to the external influence of the electricity, so that
its magnitude may be different for different kinds of glass, whilst
m has reference to the time in which this resistance is gradually
overcome. The’ circumstance that m has the same magnitude
for the different glasses of the differently-shaped charging appa-
ratus, seems to indicate that the function of the time, which dif-
fers little from the square root, was justly introduced into the
formula, and that the resistance is a mechanical one, proceeding
from the molecular forces on each particle of glass, as in the
analogous case of elastic secondary action. The number p ex-
presses what part of the charge which is then present could be
detained by the electric moment of the glass if the state of equi-
librium were attained. The magnitude of p depends, therefore,
on 4, and at the same time on the thickness of the glass. As
the relation between p and 6 is still unknown, it does not appear
possible at present to obtain the equation of the residue with
only two constants.

Whatever opinion may be entertained with respect to these
constants, or even to what has here been termed an electric mo-
ment, this much is at least certain, the electric residue can be
calculated from the equation III. As soon as, for any particular
jar, the constants shall have been determined according to § 11,
we can give an equation for its disposable charge, which, if not
strictly expressive of the precise law, will at any rate secure an
approximation sufficiently correct for practical purposes. Prac-
tice, for example, may demand the calculation of the disposable
charge, which, in a given time after a known charge had been
imparted to the jar, was employed for some purpose or other,
without being able directly to observe its magnitude. On the
other hand, the magnitude of the disposable charge being known,
that of the original charge, which was suddenly imparted to a
jar at a certain earlier period, may be required. We will deduce
the equation, and at the same time consider a particular example,
from the data furnished by the jar a, and given in the Tables a,
a’, a" and al".

According to the calculation of these observations, we have
(see Table a, and the calculation of Table a" given in Appen-

dix III.),—

Q,=0°4742 ; V=0-0409; F=228:086; =80:767 ;
T=680 ; p=0°4289 ; b=0:0397; m=—05744.

Herein T is the time at which the jar was first discharged.

Phil, Mag, 8.4, No, 48. Suppl. Vol. 7. 2K

482 M. R. Kohlrausch’s Theory of the

The line v,, which in Plate VI. fig. 2, represents the curve of
the loss of electricity, does not differ much from a right line,
although the corresponding observations lasted an hour and a
half. In the present case, where the observations lasted only
eleven minutes, the curve will differ much less from a right line,
so that we shall incur little error by assuming the loss to be
proportional to the time.

If the loss during the whole operation was V,.then up to the
time T, when the jar was first discharged, it would be

F
Vv.
F+¢
and hence, approximately,
zadirap gal
v= T . . F+¢

If, in another experiment, the primitive charge had been Q,!
instead of Q,, but the condition of the atmosphere the same, then
pe eR RY DATE

epi» F+¢° Q

This expression, however, requires a correction if the condition
of the atmosphere with respect to the loss of electricity be dif-
ferent. To this end the loss of electricity which is sustained by
any insulated freely placed body must be determined by means
of the torsion balance. Let « represent this loss in the original
observations on the jar to which the Tables a and a! and the un-
accented letters Qo, V, F, ¢ refer; and y’ the loss in the expe-
riment now under consideration, then

! 7 !
hi op Vv _F Q)
v, EO’ RE ge
Further,
L!=Q,'—r/—»/,
therefore

1 ! ! ! eectit ink !
L/=Q) —p (Q'—Que m+1 ) =o}.

If for Q/ we substitute its value Q,’—v/, and for v/ the above
expression, we have

6 m+
IV. L!=Q)[1—p(i-ewa”” )
TS F + |
—(l—p)—.-,V.—7— -~ |.
(1—p) ayy F+$6°Q,
Hence if the charge Q,' which was originally imparted be
known, L/ can be found; or if the latter be given, Q,' can be
found.

Electric Residue in the Leyden Jar. 483

In order to show how far this formula agrees with the obser-
vations, we will calculate from it the Table a of § 1, whereby, of
course, p!/ = and Q,'=Q, :—

Table av.
1; Ay
b. ealculated.| observed.

0 0:4742 | 0:4742
18 04184 | 0°4133
50 0°3989 | 0:3896

110 03700 | 03692
160 0°3571 | 0°3516
215 03462 | 03461
265 0:3381 | 0:3373
330 0°3291 | 0:3290
382 0:3230 | 0:3223
450 03158 | 0:3141
523 0:3090 | 03080
577 03044 | 0°3029
680 0-2964 | 0-295]

wetter Viens meer
The deviation is here so small, that this approximate formula
may be regarded as a very suitable substitute for the true equa-
tion of the disposable charge which has not yet been discovered.
If in any practical application a few minutes only are con-
cerned, and if on the whole the jar suffers little loss, the equation

6 yor
L,=pQ) (ean ),

followed by a few reductions, will be sufficiently correct.

The curve for the reappearing residue remains yet to be deter-
mined by calculation. Attempts have been made to this effect,
and the formule deduced from the same principles completely
fulfill the conditions. As it is not probable, however, that an
application of these calculations will be made in practice, we
withhold them, more especially as the subject has already occu-
pied too much space.

Apprnpix I.

A battery of five jars (Plate VI. fig. 1), each containing a
square foot of coating, stood in its box. At some distance was
the single jar, F, which was to be examimed ; the outer coatings
of these six jars were carefully connected with each other, and a
wire led from them to the moist earth in the garden. In order
to charge the single jar by means of the battery, a thick wire 4,
to which two thin spring-wires c, and d were soldered, was
fastened with shell-lac to a lever a; when this lever fell, the two
spring-wires connected, for a very short time, the inner coating
of the battery and the knob of the single jar. The conducting

2K2

484 M. R. Kohlrausch’s Theory of the

wire of the sine-electrometer 8, which was 3 feet long, was con-
nected with this jar by letting one extremity into a shallow cavity
made in its knob. As long as the jar contains no electricity, the
magnetic needle of the instrument stands in the meridian, making
an acute angle « with a revolving metallic arm. At the moment
of imparting a charge to the jar, the electricity would be carried
to the needle and arm, and the former, being forcibly repelled
from the latter, would be sct in violent oscillation; but before
the needle came to rest, and before the angle of observation «
could be again produced by turning the arm, exactly the most
important time for observation would be past. The object there-
fore was to bring the electrometer into such a condition, before
any electricity was imparted to the jar, that observations might
commence from the moment when, by falling, the lever effected
the charge. This is not difficult if we know beforehand the
angle @ through which the magnetic needle will be deflected
from the meridian by electric repulsion, in order that it may
make an angle « with the repelling arm, in other words, pro-
vided we already know what charge the jar will receive. Con-
sequently if mn (fig. 1) is the position of the magnetic needle in
the meridian, ad the line of vision which by means of reflexion
is placed at right angles to the needle, and pg the arm which is
connected in a fixed manner with the line of vision, the above
object will be effected by turning the latter, and with it the arm,
through an angle ¢, and then, by means of a neighbouring gal-
vanic current, deflecting the needle until it is again in its proper
place, 7. e. perpendicular to the line of vision. To this end the
current is made to traverse a multiplying coil M, and moderated
in the requisite manner by means of a rheostat or rheochord R.
At the moment when, by the fall of the lever, electricity is con-
veyed from the battery to the single jar, the knob of shell-lac e
breaks the circuit. ‘The mechanism necessary thereto is very
simple. One pole of the circuit is led to the strong wire h fixed
to a board, the other to a spring-wire g (in the foreground of the
drawing), which being properly bent requires only to be hooked
on to / in order to close the current. When the knob of shell-
lac strikes the end f of the wire g, it immediately interrupts the
current, whose deflecting force will now be replaced by the repul-
sive force of the electricity which has entered the electrometer.
In order to know beforehand what charge the jar under exami-
nation will receive from the battery, the experimenter must
already know in what proportion the electricity divides itself
between these two bodies. In Appendix II. a better method for
determining this proportion will be given; for the present the
following method may suffice, which, for reasons there given,
will always admit of sufficient exactitude when the whole coating

Electric Residue in the Leyden Jar. 485

of the battery is great in comparison to that of the jar. It con-
sists simply in determining the quantity of electricity which will
be withdrawn from the battery by the jar.

Before the beginning of the experiment whose description we
have commenced, the sine-electrometer was connected with the bat-
tery of five jars, and the latter char ged. After properly adjusting
the needle of the instrument it was moved a little backwards, 2. e.
to an angle somewhat too small, and which amounted to 17° 52/,
and allowed to remain, until, by the gradual loss of electricity in
the air, the image in the mirror coincided exactly with the mark.
At this moment the lever was allowed to fall by releasmg a
hook 7 attached to a string; a part of the electricity passed over
from the battery to the single jar, and the electrometer, which was
again adjusted with the least possible loss of time, in 15 seconds,
showed a deviation of 12° 13’. The square roots of the sines of
these angles are proportional to the charges Q and (Q! of the
battery before and after the charge was imparted to the single
jar. The latter charge amounts to Q—Q!, and the proportion
between this and the quantity Q which was at first in the bat-

I
sai , was calculated at 0°1695.

tery, that is to say, the quotient

This method was often repeated, and gave the following results :—

Daten of the magnetic needle, | Q-q
A | For Q For Q’ Q |
° ‘ | ° /
17 52 | 12 13 01695
12 13 8 29 01651
8 29 5 27 01617 |
Ph GT tn Ne ONT Rolls pA LGB 5).
ll 55 b taba 17 | 0:1647
| Means v2ittt| Girieis 0°1654

In Appendix IT. the cause of the difference which still exists
between the several determinations of the quotient, amounting
almost to 5 per cent., will be further discussed. As, however,
the value of this quotient, according to the more trustworthy
method there adopted, is 0°1647, or very near the ubove, we
may set

Q
We now know, therefore, that if at first the battery has a
charge Q, this will sink to

Q! =Q(1—0°165) =0°835 Q
at the moment when the single jar is charged. At the same

Q-Q'_ o.165,

486 M. R. Kohlrausch’s Theory of the

time, however, we know that at the moment of transferring the
electricity, the single jar will show a tension on the knob equal
to that of the battery itself; hence, also, that the indication of
the electrometer will be the same at this moment whether it be
connected with the battery or with the single jar, for the quan-
tity of electricity which this instrument withdraws from the bat-
tery always vanishes in comparison to the quantity in the latter.

To return to the experiment, therefore, the followimg method
was pursued.

A second electrometer S! was placed near the battery, though
at so great a distance from the first S that their needles did not
irritate one another. Both were at first connected with the bat-
tery of five jars, and the latter charged. By the help of an
assistant both instruments were adjusted at the same moment.
The electrometer 8 showed thereby a deflection of 18° 49’. The
angle of deflection in the instrument 8! was of no importance, it
being intended to remain undisturbed, so as, on subsequently
charging the battery, to indicate the moment when the electro-
meter S, if the latter were still connected with the former, would
show an angle of deviation equal to 18° 49’, or in other words,
when the charge in the battery amounted to Q= “sin 18° 49.

These preparations being made and everything discharged,
the instrument S was on another day connected with the single
jar, and by means of the galvanic current deflected to 13°. This
is the angle of deflection which would be produced if the charge
Q= sin 18° 49! in the battery spread itself over the single jar,
and corresponds to the value of z im the equation

Q'= Vsin 7=0°8385 sin 18° 49!

The battery was now charged again, the charge, which was at
first too great, weakened by contact with a rod of dry fir-wood
until the electrometer 8S! showed almost the requisite deflection,
and then the whole allowed to remain until, by loss of electricity,
exactly the former charge reappeared. At this moment, which
was communicated by an assistant, the falling lever substituted
the deflecting force of the electricity which was transferred to
the electrometer S for that of the galvanic current. The disturb-
ance of the needle was scarcely perceptible at first, but it soon
moved quickly towards the nieridian, so that a new and correct
readjustment could only be made after 18 seconds*, when the
angle of deflection was 9° 50’.

An assistant noted the time when the first charge was im-
parted to the jar, as well as the moments whenever the sine-
electrometer was readjusted, he also wrote down the correspond-

* In this case the loss of so much time was due to bad manipulation.
In other observations the readjustment was often completed in 5 seconds.

Electric Residue in the Leyden Jar. 487

ing angles of deflection as the latter were dictated to him. The
following series of observations thus resulted, which in the third
column, under the title charge, contains the square roots of the
sines of the angles of deflection.

Time in seconds | Angle of deflec-

after imparting | tion in sine-
the ate papas —
0 13 0 0°4742
18 9 50 0:4133
50 8 44 0°3896
110 7 50 0:3692
160 “rally / 0°3561
215 6 53 0-3461
265 6 32 0°3373
330 6 13 0°3290
382 5 58 0°3223
450 5 40 0°3141
523 5 27 0:3080
577 5 16 0:3029
680 ei ht 0-2951

Apprnnpix II.

Description and use of the Multiplier.

A very strong copper damper of an elliptical form was sur-
rounded by 1000 coils of good copper wire about 0:25 millim.
thick, covered with silk, and coated with collodion ; the bed of
every coil was also well saturated with collodion. The ends of
the wires were led to clamping screws, which were cemented
with shell-lac into the same board that carried the multiplier.
In the elliptical opening of the damper, which was 8°5 centims.
long and 3:3 centims. high, a very strong cylindrical steel mag-
net 6 centims. in length and 1 centim. in diameter was suspended
by means of a cocoon thread, stirrup and fork. The fork on
which the magnet hung carried a mirror, in order that observa-
tions might be made in magnetometer fashion. The whole was
well enclosed in a case provided with glass windows, so that the
needle could not be disturbed by currents of air. The damping
action was so strong, that oscillations of one degree elongation
were quieted in one minute.

In using it for our purpose, one end of the multiplying coil
was connected by an intermediate wire with the outer coating of
the battery, which, besides this, was in good connexion with the
earth. The other end of the multiplying coil was connected
with the wire of a lever similar to that drawn in Plate VI. fig. 1 a,
though between them a glass tube filled with water, and not too
short, was interposed. The discharge which deflected the mag-
net was effected by the fall of the lever. The velocity with which

488 On the Theory of the Electric Residue in the Leyden Jar.

the lever descended could be regulated by the height-of its:fall,
or by a moveable weight made to act against cords of vuleanized
caoutchoue. Without doubt a greater stability in the indications
of this instrument would be obtained by using a heavier magnet,
which would involve, however, a small increase in the other
dimensions. Even with these dimensions the multiplier is an
excellent electrometer for currents of discharge, provided it be
properly retarded when very strong charges are employed.

Such an apparatus may be used with advantage to determine
the proportion in which electricity has divided itself between two
Leyden jars. A sine-electrometer is connected with one jar
only, and as soon as the former indicates a certain deflection, the
latter is discharged through the multiplier. A second jar is
then connected with the first, and both are simultaneously dis-
charged as soon as the sine-electrometer has attained its former
position. If in the first case the needle of the multiplier be
deflected to an angle «, and in the second case to «+8, then by
equal tension on the knobs, the quantities of electricity in the
two jars will be as a to 8. In general, instead of the angles «
and 8, the number of scale-divisions which are deflected into
the field of the telescope may be taken.

In Appendix I. we have described a method for finding the
proportion in which the charge divides itself between two jars
by means of the sine-electrometer alone. This method suffers
from the disadvantage of the charge in the battery being change-
able. When a part of the charge is transferred to the single -
jar, some time must elapse before the electrometer can be read-
justed for measurement. At first the charge imparted to the jar
appears on this account too great, because during this time,
besides the loss of electricity in the air, a residue will also have
formed itself; afterwards it appears too small, because the residue
already formed is too great to be detained by the remaining
charge in the battery, and as a consequence it is partly set, at
liberty before the electrometer can be readjusted. The present
method is free from such disadvantages. In order to show its
exactitude, we will give the numbers which determine the pro-
portion in which the charge distributed itself between the jar F
mentioned in Appendix I., and the battery B of five jars.

Deflection of the needle in the multiplier in scale divisions.

By B alone. By B and F connected.
66°3 :
66°5 79°6
66°5 79°4:
66:2 79°2
Mean 66-4 79°8

Meéan~ 79°5

On a new Electro-magnetic Engine. 489
Let Q'=66'4 and Q=79°5, then
Q-—Q' 13:1

ings 795 01647.

Apprenpix III.

In order to calculate how the loss of electricity distributes
itself over the several times of observation, a few indications
which have reference to the calculation of the Table a" will suffice.

The loss V is the difference between the primitive charge and
that which we know to have been withdrawn. According to the
Table a, the primitive charge was 0°4742 ; at the first discharge
0°2951 was withdrawn ; then, according to Table a’, the collected
residues amounted to 0:1307, to which we may add 0:0075,
equal to the last residue, as the quantity which probably still
remained in the jar but could not be collected. Then. is

V=0°474.2 — (0:2951 + 0:1382) =0:0409.

The superficial area F enclosed by the curve of disposable
charge is
F=f,+fot+fgt+&e....

=7[(0'4742 + 0:4133)18 + (0-4133 + 0°3896) (50—18) +... ]
= 228-086.

The area ¢ enclosed by the curve of collected residues is
g=fi tf" +f" +&e....
=1/0-0443 . 65+0:0166. (153—65)+..... ]
=30°767.
Hence the constant for the loss of electricity is
V 0:0409

*~ F4o 258°863
Everything else is immediately given.
Marburg, Oct. 1853.

=0-000158.

LXXVI. Onanew Electro-Maynetic Engine invented by M. Marié
Davy. By M. Becquere.*,

pide ieee have been made for the last twenty years, to
construct machines in which the magnetic property im-
parted to soft iron by the electric current, should be employed
as a motive power; but the electromotive machines hitherto
brought forward have been far from presenting any ceconomical
advantages over steam-engines.

* From the Comptes Rendus, for May 15, 1854, p. 853.

490 M. Becquerel on a new Electro-magnetic Engine

Any electro-magnetic engine.must be composed essentially
of a series of electro-magnets of soft iron, of armatures also ot
soft iron, or arranged as electro-magnets, with various adjuncts,
for the transmission of the electricity furnished by a battery or
electro-magnetic machine, and of a commutator or breaker, for
the purpose of producing a continuous circular or backward and
forward motion.

In the machines hitherto constructed, these various parts do
not combine all the conditions desirable for making use of all
the power set in action ; a cheap, constant, and powerful source
of electricity does not yet exist; the soft iron, never being pure
or perfectly malleable, retains for a longer or shorter period
after each interruption a portion of the magnetization which
had been communicated to it by the current; the primitive
current and the extra current produce contrary effects, causing
a mutual injury; and the commutators often present alterations
when the circuit is closed. «

M. Jacobi, moreover, wao has carefully studied the subject of
the practical employment of electro-magnetic engines, has
arrived at this result,—that the mechanical effect or amount
of work, considermg the expenses necessary to keep them in
action, is far inferior to that of the other motive powers in use.
But this does not set the question at rest ; for, if we succeed in
discovering sources of electricity more ceconomical and powerful
than those at present in use, and in avoiding a portion of the
inconveniences already mentioned, electricity and magnetism
may take their place with heat as motive forces.

These considerations show that all researches having for their
object the removal of some of the difficulties encountered in the
employment of electricity as a motive power, should be received
favourably ; and the memoir recently presented by M. Marié
Davy to the Academy contains some new views worthy of atten-
tion, as will be seen from the following report.

M. Marié thought, and with reason, that, in order to obtain
the maximum of effect in electro-magnetic engines, the electro-
magnets and the armatures must act up to the point of contact,
seeing that the electro-magnetic force, as he found by calcula-
tion and experiment, decreases so rapidly with the distance, that
in employing two electro-magnets, when these are brought to-
gether from a distance to the point of contact, they develope an
amount of work in such a manner that five-sixths are produced
in the last millimetre, and the half of the remainder in the last
but one; when the second electro-magnet is replaced by an
armature of soft iron, three-fourths of the quantity of work are
produced in the last millimetre through which the armature
passes, and more than half the remainder im the last but one.

invented by M. Marié Davy. 491

In most of the rotatory electro-magnetic machines hitherto
constructed, the moveable armatures pass rapidly before the
fixed electro-magnets, following a line perpendicular to the axis,
without coming into contact; thus the entire amount of work
that might be obtained is not made use of. We must, however,
refer to the fact, that M. Froment, who has paid much attention
to electro-magnetic motor apparatus, has constructed a machme
in which an interior wheel, furnished with armatures of soft
iron, revolves upon the terminal faces of the fixed electro-
magnets, so as to make use of the magnetic attraction even up
to the point of contact of the magnetized surfaces; but this
arrangement produces, during the action of the machine, a
series of shocks or concussions, which are opposed to the con-
struction of a powerful machine upon this model.

M. Marié makes the moveable electro-magnets or armatures
revolve in such a manner as to approach the fixed electro-
magnets in the direction of the axis up to the point of contact,
without any shock. Upon this principle are constructed the
two electromotive machines described in his note, one of which
has a continuous rotatory, the other an oscillatory motion. We
shall only refer to the former apparatus, of which he has pre-
pared a model, which has worked in our presence.

This machine consists of sixty-three electro-magnets arranged
at equal distances round a circle of wood, furnished internally
with a circle of copper. All the electro-magnets have their axes
directed towards the centre of the wheel, and their surface
coincides with the concave surface of the copper circle.

In the interior of this large wheel there are two others, of
which the radius is one-third of that of the former; these are
also furnished with a circle of copper, and bear each twenty-one
equidistant electro-magnets, of which the axes are directed
towards the centre, and the polar surfaces comcide with the
concave surface of the copper wheels; these little wheels can
then revolve, without slipping, in the interior of the large wheel,
and carry round by their movement the axle of the machine,
which corresponds with the axis of the large wheel. The move-
able electro-magnets come successively in contact with the fixed
electro-magnets. The large and small wheels are furnished
with teeth for the maintenance of the coincidence, when this is
once established.

The machine is also provided with various pieces of apparatus
for putting each of the electro-magnets successively in commu-
nication with the battery, and giving a different magnetization
to the two electro-magnets at the moment when they act upon
each other.

M. Marié has made a change which appears advantageous,

492 Sir W. R. Hamilton on some

by replacing the internal wheels by others, which, instead of
bearing electro-magnets, are surrounded by a ring of soft iron,
which forms the armature ; the moveable portion is thus rendered
lighter, and the teeth are rendered unnecessary. It is this
modification of the machine that we have seen in action.

The circular electro-magnets of M. Nicklés will here find an
interesting application ; and, at our suggestion, M. Marié pro-
poses to make some experiments with this addition, which will
enable him to augment the power of the machine without
increasing the expense.

The construction of the machine is somewhat affected by
the inexperience of the maker, so that it required a battery of
twenty-four Bunsen’s elements to produce ;, horse-power.
But, according to M. Marié’s calculations, one of the same
energy, or perhaps even one of less intensity, would be suffi-
cient, with a machine of large size, to produce 300 times the
power, seeing that the friction would not increase in the same
proportion as the force of the machine; the means of electrical
communication not being changed, and the power produced by
the attraction of the magnets being capable of multiplication in
a great degree, by making use of electro-magnets formed of
large cylinders of soft iron. The model was constructed with
a view to show the relations between the effect calculated from
the magnetic force developed in the electro-magnet and the actual
force produced. The proportion was as 4 to 3, which is already
a very close approximation, considering the numerous imperfec-
tions resulting from the bad construction of the machine.

LXXVII. On some Extensions of Quaternions*. By Sir W1LL1AM
Rowan Hamiuton, LL.D., M.R.IA., F.R.A.S., Correspond-
ing Member of the French Institute, Hon. or Corr. Member of
several other Scientific Societies in British and Foreign Coun-
tries, Andrews’ Professor of Astronomy in the University of
Dublin, and Royal Astronomer of Ireland+.

[1.] CEE that in the polynomial expressions,

PY Sige! ta + .. +iynz, =D’,
PY ge yt oa" +e. tage! = dea",
the symbols zy)... 2,, which we shall call the constituents of the
polynome P, and in like manner that the constituents a! .. 2’,

P =to%y +42, + -. toate SDT, i
(1)

* See the work entitled, “ Lectures on Quaternions,” by the present
writer. (Hodges and Smith, Dublin, 1853.)
+ Communicated by the Author.

Extensions of Quaternions. 493

of P!, and x", ..2", of P", are subject to all the usual rules of
algebra, and to no others; but that the other symbols, u.. ¢,,
by which those constituents of each polynome are here symboli-
cally multiplied, are not all subject to all those usual rules: and
that, on the contrary, these latter symbols are subject, as a
system, to some peculiar laws, of comparison and combination,
More especially, let us conceive, in the first place, that these
n+1 symbols, of the form ¢,, are and must remain unconnected
with each other by any linear relation, with ordinary algebraical
coefficients ; whence it will follow that an equality between any
two polynomial expressions of the present class requires that all
their corresponding constituents should be separately equal, or that
iP! = P; then al Sage Sag ca wea, el ®)
and therefore, in particular, that the evanescence of any one such
polynome P requires the vanishing of each constituent separately ;
so that
Oren fate Ua hg ee noi ede AO)
Tn the second place, we shall suppose that all the usual rules
of addition and subtraction extend to these new polynomes, and
to their terms; and that the symbols ¢, like the symbols 2, are
distributive in their operation; whence it will follow that

Pi4-P 1, (ao 45) ee ue tea) 2 )
or that
Bae fe Ser Se eye Ae ORONO TH)

and as a further connexion with common algebra, we shall con-
ceive that each separate symbol of the form ¢ may combine com-
mutatively as a factor with each of the form 2, and with every
other algebraic quantity, so that ww=av, and that therefore the
polynome P may be thus written,
DP Swot Raye he ape Dawe. WS, U6)
But, third, instead of supposing that the symbols « combine
thus in general commutatively, among themselves, as factors or as
operators, we shall distinguish generally between the two inverted
(or opposite) products, w' and ct, or fig and t,t¢; and shall con-
ceive that all the (n+ 1)? binary products (uw), including squares
(?=w), of the n+1 symbols ¢, are defined as being each equal
to.a certain given or originally assumed polynome, of the general
form (1), by (7+ 1)? equations of the following type,

Uptg=(fg)tot (fgl)ut +» + (fgh)int --+Ugn)ins + (2)
the (n+ 1)? coefficients, or constituents, of the form (fyh), which
we shall call the “constants of multiplication,” bemg so many
given, or assumed, algebraic constants, of which some may vanish,
and which we do not here suppose to satisfy generally the rela-

494. Sir W. R. Hamilton on some

tion, (fgh)=(gfh). And thus the product of any two given poly-
nomes, P and P', of the form (1), combined in a given order as
factors, becomes equal to a third given polynome, P", of the same
general form,

Pl PP! = Sarpop a Dal peg e= Dallyagge. alin cov. G48)
the summations extending still from 0 to n, and the constituent
zx", of the product admitting of being thus expressed :

Th = JOREFE we otcn %.) pashan al
As regards the subjection of the symbols « to the associative law

of multiplication, expressed by the formula,

ood Mase ol,

we shall make no supposition at present.
[2.] As a first simplification of the foregoing very general*
conception, let it be now supposed that
7h Ne eae Mant at Se ks
the n other symbols, ¢,, é9, . - tn, beimg thus the only ones which
are not subject to all the ordinary rules of algebra. Then
because
Ie be las api gatyy. 6 a nae
it will follow that if either of the two indices f or gy be =O, the
constant of multiplication (fg) is either =1, or =0, according
as h is equal or unequal to the other of those two indices; and
we may write,
(Ofh) = ( fOh) =0, if h om f ot UAT oe an
(Offi ( POF ae ide 208 So, TER a
With this simplification, the number of the arbitrary or disposable
constants of the form (fgh), which are not thus known alread
to have the value 0 or 1, is reduced from (n+1)° to (n+1)n?;
because we may now suppose that f and g are each > 0, or that
they vary only from 1 to x. For we may write,
P=p+o, Ppi+a', . 2. See (14)
where
P=e )=2 PS Gt yt. bee gee ins
and then, by observing that p and p! are symbols of the usual

and algebraical kind, shall have this expression for the product
of two polynomes :

P!=PP!=(p+a)(p'+oa')=pp't+po'tpla+oaa'; . (16)
* Some aceount of a connected conception respecting Sets, considered

as a i Quaternions, may be found in the Preface to the Lectures already
cited,

Extensions of Quaternions. 495

where the last term, or partial product, wa’, is now the only one
for which any peculiar rules are required.

[3.] When the polynome P has thus been decomposed into
two parts, p and a, of which the one (p) is subject to all the
usual rules of algebraical calculation, but the other (a) to pecu-
liar rules ; and when these parts are thus in such a sense heéero-
geneous, that an equation between two such polynomes resolves
itself immediately into two separate equations, one between parts
of the one kind, and the other between parts of the other kind;
so that

if P=P’, or p+a=p'+a’, then p=p', andaw=a'; . (17)
we shall call the former part (p) the scalar part, or simply THE
SCALAR, of the polynome P, and shall denote it, as such, by the
symbol S . P, or SP ; and we shall call the latter part (a) the vector
part, or simply THE vecToR, of the same polynome, and shall
denote this other part by the symbol V.P, or VP: these names
(scalar and vector), and these characteristics (S and V), being
here adopted as an extension of the phraseology and notation of
the Calculus of Quaternions*, in which such scalars and vectors
receive useful geometrical interpretations. From the same cal-
culus we shall here borrow also the conception and the sign of
conjugation; and shall say that any two polynomes (such as
those represented by p+a@ and p—a) are consucare, if they
have equal scalars (p), but opposite vectors (+a): and if either
of these two polynomes be denoted by P, then the symbol K . P,
or KP, shall be employed to represent the other; K being thus
used (as in quaternions) as the characteristic of conjunction.
With these notations, and with the recent significations of panda,

p=S(p+a), w=V(p+a), p—w=Ki(p+a);.. (18)
or, writing P and P! for p+ and p—a,

P=KP. if SP'=SP, endiM Sra VRS) eriinne ole (SQ)
_ and generally, for any polynome P, of the kind here considered,
P=SPH VE) Pee BE VP i fl bets 5 dmb | (RO)

We may also propose to call the n symbols ¢, . . ¢, by the general
name of VECTOR-UNITS, as the symbol ¢ has been equated in
(16) to the scaLar-unIt, or to 1; and may call that equation
(10) the unrr-Law, or more fully, the Jaw of the primary unit.
[4.] Already, from these few definitions and notations, a
variety of symbolical consequences can be deduced, which have
indeed already occurred in the Calculus of Quaternions, but
which are here taken with enlarged significations, and without
reference to interpretation in geometry. For example, in the
general equations (20), we may abstract from the operand, that

* See Lectures, passim.

496 Sir W. R. Hamilton on some

is, from the polynome P, and may write more briefly (as in qua-
ternions),
1=S8+V, K=S=V3% 8s yo 2)
whence
S=3(14+K), V=3(1—K); ws. (22)
or more fully, yeah
SP=1(P4 Ph, VP=2(P =P); ifP=KP. .° (28)
Again, since (with the recent meanings of p and a),
Sp=p, Vp=0, Kp=p, Sa=0, Vo=a, Ka= rte (24)
S(p—o) =p, V(p—@)=—@, K(p—e)=pts,
we may write

SSP=SP, VSP=0=SVP, VVP=VP,

SKP=SP=KSP,’ VEP=—VP=KVP, KKP=P; (25)
or more concisely,
S=8, VS=SV¥=0, Nev, 6 aa (26)
SK=KS=S, VK=KV=—V, K?=

The operations S, V, K are evidently one)

SESS, § Vesey re ese ail py ane
and hence it is permitted to multiply together any two of the
equations (21) (22), or to square any one of them, as if 8S, V, K
were ordinary algebraical symbols, and the results must be found
to be consistent with those equations themselves, and with the
relations (26). Thus, squaring and multiplying the equations
(21), we obtain

1?=(S+ V)?=S*?4 V?+28V=S+V=1, 5

K?=(S—V)?=8?4 V?—28V=8+V=1, 4,taacf (96)

=(S+V)(S—V)=S?—V?=S—V=K;

and the equations (22) give similarly,

S*=1(14 K)?=4(1+ K?+2K)=3(14+K)=S8; hy
V?=1(1—K)?=1(1+ K*-—2K) =i (1-K)=V; } (29)
SV=VS=i(1 +K) (l —K) =4(1 — K?) =H(1 —1)=0.

Again, if we multiply (22) by K, we get
KS=3K(1+K)=3(K+K*%)=1(K+4+1)s8, .
KV=23K(1—K)=1}(K—K?’)=1(K—1)=—V;

all which results are seen to be ayniVolléally true, and other veri-_

fications of this sort may easily be derived, among which the
following may be not unworthy of notice :

(S+V)™=1, S£V)™H=S+V, poe pe

Pal agor iL (31)
where m is any positive whole number.

(30)

Extensions of Quaternions. 497

[5.] As a second simplification of the general conception of
polynomes of the form (1), which will tend to render the laws
of their operations on each other still more analogous to those of
the quaternions, let it be now conceived that the choice of the
“constants of multiplication,” ( fyi), is restricted by the follow-
ing condition, which may be called the “ Law of Conjugation :”

KN dd 0 0 Ore. i, Shp) AG a 2 (82)

namely the condition that “ opposite (or inverted) products of
any two of then symbols 4,, . . ¢,, shall always be conjugate poly-
nomes.” The indices f and g being still supposed to be each
> 0, the constants of multiplication (fyh), which had remained
arbitrary and disposable in [2.], after that first simplification
which consisted in supposing ¢j=1, come now to be still further
reduced in number, from (2+1)n? to in(n?+1). For we have
now, by operating with S on the equation (32), the following
formula of relation between those constants,

(fo0)=(9f0); «se se ee (88)

and by comparing coefficients of ¢,, this other formula is obtained,
—(fgh)=(gfh), fh>0; . . . (84)
(ffr)=0,ifh>0. 2 2... (85)

Writing, for conciseness,
(f90)=(f9), (FA=(f), - + + (86)

the squares, e*, of the n vector-units +, will thus reduce themselves
to so many constant scalars,

t= (1), P= (2), .-P=(f),--m'=@)53 + (87)
n(n—1)
2
other scalars, as constants of multiplication; namely the consti-
tuents (fyh) of the polynomial expansions of all the binary pro-
ducts, ev’ or tt, of unequal vector-units, taken in any one
selected order, for instance so that g>/f; it being unnecessary
now, on account of the formule of relation (33) (34), to attend
also to the opposite order of the two factors, if the object be
merely to determine the number of the independent constants,
which number is thus found to be n+2(n?—n)=}(n®+7), as
above stated. Such then is the number of the constants of mul-
tiplication, including n of the form (f), and 3n(n—1) of the
form (fg), besides others of the form (fg), which remain still
arbitrary, or disposable, after satisfying, first, the Unit-Law,

to=1, and second, the Law of Conjugation, K .cl=c' t.
[6.] From this law of conjugation, (32), several general con-
sequences follow. For, first, we see from it that “the square of
Phil, Mag. 8.4. No. 48, Suppl. Vol. 7. 21

whence

and besides these, we shall have (n+1) x =1(n3—n)

498 On some Extensions of Quaternions.

every vector is a scalar,” which may be thus expanded :
= (0,2, + « « Un®n)®*= (1) ay? + (2)ag?+ «. tae (38)

+ 2(12) aap +2(18)aya5+ .. $2( fy) pty » «3

that is, more briefly,
(Sux) =E(e)e2+2E(fy)ayz, - - . + (89)
the summations extending to values of the indices > 0, and g
being >f. In the second place, and more generally, “ inverted
products of any two vectors are equal to conjugate polynomes ;”
or in symbols, dite
wasK.an', .. ++ ees (40)
whatever two vectors may be denoted by w and a!. In fact,
these two products have (according to the definition [3,] of con-
jugates) one common scalar part, but opposite vector parts,
S.clonS.we!=Z()na't 0a te! a
—V.a's=V .ao! = (fgh) (ape!, —a,2' py:
whence also we may write, as in quaternions,

S. ae! =1(o0'+a'a), Vv aa! =1(aa!—a'a). . (42)
And, thirdly, the result (40) may be still further generalized as
follows :—“ The conjugate of the product of any two polynomes is
equal to the product of their conjugates, taken in an inverted
order ;” or in symbols,

Rowe Si cs ee ne ee
In fact, we have now, by (16), (24), (27) and (40),

KP’/=K. PP’=K. (p+a)(p' +e)
=K(pp'+po't+p'o+aa')
=pp'—po'—p'a+a'a
=(p'—o')(p—o)=KP’. KP, . . (44)

as asserted in (43). It follows also, fourthly, that “the product
of any two conjugate polynomes is a scalar, independent of their
order, and equal to the difference of the squares of the scalar
and vector parts of either of them ;” for,

if P'=KP, then PP’=(p+a)(p—w)=p?—ow*; . (45)

where #” is, by (38) or (39), a scalar. And if we agree to call
the square root (taken with a suitable sign) of this scalar pro-
duct of two conjugate polynomes, P and KP, the common TENSOR
of each, and to denote it by the symbol TP; if also we give the
name of veRsoR to the quotient of a polynome divided by its own
tensor, and denote this quotient by the symbol UP: we shall
then be able to establish several general formule, as extensions

Description and Analysis of two Mineral Species. 499
from the theory of quaternions. For we shall have

TP=TKP= /(PKP) = {(SP)?—(VP)2}7; . . (46)

T(pto)=(p?—o°)}; Tp=(p*)*, To=(—o)*; (47)

P
Bese UP SUB pile e seute s. ccas cee Ghia)
TUP=UTPS1 5: TTP=TP; UUPRUP ee 0 v\as(60)

with some other connected equations. But, although the chief
terms (such as scalar, vector, conjugate, tensor, versor), and the
main notations answering thereto (namely 8, V, K, T, U), of the
calculus of quaternions, along with several general formule result-
ing, come thus to receive extended significations, as applying to
certain polynomial expressions which imvolve n vector-units, and
for which as many as }(n?+~2) constants of multiplication are
still left arbitrary and disposable ; yet it must be observed, that
we have not hitherto established any modular property of either
of the two functions, which have been called above the tensor and
versor of a polynome ; nor any associative law, for the multipli-
cation of three such polynomes together.
Observatory of Trinity College, Dublin,
June 6, 1854.
[To be continued. ]

LXXVIII. Description and Analysis of two Mineral Species.
By T. 8. Hunt, of the Geological Commission of Canada*.

oe the specimen which afforded the minerals here described

I am indebted to the kindness of Professor Williamson of
Queen’s College, Kingston, C.W., to whom it was given by
Dr. James Wilson of Perth. The locality assigned to it is the
second lot of the ninth concession of the township of Bathurst,
and it is probably derived from the crystallme limestone of that
region. It consists of a white, massive pyroxene or diopside,
with small crystals of silvery-gray mica, prisms of bluish-green
apatite, portions of copper pyrites, and of a milk-white cleavable
calcite, together with a rose-red species, having in its aspect
some resemblance to a common variety of Wollastonite. It occurs
massive, with cleavages which indicate an oblique system of cry-
stallization ; according to Prof. E. C. Chapman of the University
of Toronto, who has examined a specimen of the mineral in the

* From the Report of the Survey for 1852-53; communicated by the
Author.
2L2

500 Deseription and Analysis of two Mineral Species.

collection of the Canadian Institute, the cleavage prism is appa-
rently right rhomboidal ; the inclination of M : T=110° to 125}.
The cleavages with M and P are perfect, and easily obtained,
giving to the mass a fibrous aspect; with T the cleavage is im-
perfect. Hardness, 3°5; density, 2°765 to 2:776. Lustre vitreous,
shining, occasionally pearly on the cleavage surfaces. Colour,
rose-red to peach-blossom red ; subtranslucent ; fracture uneven,
Before the blowpipe it becomes white and opake from the loss
of water, and fuses easily with intumescence into a white enamel.
When pulverized and boiled with hydrochloric acid, it is partly
decomposed with separation of pulverulent silica. A qualitative
analysis showed the presence of silica, lime, magnesia and
alumina, with a little iron and traces of manganese, besides a
large quantity of potash. The results of three quantitative
analyses are subjoined; the earthy mgredients were determined
by fusion with carbonate of soda; the alkalies in the first ana-
lysis were separated by a method for which I am indebted to
Dr. A. A. Hayes of Boston. It consists in fusing the pulverized
mineral for half an hour with one part of pure lime and four
parts of chloride of calcium in a platinum crucible ; the fusion
was effected over a spirit-lamp. When cold, the mass was di-
gested with water, and the solution then contained all the alkalies
as chlorides, mixed with chloride of calcium. The lime-salt was
decomposed by carbonate of ammonia, and the sal-ammoniac
separated by sublimation from the evaporated residue, leaying
the alkaline chlorides in a state of purity. The whole amount
of water in the mineral is only expelled by a heat which produces
incipent fusion. The small portion of silica, which in the ordi-
nary process of analysis adheres to the alumina, was not sepa-
rated except in the third of the following analyses :—
1h II. 1 die
Dilieay sh Sigua aldesiWintarnAd OO 43°00 43°55
Afomina wth ale. menial YoeS LO 27:80 27°94
Oxides of iron and Mindi eee ‘70 20
grasa oat Ar ie hee E ord 6°72 6:50
Marnesiay; 4 2! (0 ee) Oe 3°83 3°81
Poiana. ME lh Wes eee 8°27 8°37
OG ae eavestaels ig Merge Ui “95 “95 1:45
Water tate eres eRe 9-40 861

10015 10067 100:43

As this interesting mineral appears to constitute a new species,
I have named it Wilsonite after its discoverer, Dr. Wilson, who
has long been known as a zealous student of the mineralogy of
his district. It is to be wished that further examinations may
detect distinct crystals of the mineral; a single imperfect one

Dr. Stenhouse on Araxziine. 501

only was found in the calcite ; small masses of the species, are
often completely imbedded in the accompanying pyroxene. This
pyroxene is massive, crystallme, and affords cleavage prisms
having the ordinary angles of the species ; in a crevice it was
observed in small crystals. Hardness=6°5 ; density 3°186, to
3192. Lustre vitreous, pearly ou the cleavage surfaces; colour-
less or grayish-white ; translucent to semitransparent ; fracture
uneven, subconchoidal. Before the blowpipe the grayish por-
tions become colourless ; it retains its transparency and. lustre,
and fuses with some difficulty, and with intumescence, into a
colourless glass. The results of two analyses were as follows :—

PERE Ge tee ee ee) 50°90

Algae... re es 6°77

Peroxide ofiron . . * ‘3

pine Ree oe ee oO OU 23°74

Wa Hes ny ye, hie tt OD 18°14

Loss by ignition . . . 110 “90
100°59 100°45

This pyroxene is peculiar from the amount of alumina, which
has not hitherto been observed in any considerable quantity
except in the dark-coloured ferruginous varieties. The alumina
in these is supposed to replace a portion of silica, and admitting
a similar relation in the present variety, we have the ordinary
formula of pyroxene. The silica of the first analysis (SiO? =
45°3) corresponds to 27°28, and the alumina to 2°87 of oxygen
30:05 ; while the oxygen of the other constituents, including
the water, amounts to 14°95. The ratio of 30:05 : 14°95 is very
nearly 2 : 1, conducing to the formula (Si 03, Al? 0%)?, (MO).

eee

LXXIX. On Fravxinine, the crystallizable principle in the Bark
of the Fraxinus excelsior, or Common Ash By Joun StEN-
pousE, LL.D., F.R.S.*

T is stated in most systems of chemistry, such for instance as
Lowig’s, Liebig’s, &c., on the authority of Messrs. Keller,
Herberger and Buchner, that the bark of the Fraxinus excelsior
contains a neutral, crystallizable, bitter principle, to which they
have given the name of fraxinine.

Their mode of extracting this principle was to treat an infu-
sion of ash-bark, so long as a precipitate fell, first with neutral,
and then with basic acetate of lead. The whole was then thrown
upon a filter, and the clear liquid which passed through was
treated with a current of sulphuretted hydrogen till all excess of

* Communicated by the Author.

502 Prof. Thomson on the Uniform Motion of Heat

lead was removed. The aqueous solution, when free from sul-
phide of lead, on being sufficiently concentrated, yielded crystals
of fraxinine on standing for a few days in a cool place. 1 ope-
rated on 38 lbs. of ash-bark exactly m the way just described.
The impure crystals obtaimed from the aqueous solution were
dried with blotting-paper, and when crystallized out of spirits
of wine, were colourless. They had lost their bitter, and had
acquired a sweetish taste. They had all the characteristics of
mannite ; and when they were subjected to analysis the following
were the results :—

0°273 grm. substance, dried at 212° F., gave 0°194 grm. of
water, and 0°389 grm. of carbonic acid.

Calculated. Found.
C2="72 39:5 38-897
H¥= 14 yey. 7°882
O#%= 96 52°8 53°22]

182 1000 100-000

The so-called fraxinine therefore is merely mannite. The
reason why previous experimenters had mistaken it for a new
bitter principle was simply this, that they had not freed it
entirely from adhering impurities. ‘

LXXX. On the Uniform Motion of Heat in Homogeneous Solid
Bodies, and its connexion with the Mathematical Theory of
Electricity*. By Professor Witt1am THomson.

[@INCE the following article was written}, the writer finds
that most of his ideas have been anticipated by M. Chasles
in two memoirs in the Journal de Mathématique; the first in

* This paper first appeared anonymously in the Cambridge Mathema-
tieal Journal in February, 1842. The text is reprinted without alteration
or addition. All the foot notes are of the present date (March 1854), The
general conclusions established in it show that the laws of distribution of
electric or magnetic force in any case whatever must be identical with the
laws of distribution of the lines of motion of heat in certain perfectly
defined circumstances. With developments and applications contained in
a subsequent paper on the Elementary Laws of Statical Electricity (Cam-
bridge and Dublin Mathem. Journ. Nov. 1845), they constitute a full theory
of the characteristics of lines of force, which have been so admirably inves-
tigated experimentally by Faraday, and complete the analogy with the theory
of the conduction of heat, of which such terms as “ conducting power for
lines of foree ” (Exp. Res. §§ 2797-2802) involve the idea.

+ This preliminary notice was written some months later than the text
which follows, and was communicated to: the editor of the journal to be
prefixed to the paper, which had been in his hands since the month of Sep-
tember, 1841. The ideas in which the author had ascertained he had been
anticipated by M. Chasles, were those by which he was led to the determi-

in Homogeneous Solid Bodies. 503

vol. iii., on the Determination of the Value of a certain Defi-
nite Integral; and the second, in vol. v., on a new Method of
Determining the Attraction of an Ellipsoid on a Point without
it. In the latter of these mémoires, M. Chasles refers to a paper,
by himself, in the twenty-fifth cahier of the Journal de lV’ Ecole
Polytechnique, in which it is probable there are sti!l further an-
ticipations, though the writer of the present article has not had
access to so late a volume of the latter Journal. Since, however,
- most of his methods are very different from those of M. Chasles,
which are nearly entirely geometrical, the following article may
not be uninteresting to some readers. |

If an infinite homogeneous solid be submitted to the action
of certain constant sources of heat, the stationary temperature at
any point will vary according to its position ; and through every
point there will be a surface, over the whole extent of which the
temperature is constant, which is therefore called an isothermal
surface. In this paper the case will be considered in which
these surfaces are finite, and consequently closed.

It is obvious that the temperature of any point without a
given isothermal surface depends merely on the form and tem-

erature of the surface being independent of the actual sources
of heat by which this temperature is produced, provided there

nation of the attraction of an ellipsoid given in the latter part of the paper.
He found soon afterwards that he was anticipated by the same author in an
enunciation of the general theorems regarding attraction ; still later he
found that both an enunciation and demonstration of the same general
theorems had been given by Gauss, whose paper appeared shortly after
M. Chasles’ enunciations; and after all, he found that these theorems had
been discovered and published in the most complete and general manner,
with rich applications to the theories of electricity and magnetism, more
than ten years previously, by Green! It was not until early in 1845 that
the author, after having inquired for it in vain for several years, in conse-
quence of an obscure allusion to it in one of Murphy’s papers, was fortu-
nate enough to meet with a copy of the remarkable paper (“An Essay on
the Application of Mathematical Analysis to the Theories of Electricity and
Magnetism,” by George Green, Nottingham, 1828) in which this great
advance in physical mathematics was first made. It is worth remarking,
that, referring to Green as the originator of the term, Murphy gives a mis-
taken definition of “potential.” It appears highly probable that he may
never have had access to Green’s essay at all, and that this is the explana-
tion of the fact (of which any other explanation is scarcely conceivable),
that in his Treatise on Electricity (Murphy’s Electricity, Cambridge, 1833)
he makes no allusion whatever to Green’s discoveries, and gives a theory
in no respect pushed beyond what had been done by Poisson. All the
general theorems on attraction which Green and the other writers referred
to, demonstrated by various purely mathematical processes, are seen as
axiomatic truths in approaching the subject by the way laid down in the
paper which is now republished. The analogy with the conduction of heat
on which these views are founded, has not, so far as the author is aware,
been noticed by any other writer.

504 Prof. Thomsou on the Uniform Motion of Heat

are no sources without the surface. . The temperature of an ex-
ternal point is consequently the same as if all the sources were
distributed over this surface in such a manner as to produce the
given constant temperature. Hence we may consider the tem-
perature of any point, without the isothermal surface as the sum
of the temperatures due to certain constant sources of heat distri-
buted over that surface.

To find the temperature produced by a single source of heat,
let 7 be the distance of any point from it, and let v be the tem-
perature at that point. Then, since the temperature is the same
for all points situated at the same distance from the source, it is
readily shown that v is determined by the equation

— 22 =— 4
ip A
Dividing both members by 7?, and integrating, we have

Mater Wa
r

Now let us suppose that the natural temperature of the solid,
or the temperature at an infinite distance from the source, is
zero ; then we shall have C=0, and consequently

— See meu.
= (1)
Hence that part of the temperature of a point without an iso-
thermal surface which is due to the sources of heat situated on
. pidw,? : '
any element, dw,?, of the surface, is om. where 7, is the di-
1 .
stance from the element to that point, and p, a quantity mea-
suring the intensity of the sources of heat at different parts of
the surface. Hence, the supposition being still made that there
are no sources of heat without the surface, if v be the tempera-
ture at the external point, we have

va ff, oa a

the integrals being extended over the whole surface. The quan-
tity p, must be determined by the condition

Daye Latent swe oeeeantn aauatte

for any point in the surface, v, being a given constant tempe-
rature.

Let us now consider what will be the temperature of a point
within the surface, supposing all the sources of heat by which
the surface is retained at the temperature v, to be distributed
over it. Since there are no sources in the interior of the surface,

in Homogeneous Solid Bodies. 505

it follows that as much heat must flow out from the interior
across the surface, as flows into the interior from the sources of
heat at the surface. Hence the total flux of heat from the original
surface to an adjacent isothermal surface in the interior is nothing.
Hence also the flux of heat from this latter surface to an adja-
cent isothermal surface in its interior must be nothing; and so
on through the whole of the body within the original surface.
Hence the temperature in the interior is constant, and equal to
v,, and therefore, for points at the surface, or within it, we have

Sf? =n Se ong tot aes eat)

Now, if we suppose the surface to be covered with an attractive
ae whose Beasity at different points is proportional to p,,

—Z Sf pile,” will be the attraction, in the direction of the

axis FR; z,on a point whose rectangular coordinates are 2, y, 2
Hence it follows that the attraction of this medium on a point
within the surface is nothing, and consequently p, is proportional
to the intensity of electricity in a state of equilibrium on the
surface, the attraction of electricity in a state of equilibrium being
Wnts on an interior point. Since at the surface the value of

Si Be ate constant, and since on that account its value within

the ite’ is constant also, it follows, that if the attr actine force on
a point at the surface is perpendicular to the surface, the attraction
ona point within the surface is nothing. Hence the sole condition
of equilibrium of electricity distributed over the surface of a body
is, that it must be so distributed that the attraction on a point
at the surface oppositely electrified may be perpendicular to the
surface.

Since at any of the isothermal surfaces v is constaut, it follows

that — 2, where z is the length of a curve which cuts all the

surfaces perpendicularly, measured from a fixed point to the
point attracted, is the total attraction on the latter pomt; and
that this attraction is in a tangent to the curve n, or in a normal
to the isothermal surface passing through the point. For the
same reason, also, if p, represent a flux of heat, and not an elec-
trical intensity, — 2 will be the total flux of heat at the variable
extremity of n; and the direction of this flux will be along n, or
perpendicular to the isothermal surface. Hence if a surface of
an infinite solid be retained at a constant temperature, and if a
conducting body bounded by a similar surface be electrified, the

506 Prof. Thomson on the Uniform Motion of Heat

flux of heat at any point in the first case will be proportional to
the attraction on an electrical poimt similarly situated in the
second ; and the direction of the flux will correspond to that of
the attraction.
dv, dv wd
Let — at be the external value of — mm at the original sur-
|

face, or the attraction on a point without it, and indefinitely near
it. Now this attraction is composed of two parts; one, the
attraction of the adjacent element of the surface, and the other
the attraction of all the rest of the surface. Hence, calling the
former of these a, and the latter 5, we have

Now, since the adjacent element of the surface may be taken as
infinitely larger, in its linear dimensions, than the distance from
it of the point attracted, its attraction will be the same as that of
an infinite plane, of the density p,. Hence a is independent of
the distance of the point from the surface, and is equal to 27p,.
Hence .
sa =27p,+0

dn, sisi

Now, for a point within the surface, the attraction of the adja-
cent element will be the same, but in a contrary direction; and
the attraction of the rest of the surface will be the same, and in >
the same direction. Hence the attraction on a point within the
surface and indefinitely near it is —27p,+06; and consequently,
since this is equal to nothing, we must have J=27p,, and
therefore ;

— ~1=4rp, 2 2. we 5)
i

Hence p, is equal to the total flux of heat at any point of the
surface divided by 47.

It also follows, that if the attraction of matter spread over the
surface be nothing on an interior point, the attraction on an
exterior point indefinitely near the surface is perpendicular to
the surface, and equal to the density of the matter at the part of
the surface adjacent to that point multiplied by 4r.

If v be the temperature at any isothermal surface, and p the
intensity of the sources at any point of this surface which would
be necessary to sustain the temperature v, we have, by (5),

which equation holds, whatever be the manner in which the .

in Homogeneous Solid Bodies. 507

actual sources of heat are arranged, whether over an isothermal
surface or not; and the temperature produced in an external
point by the former sources is the same as that produced by the
latter. Also the total flux of heat across the isothermal surface,
whose temperature is v, is equal to the total flux of heat from
the actual sources. From this, and from what has been proved
above, it follows that if a surface be described round a conduct-
ing or non-conducting electrified body, so that the attraction on
points situated on this surface may be everywhere perpendicular
to it, and if the electricity be removed from the original body
and distributed in equilibrium over this surface, its intensity at
any point will be equal to the attraction of the original body on
that point, divided by 4:r, and its attraction on any point with-
out it will be equal to the attraction of the original body on the
same point*.

If we call E the total expenditure of heat, or the whole flux
across any isothermal surface, we have, obviously,

Banff do?

Now this quantity should be equal to the sum of the expen-
diture of heat from all the sources. To verify this, we must, in
the first place, find the expenditure of a single source. Now the

temperature produced by a single source is, by (1), o=4, and
hence the expenditure is obviously equal to = x 4arr?, or to
477A. If A=p,da,?, this becomes 47rp,do,*._ Hence the total

expenditure is //4mp,dw,?, or — Sf = dw,?, which agrees with
1
the expression found above.

The following is an example of the application of these prin-
ciples.

Uniform Motion of Heat in an Ellipsoid.

The principles established above afford an easy method of de-
termining the isothermal surfaces, and the corresponding tem-
peratures in the case in which the original isothermal surface is
an ellipsoid.

* After having established this remarkable theorem in the manner shown
in the text, the author attempted to prove it by direct integration, but only
succeeded in doing so upwards of a year later, when he obtained the de-
monstration published in a paper, “ Propositions in the Theory of Attrac-
tion’ (Camb. Math. Journ. Noy. 1842), which appeared almost contempo-
raneously with a paper by M. Sturm in Liouville’s Journal, containing the
same demonstration ; exactly the same demonstration, as the author after-
wards (in 1845) found, had been given fourteen years earlier by Green.

508 Prof. Thomson on the Uniform Motion of Heat

The first step is to find p,, which is proportional to the quan-
tity of matter at any point in the surface of an ellipsoid, when
the matter is so distributed that the attraction on a point within
the ellipsoid is nothing. Now the attraction of a shell, bounded
by two concentric similar ellipsoids, on a point within it is no-
thing if the shell be infinitely thin; and its attraction will be
the same as that of matter distributed over the surface of one of
the ellipsoids, in such a manner that the quantity on a given
infinitely small area, at any poimt, is proportional to the thick-
ness of the shell at the same pomt. Let a,, b,, c, be the semi-
axes of one of the ellipsoids; a,+6a,, b,+6d,, c,+ 5c, those of
the other. Let also p, be the perpendicular from the centre to
the tangent plane at any point on the first ellipsoid, and p, + dp,
the perpendicular from the centre to the tangent plane at a point
similarly situated on the second ; then §p, is the thickness of the
shell, since the two ellipsoids being similar, the tangent planes at
the points similarly situated on their surfaces are parallel. Also,
on account of their similarity,

da, _ 5b, 8c, Sp,

aq by py’
and consequently the thickness of the shell is proportional to p,.
Hence we have, by (5),

1 dv
rot oleae, sek Dog ty -Ha)

where /, is a constant to be determined by the condition v=7,
at the surface of the ellipsoid.

‘To find the equation of the isothermal surface at which the
temperature is v,+dv,, let —dv,=C in (a). Then we have
k, pany = mo p,dn,=80,, where @, is an infinitely small con-
stant quantity; and the required equation will be the equation
of the surface traced by the extremity of the line dn,, drawn
externally perpendicular to the ellipsoid. Let 2’, y/, 2! be the |
coordinates of any point in that surface, and a, y, z those of the
corresponding point in the ellipsoid. Then, calling a, 8), y,
the angles which a normal to the ellipsoid at the point whose
coordinates are 2, y, z makes with these coordinates, and sup-
posing the axes of 2, y, z to coincide with the axes of the ellip-
soid 2a,, 2b,, 2c, respectively, we have

a! —x=dn, cos a, =

in Homogeneous Solid Bodies. 509

Or a!—2= Zt 0,, since @, is infinitely small, and therefore also

i
z'—x; whence

va! 1-4). aw :
a, 1% a,
a,
In a similar manner we should find
! '
y= #-, and FS = :
i Sal RIBS 213
“4.6? ce,”
But
- ay? 2
az b? of ey? aah
and hence we have
yi? 12 ,!2
pane ; a + Si pu
as(itZy) b2(L+ gh) ee (E4ed)
or
72 y? 12
a2420, + 52-420, o2 420, =»

for the equation to the isothermal surface whose temperature is
v,+dv,, and which is therefore an ellipsoid described from the
same foci as the original.isothermal ellipsoid. In exactly the same
manner it might be shown, that the isothermal surface whose
temperature is v, + dv, + dv’, is an ellipsoid having the same foci
as the ellipsoid whose temperature is v, + dv,, and consequently
as the original ellipsoid also. By continuing this process it
may be proved that all the isothermal surfaces are ellipsoids,
having the same foci as the original one.

From the form of the equation found above for the isothermal
ellipsoid whose temperature is v, + dv,, it follows that 0, or p,dn,
is =a,da,, where da, is the increment of a, corresponding to the
increment dn, of n,. Hence if a be one of the semiaxes of an
ellipsoid, a+du the corresponding semiaxis of another ellipsoid
haying the same foci, dn the thickness at any point of the shell
bounded by the two ellipsoids, and p the perpendicular from the
centre to the plane touching either ellipsoid at the same point,
we have

tp tt tO

All that remains to be done is to find the temperature at the
surface of any given ellipsoid having the same foci as the given

510 —— Prof. Thomson on the Uniform Motion of Heat

ellipsoid. For this purpose, let us first find the value of +2

at any point in the surface of the isothermal ellipsoid whose
semiaxes are a, b,c. Now we have from (a)

dv

dn

where & is constant for any point in the surface of the isothermal
ellipsoid under consideration, and determined by the condition
that the whole flux of heat across this surface must be equal to
the whole flux across the surface of the original ellipsoid. Now
the first of these quantities is equal to 47k Mf pdw* (dw being
op
=
But Sf Spdw? is equal to the volume of a shell bounded by two
similar ellipsoids, whose semiaxes are a, b, c and a+6éa, b+58,

=4arkp, |

ka : a
an element of the surface), or to 4ar 57 Sj {f dpdw*, since ois

c+6c, and is therefore readily shown to be equal to 4ar abe.
ka 4
Hence dor Sf Spdw?, or 4k ST: pdw* is equal to 4°? kabe. In

a similar manner, we have for the flux of heat across the original
isothermal surface 477r?k,a,b,c,, and therefore

4Pnr*kabe = 4?1rk,a,b,c,,

which gives
ini a,b,c,
Sehi abe *
Hence we have
dv a,b,c
=e an = ky at a . . . . . (c)

The value of v may be found by integrating this equation.
To effect this, since a, b, ¢ are the semiaxes of an ellipsoid pass-
ing through the variable extremity of n, and having the same
foci as the original ellipsoid, whose axes are @,, b,, ¢,, we have

a —a? =? —b?=c?—¢,*,

which gives

=a? —f?

c=a? —g? i. rear wens
where fi=a?—b?, g?=a?—e,;?
Hence (c) becomes

dv re a,b,c, p
dn CV e—Pyv (C-9)

in Homogeneous Solid Bodies. 511

Now by (4) dn= a and hence
a,b,c,da
PV (E—¥#)

dv= —Arrk, V@—
Integrating this, we have
da
v= —4akane [ apa +C. (e)

The two constants, k, and C, must be determined by the con-
dition v=v, when a=a,, and v=0 when a=; the latter of
which must be fulfilled, in order that the expression found for v

2 2
may be equal to SL -
1

To reduce the expression for v to an elliptic function, let us
assume
a =f cosec h

a,=f cosecp, JS? ~ eS SITE)

which we may do with propriety if f be the greater of the two
quantities f and g, since a is always greater than either of them,
as we see from (d). On this assumption, equation (e) becomes

__ 4k, a,b,c, dp _ Arkyaybye, 5
ilies Fic dard ets) deh cP meni & oat

where g
C= Mee Me Oe eS
7 (9)

Determining from this the values of C and k, by the con-
ditions mentioned above, we find C=O, and

2 fr :
k= Baste clea ths hcls OS" (A)
hence the expression for v becomes
Fy
m=O tae Piece MA Ag 7 3 Re ee (A)

The results which haye been obtained may be stated as fol-
lows :—

If, in an infinite solid, the surface of an ellipsoid be retained
at a constant temperature, the temperature of any point in the
solid will be the same as that of any other point in the surface
of an ellipsoid described from the same foci, and passing through
that point ; and the flux of heat at any point in the surface of
this ellipsoid will be proportional to the perpendicular from the
' centre to a plane touching it at the point, and inversely propor-
tional to the volume of the ellipsoid.

This case of the uniform motion of heat was first solved by

512 Prof. Thomson on the Uniform Motion of Heat.

Lamé, in his memoir on Isothermal Surfaces, in Liouville’s
Journal de Mathématique, vol. ii. p. 147, by showing that a
series of isothermal surfaces of the second order will satisfy the
equation

dy dv dv _

dat hye * ae =
provided they are all described from the same foci. The value
which he finds for v agrees with (e), and he finds for the flux of
heat at any point the expression

KA .

Vv (He—v*) 7 (He —p*)?

or, according to the notation which we have employed,
4ark,a,b,c,

Vv (a? —v*) (a? —p*)’
where y is the greater real semiaxis of the hyperboloid of one
sheet, and p the real semiaxis of the hyperboloid of two sheets,
described from the same foci as the original ellipsoid, and pass-

ing through the point considered. Hence a*, v*, p? are the
three roots of the equation

0,

x? y? 2

U u—f? sar tiga fs
or
uz— + de +9? +2 +y?+27)u? + { f79?+ a +9*)x? +9?y* + f?2"}

u—f%g?a®=0,
Hence
a°y*p?= f 29222,

and

a?y? +a?p? ae Pp ayy? are Cf? + 9°) x? + 97y? +f22*.
Therefore

2122
(a? —v®) (a? —p?) = a4 — ay? — ap? — vp? + 2a*v"p

2

=t—{ Pet (fr+g?)e+ Py + fre} +2 2

== at — (a2 —b) (a2—c2)—(2a2—b? —?) 22 — (a2 — 02)? — (a2 —B) 22
+2(a?—b?) (0),

=at—(a?—b*)(a? — 2) i (2? + c*)a®— (a? —c*)y? — (a? —b?) 2*
+ 20%? 1-4-5)

= a'—(a®—b?) (a?@—c?) — (b? +c?) x? — (a? +c?) y*@— (a? +b?) 2? + 20%c?

= 070? + ae? B22 — { (b2+.62)a®+ (a2 +c) y? + (a2 +52) 2%} 5

in Homogeneous Solid Bodies. 518

which is readily shown, by substituting for a6? + ac? + bc? its
2. 2 2 2f2 2

equal (a7? + a?c? + 6c?) hes + 73 + =) , to be equal to a :

d dv.
Hence the expression for — Tn elven above, becomes
In

which agrees with (c).

Attraction of a Homogeneous Ellipsoid on a Point within or
without it.
; da, dv , ‘
If in (c) we put k,= rad the value of — Tn ot any point will
: 1 Sh las
be the attraction on that point of a shell bounded by two similar
concentric ellipsoids, whose semiaxes are

a, a,V (1—e*), aVW(1—e”),

and
a, +da,, (a,+da,)/(1—e*), (a,+da,) ¥(1—e”),
where
arian Meas) (1)
and @—?=a2—¢2=a,2e? 3

the density of the shell being unity. Now this attraction is in
a normal drawn through the point attracted to the surface of
the ellipsoid whose semiaxes are a, b, c. If we cail a, B, y the
angles which this normal makes with the coordinates wz, y, z of
the point attracted, we have

x
3
a px
cos a= =—
VAC ii ¥ =) a
ae” Be

and similarly,

u z
cos B= FF, cos y= os

Hence, calling dA, dB, dC the components of the attraction
parallel to the axes of coordinates, we have, from (c),

dA=4rrx ee pda,

ab
AB = Amy 12 pda, nh pea oe (2
dC =4arz ai prda,

Phil. Mag. 8. 4, No. 48. Suppl. Vol. 7. 2M

514 Prof. Thomson on the Uniform Motion of Heat.

The integrals of these expressions, between the limits a4,=0
and a,=a',, are the re ae of the attraction of an ellipsoid
whose semiaxes are @!,, bj, cy, or a’), a’) /(1—e?), a’, /(1—e?)
on the point (2, y, 2). Now by (1) we may express each of the
quantities 6, c, b, c, in terms of a and a,, and the equation

2 2?

+5=1, or eR ee . (3)

2— 2,7 ° a®*—ea,

ay?
ate
enables us to express either of the quantities a, a, in terms of

the other. The simplest way, however, to integrate equations
(2) will be to express each in terms of a ‘third quantity,

=— Ry phe antes itt Ee be
epee (4)
Eliminating a from (3) by means of this quantity, we have

9 22 ye 2?
2

a.7=u"x se ea ae ee

2 u-2—e? — 2

Hence
ag? gn 8a
a,da,= + ua?+ weet Ga eee
2
= (4 ue +5 =) a;tu-*du=a,4p—2u-%d,
Also from (4) we have a= “t ; from which we find, by (1),

= 4yV(l =u"), C= “Ly (1—e?u’).

By (1) also, 6;=a,/ (1—e*), cy=a,/(1—e?). Making these
substitutions in (2) and integrating, we have, calling a! the vaiue
of a when a,=a’,,
A=4arz V (1—e?) v(1—e) 7 sua |
WV (1—e?u?) ¥ (1 —e?u?)
urdu

B=4ryV(1—e*) 7 ae + (5)

C=4rzV/ (1—e) ¥(1—e » (ae |

If the point attracted be within the ellipsoid, the attraction of
all the similar concentric shells without the point will be nothing,

and hence the superior limit of wu will be the value of “1 at the

surface of an ellipsoid similar to the given one, and passing
through the point attracted.
Now in this case a,=a, since a is one of the semiaxes of an

Royal Society. 515

ellipsoid passing through the point attracted, and having the
same foci as another ellipsoid (passing through the same point)
whose corresponding semiaxis is a,. Hence, for an interior
point, we have

1 2]; 7)
A=dnev (1-8) ¥(1—¢8) | JUL 7a)
1 urdu
B=4 —e —¢!? ( 3 1 ‘ 6
my V7 (1—e?) /(1—e )\ (1 —e2u2)2(1—e!2u2)3 (6)
urdu

1
C=4rzV/ (1—e?) /(1—e?
V (1—e?) /( ){ (1 — u2)3(1 —eu2)3 J
These are the known expressions for the attraction of an ellip-
soid on a point within it. Equations (5) agree with the expres-
sions given in the supplement to liv. v. of Pontécoulant’s Théorie
Analytique du Systéme du Monde, where they are found by direct
integration by a method discovered by Poisson. They may also
be readily deduced from equations (6) by Ivory’s theorem. Or, on
the other hand, by a comparison of them, after reducing the limits

!
of the integrals to 0 and 1, by substituting Fe for uw, with

equation (6), Ivory’s theorem may be readily demonstrated.

LXXXI. Proceedings of Learned Societies.

ROYAL SOCIETY.
[Continued from p. 441.]
March 30, 1854.—Thomas Bell, Esq., V.P., in the Chair.

TH following paper was read :—*‘ On the Structure and Affini-
ties of Trigonocarpon (a fossil fruit of the Coal-measures).
By Joseph D. Hooker, M.D., F.R.S.

Having been for some time engaged in examining the structure
and affinities of some fossil fruits of the coal formation, included
under the name Trigonocarpon, and the progress which I am enabled
to make being extremely slow (owing to the difficulty of procuring
good specimens), I am induced to lay before the Royal Society such
results as I have arrived at, for publication in their Proceedings (if
thought worthy of that honour). The details and illustrations of
the subject will, when complete, be offered to the Geological Society
of London.

My attention has for many years been directed to the genus Jyi-
gonocarpon; as, from the period of my earliest acquaintance with
the flora cf the carboniferous epoch, I have felt assured, that bota-
nically, this was the most interesting and important fossil which it
contained in any great abundance, and that until the affinities of this
were determined, the real nature of the flora in question could never
be regarded as even approximately ascertained.

2M 2

516 Royal Society.

In the first place, Trigonocarpon is so abundant throughout the
coal-measures, that in certain localities some species may be pro-
cured by the bushel; nor is there any part of the formation in which
they do not occur, except the underclays and limestone. The sand-
stone, ironstones, shales and coal itself, all contain them.

Secondly. The symmetry in form and size which many of them
display, the regularity of the sculpturing on their surfaces, and
various other points, suggested their belonging to a class of highly
organized vegetables.

Thirdly. The fact of our being wholly unacquainted with the
organs of fructification belonging to the exogenous vegetation, which
also abounds in the coal formation, coupled with the assumed highly
organized nature of Trigonocarpon, favoured the assumption that
these might throw light upon one another, and seemed to afford a
legitimate basis upon which to proceed, should I ever procure speci-
mens of Trigonocarpon displaying structure, which I had long hoped
to do.

It is, however, only since my return from India that I have been so
fortunate as to obtain good specimens, and for these I am indebted
to my friend Mr. Binney of Manchester, who has himself thrown
much light upon the vegetation of the coal epoch, and whose exer-
tions indeed have alone enabled me to prosecute the subject; since
he has not only placed his whole collection of Trigonocarpons at my
disposal, but has shared with me the trouble and expense of their
preparation for study. All the specimens were found imbedded in
a very tough and hard black-band or clay ironstone, full of frag-
ments of vegetable matter, and which appears originally to have
been a fine tenacivus clay.

The individuai Trigonocarpons are exposed by breaking this rock,
and are invariably so intimately adherent to the matrix as to be
fractured with it. A great many of these lumps of ironstone, con-
taining partially exposed Trigonocarpons, have been sliced by a lapi-
dary in the usual manner, and excessively thin sections taken on
slips of glass. The sections were made necessarily very much at
random, but as nearly as possible parallel, or at right angles to the
long diameter of the fruit. Five of the specimens thus operated
upon have proved instructive, presenting the same appearances, and
all being intelligible, and referable to one highly developed type of
plants. As, however, the term highly developed may appear ambi-
guous, especially with reference to a higher or lower degree in the
scale of vegetable life, I may mention that by this term I mean to
imply that there are in the fruit of Trigonocarpon extensive modifi-
cations of elementary organs, for the purpose of their adaptation to
special functions, and that these modifications are as great, and the
adaptation as special, as any to be found amongst analogous fruits
in the existing vegetable world.

Thus, I find that the integuments of the fruit of Trigonocarpon are
each of them a special highly organized structure ; they are modifica-
tions of the several coats of one ovule, and indeed of the same num-
ber of integuments as now prevail in the ovules of living plants.

Royal Society. 517

The number, structure and superposition of these, are strongly
indicative of the Trigonocarpons having belonged to that large sec-
tion of existing coniferous plants, which bear fleshy, solitary fruits,
and not cones ; and they so strongly resemble the various parts of the
fruit of the Chinese genus Salisburia, that, in the present state of our
knowledge, it appears legitimate to assume their relationship to it.
In all the five specimens alluded to, there are more or less perfect evi-
dences of four distinct integuments, and of a large cavity, which is
in all filled with carbonate of lime and magnesia; these minerals, I
presume, having replaced the albumen and embryo of the seed.

The general form of the perfect fruit is an elongated ovoid (rather
larger than a hazel nut), of which the broader or lower end presents
the point of attachment, while the upper or smaller end is produced
into a straight, conical, truncated rostrum or beak, which is per-
forated by a straight longitudinal canal. The exterior integument
is very thick and cellular, and was no doubt once fleshy; it alone is
produced beyond the seed and forms the beak ; its apex I assume to
have been that of the primine of the ovule, and its cavity the exo-
stome. The second coat appears to have been much thinner, but
hard and woody or bony; it is impervious at the apex; is also ovoid,
and sessile by its broad base within the outer integument, with
which it is perhaps adherent everywhere except at the apex. This
is marked by three angles or ridges, and being that alone which
(owing to its hard nature) commonly remains in the fossil state, has
suggested the name of Trigonocarpon. Within this are the third
and fourth coats, both of which are very delicate membranes; one
appears to have been in close apposition with the inner wall of the
second integument, and the other to have surrounded the albumen.
These are now separated both from one another, and from the inner
wall of the cavity, by the shrinking of the contents of the latter, and
the subsequent infiltration of water charged with mineral matter. I
may remark, however, that these two membranes may be due to the
separation of one into two plates, in which case the original one was
formed of several layers of cells. Hitherto I have not been able to
trace any organized structure within the cavity of the fruit, and its
real nature therefore remains doubtful. It is only from the strong
resemblance, in structure, appearance and superposition, which these
integuments present to those of Taxoid Conifer, that I assume their
probable relationship. Salisburia, especially, has the same ovoid
fruit, sessile by its broader end, and its outer coat is perfectly ana-
logous, being thick, fleshy, and perforated at its apex by a longitu-
dinal canal (the exostome of the ovule); within this is a perfectly
similar, woody, two or three angled, impervious integument, form-
ing the nut. This again is lined with one very delicate membrane,
and contains a mass of albumen covered with a second similar mem-
brane. A marked analogy is presented to the European botanist by
the fruit of the Yew, which has the same integuments though some-
what modified; the outer, fleshy coat in the Yew is however a cup-
shaped receptacle, and not drawn up over the nut so as to leave
only a swall canal at the top, as in Salisburia and Trigonocarpon.

518 Royal Society.

The nut also does not adhere to the fleshy cup except below its
middle. ‘The internal structure is the same in all three.

Such are the main facts which I have been able satisfactorily to
establish. There are many others yet to be worked out, especially
those connected with the individual tissues of which those bodies are
composed; and it is particularly to be borne in mind that the disco-
very of some structure indicative of albumen or embryo, is abso-
lutely essential to the complete establishment of the affinity I have
suggested.

It must not be overlooked, that the characters through which I have
attempted to establish an affinity between Trigonocarpon and Conifere
are equally common to the fruits of Cycadee; and in connexion with
this subject I may remark, that M. Brongniart* has referred the
genus Noggerathia, which is also found in the coal-measures, to
that natural order, together with some associated organs which are
probably Trigonocarpons in a mutilated state. The leaves of Nog-
gerathia are, however, alone known, and Dr. Lindley, when figuring
those of one species (Lindley and Hutton, Fossil Flora, 28, 29),
pointed out their great resemblance to those of Salisburia, thus
affording collateral evidence of the view I have been led to adopt
from an examination of the fruit alone.

April 6.—Thomas Graham, Esq., V.P., in the Chair.

The following communication was read :—‘‘ On a new Series of
Sulphuretted Acids.” By Dr. August Kekulé.

Adopting the idea that the series of organic compounds of which
sulphuretted hydrogen is the type, corresponds in every respect with
the series of which water is the type, I concluded that not only
mercaptans and neutral sulphides which correspond to the alcohols
and ethers, but also compounds corresponding to the acids, anhy-
drous acids and ethers of acids might be produced; I therefore
endeavoured to obtain reactions which would enable me to replace
oxygen in the compounds of the latter series by sulphur.

Such reactions are produced by the compounds of sulphur with
phosphorus—the tersulphide (P? S’) and the pentasulphide (P? S*)—
which are easily obtained by fusing together amorphous phosphorus
and sulphur in an atmosphere of carbonic acid; no explosion takes
place, although the combination is attended with a very violent
action.

Experiment has proved that these combinations of sulphur and
phosphorus act on the members of the series of water in the same
manner (although less violently) as the corresponding compounds
of chlorine and phosphorus ;—however, with this difference, that by
using the chlorine compounds the product is resolved into two groups
of atoms, while by using the sulphur compounds there is obtained
only one group; a peculiarity, which, according to the bibasic nature
of sulphur, must have been expected. By acting on these com-
pounds of sulphur and phosphorus with water one atom of sulphu-

* Annales des Sciences Naturelles, 2" Series, vol. y. p. 52.

Royal Society. 519

retted hydrogen is obtained, while the chlorides give two atoms of
hydrochloric acid,

H H
ort O+P:S ey S42P0s Hs

ot 0+ 2P Cb=6H Cl+2P0: H.

Similar reactions are observed with organic compounds belonging
to the series of water with the formation of phosphorous and phos-
phoric acids respectively, or a conjugate acid. By acting in this
way, the following series of sulphuretted organic compounds is ob-
tained, by the side of which are placed for comparison the products
formed by the action of the chlorides of phosphorus on the same
substances.

Sulphuretted Hydrogen.
ulphuretted Hydrogen Hydrochloric Acid.

H
. \ S. 2H Cl.
Lees Chloride of Aithyle+-Hydrochloric Acid.
e \s. C?H> Cl+H Cl.

oo. anyle. Chloride of Aithyle.
ae S. 2C? H? Cl.

-Hyd ] ic Acid. :
Othyl-Hydrosulphuric Acid Chloride of Othyle-+ Hydrochloric Acid.

Or S. C2? H3 0,Cl+H Cl.
pas soe of Othyle. Chloride of Othyle
C2 Hs ‘
Lato \ S. 2C? H3 O, Cl.
a = Chloride of Othyle+Chloride of Athyle.
a \ S. C2 Hs O, Cl+- C2 H Cl.

Mercaptan is obtained by the action of tersulphide or pentasulphide
of phosphorus on alcohol with extreme facility. Sulphide of zthyle
may also be prepared by acting on ether in a similar manner.

Thiacetic Acid,—Sulphuretted Acetic Acid,—has been obtained by
me by acting on monohydrated acetic acid with tersulphide of
phosphorus. It is a colourless liquid, boiling at about 93°C., and
has a peculiar odour resembling sulphuretted hydrogen and acetic
acid. It dissolves potassium in the cold and zinc on heating with
the evolution of hydrogen, and gives with lead a salt less soluble
than the ordinary acetate, so that it gives a precipitate with acetate
of lead. By recrystallization from water or alcohol, the lead salt is
obtained in fine silky needles, which, though quite colourless at first,
are rapidly decomposed (whether in solution or in the solid form)
with the formation of sulphuret of lead.

By analysis I found the lead salt contained—

Lead 58'8 per cent. ‘Theory requires 58°0 per cent.

520 Royal Society.

The acid contained—

Sulphur 41°3 percent. Theory requires 42°] per cent.

Thiacetic acid is also formed in small quantity and by secondary
action, by distilling pentasulphide of phosphorus with fused acetate
of soda, Pentachloride of phosphorus gives a violent reaction with
thiacetic acid, yielding sulphochloride of B sani: whe chloride of
othyle, and hydrochloric acid,

C°H°0 S 5—(C2 Hs 5 Cls
Hyp StPCE=C*H OC1+HCL+PS Cr.

Thiacetate of Othyle.—Sulphide of Othyle.— Anhydrous Sulphuretted
Acetic Acid.—Pentasulphide of phosphorus acts but very feebly upon
anhydrous acetic acid in the cold, but on heating a violent reaction
takes place. By distilling the product, the anhydrous acid is obtained
in the form of a colourless liquid, boiling at about 121° C., and having
an odour greatly resembling sulphuretted acetic acid. On mixing
with water it falls to the bottom, without, at first, suffermg any
change; on standing, however, it is slowly dissolved and decom-
posed into sulphuretted acetic acid and ordinary acetic acid. This
change takes place much more rapidly on heating,

C? H3O H C2 H8O0 C?H3 0

It appears that anhydrous sulphuretted acetic acid is also pro-
duced by acting on the othyle-sulphide of lead with chloride of othyle,
at all events chloride of lead is formed. Chloride of benzoyle gives
with the lead salt a similar reaction, and it is probable that an inter-
mediate sulphuretted acid is formed, having the formula

C:H3O0 \ S
C7 HO

Thiacetate of Athyle.—Sulphuretted Acetic Ather.—This compound
may be prepared by the action of pentasulphide of phosphorus on
acetic ether, It is a liquid lighter than water, and possesses an
odour resembling acetic ether and sulphuretted hydrogen. It boils
at about 80°C.

It will be seen that the action of tersulphide and pentasulphide of
phosphorus above described produces sulphuretted organic com-
pounds by substituting sulphur for oxygen. ‘The compounds ob-
tained in this way may also be formed by replacing one or two
atoms of hydrogen in sulphuretted hydrogen (H®S), or one or two
atoms of metal in sulphide of potassium (K?S), or in sulphide of
hydrogen and potassium (KHS), by organic radicals. Mercaptan,
and the sulphides of alcohol radicals have, in fact, been long ob-
tained in this manner.

The formation of a sulphuretted compound containing an acid
radical has been observed by Gerhardt by acting on sulphide of
lead with chloride of othyle. I have not made many experiments of
this kind, but I have observed that chloride of benzoyle is not de-
composed by sulphuretted hydrogen, while it (as well as chloride of
othyle) gives a reaction with sulphide of hydrogen and potassium
vielding chloride of potassium.

Royal Society. 521

I am continuing these researches, and believe the above:reactions
will furnish many new compounds, and will tend to complete our
knowledge of some of those organic and inorganic compounds now
known.

April 27, 1854.—The Earl of Rosse, President, in the Chair.

The following papers were read :—

1. “On the Changes produced in the Blood by the administration
of Cod-liver Oil and Cocoa-nut Oil.” By Theophilus Thompson,
M.D., F.R.S.

The author has found that during the administration of cod-liver
oil to phthisical patients their blood grew richer in red corpuscles,
and he refers to a previous observation of Dr. Franz Simon to the
same effect. ‘The use of almond-oil and of olive-oil was not fol-
lowed by any remedial effect, but from cocoa-nut oil results were
obtained almost as decided as from the oil of the liver of the Cod,
and the author believes it may turn out to be a useful substitute. The
oil employed was a pure cocoa oleine, obtained by pressure from
crude cocoa-nut oil, as expressed in Ceylon and the Malabar coast
from the Copperah or dried cocoa-nut kernel, and refined by being
treated with an alkali and then repeatedly washed with distilled
water. It burns with a faint blue flame, showing a comparatively
small proportion of carbon, and is undrying.

The analysis of the blood was conducted by Mr. Dugald Camp-
bell. The whole quantity abstracted having been weighed, the
coagulum was drained on bibulous paper for four or five hours,
weighed and divided into two portions. One portion was weighed
and then dried in a water-oven, to determine the water. ‘The other
was macerated in cold water until it became colourless, then mode-
rately dried and digested with ether and alcohol to remove fat, and
finally dried completely and weighed as fibrine. From the respective
weights of the fibrine and the dry clot that of the corpuscles was cal-
culated. The following were the results observed in seven different
individuals affected with phthisis in different stages of advance-
ment :—

Red corpuscles. Fibrine.
First stage, before the use f Female 129°26 4:52
of cod-liver oil ...... Male 116°53 13°57
First stage, after the use f Female 136°47 5-00
of cod-liver oil ...... Male 141°53 4:70
Third stage, after the use Male 138°74 2:93
of cod-liver oil ......
Third stage, after the use [Male 139°95 2°31
of cocoa-nut oil...... Male 144°94 4°61

2. “On a Property of Numbers.” By the Rev. James Booth,
LL.D., F.R.S. &c.

I know not whether the following property of numbers has been
made public.

A number of six places, consisting of a repetition of a period of

522 Royal Society.

any three figures, is divisible by the prime numbers 7, 11 and 13.
Thus 376376, 459459, 301301 are so divisible.
A number N of six places may be thus written :—

N=100.000 a+ 10.000 6+ 1000 c+ 100d+10e+f,

which, when divided by 7, will give a quotient g and a remainder
5a+46+ 6c+ 2d4+ 3e+/f.

Now if d=a, e=b, f=c, this remainder may be written 7(a+b+c),
which is divisible by 7, whatever be the values of a, b, ¢.

In like manner if a number of six places be divided by 13, the
remainder will be

4a+3b+12c+9d+10e+/; and, as before, if d=a, e=b, f=c,
the remainder may be written 13(a+6+c), which is divisible by 13,
whatever be the value of a, 6 and c.

In the same way it may be shown that a number of this kind is
divisible by 11.

When the first figure of the period is 0, and the second any what-
ever i and j, the number is 0//0ij=i0i; or any number of five places,
the first two and the last two being the same, while the middle place
is 0, is divisible by 7, 11 and 18. Thus 34034, 14014 are so
divisible.

When the first two places are 0, the number may be written
00i00i=7i00i, or any number of four places, the first and last figures
being the same, while the two middle places are 0, is divisible by
7, 1l and 13. Thus 5005, 8008 are so divisible.

Like properties may be found for 17, 19, 25, but the periods are
longer. The prime divisor being 2n+1, it is manifest the number
of places in the period cannot exceed, however it may fall short of x.

Thus when the divisor is 17, the number of places in the period is
eight.

3. “On Fessel’s Gyroscope.” By C. Wheatstone, Esq., F.R.S.

Since the announcement of M. Foucault’s beautiful experiment
which has afforded us a new mechanical proof of the rotation of the
earth on its axis, the phenomena of rotary motion have received re-
newed attention, and many ingenious instruments have been con-
trived to exhibit and to explain them. One of the most instructive
of these is the Gyroscope invented by M. Fessel of Cologne, de-
scribed in its earlier form in Poggendorft’s Annalen for September
1853, and which, with some improvements by Prof. Pliicker and
some further modifications suggested by myself, I take the present
opportunity of bringing before the Royal Society.

It is thus constructed: a beam is capable of moving freely round
a horizontal axis which is itself moveable round a vertical axis, so
that the beam may move in any direction round a fixed point; at
one end of the beam is fixed a horizontal ring which carries a heavy
disc, the axis of rotation of which is in a line with the beam ; at the
opposite extremity is a shifting weight by means of which the equi-
librium of the beam may be established or disturbed at pleasure.

If the beam be brought into equilibrium, and the disc be rapidly
rotated, by means of a thread unrolled from its axis, it will be seen

Royal Society. 523

that the beam has no tendency to displace itself in any direction.

The Gyroscope.

Not so, however, if the equilibrium be in any way disturbed; on
moving the weight towards the centre of the beam, thus causing
the disc to preponderate, it will be observed that if the disc ro-
tates from right to left the beam will move round the vertical
axis also from right to left; and if the motion of the disc be
reversed the rotation of the beam will be reversed also. On
causing the equipoise to preponderate contrary effects will take
place. The velocity of the rotation of the beam round the ver-
tical axis increases in proportion to the disturbance of the equili-
brium. It will also be observed that, notwithstanding the increased
or diminished action of gravity on the disc, its axis of rotation
always preserves the same inclination to the vertical axis at which
it has been originally placed. The effect produced is a seeming
paradox. When the equilibrium is disturbed while the disc is at
rest, the beam being placed in any other position than the vertical,
gravity acts so as to turn it round a horizontal axis; but when the
disc is in motion the usual effect of gravity disappears, and there is
substituted for it a continued rotation round a vertical axis, that is,
round an axis perpendicular to the plane which contains the axes of
the two original rotations.

A similar composition of forces takes place when the disc is caused
to rotate while the equilibrium of the beam is maintained, by im-
pressing on the beam a rotation round the vertical axis. When the
disc rotates from right to left, the slightest pressure tending to pro-
duce rotation round the vertical axis in the same direction, causes
the end of the beam carrying the disc to ascend, and a pressure in
the opposite direction causes it to descend, that is, the beam is con-
strained to move round a horizontal axis perpendicular to the vertical

524 Royal Society.

plane which contains the two axes of impressed rotation, a case exactly
analogous to the preceding. The beam ascends and descends in like
manner, after rotation has spontaneously taken place round the ver-
tical axis in consequence of the equilibrium being disturbed, when-
ever this rotation is any how accelerated or retarded; the disc ro.
tating from right to left and its weight predominating, the rotation
round the vertical axis is from left to right; accelerating the latter
motion will cause the disc to descend, and retarding it will occa-
sion it to ascend.

As the centre of gravity of the beam is below its point of suspen-
sion, even when equipoised it is in perfect equilibrium only when it
is horizontal, consequently, if it be elevated above or depressed be-
low this position it will endeavour to resume it, tending to produce
in the two cases rotations in opposite directions round a horizontal
axis; the rotation of the disc combined with this tendency gives
rise, as in the other cases I have mentioned, to a continued rotation
round the vertical axis. If the disc rotate from right to left, and
the end of the beam carrying it be elevated above the horizontal
position, the rotation round the vertical axis will be from right to
left; if, on the contrary, the same end of the beam be depressed
below the horizontal position, that rotation will be from left to right.

In all the experiments above mentioned the axis of the ro-
tating disc has remained in the prolongation of the beam, but, by
means of an internal ring moveable round a line perpendicular
thereto, this axis may be placed at any inclination and at any azi-
muth with respect to it. Very obvious considerations show that the
inclination of this axis should produce no difference in the character
of the effects but merely in their intensity, since in any inclined po-
sition of the disc its rotation is resolvable into two others, one per-
pendicular to the beam, and the other, which is incapable of pro-
ducing any effect, in a plane containing it. When the axis of the
rotating disc is vertical and at right angles to the beam, no rotation
on the vertical axis ought to take place in any case; but, contrary to
this expectation, although the beam be horizontal and in perfect
equilibrium, a motion round the vertical axis results, which is in
opposite directions according as one or the other end of the axis of
the disc is uppermost. It is, however, easy to see that this rotation
is not owing to the same cause which gives rise to the phenomena
hitherto considered, for whether it be accelerated or retarded no
change is produced in the horizontal position of the beam; it is, in
fact, occasioned by the friction of the pivots of rotation dragging
the beam into a corresponding motion. Attention to this extraneous
cause of rotation will explain numerous anomalies which present
themselves in many of the instruments contrived to exemplify the
phznomena of combined rotary motions. It is one of the advantages
of Fessel’s apparatus that the phenomena may be exhibited in their
more important phases without being affected by this source of error.

We may form a clearer conception of these phenomena by first
considering some simpler facts which do not appear to me to have
been hitherto sufficiently attended to. For this purpose let the

Royal Society. 525

system of rings carrying the disc be removed from the rest of the
apparatus, and by unfastening the tightening screw let the inner
ring be allowed to move freely within the outer. Having set the disc
in rapid rotation, hold the outer ring at the extremities of the dia-
meter which is in the plane in which the axis of motion of the disc
is free to move, then giving to the outer ring a tendency to rotation
round that diameter, it will be observed that, in whatever position
the axis is, it will fly to place itself in the fixed axis thus determined,
and rotation will take place round it in the same direction. Consi-
derable resistance is felt so long as the moveable axis is changing
its position, but when once it coincides with the fixed axis the
rotation of the external ring round its diameter is effected with
facility. A slight alternate motion of the outer ring, tending to
give to it rotations in opposite directions, will occasion a continued
rotation of the moveable axis. The same result takes place when
an endeavour is made to rotate the outer ring round an axis per-
pendicular to its plane. In all cases when the axis of the rotating
disc is free to move in a plane, and the outer ring is constrained to
rotate round a line in this plane, the moveable axis will place itself
so as to coincide with that line, and so that the disc shall rotate
in the same direction as the ring; if the fixed axis be in a different
plane the moveable axis will assume permanently that position in its
plane which approaches nearest to the former. The moveable axis
is thus apparently attracted towards the fixed axis if the rotations
are in the same direction, and repelled from it if the rotations are
in opposite directions.

In the experiments just described the free and constrained axes of
rotation intersect, but in Fessel’s apparatus they are distant from each
other. In the latter case the rule must be thus modified, that the
free axis of rotation tends to place itself parallel to the constrained
axis of rotation, or to as near a position thereto as possible. By this
principle all the results manifested are easily explained. The beam
being in equilibrium, a motion impressed on it round the vertical axis
causes it to ascend or descend, because the axis of the rotating disc
tends to place itself parallel to the vertical axis of rotation and so that
the dise rotates in the impressed direction. When the equilibrium of
the beam is destroyed, gravity tends to make it rotate round a horizon-
tal axis; the axis of the disc endeavours to place itself parallel with
that axis, but both being unchangeably at right angles to each other,
the tendency to place itself there gives rise to a continued rotation.
Other results with this apparatus, to which I have not yet adverted,
are similarly explained. Fix the outer ring horizontally and loosen
the inner ring, keeping them both however in the same plane ; then,
on moving the beam round the vertical axis, the axis of the rotating
disc will immediately fly to place itself parallel thereto, with rotation
of the disc in the impressed direction. The rings being placed in the
vertical plane, the same result will take place if the beam be moved
in a vertical plane, 7. e. round a horizontal axis.

The following additional experiments may be made with the rings
detached from the apparatus. The results are necessary conse-
quences of what has been previously explained :-—

526 Intelligence and Miscellaneous Articles.

1. Suspend, by means of a string, the outer ring at the extremity
of a diameter perpendicular to the axis of the inner ring; and,
having loosened the latter, place it at right angles to the former.
On causing the disc to rotate, its axis will retain its original posi-
tion; but if the slightest effort be made to turn the outer ring round
the vertical line, the axis of the rotating disc will instantly fly into
this position, and the disc will move in the same direction as that of
the impressed rotation.

2. The horizontality of the loose inner ring being restored, if a
weight be suspended from either end of the axis of the disc, that axis
will, while it preserves its horizontal or any inclined position, re-
volve round the vertical line; the direction of the motion will change
if either the weight be applied to the opposite end of the axis or the
disc rotate in the opposite direction. If this rotation be arrested,
gravity will immediately cause the weighted end of the axis to
descend.

3. Clamp the rings together either in the same plane or at right
angles to each other, and fasten a string, in the first case, at the ex-
tremity of a diameter coinciding with the axis of the inner ring, and
in the latter case at the extremity of a diameter perpendicular thereto.
Having set the disc spinning, if a rotation round the vertical line be
given to the system the axis of the disc will ascend, carrying with it
the disc and rings notwithstanding their weight, and, even when the
impressed rotation has ceased to act, will continue to rotate in the
same direction until the motion of the disc ceases.

In this note I have purposely avoided entering into fhe mathema-
tical theory of the phenomena, my intention having been solely to
describe the apparatus exhibited and to give an intelligible account of
its effects. Those who wish to investigate the subject more pro-
foundly, will find the best guide in the Astronomer Royal’s essay
on Precession and Nutation published in his Mathematical Tracts.

LXXXII. Intelligence and Miscellaneous Articles.

SECOND NOTE ON THE DECOMPOSITION OF WATER BY THE PILE.
BY M. JAMIN.

N the last communication* which I laid before the Academy, I
announced that I was in possession of some new facts; I now
bring forward one of them :—

I decompose water in a voltameter constructed in a particular
manner, collect the hydrogen in a graduated receiver, and transfer
this to a vessel filled with water, either pure or containing a few
drops of nitric acid.

I place in the same vessel an exactly similar receiver, containing
the same quantity of hydrogen gas disengaged by the action of sul-
phuricacid upon zine. This done, I cut a platinum wire into two ex-
actly equal parts, heat them in a spirit-lamp, and place them in the two
receivers so as to establish a metallic communication between the gas

* Phil. Mag., p. 298 of the present volume.

Intelligence and Miscellaneous Articles. 527

and the liquid. The volume of the gas disengaged by zinc under-
goes no change in the course of several days; the volume of the gas
produced by the pile diminishes rapidly. The following are the
numbers furnished by the experiment :—

4h 20™ Aap bie 4h 49™ 5 5™ 54 55™ 128
84 80 77 70 66 50

The action was afterwards prolonged indefinitely, but the remainder
of the gas was no longer absorbable; the gas is consequently com-
posed of an absorbable portion, and of a portion which behaves like
ordinary hydrogen. The absorbable portion sometimes amounted to
three-fourths of the total volume, but most frequently it was less
than half; occasionally no absorption took place.

To ascertain the relation existing between the formation of this
absorbable gas and the current, I measured the intensity (of the
latter) with a tangent compass, and reduced the results to the
unities of time and intensity. I ascertained that the volume of hy-
drogen may attain a maximum or remain at a lower value; in the
former case it was not absorbable, in the latter, absorption took
place. We may say, therefore, that in order to disengage a volume
of absorbable gas, we must employ more electricity than in the pro-
duction of a similar volume of ordinary gas.

These facts may be interpreted in two ways; we may suppose
that the hydrogen disengaged by the pile is produced in a peculiar
molecular condition whilst taking the gaseous form under the influ-
ence of the electric current, nearly as in the case of the oxygen
which is electrified and modified at the positive pole. This con-
clusion is the only possible one if the gases disengaged be chemi-
cally pure.

But if, contrary to the generally received opinion, the gas collected
at the negative pole be a mixture of the two constituent elements
of water, we should have in contact two bodies which may combine
under the influence of the platinum wire to reconstitute water.

Further experiments must decide the question, but whatever solu-
tion may be arrived at, the fact is important, as from it we shall
derive the knowledge either of a new state of hydrogen, or of a mode
of decomposition of water by the pile, in which both gases are dis-
engaged at the same time.—Compies Rendus, March 6, 1854, p. 443.

HANSEN’S ELECTRO-MAGNETIC ENGRAVING MACHINE.

This machine is somewhat on the principle of the well-known
planing machine. The drawing to be copied and the plate to be
engraved are placed side by side, on the moveable table or lid of the
machine; a pointer or feeler is so connected, by means of a hori-
zontal bar, with a graver, that when the bar is moved, the drawing
to be copied passes under the feeler, and the plate to be engraved
passes in a corresponding manner under the graver. It is obvious
that in this condition of things, a continuous line would be cut on
the plate, and, a lateral motion being given to the bed, a series of

528 Intelligence and Miscellaneous Articles.

such lines would be cut parallel to and touching each other, the
feeler of course passing in a corresponding manner over the drawing.
If, then, a means could be devised for causing the graver to act only
when the point of the feeler passed over a portion of the drawing, it
is clear we should get a plate engraved, line for line, with the object
to be copied. This is accomplished by placing the graver under the
control of two electro-magnets, acting alternately, the one to draw
the graver from the plate, the other to press it down on it. The
coil enveloping one of these magnets is in connexion with the feeler,
which is made of metal. The drawing is made on a metallic or
conducting surface, with a rosined ink or some other non-conduct-
ing substance. An electric current is then established, so that when
the feeler rests on the metallic surface, it passes through the coils of
the magnet, and causes it to lift the graver from the plate to be en-
graved. As soon as the feeler reaches the drawing, and passes over
the non-conducting ink, the current of electricity is broken, and the
magnet ceases to act, and by a self-acting mechanical arrangement
the current is at the same time diverted through the coils of the
second magnet, which then acts powerfully and presses the graver
down. This operation being repeated until the feeler has passed in
parallel lines over the whole of the drawing, a plate is obtained en-
graved to a uniform depth, with a fac-simile of the drawing. From
this a type-metal cast is taken, which, being a reverse in’all respects
of the engraved plate, is at once fitted for use as a block for surface
printing.—Journal of the Society of Arts; and Atheneum, June 17,
1854. Saeboa

ON THE FORCE WHICH GOVERNS CHEMICAL ACTIONS,
BY M. WITTWER.

My object is to show that the force which governs chemical actions
is completely analogous to those which rule the actions of light, heat,
electricity and magnetism.

Physicists determine the force of an electric current by the mag-
netic energy excited or by the deviation of the magnetic needle.
This deviation and Melloni’s pile afterwards furnished them with the
means of measuring radiating heat. In my turn, I think it possible,
by the assistance of light and heat, to obtain the means of measu-
ring chemical force, whether we have disengagement of light and heat
in a combination, or an absorption of these matters in consequence of
the separation of the chemical components. Bodies are either in a
state of stable equilibrium, when their separation requires a con-
tinued application of light, &c., as for instance, chlorine gas ab-
sorbed by water; or in a state of unstable equilibrium, when they
only require the instantaneous application of these agents to modify
their condition (as for example, the explosive compounds) ; chemical
reactions may therefore be expressed as functions of light, heat, &c.
To arrive at the law which rules affinity when an atom of A com-
bines with several atoms of B, I admit the three following laws :—

1. Two heterogeneous bodies exercise upon each other a chemical
action which decreases as the inverse square of the distance.

Intelligence and Miscellaneous Articles. 529

2. ‘The reciprocal action of two homogeneous bodies is of the
same nature.

3. When an atom of A combines with several atoms of B, the
latter arrange themselves in such a manner that the reciprocal action
becomes a minimum.

When in a combination of two heterogeneous bodies the recipro-
cal action is represented by a, and the reciprocal action of the homo-
geneous atoms by /, taking z and m to signify the coefficients de-
rived from the number of atoms B, r for the distance, and /(w) for
some function of heat, &c., we arrive at the following equation :—

= mB (w).

As regards heat, I find @ posteriori, that 7 is equal to the product
of the mass of the combination and the specific heat; /(w) is equal
to the elevation of temperature. As to light, I have abstained from
determining /(w), because the fundamental experiments are still
wanting.

i could only make use of three experiments to check the correct-
ness of my calculation, because all others at present known only
furnish two numbers of atoms of B in a series; or it was necessary
to determine the latent heat by calculation, for which purpose the
data are still wanting. The three series of which J have been able
to make use are, the combinations of sulphuric acid with water de-
termined by Favre and Silbermann, and those of hydrate of potash
with arsenic and phosphoric acids determined by Graham.

To my great satisfaction I find that these experiments agree, as
nearly as could be desired, with the formula which I have employed.
I obtained the relative numbers which express the affinity of the
bodies which were experimented upon. The affinity between the
alkali and the arsenic acid is nearly equal to the affinity between
this base and phosphoric acid, but the distance between the atoms
of the base and those of the acid is 1 for arseniate of potash to V2
for the phosphate of potash. The affinity between sulphuric acid
and water in comparison to that of these two salts is only as
208 : 860.— Comptes Rendus, April 17, 1854, p. 750.

NOTE ON THE MAGNETISM OF LIQUIDS. BY M. QUET.

M. Pliicker’s method of ascertaining whether a liquid be magnetic
or diamagnetic does not always furnish very well-marked results,
especially with diamagnetic fluids. It appears to me that this may be
effected in a simple and direct manner by the following experiment.

A slender glass tube containing a long column of the fluid to be
tried is placed between the poles of one of M. Ruhmkorff’s electro>
magnets; it is placed perpendicularly to the line of the poles in an
horizontal direction, and the commencement of the liquid index is
brought very close to the polar pieces. As soon as the electro-
magnet is set in action by a galvanic current, if the column of fluid
be magnetic, it advances the whole length of the polar pieces, and

Phil. Mag. 8. 4. No. 48. Suppl. Vol. 7. 2M

530 Intelligence and Miscellaneous Articles.

quickly attains a position of permanent magnetic equilibrium. When
the galvanic current is stopped, the index returns and recovers its
original position. The magnetic attraction is in this case shown by
a very sensible effect, that is to say, by a displacement of four or five
centimetres. This is supposing that the column of fluid is of suffi-
cient length to produce the maximum oe action, but very short
columns may be employed.

When a diamagnetic fluid is to be tested, and the experiment is
arranged as just “described, the index is repelled by the electro-
magnet; but in this case the movement is less energetic, and-the
index only moves to a short distance, as the diamagnetic action is
weakened in proportion to the distance of the liquid. “If it be desired
to give the experiment a very marked character, and even as distinct
as for magnetic attraction, the index is to be brought between the
polar pieces so as to cover their whole length; then, as soon as the
electric current passes, the liquid is strongly repelled, and does not
stop until it has passed the polar pieces to a greater or Jess distance.
This movement, which may be produced to the extent of four or five
centimetres, can leave no doubt as to the consequences of the Panes
riment.

The sensibility of this kind of ,magnetoscope is sufficient to enable
one to recognize the diamagnetic property of water, even when em-
ploying only a single Bunsen’s element of middling energy.

With eight Bunsen’s elements, a solution of chloride “of manga-
nese remains in a position of permanent magnetic equilibrium, even
when the tube is made to slide rapidly in the direction of its axis.

If the pressure of the air be increased on one of the extremities of
the fluid column, the index retrogrades between the polar pieces,
and it may thus be brought to a position of unstable equilibrium.
The excess of pressure which I have employed to produce this effect
was about ;1,th of an atmosphere. This number shows the mag-
netic energy of the chloride of manganese, and at the same time that
the magnetoscope may be readily converted into an apparatus of
measurement.

As a last instance of the sensibility of this method, I will mention
.that the solution of chloride of manganese diluted with one hundred
times its volume of water still retains appreciable magnetic proper-
ties; but if it be diluted with twice this quantity, the magnetism of
the salt is concealed, the diamagnetism of the water becoming pre-
dominant.

Theory shows that the elevation of a fluid in a capillary tube is in
an inverse ratio to its weight. Hence we may believe that magnets
may exert an appreciable influence upon the capillary elevation of
liquids. ‘This I have verified. One of the branches of a capillary
siphon is placed between the poles of an electro-magnet; the capil-
lary surface of a magnetic liquid is brought a little below the polar
pieces and the electric current is then passed; the capillary surface
immediately rises to a new position of equilibrium. With a dia-
magnetic fluid, of which the capillary surface is brought to a level
with the poles, we get a depression of the column.—Comptes Rendus,
March 20, 1854, p. 562.

oO

INDEX to VOL. VII.

ACIDS, on a new series of sulphu-
retted, 518.

Acoustic phenomena produced by the
motion of liquids through short
efflux tubes, on some, 186.

Aduiteration of oils, on some methods
of detecting the, 101.

sa on the action of, on rocks,

Aluminium, on the electro-deposition
of, 227; researches on, and its
compounds, 230.

Ammonia, on the supposed conver-
sion of, into nitric acid in the ani-
mal organism, 381.

Amphibole, analyses of, 303.

Astronomical observations, account of
some, 66.

Barlow (Rev. J.) on silica and some
of its applications to the arts, 375.

Barry (Dr. M.) on the penetration of
the spermatozoon into the interior
of the ovum, 346.

Beequerel (M.) ona new electro-mag-
netic engine invented by M. Marié
Davy, 489.

Beer, on the acidity, sweetness and
strength of, 143.

Benzoic acid, 27.

Blood, on the changes produced in
the, by the administration of cod-
liver oil and cocoa-nut oil, 521.

Blowpipe flame, on the electricity of
the, 47.

Boole (Prof. G.) on the solution of a
question in the theory of probabili-
ties, 29; on the theory of chances,
465.

Booth (Rev. J.) on a particular case
of elliptic integrals whose parame-
ters are imaginary, 213; on a pro-
perty of numbers, 521.

Bouis (J.) on the products of the
decomposition of rocks under the
influence of sulphurous thermal
waters, 68.

Brewster (Sir D.) on the date of the
discovery of the optical properties
of chrysammate of potash, 1/1; on
barometrical, thermometrical, and
hygrometrical clocks, 358.

Brodie (B. C.) on the melting-point
and transformations of sulphur, 439.

Buff (Prof. H.) on the electricity of
plants, 122.

Caffeme, on the presence of, in the
leaves of the cotfee-plant, 21.

Callan (Rev. N. J.) on the results of
a series of experiments on the de-
composition of water by the gal-
vanic battery, with a view to obtain
a constant and brilliant lime light,

E¥

Calvert (F. C.) on the adulteration of
oils, 101.

Cambridge Philosophical Society, pro-
ceedings of the, 442.

Carbolie acid, on some compounds of,

Cartesian barometer, remarks on the,
410,

Cayley (A.) on the theory of groups,
as depending on the symbolic equa-
tion 6"=1, 40, 408; on the homo-
graphic transformation of a surface
of the second order into itself, 208 ;
on the porism of the in-and-cir-
cumseribed polygon, 339.

Challis (Prof.) on two new theorems
relating to the moon’s orbit, 278,
429,

Chances, on the theory of, 465.

Chemical actions, on the foree which
governs, 528.

2N'2

.

532

Chemical affinity among substances in
solution; researches'on, 372.

compounds, on the influence of
pressure upon the formation of, 150.

Chloro-hydrated sulphuric acid, on
ope preparation and properties of,
367.

Chrysammate of potash, on the date
of the discovery of the optical pro-
perties ‘of, 171.

Chureh (A. H.) on the spheroidal state
of bodies, 275.

Clausius (R.) on the heat produced
by an electric discharge, 297.

Clocks, notice on barometrical, ther-
mometrical,and hygrometrical, 358.

Cobalt, on the occurrence of, in some
mineral springs, 149 ; on the sepa-
ration of nickel from, 461.

Cockle (J.) on the method of sym-
metric products, 130.

Cocoa-nut oil, on the changes pro-
duced in the blood by the admini-
stration of, 521.

Coffee leaf of Sumatra, on the, as a
substitute for tea or for the coffee-
bean, 21. .

Collins (M.) on the attraction of ellip-
soids considered geometrically, 401.

Collodion plates, method for preser-
ving the sensitiveness of, for a con-
siderable time, 349.

Colours, on the theory of compound,
254.

Columbite, on the nomenclature of
the metals contained in, 461.

Comet, notice of a, seen off the coast
of South Africa, 68.

Connell (Prof. A.) on the voltaic de-
composition of water, 426; on the
nomenclature of the metals con-
tained in columbite and tantalite,
461.

Cooling of buildmgs, on the ceconomy
of the, 138.

Coralline crag, on some tubular cavi-
ties in the, at Sudbourn and Ged-
grave near Orford, 320.

Crookes (W.) on a method for pre-
serving thesensitivenessof collodion
plates for a considerable time, 349.

Davy (Dr. E.) on some new and sim-
plemethods of detecting manganese
im natural and artificial compounds,
and of obtaining its combinations
for ceconomical or other uses, 221 ;

INDEX.

on a newand simple method of de-
termining the amount of urea in
the urinary secretion, 385.

Davy (M.) on a new electro-magnetic
machine, 489. '

Delesse (M.) on the action of alkalies
on rocks, 100.

Devillé (M.) on aluminium and its
compounds, 230.

Deville (C. Ste.-Claire) on lithologic
studies, 300.

Dobson (T.) on the storm-tracks of
the South Pacifie Ocean, 268.

Donkin (W. F.) on a class of differ-
ential equations, including those
which occur in dynamical problems,
360.

Edwards (W. B.) on a comet seen off
the coast of South Africa, 68.

Electrie discharge, on the heat pro-
duced by the, 347, 348.

— induction, researches on, 197.

residue in the Leyden jar, theory
of the, 305, 412, 476.

Electricity, on the mechanical values
of distributions of, 192; on the ve-
locity of, 204; on the generation
of heat by, 428.

of the blowpipe flame, on the, 47.

— of plants, on the, 122.

Electro-magnetie engine, on a new,
489.

Electro-magnetic engraving machine,
description of an, 527

Electro-telegraph wires, on some phe-
nomena presented by, 396.

Ellipsoids, on the attraction of, con-
sidered geometrically, 401.

Elliptic integrals, on a particular case
of, 213.

Equations, on a class of differential,
360; on some points in the theory
of differential, 450.

Euclid, on the geometry of the first
three books of, 442.

Faraday (Prof.) on electric induction,
197; on electro-dynamic induction
in liquids, 265; on some phno-
mena presented by subterraneous
electro-telegraph wires, 396.

Fessel’s (M.) gyroscope, observations
on, 522.

Fisher (Prof.) on the development of
the vertebral system, 447.

Flame, on the electricity of, 47.

Forbes (E.) on an indication of depth

INDEX. 533

of primeval seas, afforded by the
remains of colour in fossil Testacea,
437.

Foucault’s pendulum experiments,
observations on, 379.

Franz (R.) on the conductibility of
metals for heat, 33.

Fraxmine, on the nature of, 501.

Galvanism, on the mechanical values
of distributions of, 192.

Gassiot (J. P.) on some experiments
made with Ruhmkorff’s induction
coil, 97.

Genth (Dr. F. A.) on a new meteorite
from New Mexico, 378.

Geology of Suffolk, on the, 447.

Gillett (W.S.) on a new and more
correct method of determining the
angle of aperture of microscopic
object-glasses, 368.

Gilliss (Lieut.) on a series of mag-
netical observations made across
the Pampas, 53.

Gladstone (Dr. J. H.) on chemical
affinity among substances in solu-
tion, 372.

Gold, on the detection of, in lead and
its compounds, 126.

Gore (G.) on the electro-deposition
of aluminium and silicium, 227.
Goret (M.) on the production of ozone
by the decomposition of water at

low temperatures, 459.

Grassmann (Prof.) on the theory of
compound colours, 254.

Groups, on the theory of, 40.

Grove (W. R.) on the electricity of
the blowpipe flame, 47.

Gyroscope, observations on Fessel’s,
522. :

Haidinger (W.) on the colours of
mausite, 215.

Hamilton (Sir W. R.) on some ex-
tensions of quaternions, 492.

Hansen’s electro-magnetic engraving
machine, description of, 527.

Haughton (Rev. S.), account of ex-
periments to determine the veloci-
ties of the rifle bullets commonly
used, 390.

Heart, on the nerves which supply
the muscular structure of the, 51.
Heat, on the mechanical action of, 1,
111, 172, 249; on the conducti-
bility of metals for, 33; on the
geometrical representation of the

expansive action of, 288; produced
by an electric discharge, on the,
297, 347, 348, 428; on the uniform
motion of, im homogeneous solid
bodies, and its connexion with the
mathematical theory. of electricity,
502.

Heating of buildings, on the ceconomy
of the, 138.

Helicea, on the growth of the, 364.

Henry (M. O.) on the occurrence of
nickel and cobalt in some mineral
springs, and on a method for their
isolation, 149.

Herapath (Dr. W. B.) on the manu-
facture of artificialtourmalines, 352.

Hirst (Dr.) on the progress of the
physical sciences, 153.

Hooker (Dr. J. D.) on the structure
and affinitiesof Trigonocarpon,515.

Hunt (T. S.) on the composition and
metamorphoses of some sedimen-
tary rocks, 233; on the chemical
composition of recent and fossil
Lingule, and some other shells,
335; description and analysis of
two mineral species, 499,

Hydroferrocyanie acid, on the prepa-
ration of, 461.

Induction, on electro-dynamic, in
liquids, 265.

Iron, on a new methad of protecting,
from the action of the weather and
various corroding substances, 83.

Jaffé (C.) on the supposed conversion
of ammonia into nitric acid in the
animal organism, 381.

Jamin (J.) on the decomposition of
water by the pile, 298, 526.

Jones (Dr. H. B.) on the acidity,
sweetness and strength of wine,
beer and spirits, 143.

Kekulé (Dr. A.) on a new series of
sulphuretted acids, 518.

Kinone, on new sources of, 24.

Kohlrausch (R.), theory of the electric
residue in the Leyden jar, 305, 412,
476.

Lead, detection of gold in, 126.

Lee (Dr. R.) on the nerves which
supply the muscular structure of
the heart, 51.

Leyden jar, on the electric residue in
the, 305, 412, 476.

Liebig (Prof.) on the separation of
nickel from cobalt, 461; on the

534

“preparation of
acid, ib.

Lingule, on the chemical composition
of recent and fossil, 335.

Liquids, on some acoustic phenomena
produced by the motion of, through
tubes, 186; on electro-dynamie in-
duction in, 265; on the magnetism
of, 529.

Logan (W. E.) on the chemical com-
position of recent and fossil Lin-
gule, and some other shells, 335.

Lowe (E. J.) on a new method of
propagating plants, 145; on the
growth of land shells, 363.

Magnetic direction, on the influence
of the moon on the, 52.

Magnetic inclination, on the applica-
tion of magnetic induction to the
determination of the, 153.

Magnetical observations, on a series
of, 53, 66.

Magnetism, on the mechanical values
of distributions of, 192.

Magnus (Prof.) on an improved con-
struction of an apparatus for the
illustration of various phenomena
of rotating bodies, 272.

Manganese, on some new and simple
methods of detecting, in natural
and artificial compounds, and of
obtaining its combinations for ceco-
nomical or other uses, 221.

Martin (P. J.) on the anticlinal line
of the London and Hampshire
basins, 166.

Mausite, on the colours of, 215; com-
position of, 216.

Maxwell (J. C.) on the transforma-
tion of surfaces by bending, 449.
Metals, on the conductibility of, for
heat, 33; on some peculiar reduc-

tions of, in the humid way, 297.

Meteorite, on a new, 378.

Meteorological observations, 66, 71,
151, 231, 303, 383, 463.

Minerals, analyses of two new, 499.

Moon, on the influence of the, on the
magnetic direction, 52; on two
new theorems relating to the orbit
of the, 278, 429.

Morgan (Prof. De) on some points in
the theory of differential equations,
450; on an error committed by M.
Cauchy in a very remarkable theo-
rem, 458.

hydroferrocyanic

INDEX.

Nickel, on the occurrence of, in some
mineral springs, 149; on the sepa-
ration of, from cobalt, 461.

Nitrotoluylic acid, on some of the
products of the decomposition of,
142.

Noad (Dr. H. M.) on some of the
products of the decomposition of
nitrotoluylic acid, 142.

Normandy (A.) on the spheroidal
state of water in steam-boilers, 283.

Numbers, on a property of, 521.

Object-glasses, microscopic, on a me-
thod of determining the angle of
aperture of, 368.

Oil of bitter almonds, on a crystalline
deposit from, 26.

Oils, on the adulteration of, 101; on
the action of diluted sulphuric acid
on, 104; action of nitric acid of
different strengths on, 105.

Ovum, on the penetration of the sper-
matozoon into the interior of the,
346.

Ozone, on the production of, by the
decomposition of water at low tem-
peratures, 459.

Paraguay tea, analysis of, 23.

Pendulum experiments, observations
on M. Foueault’s, 379.

Perey (Dr. J.) on the detection of
gold in lead and its compounds,
126.

Phear (J. B.) on some parts of the
geology of Suffolk, 447.

Phenyle, on some new compounds of,
370.

Photography, on some early experi-
ments in, 326.

Plants, on the electricity of, 122; on
a new method of propagating,
145.

Pollock (Sir F.) on certain properties
of square numbers and other qua-
dratic forms, 147, 287, 358; on a
proof of Fermat’s first and second
theorems of the polygonal num-
bers, 358.

Polychroism, on the artificial produe-
tion of, in erystallized substances,
228.

Polygon, on the porism of the in-and-
circumscribed, 339.

Powell (Rev. B.) on certain pheno-
mena of rotatory motion, 291, 398.

Probabilities, on the theory of, 29. -

INDEX. 535

‘Pyroxene, on a peculiar variety of,

501

Quaternions, on some extensions of,
492.

Quet (M.) on the magnetism of li-
quids, 529,

Rankine (W. J. M.) on the mecha-
nical action of heat, 1, 111, 172,
239; on the geometrical represen-
tation of the expansive action of
heat, and the theory of thermo-dy-
namie engines, 288.

Reade (Rey. J. B.) on some early
experiments in photography, 326.
Retina of the human eye, on some of
the circumstances and principles
which regulate the production of

pictures on the, 218.

Riess (P.) on the generation of heat
by electricity, 348, 428.

Rifle bullets. on some experiments to
determine the velocities of, 390.
Rocks, on the decomposition of, by
sulphurous waters, 68; action of
alkalies upon, 100; on the natural

ciassification of igneous, 300.

Rosse (Harl of), anniversary address
of the, to the Royal Society, 57.

Rotating bodies, on an apparatus for
the illustration of various pheno-
mena of, 272, 291, 398.

Roxburgh (Dr. W.) on the Cartesian
barometer, 410.

Royal Institution of Great Britain,
proceedings of the, 223, 291, 372.

Royal Society, proceedings of the,
ol, 142, 218, 287, 358, 437, 515;
anniversary addyess of the Presi-
dent, 57.

Ruhmkorff’s induction coil, on some
experiments made with, 97.

Sabine (Col. E.) on the influence of
the moon on the magnetic direction,
pee

Savart (F.) on some acoustic phzno-
mena produced by the motion of
liquids through short efflux tubes,
186.

Scoresby (Rev. W.) on the production
of pictures on the retina of the hu-
man eye, 218.

Scrugham (Mr.) on some new com-
pounds of phenyle, 370.

Sénarmont (M. de) on the artificial
production of polychroism in ery-
stallized substances, 228,

Shells, fossil and recent, on the che-
mical composition of some, 335 ;
on the growth of land, 363.

Siemens (M. W.) on some remark-
able phenomena presented by sub-
terraneous electro-telegraph wires,
396.

Silica, on some of the applications of,
to the arts, 375.

Silicium, on the electro-deposition of,
227;

Silvester (Dr. T. H.) on the typical
forms of the large secreting organs
of the human body, 54.

Smith (R.) on the detection of gold
in lead and its compounds, 126.
Spermatozoon, on the penetration of
the, into the interior of the ovum,

346

Spheroidal state of bodies, on the,
275; of water in steam-boilers,
283.

Spiller (J.) on a method for preser-
ving the sensitiveness of collodion
plates for a considerable time, 349.

Spirits, on the acidity, sweetness and
strength of, 143.

Square numbers, on certain properties
of, 147, 287, 358.

Steam, on the mechanical action of,
treated as a perfect gas, 172.

Steam-boilers, on the spheroidal state
of water in, 283.

Steam-engines, on the power and
ceconomy of single-acting expan-
sive, 239.

Stenhouse (Dr. J.) on the dried coffee-
leaf of Sumatra, as a substitute for
tea or for the coffee-bean, 21; on
the erystalline deposit which forms
in oil of bitter almonds, 26; on
xanthoxyline, 28; on the erystal-
lizable principle in the bark of the
Fravinus excelsior, 501.

Storm-tracks of the South Pacific
Ocean, on the, 268.

Sulphur, on the melting-point and
transformations of, 439.

Sulphuric acid, on the decomposition
of, by pentachloride of phosphorus,
365.

Sulphurous waters, on the decom-
posing action of, upon rocks, 68.
Surfaces, on the transformation of,

by bending, 449.
Sylvester (J. J.) on a point of nota-

on

tion, 50; on the enumeration of
the contacts of lines and surfaces
of the second order, 331; on a
formula by aid of which and of a
table of single entry the continued
product of any set of numbers may
be effected without the use of loga-
rithms, 430.

Symmetric products, on the method
of, 130,

Tantalite, on the nomenclature of the
metals contained in, 461.

Testacea, on the remains of colour in
fossil, as an indication of the depth
of primeval seas, 437.

Thermo-dynamie engines, on the
theory of, 288.

Thiacetic acid, on the preparation and
composition of, 519.

Thompson (Dr. T.) on the changes
produced in the blood by the ad-
ministration of cod-liver oil and
cocoa-nut oil, 521.

Thomson (Prof. W.) on the ceconomy
of the heating or cooling of build-
ings by means of currents of air,
138; on the mechanical values of
distributions of electricity, mag-
netism and galvanism, 192; on the
heat produced by an electric dis-
charge, 347 ; on the uniform mo-
tion of heat in homogeneous solid
bodies, and its connexion with the
mathematical theory of electricity,
502.

Tourmalines, on the manufacture of
artificial, 352.

Trigonocarpon, on the structure and
affinities of, 515.

Tyndall (Dr. J.) on the progress of
the physical sciences, 33; on the
vibration aud tones produced by
the contact of bodies having differ-
ent temperatures, 223.

Urea, on a new and simple method of

36 INDEX.

determining the amount of, in the
urinary secretion, 385.

Vertebral system, on the development
of the, att

Vogel (Dr. E.) on some astronomical,
meteor ological and magnetical ob-
servations, made between Tripoli
and Mourzuk, 66.

Voltameter, description of a new, 77.

Water, on the decomposition of, by
the galvanic battery, 73, 298, 426,
526.

Weber (Prof. W.) on the application of
magnetic induction to the determi-
nation of the magnetic inclination,
153.

Wedgwood (Mr.) on the geometry of
the first three books of Euclid, 442.

Wheatstone (C.) on Fessel’s gyro-
‘scope, 522.

Wiedemann (G.) on the conductibility
ot metals for heat, 33.

Wilbraham (H.) on the theory of
chances developed in Prof. Boole’s
* Laws of Thought,”’ 465.

Williamson (Prof. A.) on the decom-
position of sulphuric acid by pen-
tachloride of phosphorus, 365; on
a new compounds of phenyle,
370.

Wilsonite, on the composition of, 500.

Wine, on the acidity, sweetness and
strength of, 143.

Wittwer (M.) on the force which
governs chemical action, 528.

Wohler (Prof.) on the influence of
pressure upon the formation of
chemical compounds, 150 ; on
some peculiar reductions of metals
in the humid way, 297.

Wood (S. V.) on some tubular cavi-
ties in the coralline crag at Sud-
bourn and Gedgrave near Orford,
320.

Xanthoxyline, analysis of, 28.

END OF THE SEVENTH VOLUME.

PRINTED BY TAYLOR AND FRANCIS,
RED LION COURT, FLEET STREET.

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