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THE
LONDON, EDINBURGH, anv DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
CONDUCTED BY
SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & EH. &e.
SIR ROBERT KANE, M.D., F.R.S., M.R.LA.
WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S.'F.C.S.
JOHN TYNDALL, F.R.S. &c.
“Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster
vilior quia ex alienis libamus u apes.” Just. Lies. Polit, lib.i. cap. 1. Not.
VOL, XXTII.—FOURTH SERIES.
JANUARY—JUNE, 1862.
LONDON.
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Printers and Publishers to the University of London ;
SOLD BY LONGMAN, GREEN, LONGMANS, AND ROBERTS ; SIMPKIN, MARSHALL
AND CO.; WHITTAKER AND CO.; AND PIPER AND CO., LONDON :—
BY ADAM AND CHARLES BLACK, AND THOMAS CLARK,
EDINBURGH; SMITH AND SON, GLASGOW ; HODGES
AND SMITH, DUBLIN; AND PUTNAM,
NEW YORK,
* Meditationis est perscrutari occulta; contemplationis est admirari
perspicua..... Admiratio generat queestionem, queestio inyestigationem,
investigatio inventionem.”—Hugo de'S. Victore.
9
\
—“ 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.” ee
J. B. Pinelli ad Mazonium.
CONTENTS OF VOL. XXIII.
(FOURTH SERIES.)
NUMBER CLI.—JANUARY 1862. Page
Archdeacon Pratt.on Chinese Astronomical Epochs ...... 1
Prof. Marcet on the Comparative Effects of Nocturnal Radiation
from the Surface of the Ground and over a large Sheet of
RMSE Uae Fes thee US lee ve tee eh Wes as toe bP ie 9
Prof. Maxwell on Physical Lines of Force ............0-- 12
The Astronomer Royal on the Direction of the Joints in the
Faces of Oblique Arches ...... Phd die ood
M. G. Kirchhoff on the Relation of the Lateral Contraction to
the Longitudinal Expansion in Rods of Spring Steel. (With
MCU i il WOR we pick Milas SEW oie te oie eats 4S sersst pe 2S
The Rev. S..Haughton’s Notes on Mineralogy. 47
Prof. Potter on the Fourth Law of the Relations af oe “Blastic
Force, Density, and Temperature in Gases .......-...0'.0 52
Prof. Roscoe on the Solar Spectrum, and the aay of the
Chemical Elements ...... sidan 63
Sir R. I. Murchison on the inapplicability of ‘the new term
“Dyas” to the “‘ Permian” one of Rocks, as proposed by
[ON Ci 7a ers re Seer eee een ere ia 65
Notices respecting New Books:—Mr. R. Potts’s Euclid’s
Elements of Geometry, designed for the use of the ae
Forms in Public Schools and ‘Btudentsa in the Universities. 70
Proceedings of the Royal Society :—
The Rev. H. Moseley on the Motion of a Plate of Metal
on an Inclined Plane, when dilated and contracted; and
on the descent of Glaciers. . d 72
On the Conductibility of Saline Solutions, by M. Marie-Davy. 79
NUMBER CLII.—FEBRUARY.
Drs. Russell and Matthiessen on the Cause of Vesicular Struc-
eR ME MIRE Sees HA oth tub: wh 5 san cr cand aaa & ei Wee Baus ee 8]
Prof. Maxwell on Physical Lines of Force ..........++00+- 85
Mr. A. H. Church on the Composition, Structure, and Forma-
lame woeciaive. (With 2 Plate.) . «3. «iene ise devas s+ sive 95
Prof. Regnault on the S inaees Heat of some Simple Bodies.
CTE EL ERR aa ea ik delta ie ewe) pee Ce
IV CONTENTS OF VOL. XXITI.—FOURTH SERIES.
Mr. T. Tate’s Experimental Researches on the Laws of Evapo-
ration and Absorption, with a Description of a new Evapora-
meter and Absorbometer; 1. si hee fe fies See eee 126
Mr. J. Cockle on Transcendental and Algebraic Solution.—
Supplementary, Papers ix .:c.0c8 2.5 ads pe.sa 2 /tlei Some oe ieee 135
MM. Van Breda’s and Logeman’s Remarks on Ampére’s Expe-
riment on the Repulsion of a Rectilinear Electrical Current
OMELET oie oe epsiniess oe iene So1ee'd oie his, cle RO eee 140
Mr. G. B. Jerrard’s Remarks on M. Hermite’s. Argument rela-
ting to the Algebraical Resolution of Equations of the Fifth
Degree Sees Saeed sat te SSW Kis cee eR Pee Reed eee 146
Proceedings of the Royal Society :—
Messrs. A. Smith and F. J. Evans on the Effect produced
on the Deviation of the Compass by the Length and
Arrangement of the Compass Needles ............ 149
Lieut. -Colonel Richard Strachey on the Distribution. of
_Aqueous Vapour in the Upper Parts of the Atmosphere. 152
Physical Considerations regarding the possible Age of the Sun’s
Heat, by Professor; W.. Thomsoni< i: x.0-08 fees 158
Description of a New Mineral from the Ural, orbit M. Rodosz- »
kovski; 2.232% 7». Siete ian ae ove acre, anciee
NUMBER CLIII.—MARCH.
Mr. S. V. Wood on the Form and Distribution of the Land-
tracts during the Secondary and Tertiary periods respectively ;
and on the effects upon Animal Life which great Changes in
Geographical Configuration have probably produced ...... 161
Drs. Matthiessen and Vogt on the Influence of Traces of Foreign
Metals on the Electric Conducting Power of Mercury .... 171
Dr. Sehunck on,Sugar,inUrine ».. .... 268 Welesgectts ee ee 179
Mr. F. A. Abel on the Composition of the Great Bhurtpoor. Gun,
stationed on the Royal Artillery Parade Ground, Woolwich ;
and of some other interesting Cannon . 2... j.isi-s.bscs sade 181
Mr. C. Tomlinson on the Cohesion-Fi igures of Liquids ...... 186
Mr. A. Cayley on the Solution of an Equation of the Fifth Order. 195
Mr. J. Cockle’s Note on the Remarks of Mr. Jerrard ...... 196
The Rev. T. P. Kirkman on the Puzzle of the Fifteen Young
WANES 5 oss '05. 54
Mr. T’. Graham on Liquid Diffusion applied to Analysis. 204
Proceedings of the Royal Society :—
Major-General Sabine on the Secular Change in the Mag-
netic Dip in London between the years 1821 and 1860. 223
Proceedings of the Geological Society :—
M. Marcel de Serres on the Bone-Caves of Lunel-Viel,
RT CPAME ovis te 5) hai swiss oy cea es 0 on ete
Dr. A. Gesner on the Petroleum-springs in North America. 939
CONTENTS OF VOL. XXIII.——-FOURTH SERIES. Vv
age
Dr. Dawson on the Discovery of some additional Land Ani-
_-matls in the Coal-measures of the South Joggins...... 239
Mr. J. G. Veitch on a Volcanic Phenomenon observed at
soberly. silyl Ge Go itestecdt Seasick asa Sade Ree ok. ». 240
Mr. J. H. Key on the Bovey Basin, Devonshire........ 240
Signor G. G..Gemmellaro on two Volcanic Cones at the
ig: ce Ee ee oa etre 241
Mr. T. Davidson on some Fossil Brachiopoda of the Car-
boniferous Rocks of the Punjab and Kashmir........ 241
The Rev. O. Fisher on the Bracklesham_ Beds of the Isle
of Wight Basin ..... 241
Prof. Morris and Mr. G. E. Roberts on n the Carboniferous
- Limestone of Oreton and Farlow................-- 243
Mr. E. W. Binney on some Fossil Plants from the Lower
Woal-measures of Lancashire. ....2...:.2 0a. cess ee 244
The Rev. S. Hislop on the Plant-beds of Central India .. 244
On a Dew-bow seen on the surface of Mud, by W.J. M. Rankine. 245
Note on the Theory of Spherical Condensers, by J. M. Gaugain. 245
On the Action of Nitrate of Sodium on Sulphide of Sodium at
different Temperatures, by Dr. Ph. Pauli_......... apexes 248
~ NUMBER CLIV.—APRIL.
Prof. Magnus on the Passage of Radiant Heat through moist
Air, and on the Hygroscopic Properties of Rock Salt...... 249
_ Prof. Tyndall on Recent Researches on Radiant Heat ...... 252
Mr. A. Cayley on the Transformation of a certain Differential
Piprsmmnmrenen af: I A CE PO De sale 266
Sir W. R. Hamilton’s Elementary Proof, that Eight Perimeters,
of the Regular inscribed Polygon of Twenty Sides, exceed
Twenty-five Diameters of the Circle. . 267
Mr.S. V. Wood on the Form and Distribution of the Land-tracts
during the Secondary and Tertiary Periods respectively ; and
on the effects upon Animal Life which great Changes in Geo-
graphical Configuration have probably produced. . « 269
Mr. W. H. L. Russell’s ‘Theorems in the Calculus of Symbols. 282
Mr. T. Tate’s Experimental Researches on the Laws of Evapo-
Beummaneerbsorption 3-7/2 09. Lee eh eee 283
Mr. IT’. Graham on Liquid Diffusion applied to Analysis...... 290
Col. Sir H. James and Capt. A. R. Clarke on Projections for
Maps applying to a very large extent of the Earth’s Surface.
(With a Plate.)...... Rotates ta aa, eat
Prof. Tyndall on the Regelation of Snow-gr anules .......... 312
Prof, Challis on the Principles of T heoretical PIySIESS 2st & 2'sis 313
_ Notices respecting New Books :—Mr. W. Odling’s Manual of
-Chemistry, Descriptive and Theoretical .............00: 322
vi CONTENTS OF VOL. XXIII.—-FOURTH SERIES, —
Page
Proceedings of the Royal Society :—
Mr. M. Simpson on the Synthesis of Succinic and Pyro-
tartaric’ Acide isis ote OL SS Re See ee 326
Mr. B. Stewart on Internal Radiation in Uniaxal Crystals. 328
Proceedings of the Geological Society :—
Messrs. Whitley and Wyatt on some further Discoveries of
Flint Implements ..... riches
Mr. W. B. Dawkins on a Piyenaden 7 near - Wells Biore 332
Messrs. Palmieri and 'Tchihatcheff on the Recent man
OF Vesuviusies elie 00 I ee 332
Mr. E. Hull on the Distribution of Sedimentary Strata.. 333
On the Probable Cause of Electrical Storms, by Dr. J. P. Joule. 334
On the Influence of Heat on Phosphorescence, by M. O. Fiebig. 335
On the Resistance to the Conduction of Heat, by J.M. Rankine. 336
NUMBER CLV.—MAY.
M. V.. Regnault on some Apparatus for determining the Densi-
ties of Gases and Vapours. (With a Plate.) . 337
Mr. G. J. Stoney on the Correction for the Length of ‘the
Needle in Tangent-galvanometers....... 345
Prof. Chapman on the Position of Lievrite i in the Mineral Series. 348
Mr. A. Cayley on a Question in the Theory of Probabilities... 352
Mr. J. Croll’s Remarks on Ampére’s Experiment on the Repul-
sion of a Rectilinear Electrical Current on itself......... . 865
Mr. T. Graham on Liquid Diffusion applied to Analysis...... 3868
Mr. R. T. Lewis on the Changes in the Apparent Size of the
MOM ering is isje aisu fre) 5s le cleave Mawinelee pared «ine 8 oie) ete eee 380
Mr. S. V. Wood on the Form and Distribution of the Land-tracts
during the Secondary and Tertiary Periods respectively ; and
on the effects upon Animal Life which great Changes in
Geographical Configuration have probably produced...... 382
Mr. B. Stewart on the Occurrence of Flint Implements in the
DYE. +, 0.6. d16 io) sy0 ie. 4 bide ¥'se sigalg Uo othe AEE ope O94
Proceedings of the Royal Institution : —
Rear-Admiral FitzRoy on Meteorological Telegraphy.... 395
Proceedings of the Royal Society ;—
Prof. J. Thomson on Regelation \% .\siis sick: eee 407
Proceedings of the Geological Society :—
The Rev. W. Lister on the Drift containing Arctic Shells
in the neighbourhood of Wolverhampton... ......+.+: 412
Mr. J. Smith on a Split Boulder in Little Cumbra...... 412
Mr. T. F. Jamieson on the Ice-worn Rocks of Scotland.. 412
Prof. Ramsay on the Glacial Origin of certain Lakes in -
witzerland Boers igi ge tbie al aictdcwlone gerd Uae eet 413
On the Phosphorescence of Rarefied Gases, by M. Morren .. 415
On the Spectra of Phosphorus and Sulphur, by M. J. M.-Seguin. 416
. CONTENTS OF VOL. XXIII.—FOURTH SERIES. yi
NUMBER CLVI.—JUNE.
hae | Page
Prof. Clausius on the Conduction of Heat by Gases ........ 417
Prof. Challis on the general Differential Equations of Hydrody-
ie EIN ora oo oo ac sen ins! ps6 Bije sn'e ing! Haters) 4 kul 436
Archdeacon Pratt’s Calculation of the Undulation of an Unstif-
fened Roadway in a Suspension Bridge as a heavy Train
passes over it; and Remarks upon the effect of a suspended
fron Girder in deadening the Undulation..........:..... 445
Mr. R. Sabine’s remarks on a Paper by Dr. A. Matthiessen,
F.R.S., and C. Vogt, Ph.D., ‘‘On the Influence of Traces of
Foreign Metals on the Electric Conducting Power of Mercury. 457
Messrs. J. H. and G. Gladstone on Collyrite, and a native Car-
aeeOnrAtminag and LIME: . . « seco cou; oc ute ace ergs «a csuene 461
Prof. Schonbein on the Allotropic States of paren) and on
= Nitriucation: ."..”,. . 466
Mr. G. B. Jerrard’s ‘Supplementary Remarks on M. Hermite’s
Argument relating to the Algebraical Resolution of Equa-
fmermamCc PE REN ICETCC e's orale. ube asin - pin tym secs 44h OR 469
Mr. A. Cayley on a Question in the Theory of Probabilities... 470
Dr. Atkinson’s Chemical Notices from Foreign J ournals sdee gee he
‘Procéedings of the Royal Society :—
M. A. Schrauf on the Determination of the Optical C Con-
Srasiessor Orystallized. Substances 252 2)... .;. sc cies se 478
Sir W. S. Harris on some new Phenomena of Residuary
Charge, and the Law of Exploding Distance of Electrical
meecumulation on Coated, Glass.,...cn0¢+ o<06 ++ ee0 «20 484
Proceedings of the Geological Society :—
~Prof. Harkness on the Sandstones, and their associated
Deposits, in the Valley of the Eden, &c.............- 492
Mr. A. Geikie on the Date of the Last Elevation of the
Sema Vvalley of scotland: 0. oc. ee woe ce we ae Oe 493
Note on the Electricity developed during Evaporation and du-
ring Effervescence from Chemical Action, by Professor Tait
eter Vanilvn, sq. 20. 2b. pe. ees cece elcwe ss be 494
On Chinese Astronomical Epochs, by Archdeacon Pratt. sicieae to0
NUMBER CLVII.—SUPPLEMENT TO VOL. XXIII.
Mr. J. J. Waterston’s Account of Observations on Solar Radia-
PRamme UAE IALC.). i. 3%) ss Siara'aiy'c scales sain 02 eee spe 497
Prof. Clausius on the Conduction of Heat by Gases ........ 512
Mr. W. Baker on the Metallurgy of Lead ...5......-+ee: 534
MEV. Regnault on an Air-Thermometer used as a Pyrometer
in measuring High Temperatures. (With a Plate.)........ 537
M. H. Karsten on the Oxidation of Gaseous Hydrocarbon-com-
pounds contained in the Atmosphere ..........-- me eM
vill CONTENTS OF VOL, XXIII.—FOURTH SERIES.
Page
M. A. de Ja Rive on the Aurore Boreales, and on Phenomena
which attend them, ..s. .. . o's ase cvs 0 se bine lyl a gle Cig nen
Proceedings of the Royal Society :—
Mr. P. Griess on a New Class of Organic Bases, in which
Nitrogen is substituted for Hydrogen .............. 553
Mr. P. Griess on the Reproduction of Non-nitrogenous
Acids from Amidic, Acids .. . .,.< ia. ss esse 595
Proceedings of the Geological Society :—
Mr. J. W. Kirkby on some remains of Chiton from the
Mountain Limestone of Yorkshire’.<\.). 3-2 <. soeneeee 958
Prof. Owen on some Fossil Reptilia from the Coal-measures
of the South Joggins, Nova Scotia ............ “Gta ie OO
The Rev. W. B. Clarke on the occurrence of Mesozoic and
Permian Faune in Eastern Australia ........0.-+ 02 908
Mr. A. Tylor on the Foot-print of an Jguanodon lately
found at Tastings ..2)0.c)em- Sate ale! 0)s ibe See a ie 559
On the Connexion between Earthquakes and Magnetic Disturb-
ances, -by. Dr.J,, Lamont “a. Sa kane wei 6 one reteset
On the Freezing of Saline Solutions, by Dr. Ridorff........ 560
On the Composition of Minerals containing Niobium, by Prof.
FL. ROSe os ss... +5, « = 0, Te-eolee.s, sete nies) « orotate ks eye rr
FAUX, oie 0 win 0:0 ¥ s0ss' o's 95046 @ viol so twlaha Bebe hie erolis ieee 564
ERRATA IN VOL. XXII.
Page 200, line 9 from top, for 0° =100 read 0° = 226.
PLATES.
I, Illustrative of M. G. Kirchhoff’s Paper on the Relation of the Lateral
Contraction to the Longitudinal Expansion in Rods of Spring Steel,
and of MM. \ n Breda and Logeman’s Paper on the Repulsion of
a rectilinear Electrical Current on itself.
IJ. Illustrative of Prof. Regnault’s Papers on the Specific Heat of some
Simple Bodies; on new Apparatus for determining the Densities
of Gases and Vapours; and on a new Pyrometer. — .
III. Illustrative of Mr. A. Church’s Paper on the Structure and Composi-
tion of Beekite.
IV. Illustrative of Colonel Sir H. James and Captain Clarke’s Paper on
Projections for Maps.
V. Illustrative of Mr. J. J. Waterston’s Paper on Solar Radiation.
THE
LONDON, EDINBURGH ann DUBLIN
PHILOSOPHICAL MAGAZINK
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
JANUARY 1862.
I. On Chinese Astronomical Epochs.
By Archdeacon J. H. Prarz, M.A.
To the Editers of the Philosophical Magazine and Journal.
GENTLEMEN,
‘YN the absence of authentic history, astronomy sometimes lends
valuable aid in enabling us to fix dates by independent means,
if certain facts have been handed down to us regarding the posi-
tions of the heavenly bodies. There are two eras in Chinese
history which it has been attempted to fix in this manner :—one,
the reign of the emperor Tcheou-kong, said to have lived about
1100 3.c.; the other, that of the emperor Yao, many centuries
earlier, about 2357 B.c. The traditions regarding these persons
are vague and altogether uncertain. My object in the present
communication is to show what degree of reliance can be placed
on the astronomical determinations. However perfect the methods
may be which modern science puts into our hands, the results to
which they lead us can be of no value if the data are not sufli-
cient and also trustworthy.
On the determination of the Era 1100 B.c.
2. M. Gaubil, a jesuit missionary at Pekin, sent to Paris in
1734a MS. of Chinese astronomical observations, which Laplace
published in the Connaissance des Tems for 1809. The oldest
observations which Laplace considered to be of any value for
astronomical purposes (as he there tells us) are two observations
of the length of shadow cast by a gnomon at the summer and
winter solstices in the time of Tcheou-kong at a place Tching-
tcheou, called also Loyang and Hon-an-fou. The latitude of this
place was observed by the missionaries in 1712 three times, and
found to be 34° 52! 8" by one observation, 34° 46! 15” by the
second, and 34° 43! 15" by the third, the last being considered
the best. The vertical style or gnomon was 8 feet (pieds) high,
Phil. Mag. 8. 4. Vol. 28. No. 151. Jan. 1862. B
2 Archdeacon Pratt on Chinese Astronomical Epochs.
and the shadows were 1 foot 5 inches (pouces) and 13 feet long,
there bemg 10 pouces in | pied. These data give at once, by a
table of tangents, 79° 7’ 11” and 31° 18! 42" for the altitudes of
the sun. To these Laplace applies corrections for refraction,
parallax, and the sun’s semidiameter, and makes them finally
79° 6' 52" and 31° 18/ 48". Half the sum and half the differ-
ence of these should give the colatitude of the place of observa-
tion and the obliquity of the echptic. They give the latitude
= 34° 47! 10", and the obliquity =23° 54! 2”. This latitude is
equal to the mean of the three observations mentioned above,
but is greater by 4! than the best of the three. Laplace
shows, by a formula in Adécanique Céleste, that 23° 51! 58" was
the obliquity in 1100 z.c. This differs by 2! 4” from that
obtained from the observations, which, at the rate of 48" a cen-
tury (the mean decrease of obliquity, see Herschel’s ‘Astronomy,’
art. 640), would throw the date back to 1858 B.c. Laplace
thinks the obliquity deduced from the observations as perfect an
accordance as could be desired, “seeing the uncertainty which
this kind of observations presents, especially because of the iil-
defined limit of the shadow ” (Con. des Tems, 1809, pp. 433,434).
3. Itis the extent of uncertainty arising from this cause which
Iwish nowto determine. Let be the height of the style, s and
w the Jengths of the shadows at the summer and winter solstices,
Zand @ the latitude and obliquity, a and 6 the altitudes of the
sun. Then
1 eee: h 1 1 Sead h
Oe faa Be A Tis! =) Sioa 2 aha ase
90 i= 5 tan 5 1 5 tan ie ) 5 tan 9 tan oo
st h? ae h? dw __1—cos2ads | 1—cos 2B dw
ee Oe teh Rees ee ge a a ae
Similarly,
r5) _ __ l—cos 2a ds i 1—cos 2p 28 Ow
Jeeesiray weet eee Se 7
Put
a=79° 6 52", B=31° 18! 48", cos 2a= —0:92867, cos280=0-45978'
Uo BIOS a OWL, oa OS 0.9 OW
ss 61=0°482 5 +0365 S- = 27 6—- + 20 IF
and
Of = —-27°°6 S + 20°°9 a
h h
The recorded lengths of the shadows contain no fractions of
an inch. It may therefore be supposed that fractions equal to,
or less than half an inch, were thought too trifling to observe ;
or the undefined appearance of the shadow made greater niccty
impracticable. Put, therefore, ds and dw each equal to half an
inch, in excess or in defect, as errors to which the measure of the
Archdeacon Pratt on Chinese Astronomical Epochs. 3
‘shadows is liable. It then appears that the latitude and the
obliquity, determined from these observations, will be free from
error only within the limits —0°-25 and +025, that is, within
a range of 0°5. Now this variation in the obliquity, at the
rate of 48" in a century, is equivalent to a range of 30! x 60
--48!'=374 centuries! This astronomical observation, therefore,
really gives no independent information whatever regar ding its
date. All we can gather is, that if History points out that 1100
B.c. was the era when this observation was made, Astronomy
presents na obstacle to this determination.
On the determination of the Era 2357 B.c.
4. An attempt has been made by M. Biot (see Journal des
Savants, 1840, 1859) to fix the date of the Emperor Yao by
reconstructing the celestial sphere (as he imagines it to have
been at that time), and reasoning from the change in the posi-
tion of the equinoxes. He fixes the date at 2357 B.c. I will
briefly explain his process, and then show in what I think it
inconclusive. He states that the ancient Chinese astronomers
divided the equator into 28 unequal parts (called stew or man-
sions) by declination circles drawn through certain stars chosen
for the purpose. M. Biot has evidently bestowed much atten-
tion on the subject, and has endeavoured to identify these stars,
which the ancient Chinese astronomers are supposed to have
used so far back as 4000 years ago! In the next page, in Tables
I. and II., I have gathered together some of his results, and in
the two following pages some further calculations, the use of
which will be explained.
In Table I. are given the names of these twenty-eight stars,
and their positions at the era, and the consequent widths of the
mansions. (The figures in the second column show the magni-
tudes of the stars.) In the choice of stars two things surprise
one: (1) that their intervals in AR are so very unequal, and (2)
that im many instances such unimportant stars are chosen. Thus,
while the width of the fifth mansion is more than 30°, the width
of the third is less than 3°. Indeed the stars at the beginning
and end of the third mansion are so near in AM, that in the
column of longitudes for 1750 a.p. the fourth star falls behind
the third! For this reason apparently M. Biot goes far back
into time past for his epoch, that the line joining the two stars
may have as large a projection as possible on the equator of the
time, so as to give the greatest advantage to this, at best, very
ill-conditioned mansion. The fourth is Galea a narrow mansion,
though not quite so narrow as the third. It will be seen that it
is the introduction of the star % Orion (instead of some other,
perhaps between Nos. 4 and 5) which makes these mansions so
narrow.
B2
4 Archdeacon Pratt on Chinese Astronomical Epochs.
TaBLe [.
l : a
No. of Latitude. Longitude. Dedlination,| , Fight ee
a Star at its commence- |. ies patie OB
. ment. 1750 A D. 2357 B.C. { 2357 BC.
1 | » Pleiades... 3.44 9) 5631 | + 3 10) S56 sonore
2 BRUNE 2oeck 3,4, — 236) 64 58 | + 0 30 8.55 | 18 5
3 NIOrIONs ves A oe: 80 13 | — 3 38 97 OO 2 48
4 Oo Orion. 2e.< 2) —23 35 78 52 | —I138 32 29 43 | 3 36
5 pt Gemini ...... Si Oak 91 49 | +12 11 33 19 | 80 35
6 6 Cancer ...... 5,6) — 0 47 | 122 15 | +20 28 63 54 6 38
7 Oydra ss... 4, —J]2 25 | 126 49 | + 9 44 10: 321 17
8 a Hydra. 08 2| —22 24 | 143 48 | + 113 87 37 7 39
9 |397,Hydra ...... 5| —26 5 | 152 13) — 2 29 95 16 | 16 40
10 a Crater ...... 4| —22 43 | 170 15 | — 039 | 1kl 56] 17 27
i y Gonvuse sc. 3 3| —14 29°) 187.15 | + 4° 4) Yo9u2s lan iZ
ig @ Virgoresiccnes }) = 2 -2 |/200 21" =E 12 125) Maksse tae
13 K) Nii conssceenes 4, + 256; 211 0} +13 9 | 157 35 8 58
14 ae Mabrays Sse 4) + 0 22 | 221 36 | + 6 46/ 166 383 | 14 5
15 aw Scorpio...... A) — 5 26 | 239 27 |-— 5 39.) WsOsssnieeaee
16 o Scorpio...... 3,44 — 4 0} 24419} — 617 | 185 40} 3 5&
17 Hy Scorpio...... Al —¥5 2) | 252.46 | —20> 1 Jotes45yi aige49
18 Y2 Sagittarius 3,4) — 6 57 | 267 47 | —18 3 | 206 34 | 9 52
19 @ Sagittarius 3,4| — 3 55 | 276 41 | —18 19 | 216 26 | 26 29
20 @Capricornus 3} + 4 37 | 300 33 | —i6 23 | 242 55 | 8 24
21 e Aquarius ... 4| + 8 7 | 308 14 | —14 12 | 251 19 | 11 50
22 8 Aquarius ... 3] + 8 388 | 319 55 | —14 49 | 263 14 | 10 10
23 a Aquarius ... 3) +10 41 | 329 52 | —12 58 | 273 24 | 18 48
24 a Pegasus 2} +19 25 | 349 59 | — 2 39 | 292 12 | 16 IT
25 y, PESaSUS -2n6r2 2} +12 36 5 40 | — 6 17 | 308 23 9 13
26 Z Andromeda 4) +17 37 17 6| +135 | 317 36 | 15 19
27 [SOATICS coseeecee 3 8 29 |__30 29 | — 2 42 | 332 55 | 10 48
238 35 Aries ...... 4, +11 17 | 48 27 | 4+ 4 42 | 343 48 | 14 47
RICAN ee ee ee koe. me bel oat — 2 28
Tasre II.
Position of Equinoxes and Solstices, 2857 B.c.
| 1. 4 Pleiades.a... 1 30 behind Vena Dauner
So. a Hydra, vat-. 2 23 behind Summer Solstice.
15. 7 Scorpio...... 0 388 before Autumnal Equinox.
22. (3 Aquarius ... 6 46 behind Winter Solstice.
Archdeacon Pratt on Chinese Astronomical Epochs,
TaB.eE III,
3 é Right Wid : e Right Width of
No. of Declination. acme Seas Declination. ee mansion.
mansion. —
In the year 1729 B.c. In the year 1100 B.c.
Me 535) 5.98 | 10 50u1, 1h 21 | 13.28 | 16 53
eens M4) | 1G 131-18 1 4 32.) 24321") F755
= == RR} 34 14 eee + 2 29 42 16 1 58
4 =) Ve 36 37 4 29 — §. 35 44 14 5 39
5 +15 24 Ale Otiirc oe +17 48 49 53 eee
6 +22 8 72 30 5 55 +22 51 81 57 5 1s
7 +11 27 78 25 16 34 +1i 23 87 10 15 53
8 Bit oG |) os 59 1-724 14 0 47-| YOae TTS
9 = % Ale 102 23 16 45 = 3 Hh 110 12 16 47
10 eek 119 8 17 41 a 126 59 17 51
11 22) ae | 135 49 16227, — iF 144 50 16 31
12 +6 9 153 16 Il 55 + 5 29 161 21 jl 53
13 + 9 42 165 1] 8 43 + 6 1] 173 14 8 Al
14 +3 6 173 54 141 One 181 55 14 .9
15 ==. 19-26 187 55 6 40 52 9G et 5 10
16 =F) 3 194 35 EZ — > oe OL Te e 39
17 = 93) Sy 186 7 1S-57 —24 4 04 53 18 32
18 aa Days |) DUG UA 9 26 ASN OM eo 3s 10 13
19 = 2122 | 224 .30)) 25 42 —23 37 | 233 38 26 46
20 17 OE AAS al 9 20 — le po! 2O0L24 § 8
21 = | 259 32 12°06 —— iy 45) 268 of i easy;
22 == 271 32 10 0O —14 50 | 280 29 9 47
23 = IPAG 25 “oz Sete —I1 43 | 290 16 gL |
QA + 0 27 299 35 16 20 + 0 47 | 307 37 16 24
25 = Be | en a 8 50 a Olas ee 8 25
25 4 21 324 45 15 29 a oy fe; | 332 26 15 30
27 + 0388 | 340 14 10 38 +4 5 347 56 10 54
28 + 8 18 330 52 14 31 +11 51 308 50 14 38
op eS ee eee — 248 |
TaBLeE LV.
Position of Equinoxes and Solstices.
2357 B.C.
° ‘
\Vernal Equinox ...|] 30 before No. 1.
‘Summer Solstice...;2 23 before No. 8.
Autumnal Equinox. |0 38 behind No.15.
2.
Winter Solstice ...
6 46 before No. 2
5
4
7
1
2
5
3
3
3
9
5
2
1729 B.C,
1100 B.C.
—
behind No. 1.1 10 before No. 28.
behind No. 8.250 before No. 7.
behind No. 15.1 55 behind No. 14.
behind No. 22.1 28 before No. 21.
5
6 Archdeacon Pratt on Chinese Astronomical Epochs.
TABLE V.
: Their differences of Right Ascension,
Nos. of mansions
compared.
2357 B.C. 1729 B.C. 1100 B.C.
1 and 15 182 8 182 32 182 36
2, 16 176 45 178 24 176 53
Se ae 16] 45 161 53 162 37
Ee Ke 176 51 178 27 179 11
Go 1G 183 7 183 24 183 45
6 is 20 179 1 177 42 178 27
7 4 Of 180 47 181 7 181 22
§ 5. 99 175 37 176 33 177 26
9°. 798 178 8 179 9 180 4
10550724 180 16 180 27 180 38
Re haere 179 0 179 6 179 11
12. YG 172 1 171 29 W715
1c ee 107 175 20 175 3 174 42
PM see 177 10 176 58 176 55
M. Biot attempts to illustrate the correctness of his list of
stars, though so irregularly distributed and in many instances so
inferior in importance, by stating that there is evidently a law in
their selection, and that a narrow mansion in one part of the
heavens corresponds to a narrow mansion in the opposite part ;
so also with the wider mansions; so that the stars, at the epoch,
were situated in pairs on the same meridian.
5. It is by the application of this test, which is to some extent
approximately true, that I think I can detect a flaw which destroys
the necessity of passing so far back into past time as the twenty-
fourth century B.c. In the first of the three columns in Table
V., IL have given the differences of MR for 2357 B.c. gathered
from M. Biot’s results in Table I. It will there be seen that the
pairs of stars deviate from beimg on the same meridian by an
average =about 3°, 2f we except the third pair in which the
deviation is as much as 18° 15’. There must be some reason
for this exception. ‘The fact is, both the limiting stars of that
mansion are exceptional; No. 3 being so near Nos. 2 and 4 (as I
have already pointed out), and No. 17 having so large a declina-
tion. (No.6 hasas large a declination, see Table I.; but that star
is close upon the ecliptic, which No. 17 is not, which may be
some reason for its use, there being no nearer star.) These two
stars, moreover, are both small, being only of the fourth order of
magnitude. I conclude, therefore, for these reasons that they
have been wrongly determined. If X% Orion is rejected, the
necessity for pushing back the epoch so far is removed.
6. In Tables III., [V., V. I have given the results of calcula-
tions I have made for two other epochs, viz. 1100 3.c. and 1729
B.C. (halfway between 1100 B.c. and 2357 B.c.), in order to see
Archdeacon Pratt en Chinese Astronomical Epochs. 7
whether there is any special reason for so remote an epoch as
2357 B.c. being selected. I can see no special reason. (1)
Even if X Orion is not rejected, it will be seen that the width of
the third mansion is 2° 23! and 1° 58! at those two later dates,
and these are not so inferior to 2° 43/, the width in 2357 B.c.,
as to induce any great preference for that epoch. (2) By com-
paring the columns of declinations in Tables 1. and III., it will
be seen that the twenty-eight stars lie very much alike with
reference to the equators of the three epochs, without any decided
advantage for 2357 B.c. In allof them the mid-line is south of
the equator; the distance is 2° 28/, 2° 26!, 2° 48’ in the three
cases. (3) M. Biot points out that the arrangement of stars
chosen by the Chinese is equatorial, and not ecliptical; and he
well illustrates this by showing that « Hydree has been chosen,
though only of the second magnitude, as the eighth star in pre-
ference to the much brighter star Regulus in the same hour-
angle, but on the ecliptic and about 24° from the equator. But
he departs from this idea when he draws an argument for his
ancient epoch from the circumstance that 7 in Pleiades is the
jirst of the twenty-eight stars, and that therefore when the
system was chosen that star must have been the vernal equinox.
The Pleiades, in their sevenfold group, are so conspicuous and
marked an object, that it is very easy to understand that, being
chosen as one of the twenty-eight determining stars, they should
be fixed upon, for that reason, as the point of departure. At
the three dates in my Tables, the declination of 7 is only 3° 10’,
7° 53/, 11° 21'; the largest of which is smaller than that of
twelve of the twenty-eight stars as laid down by M. Biot for
2357 B.c. In passing backwards to obtain as great a width as
possible for his third mansion, he seems to have stopped short at
» in Pleiades for no other reason than that, being first of the
equatorial series, it might also be the equinox; whereas by
going further back he might have somewhat further widened
his third mansion. {4} M. Biot also observes that four of the
chosen stars, the ist, 8th, 15th, and 22nd (see Table I1.), fall
very near the equinoxes and solstices of 2357 B.c., and that this
is an argument in favour of that epoch. But my Table IV. shows
that in 1100 z.c. four others of the twenty-eight’ stars, also at
equal intervals in point of number, viz. the 7th, 14th, 21st, and
28th, were still nearer to the equinoxes and solstices. So that
no argument can be drawn from this source in favour of his
epoch: rather the contrary. He says that the four stars he
names are mentioned in the Chou-king*, an ancient work on
* For what is known of this work Chou-king, or Shoo-king, see Encye.
Brit., word China, p. 640: also see “ History of Astronomy” in ‘ Library
of Useful Knowledge.’
>
8 Archdeacon Pratt on Chinese Astronomical Epochs.
astronomy, as being at the equinoxes and solstices in the time of
Yao. As one of the points (see Table II.) is wrong by 6° 46',
this commits the Chou-king to.an error of 487 years. Moreover,
these traditions are not to be relied upon as facts. We have in
Indian astronomy an instance of an ancient conjunction of sun,
moon, and planets stated as if an observed phenomenon, whereas
it is clear that the idea (which is false in fact) was come at by
caleulatmg backwards, and that upon defective data. (5) An-
other thing which M. Biot appears to think confirmatory of his
epoch is this. He states that the Chinese used to observe with
care the motion of the circumpolar stars in the Dragon, the
Great Bear, and the Lesser Bear, and two in Lyra; and conjec-
tures that the position of the declination-circles passing through
them at that epoch influenced the astronomers in the choice of
the stars which define the twenty-eight mansions. Eleven, how-
ever, of the mansions have none of these circles passing through
them, and the angular distances of the others from the nearest
stars vary through all degrees of magnitude between 0° 8! and
7° 26'; of these approximate conjunctions on the same meridian
twelve take place at the inferior passage of the cireumpolar star.
There does not appear to be anything at all remarkable in these
approximate relations. Other positions of the pole and other
epochs may be no doubt found where even a nearer approxima-
tion of the kind exists. (6) Another argument of M. Biot in
favour of his epoch is, that a star is spoken of by Chinese
astronomers as the “ Unity of the Heavens,” which name is sup-
posed to indicate that it was at the pole of the equator when first
so designated: and the French chronologist Freret thinks the
star must be « in the Dragon, though M. Biot thinks it may be
another star close to it. It is very easy to show that, as the
longitude of this star was in 1750 a.p. 153° 54’, it must have
been 63°9 x 72=4601 years before that epoch (that is, 2850
B.C.) when it was at the pole, or at its nearest point only a few
minutes from it. This is 500 years before M. Biot’s epoch. In
this time, however, it would not have moved away more than
about 2° 46/, and therefore might still be regarded as the pole-
star. But this shows the uncertainty of such means of fixing
dates, even by the best astronomical means, if the data are not
precise. The star would continue within a distance of 2° 46,
taking both sides of the pole, for no less a period than 1000
years. The fact, therefore, of its being regarded as the pole-
star, if such errors are allowed (and we see larger errors allowed
in this approximation to a system), would not fix the date within
1000 years. ‘There is a tradition that the Chaldee astronomers
had observed @ Draconis in the pole. It is quite possible that
such a circumstance might be handed down, one so easily observed,
Prof. Marcet on the Effects of Nocturnal Radiation. 9
even from antediluvian times. But it is still more probable that
it has been calculated backwards, a matter of no difficulty when
once the precession of the equinoxes was known, and the epoch
when it occurred assigned with more or less accuracy according
to the means of calculation.
7. This reconstruction of the celestial sphere in the time of
the Emperor Yao, even supposing he was a historical character,
appears to me to be based upon such uncertain data as to make
it altogether untrustworthy. If the data were more exact, the
case would be different. Unless, however, reliable data can be
procured, it seems a pity to prostrate the science of astronomy
by using it in such a cause, lending its name and high character
to prop up the conclusions of vague and uncertain traditions,
enveloped too often in fable and falsehood.
J. H. Prarv,
Calcutta, October 19, 1861.
If. Experiments on the Comparative Effects of Nocturnal Radia-
tion from the Surface of the Ground and over a large Sheet of
Water. By Professor Marcet of the Academy of Geneva*. ©
i. is acknowledged that about the period of sunset, provided
the sky be clear, the temperature of the air in contact
with the earth’s surface is cooler than that of the atmosphere
at a certain height above the ground. This fact was first noticed
by Pictet and Six, towards the end of the last century; but as
the theory of radiant heat had not yet been established, no
satisfactory explanation of the phenomenon was offered until
1814, when Dr. Wells published his valuable ‘Essay on Dew.’
Many years afterwards (in 1842) a series of observations, on
the same subject, [ had made in the neighbourhood of Geneva,
was published in the eighth volume of the Mémoires de la Société
de Physique et d’ Histoire Naturelle, tending to prove that during
clear and calm nights the atmosphere becomes gradually warmer
on ascending above the surface of the earth, until a certain
height be attained, which varies according to circumstances, but
is generally not less than from thirty to forty yards. The obser-
vations I made in 1842 have just been fully confirmed by an
elaborate treatise on the subject published by Professor C.
Martins of Montpelliert. The results obtained are, no doubt,
attributable to the gradual cooling of the earth’s surface arising
from its nocturnal radiation into empty space; which radiation,
when the sky is clear, is not compensated by the transmission of
* Communicated by the Author.
+ Vide Mémoires de l’ Académie des Sciences et Belles Lettres de Mont-
pellier, vol. v.
10 Prof. Marcet on the Comparative Effects of Nocturnal Radiation
caloric from the higher regions of the atmosphere. The cooling of
the surface of the earth naturally gives rise to a corresponding
diminution of temperature of the stratum of air in its immediate
vicinity ; the effect is transmitted to the stratum above, though
naturally in a less degree, and so on from one stratum to another,
until a height be attained at which the temperature of the atmo-
sphere is found to be equal to that of the stratum of air in con-
tact with the earth.
I had often thought of inquiring whether the effects of noc-
turnal radiation, tending as they do to produce a gradual in-
crease of temperature on ascending above the earth’s surface,
are entirely dependent on the radiation of the ground, properly
so called, or whether they would be equally perceptible above a
large sheet of water, such as the sea oralake. The exceptionally
fine clear weather of October last afforded mea favourable oppor-
tunity for making some experiments on the effects of nocturnal
radiation from the surface of the lake cf Geneva.
Let me, however, be allowed to remark that experiment alone
could determine to what extent a large surface of water is
capable of producing, by the radiation of its caloric, the whole,
or at least a part of the effects due to the nocturnal radiation
of the earth. Water, it is well known, possesses a consider-
able radiating power; Leslie, in his ‘Researches on Heat,’
found it to be equal to that of lampblack, and superior to that
of paper. Itis not, therefore, because water does not radiate suf-
ficiently that we can be authorized to conclude @ priori that the
nocturnal increase of temperature is not as likely to take place
over a liquid surface as over the solid ground; but there is an-
other fact, depending upon the peculiar constitution of liquids,
which must also be taken into consideration. The particles of
liquids, it is well known, are essentially moveable, and their dif-
ferent strata subject to a constant interchange of position when
affected by the slightest changes of temperature. The conse-
quence is, that the moment the upper surface of a given extent of
water has begun to cool by the effect of nocturnal radiation, it
will become denser than the stratum immediately below it ; it
will therefore descend and be replaced by this stratum, which,
becoming heavier in its turn, will be replaced by the following,
and in the same way successively from one stratum to the other ;
so that in fact there is no reason why the temperature of the sur-
face of the water should undergo any appreciable change. Under
these circumstances it will, I think, be admitted that the effect
of nocturnal radiation (inasmuch as it would tend to lower the
temperature, first of the surface of the water, and next that of the
stratum of air in immediate contact with this surface) will become,
if not entirely imperceptible, at least far less apparent than on
from the Surface of the Ground and over a Sheet of Water. 11
land. The following experiments made during last October on
the Lake of Geneva entirely corroborate this view.
Three Centigrade mercurial thermometers, capable of showing
the tenth part of a degree, were fixed at different heights round
a vertical pole about 16 feet long. Hach thermometer was
attached to the extremity of a horizontal rod fixed to the pole,
and sufficiently long to ensure the thermometers being sus-
pended, not over the boat from which the experiments were to
be made, but directly over the surface of the water. One of the
thermometers was placed at a height of about 3 inches above
the surface of the water, the second at about 6 feet, and the
third at 15 feet. Three series of observations were made du-
ring the evenings of the 26th and 28th of October, at about
600 yards from land, under the most favourable circum-
stances—the sky being beautifully clear, and the surface of the
lake unruffled by the slightest breeze. The observations were
commenced a quarter of an hour before sunset, and renewed
every half hour until three-quarters of an hour after sunset.
The following is the average result of the observations noted
during the evening of the 26th of October :—
Temperature of the atmosphere 3 inches above the water. 11-65 C.
: re 6 feet a . 11°62
sf ‘15 feet 3 » 11°80
Temper ature of the water at the surface of the lake . 12
The average result obtained during the evening of the 28th
was as follows :—
Temperature of the atmosphere 3 inches above the water. 11: 35 C.
a 53 6 feet si - 11°29
%; 15 feet ay yilie32
Temperature of the surface of the water 2-45
The consequence to be drawn from these results is, I appre-
hend, that the comparative temperature of the successive strata
of air above the surface of the lake up to the height of 15
feet, undergoes no sensible change from the effects of nocturnal
radiation. The almost imperceptible differences indicated by
the thermometers in no case exceeding a few hundredths of a
degree, may be fairly attributed to errors arising from accidental
currents, which it is difficult to guard against completely in
observations of this nature.
The following is the mean result of comparative observations
made at the same moment in the centre of a large field about
700 yards from the borders of the lake :— :
Temperature of the surface of the ground. . 6:98 C,
Temperature of the air 3 inches above the ground . 8:00
rf 9 6 feet 33 won ali
ve a 15 feet a « - 9°65
12 Prof. Maxwell on the Theory of Molecular Vortices
Finally, comparative observations made simultaneously on the
borders of the lake, within a few feet of the water, gave the fol-
lowing result :—
Temperature of the surface of the gravel . . . 9-90 C.
‘Temperature of the air 3 inches above the ground. 10°40
4 3 6 feet 3 . 1:39
a 15 feet = 5 LORe
showing that the immediate neighbourhood of the water is suf-
ficient to modify the results generally obtained on land.
The following conclusions may, I think, be safely drawn from
the foregoing observations :—
1. The gradual increase of temperature occurring cn ascending
through the lower strata of the atmosphere, which appears con-
stantly to prevail on land about and after sunset, is not apparent
above a large surface of water.
2. The immediate vicinity of a large sheet of water is suffi-
cient to modify to a considerable extent the effects of the noc-
turnal radiation of the earth, and thereby materially diminish
the increase of temperature observed under ordinary cireum-
* stances on ascending above the surface of the ground.
3. One cannot help being struck by the great difference
(amounting to between 2 and 3 Centigrade degrees) constantly
observed between the temperature of the atmosphere a few feet
above the ground, and that of the air at the same height above
a large sheet of water.
III. On Physical Lines of Force. By J.C. Maxwett, FR.S.,
Professor of Natural Philosophy in King’s College, London*,
Part Iil.—The Theory of Molecular Vortices applied to
Statical Electricity.
ie the first part of this paper+ 1 have shown how the forces
- acting between magnets, electric currents, and matter capa-
ble of magnetic induction may be accounted for on the hypothesis
of the magnetic field being occupied with innumerable vortices
of revolving matter, their axes coimciding with the direction of
the magnetic force at every point of the field.
The centrifugal force of these vortices produces pressures di-
stributed in such a way that the final effect is a force identical
in direction and magnitude with that which we observe.
In the second part{ I described the mechanism by which
these rotations may be made to coexist, and to be distributed
according to the known laws of magnetic lines of force.
* Communicated by the Author.
+ Phil. Mag. March 1861. Phil. Mag. April and May 1861.
applied to Statical Electricity. 13
~ I conceived the rotating matter to be the substance of certain
cells, divided from each other by cell-walls composed of particles
which are very small compared with the cells, and that it is by
the motions of these particles, and their tangential action on the
substance in the cells, that the rotation is communicated from
one cell to another.
I have not attempted to explain this tangential action, but it |
is necessary to suppose, in order to account for the transmission
of rotation from the exterior to the interior parts of each cell,
that the substance in the cells possesses elasticity of figure,
similar in kind, though different in degree, to that observed in
. solid bodies. The undulatory theory of light requires us to
admit this kind of elasticity in the lumimiferous medium, in
order to account for transverse vibrations. We need not then
be surprised if the magneto-electric medium possesses the same
property.
According to our theory, the particles which form the partitions
between the cells constitute the matter of electricity. The
motion of these particles constitutes an electric current; the
tangential force with which the particles are pressed by the
matter of the cells is electromotive force, and the pressure of
the particles on each other corresponds to the tension or poten-
tial of the electricity.
If we can now explain the condition of a body with respect to
the surrounding medium when it is said to be “charged” with
electricity, and account for the forces acting between electrified
bodies, we shall have established a connexion between all the
principal phenomena of electrical science.
We know by experiment that electric tension is the same
thing, whether observed in statical or in current electricity ; so
that an electromotive force produced by magnetism may be
made to charge a Leyden Jar, as is done by the coil machine.
When a ditference of tension exists in different parts of any
body, the electricity passes, or tends to pass, from places of
greater to places of smaller tension. If the body is a conductor,
an actual passage of electricity takes place; and if the difference
of tensions is kept up, the current continues to flow with a
velocity proportional inversely to the resistance, or directly to the
conductivity of the body.
The electric resistance has a very wide range of values, that
of the metals being the smallest, and that of glass being so
great that a charge of electricity has been preserved* in a glass
vessel for years without penetrating the thickness of the glass.
Bodies which do not permit a current of electricity to flow
through them are called insulators. But though electricity does
* By Professor W. Thomson.
14 Prof. Maxwell ou the Theory of Molecular Vortices
not flow through them, electrical effects are propagated through
them, and the amount of these effects differs according to the
nature of the body; so that equally good insulators may act
differently as dielectrics*.
Here then we have two independent qualities of bodies, one
by which they allow of the passage of electricity through them,
and the other by which they allow of electrical action being
transmitted through them without any electricity being allowed
to pass. A conducting body may be compared to a porous
membrane which opposes more or less resistance to the passage
of a fluid, while a dielectric is like an elastic membrane which
may be impervious to the fluid, but transmits the pressure of the
fluid on one side to that on the other.
As long as electromotive force acts on a conductor, it produces
a current which, as it meets with resistance, occasions a continual
transformation of electrical energy into heat, which is incapable
of being restored again as electrical energy by any reversion of
the process.
Electromotive force acting on a dielectric produces a state of
polarization of its parts similar in distribution to the polarity of
the particles of iron under the influence of a magnett, and, like
the magnetic polarization, capable of being described as a state
in which every particle has its poles in opposite conditions.
In a dielectric under induction, we may conceive that the
electricity in each molecule is so displaced that one side is ren-
dered positively, and the other negatively electrical, but that the
electricity remains entirely connected with the molecule, and
does not pass from one molecule to another.
The effect of this action on the whole dielectric mass is to
produce a general displacement of the electricity in a certain
direction. ‘This displacement does not amount to a current,
because when it has attained a certain value it remains constant,
but it is the commencement of a current, and its variations con-
stitute currents in the positive or negative direction, according
as the displacement is increasing or diminishing. The amount
of the displacement depends on the nature of the body, and on
the electromotive force; so that if h is the displacement, R the
electromotive force, and E a coefficient depending on the nature
of the dielectric, R= —4rFE2A ;
and if 7 is the value of the electric current due to displacement,
at
=
* Faraday, ‘ Experimental Researches,’ Series XI.
T See Prof. Mossotti, *Discussione Analitica,’’? Memorie della Soc. Ita-
liana (Modena), vol. xxiv. part 2. p. 49.
applied to Statical Electricity. 15
These relations are independent of any theory about the internal
mechanism of dielectrics; but when we find electromotive force
producing electric displacement ina dielectric, and when we find
the dielectric recovermg from its state of electric displacement
with an equal electromotive force, we cannot help regarding the
phenomena as those of an elastic body, yielding to a pressure,
and recovering its form when the pressure is removed.
According to our hypothesis, the magnetic medium 1s divided
into cells, separated by partitions formed of a stratum of particles
which play the part of electricity. When the electric particles
are urged in any direction, they will, by their tangential action
on the elastic substance of the cells, distort each cell, and call
into play an equal and opposite force arising from the elas-
ticity of the cells. When the force is removed, the cells will
recover their form, and the electricity will return to its former
position.
In the following investigation I have considered the relation
between the displacement and the force producing it, on the
supposition that the cells are spherical. The actual form of the
cells probably does not differ from that of a sphere sufficiently
to make much difference in the numerical result.
I have deduced from this result the relation between the
statical and dynamical measures of electricity, and have shown,
by a comparison of the electro-magnetic experiments of MM.
Kohlrausch and Weber with the velocity of light as found by
M. Fizeau, that the elasticity of the magnetic medium in air is
the same as that of the lumimiferous medium, if these two coex-
istent, coextensive, and equally elastic media are not rather one
medium. |
It appears also from Prop. XV. that the attraction between
two electrified bodies depends on the value of E?, and that there-
fore it would be less in turpentine than in air, if the quantity of
electricity in each body remains the same. If, however, the
potentials of the two bodies were given, the attraction between
them would vary inversely as E*, and would be greater in turpen-
tine than in air.
Prop. X\1.—To find the conditions of equilibrium of an elastic
sphere whose surface is exposed to normal and tangential forces,
the tangential forces being proportional to the sine of the distance
from a given point on the sphere.
Let the axis of z be the axis of spherical coordinates.
Let &, 7, be the displacements of any particle of the sphere
in the directions of 2, y, and z.
Let Pix, Pyy, Pzz be the stresses normal to planes perpendicular
to the three axes, and let p,., Pex, Pry be the stresses of distortion
in the planes yz, za, and ay.
16 Prof. Maxwell on the Theory of Molecular Vortices
Let « be the coefficient of cubic elasticity, so that if
Psx=Pyy =Pzz =P)
d— dy
p= =.(¢ +74). ee (80)
Let m be the coefficient of rigidity, so that
Pex —Pyy=™ & = a NGC; Ae co (81)
Then we have the following equations of elasticity in an isotropic
medium,
ponte nn(E eS) and.
with similar equations in y and z, and also
Dice fie z): ke
In the case of the sphere, let us assume the radius = a, and
, E=erz, n=exy, C=f(a?+y*)+yge2+d. . (84)
Then
Pee=2(m—3Zm)(e+9)2+ mez=Ppyy, |
Prz=2(U—gm)(C+9)2 +2mgz,
m
Py= x (e+e )y, ea Res
m
|
Pzxe= gy e+ 2f)e, |
Pry=09.
The equation of internal equilibrium with respect to z is
d d d
gba dyeee* qa b= eae eae (86)
which is satisfied in this case if
me+2f+2g)+2(u—im)(e+g)=0. . (87)
The tangential stress on the surface of the sphere, whose
radius is a at an angular distance @ from the axis in plane zz,
T= (Prer—Pzz) Sin 8 cos 0+ pre (cos*@—sin? A). . (88)
=2m(e+f—yg)a sin 0 cos? 0— = (e+2f) sin @. . (89)
In order that T may be proportional to sin 0, the first term must
vanish, and therefore
g=et+f, ie ite: Rite ° eo (90)
T=— > (e+2f) sin 8. ee
applied to Statical Electricity. 17
The normal stress on the surface at any point is
N =P, sin? 8+ pyy cos? 8 + 2p, sin 8 cos 8
=2(u~—4m)(e+g)acosé + 2macosO((e +f)sin?6 + gcos? 0); (92
or by (87) and (90),
N=—mal(e+2f)cos@. -. s .-. -(93)
The tangential displacement of any point is
t=£cos 0—Csin €=—(a*f+d)sn@ . . . (94)
The normal displacement is
n= €sin 0+ fcos 0=(a%(e+f) +d) cos 0. Ra, CN)
If we make
Get) Pda Or ai oa ee OO)
there will be no normal displacement, and the displacement will
be entirely tangential, and we shall have
(a0 SRS OES res har tiga ne 55/7)
The whole work done by the superficial forces is
U=32>(TAdS,
the summation being extended over the surface of the sphere.
The energy of elasticity in the substance of the ae is
of dg dn ) dé
U= 23(F pat 2 dye Wz bet dz 5 = dy Pyzt . a an): Ze
- (+ i)Pa)
the summation being extended to the whole contents of the
sphere.
We find, as we ought, that these quantities have the same
value, namely
—2rra°me(e+2f). . . « « (98)
We may now suppose that the tangential action on the surface
arises from a layer of particles in contact with it, the particles
being acted on by their own mutual pressure, and acting on the
surfaces of the two cells with which they are in contact.
We assume the axis of z to be in the direction of maximum
variation of the pressure among the particles, and we have to
determine the relation between an electromotive force R acting
on the particles in that direction, and the electric displacement 2
which accompanies it.
Prop. XI11.—To find the relation between electromotive force
and electric displacement when a uniform electromotive force Rt
acts parallel to the axis of z.
Take any element 6S of the surface, covered with a stratum
Phil, Mag. 8, 4. Vol. 23, No. 151, Jan, 1862.
18 Prof. Maxwell on the Theory of Molecular Vortices
whose density is p, and having its normal inclined @ to the axes
of z; then the tangential force upon it will be
pROS sin O=2TOS, ...,... ss:
T being, as before, the tangential force on each side of the sur-
1 ,
face. Putting p= 5, a8 In equation (34)*, we find
R=—2arma(et+2f). . °. 5. 2) AS)
The displacement of electricity due to the distortion of, the
sphere is
Yd8i pt sin 6 taken over the whole surface; . (101)
and if h is the electric displacement per unit of volume, we shall
have |
4mah= fate, ee) Ge Le
or
. 1
= on ae; - . 5 5 5 : (103)
so that
Rader? LL p, eee le,
or we may write
R= 4arH*h,, . «jes | ote a
B= — mt) . ake SEED
provided we assume
Finding e and f from (87) and (90), we get
; g
K?=7m
(107)
The ratio of m, to mw varies in different substances; but in a
medium whose elasticity depends entirely upon forces acting
between pairs of particles, this ratio is that of 6 to 5, and in this
case
Wace... |. ie
When the resistance to compression is infinitely greater than the
resistance to distortion, as in a liquid rendered slightly elastic
by gum or jelly,
HP Birt 4. +) ok. log ae
The value of HK? must he between these limits. It is probable
that the substance of our cells is of the former kind, and that
we must use the first value of E?, which is that belonging to
* Phil. Mag. April 1861.
applied to Statical Electricity. 19
a cima “perfect ” solid*, in which
ieee rears 3 SELIG)
so that we must use equation (108).
Prop. X1V.—To correct the equations (9) + of electric currents
for the effect due to the elasticity of the medium.
We have seen that electromotive force and electric displace-
ment are connected by equation (105). Differentiating this
equation with respect to ¢, we find
dk dh |
Te a! ae hee ae ale Serene (111)
showing that when the electromotive force varies, the electric
displacement also varies. But a variation of displacement is
equivalent to a current, and this current must be taken into
account in equations (9) and added tor, The three equations
then become
1 (2 ads 4 dP |
Tor 3
ele Batata | ot) le
where p, g, r are the electric currents in the directions of 2, y,
and z; a, 8, y are the components of magnetic intensity ; and
P, Q, R are the electromotive forces. Now if e be the quantity
of free electricity in unit of volume, then the equation of conti-
nuity will be
die 500s. Ee. A
Reh fy dedeadi cae FAT: AD Ne
Differentiating (112) with respect to z, y, and z respectively, and
substituting, we find
« = AG+S dQ =
= iat dt
(113)
yn a EE)
whence
Se Karr dQ: din
-oalS Ting trg ay iam ay lina 2)
the constant being omitted, because e=O when there are no elec-
tromotive forces.
i ? XV.—To find the force acting between two electrified
odies
The energy in the medium arising from the electric displace-
* See Rankine “ On Elasticity,” Camb. and Dub. Math. Journ. 1851,
fT Phil. Mag. March 1861,
C2
20 ~~ Prof. Maxwell on the Theory of Molecular Vortices
ments Is
3 U=—S3(Pf+Qg+Rh)dV, . . . (116)
where P, Q, R are the forces, and f, g, h the displacements.
Now hai there is no motion of the bodies or alteration of
forces, it appears from equations (77) * that
dV Ee dy
meade las ee
and we know by (105) that
P=—4rE?f, Q=—47E?9g, R=—4rk?h; . (119)
whence
3 ee ae ees] )
=o =( = bV. . (120)
Integrating by parts throughout all space, and remembering that
W vanishes at an infinite ae
eee DGS ay eee ~
7 Bn sm oe! dye
(118)
<2) Vs (121)
or by (115),
Uaiswasve ae
Now let there be two electrified bodies, and let e, be the distri-
bution of electricity in the first, and V, the electric tension due
to it, and let
wb (ah, oY ae,
1 4arB?\ dx? dy? dz? ):
Let e, be the distribution of electricity in the second body, and
‘VY, the tension due to it; then the whole tension at any point
will be YW, + ay and the expansion for U will become
=43 (Vie, + Voe.t Veg t+ Voe,)6V. . . (124)
Let the om whose electricity is e, be moved in any way,
the electricity moving along with the body, then since the dis-
tribution of tension Y, moves with the body, the value of Wye,
remains the same.
W.e,-also remains the same; and Gieen has shown (Essay on
Electricity, p. 10) that V,e,=W,¢,, so that the work done by
moving the body against electric forces
And if.e, is confined to a small body,
Waco,
* Phil, Mag. May 1861,
(128)
applied to Statical Electricity. 21
or
Fdr= os 2dr, e ° e @ ° r (126)
where F is the resistance and dr the motion.
If the body e, be small, then if r is the distance from e., equa-
tion (123) gives
ee €
Y,=E*- :
whence
BoB; 6 ee we (12%)
or the force is a repulsion varying inversely as the square of the
distance. — ;
Now let 7, and 7, be the same quantities of electricity mea-
sured statically, then we know by definition of electrical quantity
Pe A ee Bet ae Ae)
pee
and this will be satisfied provided 7
Hee, ANG a= Wes side se en moe)
so that the quantity E previously determined in Prop. XIII. is
the number by which the electrodynamic measure of any quan-
tity of electricity must be multiplied to obtain its electrostatic
measure. ;
That electric current which, circulating round a ring whose
area is unity, produces the same effect on a distant magnet as a
magnet would produce whose strength is unity and length unity
placed perpendicularly to the plane of the ring, is a unit current ;
and E units of electricity, measured statically, traverse the
section of this current in one second,—these units being such
that any two of them, placed at unit of distance, repel each other
with unit of force.
We may suppose either that E units of positive electricity
move in the positive direction through the wire, or that E units
of negative electricity move in the negative direction, or, thirdly,
that }E units of positive electricity move in the positive direction,
while 3E units of negative electricity move in the negative dircc-
tion at the same time.
The last is the supposition on which MM. Weber and Kohl-
rausch* proceed, who have found
4 =155,370,000,000, . . . . (180)
the unit of length being the millimetre, and that of time being
one second, whence ,
: B=810,740,000,000. . « . . (dl)
* Abhandlungen der KGnig. Sdchsischen Gesellschaft, vol. iii.(1857), p, 260,
22 Prof. Maxwell on the Theory of Molecular Vortices
Prop. XVI.—To find the rate of propagation of transverse’
vibrations through the elastic medium of which the cells are
composed, on the supposition that its elasticity is due entirely to
forces acting between pairs of particles.
By the ordinary method of investigation we know that
va4/%, | ee
where m is the coefficient of transverse elasticity, and p is the
density. Byreferring to the equations of Part I., it will be seen
that if p is the density of the matter of the vortices, and yu is the
“ coefficient of magnetic induction,”
=Tp; >... ON
Tm= Vp; ~ 0 hab yo. a eae
whence
and by (108), if
ee , EHV peach. ao eee CL ‘i
By the aid of these expressions the values of a',, a", . be ;
may be formed from equations (6) and (7). I willnot draw up
these values themselves, but instead of them the values of four
magnitudes which I denote by (X’), (¥’), (X"), (Y"), and which
i define by the following equations :—
|
| aii, Chey
(X') =a! —2C (, ae
(x!) =0' —20( 84, +
J
(X") = al! —20(a!,+
Ae iu al iw aS
ee
(Y") = pl —2C ( B'o+
On the one hand we get from this
6(X') =—2Cbe',, 8(Y') =—2C88',,
6(X"j=—2CSa",, 8(¥") = —2C88", ;
and also taking into account the equation (3),
6 6(Y" Yous
1+ = = SK ae Sil) \oh ewatagies
On the other hand there is obtained from equations (12),
40 M. G. Kirchhoff on the Relation of the Lateral Contraction
taking into account equations (6) and (7),
(X’) =! —2C =>)
(X") =a" —20—_,
I
(v") —pr_ag ©,
Taking now equations (11), and placing for 9! and y" the
approximate values,
— (X'—a')? + (Y'—U)?
8C? .
arian (X?—g!l\24 (Y"—9")2
Vo S)h a» [SOR
which are obtained from equations (10), and neglecting further
small values of higher order, we obtain
8 Fe She ar)
(Y') =Y! 4.(¥! —}') F,
(X") =X" 4 (X" a!) BM,
(Y?) — Y!! au ee es b!') ne
where
h ]
P= — G+ gqs| @! ely? (V—y)2—3 [Xa + (WB
+ (3 s+4'—a!) Cg Se +5 5(X! —X7) |
3
and
PF’ - 4 = [ (xa) + (Y"—H")2— 38 [(X"—al)2 4 (Y" — oN]
—s(X!—X) — (js—4e"- “')) ("x") | :
The observations made are calculated according to these formule.
Of the magnitudes occurring in them, X’, Y', X”, Y", X’, Y',
X", Y" were obtained directly from readings of the images of
the scale; a!, b', a’, b from the measured distances of the
plummets 7, i (fig. 2, Plate I.), and of two plummets formed
of the threads f, f; &—da' and &’—a" were measured with a
circle. There only remains for further discussion the manner
to the Longitudinal Expansion in Rods of Spring Steel. 41
in which the magnitudes C and h, or the magnitudes C’, Cl,
which are connected with them by the equations (8), were de-
termined.
On the bracket which supported the rod submitted to experi-
ment, a point was fixed, the depth of which below the scale was
once for all determined on a large scale. In front of the elastic
rod a cathetometer was adjusted ; after the rod had been fixed
and made straight in the manner previously described, the depth
of a certain point of each reflecting surface below the above
point was measured with the cathetometer; for after the height
of the point had been read off on the scale of the cathetometer,
its telescope was so arranged by turning around its vertical axis
that its vertical thread covered one of the plummets 7, and then
it was lowered until the intersection of its threads appeared to
fall on the front edge of the corresponding reflecting surface.
The point upon which the telescope was then set, is the intersec-
tion of three planes, the equations of which have to be formed.
One of these planes is the reflecting surface; it has the equa-
tion (if the mirror is the first)
(E—a'a' + (q@—0)B' + (E—)y'=0.
A second plane is the vertical laid through the anterior edge of
the mirror ; let its equation be
n—r'=0.
The third plane is that which passes through the plummet 7,
and the axis of rotation of the cathetometer ; if a!" and 0!" are
the & and 7 ordinates of this axis of rotation, the equation of
this plane is
(E—al) (o!"—B) — (6) (a"—a!) =0.
If Z' be the € ordinate of the point upon which the telescope of
the cathetometer was set, we i a these three equations,
saa’! (es ra}?
TES fake
or approximately,
J Tokay oy vee Wi cat fiestas
cl =Z! a (VU) + Fray (X—al)).
By a similar notation we may obtain in the same manner,
pt
jl (Ye = DM) 4 Nien (X!—a!)) ;
OC + oir b! . I
e and e’ are calculated from these equations by taking an ap-
proximate value for C.
A
42 M. G. Kirchhoff on the Relation of the Lateral Contraction
I now pass on to a statement of the numerical results which the
observations and measurements have given.
As far as the scale is concerned, the parts of each axis were
not found exactly equal, yet the dilferences which they exhibited
were so small that they may be here neglected. The differences
of the mean value of one part of the & axis, and of the mean
value of a part of the 7 axis, were, however, more considerable.
From the measurements made the former is 1:7993 millim., the
latter 1:8086 millim.
An approximate value for C is 2357 millims. In the experi-
ments the particulars of which I here communicate, we had in
millimetres, |
ad=—241, b'=—147:0, a'=829°6, b"=—152°3,
ge AAT-by OS — 1512; “27108 Sa:
With a steel rod of about the dimensions given at the com-
mencement, which I will indicate by No. 1,
s=145-04 millims. ;
and in the first adjustment,
X'=143:2, Y’=93°3, X"=12-4, Y’=98-0,
Z' =2355'2 millims., Z"=2355'5 millims.,
f—h=—21, r'!—d"=—20,
E'—g=35, #—a'!=—29.
Using weights of 100 gr., the following readings were ob-
tained :—
a, Yi x ve";
RAPES rhs F7°/27- 88°2 25°8 92°5
POG). haz) 420152 122°9 63°0 56°4
LPO Oa pal 88°1 25°6 92°4
WS ee eet gs 53°0 61°8 127°3
Cees 2. Porte 88°5 25°7 92°8
IDGn as» 2 122°8 62°9 56°4
Bers. Sk Apis 88°0 25°6 92°3
G2. 6 DOE 52°8 61°4 127°1
i See dO 88°2 25°5 92°6
The readings were made first without the weights, then after
these had been suspended at D! and D" (fig. 1), then after
removing them, then when they acted at B' and B", then again
after their removal, then after they had been again placed at D!
and D", and so on, I have observed the rod several times under
similar conditions, first, in order to obtain greater accuracy
than one observation would afford; and secondly, in order to
notice whether if, after the weights had been removed, a per-
ceptible part of the flexion or torsion produced by them remained.
to the Longitudinal Expansion in Rods of Spring Steel. 43
If this was the case, it showed itself in a difference of the differ-
ences X’—X" and Y'—Y", on the observations in which the
weights did not act. There was such a difference, but in all sets
of observations it seldom exceeded 0°2 of a division of the scale,
and can therefore be readily accounted for from errors of obser-
vation and accidental disturbances.
From the directly observed values of X’, Y', X”, Y", I have
formed the following values by taking the mean between those
which held for the same conditions :—
x, Xi. DUE ve
ee. Lode LO 88°20 25°64 92°52
Be). |» LO120 122°85 62°95 56°40
TOOw: so 3. 101°60 52:90 61°60 127°20
From these are obtained
(X’). (¥'). (X"), (Y").
fees... 136-00 86:96 26°91 91:08
jean 22° * © 300-20'°°*-191-07 63°45 55°81
100 . . . 10120 52°43 62°67 125°42
From the first and second of these horizontal series it
follows that,
Ny Sry My _ sry
ABE) _s17, SUB) _ _ suo,
from the first and third,
My _ s(x Ny _svyt
oO) 35-28, SAY) _ sae,
My _ S(xXt
Half the sum of the two values of SS ak 3 CL, I will designate
I
by B, half the difference of the two values of iy a;
we have then
B=35:72, T=34:56.
Using weights of 200 gr. there were obtained,—
x! XS De » ay
Celts) rk: Lol’5 93°1 20°1 97°5
euler is) a)... 65°8 157°2 LOO sS) 20
Paes 1.) 130s 87°7 25°5 a1°9
Ue Rs sf Wy OAC 16°7 95°4 161°0
1 Ss iiareaian (57/0) 89°2 25°7 93°6
ON ai pe OL 156°8 100°5 19°6
CL AR stpradte 81520 87°3 25°3 91°5
POU ss OT O 17°7 98°0 162:0
oa a 77. 88°2 25°8 92°5
44 M. G. Kirchhoff on the Relation of the Lateral Contraction
Hence in the mean,—
ite: de 5 OOS 89°10 24°48 93°40
oot Apt aetiebe oH apt 5 15700 100°40 19°80
See ee EO OO 17°20 96°70 161°50
From which follows,—
(X'). (Y’). (X"). (Y”).
Oa .8 eh) 13474 87°86 25°75 91°96
2O0t 5) S, 63°05 154°28 100°51 19°66
200. . « °65°52 17°10 97°76 158°47
And further,
B=71-42.0)) —69 On.
Caleulating the values of B and T for 100 gr., by dividing
the above values by 2, we find, in close approximation with the
numbers previously found directly,
B=35°71, T=34-50.
The bar was then turned 90 degrees about its axis, the cross-
rods were again fastened horizontally to it, and then experiments
made just in the same manner. There were obtained—
X’=138:2, Y'=100-2, X"=23'7, Y"=94-0,
Z! =2355°4 millims., Z"=2355°3 millims.,
A7—'=—26, r!'—d'=—20,
E'—q'=32, F!—a!=—32 :—
X!, WE bs bee
0 - erac sis 98°7 33°9 92°6
NGO” «. 2) *%. SSbe2 133°7 68°5 57°0
DO oy wz 4) eRe 98°7 33°6 92°6
“6 ear ha aa 84°6 62°9 68°7 127-0
Or 4. 1220 98°6 33°4 92°6
160+ a - Fe 133°7 66°5 57°0
OC "% . s2oe 98°7 32°0 92°6
1062). ee 63°1 69°3 127°2
Do. in 5 Reap 98°8 33°8 92°8
Hence in the mean,—
X!. D'Gp b GS ye
Oise, «thee Ob 98°70 33°34 92°64
100... . «84°20 133°70 67°50 .. 57a
TO0i, « - on. ntOe 99 63°00 69:00 ~=127:10
(X’). (Y’). (X"). (Y").
Gee 4! Seg 21°O5 97°35 34°49 91-27
1G Se" sa. Oa2e 131°68 67°95 56°45
1GO: eis 5 eBeST 62°44 70°07 123-11
B=385'82, T=34°48.
_
to the Lonyitudinal Expansion in Rods of Spring Steel. 45
xX’. nf xm ES
Meee se 5 1225 99°6 33°6 93°95
eee 49°) 170°0 103°9 22°3
ieee eS b2)-3 99°35 32°5 93°3
PRR a RP e841 2 27°7 97°5 161°9
OP 2 cetirssi 24-5 99°6 39°8 93°5
Paes, =. =~ DOD 169°6 104°7 21:9
eee ee D2 7 99:0 34:0 92°8
Ae. =. 48°6 27°6 105°0 161°8
ee. ; =£22°6 98°7 33°9 92°6
Hence in the mean,—
me | 122-72 99:28 33-96 93°14
2000 . . . 49°55 169°80 104-30 22:10
200 . . . 44:90 27°65. —«:101-25—S-—s«16 1°85
/ (X’). (Y') (X”). (Y").
pies oS 421-71 97°93 35:11 91°77
oom | Cw 48°75, 11) 1666R) 7s 2104-39 21:97
Bie . : «44-82 29750 102:23 158-90
B=7' 56>" f£=69'01 ;
and for P=100 gr.,
B=3o 76, “T3451.
In the following Table I give the values of B and T for
P=100 gr., as they have subsequently been found; at the same
time I will give the temperatures at which the experiments were
made :—
B. T.
o71 3450 + i one Postion; 21°7 C
30°82 34°48
35.78 34-5] ( im another position ; a2 OC,
Hence in the mean,
B=35°76, T=3451.
The units which form the basis of these statements are, however,
not the same, since, as mentioned above, the divisions of the &
axis and of the 7 axis in the scale used were distinctly different
from one another. Taking the mean values of the divisions of
the scale as given above, we get
B= 64°34 millims., T=62°41 millims.
But from equation (13) we get
| DE
{+——— = Bs
46 On the Contraction and Expansion in Rods of Spring Steel.
from which is obtained for the steel rod No. 1,
0
——$___. == YC ‘
rw
Two other steel rods of almost the same dimensions as the rod
No. 1, were submitted to the same experiments. I content
myself with adducing the following results :—
Steel rod No. 2.
B. Ty
oe eae in one position; 12°4 C.
an one in another position; 16°°8 C.
Mean.... B= 35:99, T=384-80,
= 64°76 millims., =62:94 millims.,
s=145-:01 millims.
0 - e
Steel rod No. 3.
eos aoa in one position; 22°6 C.
oriae la in another position; 22°-9 C,
Mean.... B= 36:37, T=35:10,
= 65°43 millims., =63°48 millims.,
s=145°16 millims.
7
1.90 =0°294.
Hence in the mean for the three steel rods, the relation of the
lateral contraction to the longitudinal expansion is
0:294.
It would be interesting to ascertain whether with rods of a
different section to that of those here investigated, the above rela-
tion would be as great. If that were the case, the assumption
here made would be thereby confirmed, that a hardened steel
rod may be considered homogeneous, and of the same elasticity
in different directions. Objections may be raised against this
assumption ; in fact it may be assumed that in the hardening, in
which heat flows from the axis towards the periphery, the elas-
ticity in the direction of the axis is different to what it is in direc-
tions rectangular thereto, and that the molecules in the external
The Rev. S. Haughton’s Notes on Mineralogy. 47
layers have a different arrangement to those nearer the axis. If
this is the case, it is probably also the case in different directions
according to the thickness of the rod, and accordingly the latter
relation will be different in thick from what it is in thin rods.
In conclusion I mention some experiments made with a hard-
drawn brass rod of almost the same dimensions as those of the
three steel rods. The experiments are of exactly the same kind
as those made with each of the steel rods, excepting that weights
of 50 gr. and 100 gr. were used instead of weights of 100 gr.
and 200 gr. The following values of B and T were found for
P=50 er. :—
B. T;
eo See in one position; 24°1 C.
Sige oer ‘in another position; 25°-0 C.
Mean.... B=385:75 T—37°12
64°33 millims., =67:13 millims.
Here s=144°65 millims. Hence using equation (14), we have
77907” 387.
This number has certainly not the same importance as that
which I have thought myself justified in assigning to the corre-
sponding numbers in the case of steel rods, for the elasticity of
a drawn brass rod is certainly different in the direction of the
axis to what it is in others.
Heidelberg, June 1859.
VI. Notes on Mineralogy. By the Rev. Samvurt Haveuton,
M.A., F.R.S., Fellow of Trinity-College, and Professor of Geo-
logy in the University of Dublin*.
No. IX. On the Shower of Aéroliths that fell at Killeter, Co.
Tyrone, on the 29th of April, 1844.
Q* the 29th of April, 1844, a shower of meteoric stones fell,
in the sight of several people, at Killeter, near Castlederg,
co. Tyrone: they broke into small fragments by the fall, one
piece only being found entire; it was (according to the testimony
of a resident) “about as large as a joint of a little finger.” The
stones were hot when found. The account given by three gen-
tlemen, who, however, did not actually see the shower fall, was
that they were at a distance of three or four miles, up the hills
in the neighbourhood ; it was a fine sunny afternoon (three or four
* Communicated by the Author,
48 The Rev. S. Haughton’s Notes on Mineralogy.
o’clock) ; they heard “ music” towards Killeter, which they sup-
posed to proceed from a strolling German band which they knew
to be in the neighbourhood ; they are under the impression that
they heard the music several times in the course of the evening ;
they remember also to have noticed clouds in the direction of
Killeter. On reaching Killeter the same evening, they were told
of the wonderful shower of stones which had spread over several
fields. I received the fragments of these stones from the Rey.
Dr. M‘Ivor, Ex-Fellow of Trinity College, Dublin, and Rector
of Ardstraw: he writes to me that “it is now very difficult to
get either a specimen of a stone, or any very distinct intelligence
of them: even the very rumour of them has nearly died out, and
you might ask intelligent middle-aged men about the neigh-
bourhood who had never heard them mentioned.” He adds
that the people of that locality are very “ uncurious,” and that,
if there were a veritable burning bush thereabouts, few would
“turn aside to see.”
The largest specimen given to me by Dr. M‘Ivor weighed
22°23 grs. in air, and 16°32 grs. in water, showing that its specific
gravity is 8°761. Both it and the smaller fragments presented
the usual black crust and internal greyish-white crystalline
structure and appearance, with specks of metallic lustre, occa-
sioned by the iron and nickel alloy that was present. I analysed
it in the usual manner, but, owing to an accident, I was unable to
determine the composition of the earthy portion soluble in mu-
riatic acid. .
The following is the mineralogical composition of these Aéro-
liths :—
. Hornblendic mineral (insoluble in acid). 84°18
Karthy mineral (soluble in acid) . . . 80°42
MIN ys <2 pal? syerde adh. ales Uederete eae Oe
Nickel . ee Pe re ey
» Nesquioxide: of Chromen..<') oi eytae wee
Cobalt . Meer ee ren Af eNGE
PO MAgTIELIC PYEIGES.. on acs es. sesh coe eee ies
100-00
The earthy portion, insoluble in muriatic acid, had the follow-
ing composition :—
NED OUR 09 29
Atoms.
PUT CAL hea ac ih se in ty hap ete OAL 1:22
NATE ss es al POG D 0:10
Protoxide of iron. . 12°18 0:34
° RTS op nope eam ree BE 0-12 +1:66
MaSN6sI2) certs ence A4g08 1:20
99°93
The Rev. 8. Haughton’s Notes on Mineralogy. 49
Omitting the alumina, the preceding analysis gives the rational
formula of the Hornblende family,
4RO, 3 Si03,
and, taken as a whole, it agrees with the analysis of many Horn-
blendes. The variety of Hornblende with which it has the
closest relation is Anthophyllite.
According to Mr. Greg’s ‘ Catalogue of Meteoric Stones and
Trons,’ three other falls of aéroliths are recorded as having oc-
curred in Ireland :—
1. a.pd. 1779, at Pettiswood, Westmeath; 6 oz.
2. August, 1810, Mooresfort, Co. Tipperary; 72 lbs. Spec.
grav. = 3°670. |
3. September 10, 1813, Adare, Co. Limerick; 17 lbs. + 65
Ibs. +24 ]bs.; moving H. to W. Spec. grav. =3°64.
4. April 29, 1844, Kalleter, Co. Tyrone; fragments of one
stone. Spec. grav. = 3°761.
Of the meteorite that fell at Mooresfort, co. Tipperary, in
1810, the only analysis on.record is one published by the late
Professor Higgins, in the forty-seventh volume of the ‘ Proceedings
of the Royal Dublin Society,’ in whose museum the greater part
of this stone, and a cast of the entire, are carefully preserved.
My friend Mr. Robert H. Scott has undertaken to analyse a
portion of it afresh.
Professor Higgins considered 35 per cent. of the stone to con-
sist of metallic particles separable by the magnet. This would
include the magnetic pyrites, iron, nickel, and chrome. In the
Tyrone meteorite examined by me, the iron, nickel, chrome
oxide, and magnetic pyrites amounted to 85°40 per cent., which
is very nearly the same proportion.
Dr. Apjohn has published a detailed account of his analysis of
the Adare meteorite in the eighteenth volume of the ‘Transactions
of the Royal Irish Academy,’ from which it appears that the fol-
lowing is the mineralogical composition of that meteorite :—
1. Meteoric iron and nickel . 23°07
a. Mapnetic pyrites > «. . - . 438
oe Onrome WO « «2c le 3 Oe
AP Matti Wain. 3 (eke 3 OOS
iy, Alkavies and loss 2"... SOT:
100-00
Its specific gravity varied from 3°621 to 4°230. The compo-
sition of 200 grs. of the matrix was found to be,—
Plul, Mag. 8. 4. Vol. 23. No. 151, Jan, 1862. EK
*
50 The Rey. 8. Haughton’s Notes on Mineralogy.
Atoms.
Sita Soe. eee 1:717
Riisatesia 90s sy eas ong f 2390
Protoxide of iron . . 15°62 ,, 0:434:
186'94.
This analysis would make the earthy matrix, taken asa whole,
have the composition of pyroxene,
3RO, 28i0°.
No. X. Additional Notice of Hislopite and Hunterite.
I published in the Philosophical Magazine of January 1859,
an account of two new minerals, found by the Rey. Messrs.
Hislop and Hunter near Nagpur, Central India. Being anxious
to obtain additional information respecting the geological mode
of occurrence of these minerals, I wrote to Mr. Hislop, who fur-
nished me with information respecting them, from which I extract
the following particulars. —
Hislopite.—This mineral was found in a small stream which
flowed down from a trap-hill at Takli. It was discovered by a
servant of Major Wapshaw, an officer of the Madrasarmy. Mr.
Hislop believes its position in situ to have been: in trap-rock,
“probably in the thin stratum of freshwater tertiary which is
imbedded in the volcanic rock, which has been dispersed in
strings by the effusion, and which, generally speaking, contains
a-pretty equal proportion of calcareous and siliceous ingredients.”
Mr. Hislop also forwarded to me a specimen of cale-spar,
clouded lke plasma with pale greenish streaks of a siliceous
mineral, sent to him by Dr. Carter from Bombay. Its chemical
examination gave me the following result :—
Carbonate of hme .. . 97°19
Green siliceous mineral. . 2°81
100-00
The quantity of colouring mineral was too small for examina-
tion, and its per-centage much less than that of the Glauconite .
which gives its rich green colour to Hislopite, in which mineral
17°36 per cent. of Glauconite was found by me.
Hunterite.-—This remarkable mineral was found in situ na
watercourse between Mr. Hislop’s house and the city of Nagpur ;
“it was broken off a pegmatitic dyke, which, like many others,
runs at right angles to the apparent strike of the gneiss which
it has penetrated.” Mr. Hislop regards this gneiss as metamor-
phic ‘Mahadewa Sandstone’ (of Oldham), which is probably of
the age of the lowest tertiary or highest secondary beds; it was
- The Rev. S, Haughton’s Notes on Mineralogy» ~— 51>
probably once completely covered by a considerable thickness of.
trap-rock, which still remains as an outlier in Sitdbaldi Hill,
about 300 yards from the watercourse in which the pegmatite
dyke penetrates the gneiss. The trap-rocks of this hill are hori-.
zontally bedded, and interstratified with a freshwater stratum
containing Physa and other shells. ;
It is certain, from the occurrence of such a mineral as Hun-
terite in the dyke penetrating the gneiss, that this dyke must be
regarded as a fissure filled by the action of water holding mineral
matter in solution under pressure and at a high temperature ;
and as the gneiss (10) itself contains Hunterite, it also must have.
been to some extent subjected to the same Neptuno-Plutonic
agency.
No. XI. On some Irish Dolomites of the Carboniferous age.
Beds of dolomite limestone are found in many places in Ireland
stratified conformably to the ordinary crystalline limestones of
the carboniferous age. These dolomites are developed particu-
larly in the lower and in the upper portions of the carboniferous.
limestone. The following analyses will give some idea of their.
composition.
No. 1. Dolomite, of a pale cream-colour, saccharoid ; forming
the uppermost bed of carboniferous limestone immediately under-
lymg the coal-measure white sandstone of Belmore Mountain,
co. Fermanagh. ‘wo specimens, four miles apart, analysed,
gave :—
Per-centage. Atoms.
ag (2) (6) (a) (2)
Carbonate of lime . . . 61:20 62°48 1°224 1-249
Carbonate of magnesia . 37°80 86°30 0900 0-864
Silica. . nu g'20 ~ O28
Peroxide of iron be 9 60 0-60
present as carbonate
Pofale. <=) 99°30. 99°66
No. 2. Dolomite, of a rosy cream-colour, saccharoid, flaky,
and crystalline ; forming the uppermost bed of the carboniferous
limestone immediately underlying the coal-measure shales of
Raheendoran, Clogrennan Hill, co. Carlow —.
Per-centage. Atoms.
Carbonate of lime . . . 54°15 1:083
Carbonate of magnesia. . 43°01 1-024
Piast i are ham nh ue Ok
100:00
- The occurrence of beds of dolomite, so pure as those just
52. Prof. Potter on the Fourth Law of the Relations of the
described, occupying precisely the same geological position, in
localities so far apart as the counties Carlow and Fermanagh,
suggests the possibility of a dolomite horizon, marking the
upper limit of the carboniferous limestone of Ireland.
In the lower parts of the carboniferous limestone of Ireland,
where the limestone abuts against the granite of the Leinster
chain, dolomites are locally abundant, which differ from the do-
lomites of the upper limestone in containing a much larger pro-
portion of argil.
I here give the analyses of two specimens from localities far
asunder. |
No. 3. Dolomite from Brown’s Hill Quarries near Carlow,
within a quarter of a mile of the junction of the limestone and
granite; much used as a building-stone, but known to make bad
lime. This dolomite is of a bluish-grey colour, is not crystalline,
and contains numerous geodes filled with yellow clay, lined with
crystals of Bitter-spar, and containing loose double-pyranudal
erystals of quartz, many of which include cavities partially filled
with fluid, enclosing small spherical bubbles, which are moveable
on changing the position of the crystal. Spec. grav. =2°781.
Per-centage. Atoms.
Carbonate of lime . . . 49°84 0:997
Carbonate of magnesia . . 89°36 0:937
Carbonate ofaren ~. . ... 5 0:99
ATA Sos He ee we wt ee TOIOO
, 98°79
No. 4. Dolomite from Booterstown, co. Dublin; within a few
yards of the granite which appears at the Black Rock station of
the Dublin and Kingstown Railway. Dark grey, not crystalline.
Per-centage. Atoms.
Carbonate of lime . . 47°21 0:944.
Carbonate of magnesia . 25°64 0:600 0-805
Carbonate of iron . . 11°89 0°:205 ”
bel oo wees ee + AOS
100°40
VII. On the Fourth Law of the Relutions of the Elastic Force,
Density, and Temperature in Gases ; as sequel to a Paper on
the same subject in the Philosophical Magazine for September
1853. By Professor Porrer, A.M.*
§ keg is no need to be surprised that our knowledge of the
relations of heat and dense matter has progressed slowly ;
for in examining these relations we are striving to learn the con-
* Communicated by the Author.
Elastic Force, Density, and Temperature in Gases. 53
nexion of the ponderable and imponderable elements of the uni-
verse. We are indeed striving to carry the domain of the induc-
tive experimental philosophy into the properties of the subtile
matters called, often, the imponderables, and searching for the
causes of the development of mechanical force in the actions,
reactions, affinities, incompatibilities, &c. of these subtile agents,
which are struggling to pass from the state of instability which
has been impressed upon them by an omnipotent power toa state
of stable equilibrium, through the properties which they possess,
The phenomena of the actions of these properties in their inde-
finitely varying states constitute the phenomena of nature; and
in investigating them we are striving to attain the highest degree
of knowledge within the reasoning powers which have been con-
ferred upon us. We must therefore be content with the progress
of knowledge which the inductive philosophy affords to us, and
leave wild dreams and speculations to the day-dreamers and spe-
culators, and receive as probable only such theories and hypo-
theses as have an experimental basis, and for the probability of
which good reasons can be advanced.
From the time of the discoveries of Dr. Black in heat, about a
century ago, the advance of our knowledge has been great,
although apparently slow, and often deviating from a straight
course. The properties now proposed to be discussed are amongst
those which require peculiar watchfulness of our instruments, as
changing properties are to be learnt, and evanescent results are
to be noted. °
It has long been known that, in popular language, high-pres-
sure steam blows cold. Now this means that a jet of steam from
a boiler in which it exists of high temperature and elastic force,
on being allowed to escape through an aperture into the air, soon
loses its high temperature and gives a feeling of cold to the hand
on which it strikes. The sensible heat of the steam has dimi-
nished, because its capacity for caloric has increased by its ex-
pansion in volume and diminution of elastic force. It is now
the question for consideration whether the change of capacity for
caloric is instantaneous on the sudden escape of the steam from
a high to a low pressure. We see that the change is not instan-
taneous, but is developed in time; for on bringing the-hand or
a thermometer nearer to the aperture from which the steam
issues, the sensible heat increases, and the capacity in the jet of
course diminishes, so that we must conclude that the change of
the capacity for caloric is devetoped only in some time after the
steam is relieved from the pressure balancing its elastic foree in
the boiler. To determine this time is a very important point in
the theory of the mechanical force of steam, and its applications
in the steam-engine. The corresponding properties of air are
54 Prof. Potter on the Fourth Law of the Relations of the
also in this respect important practically ; for considerable ex-
penses have been incurred, and may again be incurred, from
misapprehensions of these properties.
That the properties of gases are analogous to those of steam,
as related above, there can be no doubt; that is, on expanding
from a state of more to a state of less condensation, the sensible
heat is diminished, or, as Dr. Black would say, has become latent
heat. The important points to be determined are the amount
and the laws of the changes of temperature in respect to sudden
changes of density and elastic force, as well as the interval of
time in which such changes are completed, since they are evi-
dently not instantaneous.
We are not without popular results which we may treat as
preliminary experiments. Some years ago two young gentlemen,
brothers, possessing talents, ingenuity, and perseverance, the one
a scientific chemist, and the other a civil engineer, undertook,
after a mild winter, the experiment of trying to make ice on the
large scale artificially and economically, by passing air from a
high state of condensation in a strong and large receiver to the
atmospheric pressure, through water. ‘To their disappointment,
and mistrust of the theory, they found the water cooled only a
few degrees of temperature when they expected the formation
of ice. On the contrary, we have lately heard that in the rail-
way tunnel which the Sardinian government is carrying through
the Alps, by using condensed air-engines to work the bormg
machinery, that a degree of cold is produced which causes water
to freeze, by the expansion of the air after escape from the
engine,—the moderate condensation being performed at the en-
trance of the tunnel, and the condensed air carried in pipes to
the air-engine at the workings. We may ask how are these
results to be reconciled. Is it not a case analogous to the high-
pressure steam-jet, where the change of temperature occupies a
short but sensible interval of time? This seems to me the solu-
tion of the question. :
To discuss experiments made with scientific views: we find
that when MM. Gay-Lussac and Welter were trying experiments,
at the suggestion of M. Laplace, on the sensible heat lost in
the sudden rarefaction of air, they found it so great that the
ratio of the specific heat under a constant pressure was to that
under a constant volume as 1°3748 to 1; but when the air was
allowed to escape from its state of condensation to atmospheric
pressure through an aperture, there was no change of tempera-
ture due to the expansion*. ‘This latter experiment was evidently
a hasty one; for the scientific gentlemen attempting to form ice,
® Herschel ‘On Heat,’ art. 121.
Elastic Force, Density, and Temperature in Gases. 55
Mr. Joule*, Professor W. Thomson, and myself} have all found
a certain but small change of temperature; and I have also, in
the paper to which the present is a sequel, investigated the law
of the chauge, which, I believe, 1 is the true law for the instanta-
neous result.
This law is as follows :—
Let v be the volume of a gas when the pressure is p and the
density p,
v' be the volume of a gas when the pressure is p! and the
density p!
after an expansion; and since the mass is the same, we have
x aes pl,
Also let 6 be the rarefaction or negative condensation; and
since the change of temperature is small, we have by Boyle’s law,
p=Kp, p'=xp';
then
!
pa reas ag egal
and it was found by the experiments that if w, was the number
of Fahrenheit’s degrees through which the temperature fell for
an expansion unity or for 6=1, and the degrees it fell for an
expansion 6, then
= ()
Gh NEL
or
and the experiments gave the value of the constant,
@, =0°2077.
From this formula the ratio of the specific heats was deduced
to be
specific heat of air under a constant pressure
specific heat of air with a constant volume ng:
¢
52
2359(1 +00)’
where a= Be and @= degrees of Fahrenheit’s scale above the
freezing temperature.
In the paper to which the present is a sequel, I stated that I
* Phil. Trans. for 1853, and Phil, Mag. for September 1853, p. 230,
- > Phil, Mag. for September 1853, p. 161.
56 Prof. Potter on the Fourth Law of the Relations of the
had other experiments in view on the same subject, and soon
after I procured one of M. Breguet’s exceedingly sensitive me-
tallic helix thermometers, by means of which I hoped to ascer-
tain directly the temperature of an expanding jet of air entering
the exhausted receiver of an air-pump, but was disappointed in
obtaining anything more than confirmatory results, and should
not by means of it have ascertained the law. ‘This arose from
the unsteadiness and vibrations of the helix and index-needle
when a jet passed through them, even when an addition had
been made to the instrument to steady the index-needle at the
expense of a small loss of sensibility. This addition consisted of
a small brass vertical pillar screwed into the pedestal under the
centre of the helix, with a small cylindrical hole down a part of
its axis, which was directly over a small polished agate cup on a
part of the pillar which had been filed away so that it was directly
under the cylindrical hole. The vertical needle of the helix
which carries the horizontal index-needle being raised and passed
down the fine cylindrical hole, its sharp point rested on the agate
cup. A very small loss of sensitiveness was found, but great
additional steadiness, from this arrangement. The helix in the
experiments was surrounded with a cylinder of gilt paper rather
larger than itself, which was attached air-tight to the part of the
instrument where the upper end of the helix is screwed fast.
This part turns round in a step to adjust the index-needle to any
point in the horizontal circle of degrees, and has a hole down its
axis. This hole was used in the experiments to pass a jet of air
through. A long fine brass tube, small enough to go into the
hole just named, passed through a stuffing-box in a brass plate
covering the opening in the top of a large glass receiver of an
air-pump within which Breguet’s thermometer was placed. The
fine brass tube had its lower end prepared with an aperture
which could be opened and shut by a plug at the end of a brass
wire passing down it, which was somewhat longer than the tube.
The tube being smaller than the hole in the moveable part of the
thermometer, was packed tight in it at its lower end with lint.
A light cup of paper was, after some experiments, also placed to
rest on the index-needle, to turn with it and envelope the lower
end of the vertical cylinder of gilt paper without touching it.
This was intended to retain the expanded air of the jet around
the helix. When the receiver of the air-pump was partially ex-
hausted, and the plug raised by means of the long wire passing
down the brass tube, the external air rushed into the receiver
through the cylinder of gilt paper, and communicated its tempe-
rature to the helix; the temperature was thus shown by the
degree on the scale to which the index-needle pointed. It will
be easily conceived that the helix, of which the thickness (con-
Elastic Force, Density, and Temperature in Gases. 57
taining silver, gold, and platinum) is less than ;2.,th of an inch*,
was considerably agitated by the jet, and the index-needle set
into vibration, so that tenths of degrees could not be read off
with quickness and certainty.
In January 1854 I used a method of experiment similar to
that with Marcet’s boiler, described in the paper of 1853, namely,
the exterior thermometer having been compared with Breguet’s
within the reciver, this latter fell on the pump being worked ;
and when it had risen gradually to some particular degree, the
jet was allowed to pass for about one second, and the effect upon
the -index-needle noted. When the barometer-gauge of the air-
pump stood about half the height of the barometer, we had
bea.
§=/ i =1 nearly; and if Breguet’s thermometer stood 4°,
3°, 24°, 14° or 1° degree below the exterior thermometer,
it rose Instantly on the jet passing through the helix; but when
the difference was only ;4,° it fell. These are in accordance
with the former results, which gave 1° as the temperature of
such a jet; but the actual readings of the index, contrary to
what I had hoped for, were irregular and uncertain.
Experiments were then tried of rarefactions about five and
three; or if the barometer stood at 30 inches, the jet was passed
through the helix when the barometer-gauge stood at about 25
al
inches and about 23 inches, for then 6=! mi became
!
_ 80-5 30—7
= aaah, and $=—,— =37.
The first motion of the needle was always in the direction due
to cold; but the very great agitation of the helix and index-needle
from the violence of the jet, prevented a reading being obtained
before the temperature approached that of the external air.
Accordingly this method of experiment only confirmed the
results of the paper of 1858, without adding anything to them.
. The next method of experiment which I adopted was with a
Newman’s air-pump, and the Breguet’s thermometer placed
under a glass receiver upon the plate. Newman’s air-pump
having a single barrel of large dimensions, a considerable ex-
haustion of a moderate-sized receiver is obtained by the first
stroke of the piston; and this can be easily performed, and the
communication cut off by the stopcock in one second of time.
The object was to find the effect of such rapid exhaustion on the
thermometer, and then by using receivers of different sizes
giving different degrees of exhaustion for the same single stroke
of the pump, to find the law for the corresponding changes of
s . . * 3th of a millimetre,
58 Prof. Potter on the Fourth Law of the Relations of the
temperature. A considerable degree of cold was produced by
even a small amount of expansion; but the time required was
eight or nine seconds before the thermometer reached its mini-
mum. ‘This slowness in a great measure no doubt arises from
the quiescence of the remaining air in the receiver, which only
then acts slowly by radiation and convection on the helix of the
thermometer. This slowness renders the results of little value,
beyond showing that a considerable degree of cold is produced
by a moderate rarefaction after a short interval of time.
Many experiments gave nearly the same results; and averages
of five successive good experiments were as follows:—The tem-
perature in the receiver in degrees of Breguet’s thermometer
54°42: after one stroke of the piston of the pump, in eight
seconds the index arrived at the minimum 47°82; after eight
seconds more it stood at 49°46; in eight more at 51°04; in
eight more at 52°33; in eight more at 53°16; in eight more
at 53°72; in eight more at 54°:02; after some time more at
54°32. The differences in the successive intervals of eight
seconds after the completion of the exhaustion were thus 6°60,
1°64, 1°58, 1°29, 0°:83, 0°56, 0°30, 0°30. If we suppose
the heat lost in the first interval of eight seconds equal to that
in the second, we have 6°°60 + 1°°64=8%24 for the maximum of
cold on Breguet’s scale with the circle divided into 360 parts.
The barometer- -gauge rose 1°9 to 2 inches, and therefore the
expansion 6 was as follows:
a al a OU 207 2
f= 38 =, th.
Hence 1 depaee of cold on the scale was produced by a sae
1 1
tion ii. sa 1178? which, supposing with M. Prony that
these degrees are each j7,ths of a degree Centigrade when the
7 1 a 7
circle is divided into 100 parts, gives 10 * 360 = 36 of a degree
Centigrade as the value of each degree of the thermometer used.
While Poisson supposed 1 degree Centigrade of cold to be pro-
duced by a rarefaction “= we have only found by this method
one-fifth of that quantity. !
Experiments were also undertaken with dry air. The receiver
being exhausted, it was allowed to refill slowly with air passing
through a V-tube of glass containing pumice-stone moistened
with strong sulphuric acid. The results were not greatly dif-
ferent from those obtained with the ordinary air of the room,
which was the experimental lecture-room of University College,
and was heated by a stove. With the dry air the temperature
Elastic Force, Density, and Temperature in Gases.- 59
was 57°°6 in the receiver, the barometer 29°95 inches; after one
stroke of the piston completed in one second, in nine seconds
the thermometer attained its minimum, on the average of six
good consecutive experiments, of 6°73 below the original tempe-
rature, and in the succeeding eight seconds rose, on the average,
1°25. The rarefaction was sensibly the same, ,th, as with
common air.
The two methods above detailed for finding the temperature
directly being objectionable, I laid aside Breguet’s thermometer,
and have only resumed its use lately from having found a
method in which it reaches its maximum of temperature for
eondensations in one second, as will be found further on in the
paper.
On the want of success by the direct methods, in the beginning
of 1854 I recurred to the imdirect method of observing the
barometer-gauge of the Newman’s air-pump in the case of
sudden rarefactions, which is in principle the same as the
method of MM. Desormes and Clement, and of MM. Gay-
Lussac and Welter, also of Mr. Meikle, and as adopted by M.
Poisson in his Traité de Mécanique, vol. 1. p. 643; that is, by
finding the temperatures through the pressures, and considermg
them connected by the law of Amontons. In this manner the
objection to using a light fluid having a long space to move
through as a barometer-gauge was avoided, so that the effect
of the momentum acquired in moving through a long space, but
opposed by the capillary attraction of watery fluids for glass, was
not incurred; and by noting the extremes of the first two oscil-
lations of the mercury in the gauge, the mean might be taken
as the correct result; but still the attraction of aggregation of
the mercury and its adhesion to the glass are defects, preventing
the mercury ascending so high as it might have done.
Assuming the accuracy of Amontons’s law, let p, p, ¢° be the
pressure, density, and degrees of temperature above the freezing-
point of water, « and « known constants, then
p=Kp(l+ai°) ;
similarly, for another state of the same gas we have
p'=xp'(1+at'°)
and
p_pi(l+ae) |
p p(itai?)’
and in the experiments p and p’ are so nearly equal, that we may
/
take 2 =1, since the volume of gas changes only by the small
space of the barometer-gauge through which the mercury moves,
60 Prof. Potter on the Fourth Law of the Relations of the
Taking «= = as given by M. Rudberg’s experiments, for
Fahrenheit’s degrees of temperature, we have
(Oe oe eee
: ee ed eee Se
an
pe Le 0 2
% id
Applying this formula to an experiment made on the 25th of
January, 1854, when the barometer stood at 30°30 inches and the
thermometer at 58°°5, we have as follows :—By a stroke of the
piston performed in one second with a large receiver and New-
man’s air-pump, the mercury in the barometer-gauge rose, on the
average of seven experiments which differed only slightly, to
2°64 inches, and falling gradually during some minutes rested at
2°01 inches; then
f° =58°5 —32° =26°'5
p =30°30—2:01=28:29 inches of mercury
p! =30:°30—2°64=27°66 _,, »
and
26:5 27°66
Tae eS SS - Qo oa
io—?¢ =494(1+ 27) (1 98-29
63
a AG) 5b PERS oy
=520°5 x 53-99
—11°59,
Now Poisson’s assumption was that the temperature 116° 6
Centigrade, or 209° 6 nearly Fahrenheit, would be lost by an
expansion 6; and in the above experiments we should have
PR aR Une Bic oae
| 209° x 38-99 = 14°85,
which differs a little from the experiment, in which we have
reason to expect a loss of heat.
In other experiments with the same receiver, the air dried by
passing through a V-tube with pumice moistened with sulphuric
acid, the results gave
t°— f/° = 13° 5,
and Poisson’s formula 14°°8; which are closer than the former.
When smaller receivers were used and more rarefaction pro-
duced by the single stroke of the piston, the results did not so
well accord. In one set of experiments
£9 — t!° = 29""4
was found, whilst the formula gave 54°°3.
Elastic Force, Density, and Temperature in Gases. 61
With the smallest receiver, the result
19 —7{!° = 4.32 ;sx
and by Poisson’s formula the result is 53°7.
In another experiment with the smallest receiver the result
was
t°—7!°=50°5,
for which case Poisson’s formula gave 92°4.
Although the results at the smaller rarefactions were not very
different from Poisson’s rule, yet those at greater rarefactions
did not appear to accord with it. In this state of the experi-
ments I laid the results aside until lately, when I wished again
to try if any better method of using Breguet’s thermometer could
be found, and more decisive results obtained.
On placing Breguet’s thermometer in the large receiver of
the air-pump, its canacity being about 650 cubic inches, with an
opening of 24 incaes diameter at the top, to be closed by a cir-
cular plate of glass smeared with grease, I found that, having
exhausted the receiver to a given degree, then when the plate of
glass was slid away suddenly (say, in one tenth of a second) the
agitation of the air in the receiver caused the thermometer to
arrive at its maximum in one second of time, and therefore pro-
bably indicated the true result very nearly. It was thus desi-
rable to make the experiments with all possible accuracy, and
carefully allow for the capillary depression of the mercury in a
new barometer-gauge Experiments were also made by using a
separating diaphragm of tissue paper in a bag-form at the upper
part of the receiver, and held up by an elastic ring of wire press-
ing it tothe glass. The diaphragm yielded to the re-entering air,
but kept it separate from the larger part of the rest. With the
small condensations the thermometer resumed its sluggishness,
arriving at its maximum only in four or five seconds; but as
the condensation increased, it acted more rapidly, and at the
greatest condensation arrived at its maximum nearly as quickly
as without the diaphragm, and with nearly the same indication
of heat. I consequently conclude that the phenomenon of
quickness was not due to the re-entering air, otherwise than as
producing agitation and a rapid effect upon the helix of the
thermometer. Other experiments were tried with the bell-glass
of the thermometer left over the helix, but raised on pieces of
card, and others, again, with the bell-glass raised out of its
groove and moved sideways, leaving considerable space for the
air to pass. These gave the maxima results smaller than when
the helix was uncovered, but they occurred in one second of
time.
62 On the Relations of the Elastic Force, Density, and Temperature.
A preliminary set of experiments, taken on the 26th of Sep-
tember 1861, the barometer 29°61 inches, with the air-pump
and large receiver, and. a new barometer-gauge before it was
measured to allow for the capillary depression, gave results, con-
verted to Fahrenheit’s degrees, as follows :—
Height of mercury in the gauge} j theair reventering eee 4-0
75
gave, the level: . vcisc ie wiv oe temperature TIS€S eoveesee
33 33 33 3) a
33 33 3 33 ' 33 12:0
3 33 4 33 3? 15°1
These are nearly i in arithmetic progression for condensations
in arithmetic progression, according to Poisson’s law. On the
27th of September, with the capillary depression of the gauge
carefully allowed for, the following were obtained, the barometer
standing at 29°88 inches, and the thermometer at 60° :—
Height of mercury Increase of tempe-| Approximate
in the gauge. Number of trials, { Tture in Fahren- | ¢ondensations,
heit’s degrees.
inches, 2
7 22:2 4th
5 3 18-2 Zth
4 3 13:9 seth
3 3 11-4 5th
2 3 7A th
1 3 37 sth
The experiments differed only slightly amongst themselves, and,
with the exception of those where the height of the gauge was
4 inches, they form a very certain arithmetic progression in
accordance with M. Poisson’s rule; but the absolute increase of
temperature is very little more than half what his expression
209° 6 requires; for 6= f SP = 5 30 gives 6°96 Fahrenheit,
whilst the observed increase of temperature was only 3°7,
occurring in one second of time after the condensation had
taken place.
The law of the increase of temperature being as the conderiahs
tion, is the important poimt shown in these experiments, and
which the other methods did not show; whilst the time in which
it occurred may have been much less than one second, as exhi-
bited by the thermometer.
Hin 68)
VIII. On the Solar Spectrum, and the Spectra of the Chemical
re Elements. By Professor H. E. Roscoz.
— To the Editors of the Philosophical Magazine and Journal.
=e Owens College, Manchester,
GENTLEMEN, December 21, 1861.
ae following extract from Professor Kirchhoff’s interesting
memoir “ On the Solar Spectrum, and the Spectra of the
Chemical Elements,” just published, with magnificent maps of
the lines, in the ‘ Transactions of the Berlin Academy,’ and about
to appear in English, may interest your readers as helping to
explain the appearance of the blue band in the spectrum of in-
tensely ignited lithium vapour, first noticed by Dr. Tyndall, and.
referred to in your Number of last month by Dr. Frankland.
“The position of the bright lines (or, to speak more precisely,
the maxima of light in the spectrum of an incandescent vapour)
is independent of the temperature, of the presence of other sub-
stances, and of all other conditions except the chemical compo-
sition of the vapour. The truth of this assertion has been
well tested by experiments made by Bunsen and myself with
special regard to this point, and it has been confirmed by
many observations which I have had occasion to make with
the extremely sensitive instrument above described*. Never-
theless the spectrum of the same vapour may, under different
circumstances, appear to be very different. Even the alteration
of the mass of the incandescent vapour is sufficient to give another
character to its spectrum. If the thickness of the column of
vapour whose light is being examined be increased, the luminous
intensities of all the lines increase, but in different ratios. In
accordance with a theorem which will be considered in the next sec-
tion, the intensity of the bright limes increases more slowly than»
that of the less visible lines. The impression which a line produces
on the eye depends upon its breadth as well as upon its brightness,
Hence it may happen that one line, being less bright although
broader than a second, is less visible than the latter when
the thickness of incandescent gas is small, but becomes more
distinctly seen than the latter when the thickness of the vapour
is increased. Indeed if the luminosity of the whole spectrum be
so lowered that the most striking of the lines only are seen, it
may happen that the spectrum appears to be totally changed
when the mass of the vapour is altered. Change of temperature .
seems to produce an effect similar to this alteration in the mass
ofjthe incandescent vapour. If the temperature be raised, no
deviation of the maxima of light is observed; but the intensities
of the lines increase so differently, that those which are most
plainly seen at a high temperature are not the most visible at a
* With the magnificent instrument here referred to, Kirchhoff was able
to-separate the two “ D” lines by a width of 4 millimetres.—H, E. R.
64 Prof. Roscoe on the Spectra of the Chemical Elements.
low temperature. This influence on the mass of the temperature
of the incandescent gas explains perfectly why, in the spectra of
many metals, those lines which are the most prominent when the
metal is placed in the colourless gas-flame, are not the most di-
stinct when the spectrum of the induction-spark from the metal
is examined. This is most clearly seen in the case of the calcium
spectrum. I have found that if a wet string or a narrow tube
filled with water be placed in the circuit of the Leyden jar which
gives the spark, and if the electrodes be moistened with a solu-
tion of chloride of calcium, a spectrum is obtained which coin-
cides exactly with that seen when a chloride-of-calcium bead is
placed in the colourless gas-flame. Those limes appear absent
which are the most distinct when an entire metallic ‘circuit is
employed. If the narrow column of water be replaced by a
column of larger sectional area and of shorter length, a spectrum
is produced in which both those lines which are seen in the flame
and those obtained by the intense spark are equally plainly
visible. In this experiment we see the mode in which the cal-
cium spectrum, as given in the flame, may be converted into that
produced by the bright electric spark.”
I may likewise add that, in lately examining the spectrum
of lithium obtained by the induction-spark from a Ruhmkorff’s
coil with one of Steimheil’s prisms, Professor Clifton and I ob-
served the appearance of two blue lines, one of which (probably
the line noticed by Dr. Tyndall) we found to be coincident with
the common blue strontium line 6, whilst the other coincided
with a seeond blue strontium line, which became first apparent
in the spark-spectrum of this metal. Whether the lines thus
produced in the spectra of lithium and strontium will prove to be
coincident when examined with a larger number of prisms and
with a higher magnifying power we are unable at present finally
to decide; but by employing three of Steimheil’s prisms, each
having a refracting angle of 60°, there appeared to us a slight
difference in refrangibility between the first blue lithium line and
the line Sr 6,—this difference, however, not being so large as that
between the two sodium lines. We hope to be able before long to
give a definite answer to this important and interesting question.
The explanation of the coincidence by possible presence of strontia
in the lithia, is disposed of by the fact that when the blue lines
are most intense no trace of the orange or red strontium lines a,
8, and y can be observed. The lithium-salt which I used was the
sulphate, being a portion of some pure salt sent me by Professor
Bunsen ; the strontium-salts employed were the chloride and ni-
trate, and with both of these.the same coincidence was observed.
I remain, Gentlemen,
Yours truly,
Henry E. Roscog. °
IX. On the inapplicability of the new term “ Dyas” to the “ Per-
mian”’ Group of Rocks, as proposed by Dr. Geinitz. By Sir
Roperick Impry Murcuison, F.R.S., D.C.L., LL.D. &c.,
Director-General of the Geological Survey of Britain*.
; ae the year 1859 M. Marcou proposed to substitute the word “Dyas”
for ‘‘ Permian,’ and summed up his views by saying that he re-
garded “the New Red Sandstone, comprising the Dyas and Trias,
as a great geologic period, equal in time and space to the Paleozoic
epoch of the Graywacke (Silurian and Devonian), the Carboniferous
(Mountain-limestone and Coal), the Mesozoic (Jurassic and Creta-
ceous), the Tertiary (Eocene, Miocene, and Pliocene), and the recent.
deposits (Quaternary and later)” !! 7.
As that author, who had not been in Russia, criticized the labours
and inductions of my associates de Verneuil and von Keyserling, and
myself, in having proposed the word ‘«‘ Permian ” for tracts in which
he surmised that we had commingled with our Permian deposits
much red rock of the age of the Trias, I briefly defended the views
I had further sustained by personal examination of the rocks of
Permian age in various other countries of Europe.
It was, indeed, evident that M. Marcou’s proposed union of the so-
called Dyas and Trias in one natural group could not for a moment
be maintained, since there is no conclusion on which geologists and
paleontologists are more agreed, than that the series composed of
Roth-legende, Kupfer-Schiefer, Zechstein, &c., forms the uppermost
Paleozoic group, and is entirely distinct in all its fossils, animal and
vegetable, from the overlying Trias, which forms the true base of
the Mesozoic or Secondary rocks.
Owing to such a manifest confusion respecting the true paleonto-
logical value of the proposed ‘‘ Dyas,” we should probably never have
heard more of the word, had not my distinguished friend, Dr. Geinitz
of Dresden, recently issued the first volume of his valuable pale-
ontological work, entitled ‘ Dyas, oder die Zechstein-Formation und
das Rothliegende’§. In borrowing the term “ Dyas” from Marcou,
Dr. Geinitz shows, however, that that author had been entirely
mistaken in grouping the deposits so named with the Trias or the
Lower Secondary rocks, and necessarily agrees with me in con-
sidering the group to be of Paleozoic age.
As there is no one of my younger cotemporaries for whom I have
a greater respect as a man of science, or more regard as a friend,
than Dr, Geinitz, it is painful, in vindicating the propriety and use-
fulness of the word “ Permian,” to be under the necessity of point-
ing out the misuse and inapplicability of the word ‘‘ Dyas.”
* Communicated by the Author.
t See “‘ Dyas et Trias de Marcou,’”’ Bibliothéque Universelle de Genéve, 1859.
t See ‘ American Journal of Science and Arts,’ 2nd ser. vol. xxviii. p. 256,—
the work of M. Marcou having attracted more attention in America than in
England.
§ Leipzig, 1861.
Phil, Mag. 8. 4, Vol. 23, No, 151, Jan, 1862. F
66 Sir R. I. Murchison on the inapplicabity of the new
The term “ Permian” was proposed twenty years ago for the
adoption of geologists, without any reference whatever to the litho-
logical or mineral divisions of the group; for I well knew that a
certain order of mineral succession of this group prevailed in one
tract, which could not be followed out in another. After surveys,
during the summers of 1840 and 1841, of extensive regions in
Russia in Eur ope, in which fossil shells of the age of the Zechstein of
Germany, and the Magnesian Limestone of England, were found to
occur in several courses of limestone, interpolated i in one great serves
of red sandstones, marls, pebble- beds, copper-ores, gypsum, &c., and
seeing that these varied strata occupied an infinitely larger super-
ficial area than their equivalents in Germany and other parts of
Europe, I suggested to my associates, when we were at Moscow in
October 1851, that we should employ the term “‘ Permian” as de-
rived from the vast Government of that name, over which and several
adjacent Governments we had traced these deposits.
In a letter addressed to the late venerable Dr. Fischer von Wald-
heim, then the leading naturalist of Moscow, I therefore proposed
the term “ Permian” *, to represent by one unambiguous geogra-
phical term a varied mineral group, which neither in Germany nor
elsewhere had then received one collective namey adopted by geolo-
gists, albeit it was characterized by one typical group only of animal
and vegetable remains. As the subdivisions of this group in Ger-
many consisted, in ascending order, of Roth-legende, with the sub-
ordinate strata of Weiss-liegende, Kupfer-Schiefer, and Lower and
Upper Zechstein, and in England of Lower Red Sandstone and Mag-
nesian Limestone, with other accompanying sands, marls, &c., so well
described by Sedgwick +t, the name of “‘ Permian”—purposely de-
signed to comprehend these various str ras readily adopted, and
has since been generally used. Even Geinitz himself, as well as his
associate, Gutbier, published a work under the name of the ‘ Per-
mische System in Sachsen’§, Naumann has also used the term in
reference to the group in other parts of Saxony; whilst Goppert has
clearly shown that the rich Permian Flora is peculiar and charac-
teristic of this supra-carboniferous deposit. In England, France, and
* See Leonhard’s ‘ Jahrbuch’ of 1842, p.92; and the Philosophical Magazine,
vol. xix."p.418, “Sketch of some of the Principal Results of a Geological Survey
of Russia.”
ft It is true that the term Pénéen was formérly proposed by my eminent
friend, M. d’Omalius d’Halloy; but as that name, meaning sterile, was taken
from an insulated mass of conglomerate near Malmédy in Belgium, in which
nothing organic was ever discovered, it was manifest that it could not be con-
tinued in use as applied to a group which was rich in animal and vegetable
productions.
{ Trans. Geol. Soc. London, New Series, vol. iii. p. 37. .
§ I may here note that the great Damuda for dation of Bengal, with its fossil
flora and animal remains, including Saurians and Labyrinthodonts, described by
Professor Huxley, has recently been referred (at least provisionally) to the Per-
mian age, by Dr. Oldham, the Superintendent of the Geological Survey of India.
In fact, Dr. Oldham actually cites the plant Teniopteris, of the “ Permian beds
of Geinitz and Gutbier in Saxon, y,’ in justification of his opinion. See ‘ Me-
moirs of the Geological Survey of India,’ vol. ili. p, 204.
ee
¥
term “‘ Dyas” to the “ Permian” Group of Rocks. 67
America no other term in reference to this group has been used for
the last fifteen years.
The chief reason assigned by Geinitz for the substitution of the
word “ Dyas” is, that in parts of Germany the group is divided into
two essential parts only—the Roth-liegende below, and the Zechstein
above, the latter being separated abruptly from all overlying de-
posits.
Now, not doubting that this arrangement suits certain localities,
I affirm that it is entirely inapplicable to many other tracts. For,
in other regions besides Russia, the series of sands, pebbles, marls,
gypseous, cupriferous, and calcareous deposits form but one great
series. In short, the Permian deposits are for ever varying. Thus
im one district they constitute a Monas only, in others a Dyas, in a
third a Trias, and in a fourth a Tetras *.
In this way many of the natural sections of the North of Germany
differ essentially from those of Saxony ; whilst those of Silesia differ
still more from each other in their mineral subdivisions, as ex-
plained in ‘Siluria,’ 2nd edition, particularly at p.342, Near the
northern extremity of the Thiiringerwald, for example, and espe-
cially in the enyirons of Kisenach, an enormous thickness of the
Roth-legende, in itself exhibiting at least two great and distinet
parts, is surmounted by the Zechstein, thus being even so far tripar-
tite, whilst the Zechstein is seen to pass upwards to the east of the
town, by nodular limestones, into greenish and red sandy marl and
shale, the «‘ Lower Bunter Schiefer”’ of the German geologists. The
same ascending order is seen around the copper-mining tract near
Reichelsdorf, as well as in numerous sections on the banks of the
Fulda, between Rotheburg and Altmorschen, where the Zechstein
crops out as a calcareous band in the middle of escarpments of red,
white, and green sandstone ¢,.
But in showing that in many parts of Germany, as well as in
England, the Zechstein has a natural, conformable, and unbroken
cover of red rock, I never proposed to abstract from the Trias any
portion of the Bunter Sandstein or true base of the group, as re-
lated to the Muschelkalk by natural connexion or by fossils, I
simply classed as Permian a peculiar thin red band (Bunter Schiefer),
into which I have in many localities traced an upward passage from
the Zechstein, and in which no triassic shell or plant has ever been
detected,
On my own part, I long ago expressed my dislike to the term
Trias; for, in common with many practical geologists who had sur-
veyed yarious countries where that group abounds, I knew that in
* See ‘ Siluria,’ 2nd edit., 1859, and ‘ Russia in Europe and the Ural Moun-
tains,’ 1845,
+ On two occasions (1853-4) Professor Morris accompanied me, and traced
with me these relations of the strata; subsequently, when Mr. Rupert Jones
(1857) was my companion, we saw other sections clearly exhibiting this upward
transition which I have described. Since then, Professor Ramsay, when at Hise-
nach, convinced himself of the accuracy of the fact that the Zechstein passes
up conformably into an overlying red cover. My note-books contain many
additional evidences, which I haye not thought it necessary to repeat,
68 Sir R. I. Murchison on the inapplicability of the new
numerous tracts the deposits of this age are frequently not divisible
into three parts. In Central Germany, where the Muschelkalk forms
the central band of the group, with its subjacent Bunter Sandstein
and the overlying Keuper, the name was indeed well used by Al-
berti, who first proposed it; but when the same group is followed
to the west, the lower of the three divisions, even in Germany, is
seen to expand into two bands, which are laid down as separate
deposits on geological maps of Ludwig and other authors. In these
countries, therefore, the Trias of Alberti’s tract has already become
a Tetras. In Britain it parts entirely with its central or calcareous
band, the Muschelkalk, and is no longer a Trias; but, consisting
simply of Bunter Sandstein below, and Keuper above, it is therefore
a Dyas; though here again the Geological Surveyors have divided
the group into four and even into five parts, as the group is laid
down upon the map—No. 62, ‘Geographical Survey of Great Britain.’
The order of succession in the Permian group all along the western
side of the Pennine chain or geographical axis of England proves
the impossibility of applying to it the word “‘ Dyas ;” for over wide
areas in Shropshire and Staffordshire it is one great red arenaceous
series, with a few subordinate courses of calcareous conglomerate.
Following it to the north, Mr. Binney has demonstrated that the
fossils of the Zechstein show themselves in the heart of red marls
which occupy on the whole a superior part of such a red series; and
in tracing these rocks northwards he has demonstrated that there
are, besides, two great underlying masses, first of conglomerates and
breccias, and next of soft red sandstones, the latter attaining, as he
believes, a thickness of not less than 2000 feet. Here then the Per-
mian may be considered a Trias. Prof. Harkness, in a memoir he
is preparing, estimates the thickness of these Lower Sandstones and
Conglomerates to the N.E. of West Ormside, in Cumberland, at 4000
to 5000 feet, and shows that they are surmounted by marl-slates
bearing plants, thin-bedded red sandstone, grey shale, and sandstone
and limestone, the latter—the representative of the Magnesian
Limestone—being covered by red argillaceous shale*. Now in all
these cases the Permian is a series divisible into three or more
parts. But when we follow the same group into Scotland, it there
parts with its calcareous feature, and, becoming one red sandstone of
vast thickness, is again a Monas.
I have entered into this explanation because my friend, Dr. Gei-
nitz, has seized upon one illustration in my work ‘ Siluria’ which
shows that in certain tracts, where the Zechstein or Magnesian
Limestone is subordinate to an enveloping series of sandstones, the
Permian of my classification is there as much a tripartite Paleo-
zoic group as the Trias of Central Germany is a triple formation of
Mesozoic age. Unless, therefore, the data to which my associates and
* The red clay or argillaceous shale which covers the limestone is sur-
mounted at Hilton, in Cumberland, by five hundred feet of red sandstone, which,
though perfectly conformable to the subjacent Permian rocks, he considers to
belong to the Bunter Sandstein of the Trias. Here, then, as in Germany, the
limestone may have a red cover, and yet the Bunter Sandstein be intact.
= ee
term “ Dyas” to the “ Permian” Group of Rocks. 69
self have appealed, in the work on ‘ Russia and the Ural Mountains,’
and which I have further developed in Memoirs read before the
Geological Society and in my two editions of ‘ Siluria,’ be shown to
be inaccurate, I hold to the opinion that there are tracts in which
the Zechstein is simply a fossiliferous zone in a great sandstone
series, to which no division by numerals can be logically applied.
Even if I do not appeal to the natural evidences in England, Russia,
and parts of Germany, but refer to those tracts where the Zechstein
or Magnesian Limestone has no natural red cover, I may well ask,
does not the word “ Permian,” in the sense in which it was origi-
nally adopted, serve for every tract wherein the uppermost palao-
zoic fossil animals and plants are found, whether the strata of which
the group is composed form, as in Russia and Silesia, one great series
of alternations of plant-bearing sandstones and marls in parts con-
taining bands of fossiliferous limestone, or whether, as in other
tracts, the Zechstein stands alone (as near Saalfeld), or in others,
again, where the group is tripartite, and even quadripartite? Quite
irrespective, however, of the question of whether there are or are
not localities in Germany where the Zechstein passes upwards into a
red rock, which forms no true part of the Bunter Sandstein of the
Trias, we have only to look to the environs of Dresden, on the one
hand, and to Lower Silesia on the other, to see the inapplicability
of the word “‘ Dyas” to this group.
Near the capital of Saxony, Dr. Geinitz himself pointed out to
me that the Roth-liegende is there divided into two very dissimilar
parts; and these, if added to the limestone which is there inter-
polated, or to the true Zechstein of other places, constitute a Trias,
Again, Beyrich, in his Map of Lower Silesia *, has divided the vast
Roth-liegende of those mountains into Lower and Upper, the two
embracing ezght subdivisions according to that author.
In repeating, then, that the word “ Permian ”’ was not originally
proposed with the view of affixing to this natural group any number
of component parts, but simply as a convenient short term to define
the Uppermost Palzozoic group, I refer all geologists to the very
words I used in the year 1841, when the name was first suggested.
In speaking of the structure of Russia, I thus wrote :—‘“ The Car-
boniferous system is surmounted to the east of the Volga by a vast
series of beds of marls, schists, limestones, sandstones, and conglo-
merates, to which I propose to give the name of ‘ Permian System,’
because, although this series represents as a whole the Lower New
Red Sandstone (Rothe-todte-liegende) and the Magnesian Limestone
or Zechstein, yet it cannot be classed exactly, whether by the suc-
cession of the strata or their contents, with either of the German or
British subdivisions of this age +.” ™ ag * “a “g
After pointing to the Gov ernments of Russia over which such
Permian rocks ranged, I added :—*‘ Of the fossils of this system,
some undescribed species of Producti might seem to connect the
Permian with the Carboniferous era; and other shells, together with
* See also ‘ Siluria,’ 2nd edit. p, 343.
t Phil. Mag. xix. p. 419
70 Notices respecting New Books.
fishes and saurians, link it more closely to the period of the Zech-
stein, whilst its peculiar plants appear to constitute a Flora of a
type intermediate between the epochs of the New Red Sandstone or
Trias and the Coal-measures. Hence it is that I have ventured to
consider this series as worthy of being regarded as a system *.”
In subsequent years, having personally examined this group in
the typical tracts of Germany as well as of Britain, I felt more than
ever assured that, from the great local variations of mineral succes-
sion of the grovp, the word “ Permian,’’ which might apply to any
number of mineral subdivisions, was the most comprehensive and
best term which could be used, the more so as it was in harmony
with the prirciple on which the term Silurian had been adopted.
Apart from the question of the substitution of the new word
‘“‘ Dyas’’ for the older name “ Permian,” I take this opportunity of
expressing my regret that some German geologists are returning to
the use of the term “Grauwacke Formation,” as if years of hard
labour had not been successfully bestowed in elaborating and esta-
blishing the different Paleozoic groups, all of which, even including
the Lower Carboniferous deposits, were formerly confusedly grouped
under the one lithological term of the «‘Grauwacke Formation.”
Respecting as I do the labours of the German geologists who
have distinguished themselves in describing the order of the strata
and the fossil contents of the group under consideration, I claim
no other merit on this point for my colleagues de Verneuil and
.von Keyserling, and myself, than that of having propounded
twenty years ago the name of “ Permian” to embrace in one natural
series those subformations for which no collective name had been
adopted. Independently, therefore, of the reasons above given, which
show the inapplicability of the word “ Dyas,” I trust that, in accord-
ance with those rules of priority which guide naturalists, the word
“‘ Permian ”’ will be maintained in geological classification.
London: Belgrave Square.
Noy. 30, 1861.
X. Notices respecting New Books.
Huclid’s Elements of Geometry, designed for the use of the higher Forms
in Public Schools and Students in the Universities. By Rosert
Ports, M.A., Trinity College, Cambridge. Corrected and Improved
edition. London: John W. Parker, Son, and Bourn.
R. POTTS’ first octavo edition of Euclid appeared in 1845, and
since then has been gradually gaining ground in the estimation
of our best teachers as one of the most unexceptionable books of its
class at present within the reach of the students in our schools and
universities. The work is too well known to require description,
* In my last edition of ‘ Siluria’ I have spoken of the Permian as the Upper-
most Palxozoic group, but have not deemed it a system by comparison with the
vast deposits of Carboniferous, Devonian, and Silurian age.
en a ae Se a : e
Ca
rf
Notices respecting New Books. as
and little need be added to the notice already given in this Magazine
(see vol. xxxul. 5. 3. p. 69), beyond the assurance that the new edition
possesses all the best and most characteristic features of the old one,
minus many of its imperfections. ‘The conscientious care with which
the verbal defects of Simson’s text have been emended cannot be too
highly praised, and it must be a great satisfaction to Mr. Potts to
know that he has done much towards the cultivation, in our schools,
of a more correct taste, as far as the purity of geometrical reasoning
jis concerned. In fact, if we were to judge the work merely from its
author’s own point of view, that is to say, as a careful reproduction
of, and judicious commentary upon the ‘Elements of Euclid,’ we
should have little to say except in praise of the result as now offered
to the public. It is only when we take difierent, and higher ground,
when, in short, we compare this treatise on the science of geometry
with the purely ideal one which English students do not, but ought
to possess, that we find room for much criticism.
We have no desire to enter here into the question épineuse as to
the absolute merits of Euclid’s ‘ Elements;’ as a classical work it is
second to none in point of interest, and it will ever continue to be
studied by men of culture. The opinion is gaining ground, however,
that our national admiration of Euclid has been carried too far—that
it has too long deprived our schools of the advantages to be gained
from an elementary treatise on geometry which, although based upon
the old one, shall be superior to it in point of method and accuracy,
of purely English origin, and in every way worthy of the present
state of the science. Even in our universities, which are proverbially
and, on the whole, wisely conservative, symptoms of a more vigorous
and healthy criticism—too long discouraged by an inordinate notion
of Euclid’s perfection—manifest themselves more and more frequently.
Mr. Potts’ notes to the several books of Euclid might be cited in sup-
port of our assertion, whilst the frequent use in them of such words
as seems and appears, in place of the more decisive and emphatic verb
is, curiously enough indicates the state of transition to which we
have referred. Numerous instances might be given ; let one suffice.
In his notes to the 3rd book, Mr. Potts modestly informs us that
the 9th proposition ‘‘ appears to follow as a corollary from the 7th,”
whereas it is, as he well knows, a purely logical consequence of the
latter ; for if it be impossible to draw more than two equal lines
from any zon-central point to the circumference of a circle, any
competent logician, even if he were ignorant of the very nature of a
circle, would be able to conclude that the point must be a central one
from which three equal lines can be drawn to the circumference.
Having mentioned these notes, it is but just to add that in their
present improved form they constitute a very valuable feature of the
work, and on the whole are both judicious and accurate. Whilst
admitting, however, that the opposite excess would have been in-
tolerable, we cannot but think that the notes in question would have
been of far greater value had they been less purely explanatory, and
more thoroughly critical. Instead of ‘‘ exemplifying ”’ by geometrical
figures such axioms as “‘if equals be added to equals the wholes are
72 Royal Society :—
equal,” it would surely have been more profitable to have enume-
rated the several axioms which Euclid tacitly assumes. Instead of
showing, in a very questionable manner too, how the 11th and 12th
propositions of the third book might have been proved directly had
they been placed after the 18th proposition, would it not have been
better to have proposed a rearrangement of the whole book—to
have given a sketch, in fact, of a better treatment of the many beau-
tiful properties of the circle ?
The collection of geometrical exercises given by Mr. Potts is an-
other characteristic feature of his work, and has also been improved.
In order to give to evercises their full value, however, and to prevent
them from degenerating into mere riddles, they should be made sub-
ordinate to, and illustrative of geometrical methods; and this, it
must be admitted, Mr. Potts has not been able to do fully, since, for
other and good reasons, he has preferred selecting his exercises from
college and university examination-papers. Comparing his selections
with others, however, we cannot but agree with the Reviewer whom
Mr. Potts himself quotes in his preface. With respect to the first —
of the exercises ‘‘ on tangencies,”’ we will merely caution the student
against accepting the author’s analysis, either as a model for imitation
or as a specimen of Mr. Potts’ ability; it is unusually defective.
The very enunciation of the problem is objectionable, disfigured as
it is by the introduction of the perfectiy irrelevant datum “ of a line
given in position.”
We do not care to dwell longer upon imperfections which, if not
trivial, are certainly far outweighed in importance by the many
excellent features of the book. We will merely repeat, then, that
although we trust the work, considered as an introduction to the
science of geometry, will some day be superseded, we are convinced
that as a careful English reproduction of Euclid’s Elements, illustrated
by the notes of an able and judicious teacher, and enriched by a
large collection of very useful exercises, it will long maintain its
ground.
XI. Proceedings of Learned Societies.
ROYAL SOCIETY.
{Continued from vol. xxii. ]
April 11, 1861.—Major-General Sabine, R.A., Treasurer and Vice--
President, in the Chair
_ following communication was read :—
“On the Motion of a Plate of Metal on an Inclined Plane, when
dilated and contracted; and on the Descent of Glaciers.’”? By the
Rey. Henry Mosely, M.A., Canon of Bristol, F.R.S., Inst. Sc. Paris
Corresp.
The case in which the upper edge of such a plate (supposed rec-
tangular) is fixed is first discussed ; and then that in which the lower
edge is fixed. Each of these cases is considered subject to the con-
dition of friction ; first, when the plate is dilated, and secondly, when.
On the Motion of a Plate of Metal on an Inclined Plane. 738
it is contracted. Two other principal conditions arise in the discus-
sion; one being that in which a part only, and the other that in
which the whole of the plate dilates and contracts.
In the former the dilatation or contraction is represented by
Ed? cos ¢
2u(1 + Az) sin (@+0
or by EX # cos
2u(1-~Xé) sin (pe)
according as the plate is fixed at the top or the bottom.
In the latter it is represented under the same conditions by
p sin (gto, a}
a{ de 2E cos
or by
a{re— pe sin psin (+4),
~ 2E cos ¢
- In which formulee—
a represents the length of the plate.
p. its weight in lbs. per foot of its length.
i the inclination of the plane.
@ the limiting angle of resistance (the angle of friction) between
the surface of the plane and of the plate.
E the modulus of elasticity of the plate.
A the dilatation or contraction per foot of the length for each
variation of 1° of Fahrenheit.
+¢° the rise or fall of the temperature in degrees of Fahrenheit,
by which the dilatation or contraction of the plate is supposed to be
caused.
In the case in which no part of the plate is fixed, a horizontal line
may be taken in it above which it dilates upwards, and below it
downwards. ‘The position of this line is determined by the consi-
deration that, if the plate be imagined to be cut through along that
line, the thrust necessary to push the part above upwards must be
equal to that necessary to push the part below downwards.
In like manner a horizontal line may be found above which the
plate contracts downwards and below it, upwards.
The former neutral line is nearer the top than the bottom, the
other nearer the bottom than the top. The one is at the same di-
stance from the top as the other is from the bottom. This distance
is represented by the formula
1, Sin sin (¢—0)_
34
sin @ cost
When the plate is dilated, it is the longer portion which dilates
downwards ; and when it is contracted, it is the shorter portion
which contracts upwards. The lower end of the plate descends
therefore by a given increase of temperature more than it ascends
by an equal fall ; and on the whole the plate descends.
If we suppose the temperature first to be increased by ¢,°, and
then diminished by ¢,° ; then—
74 Royal Society :—
Ist. In the case in which a portion only of the plate dilates, the
descent is represented by
EX’ cos { t,° - ae \
(1+A¢,) sin(@—«) (1—Aé,) sin (+4)
2ndly. In the case in which the whole plate dilates and the whole
contracts, the descent is
tance pea sin(d+c) sin (¢—2) tane \
i £—t, )A+(¢,4+4, —
sad Ce 2) A+ (2,4 2) cane E sin’ ¢ cos ¢
The first case passes into the second.
If E be very great as compared with pa, the second term in the
above formula may be neglected. It then corresponds with the for-
mula given by the author in a former communication to the Society.
To verify the fact of the descent of a plate of metal under the
conditions supposed, a deal board 9 feet long and 5 inches broad, was
fixed at an inclination of 185° against the wall of a house having a
southern aspect, and a sheet of lead was placed upon it one-eighth
of an inch thick and weighing 28 lbs., and having its edges turned
over the edges of the board so as not to bind upon it. Near the
lower extremity a vernier was constructed, by which the position of
the lead on the board could be determined to the 100th of an inch.
Its position was observed daily between 7 and 8 in the morning and
6 and 7 in the evening, from the 16th of February to the 28th of
June, 1858.
A Table is given showing the descent for every day of that period,
from 7 a.m. to 6 p.m. and from 6 p.m. to 7 A.M.
In the months when there was no sunlight from 6 p.m. to 7 A.M.,
there was no descent in that interval. The descents from 7 a.m. to
6 p.m. were very different on different days. Sometimes they
amounted to a quarter of an inch in the day, and sometimes were
not appreciable. The greatest descents were on sunny days, and
especially when with a warm sun there was a cold wind. The least
were on days of continualrain. The average daily descents were, in
inches, —
2 I
February. | March. April. May. June.
"10000 "13306 16133 "21500 *21888
These descents were not due to the extreme temperatures of the
periods in which they took place, but to the aggregate of the variations
up and down during each interval. The difference of the highest and
lowest temperatures in any interval may have been small, and yet the
changes of temperature up and down may have been many, and their
ageregate great. It is upon this aggregate that the descent depends.
The dilatation of ice was measured in the years 1845, 1846, at the
Observatory of Pultowa, by Schumacher, Pohr, and Moritz; and the
particulars of their experiments were communicated to the Academy
of St. Petersburgh, by W. Struve, in 1848, and published in its
Memoirs (Sciences Mathém. et Phys., sér. 6. t. iv.). By exposing
The Rev. H. Mosely on the Descent of Glaciers. 75
water to the action of the frost in a mould, Schumacher obtained a
block of ice, which, after reducing it with the plane, measured 6 ft.
3 ins. in length and 6 ins. by 6} inches in section ; and he caused three
thermometers to be frozen into it with their stems projecting above
its surface. This block of ice he earried out from a room, where it
had been preserved at a uniform temperature of —2° R. during the
day, into the open air at night, and slung it in a horizontal position
from a beam supported by tressles. As its temperature fell he
measured the distance between two steel points frozen into it near
its two ends, by a measuring rod of dry wood (well-clothed), the di-
stances on which were referred to a standard measure on the wall of
a room of the Observatory which retained nearly a constant tempe-
rature of —2° R. His measurements had reference to observed
temperatures of the ice varying from —2°3 R. to —22° R. After
applying the requisite corrections, it resulted from them that the
coefficient of expansion of ice is for 1° R.
"00006466,
which is nearly twice as great as the coefficient of dilatation of lead,
and more than twice as great as that of any other solid.
We do not know the modulus of elasticity of ice, or the pressure
under which it disintegrates.
If it were as elastic as slate and did not resist crushing more than
hard brick, a block of it placed with its ends between two immoveable
obstacles, would crumble when its temperature was raised one degree
of Fahrenheit. It is its great dilatability which gives to ice this ten-
dency to disintegrate, when, not being free to dilate, its temperature
is raised*, even so slightly as this.
If the block of ice experimented on by Schumacher had been
placed upon a plank inclined at the same angle as that used in the
experiment with the lead was, and if its under side had been coated
with lead-foil so as to give it the same friction on the plank as the
lead had, then, under the same variations of temperature as the lead
experienced, it could not but have descended as the lead did, but
twice as fast, because its dilatability is twice as great.
We may conceive such a block of ice to be made up of thin plates
parallel to its upper surface, such as plates of glass would be, if glass
were as dilatable as ice and as friable, and if it possessed that pro-
perty of passing from a disintegrated into a solid state, which in ice
is called regelation. If we put the adherence of these plates to one
another in the place of friction, and conceive the variations of external
temperature (or the effects of solar radiation) to reach them in suc-
cession, each one being dilated or contracted independently of the
rest, then each would descend by a motion proper to itself, and also by
reason of the descents of those subjacent to it. The extremities of
the plates would under these circumstances overlap, and the descent
of each, proper to itself, would be increased by the overlappings of
those beneath it.
* Agassiz describes a disintegration of the transparent ice of the blue bands
of glaciers when laid bare, which appears to be due to its expansion.—Bulletin Un.
de Genéve, vol. xliv. p. 142,
76 Royal Society :—
Each plate would under these circumstances descend faster than
the one beneath ; and supposing the adherence of the lowest plate to
the board to be the same as that of the plates to one another, then, of
any number of blocks similarly placed and subject to the like varia-
tion of temperatures, the thickest or deepest would descend, at its
surface, the fastest ; and if there were a block of different depths in
different parts, the deepest parts would descend the fastest. The
differential motion thus set up would not be appreciable in a block
of ice of different thicknesses in different parts if its dimensions
were no larger than the block experimented on by Schumacher, but
in a glacier it would be appreciable.
To bring Schumacher’s block to the proportions of a glacier, it
must be converted into a slab twelve feet long, twenty inches wide, and
two inches thick. It would then represent on a scale of the 1500th
part, a glacier 2500 feet wide, 250 feet deep, and 18,000 feet long,
which are something like the dimensions of the Mer de Glace from
2300 feet below Montanvert to the Tacul. If we suppose it to be
placed at the same inclination of 18}° at which the lead was, its
under surface being coated with lead so as to have the same friction
on board as the lead had, then it may be calculated that if it had
experienced the same variations of temperature as the lead did, its
average daily descent, measured in inches, would have been
February. | March. April. | May. June.
a
*26666 36816 43022 | 37334 98368
If, now, we conceive its inclination to change from 184° to that of
the Mer de Glace, which is about 5°, and its dimensions to become
actually those of that glacier, then, supposing the glacier to experience
the same elevations and depressions of temperature as the lead did,
its average daily descents in inches would be
me ee
104°56 144:06 | 168°74 224°87 | 228°92
which rates of motion are probably twelve times greater than the
actual rates of motion of the glacier; showing that variations of the
temperature of the glacier twelve times less than those of the lead,
would be sufficient to produce its actual descent; or that it would
descend as it actually does, if the resistances opposed to its descent were
twelve times greater than the resistances opposed to the descent of
the lead—If its descent were resisted by a friction, for instance, having
twelve times the coefficient of that of the lead on the board, or such as
would cause it to rest without slipping on an incline having twelve
times the tangent of the inclination of the board ; or if the variations
of temperature were less and the resistance greater in any proportion
which would retard the descent twelve times as much. So that
we may suppose in the case of the glacier a far greater resistance in
1 Se
The Rev. H. Mosely on the Descent of Glaciers. 77
proportion than that sustained by the lead upon the board, and
variations of temperature far less, without passing the limits within
which a probability is created by the experiment that the descent of
the glacier is due to the same cause as that of the lead.
In the act of descending on the board, the slab of ice of which we
have spoken could not but be thrown into a state of extension in
some parts and of compression in another. The conditions of the
descent being in other respects given, the amount of this extension or
compression might be at any point determined. If at any point the
extension exceeded the tenacity of the ice, the slab would there sepa-
rate across its length ; and if at any point the compression exceeded
the resistance to crushing, it would there crush.
Supposing it to be thinner at the sides than in the middle, the sur-
face-motion of the middle would be faster than that of the sides, and
from this differential motion would result cracks oblique to the axis of
the slab, the explanation of which, as they exist in glaciers, is one of
the most successful attempts yet made at the solution of the me-
chanical problem of glacier-motion. These conditions of the descent
of the slab, when refeiied to a glacier, explain the formation of trans-
verse and lateral crevasses, and the fact of a glacier crushing itself
through a gorge.
The Mer de Glace moves faster by day than by night*. Its mean
daily motion is twice as great during the six summer as during the six
winter months +. It moves fastest in the hottest months, and in those
months varies its motion the most, because in them the variations of
temperature are the greatest. It moves most slowly in the coldest
months, and in those varies its motion the least, because in those
months the variations of temperature are the least. These differences
are more remarkable at lower stations on a glacier than at higher, “‘ be-
cause the lower are exposed to more violent alternations of heat and
cold than the higher : this (says Forbes) we shall find to be general.”’
It moves fastest on the hottest days. ‘‘'This I apprehend (says
Forbes) to be clearly made out from my experiments, that thaw-
ing weather and a wet state of the ice conduce to its advancement,
and that cold, whether sudden or prolonged, checks its progress {.”’
‘The striking variations in September, especially at the lower sta-
tions, which were frequently observed, prove the connexion of tem-
perature with velocity to a demonstration §.”’
It is, however, impossible to do justice to the positive character of
the evidence on which this conclusion has been founded by Professor
Forbes without reference to those diagrams, by means of which he
has compared the mean rates of the daily motions of glaciers and the
corresponding mean temperatures. This comparison is founded on
observations made by himself and Aug. Balmat, as to the motion of
the “‘ Mer de Glace,”’ at fourteen different stations in three different
years, and on observations on the mean temperature of the atmo-
sphere made at the same times at the Great St. Bernard and at
Geneva. It results from it that no change in the mean temperature
* Forbes, ‘ Occasional Papers,’ p. 12.
+ Ibid. p. 129. Tyndall, ¢ Glaciers of the Alps,’ p. 294.
¢ Forbes, ‘ Travels in the Alps,’ p. 148. § Ibid.
78 Royal Society.
of the atmosphere is unaccompanied by a corresponding change in
the mean motion of the glacier.
The glacier moves with different velocities at different depths, the
surface-motion being faster (probably two or three times) than that of
the deepest part. ‘The motions at different depths cannot but be re-
lated to one another: so that as the influence of variations of tempe-
rature is felt on the surface, it cannot but be felt throughout the glacier.
If every change of solar heat is associated with a corresponding
change of glacier-motion, it seems to follow that the two are either
dependent upon some commen cause, or that the one set of changes
is caused by the other; and the former of these conclusions being
inadmissible, we are forced on the latter. It is not necessary to show
how it is that changes of external temperature penetrate glaciers. Of
the power of the sun upon them there are, however, evidences in the
ablation of surface constantly going on and in the preservation of the
ice which is covered by the stones of a moraine, which sometimes
forms an icy ridge from 50 to 80 feet high, and some hundred feet in
width.
The sun’s rays,’ says Tyndall*, ‘striking upon the unpro-
tected surface of the glacier, enter the ice to a considerable depth ;
and the consequence is that the ice near the surface of the glacier is
always disintegrated, being cut up into minute fissures and cavities
filled with water and air, which, for reasons already assigned, cause
the glacier when it is clean to appear white and opaque. ‘The ice
under the moraines, on the contrary, is usually dark and transparent.
I have sometimes seen it as black as pitch, the blackness being a
proof of its great transparency, which prevents the reflexion of light
from its interior. The ice under the moraines cannot be assailed in
its depths by the solar heat, because this heat becomes obscure be-
fore it reaches the ice, and as such it lacks the power of penetrating
the substance. It is also communicated in great part by way of con-
tact instead of by radiation.
s oh
Ss Sg
: = —
:
: El 5
——.
SSeshe i
Ly
LL al: rs
THE
LONDON, EDINBURGH ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
FEBRUARY 1882,
XIII. On the Cause of Vesicular Structure in Copper.
By W. J. Russewz, PA.D., and A. Marrutessen, F.R.S.*
LL specimens of commercial copper, when carefully ex-
amined, are found to be more or less vesicular in their
- structure: in some cases the vesicles are so small as to require a
magnifying glass to see them, but in other specimens they are
developed on a much larger scale. Copper and silver are, we
believe, the only metals which may readily be made to assume a
vesicular structure. In the case of silver, it is well known that
the fused metal absorbs oxygen, which being again given out on
cooling, produces the vesicular structure. It appeared therefore
possible that the vesicular structure in copper might also be
caused by the absorption of some gas. Our experiments have,
however, proved this not to be the case, but have led us ta the
same conclusion with regard to the cause of this porous struc-
ture as that arrived at by Mr. Dick+. As, however, our experi-
ments on some points have been rather more extended than his,
and remove, we believe, all doubt from the subject, a short
account of them may not be without interest.
The amount of gas contained in these cavities found in copper
was evidently too small to allow of its being collected, we were
therefore obliged to carry on the investigation synthetically. It
seemed, however, probable, from the inside of the cavities always
appearing untarnished, that they did not contain any oxygen.
In order, then, first to ascertain whether the vesicular structure
was owing to any mere absorption of a gas by the melted metal,
we passed each of the ordinarily occurring gases, carefully purified
* Communicated by the Authors.
7 Phil. Mag, June 1856.
Phil, Mag.S. 4. Vol. 23. No, 152. feb. 1862. G
82 Dr. Russell and Dr. A. Matthiessen on the Cause
and dried, through fused copper for five minutes. In all our ex-
periments electrotype copper was used, as being the purest, and
each experiment was made with about 150 grammes of the metal.
The gases experimented with were hydrogen, oxygen, nitrogen,
air, carbonic acid, and carbonic oxide. With each gas the expe-
riment was made. under three different circumstances :—Ist, the
gas was passed through when the melted copper was without
flux or covering ; 2nd, when it was under a flux of salt; and
ord, when covered with charcoal, We need not describe ‘sepa-
rately each experiment; it will be sufficient to state the general
result obtained from this series of experiments, which is, that
the vesicular structure in the copper is only developed when
either oxygen or air is passed through the melted metal under
charcoal. Under these circumstances, not only did the metal
become very porous, but when solid the surface was found to
have risen or vegetated, often to a very considerable extent. In
some cases even small particles of the melted copper, on the
cooling of the mass, were projected out of the crucible. A similar
phenomenon is known to copper-smelters, and called by them
copper rain. In order to obtain satisfactory results, a consider-
able amount of care is necessary in performing these experi-
ments; for if the surface of the melted copper towards the end
of the experiment be exposed, by the burning off of the charcoal
or any other accidental circumstance, only for a very short time
to the air, that alone is sufficient to induce the vesicular struc-
ture in the metal. Again, we found that the same phenomenon
was produced when any of the fuel fell into the melted copper.
Having satisfactorily proved that air and oxygen were the only
gases which caused the copper to become vesicular, and in fact
these only when carbon was present, we naturally concluded that
the vesicular structure could not be owing to any mere absorp-
tion or chemical combination of the melted copper and gas, but
was probably due to the formation of carbonic oxide arising from
the reduction of the suboxide of copper by means of the charcoal.
The following experiments show, we-think, that this supposition
is correct :—
Copper was fused alone in air: immediately on removing it
from the furnace, powdered charcoal was thrown on the surface ;
considerable vegetation ensued, and on being fractured it was
found to be very vesicular.
Another specimen of copper was fused, as before, in the air;
but now, on removing it from the furnace, instead of throwing
charcoal on the surface of the melted metal, a jet of coal-gas was
allowed to play upon it. The result was precisely similar to
that obtained with the charcoal, the carbon from the coal-gas
reducing the suboxide,
of Vesicular Structure in Copper. 83
~ In another experiment of the same kind we varied the condi-
tions by throwing on the charcoal before the fused copper had
been removed from the furnace; a vegetation in bulk nearly
equal to half that of the copper used took place. In order to
give a more definite idea of the great extent to which the metal
becomes porous, we have taken the specific gravity of several of
these specimens of copper in which we have developed the vesi-
cular structure. The specific gravity of the copper operated on
in the last experiment was found to be only 5°683, whereas that
of pure copper is 8°952. Mr. Dick, in the paper before alluded
to, describes some very interesting experiments which he made
by casting copper which had been fused under charcoal in an
atmosphere of coal-gas, thus not allowing the melted metal to
come in contact with the air; the result was that he then ob-
tained a perfectly solid casting; but if, instead of using coal-gas,
he made the casting in air, using even metal out of the same cru-
cible in both experiments, he in the latter case always obtained a
casting which was very vesicular. Our experiments entirely
confirm these results of Mr. Dick. The specific gravity of the
casting thus obtained shows in a striking manner the great altera-
tion in the density of the copper. A specimen of the electrotype
copper which we used, simply fused and allowed to cool under
charcoal, gave us a specific gravity of 8-952. The casting made
in coal-gas had a specific gravity of 8°929; another made in the
same way had a specific gravity of 8°919; whereas a third spe-
cimen, also made with metal out of the same crucible, but cast m
air, had a specific gravity of 6°-193. To render our experiments
still more conclusive, we now fused copper, allowing the air free
access to it, and cast one portion of the metal m moulds contain-
ing air, and the other in moulds filled with coal-gas. Two spe-
eimens of the copper cast in air had respectively the specific
gravities 8°618 and 8°665, while the specimens which had been
cast in coal-gas had a specific gravity of only 6°926 and 6:438.
The cause, then, of the vesicular structure in copper appears
to be due to the reduction of the suboxide of copper by the car-
bon mechanically drawn down into the mass of the metal by the
currents continually formed from the cooling of the surface.
The carbonic oxide thus produced throughout the whole mass of
the copper is given off as long as the surface remains fused; but
as soon as it solidifies, the crust is lifted-up, and breaking, pro=
duces vegetation. The carbonic oxide formed at the time of soli-
dification not being able to escape, remains dispersed through
the metal, giving it the vesicular structure. With lampblack
(carbon in a finer state of division) instead of powdered charcoal,
the action appears to be still more intense; and on throwmg
some of it on melted copper, the evolution of gas may be easily
G2
84. On the Cause of Vesicular Structure in Copper.
seen. That the vesicular structure is not owing to any especial
affinity of melted copper for carbonic oxide, is shown by the fact
that when copper is fused under charcoal or a flux of salt, and
carbonic oxide passed through it, the metal, on cooling, is found
to be entirely devoid of all porous structure, as proved by its
specific gravity, which we found to be 8°943.
That carbon can exercise an influence of the kind attributed
to it in the foregomg experiments, is shown by its action on
melted silver; for if silver be fused under a layer of charcoal,
and oxygen gas passed through it for any length of time, still
no spitting will take place on the cooling of the metal. Again,
when silver is fused in air, if charcoal be thrown on the melted
surface no spitting occurs, a fact well known to assayers: sand
or any other body of that kind does not exercise a similar influ-
ence on the silver*.
We next tried the action of sulphur on suboxidized copper,
and found that it also produced the vesicular structure, and even
caused the copper to vegetate to a very considerable extent. In
fact, when sulphur is thrown on copper which has been melted
with access of air, results are obtained similar to those which
carbon produces under the same circumstances.
Two specimens of copper which had been rendered vesicular
by the action of sulphur, were found to have respectively the spe-
cific gravities of 6°6 and 5:1. It is a somewhat curious fact,
that the phenomenon of copper rain is caused to a much greater
extent by the action of sulphur than it is by carbon. The sul-
phur, of course, acts on the suboxide'of copper in the same kind
of way as the carbon; and the vesicular structure and copper
rain are in this case owing to the evolution of sulphurous acid.
We also tried the action of iodine and of phosphorus on
suboxidized copper, but they did not produce any appearance of
vesicular structure.
The toregoing experiments were carried out partly in Péofessor
Percy’s, and partly i in Professor Williamson’s laboratory.
* While engaged on this subject, we also made a series of experiments
upon silver, to ascertain whether any other gas than oxygen was absorbed
by it. The melted silver was treated in precisely the same way as the cop-
per, and the gases oxygen, hydrogen, air, nitrogen, carbonic acid, and car-
bonic oxide passed through it. The spitting of the silver we found to be
caused only by oxygen or air, and, further, that, as mentioned above, this
was entirely prevented by the presence of charcoal. In Gmelin’s ‘ Che-
mistry’ (vol. vi. p. 139) it is stated that, when silver is fused under nitrate
of potash, the spitting takes place: this statement we believe to be incor-
rect; for we always found that when silver was carefully fused, so that the
air did not come in contact with it, under a layer of either nitrate or chlorate
of potash, no spitting took place. As both these salts are decomposed
below the melting-point of silver, this result is what might be expected.
Esa]
XIV. On Physical Lines of Force. By J.C. Maxwett, F.R.S.,
Professor of Natural Philosophy in King’s Colleye, London*.
Part IV.—The Theory of Molecular Vortices applied to the
Action of Magnetism on Polarized Light.
HE connexion between the distribution of lines of magnetic
force and that of electric currents may be completely ex-
pressed by saying that the work done on a unit of imaginary
magnetic matter, when carried round any closed curve, is pro-
portional to the qnantity of electricity which passes through the
closed curve. The mathematical form of this law may be ex-
pressed as in equations (9)+, which I here repeat, where «, 6, y
are the rectangular components of magnetic intensity, and p, g, 7
are the rectangular components of steady electric currents,
#9 tik ye) }
ar apna ye
ein
A Z), ©)
pa a -=).
dx dy
The same mathematical connexion is found between other sets
of phenomena in physical science.
(1) If a, B, y represent displacements, velocities, or forces,
then p, q, r will be rotatory displacements, velocities of rotation,
or moments of couples producing rotation, in the elementary por-
tions of the mass.
(2) Ifa, 8, y represent rotatory displacements in a uniform
and continuous substance, then p, g,7 represent the relative
linear displacement of a particle with respect to those in its im-
mediate neighbourhood. Sce a paper by Prof. W. Thomson
“On a Mechanical Representation of Electric, Magnetic, and
Galvanic Forces,’ Camb. and Dublin Math. Journ. Jan. 1847.
(3) If a, 6, y represent the rotatory velocities of vortices
whose centres are fixed, then p, g, r represent the velocities with
which loose particles placed between them would be carried along.
See the second part of this paper (Phil. Mag. April 1861).
It appears from all these instances that the connexion between
magnetism and electricity has the same mathematical form as
that between certain pairs of phenomena, of which one has a
linear and the other a rotatory character. Professor Challis t
* Communicated by the Author.
+ Phil. Mag. March 1861.
{ Phil. Mag. December 1860, January and February 1861.
86 Prof. Maxwell on the Theory of Molecular Vortices
conceives magnetism to consist in currents of a fluid whose direc-
tton corresponds with that of the lines of magnetic force; and
electric currents, on this theory, are accompanied by, if not de-
pendent on, a rotatory motion of the fluid about the axes of the
current. Professor Helmholtz* has investigated the motion of
an incompressible fluid, and has conceived lines drawn so as to
correspond at every point with the instantaneous axis of rotation
of the fluid there. He has poimted out that the lines of fluid
motion are arranged according to the same laws with respect to
the lines of rotation, as those by which the lines of magnetic force
are arranged with respect to electric currents. On the other
hand, in this paper I have regarded magnetism as a phenome-
non of rotation, and electric currents as consisting of the actual
translation of particles, thus assuming the inverse of the relation
between the two sets of phenomena.
Now it seems natural to suppose that all the direct effects of any
cause which is itself of a‘longitudinal character, must be them-
selves longitudinal, and that the direct effects of a rotatory cause
must be themselves rotatory. A motion of translation along an
axis cannot produce a rotation about that axis unless it meets
‘with some special mechanism, like that of a screw, which con-
nects a motion in a given direction along the axis with a rotation
in a given direction round it; and a motion of rotation, though
it may produce tension along the axis, cannot of itself produce a
current in one direction along the axis rather than the other.
Electric currents are known to produce effects of transference
in the direction of the current. They transfer the electrical
state from one body to another, and they transfer the elements
of electrolytes in opposite directions, but they do not+ cause the
plane of polarization of light to rotate when the hght traverses
the axis of the current.
On the other hand, the magnetic state is not characterized by
any strictly longitudinal phenomenon. The north and south
poles differ only in their names, and these names might be
exchanged without altering the statement of any magnetic pheno-
menon ; whereas the, positive and negative poles of a battery are
completely distinguished by the different elements of water which
are evolved there. The magnetic state, however, is characterized
by a well-marked rotatory phenomenon discovered by Faradayt{—
the rotation of the plane of polarized light when transmitted
along the lines of magnetic force.
When a transparent diamagnetic substance has a ray of plane-
polarized light passed through it, and if lines of magnetic force
* Crelle, Journal, vol. lv. (1858) p. 25.
+ Faraday, ‘ Experimental Researches,’ 951-954, and 2216-2220.
+ Ibid., Series XIX.
applied to the Action of Magnetism on Polarized Light. 87
are then produced in the substance by the action of a magnet or
of an electric current, the plane of polarization of the transmitted
light is found to*be changed, and to be turned through an angle
depending on the intensity of the magnetizing force within the
substance. |
The direction of this rotation in diamagnetic substances is the
same as that in which positive electricity must circulate round
the substance in order to produce the actual magnetizing force
within it; or if we suppose the horizontal part of terrestrial
magnetism to be the magnetizing force acting on the substance,
the plane of polarization would be turned in the direction of
the earth’s true rotation, that is, from west upwards to east. -
In paramagnetic substances, M. Verdet* has found that the
plane of polarization is turned in the opposite direction, that is,
in the direction in which negative electricity would flow if the
magnetization were effected by a helix surrounding the substance,
_ In both cases the absolute direction of the rotation is the same,
whether the light passes from north to south or from south to
north,—a fact which distinguishes this phenomenon from the rota-
tion produced by quartz, turpentine, &c., in which the absolute
direction of rotation is reversed when that of the light is reversed.
The rotation in the latter case, whether related to an axis, as in
quartz, or not so related, as in fluids, indicates a relation between
the direction of the ray and the direction of rotation, which is
sunilar in its formal expression to that between the longitudinal
and rotatory motions of a right-handed or a left-handed screw;
and it indicates some property of the substance the mathematical
form of which exhibits right-handed or left-handed relations, such
as are known to appear in the externalformsof crystals having these
properties. In the magnetic rotation no such relation appears,
but the direction of rotation is directly connected with that of
the magnetic lines, in a way which seems to indicate that mag-
netism is really a phenomenon of rotation.
The transference of electrolytes in fixed directions by the elec-
tric current, and the rotation of polarized light im fixed direc-
tions by magnetic force, are the facts the consideration of which
has induced me to regard magnetism as a phenomenon of rota-
tion, and electric currents as phenomena of translation, instead
of following out the analogy pointed out by Helmholtz, or adopt-
ing the theory propounded by Professor Challis.
The theory that electric currents are linear, and magnetic forces
rotatory phenomena, agrees so far with that of Ampére and Weber;
and the hypothesis that the magnetic rotations exist wherever
magnetic force extends, that the centrifugal force of these rota-
tions accounts for magnetic attractions, and that the imertia of
* Comptes Rendus, vol. xlii. p. 529; vol. xliv. p. 1209.
88 Prof. Maxwell on the Theory of Molecular Vortices
the vortices accounts for induced currents, is supported by the
opinion of Professor W. Thomson*. In fact the whole theory of
molecular vortices developed in this paper has been suggested to
me by observing the direction in which those investigators who
study the action of media are looking for the explanation of elec-
tro-magnetic phenomena.
Professor Thomson has pointed out that the cause of the mag-
netic action on light must be a real rotation going on in the
magnetic field. A rzght-handed circularly polarized ray of light
is found to travel with a different velocity according as it passes
from north to south, or from south to north, along a line of mag-
netic force. Now, whatever theory we adopt about the direction
of vibrations in plane-polarized hght, the geometrical arrange-
ment of the parts of the medium during the passage of a right-
handed circularly polarized ray is exactly the same whether the
ray 1s moving north or south. ‘The only difference is, that the
particles describe their circles in opposite directions. Since,
therefore, the configuration is the same in the two cases, the forces
acting between particles must be the same in both, and the mo-
tions due to these forces must be equal in velocity if the medium
was originally at rest; but if the medium be in a state of rota-
tion, either asa whole or in molecular vortices, the circular vibra-
tions of light may differ in velocity according as their direction
is similar or contrary to that of the vortices.
We have now to investigate whether the hypothesis developed
in this paper—that magnetic force is due to the centrifugal force
of small vortices, and that these vortices consist of the same
matter the vibrations of which constitute light—leads to any
conclusions as to the effect of magnetism on polarized light.
We suppose transverse vibrations to be transmitted through a
magnetized medium. How will the propagation of these vibra-
tions be affected by the circumstance that portions of that me-
dium are in a state of rotation ?
In the following investigation, I have found that the only effect
which the rotation of the vortices will have on the light will be
to make the plane of polarization rotate in the same direction as
the vortices, through an angle proportional—
A) to the thickness of the substance,
B) to the resolved part of the magnetic force parallel to theray,
C) to the index of refraction of the ray,
D) inversely to the square of the wave-length in air,
E) to the mean radius of the vortices,
F) to the capacity for magnetic induction.
(
(
(
(
(
(
* See Nichol’s Cyclopedia, art. “‘ Magnetism, Dynamical Relations of,”
edition 1860; Proceedings of Royal Society, June 1856 and June 1861;
and Phil. Mag. 1857.
applied to the Action of Magnetism on Polarized Light. 89
A and B have been fully investigated by M. Verdet*, who has
shown that the rotation is strictly proportional to the thickness
and to the magnetizing force, and that, when the ray 1s inclined
to the magnetizing force, the rotation is as the cosine of that in-
clination. D has been supposed to give the true relation between
the rotation of different rays; but it is probable that C must
be taken into account in an accurate statement of the phenomena.
The rotation varies, not exactly inversely as the square of the
wave-length, but a little faster; so that for the highly refrangible
rays the rotation is greater than that given by this law, but more
nearly as the index of refraction divided by the square of the
wave-length.
The relation (E) between the amount of rotation and the size of
the vortices shows that different substances may differ in rota-
ting power independently of any observable difference in other
respects. We know nothing of the absolute size of the vortices ;
and on our hypothesis the optical phenomena are probably the
only data for determining their relative size in different sub-
stances. :
On our theory, the direction of the rotation of the plane of
polarization depends on that of the mean moment of momenta,
or angular momentum, of the molecular vortices; and since M.
Verdet has discovered that magnetic substances have an effect
on light opposite to that of diamagnetic substances, it follows
that the molecular rotation must be opposite in the two classes
of substances. |
We can no longer, therefore, consider diamagnetic bodies as
being those whose coefficient of magnetic induction is less than that
of space empty of gross matter. We must admit the diamagnetic
state to be the opposite of the paramagnetic; and that the vor-
tices, or at least the influential majority of them, in diamagnetic
substances, revolve in the direction in which positive electricity
revolves in the magnetizing bobbin, while in paramagnetic sub-
stances they revolve in the opposite direction.
This result agrees so far with that part of the theory of M.
Webert which refers to the paramagnetic and diamagnetic condi-
tions. M. Weber supposes the electricity in paramagnetic bodies
to revolve the same way as the surrounding helix, while in dia-
magnetic bodies it revolves the opposite way. Now if we regard
negative or resinous electricity as a substance the absence of
which constitutes positive or vitreous electricity, the results will
be those actually observed. This will be true independently of
any other hypothesis than that of M. Weber about magnetism
* Annales de Chimie et de Physique, sér.3.vol. xli. p. 370; vol. xliii. p. 37.
T Taylor’s ‘ Scientific Memoirs,’ vol. v. p. 477.
90 . Prof. Maxwell on the Theory of Molecular Vortices
and diamagnetism, and does not require us to admit either M.
Weber’s theory of the mutual action of electric particles in
motion, or our theory of cells and cell-walls.
I am inclined to believe that iron differs from other substances
in the manner of its action as well as in the intensity of its mag-.
netism; and I think its behaviour may be explained on our
hypothesis of molecular vortices, by supposing that the particles
of the iron itse/f are set in rotation by the tangential action of
the vortices, in an opposite direction to their own. These large
heavy particles would thus be revolving exactly as we have sup-
posed the infinitely small particles constituting electricity to re-
volve, but without being free like them to change their place and
form currents.
The whole energy of rotation of the magnetized field would
thus be greatly increased, as we know it to be; but the angular
momentum of the iron particles would be opposite to that of the
eetherial cells and immensely greater, so that the total angular
momentum of the substance will be in the direction of rotation
of the iron, or the reverse of that of the vortices. Since, how-
ever, the angular momentum depends on the absolute sizé of the
revolying portions of the substance, it may depend on the state
of aggregation or chemical arrangement of the elements, as well
as on the ultimate nature of the components of the substance.
Other phenomena in nature seem to lead to the conclusion that
all substances are made up of a number of parts, finite in size,
the particles composing these parts bemg themselves capable of
internal motion. .
Prop. XVIII.—To find the angular momentum of a vortex. -
The angular momentum of any material system about an axis
is the sum of the products of the mass, dm, of each particle multi-
plied by twice the area it describes inreont that axis in unit of
time; or if A is the angular momentum about the axis of z,
As we do not know the distribution of density within the
vortex, we shall determine the relation between the angular
momentum and the energy of the vortex which was found in
Prop. VI.
Since the time of revolution is the same Fuad the vite!
the mean angular velocity » will be uniform and = = where « is
the velocity at the circumference, and r the radius. Then
A= Xdmr*a,
applied to the Action of Magnetism on Polarized Light. 91
and the energy
{
Te |
E=32dmr*o* =; Ao,
US 2 ere be Ova sk
ae > gall V by Prop. yee ;
whence
1 |
| A=7— praV eth bik mi aha ai 6 22)
for the axis of x, with similar expressions for the other axes, V
being the volume, and r the radius of the vortex.
_ Prop. X1X.—To determine the conditions of undulatory mo-
tion in a medium containing vortices, the vibrations being per-
pendicular to the direction of propagation.
Let the waves be plane-waves propagated in the direction of z,
and let the axis of x and y be taken in the directions of greatest
and least elasticity in the plane zy. Let # and y represent the
displacement parallel to these axes, which will be the same
throughout the same wave-surface, and therefore we shall have x
and y functions of z and ¢ only.
_ Let X be the tangential stress on unit of area parallel to x Wy
tending to move the part next the origin in the direction of 2.
Let Y be the corresponding tangential
stress in the direction of y.
Let k, and k, be the coefficients of
elasticity with respect to these two kinds
of tangential stress; then, if the medium
is at rest,
i pe
dy.
ie a 2 dz
Now let us suppose vortices in the atime whose maloaiies
are represented as usual by the symbols a, 8, y, and let us sup-
pose that the value of « is increasing at the rate = on account
of the action of the tangential stresses alone, there being no
electromotive force in the field. The angular momentum in the
stratum whose area is unity, and thickness dz, is therefore in-
creasing at the rate = ae dz; and if the part of the force Y
dt
which produces this effect is Y', then the moment of Y’ is — Y'dz,
Linde
lS pe
so that Y'= in a
The complete value of Y when the vortices are in a state of
* Phil. Mag. April 1861.
92 Prof. Maxwell on the Theory of Molecular Vortices
varied motion is
‘ dy 1 de
Y= eae eae ae
Similarly, ey: dee ered ee
A Tet Bae at
The whole force acting upon a stratum whose thickness is dz
and area unity, is ae in the direction of 2, and —— ue 5 ae in di-
rection of y. The mass of the stratum 1s pdz, so aa we have
as the equations of motion,
i dX _, de, dl de
Pade — de de dz dn ae’
dty WY _, ty _ dl de
Eh ERM a
(146)
Now the changes of velocity = and = are produced by the
motion of the medium containing the ses which distorts
and twists every element of its mass; so that we must refer to
Prop. X.* to determine these quantities in terms of the motion.
We find there at equation (68),
d d d
DB OU aii yg OR ta rae . « (68):
Since 6x and dy are functions of z and ¢ only, we may write
this equation
ay OO dee)
di ‘ded’ |
and in like manner, be ae oe] eae
qB_ dy |
uated |
1
so that if we now put k,=a"p, k, =p, and vis = y=c?, we may
write the equations of motion
dz .d*x | 4 dy
de" ge *° ded? |
148
d2y 32 d?y » Bx ( )
ade dz® Oe dt ?
These equations may be satisfied by the values
x= A cos fdas Dae
y= B sin (nt—mz+a), Me
* Phil. Mag. May 1861.
applied to the Action of Magnetism on Polarized Light. 93
provided ;
(n? —m?a?) A = m?nc?B,
and (n? —m?b*) B= m?nc?A.
Multiplying the last two equations together, we find |
(n? —m?a?) (n?—m?b?) =min?c*, . =. =. (151)
an equation quadratic with respect to m?, the selution of which is
rs 2n?
~ 24 RE V (a— 02)? + ante
These values of m? being put in the equations LeU will each
give a ratio of A and B,
A @&@—l?F VW (a? —b?)? + 4n2c4
5. igh 2a eee a
. (150)
Q
(152) |
which being substituted in equations (149), will satisfy the ori-
ginal equations (148). The most general undulation of such a
medium is therefore compounded of two elliptic undulations of
different eccentricities travelling with different velocities and ro-
tating im opposite directions. The results may be more easily
explained i in the case in which a=6; then
2
m= ———, and AFB. . (158)
ane
Let us suppose that the value of A is unity for both vibrations,
then we shall have
cos a id Su) + cos (ni a )
— ae pea
me —nc V a? + nc)’
Nz
——sin Bis dl + sin (ne— —=),
( WV a? + ne?
The first terms of x and y represent a circular vibration in the
negative direction, and the second term a circular vibration im
the positive direction, the positive having the greatest velocity of
propagation. Combining the terms, we may write
a2 =2 cos (nt—pz) cos al (155)
y=2 cos (nt —pz) sin gz, ou wae cha ts
(154)
where
n nN
- 2 V7 a? —nc? |
r
and n n | oe.
= —- ——.
IV e@—ne 2Va2+nce?
These are the equations of an undulation consisting of a plane
94 On the Action of Magnetism on Polarized Light. °
vibration whose periodic time is oa and wave-length pot,
propagated in the direction of z with a velocity. “ =v, while the
plane of the vibration revolves about the axis of z in the positive
direction so’as to complete a revolution when z= an
Now let us suppose c? small, then we may write
n ae
pai and g= 555 - ea.
| LBe 7
2B sara es
and “SRGLINEH that c = ean pry, we find © |
aS wy ere (ls)
. Le 9 p 20 e ® e i
Here 7 is the radius of the vortices, an unknown quantity:
p is the density of the luminiferous medium in the body, which
is also unknown ; but if we adopt the theory of Fresnel, and
make s the density in space devoid of gross matter, then
p=, ee 8 ee
‘where 7-is the index of refraction.
On the theory of MacCullagh and Neumann,
PSS. 5 0) 5, upuaud Seema
in all bodies. |
pw is the coefficient of magnetic induction, which is \unity in
empty Space or in air.
_ y isthe velocity of the vortices at their circumference esti-
mated in the ordinary units. Its value is unknown, but it is
proportional to the intensity of the magnetic force.
Let Z be the magnetic intensity of the field, measured as in
the case of terrestrial magnetism, then the intrinsic energy in air —
per unit of volume is
87 Sar’
where s is the density of the magnetic medium in air, which we
have reason to believe the same as that of the luminiferous
medium, We therefore put -
ya hy en
TS
is the wave-length of the undulation in the substance. Now
if A be the wave-length for the same ray in air, and 7 the index
On the Composition, Structure, and Formation -of Beekite. 93
of refraction of that ray in the body, |
: Reape aay) wiids Oicicaltls (162)
a
Aina v, the velocity of light in the substance, is related to V, the
rege of light in air, by the equation
o= 5: e @_-e 4 . ® a : (163)
‘Hence if z be the thickness of the substance through which the
ray passes, the angle through which the plane of ‘polarization
will be turned will be in degrees,
te)
ae =
g= 3 ery Picweatyece | se dea
or, by what we have now staal
In this expression all the quantities are known by experiment
except 7, the radius of the vortices in the body, ands, the density
of the luminiferous medium in air.
The experiments of M. Verdet* supply all that is wanted
except the determination of Z in absolute measure; and this
would also be known for all his experiments, if the value of the
galvanometer deflection for a semirotation of the testing bobbin
in a known magnetic field, such as that due to terrestrial mag-
netism at Paris, were once for all determined.
XV. On the Composition, Structure, and Formation of Beekite.
By Artuur H. Cuurcnu, B.A. Oxon, FsC.S.+
[With a Plate. ]
Pa ea occurs in the triassic red conglomerate of Torbay
and its neighbourhood, an interesting siliceous substance
(generally considered to be a variety of hornstone), which offers
a problem not only to the geologist and palzontologist, but also
to the chemist. The Beekite is, in fact, not a mineral merely,
but a fossil which has been more or less completely mineralized,
the mineralization having, however, been effected in a way not
very easy to understand. In the present paper, after having
quoted some authorities in order to show the geological character
and position of Beekites, I shall endeavour to throw some light,
* Annales de Chimie et de Physique, sér, 3, vol, xli, p. 370.
+ Communicated by the Author.
96 7 Mr. A. H. Church on the Composition,
by means of evidence deduced from experiments and observations,
on the chemical and physical relations of these bodies.
In addition to the localities near Torbay, it has been stated
that Beekites occur near Lidcot in Somersetshire; also in the
north of Scotland; while foreign localities for them have likewise
been mentioned. ‘Their appearance varies so much that it is
scarcely possible to give such a description of their general form as
shall include all the varieties ; yet figs. 1-4 and 8-13 in Plate
III. may perhaps indicate some of their chief characteristics. We
shall have to recur to several features shown in these figures
further on. A specimen of Beekite from Vallecas near Madrid,
in the British Museum, presents a very close resemblance to some
of the more common Torbay forms, but at the same time is re-
markable for unusual translucency.
“The Beekite is not exactly a fossil, but an incrustation of
chalcedony upon a nucleus of coral, and occasionally, but rarely,
upon fragments of limestone. The chalcedony is deposited in
concentric circles around minute tubercles. These are very
sharply defined in the Beekites that are freshly dug out of the
cliff above high-water mark; but if picked up on the beach, or
taken from the cliff where tide-washed, they are smoother and
have lost much of their peculiar character. .... Their form is
irregular ; most commonly they are more or less round. They
take their shape from the fragments of coral upon which the
chalcedony has been deposited, and which having become more
or less decomposed and disintegrated, the chalcedony forms a
kind of shell or case enclosing its remains. The coral within
is found in various stages of decomposition,—in some specimens
filling the interior, in others nearly so, allowing of so much move-
ment that when shaken the contents may be heard to rattle; in
others the coral is so completely broken down that only a powder,
consisting of the carbonate of lime and some brown particles of
organic matter, remains. ‘The interior of the siliceous shell has
often the markings of the original coral.” ,
In these remarks, which I quote from a letter by Mr. Keste-
ven*, we have little more than a repetition of parts of Mr. Pen-
gelly’s paper on Beekites read before the British Association in
18567. ‘The description given of these fossils, and the theories
which have been started to account for their present state, differ
but little.
Beekites, unlike the pebbles of the conglomerate in which
they occur, do not exhibit signs of having been water-worn ; it
is allowed consequently that their organic bases must have been
silicified in situ. So say Messrs. Pengelly and Kesteven. But
* Athenzum, August 27, 1859.
+ British Association, 1856, p. 74.
Structure, and Formation of Beekite 97
by what agency was this change effected? Mr. Kesteven extends
the suggestion made in the Report of the Commission of the
French Academy of Sciences on Water-glass, concerning the origin
of flints, agates, petrified woods, &c., and applies it in the case
of Beekites. In these instances a slow decomposition of an
alkaline silicate by means of carbonic acid is supposed. Mr.
Kesteven thus describes his theory :—‘‘ Fragments of coral,
broken by the waves, and deposited with the beac now consti-
tuting rocks of red conglomerate, would retain a certain portion
of chlorides, while their decomposition would liberate the carbonic
acid which would separate the alkaline constituent of siliceous
springs, and cause the deposition of silica upon the nucleus of
coral. That a similar siliceous deposition is not found upon the
surrounding deposits is satisfactorily explained by the non-libe-
ration of carbonic acid from the pebbles, into the composition of
which its elements did not enter. This view is strengthened by
the fact of the non-silicification of the nucleus itself, the silicate
being arrested on its surface by the escape of carbonic acid.
Furthermore, where chalcedony presenting the Beekite characters
has been found upon stone, it has been limestone, from which it
is possible carbonic acid may have been disengaged at the time
of deposition. The characters of chalcedony, as presented in
Beekites, moreover, approach very closely to those of the siliceous
incrustations of the Geyser springs m Iceland.”
Mr. Pengelly’s view is as follows. He says, “It seems pro-
bable that after the formation of the triassic conglomerate, some
of the calcareous pebbles in it underwent decomposition, that
water holding chalcedony in solution, and passing through the
rock, deposited the chalcedony on the nucleus: the nucleus in
some cases continued to decompose, by which it was wholly or
partially detached from its envelope, and not unfrequently re-
duced to dust. Suppose the decomposition to have commenced
at various points or centres on the surface of the pebble, the
chalcedony deposited at these points would form central tuber-
cles; let the decaying process extend from and around these
centres, the chalcedony deposited around these centres would
form a ring,’”’—and so on.
Mr. Pengelly states in the paper just referred to, that “ the
interior of the Beekite is calcareous,” and that “the nucleus
appears to be always a fossil, and is either a sponge, a coral, a
shell, or a group of shells.....The organic structure is fre-
quently preserved on the imner or concave surface of the enve-
loping crust, even when the nucleus is reduced to powder. Oc-
easionally organic traces are discernible on the exterior surface
of the chalcedony ; but such cases are not frequent. Some of
Phil, Mag, 8. 4. Vol. 23. No. 152. Feb, 1862. i
98 Mr. A. H. Church on the Composition,
the nuclei are slightly siliceous, but in no case more so than
ordinary limestones are.”
A correspondent at Exeter first directed my attention to
these singular fossils, and not only gave me a large number of
specimens, but much valuable information and many useful hints.
The following interesting remarks are extracted from a letter
lately received from this gentleman: to some of his remarks I
shall have occasion to refer when detailing my own theory and
experiments. |
“The chief locality for them in this county is Torbay: I have
heard that they are found at the Ness near Shaldon, and I have
a few from North Tawton. Beekites proper are confined to the
New Red Sandstone, although a structure very near akin to it is
found in the Mountain Limestone (I have one specimen) ; the
same may be said of the Lias and the Greensand, but there the
rings (concentric ridges) are not so large. I have often thought
whether this peculiar arrangement is not due to the displacement
of carbonate of lime by silex which takes place in fossilization, as
the shells must originally have been carbonate of lime. The
experiment I tried with hydrofluoric acid was on mammillated
or bubble chalcedony, to see if there were any connexion between
this structure and the Beekite. I thought the latter was the
former with the tops of the mammillations either dissolved or
rubbed off ; the appearance of the chalcedony after the application
of the acid rather favoured that supposition. I have seen Beekites
with the mammillated structure on a part of them, and the
Beekite structure on the other, passing gradually from the one to
the other. The mammillated structure I speak of is found
abundantly in the interior of the flints at Haldon, and perhaps
in the Chalk also. I shall send you the Beekite which effervesces ;
you will find that as the carbonate of lime is dissolved, the rings
more and more appear. I shall also send a few specimens of
shells from the Greensand of Haldon. With your glass you
will see that they are entirely made up of rings, such as are
shown in the Beekites on a larger scale.”
Both Mr. Pengelly and Mr. Kesteven speak of the fragments
of coral and of limestone, to which they refer as the basis of
Beekite, as undergoing decomposition spontaneously ; and it
seems that most other writers who have attempted an explanation
of the phenomena presented by these singular fossils, have made
the same assumption. We meet, for instance, with such explana-
tions as the following :—“ It seems probable that, after the forma-
tion of the conglomerate beds, many of the calcareous pebbles
in them continued to decompose at the surface, and thus allowed
water, holding siliceous matter in solution, to pass through the
rock ; and that, m passing, it deposited the chalcedony on the
Structure, and Formation of Beekite. 99
diminished pebble, which in most cases continued to decompose.”
Of what nature is the decomposition of limestone which is here
spoken of ? and how did it origmate? or didit occurat all? The
whole problem before us resolves itself into two parts, which it
will be better to examine separately. We have to account for—
I. The chemical composition of Beekite; and
II. Its physical appearance.
I. The chemical constituents of Beekite vary less both im
nature and proportion than the outward appearance of different
specimens would lead one to infer. I have been unable to find
more than one recorded analysis; it is given by Mr. Kesteven in
the letter to which I have already referred, and is as follows.
A Beekite weighing 1040 grains contained, according to his
statement —
grains. per cent.
Miepounte of lime’ ~... °. °. 470 : 45°20
Bialccdony = . 6, inn ¢ 540 ‘ 51°93
Sesquioxide of iron and alumina = 5 “46
Carbonaceous matter, residue of
animal matter of coral . . 25 2°41
1040 100-00
These results, which I presume are to be regarded as approxi-
mative only, must not be taken as indicative of the general
composition of Beekite ; for I have examined qualitatively or quan-
titatively nearly twenty specimens, and in only two cases have I
found more than 3 per cent. of carbonate of hme: even where
the appearance of the mass most forcibly recalled the original
coral, the proportion was no larger. In the two cases where
carbonate of lime occurred in considerable quantity, the Beekite
was singularly compact. Parts of one specimen did not show
the characteristic concentric ridges of chalcedony until the car-
bonate of lime in which they had been imbedded was dissolved
away by means of an acid; while the other specimen, which is
given in PI. III. figs. 10, 11, 12, although showing, when cut and
polished (fig. 10), or when in thin section (figs. 11, 12), a di-
stinet coral throughout, was enveloped in a siliceous coat, but
possessed a calcareous nucleus. In this case the portions of the
coral towards the exterior of the mass had been replaced by
silica, so far as the cell-walls of the polypidoms were concerned,
the cells being partly filled with carbonate of lime, the interior
portions remaining calcareous throughout. Occasionally a
Beekite is found contaiming a purely inorganic nucleus of lime-
stone, but in a large number of specimens there is actually no
carbonate of lime whatever, all the lime present being in the
form of silicate.
H 2
100 Mr. A. H. Church on the Composition,
In consequence of their hardness, and the necessity of fusing
them with carbonate of soda, Beekites, previous to analysis,
should be disintegrated by igniting them and throwing them
into cold water. The fragments are to be ground carefully,
boiled with concentrated nitric acid (this solution being added
to the original liquid for further examination), and the residue
fused with carbonate of soda and treated in the usual way. It
would be tedious to describe the various analytical processes
found necessary in all their details; the following Table contains
the main results. The spectroscope was used with success for
the detection of minute traces of several elements present in too
small a proportion to be recognizable by reagents.
Specimens, TL. i. 1G 1 A Ve VE VII.
Maltese. cheek. cae 90°707 | 93-037 | 93°115 | 92-7 92-707 | 91:96 | 92:119
Time ew. obtebeceee “44 2°26 2°76 3031 27 1°35 3°03
Alumina & phos-
phate of alumina ‘O75 | trace 002 ‘06 "012 | trace trace
Sesquioxideofiron| 5:09 |= 1:01 097 ‘O7 ‘78 2°94 2°16
Magnesia ......... “002 ‘O14 ‘007 | trace trace trace ‘021
NOURLS ce tee- ance 03 ‘O75 ‘O19 "017 | trace trace trace
POtassa’ cif--5 086s] trace trace trace trace traco trace trace
Latha, Sesto se tof oe aN be ite trace
Waterss. cs civ: i 1-072 1:56 ‘96 1:76 21 aT
Carbonic acid and
organic matter...) 2:27 1:53 2°44 2:51 1:97 1-64 2:29
Chlorine (probably
combined with
the sodium) ... ‘04 "O91 | trace trace trace trace trace
BOSS seers reese: 656 cold fe "652 ‘O71 ‘Ol “21
eee
Specimen II. of the above synopsis contained also a minute
trace of iodine, while lithia was detected in another specimen
not further analysed. The compact specimen of Beekite figured
in PI. III. fig. 10, and to which I have already alluded, had lost
after removal of the carbonate of lime by an acid, about 3th of
its weight. The carbonate of lime was situated almost altogether
in the central portion of the specimen; the exterior did not
show any signs of its presence when touched with an acid.
In the preceding Table I have not attempted to combine the
various bases and acids together. The greater part of the lime
existed, I believe, as silicate, and the iron and traces cf other
bases were probably in a similar state. In a few mstances a
portion of carbonate of lime was present, and occasionally a
combination of lime with some organic substance. The loss
partly represents the sulphuric acid and other undetermined
constituents of the Beekites.
I have not included in the Table of Analyses the examination
Structure, and Formation of Beekite. 101
of several Beekites in which no lime whatever was found. Their
composition scarcely differed from that of flint, except m the
larger per-centage of iron which they contained.
The chemical causes concerned in the formation of Beekite
appear to me of peculiar interest. It is reasonable to believe
that the removal of carbonate of lime froma shell or a coral, and
its replacement by. silica, has been effected by the agency of
water holding carbonic acid and silica in solution together. Such
solutions occur frequently in nature, not only in springs lke
those in the neighbourhood of the Iceland Geysers, but in several
places inGreat Britain,—silica being, indeed, an almost invariable
constituent of common waters. We may argue, then, that such
a solution filtering through the débris of organic forms, not only
removes their carbonate of lime by virtue of the solvent power
of its carbonic acid, but deposits some silica instead. This sup-
position has been tested and confirmed by experiment. A frag-
ment of a recent coral was fitted into the neck of a funnel, and
al per cent. solution of silica (prepared from silicate of potash
by Graham’s dialytic method), containing a little carbonic acid
gas, was allowed to drop slowly on the coral and filter through :
after a time the liquid ceased to pass. ‘The filtrate contained no
silica, but much carbonate of lime. The fragment of coral had
lost nearly all its lime, but had retained its structure in great
measure; it was, however, covered with a thick film of gelatinous
silica, and was very soft. In such a reaction as this, it is not
unlikely that a small portion of lime would be retained as sili-
cate. Where the process of silicification has gone on to its com-
pletion, we have a tolerably exact reproduction im silica of the
original organism, the result being, in the case of corals,
sponges, &c., a light hard porous mass, occasionally hollow, of
chalecdony. But where the process has been arrested by the
stoppage of the flow of the siliceous solution, the central portions
of the Beekite have retained nearly their original composition as
well as structure ; and in some rare instances it would seem that
a subsequent deposition of carbonate of lime, in the spaces not
occupied by silica, had taken place.
IJ. Of the physical aspect of Beekite, the quotations made in
the earlier part of this paper, taken in connexion with the
illustrations in Plate III., will give some idea. The mammilla-
tions and concentric ridges (figs. 1-4, 9 & 13), though frequent,
are not invariably present. Besides the organic structure (shown
more or less distinctly in figs. 2, 9, & 10-12), Beekites often
display one or more lines and furrows on their surface, quite
independent of the mammillations. These lines indicate for the
most part certain planes of cleavage or fracture, as shown in the
upper and lower sides of fig. 2 and the light side of fig, 3.
102 On the Composition, Structure, and Formation of Beekite. °
These lines are referable rather to the effects of pressurethan to
an organic origin,—the frequent angularity of the specimens
pointing in the same direction.
In a fragment of a silicified Pecten from the Greensand of
Haldon, Devon, the elevated ridges, characteristic of the shell,
are preserved intact, notwithstanding the complete displacement
of the carbonate of lime by silica, and the assumption by the
silica of that arrangement in concentric rings characteristic of
most Beekites. In the present specimen of shell, some of the
systems of rings are partly situate in a furrow of the exterior
surface, bend upwards, and follow the curve of a ridge, and then
dip into another furrow: the inner aspect of the shell bemg
level, shows no corresponding contortions of the systems of con-
centric ridges. In like manner, in the Beekite proper, silica
displaces rather than increases the original substance,—for the
organic structure is generally traceable in every part of the
tubercles and ridges, even to their summits,—bemg im fact more
conspicuous on the exterior surface of most of the hollow speci-
mens than on their interior.
The tendency to deposition in a circular form, though not
peculiar to this substance, is seen in many other varieties of
silica—stalagmitic quartz or quartz-sinter, for instance, such as
that from the Geysers of Iceland, and the hot springs of Luzon
in the Philippine Isles. A specimen from the latter place is»
represented in figs. 5 & 6. EHyed agate (fig. 7) shows the same
arrangement. Float-stone from Menil Montant, near Paris,
when examined with a lens, often displays mimute beads and
concentric ridges ; while menilite, or liver-opal from the same
locality, presents an appearance very closely resembling that of
the Beekite No. 9.
The annexed letter from Dr. Gladstone, commenting as it does
on both the physical and chemical questions under discussion,
may not inappropriately conclude the present paper :—
“ My pear Mr. Cuurcu,—Your Beekites seem to me very
interesting, not only in a chemical and geological, but also in a
physical point of view, as affording a remarkable illustration of
the tendency of certain bodies to assume a globular form during
deposition. I say ‘ deposition,’ because it is evident that the
Beekites are not fossils owing their mammillated appearance to
the organic form which has been silicified, but are rather deposits
on some substratum, which may be a coralline, a sponge, a shell,
or even a piece of stone. Yet this deposition seems always
accompanied by the replacement of part, or the whole, of the
carbonate of lime by silica. |
“ Many of the concentric globular deposits in your specimens
bear a striking resemblance to the globular deposits of carbonate:
Prof. Regnault on the Specific Heat of some Simple Bodies. 103
of lime to which Mr. Rainey has recently drawn attention as
occurring in animal tissues during the formation of shell*,
bone, &c., and which he has artificially produced by the slow
formation of carbonate of lime in the presence of gum or albu-
men. In all probability the physical forces concerned in the
buildmg up of the calcareous and the siliceous globes are the
same. In many of the specimens of Beekite, the concentric
masses look as though they had been more perfect at one time,
but the outer portion had been disintegrated before the mass had
become thoroughly hard: at least they suggest that idea to
me; and if true, that forms another link of analogy between
them and the phenomena described by Rainey.
“Tt seems at first sight difficult to understand how, if the sili-
cification of, say a coral, begins on the outside all round, it can ad-
vance to the interiér, and how the carbonate of lime within can he
removed ; but it must be remembered that the silica, when first
deposited, was in the gelatinous condition, and permeable to
salts in solution, as Prof. Graham has shown in the case of other
of those substances-which he designates ‘ colloids.’ It is only
gradually that such a gelatinous globular mass would pass into
the rigid flint which we now handle. In the mean time, too, it
would be subject to all those changes of form, or that tendency to
cleavage, which pressure might superinduce.
“‘It may be worthy of experiment to see whether the pellicle
formed by the gradual gelatinization of silica in solution ever
assumes a form at all corresponding with that of the Beekites.
‘| remain, yours ever truly,
“23 Pembridge Gardens, “J. H. Guapstonz.”
Dec. 14, 1861.”
XVI. On the Specific Heat of some Simple Bodies.
By M. V. Reenavurt.
[With a Plate. ]
PURPOSE bringing together in the present paper the expe-
riments made in the last few years on the determination of
the specific heat of some simple bodies which I have hitherto
not been able to obtain in sufficient quantity or of adequate purity.
The methods which I have used, differ little from those which
served for my former investigations (Annales de Chimie et de
Physique, 2ud series, vol. lxxii. p. 20); I have, however, advan-
* The structure of pearls, when compared with these globular bodies,
leads one to believe in their original identity, only the former are detached.—
met. C.
+ Translated from the Annales de Chimie et de Physique, September
1861, by Dr. E, Atkinson.
104 Prof. Regnault on the Specific Heat of seme Simple Bodies.
tagcously modified the bath which I employed for raising the body
to a temperature near 100°, inasmuch as I have substituted for
the charcoal fire by which the water in a boiler was kept boiling,
a gas-lamp which effects the same purpose, and does not require
the presence of the operator.
The substance submitted to experiment is usually placed in a
brass wire-gauze basket M, provided on the inside with a cylinder
of brass-foil, in which is fitted the bulb of the thermometer T
which marks the temperature of the substance. This basket is
suspended by a silk thread, which traverses a hollow metallic
stopper R. The thermometer T is inserted. in a stopper to
such a depth that the division 100 degrees only projects above
the bath by about a centimetre.
The hot bath consists of three concentric envelopes. The
internal cylinder A, in which is arranged the basket and the
thermometer, is soldered hermetically both at the top and the
bottom to the external envelope. Its upper orifice is closed by
the stopper R; its lower orifice by a slide m, so long as the
basket with its contents is being heated. Between the external
envelope C and the cylinder A, there is an intermediate envelope
fixed to the superior lid, and reaching below to the conical part
of the external envelope. The bath is supported by a wooden
stand D D P P’, which acts besides as a screen in preventing the
radiation of heat on the calorimeter H, when this latter occupies
the place indicated in the figure (PI. II. fig. 1), at the instant
of immersing therein the heated basket.
The boiler V communicates with the bath bya tube a3, which
traverses the intermediate envelope, and by which steam reaches
the annular space BB round the internal cylinder A. This
steam escapes by the apertures oo on the side opposite that
by which it enters. The steam descends by the external
annular space CC, and the condensed water re-enters the boiler
by the tube ed. The steam which has retained its gaseous state
passes from the bath by the tube ef into the larger tube G, ter-
minated above by a narrower tube hz, which is surrounded by
cold water continually renewed. The steam is completely con-
densed in this refrigerator, and returns to the boiler by the tube
kp: its temperature on so doing is very near 100°, for at G it
traverses the steam which is constantly coming from the bath.
Ebullition is produced in the boiler V by means of a gas-lamp
W ; it goes on continuously without necessitating the presence of
the operator; the same quantity of watcr serves for an indefinite
period, for it always returns without loss to the builer. This
new arrangement renders the operation very simple, and allows
the operator to proceed with other work.
If the water in the boiler V is replaced by other velatile liquids,
Prof. Regnault on the Specific Heat of some Simple Bedies. 105
stationary temperatures, very different from 100° may he obtained
in the bath. With bisulphide of carbon the temperature is 46° ;
with chloroform 60°; with alcohol 78°; with oil of turpentine it
is 157°, &c. It is even easy to obtain in the bath a stationary
temperature perfectly fixed beforehand; for this purpose it is
sufficient to place in the boiler V a liquid whose temperature
under the ordinary atmospheric pressure is very little different
from that desired in the bath, and then to boil this liquid under
a pressure either greater or less than that of the atmosphere, so
that the thermometer exactly indicates the desired temperature.
‘In this ease the tube /2 is connected by means of a leaden pipe,
with an air-reservoir, the pressure of which may be varied at
pleasure by a suction or forcing-pump.
I shall not revert to the method of conducting these experi-
ments; it has already been sufficiently described in my previous
memoirs. -
When it is desired to determine the specific heat of a body
which liguefies or even softens much at temperatures slightly
above that of the surrounding air, it cannot be heated in the
bath, and recourse must be had to the inverse method, which
consists in cooling the body in a cooling mixture, and determi-
ning the fall of temperature which it produces by its immersion
in the calorimeter. Ihave described (Ann. de Chim. et de Phys.
vol. xlvi. p. 270*) the apparatus I used for this purpose. This
apparatus I have replaced by another, easier of manipulation,
and by which the tempcrature can be better regulated. The
cold is produced by the evaporation of a very volatile liquid in a
continuons current of air, which can be regulated at will: fig. 2,
Plate II. represents its vertical section. In a central tube A,
like that in fig. 1, and provided at both ends with the same
stoppers, is placed the basket M containing the substance
whose specific heat is to be determined. It is surrounded by a
second tube B of the form shown in the figure, and which is her-
mctically soldered above and below to the tube A. A third tube,
C, surrounds the two others, and forms a protection to the tube
B against immediate contact with the surrounding air, and pre-
vents the deposition of dew.
On the upper circular base of the tube B are two tubulures ;
on one of which is soldered the trifurcate tube badc; through
the other a bent tube e fg passes, provided with a stopcock 7, and
‘which descends to the bottom of the tube B. The whole system
is placed on a support provided with screws, like that in fig. 1.
The volatile liquid, ether or bisu!phide of carbon, is poured
into the tube B through the orifice d, which is then closed. In
order that the level of the liquid may not sink below hi in con-
* Phil. Mag. vol. xii. p. 498.
106 Prof. Regnault on the Specific Heat of some Simple Bodies.
sequence of too much evaporation during a lengthened experi-
ment, the tube B is somewhat larger towards the upper part.
A current of air is driven through the tube efg, either by
means of an aspirator adapted to the tubulure c, or by a force-
pump, or by a pair of bellows applied directly to the tube e fg.
As I have at my disposal large reservoirs in which a force-pump,
moved by a machine, compresses the air to several atmospheres
in a very short tine, the operation is very simple; a large reser-
voir of compressed air communicates with the tube efg. By
regulating the stopcock 7, a more or less rapid current of air
traverses the ether of the tube B, and escapes saturated with
vapour through the tubulure ac: the temperature rapidly sinks
in consequence of evaporation. When the ether is near the desired
temperature, which is seen by a thermometer whose bulb dips in
the ether, the stopcock is turned so as to stop the cooling, and
with a little practice the temperature may be maintained station-
ary as long as is desired. ‘The thermometer T, whose bulb is in
the basket M, is necessarily behind that which is immersed in
the ether; but the two thermometers gradually approximate when
the current of air is suitably regulated. The basket M is only
immersed in the calorimeter when equilibrium is almost established.
The temperatures obtained by this apparatus are not so lowas
those obtained by means of freezing-mixtures of ice and crystal-
lized chloride of calcium: thus, when the external temperature
is +20°, it is difficult to keep the ether stationary at a lower
temperature than —12° C.; under the same circumstances the
temperature only sinks with bisulphide of carbon to —8°:
but, from the readiness with which low temperatures are kept
stationary for a long time, more accuracy is obtained in the
determinations. 3
By a precisely similar arrangement, the temperature of a liquid
can be gradually lowered and kept stationary at any desired point.
I have often used it to determine the point at which a liquid
solidifies when this solidification takes place between—15°
and +10°. The inside tube A is closed at the bottom (fig. 3) ;
the liquid is placed in it along with a thermometer which indi-
cates the temperature and serves as an agitator. By means of a
current of air, the temperature of the ether is lowered gradually
and as slowly as required; the thermometer immersed in the liquid
sinks in a like degree to the point at which solidification begins;
its temperature then becomes stationary. Toinvert the process,
the current of air is diminished or completely stopped. The
temperature of the ether then rises; the liquid should be conti-
nually agitated with the thermometer, and it should be ob-
served whether, when it commences to rise, the solidified part
has entirely resumed the liquid state.
Prof. Regnault on the Specific Heat of some Simple Bodies. 107
If for special experiments it is desired to obtain temperatures
lower than —40°, some liquid ammonia, which is prepared
easily and in abundance by an apparatus which I have described
(Mémoires de ? Académie des Sciences, vol. xxvi.), should be placed
on the annular space. The air-current passing through the liquid
ammonia with sufficient velocity, lowers its temperature to about
—80°*. By regulating the current, the temperature may be
kept stationary at any point between —40° and — 80°; the great
latent heat of evaporation of ammonia renders it very easy to do
this.
Magnesium.
The specific heat of magnesium has not hitherto been deter-
mined. I used for this experiment a beautiful specimen of
magnesium, lent by M. Rousseau. The metal was prepared
by decomposing chloride of magnesium by sodium at a high
temperature ; a single regulus was formed with a considerable
depression in the centre. The regulus was wrapped in several
pieces of lead-foil to preserve it from contact with the air.
Magnesium can be kept for a long time in dry air without under-
going any perceptible alteration.
Mee 2! 1S O70 Q2Qer-99
ead. . . 498-410 298-69
PS! verte 98°28
PT. ve sO MOL 22°°99
Me se SO OLOU 3°-9203
fae ee. AGS 69 4668-69
eee . = sh) OSh2466 Ost-2533
Mean ofC . .. . O8t2499,
This specific heat, multiplied by 150, the number now usually
taken as the atomic weight of magnesium, gives the product
37°49. Magnesium is consequently included in the law of spe-
cific heats of simple bodies, and its specific heat confirms the
accuracy of the formula, MgO, given to magnesia.
Lathium.
In the memoir which I published (Ann. de Chim. et de Phys.
ord series, vol. xlvi. p. 276), I gave the specific heat of chloride of
lithium, and, reasoning on this datum, I endeavoured to show
that the atomic weight which has been adopted for lithium,
80°37, ought to be halved, that is, reduced to 40°18. The for-
mula of lithia would then be Li?0, like those of potash and soda,
which, according to my experiments, should be written K2O and
Na*O. But for a convincing proof in the case of lithia, it was
* MM. Loirand Drion have recently announced that by the evaporation
of ammonia in vacuo a cold of — 96° is obtained (Phil, Mag. vol. xxi. p. 495).
108 Prof. Regnault on the Specific Heat of some Simple Bodies.
desirable to determine the specific heat of metallic lithium.
M. Debray provided me with an opportunity, by placing at my
disposal a small quantity of lithium which he had carefully pre-
pared by Bunsen’s method. It consisted of a large globule
weighing about a gramme, and of 12 grams of the size of a
small pea. I endeavoured in vain to fuse these small grains
into a single globule ; but the layer of oxide with which they were
coated prevented them from completely welding. I preferred
to operate solely with the large globule, which in the cold could
be readily worked by the hammer, and presented a very lustrous
surface.
To preserve the metal from contact with the air during the
experiment, it was hermetically enclosed in a leaden box, repre-
sented in fig. 4. The globule of lithium was first formed into a
cylinder by pressure in a lapidary’s steel mortar; while at the same
time a hollow leaden cylinder abcd had been made, in which
the plunger of the mortar fitted, as well as a leaden piston P.
The cylinder of lithium L having been placed in the hollow
cylinder of lead, the piston P was inserted above it, and briskly
struck with a hammer in order to enclose the lithium completely.
The weight of the lithium being known, as well as that of the
leaden vessel, the calorific capacity of the whole arrangement
was determined by experiment; and as that of the lead is known,
it is easy to calculate the specific heat of lithium. For the sake
of greater accuracy, before placing the lithium in the leaden
vessel, several experiments were made with this vessel provided
with its piston: these determinations gave exactly the calorific
capacity found by calculation for the weight of lead in the vessel.
The following are the results of three experiments made with the
lead and lithium together :—
Matto ne (OSE O45 08-945 Os-945
iRieadk 7-2 NOSE 985 1098-985 1098"-985
Gh Via a O27. O97, Sar
Cs ee Gr a6 26°°89 26°°83
NG! 3)“. 0) 12750856 2°0555 2°:0588
AY oH. eee MOetoo. 1518-55 1518-55
Oe alo ee) sO OAL 0:9405 0:9407
Mean-o c). 2s 2e 3ORSL08:
The calorific capacity of lithium is very considerable, being
almost equal to that of water. Taking its atomic weight at
80°37, the number assigned by chemists to lithium, the product
of its specific heat into its atomic weight would be 75°61. But
assuming that the atomic weight is 40°18, which gives for lithia
the formula Li?O, we obtain the product 37°80, and lithium then
completely satisfies the law of the specific heats of simple bodies.
«
Prof. Regnault on the Specific Heat of some Simple Bodies. 109
MeEtTALS WHICIE ACCOMPANY PLATINUM.
I have had frequent occasion to determine the specific heat of
some of the metals which accompany platinum (Ann. de Chim. et
de Phys. 2nd series, vol. Ixxii.; 3rd series, vol. xlvi.), but [had
doubts as to the purity of several of the specimens used. M.
Chapuis lent me, in June 1857, several specimens of rhodium,
osmium, and iridium, which he had prepared with the greatest
eare by the methods described by him in the following Note :—
1. The osmium was obtained by roasting osmium-iridium.
Osmic acid, condensed in a solution of caustic potash, was con-
verted into osmite of potash by alcohol, and then washed for a
long time with a solution of chloride of ammonium. The double
chloride of osmium and ammonium was heated in a current of
hydrogen, and the spongy osmium thus formed united by com-
pression into a single ingot.
2. The iridium was obtained by heating with nitre the residues
of platinum-mineral previously freed from osmium. The product,
washed with water, was treated with aqua regia, and the liquors
precipitated with chloride of ammonium. ‘The double salt was
ealcined in a platinum crucible, the temperature being slowly
raised. The metallic mass was again washed with a solution of
sal-ammoniac, and then heated in the muffle; a considerable
quantity of osmium was given off. After these operations it
was found that the iridium still contained perceptible quantities
of platinum, palladium, and gold. It was again treated with
weak aqua regia; and as the presence of foreign metals was still
apprehended, it was again fused with nitre, and the oxide thus
obtained treated with aqua regia. ‘The evaporated liquors gave
well-defined crystals of the double chloride of iridium and potas-
sium: the double chloride was heated in a crucible with car-
bonate of soda, and the iridium thus obtained was compressed
into a single cylinder by percussion.
3. The rhodium was extracted from the residues of the pre-
paration of indium. These residues, exhausted by the treatment
with aqua regia, were mixed with fused salt and then heated to
redness in a current of dry chlorine. The substance was then
treated with boiling water, and the solution gave, on evaporation,
beautiful octahedral crystals of the double chloride of rhodium
and sodium. ‘These crystals were redissolved in hot water, and
- sal-ammoniac added; on cooling, needle-shaped crystals of the
ammoniacal double chloride were deposited. This substance,
heated in a muffle, gave metallic rhodium. As some doubt still
remained of its purity, it was again treated with aqua regia, the
metallic residue again fused with common salt, and the mixture
heated in a current of dry chlorine. The substance was redis-
110 Prof. Regnault on the Specific Heat of some Simple Bodies.
solved in boiling water ; and the solution gave, by boiling, the
erystallized chloride of rhodium and sodium. From this salt,
treated as before, metallic rhodium was obtained, which was
compacted by percussion.
Osmium.
‘The osmium consisted of a single cylinder strongly compacted
by hammering. I only made one determination, the results of
which are as follows :—
My go ed Sas Wein OO AeS
Po os aw Le yeelges a GES Oas
Dy fete eb Se eee . . 548-980 548™-980
fate) 6 ORPOHIS er-Q515
Mem s 2°°97°40 96°°91
ieee ie, =. YB10 14°°25
pe. — VIN To-2089 1°°2043
A> ae . 466869 4662-69
seen sd p71. O-1207 071227
Mean’ .- .- .- O:217.
The product of the specific heat 0°1217 by the atomic weight
3250 is 39°55, which is comprised within the specified limits.
It may therefore be concluded that pure manganese is as duc-
tile as iron, and that its specific heat should be about 0°114.
Nickel.
In my first memoir “ On the Specific Heat of Simple Bodies,”
I gave the specific heat of a specimen of nickel which had been
prepared by calcining at a strong furnace-heat oxalate of nickel
contained in a closed porcelain crucible, this being enclosed in a
crucible lined with charcoal. This specific heat is 0°10863; if
multiphed by the atomic weight 350°0, which M. Dumas has
deduced from his last researches, the product 38°02 is obtained,
which agrees very well with the law of the specific heat of sim-
ple bodies. This proves the correctness of the formula assigned
to nickel compounds.
Since then I have had occasion to determine the specific
heat on some specimens of nickel which had been prepared by
different methods. M. Rousseau lent me nickel obtained by calei-
ning at furnace-heat a mixture of oxide of nickel and sal-ammo-
niae enclosed in an earthen crucible. The metal formed two
Phil. Mag. 8. 4. Vol. 23. No. 152. Feb. 1862.
114 Prof. Regnault on the Specific Heat of some Simple Bodies.
ingots, readily scratched by the file, and which were flattened
under the hammer. This nickel gave the following results :—
NES teca ke 8 LLETSOO 3118-00
ye ee. OOS KE, 97°°88
Cee Se AS 18°81]
EAGT Mae he 6°°2413 6°-1315
Alf ato .! 54 je4erOs 4.34898
OC atisewis. a6 010659 0°10845
Mean) eam O710758;
The product of the specific heat by the atomic weight 350 is
37°62. 3
The second specimen was lent me by M. Dumas, who had
great confidence in its purity. It consisted of three almost
spherical bullets, and could be readily filed :—
M . 229888 = 229888 = 2298-88 =. 22.9888 =. 8298-88
p . 10015. 18-5015, ; 25015 1e-50lo) ees Gis
er Aa 9 260 97°°45 97°°20 97°45
Ge 12:32 14°°54, 10°53 10°-69 11°12
Ad! -5°-4547 5°°3615 5°°5610 5°°5210 5°°5287
A . 422830 89 422830 0 42830 0 = 4.228780 = 422 8-30
C . 010970. O11169 ~O7:1100 (OLLO7G eG aeaitZ
Mean .. . -O-1108.
The product of this specific heat by the atomic weight is 38°78,
a number perceptibly higher than that found for the other speci- |
mens of nickel.
Cobalt.
In my first memoir I found 0°1071 for the specific heat of
cobalt. The metal had been prepared by heating at a strong
furnace-heat oxalate of cobalt pressed in a porcelain crucible,
which was itself enclosed in a crucible lined with charcoal. I
recently examined two ingots of the same metal which had been
prepared by M. Rousseau, by calcining at furnace-heat a mixture
of oxide of cobalt and sal-ammoniac. This metal was malleable,
and readily scratched by the file.
Mee) cee Se S05
pen eae date Oils
he, ewOreS
Bila eae co eaocrey
NBT hein yet! (i Np 2e:B OR
Rar yi. y ASAE OS
Corea os NOUS
1188-805
18-5015
97°-09
12°43
2°°5260
4348-98
0:10075
Mcatin ails yaks cD LODOAE
Prof. Regnault on the Specific Heat of some Simple Bodies. 115
This specific heat is much lower than that which I found for
metal prepared with the oxalate, and the product of the specific
heat by the atomic weight 350 is 35°33. I think that the
metal contained some foreign body.
M. Dumas placed at my disposal another quantity of cobalt
which he considered to be pure. One portion of it consisted
of small bars; the other formed three almost spherical bullets.
The metal was malleable enough to be flattened in the cold by
the hammer, and the file readily cut it; but the small ingots
grasped in a vice were broken when struck transversely by a
hammer.
The metal in bullets gave the following results :—
M . 225817 220817 220817 225817
a 18-5015 18-5015 187-5015 18-5015
apie) 97?-90 97°90 97°°35 97°°45
ae 8°39 9°57 10°56 10°°44.
A@' . 5°°3267 5°°3034. 5°:2338 5°°2920
A. 4228"-30 4.22830) 4228-3U 4.22830
CP: 0°10494. 0-10593 0-10653 0-10740
Meanee. 0424. -O:0626:
The product by the atomic weight 350 is 37°17.
The cobalt in bars gave—
Mees . .-.. ,EGAE-65 1648"-65
PE be shi. 18-5015 1s™-5015
97°°55D 97745
ae 8°14. 8°-08
a ae 4°:0782 4,°°(J)127
A 4228-30 4.222730
Ci eh sx 0°10772 0:10682
Mean. Meteo. ‘O1LO727.
This specific heat scarcely differs from that found above.
The following are the numbers which I have successively ob-
tained for the specific heats of cobalt and of nickel, excluding
some numbers which refer to metals evidently impure :—
Cobalt. Nickel.
peas. |... se OEOZO 0:1086
A ane ante ir LOOe 0:1075
BOAO chew te ice 1 OTLOLS 0-1108
The specific heat of cobalt is hence in all cases a little less than
that of nickel ; and it might be concluded that the atomic weight
of cobalt should be higher than that of nickel. The recent ex-
periments of M. Dumas have given the same atomic weights for
these two metals. M. Schneider, who has made some new
12
116 Prof. Regnault on the Specific Heat of some Simple Bodies.
determinations (Phil. Mag. vol. xv. p. 115, and vol. xvin. p. 273),
gives cobalt a higher atomic weight. My determinations of the
specific heats favour the latter conclusion; but the differences in
question are so small that it is impossible to decide the question
by a determination of the specific heats, until the experiments
can be made with absolutely pure metals.
Tungsten.
The specific heat of tungsten was given in my first memoir.
The metal was obtained by calcining, at furnace-heat in a lined
crucible, oxide of tungsten previously reduced by hydrogen. It
was to be feared, however, that the metal had by this process
absorbed carbon and silicon. I found, in fact, the specific heat to
be 0:03636, which, multiplied by the atomic weight 1150, now
usually admitted for tungsten, gives 41°81, a number distinctly
too high for the law of specific heats.
M. Rousseau placed at my disposal a large quantity of tungsten.
He had prepared it by reducing tungstic acid at a high and
steady long-sustained temperature by means of hydrogen. This
tungsten is crystalline, but pulverulent. To determine its
specific heat, it was pressed in a circular brass vessel weighing
358-60, and the calorific equivalent of which was 38-3428. The
following are the results of the two experiments which have been
made upon this substance :— :
Meee en axa O8t- 30) 4.25805
TO, sodas Baa 387-3428 38°-3.4.28
EE RD RE oie ol 9 ROS Bese 98°16
GI 3 Seas 12°:09
VAN ere 3°°5512 3°°5625
ARE A 2er-3() 4.22830
CH ue yee 0:03358 -—0:038826
Meaniinie ast 00542,
This specific beat, multiplied by 1150 0, the atomic weight of
tungsten according to M. Dumas’s last experiments, gives the
product 38:43, which is quite within the limits of the law of
specific heats.
Silicon.
Chemists are at present quite uncertain as to the formula
which should be assigned to silicic acid, and therefore as to the
true equivalent of silicon. The majority write the formula Si0°,
and the equivalent is then 266°7; others write it Si0?, which
puts the equivalent at 177°8; lastly, the formula S10 has been
proposed, which makes the equivalent 88°9.
It has hitherto been possible to form only a few definite com-
Prof. Regnault on the Specific Heat of some Simple Bodies. 117
pounds of silicon ; and the chemical and crystallographical ana-
logies which have been sought to be established between these
compounds and other similar compounds whose formule are
definitely known, are by no means certain. Hence it becomes
interesting to determine the specific heat of silicon; and during
the last few years I have neglected no opportunity of doing so.
I worked on two varieties of silicon; crystallized silicon, pre-—
pared by M. St.-Claire Deville’s method, and the same silicon
melted at a very high temperature.
First specimen of crystallized silicon lent by M. Deville; it
was in small lustrous crystals, from which the unerystallized
part had been separated as completely as possible :—
Nips 6S 44er] 4} Ale-06 388-74
Pare ant iek 287-027 Qer-)27 Qet-0.27
ieee. 97°83 97°70 97°83
fee a 21-O2 19°34 _ 19°31
Bee <<) - 1-5856 1°5032 1°-4359
Meee oe . 466869 AG 68-69 4668-69
eee, t 0°1655 01686 0:1679
Mean“ .30) 2 £021673.
Second specimen of crystallized silicon lent by M. Rousseau ;
it had been prepared by M. St.-Claire Deville’s method, and the
best-defined and most lustrous crystals were selected :—_
Nera cele ise BBEE88 348-08
Wii tees iss QEFODT Q2r-()27
Mais oils 1972-50 97°-50
Pei yi sol P4e-95 15°65
PRE 8 TO OG | 1°-5161
I ag 1434058 4348°-58
Byte hien nn O21 707 0:1767
Wean 3 isa | isd eon:
Third specimen of crystallized silicon from another prepara-
tion, which M. Rousseau made by the same method :—
M 448-53 AQe-515 438-815
ae Qer-)27 Qet-()27 Qer-()27
eM ishicny .09°-67 99°'77 99°82
) 12°-85 13°:70 11°:37
Aé' 1°-9714. 1°-9275 2°:0017
A . 4228-96 42.28"-96 4228-96
0:1712 01751 01722
Mean 3g 769 SO T7490:
_ Lastly, Captain Caron lent me a large quantity of crystallized
silicon, remarkable for its lustre and the distinctness of its cry-
8 Prof. Regnault on the Specific Heat of some Simple Bodies.
stals. I give in a note* the method of its preparation as de-
scribed by Captain Caron.
141 Bis sia ae oY gtaa 6 908" 12 938-07
p. . . . Ie"6648 le-6648 ‘18-6648
eet. O9e-40 99°81 99°-20
Gi Wott aoc 21°06 19°-95
AG. 8 oO 3°°0303 3°°1135
A... 464848 4648-48 464848
Cy eye FOS 0°17986 0°17818
Meaniy:. art. ain SOM S7-
I have therefore obtained for the specific heat of crystallized
silicon—
* A mixture is made of—
Dried silicofluoride of potassuum.... 300
Granulated zinc.........++.+++++- 400
These proportions are not absolutely necessary, but they seem to give the
best yield of silicon. The mixture thus made is projected into a crucible,
which, along with its cover, 1s red-hot. The reaction is brisk, although
when the cover is not sufficiently hot it is often necessary to press the mix-
ture with aclay pipe. When the whole is liquid, the crucible 1s removed and
allowed to cool. It is necessary to execute the operation as rapidly as pos-
sible, otherwise the crucible is liable to be perforated, and part of the zine
and the silicon lost.
The cooled crucible is broken to extract the ingot of zine, which will
have settled down well if the operation has been successful: the erystal-
lized silicon is almost entirely at the upper part of the zinc. The pieces of
the crucible and scoriz adhering to the regulus are removed, and the latter
is melted at as low a temperature as possible, so that the zine is liquid
while the silicon is solid. The zine is run out and granulated, and can be
used for another operation: crystals of silicon remaim in the crucible sur-
rounded by a little zinc. ‘This residue is treated with concentrated hydro-
ehloric acid, which removes zine and iron, and crystallized silicon is left
still containing a little lead (if the zie was not quite pure), and always a
little protoxide of silicon. The lead is removed by boiling with strong
nitric acid and washing, and the protoxide of silicon, as well as any of the
mass of the crucible, are removed by treatment with hydrofluosilicie acid.
The pure silicon which remains is washed with water and dried.
To melt this silicon, it is mixed with silicofluoride of potassium and placed
m a double crucible, having been previously covered with a thick layer of
coarsely powdered elass. It is next heated to the melting-point of iron
for some time, and is then immersed while hot in cold water in order to
render the glass more friable. The crucible is then carefully broken, and
the globule of silicon is found surrounded by glass, which is easily removed
either by a hammer or by means of a sharp-pointed steel. To purify it
completely, it must be boiled for some time with concentrated hydrofluoric
acid, which completely removes any slag, provided it is notin the centre of
the regulus.
The. only acid which attacks melted or crystallized silicon is nitrofluoric
acid.
Prof. Regnault on the Specific Heat of some Simple Bodies. 119
First specimen . . . 0:1673
Second specimen. . . 01762
Einrd specmmen . -. : O:1742
Raurcth specimen... ... - 01787
Meany more 2 Oskaa
Fused Silicon.
M. St.-Claire Deville lent me a specimen of silicon which had
been fused in a strong furnace. It constituted a single bar, all
the parts of which were firmly welded together. There were,
however, some cavities, one of which was filled with a vitreous
matter very different from the rest of the mass, and which it was
impossible to detach.
Mee... 208228 288228 288-228
Paes 1. 2827 28-027 28-027
epee: . | 97°63 97°63 97°50
gee.) 2063 20°68 21°°26
Piguet oa 10647 1°:0479 i 0a95
meme = ©. “4668-69 4662-69 4.66869
Cae 3): 601568 0°1533 0:1571
Vecatiinus | bectice be. OPhO Os
A second specimen of fused silicon was lent to me by M. Caron ;
it consisted of a single globule, apparently quite homogeneous,
with a facette which wasa perfect mirror.
Mp ho. L620 118-620
ENE Ai) 1). 2 OOPAD 99°52
ee eats 2, ODS 12°27
PEGE TORE E Y IN NITY ABB 1°:4.436
PA Mes iy yo Loe A) 112840
Cee eye 5 OMG LT 0°1648
Means si beeleay oO L630
M. Caron lent me recently a larger quantity of fused silicon
forming several reguli, and in which no foreign matter could be
detected. I obtained—
ivy bea peal Esa id 818"-67
Wl ee ENB 287, 13287
ie he OOO 99°-55
Be eh £992.90 20°-99
A6l. . . . 2°6069 2°-6257
Be Geagder As 4648-48
Bie elope eR a Warts 0:1738
ican atten pl ecuih la 47
120 Prof. Regnault on the Specific Heat of some Simple Bodies.
At my request M. Caron was good enough to melt this intoa
single regulus. I then obtained the followmg results :—
VD wens ejy os: AESEETOO 78°°700
NEA: > owe. (ROO GAO 99°:49
By Sey ne eeOn 22°°70
BG 8 eee a 2°-2986
A... « 464848 4642-48
Giiosiv ic ei gpOaT2 ae 0°1767
Mean’ °S? 25 3 O-1750
The experiments made with the silicon melted by M. Caron
are evidently the most reliable, because they were made with a
sufficient quantity of substance. They lead to the result that
the specific heat of silicon is 0°1750, which is virtually the same
as that of crystallized silicon (p. 119).
The mean specific heat, 0°176, multiplied
by the atomic weight, 266°7, gives the product 46°92
Ps . Wee} i + Oie29
is - 88°9 Bs 15°64
None of these results is comprised within the limits of varia-
tion which we have found in the case of other bodies. We must
assume either that silicic acid has none of the formule which
chemists have hitherto assigned to it, or that crystallized silicon
is not a simple body, but contains another element which has
escaped the sagacity of observers, or, lastly, that silicon forms an
exception to the law of the specific heats of simple bodies. It is
difficult to admit that this anomaly arises from a numerical error
in the determination of the equivalent of silicon; for this equi-
valent has been determined by the synthesis of silicic acid, and by
the analysis of chloride of silicon.
In order that silicon should obey the law of the specific heats
of simple bodies with the value which we have found for its
specific heat, it would be necessary tc write the formula of silicic
acid, Si? O°; it would then resemble that of nitric, phosphoric,
and arsenic acids. The atomic weight of silicon would be 222°3,
and the product of this atomic weight by its specific heat would
become 39°12, which agrees with the analogous product which
the other simple bodies give.
If we are only guided by apparent analogies, it is not difficult
to find resemblances between silicon, phosphorus, and arsenic.
Thus :—
Silicie acid being a polybasic acid, could form, like phos-
phoric and arsenic acids three kinds of salts,—monobasic, bibasic,
and tribasic ; it would thus be easier to explain the great number
of silicates with multiple bases which nature offers us in beau-
Prof. Regnault on the Specific Heat of some Simple Bodies. 121
tiful well-defined crystals. The existence of the natural hydro-
silicates would then be readily understood, &c.
Silicic acid forms, with alcohol and wood-spirit, three silicic
ethers like phosphoric acid, while the monobasic acids only form
one compound ether.
M. Wohler has recently described a siliciuretted hydrogen
which is spontaneously inflammable in the air, and presents the
greatest analogy with phosphuretted hydrogen.
The protoxide of silicon discovered by the same chemist would
correspond to phosphorous acid ; chloride of silicon to chloride of
phosphorus, &c.
But it is difficult to refer to this formula for silicic acid (Si? O°)
the numerical results which analysis assigns to many compounds
of silicon. I confine myself at present to calling the attention
of mineralogists to this subject. Moreover it is possible that
silicon presents in its calorific capacity anomalies like those
which I have met with for carbon in its different conditions.
The specific heat of crystallized or melted silicon would not be
that which appertains to silicon in its compounds.
Boron.
The atomicweight of boron is as uncertain as that of silicon; and
chemists can give no definite reason for fixing the formulaof boracic
acid. The formula BoO® is usually adopted, and then borax is
regarded as a neutral borate of soda. In the hope of elucidating
this question, a great interest attached to the determination of
the specific heat of boron, and I have successively made experi-
ments upon all the specimens of boron which I could procure.
M.H.St.-Claire Deville distinguishes three varieties of boron: —
1, amorphous boron; 2, graphitoidal boron; and 38, crystallized
boron.
I worked with all three varieties, and proceed to detail the
fesults which I have obtained.
1. Amorphous Boron.
The amorphous boron was prepared in M. St.-Claire Deville’s
laboratory. I washed it repeatedly with distilled water, and
then dried it under the receiver of an air-pump. In order to
determine with some accuracy the specific heat of this pulve-
rulent substance, I compacted it in the form of cylindrical discs,
by compressing it with the blows of a hammer in a lapidary’s
mortar. These discs were placed for six days in vacuo over sul-
phuric acid, and were then placed in a basket of brass wire. To
prevent the boron from absorbing oxygen by being raised to the
elevated temperature of the bath, the inverse method was
adopted, that is, the boron was cooled in the apparatus which I
have described.
122 Prof. Regnault on the Specific Heat of some Simple Bodies.
Several experiments made in this way have given very discord-
ant results. The reason is, that at a low temperature boron
absorbs and condenses a large quantity of air, which it disen-
gages often with a brisk effervescence the moment the basket is
immersed in the calorimeter. To avoid this source of error it
would have been necessary to press the amorphous boron im a
brass cylinder, which was then hermetically closed. I tried in
fact to make the experiment in this way; but boron in this pure
state of division is such a bad conductor of heat, that the water
of the calorimeter only assumes its maximum temperature after
a lengthened immersion; and that renders the determination very
uncertain.
I then decided to heat the boron in the water-bath. The
pulverulent boron was strongly pressed in a very thin brass
cylinder, which was closed with a circular leaden cover to pro-
tect the substance completely from the action of the air. The
brass vessel was suspended in the bath of fig. 1, the reservoir of
the thermometer occupying the central space of the vessel. I
soon found that the thermometer rose much more rapidly than
when the vessel contained another substance; after some time
it even exceeded the temperature of 100°. I thought at first that
this arose from the boron undergoing at this temperature one of
those allotropic modifications which M. Deville has mentioned ;
but I have since found that this increase of temperature simply
arises from a brisk absorption of oxygen by the boron,-which
takes place at about 100°, and changes it into boracic acid. This is
soon seen by digesting in the water of the calorimeter the boron
which filled the basket. This water, filtered, gave on evaporation
a notable quantity of boracic acid, which certainly arose from an
oxidation which the boron had experienced in the bath, spite of
fe precautions which had been taken to isolate the surrounding
; for the boron had been repeatedly washed with distilled
water, and then dried in vacuo over sulphuric acid before being
compressed i in the circular vessel.
This second method of experimenting presents therefore an
important source of error, and confidence cannot be placed in its
results. I nevertheless transcribe the elements of the three
experiments made in this manner :—
I. , Il: IIL.
Me use. wo OSHA 192-22 188-88
ee kagiokiie 1WeAAD | 11451 181451
agi oc lA) 99°70 101°-55
Oi kecea te lO 14°-19 15°14
CR VOOR a 1°-5934 19-6315
AO. RAZZ 50 A228 30 4.228"30
Prof. Regnault on the Specific Heat of some Simple Bodies. 123
In each of these experiments the quantity of boracic acid
formed was determined: in the first 0°56 grm. was found; so
that at the moment of immersion the brass vessel contained
198'-95 of boron, and 0°56 of boracic acid. In hke manner in
Experiment II. there were—
Borolineiot. Saesheeto Oe 10
BoraciG aCe ees kc, page ao
Lastly, in the third experiment there were—
Boren, |. Aeewtty aeensi A ploewe
Boracic acid . . . . O49
The specific heat of anhydrous boracic acid is 0:2374 (Ann. de
Chim. et de Phys. 3rd series, vol. 1. p. 148). If there were no
other sources either of the disengagement or absorption of heat,
the perturbation produced by the presence of the boracic acid —
could be calculated. But the boracic acid is probably formed in
the anhydrous state in the bath; in the water of the calorimeter
it changes into hydrated acid, which dissolves more or less com-
pletely in this water during the time which elapses between
immersion and the observation of the stationary temperature.
These are new sources of error which I was not able to take into
account.
Simply making the correction due to a replacement of part of
the boron by boracic acid, the specific heat of boron is found to
be—
k: reais rt OF 4058
Teas hee iis Auge 103483
Mie et ee OOS
These values agree very little with each other, and I think they
cannot even be regarded as approximate.
I then tried to study amorphous boron in the isomeric modi-
fication which it experiences, according to M. Deville, when
heated to 200° in an oil-bath in a curr ent of hydrogen. I placed
in a glass flask discs of amorphous boron which had been pre-
pared by percussion. The flask having been placed in an oil-
bath, a current of hydrogen was passed through, and the tem-
perature of the oil-bath gradually raised to 200°, where it was
maintained for about half an hour. In this experiment I did
not observe either imcandescence, or any visible phenomenon of
molecular modification. The oil-bath having been removed, the
current of hydrogen was continued for two hours. The suo-
stance had not changed in appearance; but when I was trans-
ferring the discs from the flask into a porcelain capsule, they
took fire one after the other, and burned with a lively incan-
descence. A funnel placed immediately over the ignited boron
was immediately covered with abundant drops of water.
124 Prof. Regnault on the Specific Heat of some Simple Bodies.
It appears, from this that amorphous ‘boron, in becoming
cooled in hydrogen gas, had condensed in its pores a large quan-
tity of this gas. The gas took fire in air just as is the case
when hydrogen is directed on spongy platinum.
2. Graphitoidal Boron.
This was prepared by M. Debray, by accurately following the
method described by M. Deville. It wasin small lustrous lamine,
closely resembling those of graphite.
M 13286 13887 138-56
D 687-593 68-593 68-593
T 99°-32 99°°72 99°27
Gy iy: 16°°64: 18°09 17°41]
aN cian ae AO ON, 1°°8814 1°°9272
A . 4228-96 4228-96 AQQt-OG
C 0:2299 02275 0:2481
Mean 0-2352
The results obtained by these experiments differ appreciably
from each other. This arises from the fact that, in order to
retain this pulverulent boron in the brass basket, it was neces-
sary to line the latter with lead-foil; and in order that the
basket should sink rapidly in the water of the calorimeter, it had
to be loaded with a disc of lead. The calorimetric value of p is
thus twice that of M; and the latter, which is the unknown,
necessarily bears the sum of the errors of each experiment.
3. Crystallized Boron.
Crystallized boron is prepared, according to M. St.-Claire
Deville, by heating aluminium in a porcelain tube in a current
of chloride of boron.
I worked with three specimens prepared by this method.
The first specimen was lent me by M. Deville: the quantity
was not great ; and it was necessary to take special precaution to
obtain accurate results. The following are the elements of the
three experiments which I made :—
M 78-330 72°280 78" 202
p 08-2826 08-2413 Ost-2413
Ab 97°°60 97°°73 97°67
g! LO 2, 9°35 10°26
Ad! fe eA 1°°3750 1o3500
A . 1848566 1348"'846 1418-076
C 0:2657 O:2552 02652
Mean 0:2622
Prof. Regnault on the Specific Heat of some Simple Bodies. 125
Second specimen prepared by M. Rousseau. It was treated
by hydrofluoric acid; M. Rousseau feared nevertheless the pre-
sence of a little aluminium.
Mines ie: eS ber ss 1ls-18
aie ese LE OS2 18t-332
Bee ot > e's -OS?°"25 97°95
ee ale io A 10°32
Gee ee a Ot S78 0°-7928
Pei eet OO 4.228t-30
Geer. is) «:, O:2280 0°2226
WEAN yrs) io 4a) i ee ORR COs
The specific heat of the second specimen is perceptibly less
than that of the first; and that proves clearly that even by the
same method products of different nature may be obtained.
The third specimen was prepared by M. Debray in M. Deville’s
laboratory, and by the same method. It consisted of very lus-
trous crystalline laminz, to some of which an amorphous sub-
stance adhered, from which it was very difficult to free them.
Mite... cw. » 2-00 168™-690
p ee er pile 38-3472
Ah Meet! 8s. G9O:92 99°-52
6g! Reet ie BL OZSe 16°85
PEGs 3h. se LOCAGTDS 1°-5938
tee = 5. , A 2ZE 9G 395858
C ee hee Or 2004 0°2564
Meana lit ey ns) O25 74
This value differs little from that which I found for the first
specimen. ;
In conclusion, I have but little confidence in the results
obtained for crystallized boron, and I shall assume that its spe-
cific heat is 0°250, which is about the mean of the numbers
furnished by the three specimens. If we write the formula of
boracic acid BoO®, the equivalent of boron becomes 1861, and
the product of the specific heat, 0-250, by the equivalent is 34:1.
Thus, from the specific heat of crystallized boron, the most pro-
bable formula of boracic acid is BoO®. But it would be impru-
dent to draw any such conclusion from this fact ; for crystallized
boron might well contain another simple body, which would
materially modify its specific heat.
T, ee Va
XVII. Experimental Researches on the Laws of Evaporation and
Absorption, with a Description of a new Evaporameter and Ab-
sorbometer. By Tuomas Tate, Esq.*
Evaporameter.
‘ | eee instrument enables us readily to determine with con-
siderable precision the amount of evaporation which takes
place from a given surface of water at different states of the atmo-
sphere. The most direct and probably the most accurate method
of determining this consists in exposing a known weight of
water, placed ina large shallow pan, to the action of the air; and
then, ‘after the lapse ‘ofa certain time, by weighing the pan ‘with
the residue of water, the weight of the water which has been
evaporated becomes known. This method, however, is not only
troublesome, but supplies no correction for the rain or moisture
that may have fallen during the period of exposure. The instru-
ment which I have constructed not only takes the rain-fall into
account, but is also simple in its use, and sufficiently accurate in
its indications. It consists of a large glass bell, such as are
used for aquariums, B, fig. 1, nearly filled with water, placed
Fig. 1.
upon a stout deal board GH; a glass tube, CEF, divided
into linear inches, about 18 inches long, and ;%,ths of an inch
internal diameter, supported on the pillars HH and FG in a
slightly inclined position, the extremity F having a rise of about
z'5 in 1, and having its bent extremity HC dipping into the
water contained in the glass bell; a displacement-gauge D, gra-
duated into cubic inches and parts of cubic inches, supported in
a vertical position by the sliding ring R, with its clamp-screw,
so that it may be readily raised out of or depressed in the water
contained in the glass bell; a wide graduated tube T, placed as
shown in the diagram, to catch the overflow of water from the
* Communicated by the Author.
Mr. T. Tate on a new Evaporameter and Absorbometer. 127
, tube EF. The pillar FG admits of being raised or depressed,
so as to give any desired inclination to the tube EF. A mark
is made on the surface of the glass bell at D, a little below the
ordinary level of the water, with which the graduations on the
displacement-tube are at each observation compared; also a
special mark is made on one of the graduations of the tube EF
at a, towards its outer extremity, with which the water in the
tube at each observation is made to coincide by raising or de-
pressing the displacement-gauge. Now as the water in the tube
always stands at a point depending on the height of the water in
the glass bell, any slight depression of the water in the bell, pro-
duced by evaporation or by any other means, will cause the water
in the tube to move through a comparatively large space; thus
if the tube has a rise of 54, in 5, then a fall of =,th of an inch in
the bell will cause the water in the tube to fall through the space
of an inch; that is, the scale of reading in this case will be in-
creased fifty times ; moreover, if the displacement-gauge be de-
pressed until the water in the tube is brought again to the
position a, the reading of this gauge will give the number of
cubic inches of water evaporated.
To adjust the inclination of the tube EF so as to give any
proposed scale of reading.—Let it be required, for example, to
give the tube such an inclination that one cubic inch depression
of the gauge shall cause the water in the tube to move through
the space, say, of half an inch. The zero-mark on the displace-
ment-gauge being made to coincide with the mark D on the
glass bell, water is then added until it reaches a certain mark on
the tube; the gauge is then depressed until the mark of one
cubic inch coincides with the mark on the bell, and the space
through which the water in the tube has moved will show
whether the inclination of the tube is too much or too little, and
then the moveable pillar GF is lowered or raised accordingly ;
and this is repeated until the proper inclination is found. In
order to obtain the true position of the water in the tube, it is
only necessary alternately to raise and depress the displacement-
gauge so as to cause the water to oscillate in the tube until it is
found to settle itself exactly at the same mark when the displace-
ment-gauge is brought to its desired position. This remark also
applies to all the ordinary observations made with the instru-
ment. This adjustment of inclination being once made, does
not require to be repeated, unless the place of the instrument has
to be changed, or unless some other scale of reading has to be
adopted.
The instrument is ordinarily used in the following manner :—
At the commencement of the observations the displacement- gauge
is at zero, whilst the water in the tube stands at the mark a;
128) Mr. T. Tate on a new Evaporameter and Absorbometer.
after the lapse of any proposed time, the evaporation from the ¢
surface of the water in the glass bell will have caused the water
in the tube to have moved towards E; and this distance con-
verted ito cubic inches, by a relation of scale previously ascer-
tained, will for short intervals very nearly give the amount of
evaporation; but this will in all cases be more accurately and
directly found by depressmg the displacement-gauge until the
liquid in the tube is brought back to the mark a; for the read-
ing of the mark on the gauge, coincident with the mark on the
glass bell, at once gives the number of cubic inches of water eva-
porated in the interval of time, care being taken to give a slight
oscillation to the water in the tube, as already explained, before
the reading is taken. After a series of observations it will be
found that the displacement-gauge has nearly reached its lowest
point of depression ; in this case fresh water must be added, and
the adjustment made as already described. If rain has fallen
during the interval of observation, the amount of this rain, as
determined by an ordinary rain-gauge, reduced (if necessary) to
the surface of the water of the glass bell, must be added to the
amount of evaporation indicated by the evaporameter, and then
the excess of this quantity over that which has flowed into the
tube T will give the true amount of evaporation. Should the
water in the tube extend beyond the mark a, the gauge must
in this case be depressed so as to throw a portion of water into
the tube T, and then the process may be conducted as above
described. The amount of evaporation thus determined is that
which is due to the surface of the water in the glass bell; but by
proportion the evaporation due to any other surface may be
readily found. The water-surface of the instrument which I have
constructed is equal to about 80 square inches, and the inclina-
tion of the tube is about 1 in 50: when the inclination is much
less than this, the motion of the water in the tube becomes
somewhat fitful and irregular.
With the view of testing the reliability of the instrument, I
have compared the results derived from it with those derived
from the balance, and have found that they nearly agree with
each other. Thus the evaporation during twenty-four hours was
found by the instrument to be 2-2 cubic inches, whilst the eva-
poration during the same time, as indicated by the balance, was
found to be 540 gr. or 2°14 cubic inches.
No doubt the variation of the force of liquid cohesion due
to change of temperature will form a source of error in the read-
ings of this instrument ; but this variation, slight even at extreme
atmospheric temperatures, must be exceedingly small for any
change of temperature which can take place between two conse-
cutive observations.
Mr. T. Tate on a new Evaporameter and Absorbometer. 129
A more delicate instrument, adapted for special purposes, will
be hereafter described.
Absorbometer.
This instrument is used for determining the volumes of liquid
absorbed during successive intervals of time, and generally for
finding the rate at which liquids are transmitted through the
pores of different absorbents. It consists of a graduated glass
tube A B, about ,4,ths of an inch in the bore and 20 inches long,
sustained in a horizontal position by the supports AC and BD,
and having one of its extremities bent after the manner shown
in the diagram (fig. 2); an enlarged tube E, on which is placed
Fig. 2.
TTT TTT
TTT
the absorbent to be examined, polished at its top, which is on a
level with the axis of A B, cemented or otherwise attached to the
top of the bent tube K ; and acapillary tube J, having its upper
end on a level with the upper side of the tube A B, with a funnel-
shaped top for supplying the tube with liquid as may be required.
The enlarged tube E may be replaced by tubes of different dia-
“meters and lengths. The whole tube having been filled with
liquid, the finger is applied to the extremity A, and a few drops
of water are added, so as to cause the water to cover the top of the
tube E; the absorbent is then laid on the tube H, the finger
being at the same time withdrawn from the extremity A: as the
water is being absorbed by the absorbent, the column of water
in the horizontal tube AB moves towards B; and the rate of
this motion being observed by means of a watch with a pointer
indicating seconds, gives the rate at which the water diffuses
itself through the pores of the absorbent; and so on to other
eases. The following form of the apparatus was employed when
the amount of water diffused or transmitted, as the case might be,
was unusually large :—
A graduated tube, O D, fig. 3, about 9 inches long and # of
an inch diameter, closed at the top and having a smooth welt at
the bottom,—a small perforation, O, about ;1,th of an inch dia-
meter, having been made in the tube at a short distance from its
Phil. Mag. 8. 4. Vol. 23. No. 152, Feb. 1862. K
130 Mr. T. Tate on a new Evaporameter and Absorbometer.
lower extremity, for admitting the external Fig. 3.
air into the tube as the water is being absorb- ;
ed by the absorbent e K, on which the tube
stands, thereby maintaining the water at a
constant pressure on the absorbent. The in-
strument is adjusted in the following man-
ner :—The tube is held in a vertical position,
with its mouth upwards, and filled with water;
the flat surface of the absorbent is then placed
on the orifice of the tube, and the whole is
inverted and placed upon the edge of the
table. In the case of flexible absorbents,
such as calico or cloth, the material is first
covered with a piece of polished slate, and
then the instrument is verted as above described.
A more delicate Evaporameter, answering the purpose of a
Hygrometer.
This instrument is a modification of the apparatus represented
in diagram 2. The tube AB K E being filled with filtered rain-
water, a damp piece of calico, about 8 inches square, is placed
upon the top of the tube E, and a small weight is placed over
it to keep it in position. In order to stretch this calico and to
keep its surface horizontal, tinned bent wires are passed through
its corners and inserted in wooden pegs fixed to the board C D ;
the instrument thus adjusted may remain without any further -
interference until it is found requisite to clean the calico by
washing. The calico is thus always kept in a damp condition
by absorption ; and as the moisture is being evaporated from its
surface, the water in the horizontal tube A B moves towards B
with a velocity proportional to the rate of evaporation ; this rate
of evaporation, therefore, is indicated by the space passed over
by the extremity of the water column in the tube A B in suc-
cessive equal intervals of time; and further, as the section of
this tube is known, the number of cubic inches of water evapo-
rated in any proposed time becomes known. When the liquid
has reached the extremity B of the scale, fresh water is added
to the tube by the funnel J. The delicacy of the indications of
the instrument is such, that at a mean temperature, and at an
average state of dryness of the atmosphere, the water in the tube
AB will move at the rate of about 2 inches per hour. Having
determined the rate of evaporation from the surface of water as
compared with that which takes place from the surface of damp
calico, the indications of the instrument may be readily reduced
so as to give the rate of evaporation from the surface of still
Mr. T. Tate on a new Evaporameter and Absorbometer. 131
water. By means of this instrument the following laws of
evaporation have been established :-—
1. Other things being the same, the rate of evaporation is
nearly proportional to the difference of the temperatures indi-
cated by the wet- and dry-bulb thermometers.
2. Other things being the same, the augmentation of evapo-
ration, due to air in motion, is nearly proportional to the velocity
of the wind.
3. Other things being the same, the evaporation is nearly
inversely proportional to the pressure of the atmosphere.
By means of Apjohn’s formula, or by Glaisher’s multipliers
and a special constant, this mstrument therefore may be used
as a hygrometer, giving indications vastly more delicate, if not
more reliable, than those of the wet- and dry-bulb thermometer
commonly employed. It is believed that the proposed instru-
ment would supply a desideratum in meteorological observations,
inasmuch as it would give with the utmost delicacy the evapo-
rating capacity of the atmosphere, or, what amounts to the same
thing, the comparative dryness and salubrity of the atmosphere
extending over given intervals of time; whereas other hygro-
meters only give the state of the atmosphere at the particular
time of observation. When used as a hygrometer, the instru-
ment should be placed in a situation where there are no currents
of air.
Results of Experiments relating to Absorption.
The following experimental researches form a continuation ot
those given by me in the Philosophical Magazine for 1860-61.
1. When water is diffused from a central point through the
pores of an absorbent (with a certain proviso), nearly equal
volumes of water are absorbed in equal times.
Dry calico, in four folds, was laid on the tube of the absorbo-
meter represented in fig. 2. At first the absorption was very
rapid, but after the lapse of a few minutes it became nearly uni-
form; thus the number of minutes corresponding to each suc-
cessive interval of 2 inches on the tube were 3:16, 3:3, 3:5,
36, 3°8, 3°8.
Plaster of Paris being placed on the tube, gave the following
results: the numbers of seconds corresponding to successive
intervals of 4 inches on the tube were 55, 60, 62, 64.
For a very porous sandstone, the numbers of seconds corre-
sponding to successive intervals of 4 inches on the tube were
70, 75, 80, 80.
For a sandstone of greater density and closer in its pores, the
numbers of minutes corresponding to the absorption of succes-
sive half cubic inches of water were 36, 39,41. Similar results
K 2
132 Mr. T. Tate’s Eaperimental Researches on Absorption.
were obtained for fine sand, wood, and other porous sub-
stances. s
A sector of unsized paper was placed on the absorbent tube,
first with its surface in a horizontal position, and second with its
surface bent vertically downwards. In the first case, the num-
bers of minutes corresponding to successive equal quantities of
absorption were 20, 20, 21, 21°5, 22, 23, 23:2, 23:4; whereas in
the second case the times for the same amount of absorption
were 18, 18, 19, 19, 20, 20°5, 21, 21. |
In like manner a sector of calico, in four folds, was placed on
the absorbent tube: in the horizontal position one-half of a cubic
inch of water was absorbed in 95 minutes, whereas in the vertical
position the same volume of water was absorbed in 87 minutes.
This experiment shows that the rate of absorption is slightly
affected by the gravity of the liquid absorbed. When water is
diffused from a central point in the surface of the absorbent (as
in Exp. 5, Phil. Mag. vol. xx. p. 500), the rate of diffusion
(within certain limits of range) in an upward direction is the
same, or practically the same, as it is in the horizontal direction.
But it appears from the foregomg experiment that, when the
upward and downward currents are divided, the effect of the
gravity of the liquid becomes appreciable. Within short distances
of the central point of diffusion, the force arising from the gra-
vity of the liquid absorbed is exceedingly small as compared with
the force of absorption; but as the former is an accumulative
force, whilst the latter is a constant force acting against a conti-
nually increasing resistance, the effects of the gravity of the
liquid at length become appreciable. The law of absorption,
therefore, given in the article above referred to, must only be
accepted with these limitations.
2. The rate of absorption (in the case of substances composed
of loose material) is not much affected by a reduction of the pres-
sure of the liquid on the absorbent.
Thus an experiment was made with a calico absorbent under
different pressures: viz., first, when the pressures on both sides
of the absorbent were the same, that is, equal to that of the
atmosphere; and second, when the pressure of the liquid on the
under side of the absorbent was less than the atmospheric pres-
sure on the upper side by the pressure of a column of water 7
inches high. For equal volumes of water absorbed, the times in
the two cases were 13°5 minutes and 16 minutes respectively.
3. The rate of absorption increases with the diameter of the
liquid circle in contact with the surface of the absorbent ; also,
in the case of sheets of paper and textile fabrics, it increases
with the number of the sheets, or with the thickness of the
material placed in contact with the liquid.
Mr. T. Tate’s Experimental Researches on Absorption. 133
4. Under constant pressure, the rate at which a sSIPHON-FILTER
transmits water is nearly the same for all lengths of the filter,
provided the length is not less than a certam minimum corre-
sponding to a maximum of discharge.
Let K AB (fig. 4) be a siphon-filter of calico,
transmitting water from the tube of the second
absorbometer which has been described; AB a
glass cylinder nearly filled with water, in which
the lower end of the filter is inserted. By
lowering or elevating the cylinder, any proposed
length may be given to the filter, and the times
required for discharging a cubic inch of water
from the tube OD at the different lengths of |
the filter can be accurately ascertained. Thus
it was found that the times requisite for the
discharge of one cubic inch of water were as
follows :—
viz. 25 minutes with a filter 38 inches long
20°5 ” 9 6 oe)
20 33 33 8 bP)
20 33 23 13 PP)
20°3 33 PP) 29 3)
Here the minimum length corresponding to maximum dis-
charge exceeds 3 inches; but for lengths of filter exceeding this,
the rate of discharge is very nearly constant. ‘The filter m this
experiment was fine cloth 14 inch in width.
5. When a portion of the filter of the last experiment is placed
horizontally, the rate of discharge (with a certain proviso) varies
inversely as the length of this horizontal portion.
The results of experiment were correctly represented by the
formula
here
ey
where Lis put for the length of the horizontal portion in inches,
and v is the corresponding weight of the discharge of water in
_ grains per minute.
Here a constant is added to the actual length of the horizontal
portion of the filter, this constant being the distance due to the
initial velocity ; when L=O, the initial velocity is 7°6. When
L was 12 inches, the rate of discharge per minute was found to
be 2°25, which by the formula would be 2°24; when L was 6
inches, v was found to be 3°58, which by the formula would be
3°47 ; when L=3°6 inches, v was found to be 4°49, which by
the formula would be 4°44; and go on.
6. When a siphon-filter transmits water under a reduced pres-
134 Mr. T. Tate’s Experimental Researches on Absorption.
sure, the decrements of the rate of transmission vary directly as
the column of liquid equivalent to the reduction of pressure.
Let K EC (fig. 5) represent a U-tube filled
with water; KB a siphon-filter, saturated
with moisture, placed on the orifice K in
contact with the water, a small weight being
laid upon the end of the filter to keep it
in position : then the water being discharged
by the siphon-filter causes the liquid to
descend on the side C D of the tube, so that
the reduction of pressure on the filter at
any instant is measured by the column of
descentC D. The rate of discharge is gene-
rally expressed by the formula
Fig. 5.
v=a—bh,
where v represents the velocity of discharge per minute, corre-
sponding to # the descent of the column CD. When A=0,
v=a, which is the initial velocity; and bh is the decrement of
velocity due to the descent h, which is proportional to h. —
The formula closely expressing the results of experiment was
found to be
v='35 —‘05h;
so that for h=1, 2, 3, 4, 5, 6, the corresponding values of v are
"8, °25, *2, °15, -1, and °05 respectively; but by experiment
these velocities were found to be ‘3, °25, °19, ‘14, -1, and ‘055
respectively.
When the extremity B of the filter is inserted in a large vessel
of water, and the length K B of the filter is less than the depth
C D of the column, the current. of the water is reversed ; that is,
the water is transmitted through the pores of the filter into the
tube, and the water D will rise in the tube. When the absorbent
is horizontal, the following law of transmission obtains :—
7. When an absorbent transmits water into a closed vessel or
tube containing water under a reduced pressure, the rate of
transmission varies directly as the column of liquid measuring ,
the reduced pressure ; that is, the rate of transmission, the length
of the absorbent beg constant, is expressed by the formula
=D -
where v is put for the rate at which the water is transmitted per
minute at the corresponding depth / of the liquid measuring the
reduction of pressure, and 4 a constant depending on the size
and nature of the absorbent, and the relative dimensions of the
essential parts of the apparatus.
Mr. J. Cockle on Transcendental and Algebraic Solution. 135
The formula expressing the results of experiment was found
to be
v='075h;
so that for h=1, 2, 3, 4, 5, 6, 7, the values of v are 075, °15,
‘220,70, “O15, 45, 525 respectively ; but by experiment these
velocities were found to be respectively °078, °15, °22, °3, °36,
"43, +52.
[To be continued. |
XVIII. On Transcendental and Algebraic Solution.— Supplement-
ary Paper. By James Cock1t, M.A., F.R.A.S., FCPS. &e.*
ii is not, for the purposes of my paper in the last May Num-
ber, necessary to deal with more than one root of fr=0.
Assume
dae _ spe ty”).
mae en a speaatel ict Odln iat:
form the equation
=(ptqetra?+...+ ta )Fx,
and put it under the form+
| P+Qr+Ra?+...4+T2™=0
by eliminating 2”, 2"*!, 2"*?, &. Then the n linear equations
EO) 5Q-— 0.0 —O072 0
will determine the n quantities p, g, 7,...¢. Thus, forthe cubic
TOGA COM fy) ace! omni alos ae)
we have
fe=2, Fr=3(1—2”),
dx
Bia =p+qzrt+ra?, P=3(p+2aq)—2,
Q=6(ar—q), R=—3(p+2r),
whence {, clearing of fractions, &c.,
* Communicated by the Author.
+ The deduced form
P+Q2+Ra2?+...+Taxr-!
of a rational function of z is the remainder after a division by fx. Hence
it is attainable by division and readily (more particularly where the coeffi-
eients are all numerical) by Horner’s synthetic division. When 2”, 2+1,
&c. are eliminated by substitution, the higher powers should be eliminated
first, and in order of magnitude.
{ For
2 —a —]
A a2\ met Boa)» 4 wala),
136 Mr. J. Cockle on Transcendental and Algebraic Solution.
3(a?—1) @ =a° + ax—2. site, anole eth ee
Differentiating this, and transposing,
d*x dx
3(a? hers = (2a— ba) > +
Multiplying this result into 3(a?—1), and reducing by means
of (a), we find
2
3°(a?— 1)? a = (24—5a) (a? + aw —2) + 3(a?—1)z
= —d8ax*—(20?+1)r+6a; . . « (b)
whence, putting =m VW —1,
= men = ia Ue
Te eee Oe ie (2)
the differential resolvent to which, in the Number for November
1860, we were led by an entirely different process*. But (2) is
equivalent to the symbolical equation
ented 2 a ae
( vin@.t+m)( vise. 5 Fm)a=0,
whencet+
=a d ;
z= ( l—a’. < =m) ee Fae “0
="
=( vine. £ Fm) ermsn-
glaienee
—_ —— eFmsin-la_
a am
Hence, introducing arbitrary constants and substituting for m,
the general expression for x is f
sin-la sin-la 1
ar ae sin-!a
o— Kees 14K, 3V¥—1—= A sin 3 +B}. (3)
* The process given in the May Number leads to
= 2 x£ @(a—X_)(a—#3) We ax?— 2a
= 301-2) 3(a—2) ~ 3(a—a)\(a—2,)\(a—2,) (eae
aa eae itself to the result (a) of the text.
+ I have found it often convenient to represent by (a][6) the product of
a and btreated as ordinary algebraical quantities. Thus we see at once
that
(Vize. tm | vima. 2 Fm) = 0-0) & — nr,
and the accuracy of the symbolical decompositions given in the text are
manifest.
+ If the first coefficient of a linear differential equation of the second
Mr. J. Cockle on Transcendental and Algebraic Solution. 137
Next, to determine these arbitrary constants. Multiply (1)
into 4, and in the product substitute for 2 its value given by (3).
Then, ‘eliminating the cube of the sine by the known formula of
trigonometry, the result is
3(A—4A) sin oe +B)
— A? sin ome +3B)+8a=0,
which is satisfied if
Aaa), AS=8, cossB=1, smob=0;
that is, r being an integer, if
A=2; 38B=2rz.
Hence . (sin at 2rar
2=2smn ———— ) -
This discussion embraces the “ irreducible case ;” but if a be
greater than 1 we must employ logarithmic in place of trigono-
metric forms. Putting (2) under the form
dx da
(a2— 1) 4 +a —mx=0,.. . . . (4)
where m=4, we find that (4 (4) is* equivalent to the symbolical
equation P :
| Sey Dee LOK /
(vei ay +m) ( Va?—1 4, Fm)a=0,
whencet+
order be divided by the last, and the square root of any multiple of the
quotient be integrated, the form of the integral occasionally suggests a
convenient transformation. Thus, for (2) let |
da
—_—__— 1
Virgo any a;
then, a being determinable as a function of ¢ (for a=sinZ), if ¢ be made
the independent variable, we see @ priori that the first and last coeftticients
of the transformed equation will be constant. In the present case, indeed,
all three are constant.
* Tn this case
i
da ——_
[= ———— © lo a+Nv a—1);
{7 a*—| gx /
and, as before, a is determinable as a function of t, and all the coefficients
of the transformed equation are constants, the middle one vanishing.
+ In the equation
d SARE eT,
(ye eo +x0) px=W,
W is always determinable as a function of z. For
Wo. oN exe .W=pz
is a hnear differential equation.
1388 Mr. J. Cockle on Transcendental and Algebraic Solution.
= (VERT. Sem) (VFR cH
t= a*— ate a*— ears |
, 34
=(Ve=1 LE) (axe Va?—1)\™
af) 4) 1
=F an! Gaver
Hence, introducing arbitrary constants, effecting an obvious
reduction, and substituting for m, the general expression for x is
——— 1
e=C,VatVe—1 tO yeaa aod
=C, Vat Va?—1+4+C, Vat Va2?—1.
By substitution in (1) we are led to
O= (C7+C,3+2)a+
3(C,2C.—C,)V a+ Va2—143(C,C,2—-C,)/ at Ve,
the dexter of which will vanish, independently of a, if
C,?+C,3+2=0, and C,C,=1.
Hence the values of the arbitrary constants may be written
Q=(-)b C,=(-Hf,
and we may put
a=(—1)*R,+(—1)*R,.
These agree with known results. Further, assuming for the
solution of (2), or rather of (4), the series
La,a",
r being taken from zero to infinity, the form of those differential
equations shows that the above breaks up into two independent
series, and that we may assume
Ys DS ao,a2” + HS Boi Crs
D and E being arbitrary constants, and « and 8 being deter-
mined by the conditions
Aor+o vis (6r —1) (67+ 1)
Gor (6r+8)(6r+6)
Borsa _ (6r+2)(6r-+4)
Bort+1 (6r+6)(6r+9)’
in the sinister of which e) and a, may, in consequence of the
arbitrary nature of the multipliers D and EH, each be taken as
unity. Now, when a=Q, then
e= =O, or 4/3, OL) —/ 3:
Mr. J. Cockle on Transcendental and Algebraic Solution. 139
and, w denoting an unreal cube root of unity, we may write
— dD, =(e"—@”) V1.
Again, determining E by the condition that the whole series
must change sign when a changes sign, and that at the last of
the set of real values we have
£=— 2, 0r by or
in a succession corresponding to that given above, we find
=o" +o.
Consequently the relation
Lm= (wo — w?™) | es Sa, 02" + (a + @?")S Bo. at!
will, when m is replaced by 0, 1, and 2 successively, give the
three values of x.
The foregoimg is a complete illustration of the process in its
application to cubics. Quadratics lead to a linear differential
equation. In the case of the higher equations, series may be
obtained corresponding to that above given, even though radicals
corresponding to R, and R, have no existence. The increasing
complexity of the process as we pass the fifth degree may per-
haps be met by the following modification of it. Let there be
given
a” + la) 4+- man? +... +r=0.
Change this equation into
2” + IX(a)ae"—! + my(a)a"—2 +... +rp(a)=0,
where dA, ,..p are functional symbols which, a being replaced
by unity, or by ¢, satisfy the respective sets of conditions
A1)=1, w(1)=1,..p(1)=1,
mean (C40 (6) ie
but which are in other respects arbitrary. Then if, treating a as
the independent variable, and /, m, .. r as constants, and apply-
ing the foregoing process, we can, by means of the arbitrary con-
stitution of X(a), w(a), .. p(a), obtain the n—1 particular inte-
grals of the differential resolvent, the n values of 2 must be
sought by writing 1, orc, in place of a in those integrals, introdu-
cing arbitrary constants, and pursuing a path already traced in
the case of cubics. This modification of a process which I glanced
at inthe August (1860) Number, would render it unnecessary to
deal with more than one parameter.
4 Pump Court, Temple, London,
November 5, 1861.
or
[140 J
XIX. Remarks on Ampére’s Experiment on the Repulsion of a
Rectilinear Electrical Current on itself. By Professor Van
Brepa of Haarlem, in a Letter to Jamus D. Forzes, D.C.L.,
F.R.S., V.P.R.S.E., Principal of the United College, St.
Andrews*.,
[Plate I. fig. 7.]
To James D. Forbes, Esq., F.RS.L. & E.
SIR,
‘ie the February Number of the Philosophical Magazine for
this year, you have published the description of some expe-
riments tending to prove that, contrary to Ampére’s theory, the
contiguous parts of an electric current attract stead of repel
each other. And in the Aprii Number of the same Journal,
Mr. Croll of Glasgow endeavours to show that the experiment
by which Ampere believed he had proved the reality of this repul-
sion might be explained in an entirely different manner. The
result of experiments, partly old and partly new, which we have
made, leads us to differ from you as to the import and signifi-
cance of the results which you have obtained; and from Mr.
Croll, as to the validity of his explanation. We shall describe
these experiments and communicate the reflections which they
have suggested, requesting you to publish them in the same
Journal if they seem to you to be worth the attention of physicists.
We shall commence with Mr. Croll’s article. We shall not
discuss it from the theoretical point of view, nor ask the author
how, if he admits that two currents, one of which is directed
towards their point of intersection, and the other from it, repel
each other when they make any given angle with each other, it
is possible to deny this repulsion in the single case in which this
angle is equal to two right angles, that is, when the two currents
form part of the same rectilinear current. Such discussions
appear to us only of relative value; they can only serve to de-
cide a question when this cannot be decided experimentally. We
have resorted therefore to experiment to determine the value of
Mr. Croll’s experiment.
At a height of about 8 mches above a wooden trough A B
(fig. 7, Plate I), divided into two compartments for Ampére’s
\
* Communicated by Principal Forbes. The paper by Mr. Forbes, referred
to in this communication, appeared in the Philosophical Magazine for
February last. An interesting experiment by Professor Tait of Edinburgh,
in which the Ampérian repulsion was distinctly proved in a homogeneous
conductor composed of mercury alone, is printed in this Magazine for April
1861, but has probably escaped the notice of Professor van Breda. We are
authorized to state that Professor Tait’s experiment had already removed
all doubt from Principal Forbes’s mind as to the reality and energy of the
Ampérian repulsion.—Ep.
On the Repulsion of a Rectilinear Electrical Current onitself. 141
experiments, two small mercury cups C were placed upon a suit-
able support. In these cups were placed the two pointed ends
of a conductor of copper wire about a millimetre in diameter ;
they were bent in such a manner as to neutralize the action of
the earth’s magnetism, and to present a horizontal part DD at
right angles to the partition between the two compartments.
By altering the height of the support, the distance between this
horizontal part of the conductor and the surface of the mercury
in the compartments could be changed. Two fixed conductors,
EE, connect one end of each of these compartments with one of
the mercury cups. By connecting the two other ends of these
compartments by means of the binding-screws F F with the poles
of a battery, the current passed through the mercury from one
end of the compartment to the other, then by one of the fixed
conductors through the moveable conductor, and then returned
to the other pole of the battery through the second fixed con-
ductor, and the mercury in the second compartment. When,
first, the two cups were fixed at such a height that the part
DD of the moveable conductor was only about a centimetre
distant from the mercury in the trough (that is, about half as
distant as the same part of one of Ampére’s floating conductors),
and when the current was closed, there was no perceptible motion
m the conductor. At this distance, therefore, the crossed cur-
rents were not strong enough to displace visibly a part of a con-
ductor which a breath could deviate from its direction; and yet
an Ampére’s floater placed in the mercury in the same trough
after the moveable conductor had been removed, was briskly
repelled by the current of the same battery, which consisted of
six Bunsen’s elements united in a series of three double elements.
You see the result of this experiment is not favourable to Mr.
Croll’s point of view. To make it conclusive, it was necessary
~ to determine the mechanical force necessary to move each of the
two conductors, and to show that it was less for our moveable
conductor than for Ampére’s floater. We intended to make it,
but in repeating the experiment with this floater a very simple
expedient presented itself, which, had the idea occurred to us
sooner, would have rendered superfluous all the apparatus de-
scribed above. It is to place this conductor, so to speak, in the
contrary direction in the mercury, that is to say, so that the parts
ab and de (see the illustration to Mr. Croll’s paper, page 248,
vol. xxi. of the Philosophical Magazine), instead of being directed
from the curvature 5 c towards the points P-and N where this cur-
rent enters, should be directed towards the other end of the trough.
Now, reasoning on Mr. Croll’s hypothesis, the floater ought still
to move from the points P and N when the current is closed ; for
there has been no change in its direction either in the mercury or
14.2 Prof. Van Breda on the Repulsion of a
in the part bc of the floater. But the very opposite takes place ;
the floater moves briskly towards the points P and N, just as is
required by Ampére’s experiment. Here, it appears to us, is a
result which scarcely agrees with the explanation of the motion
of this floater by the action of crossed currents. How, then, is it
to be explained, if not by Ampére’s theory itself? If there is
any doubt on this point, we call to remembrance the experiment
which we published three years ago in the French journal Cosmos.
Permit us to describe it :—
“One of us succeeded, twelve years ago, in showing directly
the repulsion of the parts of the same current, by employing a
dozen iron bullets 8 or 9 millims. in diameter, suspended like
the ivory balls in experiments on the impact of bodies, touch-
ing each other, and so that their centres were in the same right
lme. By means of conductors suitably arranged and moveable
in mercury, the two terminal bullets could be connected with the
two poles of a battery; there was besides on each a light thin
rod, by which their motion could be read off on a graduated
scale. When the current from ten Grove’s elements was passed
through the bullets, the terminal ones were seen to diverge
about a millimetre, and between each pair of bullets small sparks
were continually seen to pass. When the battery was not too
strongly charged, and the action of the current not continued
too long, so as to prevent a permanent connexion in consequence
of a fusion of the bullets at the point of contact, the bullets, so
soon as contact was broken, were seen to approach each other
and resume their primitive position, which proved that the effect
was not due to heat, and gave a confirmation of Ampére’s law at
once simple and direct. |
“ But,” you will perhaps say, ‘‘you have appealed to facts,
and my experiments furnish facts which demonstrate an attrac-
tion instead of a repulsion of the contiguous parts of the same
conductor.” But these experiments, Sir, are they conclusive ?
You will permit us to doubt it. To justify this doubt, we com-
mence by clearly distinguishing two circumstances which are
confounded in your experiments, and which nevertheless are in.
our eyes essentially different. While a conductor remains
charged with electricity, however strongly, it does not become
heated; there is no special action on the magnetic needle,
no chemical action is produced in its interior. It is only when
and whilst the electrical condition of its particles changes, and
whilst a current traverses it, as we usually say, that all these
effects are produced. ‘These instances, and many others, would
prove to demonstration that there is a fundamental difference
between the phenomena produced by statical and dynamical
electricity, if a thesis so generally admitted required proof. But
“——
Rectilinear Electrical Current on itself. 143
whenever in your experiments you have observed a true attrac-
tion at a distance, the two parts of your conductor were neces-
sarily disjoined; that is to say, there could be no current other
than that which is propagated by the sparks; and you will
agree with us that every spark indicates a marked difference in
the electrical condition of the two surfaces between which it
springs, a difference which ought necessarily to produce an
attraction between the two. The current transmitted by these
sparks is always too feeble, in too small quantity, as would
formerly have been said, to produce any appreciable mechanical
effect. But in making contact between the two portions of your
conductor, there was certainly a current; an attraction at a
distance could not be perceived, but instead of it you have seen
an adhesion which lasted some time after the current had been
broken. Could not this persistence be an indication that this
adhesion is not a direct effect of the current (the rupture of
which ought to stop it instantaneously), but is a secondary effect ?
We think so. In our opinion the explanation of the pheno-
menon is as follows.
As soon as the current is closed, the moveable current is re-
pelled. It only, however, moves to a slight distance, which can-
not be otherwise, seeing that the force of repulsion, not very
great itself, must overcome that of torsion while only acting
during an excessively short time, and on a relatively consider-
able mass. It would go further than it does, if at the same
moment that it quits the conductor an induction spark, a small
voltaic arc, did not instantaneously pass between the two. This
arc, as is always the case when it springs between two fusible elec-
trodes placed at a very small distance, is almost entirely composed
of a kind of melted metal. It is broken after a very short exist-
ence; but the rupture of the circuit brigs about a new induc-
tion with its arc, which also quickly breaks, and so on. You
have often heard these sparks: this is the fizzing noise of which
you speak. ‘The interposition of an induction-coil in the circuit,
which, as you found, promotes the success of your experi-
ments, does so only by giving rise to stronger sparks. Without
that its effect would be absolutely inexplicable, for its presence
can only weaken the continuous current. And further, if you
still possess the conductors which you have used in your experi-
ments, be good enough to examine, through a lens, the ends by
which they touched; you will readily see the traces, the relics, so
to speak, of the melted wire of which we have spoken. This
wire prevents the two conductors from removing too far from
each other, just as a very small drop of liquid adhering to their
surfaces would, if introduced between the two. After the rupture
of the circuit, it solidifies instantaneously and keeps them soldered
144 Prof. Van Breda on the Repulsion of a
to each other. The unequal contraction of the two parts of the
conductor, of different form and often of two different metals, |
sometimes causes a spontaneous rupture of this junction after a
longer or shorter time, as you have observed.
There is fortunately one means of preventing this welding ; and
that is by using a metal, mercury, which is liquid to begin with,
and then you can observe the Ampérian repulsion. In the same
article of Cosmos, of which some lines have been cited, we have
described an experiment which has much analogy with your own.
We described it thus :— |
“On one of the arms of a small and delicate balance is suspended
a copper-wire conductor about 3 millims. in diameter, and bent
in the form of an inverted U. The other arm is loaded with
weights which almost counterbalance the conductor; that being
done, the two ends of the latter are respectively immersed in two
mercury cups, placed at such a height that they are not immersed
to a greater depth than 2 millimetres at most. As soon as the
circuit is closed so that a pretty strong current passes from the
mercury to the conductor, and from the other end of the con-
ductor to the mercury in the other cup, the conductor is briskly
repelled out of the mercury; the current is broken, and the con-
ductor falls again to be again repelled, and so on indcfinitely*.”
The current for this experiment ought to proceed from four
Grove’s elements, each presenting an active surface of 12 square
inches, and connected so as to form a series of two elements of
double the size. By using a weaker current, the repulsion is not
strong enough to throw the conductor entirely out of the mer-
cury ; it merely rises a little as soon as the current begins to
pass. We have lately improved the apparatus by fixing at the
other end of the balance a small glass disc, on which there is a
scale divided into tenths of a millimetre. This can be observed by
means of a small fixed microscope magnifying about twenty times,
and with cross-wires on its ocular. In addition to this, plati-
num wires are soldered to each of the ends of the bent conductor ;
they are about a millimetre in diameter, and are covered with
glass so as only to leave the two ends free. The results obtained
by means of the apparatus thus modified have appeared interest-
ing to us, because they have confirmed us in our point of view,
which, in the explanation of all the motions cited, as well as in that
of the phenomena observed with hollow spheres by Mr. Gore,
and in Mr. Page’s experiment with the Trevelyan instrument,
only attributes a secondary part to the heat developed by the
current ; it refers some exclusively, and others principally, to the
Ampérian, just as you have hitherto done. In the case of Mr.
* We have since learnt that this experiment had been previously made by
Mr. Faraday.
Rectilinear Electrical Current on itself. 145
Gore’s sphere, which touches each of the two rails in almost a
mathematical point, the heat developed at the point of contact
may in fact be one of the causes of motion: if we were unaware
of the repulsion which ought to be developed on this point inde-
‘ pendently of the heat, the cause of the phenomenon would have
to be attributed to the latter. In the case of the vibrating blocks
of Trevelyan this explanation becomes less probable, because the
weight of the upper block ought to render the two surfaces in
contact much greater. In fact if their surfaces are increased n
times, the heat developed, and the resultant sudden expansion,
ought to be x? times less. if now one of the two is a hquid
metal, like mercury, which assumes exactly the extent of surface
of the solid conductor immersed in it, and which ought therefore
to touch this in all points, the expansion produced by the heat
developed in these points of contact ought to be very small. We
nevertheless see that the repulsion takes place; and its effect is
readily distinguished from that produced by the heat which
causes the mercury and all the vertical parts of the conductor
to expand, by the fact that it ceases instantaneously with the
rupture of the circuit, whereas heat requires a tolerably long
time to become dissipated. In observing, through the micro-
scope, the apparatus just described, as soon as the two cups are
connected with four or six Bunsen’s elemeuts arranged in a series
of elements of double surface, as indicated for the experiments
with the floater, we see the disc suddenly sink, and then the
moveable conductor rise about a tenth of a millimetre. This
motion is immediately succeeded by another in the same direc-
tion, but far slower, due to the expansion by heat. When the
circuit is broken, either after the lapse of a few seconds or after
ten minutes, the conductor is seen at the same moment to fall
again, exactly as it had been raised at the commencement, and
then sink with great slowness in consequence of cooling.
This, Sir, is what we had to communicate to you. If our
experiments still do not seem to you entirely conclusive, you will
oblige us by saying so before the publication of this communica-
tion, so that we may, if possible, be able to modify them or am-
plify them according to your desires.
Receive, Sir, the assurances of our very distinguished con-
sideration*,
J.G. 8. van Bropa.
Teylerian Laboratory, Haarlem,
October 1861,
* Though this letter is throughout in the plural number, it bears the
signature of M. van Breda alone.—LKpir.
Phil. Mag. 8. 4. Vol. 23. No, 152. Feb. 1862. L
[ 146 ]
XX. Remarks on M. Hermite’s Argument relating to the Alge-
braical Resolution of Equations of the Fifth Degree. By G.B.
JERRARD*,
1. WAS not aware of what M. Hermite had written with
respect to the impossibility of effecting generally the
algebraical resolution of equations of the fifth degree, until I
saw an abstract of his argument in a paper by Mr. Cockle which
appeared in the last Number of the ‘ Quarterly Journal of Pure
and Applied Mathematics.’ The abstract to which I refer is
this :—
“M. Hermite’s argument may help to settle a still vexed
question. It is as follows:
“Let us assume that between the roots of the sextic réduite of
the general quintic there exist relations which render that sextic
an Abelian. These relations would, in effect, lead to the con-
clusion that the réduite is resolvible algebraically by quadratic
and cubic radicals; and without having recourse to the demon-
stration of Abel, we may at once convince ourselves that it would
follow that the equation of the fifth degree is resolvible by
radicals of the same knd. Let us call x, 2, 2, #3, %, the roots
of this equation, and put
US Hol + kyLq + Lolz + Ug%4 + LyX
VEX Ug t Lol yt UL, +L, %3 4+ LyX oq,
the quantities w+v and wy will be, the one rational, and the
other a root of an equation of the sixth degree resolvible alge-
braically by hypothesis. Then uw and v and their various values
will be expressed by means of quadratic and cubic radicals. The
same conclusion will hold with respect to the more general
functions
U, = (Xt )* + (@,%o)" + (%2%5)" + (2324) + (a%o) if:
U_= (Lo%a)* + (ayM%4)* + (Hq)? + (a y2%s)* + (H3%)",
whatever be the integral exponent a. It follows that
Lol, LiLo, Vols, Ugtg, LaXoy
for example, will satisfy an equation of the fifth degree, the co-
efficients of which will only involve radicals of the kind in ques-
tion. But with two values of u, and vq it will be possible to form
two equations of the fifth degree having a common root, for
example zgx,, the others being different. Hence we may
deduce Zp v,, and consequently the similar function z)+2,, in
terms of cubic and quadratic radicals; consequently also 2 and
Z,, so that the equation of the fifth degree would be resolvible
without quintic radicals.
* Communicated by the Author.
On the Algebraic Resolution of Equations of the Fifth Degree. 147
“Such a conclusion is of course madmissible. M. Hermite’s
argument is given, with developments, in his “ Considérations
sur la Résolution Algébrique de l’équation du 5 degré.” See
pp. 826-336 of vol.i. of the Nouvelles Annales de Mathématiques
(par MM. Terquem et Gerono), 1842.”
I propose to examine the argument in question.
2. Denoting the function
Pet Oty te ta Ce -- ie, by {(e");
and consequently*
Sot ra, +" L_+ "4+ ox, by f(),
we see that the 5 x 5 terms which compose the product
Fe) Fe”)
= (22)*,
+ (8+ 8") 2 (xy #42),
+ (e2" + 3”) (x, Leth),
> indicating, in each case, the sum of all the terms which arise on
putting A successively equal to 0, 1, 2, 3, 4, and #,, a, being
such as to take the places of x, 2, respectively in a cycle of the
roots arranged in the order: 2%, %, Xo, Ly Ly.
3. Here we at once recognize M. Hermite’s functions wand v ;
the former of which has for its general term 2, 2,4,, the latter
£, fo, Thus u and v-are linked together in the equation
fe”) Te) = G2 + (o” a “yy + (02” 2s B)y, aes (e)
as will be seen on writing, in accordance with the notation of my
‘Hssay on the Resolution of Equationst, ©2 for =(z,)*.
4. We can, too, without the aid of this equation, prove the
truth of what he says respecting the rationality of u+v.
For
will collapse into
U +v=3 (a, 2 +n) + > (a, %24n) ;
and since any one of the ten terms which enter into the two fune-
tions characterized by = differs from all the rest in both groups,
it is clear that all the : oe distinct combinations of the assigned
form are exactly comprised in the expression for w+-v. Hence
uw-+v, being a symmetrical function of the roots of the equation
in #, must admit of being expressed in rational terms of the co-
efficients A,, Ay, .. As.
* Observing that
12(42) — 5n+3n, i3(4n) == l0n+2n, (A(dn)==,15n-+7,
} Published by Taylor and Francis, Red Lion Court, Fleet Street, London.
L2
148 Onthe Algebraic Resolution of Kquations of the Fifth Degree.
But it remains to consider we.
5. From the equation (c) there spring at once
SY) FEV HS2+ (C+ eut (E+ eye,
FPP) =S2 + (0? + Fut (ot c4)v.
Now the product of the two first members of these two equa-
tions, or the function
FO) FEY A) FE),
must manifestly be symmetrical with respect to u and v. It is,
in effect, expressible by
(S2)
+ (+7484 04)62(u+r)
+ (¢ + c4) (0? 4-09) (u? + v?)
+ { (e+ 04)? + (2+ 03)?} uv.
And if from this expression we eliminate ~?+v? by means of
the identical equation
u? + vo? = (u+v)?—2Quv,
we shall immediately obtain
LOS) AO) MA HLtrAw; . . . « (4)
in which L is rational and even integral relatively to Aj, Ag,.. As;
(arts. 4, 5), and A is a numerical constant.
6. According, then, to M. Hermite’s theory,
FO) FO) FE) FE)
ought—on the hypothesis that the equation in w admits generally
of a finite algebraical sclution—to involve no radical higher than
a cubic. His conclusion, however, appears to me to be quite
untenable. It follows, indeed, from what has been demonstrated
in my ‘ Essay,’ that the fifth power of the function in question,
[POT LAE)? LA) 1? LACT?
depends directly on an Abelian equation, and therefore involves
in its solution quadratic and cubic radicals only. But although
JF) FO) F(2) f(A) 1s, as well as its fifth power, six-valued, we
cannot, with the aid of Lagrange’s theory of homogeneous
functions, establish a rational communication between the two
functions
FO MALAY FE, CAO? LAAT? LAP? AED,
as I pointed out to Mr. Cayley in the Philosophical Magazine
for May 1861.
7. Sctting aside, therefore, the objection raised from the theory
of Lagrange, we may now see clearly the way in which quintic
radicals enter into the expression for we.
Royal Society. 149
For sinee, in accordance with what has been already stated,
we are permitted to assume
[AO]? LA) LAP LAC) PRK ee (ea)
K being a root of an Abelian equation, (e,) will take the form
ni Wi Bick citi oe aA niadbendes hi (€}, €)
8. We might, indeed, without considering at all the ground of
M. Hermite’s argument, have inferred, from the very enunciation
of the result at which he had arrived, that an error must some-
where have crept into his processes. How, in effect, can we
reconcile such a result with the possibility of solving binomial
equations of the fifth degree, not to speak of any other class of
solvable equations of that degree into the expressions for whose
roots irreducible radicals of the form cee lat oan eeeeclecen | at e|0Ge, [ove | ear
= Lae ZS. (Ata Ei Ne PP Nh OTN Beeler RE.
= 08. cE. gg. log. | °° |8e. | °° 198. | 6%. | 8c. | FE.
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On the Distribution of Aqueous Vapour in the Atmosphere. 157
done in the case of the entire atmosphere, by the height of a column
of the density observed at the surface. The height of a homogeneous
atmosphere of vapour, equivalent to an independent vapour atmo-
sphere, on Dalton’s hypothesis would obviously be = of the height
of the homogeneous air atmosphere, that is £ of 26,250 feet, or about
42,000 feet.
But the vapour actually existing is much less than this. Taking
the results of Dr. Hooker’s observations, and considering the den-
sity'at the surface to be unity, the mean density of the whole vapour
below 20,000 feet will readily be calculated to be about -47; so that
the whole of the vapour up to this height would be equivalent to a
homogeneous column of 9460 feet of density 1-0. Now it may be
assumed approximately that the quantity of vapour above 20,000 feet
will bear the same relation to the entire quantity, as holds good be-
tween the densities at that height and at the surface ; and as we see
from the Table that the density at 20,000 feet is 7.5, of what it is at
the surface, we may infer that this is the proportion of the vapour
above that altitude, the remainder, or 84, being below it. Conse-
quently the whole quantity of vapour, according to Dr. Hooker’s
observations, would be equivalent to a homogeneous column of 42°
9460, or 11,260 feet. Using the balloon observations, the height
would be rather less than this, viz. 10,050 feet, so that we may infer
that the actual pressure of the vapour in the atmosphere is to that
represented by the tension at the surface of the earth, as 10,500 to
42,000, or as about one to four; and this ratio would also subsist
between the actual pressures and observed tensions at all eleva-
tions.
The problem might otherwise be solved, by comparing the dimi-
nution of density as we ascend, according to Dalton’s hypothesis,
and the observations, as shown by the series of figures in Table I.
This diminution, it will be seen, takes place in all the series, approxi-
mately in a geometrical ratio, so that the density is reduced nearly in
an equal proportion for each 2000 feet of ascent, namely, from 1:00
to *96, thatis by ~4,5, on Dalton’s hypothesis ; from 1:00 to °84, that
is by #5, according to Dr. Hooker; and from 1:00 to °82, that is
by 85, according to Mr. Welsh. Now it follows, from an obvious
mathematical law, that the entire quantities of vapour in these dif-
ferent cases are inversely proportional to the constant reduction of
density ; so that the quantity on Dalton’s hypothesis, which is that
represented by the observed tension at the surface, is to the quantity
according to Dr. Tooker, as sixteen to four, and to the quantity ac-
cording to Mr. Welsh, as eighteen to four, a result nearly identical
with the former. The subtraction of the observed tension of vapour
from the total barometrical pressure, in the hope of obtaining the
simple gaseous pressure, must consequently be denounced as an ab-
surdity ; and the barometrical pressure thus corrected, as it is called,
has no true meaning whatever.
In conclusion, I would remark that the consideration of the small
quantity of vapour that is disseminated in the upper parts of the
atmosphere, shows us that inequalities of level on the earth’s surface,
which are insignificant when viewed in relation to the dimensions of
158 Intelligence and Miscellaneous Articles.
the globe, become objects of the greatest importance in connexion
with the atmosphere which surrounds it. Three-fourths of the whole
mass of the air is within range of the influence of the highest moun-
tains; one-half of the air and nearly nine-tenths of the vapour are
concentrated within about 19,000 feet of the sea-level, a height
which hardly exceeds the mean level of the crest of the Himalaya ;
while one-fourth of the air and one-half of the vapour are found be-
low a height of 8500 feet. Thus, mountains even of moderate mag-
nitude may produce important changes in very large masses of the
atmosphere, as regards their movements, their temperature, and their
hygrometric state ; and especially in those strata that contain the
great bulk of the watery vapour, and that have the greatest effect
therefore in determining the character of climate.
XXIT. Intelligence and Miscellaneous Articles.
PHYSICAL CONSIDERATIONS REGARDING THE POSSIBLE AGE OF
THE SUN’S HEAT. BY PROFESSOR W. THOMSON*.
(THE author prefaced his remarks by drawing attention to some
principles previously established. Itisa principle of irreversible
action in nature, that, ‘although mechanical energy is indestructible,
~ there is a universal tendency to its dissipation, which produces
gradual augmentation and diffusion of heat, cessation of motion,
and exhaustion of potential energy, through the material universe.”
The result of this would be a state of universal rest and death, if
the universe were finite and left to obey existing laws. But as no
limit is known to the extent of matter, science points rather to an
endless progress through an endless space, of action involving the
transformation of potential energy through palpable motion into
heat, than to a single finite mechanism, running down like a clock
and stopping for ever. It is also impossible to conceive either the
beginning or the continuance of life without a creating and over-
ruling power. ‘The author’s object was to lay before the Section
-an application of these general views to the discovery of probable
limits to the periods of time past and future, during which the sun
can be reckoned on as a source of heat and light. The subject was
divided under two heads: 1, on the secular cooling of the sun; 2,
on the origin and total amount of the sun’s heat.
In the first part it is shown that the sun is probably an incan-
descent liquid mass radiating away heat without any appreciable
compensation by the influx of meteoric matter. The rate at which
heat is radiated from the sun has been measured by Herschel and
Pouillet independently; and, according to their results, the author
estimates that if the mean specific heat of the sun were the same as
that of liquid water, his temperature would be lowered by 1°°4 Cen-
tigrade annually. In considering what the sun’s specific heat may
actually be, the author first remarks that there are excellent reasons
for believing that his substance is very much like the earth’s. For
the last eight or nine years, Stokes’s principles of solar and stellar
chemistry have been taught in the public lectures on natural philo-
* Communicated by the author, having been read at the Meeting of the
British Association at Manchester, September 1861. 7
wy A ihe fs 2 Yio, Af ‘ 4) “ oe: -
£ r
Cru DP a
Af F &€ t
,
1
4
Intelligence and Miscellaneous Articles. 159
sophy in the University of Glasgow; and it has been shown as a
first result, that there certainly is sodium in the sun’s atmosphere.
The recent application of these principles in the splendid researches
of Bunsen and Kirchhoff (who made an independent discovery of
Stokes’s theory), has demonstrated with equal certainty that there
are iron and manganese, and several of our other known metals in the
sun. The specific heat of each of these substances is less than the
specific heat of water, which indeed exceeds that of every other
known terrestrial solid or liquid. It might therefore at first sight
seem probable that the mean specific heat of the sun’s whole sub-
stance is less, and very certain that it cannot be much greater, than
that of water. But thermodynamic reasons, explained in the paper,
lead to avery different conclusion, and make it probable that, on
account of the enormous pressure which the sun’s interior bears, his
specific heat is more than ten times, although not more than 10,000
times, that of liquid water. Hence it is probable that the sun cools
by as much as 14° C. in some time more than 100 years, but less
than 100,000 years.
As to the sun’s actual temperature at the present time, it is
remarked that at his surface it cannot, as we have many reasons for
believing, be incomparably higher than temperatures attainable arti-
ficially at the earth’s surface. Among other reasons, it may be men-
tioned that he radiates heat from every square foot of his surface at
only about 7000 horse-power. Coal burning at the rate of a little
less than a pound per two seconds would generate the same amount ;
and itis estimated (Rankine, ‘Prime Movers,’ p. 285, edit. 1859)
that in the furnaces of locomotive engines, coal burns at from 1 Ib.
in 30 seconds to 1 lb. in 90 seconds per square foot of grate-bars.
Hence heat is radiated from the sun at a rate not more than from
fifteen to forty-five times as high as that at which heat is generated
on the grate-bars of a locomotive furnace, per equal areas.
The intefior temperature of the sun is probably far higher than
that at the surface, because conduction can play no sensible part
in the transference of heat between the inner and outer portions of
his mass, and there must be an approximate convective equilibrium of
heat throughout the whole; that is to say, the temperatures at dif-
ferent distances from the centre must be approximately those which
any portion of the substance, if carried from the centre to the surface,
would acquire by expansion without loss or gain of heat.
Part II. On the Origin and Total Amount of the Sun’s Heat.
The sun being, for reasons referred to above, assumed to be an
incandescent liquid now losing heat, the question naturally occurs,
how did this heat originate? It is certain that it cannot have ex-
isted in the sun through an infinity of past time, because as long as it
has so existed it must have been suffering dissipation ; and the finite-
ness of the sun precludes the supposition of an infinite primitive store
of heat in his body. The sun must therefore either have been created
an active source of heat at some time of not immeasurable antiquity
by an overruling decree; or the heat which he has already radiated
away, and that which he still possesses, must have been acquired by
some natural process following permanently established laws. With-
out pronouncing the former supposition to be essentially incredible,
160 Intelligence and Miscellaneous Articles.
the author assumes that it may be safely said to be in the highest
degree improbable, if, as he believes to be the case, we can show the
latter to be not contradictory to known physical laws.
The author then reviews the meteoric theory of solar heat, and
shows that, in the form in which it was advocated by Helmholz*, it
is adequate, and it is the only theory consistent with natural laws
which is adequate to account for the present condition of the sun,
and for radiation continued at a very slowly decreasing rate during
many millions of years past and future. But neither this nor any other
natural theory can account for solar radiation continuing at anything
like the present rate for many hundred millions of years. The paper
concludes as follows :—‘‘ it seems therefore, on the whole, most pro-
bable that the sun has not illuminated the earth for 100,000,000 years,
and almost certain that he has not done so for 500,000,000 -years.
As for the future, we may say with equal certainty that inhabitants
of the earth cannot continue to enjoy the light and heat essential to
their life for many million years longer, unless new sources, now
unknown to us, are prepared in the great storehouse of Creation.”
DESCRIPTION OF A NEW MINERAL FROM THE URAL.
BY M. RODOSZKOVSKI.
In 1857 I discovered at Nijni-Jagurt a variety of concretionary
silicate of zinc, the existence of which, as far as I am aware, was
not previously known in the Ural Mountains.
It is in concretionary crusts. The surface is covered with small
roughnesses, which, seen under a lens, present the appearance of
tolerably lustrous indistinct crystals, which are analogous to zeolite.
The colour of these is a light blue, with a tinge of green.
The hardness is 5, the specific gravity 2°707. It is soluble with-
out effervescence in acids, gives off water when calcined; it is in-
fusible before the blowpipe, but becomes opake when submitted to
the action of the flame; it dissolves in borax, forming an insoluble
glass.
The composition of this silicate of zinc, from my analyses, is—
| Oxygen.
IMed cin: emetic ee Oud 13°507 3
Oxide of cajemma 7. 5 <0... | Bere 5) 0°43 |.
Oxide OL7inerr ers tous OUT 13°133
WY Alera meee ns irre ae, AA] oe
Oudevohicapper tive wi pas
Protoxide ofaron.;. J.32% i
and is represented by the formula
38 Zn Si+ Aq.
* This variety of silicate of zinc greatly resembles a variety of con-
eretionary carbonate of zinc which I saw at London in the British
Museum under the name Smithsonite; but as its composition, its
form, and its colour differ from those of ordinary silicate of zine, I
name it Wagite in honour of M. Waga, the venerable naturalist of
Warsaw.—Comptes Rendus, December 9, 1861.
* Popular Lecture delivered at Konigsberg on the occasion of the Kant
commemoration, February 1854.
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Phil. Mag. Ser. 4.Vol. 23 Pl IL
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THE
LONDON, EDINBURGH, anv DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
MARCH 1882.
XXIII. On the Form and Distribution of the Land-tracts during
the Secondary and Tertiary periods respectively ; and on the
effects upon Animal Life which great changes in Geographical
Configuration have probably produced. By Snartes VY. Woop,
Jun.* ;
Section 1. Introductory.—Sectrion 2. The General Geographical Configuration
of the Secondary Period.—Sxcrion 3. The Changes in the Geographical Con-
figuration which resulted from Post-cretaceous Volcanic Action.—SecrTIion 4.
The Effect produced by the Post-cretaceous Geographical Changes upon the
Secondary Fauna.—Sercrtion 5. The Preservation, at the present day, of isolated
Remnants of the Secondary Continents, and of the Secondary Fauna inhabiting
them.—Section 6, Summary and Conclusion.
Section 1.—Jntroductory.
| a attempt to restore in description the outline of the
lands and seas of a past geological period, although but in
their broadest features, and from that restoration to draw con-
clusions as to results emanating from changes in the distribution
of the continental tracts in succeeding periods, will probably in
the present state of our knowledge be, by many at least, depre-
cated as illusory. The consideration, however, of a few leading
principles to be observed in making such an attempt will, I trust,
tend to remove from the minds of some such an impression, at
least sufficiently so to induce a fair consideration of the views
here put forward.
It is obvious that if any tract, large or small, be submerged or
elevated by subterranean action, the relative levels of all parts of
the tract would, if that tract were raised or depressed by a force
exerted equally on every portion, remain the same, however fre-
quently the elevation or depression occurred. Such an elevation
or depression is, it is true, dynamically impossible, as all these
* Communicated by the Author.
Phil. Mag. 8. 4. Vol. 28. No, 153. March 1862. M
162 Mr. 8. V. Wood on the Form and Distribution of the
elevations appear to have emanated from foci of force, where the
volcanic action was the most exerted, or at least where it found
the least resistance, and produced the greatest dislocations ; ima
word, the upheaval (however prolonged) of mountain chains, has
converted large tracts falling within their influence into dry land.
Now if we can in imagination remove the inequalities produced
by any volcanic upheaval, and by so doing restore the surface as
it existed before such upheaval took place, it is clear that we
should remove the chief difficulty in arriving at a correct view of
the relative configurations of the land and water during the an-
tecedent period.
Again, consider how during every successive geological epoch
since the close of the palzozoic period, but more particularly
during the Jurassic and cretaceous epochs, the sea over the
south-east of England and north of France has returned to the
basin occupied by it during the immediately preceding geological
period, where no anticlinal has interfered to change the relative
levels of the surface: thus we see the outcrop of the jurassic and
cretaceous formations, and even of the older tertiaries over this
district, forming a series of concentric rings, the newer formation
lymg within the older*. If we can so plainly perceive this where
powerful dislocations have taken place subsequent to the older
tertiaries, which have not only interfered with the old and gra-
dually narrowing sea-basin of the secondary and older tertiary
seas, but reversed the very inclination of the surface, so that the
land, from which came the sediment that supplied the clays and
limestones of those ancient formations, now falls away to the
west under the deepening water of the British Channel towards
the Atlantic, how much more plainly ought we to perceive it in
those parts of the world where the strata have remained over
great areas undisturbed by anticlinals since they were deposited,
as in Russia, North America, &c., places in which, if the tracts
were now sufficiently depressed, the ocean would again wash
almost the same coast-line which it did in the secondary periods.
Even in England, which is a geological microcosm, and where a
more regular succession of strata exists than in any other known
tract of equal size, there is by no means that overlay of successive
deposits to the extent that apparently exists, since not only does
the whole jurassic series thin out as it recedes from those ancient
lands the drainage of which formed the sources whence was de-
rived the sediment of its deposits}, but the basins which the
* Tt is intended only to be said that this is the result of the geological
changes since the commencement of the secondary period, broadiy con-
sidered, as it is well understood that numerous local interruptions oc-
curred in this order of events, causing local absence of some of the subor-
dinate divisions of the several secondary groups.
T See Hull, Quart. Journ, Geol. Soc. vol. xvi, p. 63.
Land-tracts during the Secondary and Tertiary periods. 163
Jurassic and lower cretaceous deposits apparently fill are found
to be traversed by anticlinals of anterior origin*, which formed
either peninsulas or islands in the Jurassic and Neocomian seas
that occupied the South-east of England, and parts of France and
Belgium, during the formation of those deposits.
Further, we find, in the case of deposits since the paleozoic
period, that almost all of them have been formed in the neigh-
bourhood of land which has supplied the material for their com-
position. There are exceptions, such as the cretaceous and the
nummulitic series of Europe and Asia; but even these fall far
short of what we should conceive to be the bed of a great ocean,
_such as the Pacific, were it the case that deposits took place in it
of a thickness sufficient to ensure their preservation on upheaval.
It has been remarked by Mr. Darwin (Origin of Species, pp. 300
and 343) that seas have been seas, and continents. have been
continents, for periods far greater, geologically speaking, than
we have been apt to assign for their existence.
In applying these principles to elucidate the broader features
of the geographical configuration at any geological period, we
have to bear in mind another and even more important fact, viz.
the permanence through vast periods of the general direction of
the lmes of volcanic eruption over a whole hemisphere: I shall
at a later stage of this paper enter ito some detail upon this
subject, and therefore only refer here to the fact of this perma-
nence. Consider the chain of the Andes forming a line of vol-
canic eruption more or less active through near 60 degrees of the
earth’s cireumference, and prolonged for an equal distance by the
chain of the Rocky Mountains, and the almost continuous vol-
canic band extending from the Azores in a south-easterly direc-
tion to the centre of the Pacific, and we see that the development
of volcanic eruptions has been exhibited with a permanence and
persistency of direction over immense areas, and may therefore
well assume that the influence of this persistence upon the geo-
graphical configuration of the period during which it prevailed
must have been, perhaps beyond all other things, important and
enduring. Into the causes of this persistency of direction during -
long periods I do not pretend here to enter, further than to
remark upon the insufficiency of the adventitious action of per-
colated water upon the metallic bases to account for it. The fact
so often mooted, of the contiguity of all active volcanoes to the
sea or to great inland waters, is not only explicable on othe
grounds, but is, I venture to suggest, the necessary concomitant
of any elevatory action acting spasmodically like that of volcanoes,
® See Prestwich, Quart. Journ. Geol. Soc. vol. xii. p. 10; also vol. xiv
p- 250; and Degousée and Laurent, Quart. Journ. Geol. Soc. vol. xii.
202.
p:
M2
164 Mr. 8. V. Wood on the Form and Distribution of the
If we admit that every elevation takes place at the expense of
material removed from subterraneous places to the surface, the
void thus caused must, even if we conceive a cavernous structure,
be supplied sooner or later by other material subsiding into the
cavity, so that in such case we may assume that every volcanic
elevation is accompanied by a depression coequal in amount
(although perhaps not in area), and also contiguous. Did moun-
tain chains come into existence by one great catastrophe, instead
of their being formed (as the evidence shows) by a multitude of
minor and spasmodic volcanic outbursts, this contiguity would
not so necessarily accompany the volcanic elevations; but the
smallness of the effect produced by each volcanic elevation when
compared with the sum of their action, as seen in mountain —
chains, shows that, upon the principle stated above, the depres-
sions are contiguous. ‘Thus, as it seems. to me, every volcanic
outburst has a tendency, by the contiguous depressions that it
causes, to bring the drainage into its neighbourhood. This
drainage is generally the ocean; but, as in the Caspian, it may
be only waters having their origin from the surrounding land
collected into the depressed area. And hence is it that great
waters are not only contiguous to volcanoes at the present day,
but that in all geological periods volcanic outbursts are associated
with marine formations.
Section 2.—The General Geographical Configuration of the
Secondary Period. ?
The volcanic forces which prevailed during the later part. of
the paleozoic period, at least during the carboniferous age, appear
to have had a general direction from east to west. The convul-
sions which broke up the paleozoic deposits, and formed the
mountain systems which governed the geographical configuration
of the secondary period, have obliterated these features to a
greater extent than have the tertiary upheavals obliterated those
of secondary age; enough, however, remains to show this east
and west direction in several well-marked and extensive anticli-
nals over the northern hemisphere which originated during the
carboniferous period: witness the anticlinals of Nova Scotia, of
South Scotland, of North Devon, of the Ardennes, of some of
the Sierras of Spain, of Corbiéres in the Pyrenees*. The close
of this period, however, appears to haye been accompanied (or
* As to Nova Scotia, see Dawson, Proc. Geol. Soc. vol. iv. pp. 184, 269 ;
Quart. Journ. Geol, Soc. vol.1. pp. 26,322; vol. iv. p. 50; vol. vi. p. 349 ;
vol. viii. p. 398; vol. x. p.42. As to the Ardennes, see Austen, Quart.
Journ. Geol. Soe. vol. xi. p. 533. As to North Devon, Scotland, and
Spain, see Murchison’s ‘Siluria,’ London, 1854. As to Corbiéres, see
D’Archiac, Bull, Soc. Géol. d, France, vol. xiv.p.507. In addition to which
Land-tracts during the Secondary and Tertiary periods. 165
probably was caused) by an entire change in this alignement:
the volcanic bands which brought into existence the extensive
mountain systems which are formed out of the palzeozoic strata,
broken up and thrown into parallel ridges of immense extent,
obliterating almost entirely the alignement which the paleozoic
strata had previously possessed, appear to have burst forth, not
merely in one hemisphere, but over the whole world as far as
hitherto examined, in a direction more or less from north to
south, and to have maintained this direction during the whole
secondary period. These old volcanic bands have left their evi-
dences in several great systems which have been examined by
competent geologists, and, there is reason to believe, in other
mountain chains of similar direction not yet examined. The
well-marked and examined systems consist, in the northern he-
misphere, of the Alleghanies*, the Oural+, and of the system of
Portugal{ prolonged into the North of England; and in the
southern hemisphere, of the great system of Hastern Australia Q ;
of like origin with which appears to be the paleeozoic and schis-
tose system of New Zealand ; and lastly, the grand systems of
the Rocky Mountains|| and of the Andes.
There seems reason also ior inferring that the north and south
ridges of Central and Southern Africa, crossed by the late tra-
vellers in that region (Burton, Speke, and Livingstone), of whose
it may be added that, according to M. Abich, Bull. vol. xi. p. 116, a great
east and west axis, presumably of carboniferous date (being formed of De-
vonian rock), traverses European Russia from the meridian of Smolensk to
that of the Oural. M. Tchihatchef also describes similar axes running
through Galatia and Paphlagonia (Bull. vol. vil. p. 312), and through the
Antitaurus (Bull. vol. xi. p. 402).
* See Rogers, “ Physical Structure of the Appalachian Chain,” in
‘Reports of Survey of Massachussetts,’ p. 522 (Boston, 1838). See also
Report on Geol. Explor. Pennsylvania, 1836, 1838, 1839, 1840, 1841.
Report on Geol. Survey of Virginia, 1840, 1841.
Tt Murchison, Proc. Geol. Soc. vol. iii. pp. 398, 717. Also ‘ Siluria,’
pp. 294 to 300, and p. 333.
{ Sharpe, Quart. Journ. Geol. Soc. vol. vi. p. 135.
§ See Strzelecki’s ‘Australia,’|Lond.1845. Seealso Odernheimer, in Quart.
Journ. Geol. Soc. vol. xi. p.399. Clarke in same, p. 408. Selwyn, in
vol. x. p. 299; vol. xiv. p. 533 (wherein the north and south strike of the
palzeozoic rocks and their unconformability to the secondary coal-bearing
strata reposing on them is shown); vol. xvi. p. 147. Resales, in vol. xv.
p- 497 (showing the paleozoic strike below the drift).
|| See Hector, Journ. of Geograph. Soc. 1860; Edinb. New. Phil. Journ.
vol. xi. p. 169; Quart. Journ. Geol. Soc. vol. xvii. p. 388. Shumard,
Trans. Acad. St. Louis, vol. i. No. 3. p. 341.
§| See Forbes, Quart. Journ. Geol. Soc. vol. xvii. pp: 38, 48. See also
Darwin’s ‘South America’ (1846), pp. 237-248, who at page 247 proceeds
thus :—“ Hence it would appear that the Cordillera has been probably,
with some quiescent periods, a source of volcanic matter from an epoch
anterior to our cretaceo-oolitic formation to the present day.”
166 = Mr. 8. V. Wood on the Form and Distribution of the
structure, however, we know nothing beyond the direction of
their strike, will, when examined, present similar evidences of an
origin at the close of the palzozoic period.
The way in which the secondary formations occur upon the
flanks of these known systems, stretching from them in success-
ive outcrops, indicate that throughout the secondary period the
tracts falling within the influence of these volcanic bands were,
with some interruption, undergoing a steady contmuous eleva-
tion. Thus, to commence on the east with the Oural Mountains,
we see that the elevatory action of that chain commenced after
the close of the carboniferous period, but was in full action durmg
the last age of the palzeozoic period, the Permian, the deposits of
which spread over large tracts, and that this action, prolonged
into the secondary period, elevated the Permian deposits into
ridges subordinate to the original ridge of the Oural but parallel
with it, while the Jurassic deposits were formed in the same but
diminished basin as that occupied by the Permian Sea, these
now lying withm the Permian deposits in a concentric form,
precisely as we see the secondary deposits of England and
France forming successive concentric rings of outcrop diminish-
ing in the direct ratio of their age. ‘The system of England and
Portugal, although not so marked as the uninterrupted chain of
the Oural, is yet distinctly apparent from a consideration of the
manner in which the secondary deposits in those countries are
assembled. The chief part of the Portuguese system appears
now to have disappeared under the Atlantic; but the Jurassic
and subcretaceous deposits which, fenced on the east by the
schistose region of Eastern Portugal and Western Spain, oe-
cupy the littoral region of Central Portugal, have been shown
by the late Mr. Sharpe* to have a regular outcrop along a line
of strike from N. by W. to 8. by E., in which the earliest-
deposited Jurassic formations were elevated at intervals into
ridges having this direction until the cretaceous age; while in
England we find this line of the Portuguese strike traversing the
island, and becoming conspicuous in the midland and northern
counties of England, the volcanic outbursts appearmg in the
trappean beds of Skye, which there alternate with oolitie depo-
sits. The elevatory effect of this band upon the formations of
the great secondary gulf of England and Northern France I
have before alluded to, in the concentric outcrop of the forma-
tions deposited in that gulf, which, like the Oural region and
the secondary tract of Portugal, exhibit a gradual and successive
elevation and desiccation of the sea-bottom during the whole
period, at least until the cretaceous epoch.
Passing westward, we find under the Atlantic, within the
* Quart. Journ. Geol. Soc. vol. vi. p. 135.
Land-tracts during the Secondary and Tertiary periods. 167
distance of 400 miles from the Irish shore, ridges of consider-
able elevation apparently parallel with the line of Portugal and
England, terminating with an abrupt declivity of upwards of
7000 feet, which would appear to be the western escarpment of
the Anglo-Portuguese system. Crossing the immense valley
which is occupied by the Atlantic between this point and the
American shore, we find a magnificent development of parallel
secondary movements in the Appalachian chain and the deposits
flanking it. The elaborate surveys, by the State surveyors, of the
Atlantic border of the Appalachian chain, and of that chain itself,
enable us to speak with precision of the phenomena attending
the development of the secondary formations of that region.
The parallelism of the ridges mto which the paleozoic deposits
have been thrown in the Alleghanies is perhaps even more
marked and persistent than in the Oural chain; and the persist-
ence of outline of the shore of the secondary oceans, exhibited
by the successive outcrop of the secondary formations along the
littoral border of the Alleghanies, is almost uninterrupted, and
so nearly coincides with the present Atlantic shore, that if the
whole region were now to be depressed to the level it occupied
during any age of the secondary period, the sea would again wash
a coast-line agreeing in its main features with the outcrop of the
formation of that age. We see represented here the same fea-
tures that occur in England and France, viz. the return of sea
after sea, from the Jurassic down to and including the older ter-
tiaries, to the same, though in most cases shrunken, bed as that
occupied by its immediate predecessor. This is most conspicuous
in Virginia and the States to the south of it, the outcrop of the
tertiary and secondary strata successively disappearing under the
Atlantic as it advances northward. Here also we see that suc-
cessive desiccation to which I have adverted in the case of Russia
and England and Portugal; but the succession is less regular
in the Alleghany region, the newer secondaries more generally
overlaying the older, and exhibiting a greater alternation of level
than is the case m Europe ; indeed so considerable has this alter-
nation been, that the equivalents of the middle secondaries of
Kurope have not been well made out, being mostly either absent
or else hidden by the overlay of the newer secondary (cretaceous)
deposits.
The investigations and explorations of Marcou, Shumard,
Swallow, Heyden, Meek, and many other American geologists
and explorers of the formations on the western flank of the Ap-
palachian chain warrant an inference that the secondary sea,
particularly during the cretaceous periods, swept round the
southern termination of the chain and filled the area now occu-
pied by Texas, Kansas, and the Indian territory, extending thence
168 Mr.’8. V. Wood on the Form and Distribution of the
northwards along the eastern side of the Rocky Mountains to
the Polar Sea ; the Alleghany region forming a great peninsula
poimting southwards, and joined to a contiriental tract occupied
by what is now the paleozoic region of the northern and north-
western states of America and of Canada, and the crystalline
region of the Hudson Bay territories, but separated from the
Rocky-Mountain region by this secondary sea. Here, again, the
same changes of level during the secondary period which the At-
Jantic flank of the Appalachian region presents seem repeated,
the newer secondary (cretaceous) formations so overlapping the
middle and older secondary that they are mostly found reposing
here on the palzozoic,—the middle and older secondary forma-
tions being either absent or so far obscured that, in the present
state of their knowledge of this region, the American geologists
are at issue whether any formations really referable to the middle
and older secondary periods have yet been found west of the
Alleghanies*.
The extensive region of the Rocky Mountains, which includes
within it the whole elevated tract between the Mississippi and
Saskatchewan valleys on the east, and the Pacific on the west,
was until recently almost an unknown region ; but the report of
Dr. Hector +, who, under Palliser’s expedition, made a rapid
survey of part of this chain, shows that, hke the Alleghanies,
the core of the chain consists of mural precipices of highly in-
clined palzeozoic formations, flanked with secondary deposits
lying quite unconformably on them, and stretching away from
the chain with a very easy dip, the development of the cretaceous
formation being such as apparently to have filled the whole val-
ley lying between the Rocky Mountains on the west, and the
paleeozoic system of the United States and Canada, and the hy-
persthene system of the Lake and Hudson’s Bay region on the
east, from the coast of Texas on the south, to the Polar Sea on
the north. Here again, therefore, is exhibited a yet more marked
continental alignement from north to south during the secondary
periods.
There remain to be noticed the great systems of the southern
hemisphere, and first that of Australia. Considerable progress
has been made by the surveyor of one of the eastern colonies of
* See Marcou, ‘Geology of North America’ (Zurich, 1858) ; his views
are, how ever, repudiated by the American geologists. See Dana, in Silli-
man’s Journal, vol. xxvi. p. 323. Heyden and Meek in same, vol. xxvii.
pp- 35, 219. This overlay of the cretaceous deposits in many parts of the
northern hemisphere, together with their great extent there, appears to in-
dicate that extensive subsidences in this hemisphere preceded that general
change in the geographical alignement which in the third section I propose
considering.
t+ See Note {|, ante, p. 165.
Land-tracts during the Secondary and Tertiary periods. 169
Australia in the examination of their geological features. The
similarity of these features over a large tract, coupled with the
exhibition of similar features wherever exploring vessels have ex-
amined the eastern sea border, favours the inference that the
whole of Eastern Australia is one geological system composed of
disrupted palozoic formations, and having a strike throughout
from north to south. ‘The resemblance of this structure to that
of the Appalachian and Rocky-Mountain chains is striking.
Here, as there, the Devonian and carboniferous deposits have
been broken up into numerous parallel ridges from north to
south, showing the origin of the system to be-subsequent to the
carboniferous period, but prior to the deposit of the coal-bearing
strata of this continent, which, like those of India, appear to be
of secondary age, these coal-bearing strata resting in Australia
unconformably on the true carboniferous and older paleozoic
strata*,
The schistose system of New Zealand seems evidently due to
the same elevatory action as that which formed the Australian
system, since the coast-line of that island is almost identical with
the opposite shore of Australia in a somewhat lower latitude.
Lastly, we have the grandest mountain system of the world—
the Andes—exhibiting similar features to the other systems
above discussed. This chain exhibits the greatest constancy of —
direction of any, and in its extent it is unrivalled. The reports
and sections published of this chain, the latest of which is the
elaborate memoir of Dr. Forbes, show that this system, although
still in the height of its activity, had its origin as far back as the
oolitic period}, if indeed it do not eventually prove, as there is
reason to believe, to have been brought into existence, like the
Oural and the other systems to which I have adverted, at the
close of the carboniferous epoch. The activity of this volcanic
chain during the secondary period is shown by the forma-
tions of that period being interstratified with porphyries and
other voleanic rocks; and the direction of the volcanic band is
shown to have been, during the period, coincident with that of the
present chain, by the circumstance that these secondary deposits,
so interstratified with volcanic rocks of contemporaneous date,
lie in a band from north to south between the paleozoic forma-
tions of the central or higher region of the Cordillera and the
Pacific, forming a subordinate division of the chain of lower ele-
vation, and comprising within it the greater part of the existing
voleanoes of the Cordillera. It is worthy of remark also, as
showing the identity of this system with that of the Rocky
Mountains, that Dr. Forbes in the one, and Dr. Hector in the
* See Selwyn, Quart. Journ. Geol. Soc. vol. xiv. p. 533.
+ See Darwin’s ‘South America,’ p. 247.
170 On Land-tracts during the Secondary and Tertiary Periods.
other, have observed a remarkable absence, or at least rarity, of
voleanic rocks penetrating the paleozoic portion or core of the
chains, these rocks being developed in the lateral region where
the secondary formations were deposited,—illustrating, I venture
to think, the hypothesis mentioned in Section 1, that the con-
tiguity of the sea (as shown here by the deposits) to the volcanic
foci is due to the depressions caused by the volcanic action, its
absence from those parts of the chains deficient in volcanic rocks
being due to the steadiness of level there permitted by the absence,
during the period, of volcanic disturbances. These two great
systems of the Andes and the Rocky Mountains, although origi-
nating early in the secondary period, have preserved their aligne-
ment and activity until the present time ; for although the Andes
be the only one of them in which the volcanic force is still en-
tirely active, yet the Rocky Mountains themselves, as well as the
Cascade Mountains and the other Pacific-coast ranges (which are
but the lateral and subordinate chains of the great Rocky-Moun-
tain system), exhibit evidences of very recent volcanic activity*. ’
We thus see over half the northern hemisphere, and again in
important parts of the southern, well-marked evidences of the
continental development which prevailed during the secondary
period, sufficient, I think, to justify an mference that during
that period, when the chief part of the present Kuropeo-Asiatic
continent and of Northern Africa was sea, the continents had
an alignement from north to south as well marked as is the
EKuropeo-Asiatic continent of the present day in the opposite
direction (the great development of which from east to west
being due, as I shall presently attempt to show, to the east and
west development of tertiary volcanic bands), all the examples of
great systems of secondary origin yet studied, with the exception
of the Juraand of part of the Pyrenees (both of which originated
very late in the secondary period), having this north and south di-
rection. This inference will be greatly strengthened if further ex- —
plorations should show that the north and south ridges of Central
and Southern Africa, to which the configuration of that conti-
nent south of the Niger is due, and the north and south ridges
of Madagascar are of contemporaneous origin with those of
Australia, the Alleghanies, and the Oural, and contributed to
the geographical configuration of the secondary period. In
short, it may be asserted that the present configuration of ‘our
continents is due to the engrafting, as it were, upon secondary
continents or their remains, of post-cretaceous land, elevated by
mountain chains running from west to east which have come
into existence since the close of the secondary period,—in some
* See Geology of California and Oregon, by J. S. Newberry (Wash-
ington, 1857). Bauerman, Quart. Journ. Geol. Soc. vol. xvi. p. 198.
On the Ilectric Conducting Power of Mercury. 171
cases, as in that of the Oural, incorporating them into the body
of the new continent, but in others leaving them in the form of
peninsulas extending north and south, as in the case of South
America, or of insulated tracts, as in the case of Australia.
_ The following are the (known) important axes which governed
the geographical configuration of the secondary period; the
letters refer to the diagram below. Axes such as the Jura,
which came into existence very late in the secondary period,
and whose influence upon this configuration was but subordi-
nate, or as the principal axis of the Pyrenees, which, although
of secondary origin, preceded only the newer cretaceous epoch,
and whose influence is rather to be considered among those to
be discussed in the 3rd section as governing the post-cretaceous
configuration, are omitted in this list and diagram.
‘ Direction.
Sirwe- ot Oural).: 40-5. « Neto 8:
Chain of Andes. . . « «oN, tod,
Chain of Rocky Mountains N.N.W. t
Chain of Alleghanies . . N.E. to S.W.
N. b
N.b
* Ach ER
System of England and Portugal.
f. System of Eastern Australia .
: e
De le a:
BS
[To be continued. |
XXIV. On the Influence of Traces of Foreign Metals on the
Electric Conducting Power of Mercury. By A. Matraiessen,
F.R.S.; and C. Voer, Ph.D.*
ays fact that mercury, when alloyed with traces of foreign
metals, shows an increment, and not, as most pure metals,
* Communicated by the Authors.
172 Drs. A. Matthiessen and C. Vogt on the Influence of
a decrement of the conducting power, has induced us to make
the following experiments.
The mercury employed was purified by allowing it to stand
for a length of time under a solution of protonitrate of mercury,
and before use heating it on a water-bath for about half an hour
with dilute nitric acid, washing with distilled water, and drying
on the water-bath.
Before commencing the experiments, it was necessary to test
whether the assertion made by Siemens*, “that not only dues
the absorbed oxygen, but also all metallic impurities increase the
conducting power of mercury,” is correct. Is oxygen really
absorbed by mercury? This question may be answered by
the following experiments :—
I. Mercury which had been treated with dilute nitric acid on
a water-bath was well washed with distilled water (previously
boiled to expel the air) and carefully dried with bibulous paper ;
a part of it was heated on the water-bath for half an hour, being
well stirred during that time, and part dried in a Liebig’s
drying tube at 100° C. in a current of dry and pure hydrogen.
These specimens did not show the slightest difference in their
conducting power.
II. Another portion, after being dried in the water-bath, was
shaken with oxygen in a bottle at the ordinary temperature for
twenty minutes, and allowed to stand for three hours, during
which time it was repeatedly shaken up. This also had the
same conducting power as the above.
III. Another portion of the same mercury was boiled in an
evaporating dish in contact with air for a quarter of an hour, to
allow the formation of suboxide. This also showed no altera-
tion in the conducting power. It may be mentioned that the
apparatus we employed for the determination of the resistances
will distinctly show 0:01 per cent. difference in the resistance.
IV. If mercury absorbed oxygen, it is probable that it would
give it out again on solidification, as in the case of silver.
Rose, however, states in his paper “ On the Spitting of Silvert+,”
that he had often frozen large quantities of mercury, but never
observed the phenomena which occur with the spitting of silver.
From the foregoing it would appear that mercury does not
absorb oxygen or oxide; or if it does, only to so small an
extent that its conducting power is not altered by it. Now, as
we shall preve that a very minute quantity of foreign metal
materially affects the conducting power of mercury, we think
we are justified in stating that pure mercury will neither absorb
oxygen nor dissolve either of the oxides of mercury. That the
* Phil. Mag. January 1861.
+ Poggendorff’s Annalen, vol. lxviu. p. 290.
Foreign Metals on the Electric Conducting Power of Mercury. 173
mercury was sufficiently purified by the process we subjected it
to, was proved by comparing it with some distilled mercury,
which after distillation was treated with dilute nitric acid and
dried in a current of hydrogen. The experiments were made as
follows :— |
Thermometer-tubes were fused on to wide tubes and bent, as
shown inthe figure. The length of these
was about 300 millims. Into the wide
tubes dipped well-amalgamated copper
wires (5 millims. thick), which reached
to the bottom of the tubes at a, thereby
closing, as it were, the ends of the
thermometer-tubes with a plate of copper. It was found that
the height of the mercury in the wide tubes made no difference
in the results obtained. The weight of mercury taken for each
determination was 50 grammes.
To obtain concordant results, the precautions taken were :-—
I. The amalgam was made in the tube itself. This was filled
with the requisite quantity of mercury, and its resistance deter-
mined: this was always repeated twice, to be sure no air-bubbles
were in it; and either the solid metal was added, or, as in the
case of the poorer amalgams, a certain weight.of an amalgam
of known composition, and then heated for a quarter to half an
hour over a Bunsen-burner, during which time the mercury was
allowed to flow continually from the one arm to the other, at
the same time taking great care that the thermometer-tube
remained always full; for if it became empty, the amalgam
would leave a tail in it, and thereby injure the continuity of
the column. ‘The thick copper wires were heated before being
dipped into those amalgams, which partially solidified on cooling.
It is almost superfluous to add that the tubes were, after they
were emptied, well washed with nitric acid and distilled water
and carefully dried, and that the ends of the copper wires were
cleaned after each determination, and, when necessary, reamal-
gamated.
IJ. As the conducting power of mercury is known, and as the
resistances of the tubes filled with that metal were always deter-
mined, it was not necessary to measure the length or diameter
of the tubes; for we obtain more concordant results, when expe-
rimenting with the different tubes, by comparing their resist-
tances with that of the tubes filled with mercury, than if we had
measured their respective lengths and cliameters and brought
these data into calculation.
III. The metals used for the experiments were pure.
IV. During the determination the tube filled with the
amalgam was placed in a trough filled with water, the tempera-
174 Drs. A. Matthiessen and C. Vogt on the Influence of
ture of which was kept as near 13° C. as possible. Ofcourse, the
tube was first placed on the empty trough and allowed to cool
gradually before the water was poured in.
V. Hach amalgam was made twice, andjits resistance deter-
mined in different tubes.
In the following Tables the results obtained are given. They
have been compared with the gold-silver alloy*, whose conduct-
ing power was taken at 0°=100:—
TasLe ].—Mercury-Bismuth Series.
|
To 100
parts mer-| Volumes eae Tempera- Mean of the Fondacting pint:
cury were | per cent. i he d e. |Conducting Temper pee 2 F
added observed, | calculated.
power.
a | es ee | ee ee | ee es | eee
10-932 | 13-0 ah 2.
0:05 | 0°069 | j5039| 43-1 | 10:9382 | 13:05 | 10-908 | +0-024
5 10946 | 133 ’
0-1 0138 | i5.947 | 13-9 | 10-9465] 13:15 | 10-906 | 10-040
0-2 0-276 | 1 0-973 133 109785} 13:05 ; 10-901 | +-0:077 |
0:5 0686 | 3 1-063 13-4 | 1 10675} .13°45 | 10890 | +0:177
: : 17-199 13-2 a i: 3 | ‘
1-0 1-13 11-200 13:3 11:1995| 13:25 | 10°876 | +0:323
To 100
parts mer-| Volumes Conducting Tempera-
Mean of the Conducting
power, | Difference.
cig ae) Dex cent. | freq. | ture. Condusnne pone. peal
0-01 | 00119] Ipery 2 10-9185] 13:2 | 10-915 | +0-003
0-025 | 00298) 10029 | 13) | 10-9285] 13-05 | 10-922 | +0-006
0-05 | 00596] ieoag| igo | 10-944 | 13:2 | 10-935 | +0009.
0-1 0-119 He 133 | 109725] 133 | 10-960 |+0-012
0-2 0-238 | 11082 | 33% | 11-0375] 13-4 | 11-009 | +0028
| 08 0593 | F550 | goo | 1222 | isa | 11-157 | +0-065
| 1-0 Ie a caer joy | 11-495 | 18-15 | 11-407 | +0-083
| 2-0 2-38 Fas ty | 1-705] 1345 | 11-882 | —0-177
| ao | 455 | 11867 | 130 | 11873 | 132 | 12-809 | —0-936
* Phil, Mag. February 1861.
Foreign Metals on the Electric Conducting Power of Mercury. 175
Tasie I1J.—Mercury-Tin Series*.
To 100 . 4
parts mer-}| Volumes eee Tempera- ie es Cesar a Difference.
cury were | percent. 2 ture. Conducting) Tempera-
waded observed. power, Are. calculated.
10929 | 122 | 10.9995! 19:15 | 10-922 | 0-007
GOL | 00186 | 30-930 | 12-1
0-025 | ooses | W018 | 12% | 10-9155] 125 | 10-941 | 40-005
0:05 | 0-0930 ee 153 | 109775] 127 | 10-973 | +0-004 :
01 | o1se | tbo | ihe | 10415] 131 | 11-036 | 40-005
02 | 0-371 Habe 132 [irizi | 132 | 11-161 |-+0-010
05 | 0929 | ji2o8| 132 | 11-5285] 131 | 11-538 | 0-010
MMe ss A ree | qoq | 1782 | Had || 12-147 | 0-255
20 | 3-59 iaeay 0 | 19318 | 130 | 13335 | -1-017
40 | 693 | eee | ise | isle7 | 128 | 15-595 | 2-408
* In my paper (Phil. Mag. Sept. 1861) the conducting power of the gold-
silver alloy at 0° C. was brought into calculation by mistake as = 226,
instead of 100 as stated. The-values given in Table V. in that paper must
be divided by 2°26 in order to make them comparable with the above.
Taking, as above, the gold-silver alloy 100° at 0°, the values found for
the tin-mercury series, &c. ought to have been—
Calculated conducting
n power.
* Pure mercury conducts ........ N87 at 1S Cs
¥ alleyed with 0°1 Bi = 10°876 at 18°6 10°823
ie 3 0:01 Sn = 10:845 at 18°4 10840
4 0°02 ,, = 10°858 at 18-0 10°850
i, oe Ooi 1103898 at 1s2 10°889
4 es 01 ,, = 10-956 at 18°8 10:95]
“ " 0:2" > 5.11080 at 19°0 11-071
. bs 05 ,, = 11442 at 18°4 11-439
4 is 1:0 ,, = 11-779 at 18°6 12:031
% ; 04 pas 12289 at 18'S 13°162
Br
S
” 3 hat Lolo, fable O 15°527
“ Further, for the calculations the conducting power of tin was taken equal
to 76°146, and that of bismuth 7°9115, &c.” It must be borne in mind
that the values given in the Table were deduced from determinations made
at different temperatures from those given in the present paper; the differ-
ences may therefore be due chiefly to the temperature not being the same.
The relative results, however, are in both cases the same. The values given
for the conducting powers of tin and bismuth are those taken from my
paper “On the Electric Conducting Power of the Metals” (Phil. Trans.
1858),—A, M,
176 “Drs. A. Matthiessen and C. Vogt on the Influence of
Taste [V.—Mercury-Zine Series.
Sack Volumes |Conducting Tempera- Mean of the Conducting
cury were | percent. | POWET power, |Difference,
addni observed. CUxe, Conducting] Tempera- calculated.
power. ture.
a
10-928 | 13-2 b
0-01 | 00190 | 10-927] 13:2 | 10-929 | 13:07 | 10-943 |—0-014
10:932 | 12:8
10:949 | 13:2
0:025 | 0°0474 | 10-950 | 13:2 10:9507| 13:07 } 10:992 | —0-0413
10-953 | 12:8
10:990 | 13:2
0:05 0:0948 | 10993 | 13:4 10:992 13:13 | 11075 | —0:083
10993 | 12°8
11:079 | 13:2
0-1 0°189 11078 | 13:0 11:077 13:07 | 11:238 | —0-241
11:075 | 13:0
| 11:240 | 13:1
0:2 0-378 11:286 | 13:1 11:235 13:13 | 11°564 | —0:329
11:230 | 13-2
11:708 | 13:2
0:5 0940 11:698 | 13-2 11-696 13:2 12°538 | —0°842
11°683 | 13-2
12-462 | 13-4
1:0 1°86 12:458 | 13-0 12°450 13:27 | 14:131 | —1:681
12°431 | 13-4
13°537 | 13:2 ;
2:0 3°66 13569 | 13°90 13:566 13°0 17:247 | —3°681
13°593 | 12:8
14644 | 13:3
4-0) 7:06 14-651 | 13:0 | 14°658 13:1 23133 | —8:475
14678 | 13:0
TasLe V.—Mercury-Gold Series.
To 100 |
parts mer-| Volumes Pongucting Tempera- Mean of the Conducting canes
cury were | per cent. | ih q ture. |Conducting] Tempera- | __POWe! cara
added observed. power, ture, _ | Calculated.
te)
10°917 13:2
001 0:0070 10:917 13-4 10:917 13:3 10-913 | +0004
; : 10-929 13°4 : ay : ;
0:025 | 0:0176 10-933 12-8 10:931 13:0 10917 | +0014
10:945 13°4
005 | 00352} 19.213 | j25 | 10-9465]. 132 | 10-924 | +0022
o1 | 0070 | Jose | ike | 109775| 132 | 10937 | +0-040
o2 | oss | 37029 | 329 | 11-0315] 134 | 10-962 |-+0-069
o5 | os41 | 11200] dee | 113225] 131 | 11-041 | +0281
10 | 0-70 Tae ioe | 15715} 192 | 11180 | 40-391
Foreign Metals on the Electric Conducting Power of Mercury. 177
Taste VI.—Mercury-Silver Series.
ear Mean of the Conducting
To 100
parts mer-| Volumes Tempera- ‘ :
cury were | per cent. A uligad) perature. |Conducting) Tempera- ate Difference.
added. servers power. ture. .
ee ——<
———
10-920 | 13-2
0-01 | 00130} jo.918| 309 | 10919 | 131 | 10-917 | +0-002
0-025 | 00324] 1) 950 | iso | 10-9265] 132 | 10927 | 0-000
0-05 | 0-0648 ve HS 10-948 | 13-4 | 10-944 | +0-004
o1 | or29 | 1998) | 130 | 10-984 | 130 | 10978 | +0006
02 | 0-259 ie 32 | 1-048 | 133 | 11-046 | +0-002
05 | 0644 | Haeg| dap | 1200 | 13-0 | 11-247 | —0-047
10 | 1-28 bes 1g9 | 115665] 13:0 | 11581 | —0-015
Unfortunately, owing to the tendency of the amalgams to
solidify, or rather to crystallize, we were obliged to discontinue
the determinations in some of the series much sooner than in
the others, as it was impossible to obtain constant results. In
the mercury-bismuth series the turning-point (for there must be
one, as bismuth has a lower conducting power than mercury)
occurs between 1 and 2 per cent.; this point, however, could not,
for the above reason, be accurately determined.
For the calculations, the conducting powers and _ specific
grayities employed are given in the following Table :-—
Tase VII.
Conducting power | Specific gravity t.
PRISUIRUEIL 5s cececescanes 7915 9-822
MMEECUEY, ses pesancanc es 10-910 13°573
MICS cev'evateacdas coast 52-640 11°376
Mi aes Bie Ae cage 78°507 7294
RPGR score atadacees 184-064 /. 97148
Gold” ... B+. yt. d+e.€ + 0. f= de,
ct75, ag + 8, B+, y +8. 5 +6. +07, C= dog;
and thence 7
(4° — B°) (2° 99°) (2° 8°) (x? —e*) (a? — 0°) ¢ = Sigg —EB%. Zo
+ SB %y, Speco CS Pe +S By5d5e°, S_—Biy?6°e",
where {8° denotes the sum 6°+9°+6°+e+°; and in like
manner >%y°, &A°y°6°, = A°y°d°e? denote the sum of the pro-
ducts of the quantities 9°, y°, 65, ¢, &, taken two and two,
three and three, four and four together.
But &,, X) --- Log are symmetrical functions of a, B, y, 5, €, £5
that is, they are rational functions of the coefficients of the equa-
tion for «, or, what is the same thing, of the coefficients of the
equation of the fifth order; and the product (e#5—°)(a5—y’)
(a> — 0°) (a5— 5) (#5 —&), and the coefficients 26°, &c. qua sym-
metrical functions of 6°, y°, 6°, ¢, &, are rational functions of
a> and of the coefficients of the equation for «®; that is, they
are rational functions of « and of the coefficients of the equation
of the fifth order. The only case of failure would be if two or
more of the quantities a, B, y, 5, «, € were equal; but this is not
the case, since we are only concerned with the general equation
of the fifth order. Hence by the last equation, « is given as a
rational function of «> and of the coefficients of the equation of
the fifth order.
2 Stone Buildings, W.C.,
February 4, 1862.
XXIX. Note on the Remarks of Mr. Jerrard.
By James Cocxin, M.A. &c.*
ite HERMITEH’S results are reconciled with the possibi-
e lity of solving binomial equations of the fifth degree
* Communicated by the Author.
Mr. J. Cockle on the Remarks of My. Jerrard. 197
by the fact that, for such equations, u and v vanish, and the
réduite is not an Abelian sextic.
2. The function designated by &/K is generally expressible
im rational terms of K. The suggestion that that function is an
irreducible surd cannot be reconciled with the fact that it is a
root of an equation of the sixth degree with rational coeflicients.
Assume, however, for a moment, that it can. Then, as we learn
from a theorem of Abel, four other roots will be obtained by
multiplying ~/K into the unreal fifth roots of unity. Hence,
denoting the remaining root by @ and the absolute term by A,
we find
AY
K
Next, change the signs of the quadratic surds in K, or multiply
its cubic surds into unreal cube roots of unity, or perform both
operations simultaneously, and denote the result by K’. Then,
Co
by Abel’s theorem, 7 is a root of the sextic. Consequently, for
some of the forms of K’, we may establish the relation
A 5 ae
Kk’ = (ile KK:
in other words b, c>d, &e.,
(a—b), (c—d), (e—f), (9-4), (J), A—-D
shall be six (or for the general case of 12n+3 shall be 3n) dif-
ferent numbers > 0.
Secondly, it is required that the twelve numbers (or for the
general case the 6n numbers defined by the capitals and small
letters)
a—3, b6—3, c—7, d—7...k—11, /—-11
shall be in some order the twelve numbers 1234...12, or for
the general case the 62 numbers 123... 6n, when estimated as
residues to modulus 13 (or 6n+1).
To find the numbers a, 0, c, &c., we have only to write out
the congruences |
(a—8)”" + (6—38)" + (c—7)" + (d—T)" +... 4(A—11)" +
(2—)= 1" +22" 438"4+...412”, (mod. 138,)
for as many values of m as we require. We can thus obtain by
a solution of these congruences every possible system of the 3n
duads which can satisfy the second condition. The number of
these systems which satisfy also the first, is that of the different
‘solutions of the problem.
It is perfectly certain that for the case of 12n+8=15, the
only systems possible will thus turn out to be, for addition to the
eapitals 3, 5, 6, those read in the first lines of G,, G,, G..
Mr. Anstice’s method of constructing the n primary triplets of
the 6n+1 capitals is not proved to exhaust the solutions.
A direct and exhaustive method of finding them is to seek for
their difference circles; that is, to seek for the perfect sets of par-
titions in triplets of the prime number 6n-+ 1.
Def.—A perfect set of partitions in r-plets of N=k(r?—r) +1
is a system of k r-plets,
(Gy aq Mg-+- 0, + (ay agad'g...d ot... (a ag... duit.
such that every number, 1, 2, 3,... N—1, can be made by ad-
dition of consecutive elements of some one r-plet, the sum of the
elements of each r-plet being N. These partitions can be directly
found by the solution of a system of congruences similar to that
204 Mr. T. Graham on Liquid Diffusion applied to Analysis. .
above written. (Vede a paper of mine “ On the perfect 7-parti-
tions of N=7?—r+1,” Transactions of the Historic Society of
Lancashire and Cheshire, vol. 1x. 1857.)
For example, the perfect sets of triplets for N=18 are ob-
tained by solution of the six congruences, made with six values
of m,
ay™ + ag” + ag” + 5,” +b.” + 5” + (@, + aq)” + (dg+ ds)” + (ag+a,)™
+ (b, +b)” + (09+ 63)” + (bg + b))" = 1" 4+2"4 .. +12m, (mod. 13,)
of which one solution is
Anz + b,b.b,= 139 +265.
Perfect partitions are the following :-—
NET Lea N=j=1SS 1S. 9462 16252" NS oe ee
+2.14.344.9.6:
N=15, 122.6. 45 .1.7.2.3:. N=21 ol 3. dO ae
Neos b le A do.
N=73, 1.2.4.8.16.5.18.9.10; 1.4.7.6.3.28.2.8.14;
1.16. 22.23.4.6.8.11; 1.8.12.2.3.13.24.4.6.
Using 189+ 265, or 1264 as difference circles, we form the
triplets 1, 2,5+4, 6, 12, or the quadruplet 1,2,4,10. If we
now complete under every element the circle 12345 ...13, we
shall have two columns of triplets, or a column of quadruplets,
in which the duads are once, and once only exhausted. In the
same way all the above perfect partitions may be used.
Six solutions of the triplet problem for 12n+38=27 are given
by Mr. Anstice. They are all derangements of the same group
of the thirteenth order. The solution of the same problem by
Mr. Mease (Camb. and Dub. Journ. vol. v. 1850, p. 262) is the
sum of certain derangements of two groups of the third and
ninth order added to a derangement of unity.
The method above given, depending on the theory of differ-
ence circles, will exhaust the solutions of Mr. Anstice’s form,
and can easily be modified so as to exhaust those of Mr. Mease’s.
Croft Rectory, near Warrington,
January 14, 1862.
XXXI. Liquid Diffusion applied to Analysis.
By Tuomas Granam, F.R.S., Master of the Mint*.
HE property of volatility, possessed in various degrees by so
| many substances, affords invaluable means of separation, as
is seen in the ever-recurring processes of evaporation and distilla-
* From the Philosophical Transactions for 1861, Part I. p. 183.
Mr. T. Graham on Liquid Diffusion applied to Analysis. 205
tion. So similar in character to volatility is the diffusive power
possessed by all liquid substances, that we may fairly reckon
upon a class of analogous analytical resources to arise from it.
The range also in the degree of diffusive mobility exhibited by
different substances appears to be as wide as the scale of vapour-
tensions. Thus hydrate of potash may be said to possess double
the velocity of diffusion of sulphate of potash, and sulphate of
potash again double the velocity of sugar, alcohol, and sulphate
of magnesia. But the substances named belong all, as regards
diffusion, to the more “ volatile” class. The comparatively
“fixed” class, as regards diffusion, is represented by a different
order of chemical substances (marked out by the absence of the
power to crystallize), which are slow in the extreme. Among the
latter are hydrated silicic acid, hydrated alumina, and other
metallic peroxides of the aluminous class, when they exist in the
soluble form; with starch, dextrine and the gums, caramel, tan-
nin, albumen, gelatine, vegetable and animal extractive matters.
Low diffusibility is not the only property which the bodies last
enumerated possess in common. They are distinguished by the
gelatinous character of their hydrates. Although often largely
soluble in water, they are held in solution by a most feeble
force. They appear smgularly inert in the capacity of acids and
bases, and in all the ordinary chemical relations. But, on the
other hand, their peculiar physical aggregation, with the chemical
indifference referred to, appears to be required in substances
that can intervene in the organic processes of life. The plastic
elements of the animal body are found in this class. As gelatine
appears to be its type, it is proposed to designate substances of
the class as colloids, and to speak of their peculiar form of aggre-
gation as the colloidal condition of matter. Opposed to the
colloidal is the crystalline condition. Substances affecting the
latter form will be classed as crystalloids. The distinction is no
doubt one of intimate molecular constitution.
Although chemically inert in the ordinary sense, colloids
possess a compensating activity of their own arising out of their
physical properties. While the rigidity of the crystalline struc-
ture shuts out external impressions, the softness of the gelatinous
colloid partakes of fluidity, and enables the colloid to become a
medium for liquid diffusion, like water itself. The same penc-
trability appears to take the form of cementation in such colloids
as can exist at a-high temperature. THencea wide sensibility on
the part of colloids to external agents. Another and eminently
characteristic quality of colloids is their mutability. Their
existence is a continued metastasis. A colloid may be compared
in this respect to water while existing liquid at a temperature
under its usual freezing-point, or to a supersaturated saline
206 Mr. T. Graham on Liquid Diffusion applied to Analysis.
solution. Fluid colloids appear to have always a pectous* modi-
fication, and they often pass under the slightest influences from
the first into the second condition. The solution of hydrated
silicic acid, for instance, is easily obtained in a state of purity,
but it cannot be preserved. It may remain fluid for days or
weeks in a sealed tube, but is sure to gelatinize and become in-
soluble at last. Nor does the change of this colloid appear to
stop at that pot; for the mineral forms of silicic acid, deposited
from water, such as flint, are often found to have passed, durimg
the geological ages of their existence, from the vitreous or colloidal
into the crystalline condition (H. Rose). The colloidal is, in
fact, a dynamical state of matter, the crystalloidal being the
statical condition. The colloid possesses energia. It may be
looked upon as the probable primary source of the force appear-
ing in the phenomena of vitality. To the gradual manner in
which colloidal changes take place (for they always demand time
as an element), may the characteristic protraction of chemico-
organic changes also be referred.
A simple and easily applicable mode of effecting a diffusive
separation is to place the mixed substance under a column of
water, contained in a cylindrical glass jar of 5 or 6 inches in
depth. The mixed solution may be conducted to the bottom of
the jar by the use of a fine pipette, without the occurrence of
any sensible imtermixture. The spontaneous diffusion, which
immediately commences, is allowed to go on for a period of
several days. It is then interrupted by siphoning off the water
from the surface in successive strata, from the top to the bottom
ofthecolumn. A species of cohobation has been the consequence
of unequal diffusion, the most rapidly diffusive substance being
isolated more and more as it ascended. The higher the water
column, sufficient time being always given to enable the most
diffusive substance to appear at the summit, the more completely
does a portion of that substance free itself from such other less
diffusive substances as were originally associated with it. A:
marked effect is produced even where the difference in diffusi-
bility is by no means considerable, such as the separation of
chloride of potassium from chloride of sodium, of which the
relative diffusibilities are as 1 to 0°341. Supposing a third
metal of the potassium group to exist, standing above potassium
in diffusibility as potassium stands above sodium, it may be
safely predicated that the new metal would admit of being
* IInktos, curdled. As fibrine, caseine, albumen. But certain liquid
colloid substances are capable of forming a jelly and yet still remaining
liquefiable by heat and soluble in water. Such is gelatine itself, which
is not pectous in the condition of animal jelly, but may be so as it exists
in the gelatiniferous tissues.
Mr. T. Graham on Liquid-Diffusion applied to Analysis. 207
separated from the other two metals by an application of the jar
diffusion above described.
A certain property of colloid substances comes into play most
opportunely in assisting diffusive separations. The jelly of
starch, that of animal mucus, of pectine, of the vegetable gelose
of Payen, and other solid colloidal hydrates, all of which are,
strictly speaking, insoluble in cold water, are themselves per-
meable when in mass, as water is, by the more highly diffusive
class of substances. But such jellies greatly resist the passage
of the less diffusive substances, and cut off entirely other colloid
substances like themselves that may be in solution. They re-
semble animal membrane in this respect. A mere film of the
jelly has the separating effect. Take for illustration the follow-
ing simple experiment.
Asheet of very thin and well-sized letter-paper, of French manu-
facture, having no porosity, was first thoroughly wetted and then
laid upon the surface of water contained in a small basin of less
diameter than the width of the paper, and the latter depressed
in the centre so as to form a tray or cavity capable of holding a
liquid. The liquid placed upon the paper was a mixed solution
of cane-sugar and gum-arabic, containing 5 per cent. of each
substance. The pure water below and the mixed solution above
were therefore separated only by the thickness of the wet sized
paper. After twenty-four hours the upper lquid appeared to
have increased sensibly in volume, through the agency of osmose.
The water below was found now to contain three-fourths of the
whole sugar, in a condition so pure as to crystallize when the
liquid was evaporated on awater-bath. Indeed the liquid of the
basin was only in the slightest degree disturbed by subacetate
of lead, showing the absence of all but a trace of gum. Paper
of the description used is sized by means of starch. The film
of gelatinous starch in the wetted paper has presented no
obstacle to the passage of the crystallized sugar, but has resisted
.the passage of the colloid gum. I may state at once what I
believe to be the mode in which this takes place.
The sized paper has no power to act asa filter. It is mechani-
cally impenetrable, and denies a passage to the [mixed fluid as a .
whole, Molecules only permeate this septum, and not masses.
The molecules also are moved by the force of diffusion. But the
water of the gelatinous starch is not directly available as a medium
for the diffusion of cither the sugar or gum, being in a state of
true chemical combination, feeble although the union of water
with starch may be. The hydrated compound itself is solid, and
also insoluble. Sugar, however, with all other crystalloids, can
separate water, molecule after molecule, from any hydrated col-
loid, such as starch. The sugar thus obtains the liquid medium
208 Mr. T. Graham on Liquid Diffusion applied to Analysis.
required for diffusion, and makes its way through the gelatinous
septum. Gum, on the other hand, possessing as a colloid an
afinity for water of the most feeble description, is unable to
separate that liquid from the gelatinous starch, and so fails to
open the door for its own passage outwards by diffusion.
The separation described is somewhat analogous to that ob-
served in a soap-bubble inflated with a gaseous mixture composed
of carbonic acid and hydrogen. Neither gas, as such, can pene-
trate the water-film. But the carbonic acid, being soluble in
water, is condensed and dissolved by the water-film, and so 1s
enabled to pass outwards and reach the atmosphere ; while
hydrogen, being insoluble in water, or nearly sO, 18 retained be-
hind within the vesicle.
It may perhaps be allowed to me to apply the convenient term
dialysis to the method of separation by diffusion through a
septum of gelatinous matter. The most suitable of all substances
for the dialytic septum appears to be the commercial material
known as vegetable parchment or parchment-paper, which was —
first produced by M. Gaine, and is now successfully manufactured
by Messrs. De la Rue. This is unsized paper, altered by a short
immersion in sulphuric acid, or in chloride of zinc, as proposed
by Mr. T. Taylor. Paper so metamorphosed acquires consider-
able tenacity, as is well known; and when wetted it expands and
becomes translucent, evidently admitting of hydration. A slip
of 25 inches in length was elongated 1 inch in pure water, and
1-2 inch in water containing one per cent. of carbonate of potash.
In the wetted state parchment-paper can easily be applied to a
light hoop of wood, or, better, to a hoop made of sheet gutta
percha, 2 inches in depth and ;
8 orlO inches in diameter, so Fig. 1.—Hoop Dialyser.
as to form a vessel like a sieve
in form (fig. 1). The disk of
parchment-paper used should
exceed in diameter the hoop to
be covered by 3 or 4 inches,
so as to rise well round the
hoop. It may be bound to
the hoop by string, or by an
elastic band, but should not
be firmly secured. The parch-
ment-paper must not be po-
rous. Its soundness will be
ascertained by sponging the
upper surface with pure water, and then observing that no wet
spots show themselves on the opposite side. Such defects may
be remedied by applying liquid albumen, and then coagulating
i ii Re
gr
Mr. T. Graham on Liquid Diffusion applied to Analysis. 209
the same by heat. Mr. De la Rue recommends the use of albu-
men in cementing parchment-paper, which thus may be formed
ito cells and bags very useful in dialytic experiments. The
mixed fluid to be dialysed is poured into the hoop, upon the sur-
face of the parchment-paper, to a small depth only, such as half
an inch. The vessel described (dialyser) is then floated in a
basin containing a considerable volume of water, in order to in-
duce egress of the diffusive constituents of the mixture. - Half a
litre of urine, dialysed for twenty-four hours, gave its crystal-
loidal constituents to the external water. The latter, evaporated
by a water-bath, yielded a white saline mass. From this mass
urea was extracted by alcohol in so pure a condition as to:appear
in crystalline tufts upon the evaporation of the alcohol.
1. Jar Diffusion.
The mode of diffusing more lately followed, which I have
already alluded to as jar diffusion, is extremely simple, and gives
results of more precision than could possibly be anticipated.
The salt is allowed to rise from below into a cylindrical column
of water, and after a fixed time, the proportion of salt which has
risen to various heights in the column is observed. The water
was contained in a plain cylindrical glass jar, of about 152 milli-
metres (6 inches) in height and 87 millimetres (3°45 inches) in
width. In operating, seven-tenths of a litre of water were first
placed in the jar, and then one-tenth of a litre of the hquid to
be diffused was carefully conveyed to the bottom of the jar by
means of a fine pipette. The whole fluid column then measured
127 millimetres (5 inches) in height. So much as five or six
minutes of time were occupied in emptying the pipette at the
bottom of the jar, and extremely little disturbance was occasioned
in the superincumbent water, as could be distinctly seen when
the liquid introduced by the pipette was coloured. The jar was
then left undisturbed, to allow diffusion to proceed, the experi-
ments being always conducted in an apartment of constant, or
nearly constant temperature. When a certain time had elapsed,
the diffusion was interrupted by drawing off the liquid from the
top, by means of a small siphon, slowly and deliberately, as the
liquid had been first introduced,in portions of 50 cubic centimetres,
or one-sixteenth of the whole volume. The open end of the short
limb of the siphon was kept in contact with the surface of the
liquid in the jar, and the portion of liquid drawn off was received
in a graduated measure. By evaporating each fraction separately,
the quantity of salt which had risen into equal sections of the
liquid column was ascertained. From the bottom of two jars,
A and B for instance, a 10 per cent. solution of chloride of sodium
was diffused for a period of fourteen days. The whole quantity
Phil. Mag. 8. 4. Vol. 23. No, 153. March 1862. P
210 Mr. T. Graham on Liquid Diffusion applied to Analysis.
of salt present in each jar was 10 grammes, which was found at
the end to be distributed as follows in the different sectional
strata of fluid, numbering them from the top downwards :—
In the first or highest stratum, 0°103 and 0°105 gramme of
salt in A and B respectively ; in the second stratum, 0°133 and
0125; in the third stratum, 0°165 and 0°158; in the fourth
stratum, 0°204 and 0°193; in the fifth stratum, 0°273 and
0-260; in the sixth stratum, 0°348 and 0:332; in the seventh
stratum, 0°440 and 0:418; in the eighth stratum, 0°545 and
0:525; in the ninth stratum, 0°657 and 0°652; in the tenth
stratum, 0°786 and 0°747; m the eleventh stratum, 0°887 and
0°875; in the twelfth stratum, 0°994 and 0:984; in the thir-
teenth stratum, 1:080 and 1:100; in the fourteenth stratum,
1:176 and 1:198; in the fifteenth and sixteenth strata together,
2:209 and 2°324 grammes. With differences so moderate in
amount between corresponding strata in the two experiments,
this method of observing diffusion may claim a considerable
degree of precision.
In similar experiments made at the same time and temperate
with sugar, gum-arabic and tannin of nut-galls, the final distri-
bution of each substance was different in each case, and the
results may be placed together in illustration of unequal diffusi-
bility, as exhibited by this method of observation. T'wo experi-
ments were made on each substance, as with chloride of sodium,
but the mean result only need be stated.
Tasxie I.—Diffusion of 10 per cent. solutions (10 grammes of
substance in 100 cub. centims. of fluid) into pure water, after
fourteen days, at 10° (50° Fahr.).
No. of stratum | Chloride of
(from above eee Sugar. | Gum. | Tannin.
downwards).
1 104 - 005 003 003
2 "129 008 003 003
3 162 012 003 004
4 "198 016 004 "003
5 *267 030 003 005
6 3.40 059 004 007
7 "429 102 006 017
8 535 180 031 031
9 654 °305 097 069
10 *766 495 215 "145
11 881 *740 407 *288
12 “B91 1:075 734 556
13 1-090 1435 {| 1:157 1:050
14 1°187 1758 | 1°731 1-719
15 and 16 2°266 3°783 | 5601 6:097
—
Se ee
9°999 10°003 | 9°999 9°997
Mr. T. Graham on Liquid Diffusion applied to Analysis, 211
The superimposed column of water being 111 millimetres
(4:38 inches) in height, the chioride of sodium, it will be observed,
has diffused in sensible quantity to the top, and could have risen
higher ; the upper layer being found to contain 0°104 gramme
of salt, or 1 per cent. of the whole quantity present. The apex
of the diffusion column of sugar appears to have Just reached the
top of the liquid in the fourteen days of the experiment, for :005
gramme only of that substance is found in the first stratum,
followed. by :008, -012, -016, and -030 in the following: strata.
Again, no gum appears to be carried by diffusion higher than
the seventh stratum (2°2 inches), which stratum contams ‘006
gramme, followed by ‘031 gramme in the eighth stratum. The
minute quantities of substance shown in the first to the sixth
stratum, and which do not altogether exceed ‘020 gramme, are
no doubt the result of accidental dispersion, arising probably
from a movement of the upper fluid occasioned by slight inequali-
ties of temperature. The diffusion of tannin is even less advanced
than that of gum; but the former numbers are apparently in-
fluenced by a partial decomposition, to which tannin is known to
be liable, and which gives rise to new and more highly diffusible
substances.
‘Experiments continued, lke those last described, for a con-
stant time, do not exhibit the exact relative diffusibilities, although
these could be obtained by proceeding to ascertain, by repeated
trial, the various times required to bring about a similar distri-
bution and equal amount of diffusion in all the salts. The
numbers observed, however, may afford data for the deduction
of the relative diffusibilities by calculation.
A particular advantage of the new method is the means which
it affords of ascertaining the absolute rate or velocity of diffusion.
It becomes possible to state the distance which a salt travels per
second in terms of the metre. It is easy to see that such a
constant must enter into all the chronic phenomena of physiology,
and that it holds a place in vital science not unlike the time of
the falling of heavy bodies in the physics of gravitation. It may
therefore be not amiss to place here in a short tabular form the
results observed of the diffusion of a few more substances, con-
ducted in the same manner as the preceding.
P2
212 Mr. T. Graham an Liquid Diffusion applied to Analysis.
Tasie I].—Diffusion of 10 per cent. solutions for fourteen days.
No. of stratum | Sulphate of
‘ Albumen, at | Caramel, at
(from above magnesia, | 13°to 13°5. | 10° to 11°
downwards). at 10°. ae
1 007 j |
2 ‘O11
3 018
4 027 |
5 049 |
6 “OBB Joy Pas | 003
7 “133 005
8 218 “010 “010
9 331 015 023
10 499 *047 "033
11 *730 "r13 °075
12 1:022 "343 *215
13 1:383 *855 °705
14 1803 1:892 1:°725
15 and 16 3°684 6°725 7°206
| 10-000 10-000 10-000
The sulphate of magnesia was anhydrous. The albumen was
purified by Wurtz’s method. The caramel was partly purified by
precipitation by alcohol, as recommended by Fremy, and further
by other means which will again be referred to. It will be re-
marked that the diffusion “of sulphate of magnesia exhibited
above is very similar to that of sugar in a former Table, but is
slightly less advanced. The similarity in diffusibility of these
two substances had already been observed in the experiments of
former papers. The fall im rate on passing from these crystal-
loids to the colloids tannin, albumen, and caramel is very
striking. The elevation in the liquid column attained by albu-
men or by caramel is moderate indeed compared with that of
crystalline substances. Of albumen, which will be looked upon
with most interest, no portion whatever was found in the seven
higher strata. [It appeared to the extent of 0-010 gramme in
the eighth stratum, 0°015 in the ninth stratum, 0:047 im the
tenth stratum, 0°113 in the eleventh stratum, 0°343 in the
twelfth stratum; while the great mass of this substance remained
in the four lower strata. The diffused albumen did not appear
to lose its coagulability, or to be otherwise altered. It will be
seen immediately that the diffusion of sugar advances as much
in two days as the albumen above in fourteen days (Table IV.).
The diffusion of caramel is the slowest of all, and does not
much exceed in fourteen days the diffusion of sugarin a single day.
It was considered useful to possess examples of the progress of
diffusion, in one or two selected substances, for successive periods
of time, so as to exemplify the continuous progress of diffusion
Mr. T. Graham on Liquid Diffusion applied to Analysis. 218
in these substances. Such a chronological progress of diffusion
im a particnlar substance becomes a standard of comparison for
single experiments on the diffusion of other substances. The
substances selected were chloride of sodium and cane-sugar.
Tasie III.—Diffusion of a 10 per cent. solution of Chloride of
Sodium in different times.
In 4 days, | In 5 days, | In 7 days, | In 14 days,
No. of stratum. |.49°49102.| at 11°75. | at 9°. at 10°.
1 -004 004 -013 -104
2 004 -006 017 -129
3 -005 ‘O11 -028 -162
4 “O11 -020 “051 -198
5 023 -040 -081 -267
6 -040 -075 “134 340
iG -080 “134 211 “499
8 145 +933 318 535
9 -261 -368 -460 GE);
10 436 589 -640 -766
11 706 762 -350 -881
12 1-031 1-090 1-057 -991
13 1-416 1357 1-317 1-090
ae 1815 1°697 1527 1187
1sand16| 4-023 3-613 3-294 2-266
10-000 9-999 9:998 9-999
TasiLe [V.—Diffusion of a 10 per cent. solution of Cane-sugar
in different times.
No. of In 1 day, | In 2 days, | In 6 days, | In7 days, | In8 days, |In 14 days,
stratum. |at10°°75.| at10°. at 9°. at OS at.9°° at 10°.
tt! verece >|) cesees 001 002 002 005
PEAT aecoeds70i|) \oawnee's 002 "002 003 008
2 a 002 003 003 012
PRAY csascs | aescee 002 004 004 016
Ce i IR) eat 003 "004 007 030
AIAIE TY) Vaacece |. |, jasc 005 007 "012 059
UMN ce cert Dh suo cea 011 020 031 "102
8 002 002 024 051 072 180
9 002 008 071 121 154 305
10 005 027 170 "260 "304 "495
11 024 107 "376 507 555 °740
12 133 344 424 897 "858 1075
13 597 930 1°282 17410 1:365 1°435
14 1°850 1-940 1:930 1-950 1-955 1°758
15 and 16; 7°386 6°641 5392 4°760 4°674 3 783
9:999 See ie 9°998 9-998 Sey 10003
The scheme of the en “of the chloride of dey may
afford terms of comparison for the metallic salts, acids and other
highly diffusible substances, while the scheme of sugar will be
214 Mr. T. Graham on Liquid Diffusion applied to Analysis.
found more useful in appreciating the diffusion of organie and
other less diffusible substances. In comparing the two Tables
together, it appears that a fourteen days’ diffusion of sugar is
greater in amount than a four days’ diffusion of chloride of so-
dium, but less than a five days’ diffusion of the same substance.
The diffusion of chloride of sodium appears to be pretty nearly
three times greater (or more rapid) than that of sugar.
The followmg experiments were made upon hydrochloric acid
and chloride of sodium at a somewhat lower temperature and for
times which are different, but which give a nearly equal diffusion
for each substance.
Tasxe IV. d2s.—10 per cent. solutions.
Hydrochloric acid, |Chloride of wilh
No. of stratum. in grammes. in grammes.
3 days at 5°. 7 days at 5°. *
1 003 003
2 006. 009
3 012 010
4 022 "026
5 "043 °055
6 "086 "082
7 162 165
8 "308 "270
9 406 "403
10 595 595
11 837 "823
12 1080 1:085
13 1°163 1*270
14 1:578 1°615
15 and 16 3°699 3°589
10-000 10-000
The diffusion of hydrochloric acid in three days corresponds
closely with the diffusion of chloride of sodium in seven days.
The times of equal diffusion for these two substances, at the tem-
perature of the experiment, appear accordingly to be 1 (hydro-
chloric acid) and 2°33 (chloride of sodium). Hydrochloric acid
and the allied hydracids, with other monobasic acids, are the
most diffusive substances known. ‘The general results of several
series of experiments may be expressed approximately by the
followmg numbers :—
Approximate times of equal diffusion.
Hydrochloric acid. . . 2 meres ||
Chlonde.of sodium 3 < £2. ek a Shee
eucde Aes i
Sulphate of magnesia . kas 6
Albandena ee) (et? JO soe 2 eee
Gayomiel ci tie lisse uy Wek deere ees
Mr. T. Graham on Liquid Diffusion applied to Analysis. 215
It is curious to observe the effect of changing the liquid at-
mosphere in which diffusion takes place, which is water in all
these experiments, and replacing it by another fluid, namely
alcohol. Two substances were diffused in the usual manner,
but with this difference, that the substances were dissolved in
alcohol, and the solutions placed under a column of the same
liquid in the jar. The alcohol was of sp. gr. 0°822 (90 per
cent.).
TABLE V.—Diffasion in Aleohol of 10 per cent. solutions of
Iodine and of Acetate of Potash in seven days.
Acetate of potash,
No. of stratum. Todine at 14°. at 14° to 15°.
ef ee eer ee
1 028 °055
2 *033 *057
3 046 061
a 038 063
5 - 037 064
6 *039 066
7 ‘081 070
8 143 071
9 °263 072
10 °417 095
11 °637 *285
12 936 619
13 1°235 1157
14 1506 1907
15 and 16 4°561 5°358
i i
10-000 10:000
Tasie V. is.—Diffusion in Alcohol of a 10 per cent. solution
of Resin, for seven days, at 14°°5.
No. of stratum. | Diffusate, in grammes.
1 017
2 017
3 018
4 017
5 019
6 020
7 022
8 024
9 025
10 “080
11 210
12 498
13 “992
14 1:700
15 and 16 6°341
10°000
216 Mr. T. Graham on Liguid Diffusion applied to Analysis.
The experiments were conducted in the absence of light, and
there is no reason to believe that the iodine acted chemically
upon the aleohol. The diffusion is more advanced in the iodine
than in the acetate of potash, but in both is moderate in amount,
confirming the early experiments with phials, which appeared to
show that the diffusion process was several times slower in
alcohol than in water. The small quantities of iodine found im
each of the six superior strata are nearly equal, and were no
doubt accidentally elevated by the mobility of this fluid, arising
from its high dilatability by heat compared with that of water at
the same low temperature. The diffusion may be considered
then as confined to the nine lower strata, and considerably re-
sembles that of sugar in water for eight days.
The diffusion of acetate of potash is still less advanced than
that of iodine, and is probably confined to the six lower strata,
the salt found in the higher strata presenting in its distribution
the appearance of having been carried there by a movement of
the fluid consequent upon heat-dilatation, and not by diffusion.
The diffusion of: acetate of potash in alcohol observed during
seven days approximates to that of sugar in water during six
days (Table IV.}.
I now proceed to observations of the simultaneous diffusion of
two substances in the same fluid. ‘he great object of this class
of experiments was to separate salts of unequal diffusibility, and
to test the application of diffusion as an analytical process. A
mixture of two salts being placed at the bottom of the jar, it
may be expected that the salts wil! diffuse pretty much as they
do when they are diffused separately; the more diffusive salt
travelling most rapidly, and showing itself first and always most
largely in the upper strata. The early experiments of diffusion
from phials had shown mdeed that inequality of diffusion is in-
creased by mixture, and the actual separation is consequently
greater than that calculated from the relative diffusibilities of
the mixed substances. Chlorides of potassium and sodium diffuse
nearly in the proportion of 1 to 0°841, according to the earlier
experiments. They may afford, therefore, the means of observing
the amount of separation that may be produced by avery mode-
rate difference in diffusibility. A mixture of 5 grammes of each
salt in the usual 100 cub. cent. of water was diffused.
Mr. T. Graham on Liquid Diffusion applied to Analysis. 217
Taste VJ.—Diffusion of a mixture of 5 per cent. of Chloride of
Potassium and 5 per cent. of Chloride of Sodium, for seven
days, at 12° to 13°.
Number of Chloride of | Chloride of | Total diffu-
stratum. Potassium. sodium. sate.
1 018 °014 032
2 025 °015 "040
3 "044 14 °058
As °075 °017 "092
5 LOR, "034 135
6 7 141 "063 -204
7 "185 "104 *289
8 9252, "151 403
9 *330 dl Pe "542
10 J *349 °351 -700
11 °418 °458 °876
12 =r "559 F070
1) “jae "684 1:236
14 °615 hie 1°387
15 and 16 1°385 1°551 2°936
5°001 4:999 10:000
In the upper part of the Table chloride of potassium always
appears in excess, but not in so large a proportion in the first
three strata as in the fourth. This inequality may be partly
owing to mechanical dispersion of the mixed solution, but is to
be referred chiefly, I believe, to errors of analysis from a loss of
the chloride of potassium difficult to avoid in the determination
of minute proportions of that salt by means of chloride of platinum.
Of 92 milligrammes of salt found in the fourth stratum, 75 mil-
ligrammes, or 81°5 per cent., are chloride of potassium. The
first six strata contain together 561 milligrammes, of which 404
milligrammes, or 72 per cent., that is nearly three-fourths, are
chloride of potassium. We have to descend to the tenth stratum
before the salts are found in equal proportions. The progression
is then inverted, and chloride of sodium comes to preponderate
in the lower strata.
It is evident that the preceding experiment might be so con-
ducted as to diffuse away the chloride of potassium and leave
below a mixture containing chloride of sodium in relative excess,
to as great an extent as the chloride of potassium is found above,
in the last experiment.
Further, the mixture in which chloride of potassium was con-
centrated in the experiment described, so as to form 72 per cent.
of the whole mixture, might be subjected again to diffusion in
the same manner. In an experiment upon a mixture of 7:5
grammes of chloride of potassium and 2°5 grammes of chloride
of sodium, the six upper strata gave 640 milligrammes of salt,
218 Mr. T. Graham on Liquid Diffusion applied to Analysis.
of which 610 milligrammes, or 95°3 per cent., were chloride of
potassium. It is obvious that by repeating this diffusive recti-
fication a sufficient number of times, a portion of the more
diffusive salt might be obtained at last in a state of sensible
purity.
The preceding example illustrates the separation of unequally
diffusive metals or bases; the following example, on the other
hand, the separation of unequally diffusive acids united with a
common base. Chloride of sodium and sulphate of soda diffuse
separately in the phial experiments in the proportion of 1 to
0:707 ;
TasxLe VII.—Diffusion of 5 per cent. of Chloride of Sodium
and 5 per cent. of anhydrous Sulphate of Soda, for seven days,
at 10° to 10°75.
Wuniber of Chloride of | Sulphate of | Total diffu-
attain sodium, in soda, in sate, in
7 grammes. grammes. grammes.
1 S009 Oar eens 009
2 013 001 014
3 024 002 "026
4 038 "003 041
5 "060 "006 066
6 "095 012 107
7 "141 029 170
8 203 "059 "262
9 278 °115 393
10 *360 205 "565
ll "473 317 °790
12 560 507 1067
13 637 694 hojok
14 718 909 1°627
15 and 16 1390 2°14] as |
4:999 5000 9°999
Here the separation is still more sensible than before with the
bases. The six upper strata contain 263 milligrammes of salt,
of which 239 milligrammes, that is 90°8 per cent., are chloride
of sodium. The salt of the upper eight strata amounts to 695
milligrammes, of which 583 milligrammes, or 83:9 per cent.,
are chloride of sodium.
How long the diffusion should be continued im a liquid column
of limited height, such as in these experiments, so as to produce
the greatest separation, is a question of some interest, which can
only be answered by experiment. The last diffusion was ac-
cordingly repeated, with the difference that it was continued for
double the former time.
Mr. T. Graham on Liquid Diffusion applied to Analysis. 219
Taste VILI.—Diffusion of 5 per cent. of Chloride of Sodium
and 5 per cent. of Sulphate of Soda, for fourteen days, at
BOPT a 11°,
Mamber or Chloride of | Sulphate of | Total diffu-
eatin: | Sodium, in soda, in sate, in
grammes. grammes. grammes.
1 077 005 7082
2 "089 009 7098
3 "105 "014 “119
4 "130 "026 156
5 161 — "044 205
6 oh99 072 271
Z °240 ‘111 351
8 °289 173 462
9 337 241 578
10 392 334 °726
il 433 433 "866
12 487 539 1:026
13 “525 646 1171
14 559 745 1:300
15 and 16 979 1609 2°588
4°998 5°001 9-999
The salt contained in the three upper strata amounts to 299
milligrammes, of which 271, or 90°6 per cent. of the whole, are
chloride of sodium. The upper five strata yield 660 milli-
grammes of salt, of which 562 milligrammes, or 85:1 per cent.,
are chloride of sodium. ‘These proportions are not dissimilar to
those deduced from the former Table, and show that little is
gained in the way of separation by extending the diffusion-period
from seven to fourteen days, unless, indeed, the column of fluid
be increased in height at the same time.
It might be worth observing whether the separation of two
unequally diffusive metals can be favoured by varying the acid,
or form of combination—whether, for instance, the hydrates of
potash and soda would not separate to a greater extent than has
been observed of the chlorides of potassium and sodium, the
separate diffusibilities of the former substances being as 1 to 0-7,
while that of the latter are as 1 to 0°84]. I have not, however,
pursued this branch of the subject.
The separation of the same metals from each ober may pos-
sibly be favoured in another manner. In the preceding experi-
ments (Table VI.) the two metals were in union with the same
acid, or rather both were in the state of chloride. But the
metals might be used in combination with different acids, and
these acids themselves might be of equal or of unequal diffusi-
bility. Ifof equal diffusibility, such as nitric and hydrochloric -
acids, no reason appears why the acids should affect the amount
220 Mr. T. Graham on Liguid Diffusion applied to Analysis.
of separation. But if the acids are unlike in diffusibility, the
case is not so clear. If, for instance, the potassium were in the
form of chloride and the sodium in that of sulphate, might not
the diffusion of the potassium be promoted by the highly diffusive
chlorine with which it is associated, and the diffusion of the soda,
on the other hand, be retarded by its association with the slowly
diffusive sulphuric acid? Will, in fine, the separation of the
metals be greater from a mixture of chloride of potassium and
sulphate of soda, or even from sulphate of potash and chloride of
sodium, than from the two chlorides or from the two sulphates ?
The inguiry, it will be remarked, raises the whole question of
the distribution of acid and base in solutions of mixed salts. It
will be illustrated by a comparison of the diffusion of chloride of
potassium mixed with sulphate of soda, with the diffusion of sul-
phate of potash mixed with the chloride of sodium, the salts being
taken in equivalent proportions.
Taste [X.—Diffusion of a mixture of 5°12 per cent. of Chloride
of Potassium and 4°88 per cent. of Sulphate of Soda (equiva-
lent proportions), for seven days, at 14°.
No. of stratum. Potassium, Sulphuric acid, | Total diffusate,
in grammes. in grammes. in grammes.
1 028 002 024
2 035 002 030
3 "048 004 045
4 064 7009 "066
5 092 016 097
6 "128 "032 149
7 174 "058 215
38 242 105 316
epee line Ee at RUSSO SAR IN OMe Hoe ME Sts "441
Qe Oye Pen ee cceie 4 He te nieclester 615
ATS Wh ICE ee Se gL TV See aes 815
AB' ei b) el p peeteeduen hy) Gaal Pa iyscceas 1042
DS ete Ul Wl dike eeenes te Merlin al 4eowece 1°290
EEE eileen hg RGD wylelsiestes 1517
DDG AG TIP icone en Ae) Weeaast 3°346
10-008
The weight of the mixed salt was always 10 grammes. The
diffusions exhibited in Tables [X.andX.are strikingly similar,and
indeed may be considered as identical. It thus appears that the
diffusion of the metalsis not affected by the acid with which they
are in combination. ‘The result is quite in harmony with Ber-
thollet’s view, that the acids and bases are indifferently combined,
or that a mixture of chloride of potassium and sulphate of soda
is the same thing as a mixture of sulphate of potash and chloride
Mr. T. Graham on Liquid Diffusion applied to Analysis. 221
of sodium, when the mixtures are in a state of solution. With
two acids very unequal in their affinity for bases, the result pos-
sibly might be very different.
TasLe X.—Diffusion of a mixture of 4°01 per cent. of Chloride
of Sodium and 5:99 per cent. of Sulphate of Potash (equiva-
lent proportions), for seven days, at 14°.
No. of stratum. Potassium, Sulphuric acid, } Total diffusate,
in grammes. in grammes. in grammes.
1 028 002 023
2 034 002 030
3 049 004 044
£ 064 009 065
5 092 015 096
6 128 031 149
a 172 059 219
8 242 104 315
PGi t \escecei fies) i) || wesw 435
MO he ovsece rit) Wateane 600
Lip Ay Aes FRU a ee “LBM
mS cece ee E 1:025
Le ES) RE SU ad A Ge euro 1-261
PARR ENA A) Picvesest) bly) (ye oeenca 1-480
Li ITI LCT Sir PS eS manne Seranes 3°467
| 10°016
2. Effect of Temperature on Diffusion.
Diffusion is promoted by heat; and separations may accord-
ingly be effected in a shorter time at high than at low tempera-
tures. In a series of observations made upon hydrochloric acid,
the diffusion of that substance was carefully determined at 15°-5
(60° F.), and at three higher points, advancing by 11°11
(20° F.). The ratios of the diffusions observed were as follows :—
Diffusion of hydrochloric acid at 15°55 ( 60° F.), 1
‘; a at 26°66 ( 80° F.), 1:3545
‘ 4 at 87°77 (100° F.), 1:7732
‘3 3 at 48°88 (120° F.), 2°1812
The increments of diffusibility, 0°3545, 04187, and 0-408 for
equal increments of temperature, are probably affected by small
errors of observation, but they appear to indicate that the diffu-
sion increases at a higher, although not greatly higher, rate than
the temperature. The average increase of diffusibility for the
whole range of temperature observed is 0°03543, or 31; for each
degree (0°01969, or ;', nearly for 1° F.).
The preceding experiments were made by diffusing a 2 per
222 Mr. T. Graham on Liquid Diffusion applied to Analysis.
cent solution of hydrochloric acid from wide-
mouth phials immersed in a jar of water, as in
my former experiments*. The times were ob-
served in which an equal amount of the acid
(0:777 gramme from three phials) was diffused
out. These times of equal diffusion were 72
hours at 15°°55 (60° F.); 53°15 hours at 26°66
(80° F.) ; 40°6 hours at 37°°77 (100° F.) ; and
33 hours at 48°88 (120° F.).
The diffusate from a 2 per cent. solution of
chloride of potassium in similar circumstances
was 0°6577 gramme
In 101°75 hours at 15°55 (60° F.); and
In 41:93 hours at 48°88 (120° F.).
The diffusate from a 2 per cent. solution of chloride of sodium
was 0°65383 gramme
In 124°75 hours at 15°55 (60° F. a 3
In 49-60 hours at 48°: 88 [207 ee
In equal times the diffusate would be
For chloride of potassium at 15°55 ( 6
BS at 48°°88 (12 OF \, 5 426
For chloride of sodium at 15°55 ( 60° by ae
- » at 48°88 (120° F.), 2°5151.
As the ratio between the diffusates of hydrochloric acid, at the
same two temperatures, was 1 to 2°1812, it appears that the acid
is less increased in diffusibility than the salts at the higher tem-
perature ; chloride of sodium also is slightly more increased than
chloride of potassium. The more highly diffusive the substance,
the less does it appear to gain by heat. Chloride of sodium ap-
pears to be sensibly 24 times more diffusible at 48°88 (120° F.)
ae at 15°-55 (60° F. : :; this gives an average increase of 0-014,
or ;/, for 1 degree (0:025 for 1° F., or 7). The mequality of
diffusion which the three substances referred to exhibit at a low
temperature becomes therefore less at high temperatures ; and
it would appear to be the effect of a high temperature to assimi-
late diffusibilities. Heat, then, although it quickens the opera-
tion of diffusion, does not appear otherwise to promote the sepa-
ration of unequally diffusive substances.
The results in such experiments are less disturbed by changes
of temperature, if at all gradual, than might be supposed. A
sensible separation was obtained of hydrochloric acid and chloride
of sodium from each other, in a solution contaiming 2 per cent,
of each substance, when the water-jar was heated up from 15°55
* Philosophical Transactions, 1850, p. 25.
Fig. 2.
On the Secular Change in the Magnetic Dip in London. 223
to 95° C. in two hours, and maintained at the latter temperature
during four hours more. Diffusion appeared to be accelerated
about six times at the higher temperature.
At low temperatures, again, diffusion is proportionally slow.
The ratio of diffusibilityof the following salts at two different tem-
peratures appeared to be,—
For chloride of potassium at 5°-3 (41°°5 F.), 1; at 16°°6 (62°°0 F.), 1°4413
For chloride of sodium = at 5°°3 (41°°5 F.), 1; at 17°°4 (63°°4 F.), 1°4232
For nitrate of soda at 5°°3 (41°°5 F.), 1; at 17°°4 (63°°4 F.), 1°4475
For nitrate of silver at 5°°3 (41°°5 F.), 1; at 17°°4 (63°°4 F.), 1°3914.
The salts are unequally affected to a sensible extent ; and it
will be observed that the superiority of chloride of potassium over
chloride of sodium, in diffusibility, is increased at the low tem-
perature.
Within the range of temperature of the preceding experiments,
the diffusibility of chloride of sodium beimg taken as 1 at 17°*4
(63°°4 F.), it becomes 0°7026 at 5°°3 (41°°5 EF.) ; or it diminishes
0:0246, or .., for a depression of 1° (0:0136, or —., for a de-
: 40°79 73°5?
pression of 1° F.),
[To be continued. |
XXXII. Proceedings of Learned Societies.
ROYAL SOCIETY,
[Continued from vol. xxi. p. 552.]
March 14, 1861.—Major-General Sabine, R.A., Vice-President and
Treasurer, in the Chair.
a following communications were read :—
** On an Application of the Theory of Scalar and Clinant Radical
Loci.” By Alexander J. Ellis, Esq., B.A., F.C.P.S.
“A Seventh Memoir on Quantics.” By Arthur Cayley, Esq.,
F.R.S,
* On the Secular Change in the Magnetic Dip in London, between
the years 1821 and 1860.’ By Major-General Edward Sabine, R.A.,
Treas. and V.P.R.S,
I propose in this communication to bring together and discuss four
determinations at different epochs, in which I have myself been either
directly or indirectly concerned, which have had expressly in view the
object which forms the title of the paper. -
Epoch of 1821,—The experiments on this occasion were made in
a part of the Regent’s Park, then occupied as the nursery garden of
Mr. Jenkins: an unexceptionable locality in all respects, and far
distant at that time from buildings or iron implements, railing, or
pipes. The experiments, ten in number, were made on six different
days, between the 3rd and 10th of August 1821; and all between
8 a.m. and 4 p.m. The circle employed was 113 inches in diameter,
made by Nairne, a celebrated artist in his day for instruments of this
description: the needle was made by Dollond on Professor Tobias
224 Royal Society :—
Meyer’s principle, described in the Géttingen Transactions for 1814.
The size of the small spheres, or their distance from the needle, was
varied in the different experiments, so as to bring different parts of the
axle to rest on the agate planes. The mean of the ten experiments
was 70° 02':9 N., corresponding to the epoch 1821.65: the extremes
being 70° 001 and 70° 05'°9. The whole of the experiments were
made by myself, and are detailed in a paper in the Phil. Trans. for
1S22, Att. 1.
Epoch of 1838.—The experiments on this occasion were made on
different days in 1837 and 1838, in the course of the magnetic survey
of Great Britain, by Messrs. Robert Were Fox and John Phillips,
Captain (since Admiral) Sir James Clark Ross, Captain Edward
Johnson of the Royal Navy, and myself. The instruments employed
were those of Robinson, Gambey, and Jordan: the particulars are re-
corded in the 8th volume of the Reports of the British Association for
the Advancement of Science (1839), Table 10, p. 64. The localities in
which the experiments were made were—1. The same spot in the
Regent’s Park where those of 1821 had been made. 2. Kew Gardens.
3. Westbourne Green, a locality which has been since built over.
Separate determinations were made on 13 days between May 30, 1837,
and December 10, 1838, the mean epoch being 1838.3, and the mean
dip 69° 17'"3.N. The extremes of all the observers and of all the in-
struments were 69° 13!:3, and 69° 23'9.
Epoch of 1854.—The experiments on which this determination
rests were made by the late Mr. John Welsh, of the Kew Observatory,
and myself in August and September 1854, with two inclinometers
made by Mr. Henry Barrow (successor to Mr. Robinson), fitted
according to the modern English construction with verniers and
microscopes, and each having two needles. The localities selected
were—1l. The station in the Regent’s Park already named as that of
the experiments in 1821, and of a part of those in 1838; and 2. the |
magnetic house of the Kew Observatory. The experiments had a
double purpose, viz. 1, to ascertain the difference, if any, in the
dip in the Regent’s Park and in the magnetic house at Kew; and
2, to obtain a determination of the dip in August 1854 which might
be strictly comparable with the result obtained in August 1821. The
experiments were made on five different days, and comprised eighteen
determinations, ranging between 68° 29'-25 and 68° 33/73 ; the mean
being 68° 31'-13 N., corresponding to the epoch 1854.65. The
mean of eight determinations in the Regent’s Park was 68° 30'°55,
and of ten determinations at Kew, 68° 31'-6; the difference of either
from the mean being 0/52, which is within the limits of probable
error. A detailed notice of these experiments was published in
1855 in an Editor’s note in p. 364 of the translation, edited. by
myself, of Arago’s Meteorological Essays.
Epoch of 1859.5.—The dip corresponding to July 1, 1859 (now
first discussed), is derived from 282 determinations made in the
magnetic house at Kew on 121 different days between November 1857
and December 1860 inclusive, chiefly by four observers, viz. Mr. John
Welsh, late Director of the Kew Observatory, Mr. Balfour Stewart,
On the Secular Change in the Magnetic Dip in London. 225
“its present Director, Mr. Chambers, Assistant in the Observatory,
and Dr. Bergsma, Director of the Magnetical and Meteorological
Observatory of the Netherlands Government in Java.
There were employed in these determinations, on different occasions,
twelve circles and twenty-four needles, all of the same form and
pattern; the circles being 6 inches in diameter, fitted with verniers
and microscopes, and the needles 34 inches in length; they were
all made by Mr. Henry Barrow. Every determination was
complete in the eight different positions of the circle and needle, as
described in Appendix 2 of the Article ‘‘ Terrestrial Magnetism ”’ in
the 3rd edition of the ‘ Admiralty Manual of Scientific Inquiry.” The
individual results are shown in the subjoined Tables, whereof Table I.
contains 115 determinations comprised between November 1857 and
December 1858; Table II. 96 determinations between January and
December 1859; and Table III. 71 determinations between January
and December 1860. The results in each year are reduced to the
Ist of July in the same year, employing the proportional parts of an
annual secular change of —2!-6: those which were obtained in the four
winter months, November, December, January, and February, have
also received a correction of —0'°8, and those obtained in the summer
months, May, June, July, and August, a correction of +0'8 in
compensation for annual variation, agreeably to an investigation con-
tained in the sequel. The Tables exhibit im every case the date, the
particular circle and needle employed, the azimuths in which the
observations were made, the name of the observer, the observed dip,
the reduction to a common epoch, the correction for annual variation,
and finally, the corrected result.
The opportunity afforded at the Kew Observatory, of testing the
degree of accordance which may be expected in the results of different
instruments constructed on the plan which has been for several years
past approved and adopted at Kew, has thus been profited by, and the
conclusions appear such as to merit the consideration of those who
are desirous to possess reliable instruments. Several of the circles
are the property of foreign governments or of individuals, at whose
request they were provided subject to a verification at Kew. The
observations here recorded were for the most part made for the
purpose of such verifications, and were entered as they were made in
the books of the Kew Observatory, from which they are now taken.
No observation has been omitted. The circles were distinguished by
the numbers 20, 23, 27, 28, 30, 31, 33, 34, 35 and 36; and two
unnumbered, one known as the Kew Circle, the other an inclinometer
employed by Admiral Sir James Clark Ross in his recent magnetic
survey ofapart of England. No. 20 was made for Professor Hansteen
of Christiania, and is now in his possession ; 23 is the circle used by
the late Mr. Welsh in his magnetic survey of Scotland; 27 was
supplied to the Austrian frigate ‘ Novara’ for her voyage of circum-
navigation ; 28 was made for the Russian Government ; 30 was used
by myself in the recent magnetic survey of England, and has been
since supplied to the Observatory at the “Isle Jesus’ near Montreal
in Canada; 31 was made for Padre Secchi of the Collegio Romano,
and is now at Rome; 32 was made for the Rev. Alfred Weld of
Phil. Mag. 8. 4. Vol. 23. No. 153. March 1862, ()
226 Royal Society :—
Stonyhurst College, and is now in the Observatory of that College ;
34 was supplied to the Government of the United States of America,
and is now in the possession of Dr. Alexander Dallas Bache, Superin-
tendent of the Coast Survey; Nos. 35 and 36 were made for the
Netherlands Government, one for Utrecht, and one for Java; the
‘Kew Circle’’ was in regular use for the monthly determinations of
the Dip at Kew, from the commencement of those observations until
August 1859, when it was exchanged for No. 33, which has subse-
quently been, and is now, in regular employment for that purpose.
Besides the four principal observers already noticed, a few determina-
tions were made, as is shown in the Tables, by Mr. Valentine Magrath,
Assistant in the Observatory, by Captain Haig of the Royal Artillery,
practising at Kew preparatory to his employment on the Boundary
Commission between the United States and the British possessions
on the West Coast of North America, and by Lieut. Goodall of the
Royal Engineers, who attended at Kew to practise the manipulation
of magnetical instruments.
TasLE I.—Observations of the Magnetic Dip, at the Kew Observatory, in
1857 and 1858, with Circles of the English Construction, fitted with
Verniers and Microscopes.
$ 2a Reza SE E 3 | 22/828) 3
A 6 2 g : E 3& |ese| ec
Zi S} 2 oO oR og a OD >,
< =) fe 3 5 > ae
o) i) min
1857. ° ° ° / ‘
Noy. 2 27 I o & 180 Mr. Welsh. 68 23°4 | —1°8 —O8 | 63 20°8
2 27 Dae 45) LZ * 24°9 1°8 og D278
2 27 Tit HOW; 150 24°5 1°8 o°8 21'9
2 27 2 © 5, 180 . ee, 1°8 0°83 22°6
2 27 BAO ys T20 . 23°38 1°8 08 2125
2 27 254 60%,, 150 4 24°0 1°8 o°8 21°4
2 Kew 2 Ors Iso Mr. Chambers. 27°0 1°8 o'8 24°4
2} Kew DBM feat CoP >To) as 24°0 1°3 o°8 214
2 Kew 2,60 5, 156 A 2.4.0 1°83 o8 21°6
3 23 I © » 180 Mr. Welsh. 2.6°3 1°8 o'8 2a7
3 23 Bil 90) 5.120 Hd 26°6 1°8 o's 2.4.°O
3 22 1 | 60 ,, 150 + 25°6 1°8 o°8 2370
3 23 2 © 3, 180 5 26°6 1°8 o°8 24°0
a 23 ZN BO! 55 LZO 4 25°5 1°8 o°8 22°9
3 23 2 | 60 5, 150 25°0 1°8 o°8 22°4
3 27 3 © » 380 Mr. Chambers 2.2°0 1°8 o°8 19°4.
3 27 ela bie (sy cry see; oe 23°5 1°3 o'8 20°9
3 27 3 | 60 » 150 os 2.375 1°8 o°8 2.0°9
‘4 28 I © », 180 s 22°3 1°83 o's 19°7
4 28 rE { 305, 120 + 25% 1°8 o°8 22°5
4 28 1 | 60 5, 150 i 27°29, 1°83 o°8 246
5 23 2 © 180 te 28° 1°8 o°8 25°5
5 28 2. | 20.55 120 . 25°3 18 o°8 22°79
5 23 60 5, 150 af 28°I 1°8 o'8 2575
7 23 I &A Mer., and at Sp 25°6 1°38 o°8 2.3°0
right angles. 1°8
ie) 27 1&4) Mer., and at a 34°2 1°38 o's 31°6
right angles. bee ae ot
yi 23 I o & 180 4 24.°9 I°4, o°8 22-7
27 28 2 4 a 68 29°4.| —1°4. | —o°8 | 68 27°2
On the Secular Change in the Magnetic Dip.in London. 227
TaBLe I. (continued.)
‘ a g Schl (Ss
5 ¢ |4| $ : 2 | €2/s22| 32
2 E 3 E E F Pe | See; sa
A o 7, eI Q By ote og Ss Db
< ° = S is ae
fo) o) Or
1358. °o ° ° 4 / / ° /
Jam: 3)’ Kew I o & 180 Mr. Chambers. | 68 20°7 | —1°4 | —o°8 | 68 13°5
1} Kew 2, 35 i 24°7 1°4 o°8 22°5
5 Kew 2 ¥ a 24.6 1°4. o8 22°4
5| Kew I i Mr. Welsh. - 208 154) ]) BNORS, [4 MeT8°6
8} Kew I ~ Cap. Bedingfield, R.N. OH 1°4 o°8 22°9
14|. Kew 2 5 Capt. Haig, R.A. 24°9 1°3 0°8 22°8
14] Kew 2 + i - 24°6 ie c'8 22°5
16 Kew I 53 35 23°6 13 o°8 2) 2'5
18 23 I a ee 23°4 1°3 o°8 26°3
18 23 I +s a 22°38 3 o°8 2077,
Feb. 3 ? 5 Mr. Chambers*. 27°2 1°2 o°8 Zs)
4| Kew I op zs 2.2°9 12 o°8 20°9
4, Kew 2 op 5 2.6°9 r2 0°8 24°9
27| Kew I > Hs 20°3 1m) o°8 18°5
27 Kew 2 os - 22a ro | —o°8 2077),
Maree 1| Kew I 9 Mr. Welsh. 24°4, HO | “Oso 23°4
I Kew 2 ” ss 2Ae3 I°O (oho) 23°3
4 Kew 2 ” ” 25°4 o"9 He) 24°5
5| Kew I 3 “a 22 o'9 (oho) 21°6
22| Kew I ” “: 28a O'7 o°0 23°0
22| Kew 2 + es 25°9 O'°7 foe) 25°2
27| Kew I 5 oH 2Rn7 O'7 route) 23°0
27, Kew 2 9 . 26°1 O'7 foe) 45°.
27| Kew I i Mr. Chambers. 21°6 0'7 foe) 20°9
30 20 I + Mr. Welsh. 25°4 O°7 o’o 24°7
30 30 rt |(30°& 120 ss 23°3 O'7 foXe) 27°6
30 30 Te GGn,, 150 Hs 23°0 0'7 foxe) 2258
30 30 I © 5, 180 Ap 23°2 O°7 foxe) 225
30 2.0 ie \e3on,, 120 _ Price) O'7 o°o 20°6
30 30 TaeGon,, 150 a 25°2 O'7 o°0 24°5
30 30 2 O 5, 180 Mr. Chambers. 250% O'7 foMre) 24°4
30 30 2 | 30 ,, I20 ¥§ 26°9 o'7 (ove) 26°2
30 30 Pe eGOL,, E50 3 27°O O°7 foe) 26°3
Apr. 22 Kew 2, © ,, 180 Mr. Magrath. 23°77 o's oho) 23°2
22, Kew I Es “9 24°0 0°5 oh) eile
27| Kew I My Mr. Welsh. 2.0°9 05 | o'o 20°4
27 Kew 2 ep Mg ae 0°5 o°0 21°,
28| Kew I E Mr. Chambers. 22°8 O'S fore 2208
28 Kew 2 ~ i 23°F 0'5 foxe) 21°2
May 20| Kew I A is 22°38 0°3 | fos 22°8
20} Kew 3 + A '2.3°9 0°3 o°8 24°4,
26} Kew I c Mr. Welsh. 2.0°5 0°3 o°8 21°O
26; Kew 2 + 4 24°1 03 o°8 24.°6
27 Kew I Be Mr. Chambers. 21°6 0°3 o'8 22°%
27| Kew 2 9 “) i te 03 o°8 21°8
27\Sir J. Ross| 1 ” Mr, Welsh. 25°4. 0°%3 o'8 25°9
28|Sir J. Ross| 1 13 + 26°8 03 o'8 278
28\Sir J. Ross} 1 | 30 & 120 Ms 20°3 raphe cr8 20°8
28|Sir J. Ross} 1 | 60 ,, 150 i 24°0 0°3 o°8 24°5
June 9 30 I Oy. VIO ‘9 68 21°1 | —o'2 | +0°8 | 68 ar
* Marked “ Doubtful.”
&
>: a Royal Society :—
TABLE I. (continued.)
Ps & s & g Bes
A Ace. #e : E | de | gael | ee
7 * < 5 $013" eee
5 ian & oF
1858. | ° o aie / ‘ b
June 2 o & 180 Mr. Welsh. 68 21°6 | —o'2 | +0°8 | 68 22°2
I 7 Mr. Chambers. 19°9| || Rois Wl worm 20°6
2 ” “A 20°7 ov! o's 21°4
2 ” . 19°83 orl o'8 20°5
I ” ; * 18°2 orl o°8 18°9
I ” Mr. Welsh. 27°4. o'r o°8 28°I
2 ” - 23°0 o'l o°8 23°7
2 ” “5 grin Ost o°8 23°83
2 | 30 & 120 . pla o'r o°8 25°9
2 | 60 4» 150 a 24°7 | —o'r o°8 2.5°4.
2, © », 180 if 25°I foie) o'8 25°9
I ” Mr. Chambers. 23°4 rote) o'8 24°2
2 ” Mr. Welsh. PI s2n o'o o's 25°9
I ” ” 23°9 foe) o°8 24°7
I ” Mr. Chambers. az, (ose) o°8 2253
July © I ” 43 24°3 (ose) o°8 25°x
I ” ” 2 Gl roe) o°8 26°3
2 ” “ 22°9 foWfe) o°8 2377
2 ” a 22°7 | torr o°8 23°6
I ” ” 237% ol o°8 24°0
Aug. 2 ” ” 20°1 0°3 o°8 212
I ” ” 20°F, 0°3 o'8 21°8
2 ” ” 21a 0°73 o'8 22°4
1) 3 + 21°7|| GA j wis 22°9
2 ” ” 2B°5 04. | +o0°8 24°7
Sept. I ” ” 2254 0°6 foe) 22°7
2 ” ” 20°38 o°6 foMe) 21°4
Oct. I ” , 22°h O'7 foe) 24°1
Zz +B) ” 24°2 O°7 rome) 24°9
Noy. I ” » 20'0 | o'g | —o°8 20°1
2 ” 5 23°4 o°9 o°8 23°5
I ” ” 25°6 o"9 o°8 28°7 |
2 ” ” 26°1 o°9 o°8 26°2
2 ” A 23°0 IO o°8 25°2,
I ” ” 2A I°O o°8 24°5
Dec. 2 AA AR 20°8 Tigh o°8 21°!
I ” ” 22°3 128 o°8 22°38
2 i i. 68 2074 |-+1°3 | —o°8 | 68 20°9
July i, 1858, mean Of 115 Observations... 2.600. soca ccsncescleeen os eee enna
|
|
|
|
|
On the Secular Change in the Magnetic Dip in London. 229
Taste IJ.—Observations of the Magnetic Dip at the Kew
Observatory in 1859.
} }
| H a. i) 5 a
: e =~ : =O
z Beebe 2 e a EG) US BE | as
i =) era ae 5 lial ca Timea (ak Ss
EM Eg Uce
1859. 5 S Oy 4 / (0)
Jan, 4| 3 1 |}o & 180 Mr. Chambers. 68 22°5 | —1°3 | —o°8 | 68 2074
Aly, 31 2 - ce 21'O 1°3 0°38 13°9
t1i Kew | 1 5 Mr. V. Magrath. 23°6 vie. o°8 21°5
“sl 30 I rf Mr. Chambers. 23e7, Eh Os8 21°6
| co ae 9 24°6 | 1°73 | 08 22° 5
11| Kew | 1 i Ke 21°6 73 o°8 19°5
12} 30 2 Fs ” 23°7 1-3 o°8 2.1°6
12| Kew | 1 Bf 33 22-2, 3 o°8 20°!
12; 30 2 ” ” 24°4. 13 o°8 22°3
24| 30 I dp - 2207, re, 0°83 20°7
24| Kew | 2 3 A 19°8 1°2 o°8 17°8
24) 30 I ” ” 21°6 °2 o°8 19°6
25 30 2 ”» ” 24°1 2 os 221
25| Kew | 2 bs ” 20°4 0:2 o°8 18°4
25) 30° I » ” 22-2, 1°2 o°8 20°2
25| Kew I “fp ” 18°9 I'2 | —o'8 16'9
Mar. 7| Kew | 1 . 19°6 o°8 foMre) 13°38
7 Kew 2 ” ” 20°! o°8 foe) 19°3
3, 30 I ”? ” 21°7 o°8 foue) 20°9
ieee. 2 a A 2929, o's fone) 21°4
3; 20 I “6 ” 20°8 08 foMre) 20°0
8| 20 2 a os 22°3 o°8 o°0 22°0
Io 20 2 ” ” 24 6 o°8 joe) 23 8
IG}... 33 2 39 ” 20°5 og foxe) 19°7
II} 20 I 33 ” 24°1 o°8 foe) 237%
FG 33 I iF op 25°0 o's fone) 2A°2
PE 33 I a ” 22°2 o°$ (ooo) 214
II) 33 2 ” ” 2253 o°8 owe) 23°5
Fe Pel I Fr ” 21-0 0°83 o°o 20°2
TI] 34 2 . ” 21°6 o°8 foue) 20°8
12} 34 I P - 21°4 o°8 foMe) 20°6
EZ. 34 z r ” 2C°4. og foMe) 19°6
12) 23 i ” ” 25°O fo} rote) 24°2
FS). 23 2 a ” 21°8 o'8 owe) 21°O
14] 23 I ” ” 24°6 o°8 foto) 23°8
14] 23 2 9 ” 22°7 o°8 o°O 21°9
15| 33 I ” ” 22°9 o°8 fohfe) 22°1
I a4 2 cp ” ake o°8 foue) 20°9
15| Kew I ce ” 21°S o°8 role) 20°7
¥5| Kew | 2 a ” 2652 o°8 fowe) 2505
16| 33 I ” ” 22°9 o°8 foxe) 22°95
06) ...33 2 ” ” 21°8 o°8 route) 21°O
mG). 34. I rp ” DIS Oo o"0 20°7
16] 34 2 eh ” TOES | 4 Go o°0 18°7
wy 94 I A | ” 24°83 O7 fohze) 24°1
Eat 34. 2 » ” 13°4 o°7 o°O btn
D7). 30 I 3 99 217 o°7 foMe) 21°C
MgO (2 : ”» ” 68 24°4 | —0'7 oo | 68 23°7 |
230 Royal Society :—
TaB e II. (conéinued.)
Bo 8 eee ees
: 4 5 A ga |aqs| 8
AS = = ro =e oe-Ere gn
3 iS o 2 on, | S28 eee
A s F B | se | Ede) Bs.
ead oe
1859. ° ° ie} / / / ie} /
Mar, 18 o & 180 Mr. Chambers. | 68 23°3 | —o'7 o'o | 68 22°6
18 5s 5 25°0 O'7 fohze) 24°
| 18 + - 21°5 O'7 o"o 20°3
| 19 as as ils o'7 0°0 20°8
SS) ” ” 23°7 7 O40 2352
19 st A 2077) O'7 oxo) 26°0
April 20 a Dr. Bergsma. 22 O°5 ole) 22°0
: 55 Bt 21°2, O°5 foMe) 20°7
? ss “A 19°2 0°5 owe) 18°7
30 Ze 5) 21-7 O°5 oye) 2072
May 16 a on 18°8 o°3 | +08 19°3
16 a i 18°r 03 o'8 18°6.
16 ss Mr. Chambers. 19"0 0°3 o°8 19°5
16 go 3 19°4 03 oS), 19595
17 i Dr. Bergsma. 18°2 rome) 0°8 18°7
17 » 9 20°3 | 03] 08 20°83
17, 18 ue Mr. Chambers. 20°7 03 o'8 212
17,18 5 an 20°7 | —0°3 o'8 2a
July 7 ai 9 21°3 foMe) o'8 225
7 a a 21°9 ove) o's 227,
Aug. 10 ‘p AS 17°4. | +0°3 o°8 18°5
10 ” ”? 18°3 0°3 08 19°4.
15 ue Dice 0°3 o's 22°9
15 ” 9 17°2 |) O32 uo 18°3
22 5 9 2:5°3 311) O:Sia eure 26°4.
22 BS a 20°6 0.3 0°8 ay,
22 °° is 22°6 0°73 o°8 237
22 a op 21°9 o°3 | +0°8 23°0
Sept. 12 <2 a 21°9 06 foMe) Heder
12 <5 os 20°4. 0°6 foMfe) 21°O
21 Sy A 23°6 0°6 route) 24°2
21 = ny 22D 0°6 foMe) 22°8
Oct. 29 neh A 25°6 o"9 foKe 26°5
29 is i. 24°1 o"9 foMe) 256)
| 29 * in 22°8 °'9 0°0 23°7
29 s ” 2a, o"9 (oxo) 24°6
| Noy. 17 a - 23°9 I'o | —o'8 24°1
17 ee ” 22an I°O o'8 2203
| 17 Ge of 22°4 I°o o°8 22°6
17 oe a 24.°3 I'o o°8 24°5
17 5 Mr. Magrath. 21°O I"0 08 25-2
17 Ga ” 24°3 I'o OB i) 2455
17, 99 ” 24°3 1° o°8 24°5
17 + ” 2r2 I°o o°8 21°4
18 as ” 20°5 I'o o°8 20°7
18 3 Mr. Chambers. 20° I'O o°8 2073
Dec. 21 a 5 20°2 12 08 20°6
21 ba aoe 68 2174 | +1°2 | —0°8 | 68 21°38
June
July
On the Secular Change in the Magnetic Dip in London. 281
Tas eE I[I.—Observations of the Magnetic Dip at the Kew
Observatory in 1860.
Needle.
PRP YPN DY HAR he he DDD DAR RD DD Be ee oe DN DR DD Ree ee YN DY DD Bee DY DY YD Ye DY
Azimuth °
fo) °
o & 180
Observer,
Mr. Chambers.
Lt. Goodall, R.E.
Mr. @iainbers:
3?
99
Mr. Stewart.
”?
Mr. Chambers.
?
Mr. Stewark:
Mr. Chambers.
Dr. Bergsma.
”
”
Mr. Chambets.
Dr. Bergsma.
a s
5 =
ie} / /
68 21°9 | —1'2
22°9 1°2
20°7 b re)
21-5 I'o
20°8 o'8
25°2 o°8
21°9 o'7
24°7 7
22°38 0°6
21°6 o°6
17°3 0°5
18°5 O°5
18°6 0°5
20°4 O°5
20°6 O°5
14°8 O°5
23°9 os
13° O°5
20°5 0°3
19°5 or
20°5 0°3
19°2 0°3
19°0 0°3
18°o 03
19°7 03
20°! op i
19°I robe |
16°6 ohe
E7s7 ov!
19°3 o'r
18°8 one i
19°2 o'r
18°38 | —o'r
oH te foMe)
22-8 rome)
18°4. fox)
17°38 foxe)
19°9 foMe)
nS t fohe)
19°5 foue)
19°7 foxe)
21°7 route)
22°6 oho)
17°7 owe)
13'2 owe)
22°9 route)
15°4 foe)
68 15°7 | +o"!
© i) @s
ga8|/ AS
E igo] “+= 2 een oe
a a © gs 5 2 Sy, Sasa a +
Q oO iS) 45 77) E 3 8 S-5 S44
Zz 8 2 cs) rs Ea Le
* ° 3 = Ss >| Es
fe) Oo orm
|
1860. ° ° Onn, ‘ / Oo 7
July 91.35 1 |o&18 Dr. Bergsma. 68 20°4 | -+or1r | +0°8 | 68 2173
9] 35 2 + 1770 ol o°8 17°9
9} 36 I ” ” 14°5 o'r o°8 15°4
9} 36 2 ss % sed Oo’! o°8 14°!
251. 33 I $3 Mr. Chambers. 18°6 o'2 o°8 19°6
32} Relies Le) 2 5 a Bos o'2 o'8 22
Aug. 16} 33 I % 16°4 O'4 o°8 17°6
16] 33 2 3 169 o°4 | +0°8 13'r
Sept. 14] 33 2 3 5 19°9 0°6 foMe) 20°5
143.34 I » ” 18°9 0°6 foMe) 19°5
Oct. 391.1533 2 55 > 212 0'9 fosze) 227%
19] 33 | I 55 9 2.0°S 0'9 foe) 21°4
22| . 30 I 5 Mr. Stewart. 18°0 0°9 o"o 18°9
22\k 30 2 5 y 20°6 0'9 (oxo) Dy ial
772 30 2 - 9 Qe o'9 (owe) 22°1
22| 30 I 5 9 14°9 o°9 fohge) 15°8
23. 30 ie i ” 17°6 o'9 foxe) 13°5
21.2) (eX 1 | in 19°2 0'9 o°0 20°5
30| . 30 ea Votes ; 23°0 o°9 oe) 23°9
Nov 24 a8 I i Mr. Chambers. 2.0°3 xe) || Oris 20°5
7.5) Wee Yn Mal Vee? | He = B05 T26) o'8 21s
Decks 231.33 a Mane ” 19°I 12 o°8 19°5
19) 33 ity haba S 9 68 180 | -+1°2 | —o°8 | 68 1874
July 1, 1860, Mean of 71 observations... ciclo» 0% 2/2) ole oc uate te oo mic aioe eee 68 19°8
Correction for Annual Variation.—W herever, in the middle lati-
tudes of the northern hemisphere, observations of the dip have been
made with sufficient care, it has been found that, after elimination of
the effects of secular change, the north dip is somewhat greater in
winter than in summer. In the 3rd volume of the Toronto Observa-
tions, pp. exxiiand exxii, the following Table is given as the result of
fifteen years of careful observation made throughout at the same spot
and according to the same method of observation, comprising 1920
independent determinations nearly equally distributed in the different
months, and averaging about 128 determinations for each of the
twelve months; by combining the months equidistant from July
(or the middle of the year), the influence of secular change is elimi-
nated :— Ai ;
Mean of January and the following December .... 75 18°90 N.
Mean of February and the following November ..75 18°98 ,,
Mean of March and the following October ...... 7) TGs,
Mean of April and the following September...... 73 16°7 ies
Mean of May and the followmg August ........75 17°70 ,,
Mean of June and the following July .......... 79 17°29 5,
On the Secular Change in the Magnetic Dip in London. 283
Hence on the Ist of July the mean dip at Toronto would be derived
as follows, viz. :—
j
From the four winter months, November to February .. 75 18°97
From the four summer months, May to August ...... 75 17°47
Showing an excess of 1/"5 in the winter months above the summer
months.
The annual variation at Kew, as it may be derived from the 282
determinations in Tables I., II. and III., does not differ materially
from this conclusion. There are in these Tables 87 results obtained
in the four winter months of the different years, and 93 results
obtained in the four summer months of those years. If we collect
into separate means the results in the winter months of 1857-58,
1858-59, and 1859-60, numbering them (1), (3), and (5),—and into
separate means the results in the summer months of 1858, 1859 and
1860, numbering them (2), (4), and (6),—and if we compare (1)
and (3) with (2), (3) and (5) with (4), (2) and (4) with (3), and
(4) and (6) with (5), (by which comparisons the effects of secular
change are eliminated), we find an excess of 1'-7 in the mean dip of
the winter months over that obtained from the summer months. The
mean of the two corrections, thus separately obtained at Toronto and
Kew, is 1/6; of which the half, or 0/8, has been applied in the
Tables with the — sign to the results in the winter months, and with
the + sign to the results in the summer months.
Probable error of a single determination of the Dip.—It may be
desirable to state the probable error of a single determination as it may
be derived from the observations in the Tables, before and after the
application of the correction for annual variation. It will be seen
that the probable error is dimimished by the application that has
been made of a correction on this account,
When uncorrected When corrected
for annual variation. for annual variation.
Semin s Results in Tabled... 1-50.) .. ....' +149
From the 96 Results in Table II. +1°44.......... + 1°39
Pommeene ) 7) Results. in.Table IM. 7:1°57......... + 1°46
raat (EEO) Pees erg eA
The probable error thus obtained represents all the diversities
ascribable to the employment of different instruments (all of the one
construction),—to the supposed peculiarities of different observers,
—to the occasional presence of magnetic disturbance (for which no
correction has been attempted),—and to differences due to different
hours of observation ;—in addition to what may be more strictly
viewed as ‘observational errors.” It may thus serve in some mea-
sure as a guide to those engaged in similar researches, as to the degree
of accuracy which is attainable in such experimental inquiries, when
proper care is taken in the procurement of a reliable inclinometer
and in its manipulation.
For the purpose of comparing the probable error thus obtained
234 Royal Society :—
with inclinometers of the later English pattern with that of the
instruments of earlier construction, four of the latter were selected,
viz. a 9-inch circle by Robinson, a 9-inch circle by Barrow, and two
6-inch circles by Robinson, all in good order. Each circle was
furnished with two needles of the same length as the diameter of the
circle, and read bya lens in lieu of verniers and microscopes. Table IV.
contains the particulars of 20 determinations made with these instru-
ments in 1860 by Messrs. Stewart and Chambers. Their mean
result is 68° 20':04 reduced to the epoch 1860.5, and corrected for
annual variation. The mean result of the 71 determinations at the
same epoch in Table III. is 68° 19'"8. There is therefore no notable
difference in the mean results obtained by the two classes of instru-
ments; but there is a considerable difference in the probable error ;
as from the,20 determinations in Table IV. we obtain +3'°65 as the
probable error of a single determination with the instruments of the
earlier pattern, whilst +1':5 has been shown to be the probable error
when inclinometers of the more recent pattern were employed.
TasLe [V.—Observations of the Magnetic Dip, at the Kew Observatory, in
1860, with 9- and 6-inch Circles (Robinson’s and Barrow’s), without Verniers.
rm & = & < as
A S| 2 E: EB Se LE ee
4 © 2. le ee ee
} me 3 om
1860. ° / / / ° /
Mar. 16} Robinson’s 9-inch I Mr. Stewart. 68 29°4 | —o'8 o'o | 68 28°6
17 ” I ” 24°7 o°8 o"o 23°9
17 = I a 180 o°8 foMe) 1772
19 4. 2 - I4°2 o°8 o'O 13°4.
19 PP 2, “5 13°5 o°8 o°o 1277
16 | a 2 “ 2207, o°8. foWe) 21°9
21, Barrow’s g-inch I 5 II°O o°8 foie) 10°2
21 se I a 16°5 o'8 foMe) 15°F
21 =F 2 3 24°0 o's lowe) 23°2
21; Robinson’s 9-inch I Mr. Chambers. 16°6 o°8 four) 15°8
21 a 2 e 21°8 o°8 foe) 21°O
22| Barrow’s g-inch Z Mr. Stewart. 2.6°5 o°8 foMe) AT |
22 5 2 Mr. Chambers. 2307 o°8 foxte) 22°4.
22 i I “ 13°o o°8 rome) 172
May 2/)Robinson’s 6-inch, No.1} 1 » 2.6°3 o°5 | +0°8 26°6
4 ‘ 2 if 30°7 | 05 | +08 | 310
4 Robinson’s 6-inch, No.2} 1 43 18'r o°5 | +o°8 18°4
4 ” 2 ” 175 | 0% |p 17°8
Noy. 26 ” I Mr. Stewart. 19°o | -+1°r | —o°8 19°3
| 26 ss 2 oA 68 18°5 | +11 | —o°8 | 68 18°8
| July 1, 1860, mean of 20 observations .......--cesseececcccccereccccat «- 68 20°04
The observations were all made in the plane of the magnetic meridian.
The values obtained for the Dip at the epochs of 1821 and 1854,
having been derived from observations made at the close of August
and beginning of September in those years, require a small cor-
On the Secular Change in the Magnetic Dip in London. 235
rection for annual variation, to bring them into strict comparison
with the values at the two other epochs of 1838 and 1859, which
have beenderived from observations distributed generally throughout
the years. A correction of +0'5-has been applied to each on this
account.
Corrected Dip at the several Epochs.—We_have then the observed
Dips, finally corrected, at the several epochs as follows :—
le)
1821.65... 5) <<. 70) OBA Ninacele os (1)
M883 lo ce ds. G0 ae) Done ack (2)
1854.65... GBi 316 eis ace (3)
Megs A ol ae 68; 21 ooh stescat, oA)
Between No. 1 and No. 4 we have an interval of 37.85 years, and
a mean annual secular change of —2’:69 ; mean epoch, 1840.6.
Between No. 1 and No. 2, comprising an interval of 16.65 years,
we have a mean secular change of —2’*77; mean epoch, 1830.0.
Between No. 2 and No. 4, comprising an interval of 21.2 years, we
have a mean secular change of —2’°63; mean epoch, 1848.9.
Hence we may infer that the yearly diminution of the Dip from
secular change, though very nearly uniform throughout the whole
interval of 37.85 years, was somewhat greater in the earlier part of
the interval than in the later; and that the rate of diminution
may admit of being more exactly represented by the introduction of
a second term.
If then we take the year 1840.0 as aconvenient middle epoch=z,,
and call its dip 0,; and if we further call the observed dip at the
several observational epochs ¢,, ¢,, ¢, and ¢,, respectively 0,, 6,, 0,5 0,5
we shall have four equations of the form
6,=9,+2(t,—£,) +y(t,—t,)* >
and giving double weight to the equation furnished by the epoch
1859.5, inasmuch as it is derived from so much greater a body of
observations than the results at the other three epochs, we obtain by
least squares,
8,=69° 11°95; ) #2=—2'713; y=+0'-00057,
Hence we have the general formula for computing the dip between
the years 1820 and 1860,
6==69° 11'°95—2'-713 (¢—¢,)+0''00057 (¢—#,)’,
¢, being 1840.0, and ¢ being any other time for which the dip @ is
required.
Using this formula, we have the differences between the com-
puted and the observed dips at the several epochs of observation
as follows :—
Computed. Observed. Computed—Observed.
PBQG Sore riiveus 70 03:6 = 70: 03-4 +.0:2
SSS: ii Laavonde 69 168 69 17:3 —0°5
LS5ALGa cued 68 33:4 68 31°6 +1:8
BSDSES is dae 68 21:2 68 21°5 —0°3
236 Royal Society :—
And the dips corresponding to every tenth year within the period
specitied are as follows :—
1880.0) cates .. 70 O73
163050 aaeee 69 39-6
1840/0." 5. ok Sa OSES
1850.0). becsun 868y45-9
1860:0 = #2 eet ion
The progressive diminution of the Dip in London during the last
forty years has thus been traced and followed by the observations
recorded and discussed in this paper; and the further progress of the
research will now devolve on the systematic observations which are
made for that purpose monthly at the Observatory at Kew.
The rate of diminution in the last forty years does not appear to
differ materially from the mean rate in the preceding hundred years.
The experiments of Mr. George Graham between March and May,
1723, recorded in the Philosophical Transactions for 1725, No. 389,
give a mean dip in London at that epoch of “nearly”? 74° 40'. Com-
paring this with 69° 11'-95 in 1840.0, we have a difference of 5° 28!-1
in 116°7 years, equivalent to a uniform diminution of 2'°81 annually ;
or if the formula
6=69° 11'-95—2'-713 (¢€—t¢,)+0':00056 (¢—7,)?
be employed, it gives the dip in March 1723.3 equal to 74° 36'"1, being
a difference of less than 4’ from the result of Mr. Graham’s experi-
ments ; which difference is doubtless less than the probable error
of that gentleman’s determination with the instruments then in use.
An expectation appears to have prevailed in some quarters that the
decrease of the Dip in London should have ceased, and its subsequent
increase have commenced, contemporaneously with the alteration
which took place in the secular change cf the Declination in the
early part of this century, when the increase of west declination,
which had been continuous in the British Islands for about two cen-
turies, ceased, and was succeeded by a decrease of the same. But
this supposition is by no means in accordance with that general
view and interpretation of the phenomena of terrestrial magnetism
for which we are indebted to Dr. Halley, and which, since its pro-
mulgation in 1683, has received so much confirmation in various and
distant parts of the globe. In accordance with that hypothesis, the
diminution of the Dip in London might be expected to continue until
the epoch should arrive when, by the easterly movement of translation
of the minor magnetic system in the northern hemisphere, the dis-
parity of the magnetic force prevailing in the Kuropean and American
portions of the hemisphere should have attained its maximum :—which
is certainly not yet the case.
Is there then, in the secular change of the Dip, no feature in
which, in conformity with the Halleian hypothesis, an alteration
might be expected to synchronize with the reversal in the direction
of the secular change of the declination? Assuredly there is; and
the facts which recent investigations have brought to our knowledge
On the Secular Change in the Magnetic Dip in London. 237
manifest that such an alteration has taken place. I proceed to de-
scribe it.
If we have recourse to those extensive generalizations which, under
the name of “Isoclinal Lines corresponding to particular Epochs,”’
present a connected view of the changes which have taken place from
time to time in the magnetic lines of the Dip over large portions of
the earth’s surface, and enable us to anticipate with some degree of
confidence the changes which may be expected to take place in years
to come, we notice generally that the lines undergo two species of
modificaticn, or peculiarities of change, which it is necessary to keep
separately and distinctly im view. In the British Islands, for example,
the Isoclinal Lines for little less than two centuries past have been
steadily advancing towards the north by a gradual movement of trans-
lation. This is one feature of the secular change; but there is a
second feature, which, if not at first sight equally striking, is yet
equally regular and systematic in its operation; viz. the direction of
the isoclinal lines as they pass across our country from the south-west
towards the north-east undergoes a small but sensible change from year
to year, by which, in the lapse of several years, the angle at which
they cut the geographical meridians is materially altered. By the
joint operation of these two processes, the general configuration of the
lines over large portions of the earth’s surface, as well as their values
in particular localities, are both subject to systematic alteration; a
remark which is not limited to the isoclinal lines alone, but is the case
also in the isogonic and isodynamic lines. Those who are conversant
with Dr. Halley’s writings, will be aware that,—in correspondence
with his views,—between the epochs when the Dip in London should
attain, respectively, the maximum and the minimum amount which
constitute its limits under the system of secular change, an inéer-
mediate epoch might be anticipated, when the isoclinal lines passing
across the British Islands should attain their least angle of inclination
to the geographical meridian ; towards which they should have pro-
gressively advanced, and from which they would as progressively re-
cede. Now, if we compare the lime of 70° of dip in the Isoclinal
Map of 1780 of the Magnetismus der Erde with that of 1840 in Mr.
Keith Johnstone’s Physical Atlas, plate 23, we may fix on a point
in about 42° North Latitude and 30° West Longitude, in which the
Dip has remained nearly stationary, and through which the line of 70°
of Dip passed, at both epochs ; and we may perceive that, in its easterly
course from that point or pivot, this line passed in 1780 through the
middle of France considerably to the South of Paris (where the Dip
was then between 71° and 72°); whereas in 1840 it passed across
England considerably to the north of London (where the Dip had
diminished to little more than 69°). Therefore in the sixty years
which had elapsed between the two epochs, 1780 and 1840, the di-
rection of the lines as they impinged upon Western Europe had
become much less inclined to the geographical meridian (7. e. forming
a greater angle with the parallels of latitude) in 1840 than in 1780:
and if we consult still earlier maps, we find that a change in the same
direction had been progressive from a still earlier period. The par-
238 Royal Society.
ticular year in which this feature attained its limit, and an opposite
change commenced, cannot now perhaps be precisely determined ; it
was probably somewhat earlier than 1840. But from the comparison
of the magnetic surveys of the British Islands in 1836-37 and
1857-58, it is certain that the change in the direction of the isoclinal
lines in this part of the globe has entered upon the contrary phase
to that which had previously existed. The observations of the late
Mr. Welsh in Scotland in 1857-58 (Brit. Assoc. Reports, 1859),
when compared with those of the Scotch Survey made in 1836-37,
published in the British Association Reports for 1836, show, according
to Mr. Balfour Stewart’s calculation, that an increase of several degrees
in the angle at which the lines cut the meridians in passing across
Scotland has taken place between the epochs of the earlier and the
later surveys. The same general conclusion follows from a comparison
of the magnetic surveys of England at nearly the same epochs; every-
‘where near the west coast of England the mean annual secular change
in the twenty years has been greater, and near the east coast less than
its mean value at Kew; showing that the general direction of the
isoclinal lines more nearly approaches a parallelism to the equator now
than it did twenty years ago. The ascertainment of the exact value
of the secular change at a particular locality by a well-conducted
system of periodical observations is the duty of a magnetic observa-
tory; the direction of the magnetic lines passing across a country
is supplied by magnetic surveys ; which, for that purpose, ought to
be repeated from time to time, as they have now been in this country,
at intervals of perhaps twenty or twenty-five years.
It has been imagined that the secular changes of the magnetic ele-
ments may be due to some alteration taking place either in the dis-
tribution or in the condition of the materials in the interior of the
globe. But the regularity and uniformity with which the secular
magnetic changes coutinue through long intervals of time, together
with their sudden periodic reversals,—and their corresponding fea-
tures in the northern and southern hemispheres, which add greatly
to the apparent consistency and systematic character of the whole as
parts of a uniform general system,—wear more the aspect of effects
of some yet unascertained cosmical cause. One of the British Colo-
nial Observatories, St. Helena, having the advantage of both a large
secular change and a small amount of magnetic disturbance, has
afforded a very striking example of the great regularity with which
the secular change takes place, maintaining a steady uniformity,
traceable not only from year to year, but from month to month, and
even from week to week; so that it is not too much to say that,
from observations made during a single fortnight, an annual secular
change which has existed almost without variation for more than a
century, may be ascertained and measured with very considerable
precision. (Magnetic Observations at St. Helena, vol. il. p. ix.)
March 21.—‘ On the Relations of the Vomer, Ethmoid, and In-
termaxillary Bones.” By John Cleland, M.D.
“On the Structure and Growth of the Tooth of Echinus.” By
S. James A; Salter, M.B. Lond., F.L.S., F.G.S. i
Geological Society. 239
GEOLOGICAL SOCIETY.
[Continued from vol. xxii. p. 405.]
November 6, 1861.—Sir R. I. Murchison, V.P.G.S., in the Chair.
The following communications were read :—
1. “Note on the Bone-Caves of Lunel-Viel, Hérault.” By M.
Marcel de Serres. Communicated by the President.
These bone-caves in Miocene limestone, on the Mazet estate,
near Montpellier, discovered about 1823, and described in 1839 by
MM. Marcel de Serres, Dubreuil, and Jean-Jean, comprise a large
cave and some smaller fissures, containing a red earth with pebbles
and an abundance of bones and coprolites of Hyzna, Lion, Bear,
Wolf, Fox, Otter, Boar, Beaver, Rhinoceros, Horse, Deer, Ox, &c.,
with Birds and Reptiles. The author expressed his belief anew that
the association of pebbles with the bones in caves is a common
phenomenon, and an evidence of the accumulation of the materials,
gnawed bones and coprolites included, by the running water of violent
inundations,—the caverns being of Tertiary origin, the detritus being
contemporary with the old alluvium of the Rhone, and the fauna
indicated by the bones having been antecedent to the latter.
2. «On the Petroleum-springs in North America.’ By Dr. A
Gesner, F.G.S. |
After some observations on the antiquity of the use of mineral oil
in North America and elsewhere, and on the present condition of
the oil- and gas-springs and the associated sulphur- and brine-
springs in the United States, the author stated that 50,000 gallons
of mineral oil are daily raised for home-use and for exportation.
The oil-region comprises parts of Lower and Upper Canada, Ohio,
Pennsylvania, Kentucky, Virginia, Tennessee, Arkansas, Texas, New
Mexico, and California. It reaches from the 65th to the 128th de-
gree of long. W. of Greenwich, and there are outlying tracts besides.
The oil is said to be derived from Silurian, Devonian, and Car-
boniferous rocks. In some cases the oil may have originated during
the slow and gradual passage of wood into coal, and in its final
transformation into anthracite and graphite,—the hydrogen and some
carbon and oxygen, being disengaged, probably forming hydro-
carbons, including the oils. In other cases, animal matter may have
been the source of the hydrocarbons.
Other native asphalts and petroleums were referred to by the
author, who concluded by observing that these products were most
probably being continually produced by slow chemical changes in
fossiliferous rocks.
3. “‘ Notice of the Discovery of some additional Land Animals in
the Coal-measures of the South Joggins, Nova Scotia.” By Dr.
J. W. Dawson, F.G.S.
Two additional fossil stumps of trees have been examined by the
author from the same group of the Coal-measures as that which has
already afforded Reptilian, Molluscan, and Myriapodal specimens.
240 Geological Society :—
These trees stand on the 6-inch coal in Group XV. One (Sigillaria
Brownii) has yielded indications of six skeletons of Dendrerpeton
acadianum (one probably perfect), a jaw of a new species, two
skeletons of Hylonomus Lyelliit, one of H. Wymani, a number of
specimens of Pupa vetusta and Xylobius Sigillarie, and some rem-
nants of Insects (in coprolites).
In a lower bed (1217 feet beneath—in Group VIII.), a Stigma-
rian under-clay 7 feet thick, the Pupa was found abundantly in a
thickness of 2 inches—with fragments of Reptilian bones. The
coal-seams between the trees and this bed indicate that this Pupa
must have existed during the growth and burial of at least twenty
forests.
4. «On a Volcanic Phenomenon observed at Manilla, Philippine
Isles.” By J. G. Veitch, Esq. In a Letter to Dr. J. D. Hooker,
F.G.S.
On the lst of May 1861, the River Pasig, at Manilla, from 15 to
18 feet deep, was disturbed by a violent ebullition from 6 to 10 a.m.
for a distance extending to a quarter of a mile. Its temperature
here was 100° to 105° Fahr. (elsewhere 80°). A bank of fetid mud
was thrown up several feet above the water, and had a temperature
of 60° to 65° only.
The Chairman remarked that a bank of mud, 30 feet high, and
more than a mile long, had lately been thrown up in the southern
portion of the Caspian.
November 20, 1861.—Sir R. I. Murchison, V.P.G.S., in the Chair.
The following communications were read :—
1. “*On the Bovey Basin, Devonshire.” By J. H. Key, Esq.
The author first described the physical features of the Bovey
Basin, and then the strata, as proved by borings and diggings for
clay and lignite. Having pointed out the evidences that exist of
the basin having once been a lake in which the several strata of clay,
sand, lignite, gravel, &c. were deposited, and having considered
the probable conditions of such a lake having been gradually filled
up by fluviatile deposits brought down from neighbouring granitic
hills, the author remarked:—Jst. that the Bovey deposits are
composed of materials almost identical with the component parts of
granite. 2. The strata run, for the most part, parallel with the
outline of the marginal hills, and dip from the sides towards the
centre, often thinning away in that direction. 3. The finer mate-
rial is deposited towards the sides, and the coarser towards the centre.
4. Where the basin is contracted the finer beds often disappear,
but thicken where the basin widens. 5. That the upper beds of the
northern part are coarser than those of the middle and lower portions.
6. On the eastern side the fine-clay beds are more developed than on
the western side. 7. The various beds run in the direction of, and
seem to point to, the River Bovey as the source from whence they
were derived ; but the old outlet of the lake was towards Torbay,
and not along the Teign as it is at present. Some observations on
On the Bracklesham Beds of the Isle of Wight Basin. 241
the peculiar absence of animal-remains in these deposits, often rich
with vegetable-remains, concluded the paper, which was illustrated
by several original plans, sections, and sketches.
2. “On two Volcanic Cones at the Base of Etma.”” By Signor
G. G. Gemmellaro.
These two cones occur at Paternd and Motta (Sta. Anastasia) ;
and the existing remains of their craters and nuclei were described
in detail. The author concludes that these were two contempora-
neous doleritic volcanic cones, that were formed in the Post-pliocene
period, previous to the deposition of the calcareous tuff of the vici-
nity of Paternd,—also that they were cones of eruption, and not of
elevation, for the neighbouring strata are not disturbed—and that
they were independent eruptions, and not parasitical cones of Etna.
3. “On some Fossil Brachiopoda of the Carboniferous Rocks
of the Punjab and Kashmir, collected by A. Fleming, M.D., &c.,
and W. Purdon, Esq., F.G.S.”.. By T. Davidson, Esq., F.R.S.,
F.G.S.
Dr. Fleming’s geological researches on the Salt-range and else-
where in the Punjab, in 1842-52, are recorded in the Journal of
the Society for 1853, in the Journ. Bengal Asiat. Soc. 18538, and in
his Report on the Salt-range, 1854. The species of Carboniferous
Brachiopoda collected by Dr. Fleming and described and figured by
Mr. Davidson, are Terebratula (vel Waldheimia) Flemingii, Dav., T.
problematica, Dav., T. subvesicularis, Dav., Retzia radialis, var.
grandicosta, Dav., Athyris Royssii, L’Ev., A. (vel Merista) subtilita,
Hall, var. grandis, Dav., Spirifera striata, Martin, Spiriferina octo-
plicata, Sow., Orthis resupinata, Martin, Streptoriynchus crenistria,
Phil., var. robustus, Hall, St. pectiniformis, Dav., Productus striatus,
Fisch., P. longispinus, Sow., P. contortus, Sow.
Mr. Purdon’s collection comprises, besides several of the fore-
going, Terebratula Himalayensis, Dav., Spirifera Moosakailensis,
Dav., Sp. lineata, Martin, var., Camarophoria Purdoni, Dav., Pro-
ductus Purdonii, Dav., P. Humboldtii, D’Orb., Adulosteges Dalhousit,
Dav., and Strophalosia Morrisiana (?), King, var.
December 4.—Sir R. I. Murchison, V.P.G.S., in the Chair.
The following communication was read :—
“Onthe Bracklesham Beds of the Isle of Wight Basin.” By the
Rev. O. Fisher, M.A., F.G.S.
After noticing the researches of Prestwich and Dixon, the author
proceeded to state that most of the ‘‘ Bracklesham Beds ”’ are dis-
played at low water at Bracklesham Bay; but other and higher beds
belonging to the same series are to be observed in the New Forest,
at Stubbington, and in the Isle of Wight. By means of the fossils,
for the most part, Mr. Fisher divides the series into four groups :—
A. The uppermost abounds in Gasteropoda, and has several fossil-
beds. One of these, in the eastern part of its range, is full of Num-
Phil, Mag. 8. 4. Vol. 23. No. 153. March 1862. R
24.2 Geological Society :—
mulina variolaria (bed No. 16 of Mr. Prestwich’s Section of White-
cliff Bay, Quart. Journ. Geol. Soc. vol. i. pl. 9); the NV. variolaria
bed of Selsea and of Stubbington; and the Shepherd’s Gutter Bed at
Bramshaw, New Forest. ‘The beds above the last-named are—lIst, a
portion of No. 19 of the Whitecliff Bay section and the Coral-bed of
Stokes Bay and Hunting Bridge (New Forest) ; and 2nd, the Shell-
bed at Hunting Bridge, and Pebble-bed, with shell-casts, at High-
cliff. The lowest bed of this group is the Cyprzea-bed of Selsea,
the Cardita-bed of Stubbington, and the Brook-bed in the New
Forest. B. This group is more sandy than the last; it has two
fossil-beds, one of which contains Certthium giganteum (at Hillhead,
Stubbington; and _ half-a-mile west of Thorney Station, Brackles-
ham Bay). C. This is a sandy group, and is remarkable for the
profusion of Nummulina levigata in its principal fossil-bearing beds.
D. This embraces the lowest fossiliferous sands of Bracklesham Bay.
Its distinctive shells are Cardita acuticosta and Cyprea tuberculosa.
Some species ef Molluscs pass upwards from the Bracklesham
into the Barton series ; yet the fauna of the Bracklesham Beds has a
sufficiently distinct facies; and the following species range through
this series and are confined to it—Cardita planicosta, Sanguinolaria
Hollowaysii, Solen obliquus, Cytherea suberycinoides, Voluta Cithara,
and Turritella sulcifera. Pecten corneus is also characteristic, but is
met with higher up.
The Bracklesham Beds seen at Whitecliff Bay were first treated
of, and Mr. Prestwich’s section referred to in detail. No.6 (a
pebble-bed) of this published section is regarded by Mr. Fisher as the
base of the Bracklesham series, the upper limit being somewhere in
No. 19. Descriptions followed of the beds seen at Bracklesham Bay ;
the eastern side of Selsea; at the Mixen Rocks; at well-sinkings
near Bury Cross ; at Stubbington (including the Cerithium-bed at
Hillhead, discovered by the author in 1856); Netley; Bramshaw,
Brook, and Hunting Bridge (where H. Keeping has lately found a
fossil-bed high in the series), in the New Forest. Indications of the
western range of the marine shells of ‘“‘ Bracklesham” age were
quoted as occurring at Lychett near Poole, and as very rare (one
Ostrea) near Corfe.
Bracklesham Beds, containing marine forms, seen at Alum Bay
(Isle of Wight) and at Highcliff (mear Christchurch) were then
described in full. The Bracklesham series is regarded by Mr. Fisher
as commencing in both these sections a few feet beneath a dark-
green clay (part of No. 29 of Mr. Prestwich’s section of Alum Bay)
containing a peculiar variety of Nummulina planulata and many shells
of the Barton fauna.
Remarks were also made on the estuarine condition of the lower
Bracklesham Beds in their western area; on the probable sources of
their materials ; on the successive deepenings of the old sea-bottom,
and the formation of the pebble-beds ; and lastly on the fitness of
the Bracklesham and Barton series as a field for research in the
history of Molluscan Species.
On the Carboniferous Limestone of Oreton and Farlow. 243
The paper was illustrated by a series of Specimens from the
Author's Collection.
January 8, 1862.—Sir C. Lyell, F.G.S., in the Chair.
The following communications were read :—
1. ‘‘On the Carboniferous Limestone of Oreton and Farlow, Clee
Hills, Shropshire.” By Professor John Morris, V.P.G.S., and
George E. Roberts, Esq. With a Note upon a new species of Pte-
richthys; by Sir P. de M. G. Egerton, Bart., M.P., F.G.S.
The rocks described in this paper are a series of thin beds of
limestone and sandstone lying between the Old Red Sandstone of
South Shropshire and the Millstone Grit which forms the basement
of the Titterstone Clee Coal-field.
In consequence of the opening of new quarries and the cutting of
a roadway through the Farlow ridge, transversely to the strike of
these deposits, the authors were enabled to add somewhat to the
description of the locality given in ‘ The Silurian System.’ The
series of deposits from the Old Red “ cornstone,’’ upwards, was
shown by them to be :—1. Laminated yellow sandstones, with peb-
ble-beds and sands. 2. Bright-yellow sandstones containing Pteri-
chthys. 3. Brecciated yellow sandstones, pebble-beds, sandy layers,
and laminated sandstones. 4. Sandy and concretionary limestone.
5. Grey oolitic limestones, containing palatal teeth of great size.
6. Clays, with ferruginous bands. 7. Shaly Crinoidal limestones.
8. Clays with limestone-concretions, and shaly limestones. Against
the last-mentioned bed, the Millstone Grit rests unconformably.
These beds thicken out at Oreton,a mile East of this Farlowsection,
and are there extensively worked for various economic purposes, the
oolitic limestones, locally termed “ jumbles,” being used for decora-
tive purposes under the name of Clee Hill marble. In describing
the physical conditions of the localities, mention was made of the
“mole river,” which, losing itself at the West end of the ridge, takes
a subterranean course nearly parallel with its axis, and re-appears
at its lower end, a mile distant. An interesting fact was communi-
cated to the authors by the Rev. J. Williams of Farlow, of an acci-
dental accumulation in the hollow of its inlet, of a body of water
estimated at 1,635,000 cubic feet, the whole of which was carried
away in 48 hours by the sudden clearance of the channel.
In describing the paleontology of these rocks, the authors specially
drew attention to the fortunate discovery in the Yellow Sandstone
of Farlow, of Pterichthys macrocephalus (spec. nov., Egerton), made
while reducing the thickness of a large ripple-marked slab sent them
by Mr. Weaver Jones in illustration of the physical conditions of the
deposit. .This Pterichthys proving identical with the fragment pre-
viously found in the Farlow sandstone by Thomas Baxter, Esq,,
F.G.S., they attached to the paper a descriptive note on that fossil,
by Sir Philip Egerton, in which the Farlow Pterichthys was con-
trasted with that of Dura Den, and additional proof given of the
R 2
244 Geological Society.
identity of the genera Pamphractus aud Pterichthys. In addition to
Pterichthyoid remains, scales of two species of Holop/ychius, one
probably new, had been found by them.
The richness of the overlying limestones in palatal teeth was shown
by a fine series of examples, amongst which Orodus ramosus, of
unusual size and in perfect condition, and an undescribed Pecilodus,
of great magnitude, were most conspicuous. Other genera repre-
sented were Helodus, Psammodus, Cladodus, Cochliodus, Petalodus,
and Cieneptychius. Ichthyodorulites, of large size and rich orna-
ment, chiefly belonging to the genera Cienacanihus and Oracanthus,
accompany these teeth.
The notices of the invertebrate fauna given by the authors proved
the assumed lowness of the Oreton limestones in the Mountain-
limestone series,—the zone of Rhynchonella pleurodon being well-
marked, Crinoidal and Bryozoan remains abundant though fragmen-
tary, and Corals nearly absent.
A large series of Pterichthyes and of rock-specimens were ex-
hibited in illustration by Mr. George E. Roberts; and a collection
of palatal teeth was liberally sent for exhibition by W. Weaver
Jones, Esq,, of Cleobury Mortimer, and by Edward Baugh, Esq., of
Bewdley.
2. “On some Fossil Plants, showing Structure, from the Lower
Coal-measures of Lancashire.” By E. W. Binney, Esq., F.R.S.,
F.G.S.
After noticing the views taken of the structure of Lepidodendron
by Hooker and others, the author proceeded to describe three por-
tions of calcified stems, Lepidodendroid in external appearance, two
of which exhibit in section a central axis composed, not of cellular
tissue, but of large, transversely barred, hexagonal vessels. ‘These
two specimens the author refers to a new species, Sigillaria vascu-
laris. The third specimen differs from the others in the absence of
the thin radiating cylinder of barred vessels around the central axis ;
this he terms Lepidodendron vasculare.
Microscopical preparations and photographs of sections were sup-
plied by the author.
3. “ Supplemental Notes on the Plant-beds of Central India.” By
the Rey. S. Hislop. In a Letter to the Assistant-Secretary.
Mr. Hislop, in noticing the discovery of more remains of Plants,
Insects, and Fishes at Kota on the Pranhita, stated that he certainly
now thought that the ichthyolitic beds of Kota (probably Lower
Jurassic in age )are higherin relative position than theplant-sandstone
of Nagpur, which, with the Sironcha sandstone underlying the Kota
limestone, belong to the Damuda Group. He remarked ‘also that,
in his opinion, the Tenzopteris of Kampti would prove that the Da-.
muda and Rajmahal groups cannot be widely separated.
[ 245 ]j
XXXII. Intelligence and Miscellaneous Articles.
ON A DEW-BOW SEEN ON THE SURFACE OF MUD.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
ee was seen today (February 13, 1862) by myself and some
other persons in this neighbourhood,a very beautiful phenomenon,
of which the cause is obvious, and of such a nature that one would
expect the phenomenon to occur frequently ; but I do not remember
to have yet seen any instance of it recorded in any scientific publi-
cation. I refer to a prismatically-culoured hyperbolic iris, or bow
of the first order, exactly resembling that sometimes seen on a field
of dewy grass; but in this case it was displayed on the muddy sur-
face of a by-road near Glasgow, and on the less trodden parts of
an adjoining turnpike road, throughout a distance of more than a
mile. The time was between 12" 30™ and 1" p.m. Greenwich time;
the morning had been hazy, but the mist had cleared away, and the
sun was shining brightly.
The angular dimensions of the iris were obviously the same with
those of a rainbow of the first order; its colours were complete,
from red to violet, and very bright and distinct, especially where the
mud was softest and moistest; where a sheet of water, how thin
soever, covered the mud, the iris vanished. No trace of an iris
could be seen on the grass, in the sky, or anywhere but on the mud ;
and on those parts of the turnpike road where the mud had been
much disturbed no iris was visible.
The necessary conclusion from this appearance is, that the sur-
face of the mud must have been thickly covered with globules of pure
water, perfectly spherical, and not in absolute contact with the mud,
although resting on it; but those globules must have been extremely
minute, for they were invisible to the closest inspection with the
naked eye.
I am, Gentlemen,
Your most obedient Servant,
Glasgow, February 6, 1862. W. J. Macaquorn RanxINE.
NOTE ON THE THEORY OF SPHERICAL CONDENSERS.
BY M. J. M. GAUGAIN.
I have indicated in my preceding communications* a general
principle by means of which all questions relative to condensers may
be transformed into questions of propagation, and thus brought
within the domain of Ohm’s law. ‘The exactitude of this principle
has been already demonstrated experimentally,—1, in the case of
concentric cylindrical condensers; 2, in the case of eccentric cylin-
drical condensers; 3, in the case of plane condensers (Comptes
Rendus, Feb. 18, April 29, and June 17,1861). I have now verified
* See Phil. Mag. vol. xxi. p. 539.
246 Intelligence and Miscellaneous Articles.
it for a new class of condensers, that of concentrical spherical con-
densers.
The problem which I proposed to solve was as follows :—Given
two concentrical spheres, suppose that the inside sphere, whose
radius is 7, is placed in contact with a constant source of electricity,
and that the external sphere whose radius is R, is placed in contact
with the ground; it is required to express the charge of the inside
sphere in terms of the radii 7 and R.
In order to obtain the corresponding question of propagation, it
is sufficient to suppose that the insulating substance, which sepa-
rates the two spheres in the case of condensation, is replaced by a
medium which is a conductor, but to a far less extent than the
substance of which the spheres consist. The problem then con-
sists in finding an expression for the intensity of the current
transmitted from the internal sphere to the external one; and this
latter question is easily solved.
Suppose two concentric spheres very near each other, and having
the radius x and #+dzx (w being less than R and greater than 1r) ;
the resistance of the medium comprised between these two spheres
kd : : :
will be expressed by =, k being a constant coefficient; and this
resistance will be the differential of the total resistance of the sphe-
rical ring comprised between the spheres of the radii r and a. This
total resistance will thus have the value i(- =a -) , that of the ring
comprised between the spheres of the radius r and radius R will be
expressed by ( : oo x): and consequently the intensity of the cur-
rent transmitted will be proportional to Ee Now, from.the prin-
ciple which I have adduced at starting, the charge expressed in the
case of condensation ought to be proportional to this same expres-
sion. It was necessary to ascertain experimentally if this were so.
To do this I have compared, two by two, six concentrical spherical
condensers, the armatures of which had the following dimensions :—
Internal sphere. External sphere.
Diameter in Diameter in
millimetres. millimetres.
INO 5623) See G15 89-0
Dirt ha hs dade ae a 6155 Ses
Stirs a eer O Le 161°0
2 Nie PR AE Sad el oat pinta ee 18 189) 118°5
Bye aie: Ales owes 90°5 161°0
Gateei nies k cucr 120:0 161:°0
I charged these six apparatus successively by placing them in
communication with the same source, and 1 determined the charge
accumulated on the sphere by the methods described in my pre-
ceding Notes. ‘Through acircular aperture, 30 millims. in diameter,
Intelligence and Miscellaneous Articles. _ 247
in each of the external spheres, wires can be introduced by which
the sphere is either charged or discharged. The following are the
results obtained :—
Charge obtained Ratio of the Ratio of the
experimentally. charges calculated
obtained. charges.
es 0457 0488
Gas 0214 0811
pel... azo 0828 0812
PE sa | 0483-424
me 64 poo le eae
The differences obtained between the calculated and observed
charges are small, considering the imperfections of the modes of
measurement; and we see that the formule deduced from the
theory of propagation may be applied to the case of condensa-
tion, as well in the case of spherical condensers as in the case of the
cylindrical and plane condensers with which I have been previously
occupied. I believe that the proposition may without temerity be
generalized, and be considered applicable to condensers of any
shape.
To appreciate the interest of this principle, it is important to ob-
serve that the theory of condensers, which has been usually pre-
sented as a branch of statical electricity, comprehends really the
whole of this subject. When an insulated and electrified conductor
is placed in any room, the electricity with which it is charged is
usually called free electricity; but, as Mr. Faraday has shown by
numerous experiments, this electricity is no more free than that on
the inner coating of a Leyden jar. The insulated conductor is only
the inner coating of a large condenser, the external coating of which
is constituted by the whole of the adjacent conductors. In fine, all
questions relating to the distribution of electricity which is said to be
free, depend on the theory of condensers, and may therefore be
solved by means of the theory of propagation. By the principle
which I have propounded, all questions of statical electricity may be
resolved into questions of dynamics, and vice versd.
The want of apparatus has prevented me from investigating
whether the numerous results which Coulomb obtained in his re-
searches relative to the distribution of electricity may be made to
coincide with the ideas which I have laid down; but I have already
been able to verify the very simple law which expresses the free
charge. We have just seen that the quantity of electricity accumu-
lated on the inner coating of a spherical condenser is proportional to
Rr
KR
This expression is reduced to r if we suppose R to be infi-
248 . Intelligence and Miscellaneous Articles.
nite; but it seemed evident that if the outer armature becomes infi-
nitely large, its form becomes indifferent. We are thus led to admit
that when a sphere is placed in an envelope which is either infinite
or simply very large, the charge communicated to it by a given source
is proportional to its radius; which amounts to saying in Coulomb’s
language, that the thickness of the electric layer is inversely as its
radius. To verify this conclusion, I took four spheres of brass, the
diameters of which were 61°35, 90°5, 120, and 161 millims.; I placed
them successively on an insulating support in the centre of a very
narrow chamber, and charged them by connecting them with a con-
stant source by means of a metallic wire; I then tested them by em-
ploying, as usual, a discharging electroscope. ‘The charges obtained
were 5°2, 7°G, 11, and 14°7. The law of proportionality would
have given 5°2, 7°6, 10°1, and 13°6. ‘These two series of numbers
are not identical; but they differ so little, that we might expect
that the law of proportionality would be exactly verified in a larger
envelope.
At first we might suppose that this law of proportionality is
opposed to one of the results obtained by Coulomb; but this con-
tradiction is only apparent. In Coulomb’s experiments, in the case
of two unequal spheres, the spheres touched at the moment at which
they were electriiied, and were only separated after being charged ;
their mutual action necessarily modifies the distribution of electricity.
The problem I have treated is quite different, and much simpler, as
the spheres on which I worked were only charged successively.—
Comptes Rendus, September 30, 1861.
ON THE ACTION OF NITRATE OF SODIUM ON SULPHIDE OF SODIUM
AT DIFFERENT TEMPERATURES. BY DR. PH. PAULI, UNION
ALKALI WORKS, ST. HELENS.
The mother-liquor obtained in the manufacture of soda-ash con-
tains, as is well known, large quantities of sulphide of sodium. In
ordert o oxidize that compound, nitrate of sodium is used. As long as
the boiling-point of the liquid is between 280° and 290° F., the sul-
phide is quietly oxidized to sulphate, nitrite of sodium being formed.
But if the nitrate is added when the temperature of the boiling
liquid is about 310° F., a violent evolution of ammonia takes place,
according to the following equation :—
2NaS+ Na NO°+4HO=2 Na SO*+ Na HO?+ NH’.
As the liquor contains a large amount of sulphide, the quantity
of ammonia is so considerable that it may prove worth while to
conuect the evaporating-pot with a tower filled with coke, over
which a stream of water or dilute acid is running.
If the nitrate be added when the liquor has been heated to a tem-
perature much above 310°, a violent evolution of pure nitrogen occurs.
5NaS+4Na NO'+4HO=5 NaSO!+4Na0?H+4N.
—From the Proceedings of the Literary and Philosophical Society
of Manchester, January 21, 1862.
THE
LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
(FOURTH SERIES.]
APRIL 1862.
XXXIV. On the Passage of Radiant Heat through moist Air, and
on the Hygroscopic Properties of Rock Salt. By G. Macnus*.
aoe deportment of our atmosphere in reference to the passage
of the solar heat through it appeared especially important to
me in the investigation on the propagation of heat in gases, of
which I gave an account to the Konigliche Academie on the 30th
of July 1860}, and 7th of February 1861. Although it could be
foreseen that the small quantity of aqueous vapour which the air
can take up at the ordinary temperature would exercise a scarcely
perceptible influence on the passage of the thermal rays, yet, after
it had been made out that, under the same circumstances, olefiant
gas only transmits half as many rays as oxygen, and ammoniacal
gas still fewer, 1t appeared desirable to investigate whether that
anticipation was well founded or not. Experiment completely
confirmed it : neither by the application of a source of heat of 100°
nor by using a strong gas-flame could any difference be per-
ceived in the transmission of heat through air, whether it was dry
or saturated with vapour. This was the more surprising, inasmuch
as a paper by Dr. Tyndall{, “On the Absorption and Radiation
of Heat by Gases and Vapours,” published simultaneously with
the above investigation, coutaimed the statement that undried
atmospheric air, on a certain day, exhibited fifteen times as great
an absorption as dried air. Dr. Tyndall has subsequently been
further engaged on this subject, as appears from a letter to Sir
John Herschel§ recently published. In this Dr. Tyndall says,
“The results from which the opacity of the air has been in-
ferred are all to be ascribed to extraneous matters diffused in the
* Translated from Poggendorff’s Annalen, No. 12, 1861.
7 Phil. Mag. vol. xx. p. 510. £ Ibid. vol. xxu. p. 169.
§ Ibid. vol. xxi. p. 377.
Phil. Mag. 8. 4. Vol. 23, No. 154, April 1862. S
250 Prof. Magnus on the Passage of Radiant
atmosphere, and mainly to the aqueous vapour.” He has, he
continues, led by the experiments which I have made, again
investigated this subject, and the experiments have shown that
the action of aqueous vapour was enormous. On the 10th of
October he found that the absorption by the air of the laboratory
consisted of three components. If the first, which is due to
pure air, be designated by the number 1, the second, produced by
the transparent aqueous vapour is 40, and the third, caused by
the effluvia of the laboratory and the carbonic acid, is 27. The
total action of foreign substances on that day was certainly 67
times as great as that of the atmospheric air alone, and that of
the aqueous vapour was certainly 40 times as great.
This statement has caused me to repeat the experiments in
this direction which I published in Poggendorff’s Annalen,
vol. cxu. p. 5389 (Phil. Mag. vol. xxi. p. 85). But neither by
using the apparatus described in page 87 and depicted on Plate J.
fig 2, in which the heated bottom of a glass vessel sent its heat
to the pile through the air without the intervention of any plates,
nor even when the heat of a lamp passed through a tube closed
with glass plates, could any difference be perceived between air
saturated with aqueous vapour at 15° C., and perfectly dried air.
It follows again from this, that aqueous vapour, so long as it is
not separated as fog, exercises at 15° C. no appreciable influence
on the transmission of thermal rays, and that the rays of the sun,
so long as the air is clear, reach the earth in the same manner,
whether the atmosphere is saturated with vapour or not.
Besides the above experiments I have made similar ones with
plates of rock salt, but I soon found that the use of the latter
presents considerable difficulties; for rock salt in saturated air
readily attracts moisture, and becomes covered with a solution of
salt which may become so considerable as to drip off. Ifa plate
of rock salt be placed in an inclined position under a bell-
glass, under which is a vessel containing water, the solution
gradually collects towards the lower parts, and falls in drops
into a vessel placed underneath. The attraction of the water
was observed in this manner between 10° and 25° C.; the
water underneath the bell-glass had no higher temperature. For
the sake of comparison, a glass plate was placed each time near
the rock-salt plate under the same bell-glass, but it never showed
a trace of moisture. The plates of rock salt used were all quite
white and transparent. Plates from Northwich in Cheshire were
principally used ; but plates from Wielicza, from Stassfurth, Ischl
and Hall in Tyrol, which I happened to possess, showed the same
deportment ; and salt from Barcelona, prepared from sea-water,
behaved in a similar manner.
If the plate of salt, after it has become covered in a moist atmo-
Heat through moist Air. 251
sphere with a solution of salt, be placed in dry air, the water eva-
porates and the salt becomes again dry. In the experiments I
made, it was merely necessary to expose the plates in the labo-
ratory to obtain them quite dry in a few hours.
_ Melloni* found that a layer of pure water of a millimetre
in thickness transmits no heat which comes from an obscure
source of heat. Of the rays of ignited platinum, 5°7 per cent.
are transmitted. In Melloni’s experiments J, a saturated solution
of rock salt transmitted + more of the rays from an Argand
lamp, than a layer of water of the same thickness, and in Dr.
Franz’s experiment } more. As far as 1 know, no experiments
have been published as to the proportion of rays transmitted
through a very thin layer of solution of rock salt; but the
quantity which is transmitted must in any case be excessively
small. Hence even the thinnest layer of solution on the plate
hinders the passage of heat.
In order to investigate how far this is the case, the following
experiment was made :—A tube of strong glass, a metre in length,
was closed at both ends by plates of English rock salt a milli-
metre thick. It was first filled with dry air, by sending through
it, by means of an aspirator, such a quantity of air, which had
been dried by passing through several chloride-of-calcium tubes,
as to make it quite certain that all the origimal air had been dis-
placed. Thereupon thedeflection of the galvanometerwasobserved,
which was produced when the rays from a flask blackened on the
outside and filled with water kept boiling by passing a current of
steam through it reached the thermo-pile after passing through
the tube full of dry air. Then, while the rest of the experiment
was unchanged, air, which had previously passed through a tube
filled with moistened pumice, was sent through the same tube.
So soon as only a small quantity of this air filled the tube with
the plates of rock salt, the quantity of the heat which reached
the thermo-pile, after traversing this air, decreased. If, then, dry
air was again transmitted through the tube, the deflection again
increased and finally attained its original value. It is perhaps
superfluous again to remark that, when the tube was closed with
glass plates instead of rock-salt plates, nothing was observed of
such a difference in the transmission of the thermal rays. By a
continued transmission of moist air through the tube with the
rock-salt plates, the quantity of heat which traversed it could
easily be reduced to 7. In that case the plates, when removed
from the tube, were found to be covered on the inside with
moisture. A decrease such as Mr. Tyndall mentions{, to 3;
or to 77, has not, could not be attained in these experiments, not
* La Thermochrose, 207. + Ibid. 165.
{ Phil. Mag. vol. xxii p. ane
252 Prof. Tyndall on Recent Researches on Radiant Heat.
even when the outer sides of the plates of rock salt were simul-
taneously kept moist.
I do not venture to maintain that the remarkable results
which Dr. Tyndall obtained on the 10th of October of this year,
depend on the hygroscopic properties of his plates of rock salt,
since I neither know sufficiently the quality of these plates, nor
the precautions which Dr. Tyndall took in his experiments. My
only object is to call attention to the difficulties incidental to the
use of plates of rock salt in such experiments.
XXXV. Remarks on Recent Researches on Radiant Heat.
By Joun Tynpatt, F.R.S.*
Ore ee last Number of Poggendorff’s Annalen contains a
short paper by Professor Magnus, “‘ On the Passage
of Radiant Heat through moist air,’ a translation of which
appears in the present Number of the Philosophical Magazine.
This paper has excited considerable interest and some dis-
cussion among the scientific men of London, and it is on many
accounts desirable that I should not delay attempting to offer
an explanation of the differences which exist between my emi-
nent friend and myself. A brief sketch of the history of the sub-
ject is also considered desirable ; and this, as far as the extremely
limited time at my disposal will admit of, I shall also endeavour
to supply.
§ 2. On the first perusal of Melloni’s admirable work La
Thermochrose, which came into my hands soon after its publica-
tion, the thought of investigatmg the action of ‘gases on radi-
ant heat occurred to me. Melloni, it will be remembered, failed
to obtain any evidence of the absorption of radiant heat by
a column of atmospheric air 18 or 20 feet long. My attention
was further fixed upon this subject by the discussion carried on
in 1851 between Professors Stokes and Challis, regarding
Laplace’s correction for the theoretic velocity of sound. Pro-
fessor Challis, it will be remembered, contended that Laplace
had no right to his correction, because the heat evolved in con-
densation would be instantly wasted by radiation in a mass of
air of indefinite extension. In the first lecture of my first
course at the Royal Institution in 1853, I proposed compress-
ing air in a rock-salt syringe to decide the question; and im
a paper presented quite recently to the Royal Society, I have
solved this point in a manner which I hope Professor Challis
himself will deem conclusive, the mode of solution resembling in
some respects my device of 1853. In 1854 the action of gases
* Communicated by the Author.
Prof. Tyndall on Recent Researches on Radiant Heat. 253
and vapours on radiant heat was a frequent subject of conversa-
tion between my scientific friends and myself; and some of these
still remember my remarks at the time; the hopes I entertained
regarding the subject, and the devices by which I proposed to
meet its difficulties. I was, however, prevented by other engage-
ments from attacking the subject at this time; and not till the
early spring of 1859 were my ideas brought to practical defini-
tion. Then, however, I devised and applied the apparatus
which, with some modifications and improvements, I have used
ever since.
This apparatus immediately opened to me a large and rich
field of experimental inquiry; and the greatest pleasure this dis-
covery gave me, and which I often expressed to Mr. Faraday at
the time, was, that it placed me in possession of a subject in the
prosecution of which i could not possibly interfere with the claims
of any previous investigator. The first notice of my researches is
published in the ‘ Proceedings of the Royal Society’ for May 26,
1859. On the 10th of June following, I made the investigation
the subject of a Friday evening discourse at the Royal Institution.
The late lamented Prince Consort was present on this occasion,
and with characteristic goodness interested himself afterwards to
obtain plates of rock-salt for me. I then executed many of my
experiments in presence of a large audience ; and an account of
the discourse is published im the ‘ Proceedings of the Royal
Institution’ of the date referred to. I also communicated an
account of the investigation to my friend Professor De la Rive,
and he published a translation of my communication in the
Bibliotheque Universelle. The investigation was also described
in Cosmos, in the Nuovo Cimento, and in other Journals. When
I reached Paris in 1859, I found that the subject had attracted
a greater degree of attention than I could have hoped to see
bestowed upon it. In short, the publicity of my mode of experi-
ment and results was quite general.
I will here ask permission to cite a number of these results
obtained during the month of July 1859, after the main difficul-
ties of my apparatus hadbeen surmounted. The method employed
was substantially the same as that described in my last memoir*.
The heat passed from the radiating surface through a vacuum
into the experimental tube; the principle of compensation was
also employed; the length of the tube used to receive the gas
was 12 inches ; and from the galvanometric deflection consequent
on the admittance of the gas or vapour its absorption was deduced.
* Phil. Trans., February 1861; Phil. Mag., Sept. 1861.
254 Prof. Tyndall on Recent Researches on Radiant Heat.
I. Gases.
Name of gas. Deflection.
AMOSDNGMICIAIEE 6 dc on ibid act a OLE
Oxygen, J. a iniiinnts saben pao edit anti
Nitrogen, 20th J uly Moki nnieee pion ae oe
Para, Sent. i WG) «5 c/a apes Pcs fheapig dene mie
BP yArgmeny in. 69) of) x ys Wedd Kol Gary Onan
Carbonic oxide, S).c5. (ar) sSueltesy Ole eet
Garbonach acidia sesh nee tgs aie 37-5 ; 35° ; Byiena yen -
Nitrous oxide . . By Piya) 7/2 ie B75
Olefiant gas, 1 inch fence teen 43°,
35 5 Ounchesy:,..4)) 5. [6 1) sO coe hogan
be yf) MUCH ES be ou. in hay ee et
Coal-gas, linchtension . . 28°.
o S MCheS, 35) a.jc ty ane Wee
R aOmnehesy/ 4.) 50) 5 Wavenaee
Motaleheat ere wt UOTE rato
The figures separated on each ous by semicolons indicate
the results of different experiments; and their close agreement
shows the accuracy which, even in this early stage of the inquiry,
the experiments had attained. The above deflections represent
the following absorptions, at a common tension of 30 inches of
mercury.
If.
Name of gas. Absorption.
Atmospheric! air). 2008 Ji uou cee ao
INatrowen i, f ia) Joh My de ee)
Oxayeni shed hE i Rd CaO es
Blivdigoren 5) ua ean ee
Warbonteloxide: 02 Veevae J. eco). Meee:
@arbonie ‘acid’)):.3 63h) A eee
Nitrous oxide 155)j.)) 40) 558 ase
Olefiant gas. 20. 0 i eee
CoalzcastGre O97) 6 2 OL SAS
The vapours of the following saltiness were also examined
in the same month, at a common tension, and the annexed
results were obtained.
Ill. Vapours.
Name of vapour. Deflection.
Biswiphide of carbon: 6.) icg)cli»:'le6) cee Orel ee
Bichloride;of carbow ..) 4.0.2 +. 4/14 de enous
Todidevof methyle’,.. .'. 4). 2s OA eonenae
Cillorolorar ee! oe es Boek tay ot ae eee A1° ; 40°.
Benzoler er ee eee
Amnylene ny site Ve iia) ot ele ai) ony ROG 55°.
Prof. Tyndall on Recent Researches on Radiant Heat. 255
Table (continued).
Name of vapour. Deflection.
Wood-spiit . he OO yrs OO
Methylic alcohol (from Dr. W,) DS team ce AOD).
a Grom Dri), fo. 0a,.o);, O40 Cimpure).
Ethylic TR cece bis. «hecho, cuihicmhy EO OO GOS. «
mseinieralcohol 9). i... + | s+ 040-5 640°.
Mag ATE EL NET owls fi, dc soph fel OOS 65°.
POMREEIG (ELLIOT. og 6h) fm vi my im} oervy 67°; ae
Exapmuate of cthyle ., . .. .... + > 68°; 68°.
BURNS CLINIC orice ae Sj, Loses © buceas ch 0°; 70°:
Double brass screen . . 7928,
These deflections correspond to the following absorptions,
omitting decimals :—
LY:
Name of vapour. Absorption.
stl phide, Of €arDOw rey boyy sity evs | AF
Biehloride of carbon... -s .s0.6:: 4. 008
sipaine of methyle joo..('4 412 bape wiytoyo88
IMOLOLOEHI bite) chuck come Aten wesc e hae
Beearemlcanecnl Gyo td. iw. dtedamern ay GOO
Amylene . wt Hid 47 toe ie)
Pure methylic acono! ct} jptosipen ctl es, tape tna
PrbemCh ei ber .4:() ail poh nil hyenas ananineOO
Bein, BCH Wal cats Won acartravinwe etn LOO
Mey -amylicvether ec. 6-21) oy co) 216
BemiELIE CUCL) o05) 5 4i 08k a) |feeh es cneOon
Eropionate of ethyle.., «5 «4... 252
eperaterOl eblivle . iio < nes), 6, «ya VeOam
These results, which followed many thousand undescribed
experiments, were all obtained before the end of July 1859 ; and
I should certainly have published them and many others in ev-
tenso at the time, had I not felt that the wide circulation the
general description of the inquiry had obtained relieved me from
this necessity. I wished to impart the last finish to my apparatus,
and to pursue the subject with that deliberation and thorough-
ness which its difficulty and importance demanded. Not until
the close of 1860 was the full account of the investigation drawn
up ; and the memoir in which it was embodied bears the receipt
of the Royal Society for the 10th of January, 1861. It after-
wards formed the Bakerian Lecture for the year.
- For months I was harassed by the discordant results obtained
with gases generated in different ways. The nitrogen obtained
from the passage of air over heated copper turnings g eave me at
first many times the effect of the air itself; that obtained from
256 Prof. Tyndall on Recent Researches on Radiant Heat.
the combustion of phosphorus in air differed from both; while
the nitrogen obtained from the nitrate of potassa could not
be made to agree with its fellows. In like manner, the
oxygen obtained from the chlorate of potash and peroxide of
manganese differed from electrolytic oxygen; the hydrogen
obtaimed from sulphuric acid and zine differed from electrolytic
hydrogen ; the carbonic oxide obtained from chalk and carbon
differed from that generated from the ferrocyanide of potas-
sium, while carbonic acid from different sources showed similar
anomalies. It will be borne in mind that at this time nothing
whatever was known of the vast action which a small amount of
certain impurities can exert, and that my own experiments were
the first to exhibit this action.
Further, my drying apparatus first consisted of sixteen feet of
glass tubing filled with chloride of calcium, and a large U-tube
filled with fragments of pumice-stone moistened with sulphuric
acid. Sometimes the chloride of calcium was used alone, some-
times the sulphuric acid, and sometimes both were used together.
Every morning it was necessary to allow the air to pass through
the drying apparatus, and fill the experimental tube several times
before the results became constant; and even after they had
become tolerably constant with the chloride of caleium, the
introduction of the sulphuric acid caused a considerable variation
of the absorption. This might naturally be ascribed to the
more perfect desiccation of the air by the acid, but this does not
account for the effects which I obtained. For when both were
used, the magnitude of the absorption was found to depend on
the circumstance whether the air entered the sulphuric-acid tube
or the chloride-of-calcium tube first. I will here give an example
of this irregularity.
Absorption.
Air passed through CaClalone. . . . pea 7/
When SO? was added . Be Rares A
Through new CaCl tube . aj) gia Ph
New SO® tube added aie uals 4,
Through another CaCl tube alone . . ; Z.
A fresh tube of SO? added 5
Reversed current of air, and sent it through SO®
FU i * coop v0 esl) “Lenscien eam acd tame cen
The fluctuations above referred to are here distinctly exhibited ;
and the last experiment shows that, without changing the tubes
in any way, but merely by reversing the direction in which the
eurrent of air passed through them, the absorption was doubled.
Difficulties almost innumerable of this kind had to be overcome.
I had finally to abandon the chloride of calcium and the pumice-
stone altogether, and make use of fragments of pure marble for
Prof. Tyndall on Recent Researches on Radiant Heat. = 257
my caustic potash, and of pure glass for my sulphuric acid. But
with these also a long time elapsed before I was master of the
anomalies which from time to time made their appearance. The
dust of a cork; a fragment of sealing-wax, so minute as almost
to escape the eyesight ; the moisture of the fingers touching the
neck of the U-tube, in which the sulphuric acid was contained
—these, and many other apparently trivial causes, were sufficient
entirely to vitiate my results in delicate cases, giving me on
many occasions effects which I knew to be large multiples of
the truth. Thus, while perfectly safe as regards the stronger
gases whose energy of action masked small errors, prolonged
experiment was needed to connect these with the feebler ones, and
to refer them to air as a standard. In short, I thought it due
both to the public and myself to abstain from giving more than
a clear general account of my inquiry until I had mastered every
anomaly that had arisen. I cannot regret having exercised this
patience, more especially when I find one of the ablest and most
conscientious experimenters of modern times falling, as I believe,
into error on some of the points which most perplexed me.
A few weeks subsequent to the receipt of my paper by the
Royal Society, that is to say, on the 7th of February, 1861, an
account of experiments on the transmission of radiant heat
through gases was communicated by Professor Magnus to the
Academy of Sciences in Berlin. In this inquiry the absorption
of heat by vapours was left untouched, nor did it embrace the
reciprocity of radiation and absorption which my investigation
revealed. But as regards absorption by gases, Professor Magnus
and myself had operated on the same substances; and consider-
ing the totally different methods employed, the correspondence
between our results must be regarded as very remarkable.
Previous to occupying himself with the transmission of heat
through gases, Prof. Magnus had made an investigation on the
conduction of heat by gases, and he was led naturally by this
inquiry to take up the question of gaseous diathermancy. My
knowledge of his great skill and extreme caution as an experi
menter entirely ratifies a statement which he has repeated more
than once in his published memoir, namely, that his results on
the diathermancy of gases were already obtained at the time he
communicated his results on conduction to the Academy of
which he is a member, that is to say, in the month of July
1860; im fact the very experiments intended to determine their
conduction, really revealed the absorption of the gases. I am
quite persuaded that the results of Prof. Magnus are inde-
pendent of mine, and that, had I published nothing on the sub-
ject, his own inquiries would have led him to the discoveries
which he has announced. That my researches preceded his by
258 Prof. Tyndall on Recent Researches on Radiant Heat.
more than a year, is simply to be ascribed to the fact of my
attention having been directed to the radiation of heat through
gases long before even his researches on conduction had com-
menced. It is needless to dwell upon the value of such a general
corroboration as that which subsists between Prof. Magnus and
myself. However private interests may fare, science is assuredly
a gaimer when independent courses of experiment lead, as in
the present instance, to the same important results.
§ 3. But while furnishing, by an independent method, a
highly valuable general corroboration of my results, there are
some special pomts on which Prof. Magnus differs from me;
and one of these (the action of aqueous vapour on radiant heat)
he has made the subject of special examination. My first
experiment gave the action of the vapour of the London air on
a November day to be 15 times that of the air itself. Only a
few weeks subsequently Prof. Magnus announced, and cited very
clear experiments in support of his statement, that the amount
of aqueous vapour capable of being taken up by air at a tempe-
rature of 15° C. has no influence whatever upon the absorption.
This announcement caused me to repeat my experiments with
more than usual care ; and | found the absorption of the vapour
not 15 times, but 40 times that of the air. This result was
mentioned incidentally in my letter to Sir John Herschel; and
Prof. Magnus, induced by this mention to take up the question
again, corroborates his former result, and finds, by repeated
experiments, that the aqueous vapour of the atmosphere has no
influence whatever upon radiant heat, “and that the rays of the
sun, so long as the air is clear, reach the earth in the same man-
ner whether the atmosphere is saturated with vapour or not.”
The more I experiment, the further I seem to retreat from
the position of my friend ; for in a paper quite recently presented
to the Royal Society, I have set down the action of the air of
the laboratory of the Royal Institution, not at 15, nor at 40,
but often at 60 times that of perfectly dry air. In fact, the
more experienced I become, and the greater the precautions I
take to exclude impurities, the more does atmospheric air, in its
action on radiant heat, approach the character of a vacuum, and
consequently the greater, by comparison, becomes the action of
the aqueous vapour of the air.
In the paper which has suggested this communication, Prof.
Magnus assigns as a possible source of error on my part,
that the aqueous vapour may have been precipitated in a quid
form upon my plates of rock-salt. He cites experiments
of his own to show the hygroscopic nature of this substance ;
and refers to Melloni’s experiments in proof of the highly
opake character of a solution of rock-salt for the obscure
Prof. Tyndall on Recent Researches on Radiant Heat. 259
rays of heat. Such a solution on the surfaces of my plates
might account in part for the extraordinary absorption which ].
have observed. In a series of experiments made with the express
intention of wetting the plates of salt by precipitation, Prof.
Magnus exalts the absorption to 4 times that of air; but
though the plates were visibly wet, no nearer approach than
this could be made to my result, which makes the absorption of
aqueous vapour 40, 50, and even 60 times that of air. It was
only on the inner surface of the salt, which came into contact
with the saturated air, that the moisture was precipitated in the
experiments of Prof. Magnus; the outer surface, which was in
contact with the common air of his laboratory, remained dry ;
and even the wetted surface, when exposed for a time to the
same air, became dryalso. I would here, at the commencement,
remark that it is with this common outer air, and not with air
artificially saturated with moisture, that I find the absorption of
aqueous vapour to be 50 or 60 times that of the air in which tt is
diffused. In fact, if I am correct, the action of aqueous vapour
upon radiant heat might be applied in the construction of a
hygrometer surpassing in delicacy any hitherto devised.
I think it would be hardly possible for a person of any experi-
mental aptitude whatever, to work, as I have done, for three years
with plates of rock-salt, which must be kept polished and bright,
without becoming aware of all the circumstances referred to
by Prof. Magnus. But the truth is that I was well acquainted
with the peculiarities of rock-salt many years before this investi-
gation commenced*. A slight consideration of the conditions
of the case will, I think, show how improbable it is that a
precipitation, such as that surmised, could take place in my ex-
periments. First, then, the common air of the laboratory,
according to Prof. Magnus, does not produce the effect which
he considers may be active in my case; this, as already stated,
is the air which I have employed in all kinds of weather, dry as
well as moist. Secondly, this air is introduced into a tube >
through which is passing a flux of heat from the radiating
source. Thirdly, the air on entering the tube is heated by the
stoppage of its own motion, and thereby rendered more ca-
pable of maintaining its vapour in a transparent state. The ex-
terior surface of my terminal plate of salt was, moreover, always
open to inspection, and it was never found wet; much less
could the inner surface be wetted, because the temperature
within the tube was higher than that without.
* The action of moisture upon rock-salt was unhappily made strikingly
evident to me some months ago; for through a chink in the roof of the
laboratory some water entered, which destroyed two of my plates, and left
me more or less a cripple ever since.
260 Prof. Tyndall on Recent Researches on Radiant Heat.
But I have not relied on ‘the inspection of the outer surface
alone of my rock-salt plates. I have taken my apparatus
asunder fifty times and more, on occasions when I had most
reason to expect precipitation, but have not been able to find a
trace of moisture on my plates.
This, however, did not entirely satisfy me, and I therefore
made an arrangement of the following kind :—An India-rubber
bag was filled with air and subjected to gentle pressure. By
a suitable arrangement of cocks and T-pieces, this air could be
forced either through a succession of tubes containing fragments
of marble moistened with caustic potash and fragments of glass
moistened with sulphuric acid; or through a similar series in
which fragments of glass were moistened with distilled water.
A current of either dry air or damp air could be thus obtained
at pleasure ; and my object then was to get either the dry air or
the wet air, under precisely the same conditions, into an open
tube. ‘To effect this, matters were so arranged that either cur-
rent could be discharged into the same narrow glass tube. This
glass tube was left in undisturbed connexion with one end of my
experimental tube, while the other end was connected with the
air-pump. The plates of salt were entirely abandoned, the expe-
rimental tube was separated from the “ front chamber” de-
scribed in my memoir, and a distance of a foot intervened be-
tween the radiating surface and the adjacent open end of the
tube. In front of the other open end of the experimental
tube was my thermo-electric pile, the ‘compensating cube”
being applied in the usual way. By pressing the bag and gently
working the pump, I could, to a great extent, displace dry air
by moist, and moist air by dry. And in this way, without any
plates of rock-salt whatever, | verified all the results that I had
obtained with them. I have executed similar experiments in the
case of all other vapours that I have examined, and find that
with them, as well as with aqueous vapour, my plates of rock-
salt are perfectly to be relied on.
Whence, then, the difference between Prof. Magnus and myself ?
I am quite persuaded that no greater care could be bestowed
upon scientific work than Prof. Magnus bestows upon his; and it
is the perfectly accurate nature of his experiments which renders
the explanation of the differences between us an easy task.
Let me, however, first ask attention to what I may call a case
of internal evidence. 1 think the mere inspection of the drawing
of my apparatus in the ‘ Philosophical Transactions’ will show
that there was a good deal of thought and labour expended in
the construction of it. To one part of it especially I would di-
rect attention. In front of the experimental tube is a chamber
which is always kept exhausted, the radiant heat thus passing
Prof. Tyndall on Recent Researches on Radiant Heat. 261
through a vacuum into the experimental tube. To obtain that
chamber gave me great trouble: I had to unite its anterior wall
with silver solder to its sides ; and this, moreover, had to be done
for every special source of heat employed. I had to cause this
chamber to pass through a copper vessel, soldering it water-tight
at its place of entrance and of exit. This vessel I had to connect
by a tube 20 feet long with the water-pipes of the Institution, so
as to get a supply ; and to carry off the water, I had the stone floor
of the laboratory perforated, and one of our drains connected by
a second tube with the vessel. As already known, this vessel was
imtended to prevent the heat of the source from reaching my first
plate of rock-salt. The introducing of this plate air-tight be-
tween the front chamber and the experimental tube was also a
difficult matter, which required special means to meet it. Now
let me ask what could have induced me to go to all this trouble ?
The obtaining of suitable plates of rock-salt has been one of my
greatest difficulties; why then did I expend my time in seeking
for a pairof them? Why did I not content myself with a single
plate to stop the remote end of my tube, and allow the latter to
form a continuous whole from the radiating surface to the re-
mote end? Nay, why did I not abandon both plates, and simply
cement my pile air-tight into the remote end of my tube? All
these devices passed through my mind and formed subjects of
experiment at an early stage of this inquiry. These experiments
taught me that by bringing the gas whose deportment I wished:
to examine into direct contact with my source of heat, or into
direct contact with the face of my pile, I entirely vitiated my
results. And this arrangement, which in my case would have
been perfectly fatal as far as accuracy is concerned, is that which
Prof. Magnus has adopted, and 1s, I believe, the sole source of
the differences which have shown themselves between his results
and mine. :
His chief apparatus may be thus described* :—A glass vessel fits
like a receiver with its ground edge on the plate of an air-pump.
To the top of this receiver a second glass vessel is fused, and par-
tially filled with water. Into this water steam is conducted, which
causes the water to boil—a temperature of 100° C. being thus im-
parted to the bottom of the vessel, which is at the same time the
top of the receiver. On the plate of the air-pump a thermo-electric
plate is fixed with its face turned upwards, so as to receive the
radiation from the heated top of the receiver. The face of the
pile can be screened off at pleasure from the radiation from above.
From the pile, wires proceed through the plate of the air-pump
* The apparatus itself is drawn, and a translation of the paper to which
it refers is published, in the Philosophical Magazine, vol. xxi. pp. I, 81,
Pl. I. fig. 2.
262 Prof. Tyndall on Recent Researches on Radiant Heat.
to the galvanometer. The receiver is first exhausted and the
screen removed; the consequent deflection gives the amount of
heat radiated against the pile through a vacuum. Aijr, or some
other gas, is then admitted, and the reduction of the deflection
is regarded as due to the absorption of the gas*.
Air at the common laboratory temperature is here admitted
into direct contact with the radiating source possessing a tempe-
rature of 100°C.; chilling of that source is the immediate con-
sequence. And no matter how long the gas may remain there,
the hot surface can never attain its pristine temperature. Prof.
Magnus, it will be observed, experiments in the ordmary way,
making use of one face only of his pile. I entirely failed to ob-
tain any absorption by air or any of the elementary gases by this
mode of experiment, while Prof. Magnus obtains for oxygen and
air an absorption of 11 per cent., and for hydrogen an absorp-
tion of 14 per cent. My apparatus enables me to measure an
absorption of 0-1 per cent.; and surely with it an action so gross
as the above could never have escaped me. Nor could it have
escaped Melloni, who operated upon a column of air fifteen times
the length of that used by Prof. Magnus, and still found no ab-
sorption. With a column of air move than double the length of
his I obtain for oxygen only ;+)th of the absorption ascribed to
it by Prof. Magnus, and only 71th of what he finds for hydrogen.
The greater action of hydrogen is quite in accordance with
the known chilling-power of that gas. While ascribing their
results to a different cause, some experiments of my own, which
I have briefly described in the paper recently presented to the
Royal Society, completely corroborate those of Prof. Magnus.
In these experiments the gases were allowed to come into direct
contact with the radiating source, and here the action of hydro-
gen bore to that of oxygen the precise ratio found by Prof. Mag-
nus. The tube used in these experiments was 8 inches long ;
and had I been tempted to ascribe the results to absorption, I
should have found in a tube of the above length fifty times the
effect observed in a tube 33 inches long, in which the gases were
withdrawn from contact with the source.
The negative results of Prof. Magnus, as regards aqueous
vapour, are now sufficiently intelligible. The action which he
observed in the case of air being due to direct chilling by con-
tact—a process in which the mass of the chilling agent is the
most important consideration—the action of the minute quantity
of aqueous vapour present in the air becomes a vanishing quan-
tity. He makes air more than a hundred times what it ought
to be, and the action of the vapour practically disappears.
It is curious and instructive to observe the contrast of opinion
between Prof. Magnus and myself. He concludes that even if.
Prof. Tyndall on Recent Researches on Radiant Heat. 263
his experiments did not actually prove it, it must be evident that
the small amount of aqueous vapour in the air cannot sensibly
affect the absorption ; and I apply the same consideration of
smallness of quantity to account for the neutrality of the aqueous
vapour, when mixed with air, asa chilling agent by contact. With
regard to absorption, however, the quantity of vapour usually
afloat in the atmosphere is quite enormous in comparison with
some of the quantities with which I work. Indeed it is com-
mon with me to operate with quantities of various vapours which,
multiplied thousands of times, would not equal in volume the
vapour of the atmosphere.
Further, an inspection of my experiments showed me long ago
that those substances which, m the liquid condition, are highly
absorbent of radiant heat, are also highly absorbent in the
vaporous condition. Indeed, prompted by this fact, I have already
commenced experiments for the purpose of examining whether
the same amount of matter does not exert the same absorption,
whether it be in the liquid or the vaporous state. Now, water
is proved by Melloni to be the most opake liquid that he had
examined ; and it would be perfectly anomalous to me, on @ priori
grounds, if the vapour of this liquid proved so utterly neutral
as the experiments of Prof. Magnus would make it.
But I have also spoken of the exposure of the naked face of
the pile to the gas experimented with. My experience of this
arrangement is not without instruction.
I had a square aperture cut into a tin tube, and the face of a
pile introduced into the aperture, and cemented air-tight all
round. The tube was closed at the ends and put in connexion
with an air-pump. ‘The tube being exhausted and the needle
of the galvanometer connected with the pile at zero, on allowing
air to enter, its motion was soon arrested, and an equivalent
amount of heat was generated. This heat, communicated to the
face of the pile, was sufficient to dash my needles against the
stops at 90°. I do not entertain a doubt of being able to cause
my needles to swing through an are of 500° by the heat thus
generated. When, on the contrary, the tube was full at the
commencement, and the needle at zero, two or three strokes of
the pump sufficed to send the needle up against the stops, the
deflection now being due to the chilling of the inner face of the
pile. In fact this very deportment of a gaseous body on enter-
ing an exhausted receiver, and on being pumped out of a full
one, has enabled me to solve the paradoxical problem of deter-
mining the radiation and absorption of a gas or vapour without
any source of heat external to the gaseous body itself. The pile
of Prof. Magnus was exposed to a similar action to that here
described, though he never, to my knowledge, refers to it. It
264 Prof. Tyndall on Recent Researches on Radiant Heat.
would be quite impossible for me to carry out my experiments
with a pile thus circumstanced ; for after the instrument had
been either heated or chilled dynamically, it required in some
cases hours for the needle to return to zero. I may add that I
have made these experiments on dynamic heating and chilling
with my needles loaded with pieces of paper, so as to render
their motion visible to the most distant members of the large
audience of the Royal Institution.
§ 4. In addition to the experiments made with the apparatus
which I have described, Prof. Magnus has made two other series
with a glass tube one metre im length, and stopped at its ends by
plates of glass. His source of heat in this case was a powerful
Argand lamp, the rays of which were collected by.a parabolic
mirror placed behind it. In one series the tube was covered
within by a coating of blackened paper, while in the other this
coating was removed, the radiation through the tube being in
this case augmented by the reflexion from its sides. With the
blackened tube, Prof. Magnus corroborates the results already
obtained for air by Dr. Franz, who makes the absorption of a
column of nearly the same length as that employed by Prof.
Magnus 3 per cent. of the incident heat.
The difference between this result and that obtamed with the
other apparatus of Prof. Magnus, which gave an absorption of
1] per cent., might naturally be ascribed to the different kinds
of heat employed in the respective cases. But in the series of
experiments made with his wnblackened tube, and in which the
lamp above described was also his source of heat, he finds the
absorption of oxygen and of air to be 14°75 per cent.; and of
hydrogen to be 16:23 per cent. of the incident heat. This great
difference between the blackened and the unblackened tube,
Prof. Magnus ascribes to a change of quality which the heat has
undergone by reflexion at the interior surface of the tube, and
which has rendered the heat more capable of absorption. I have
tried to obtain this result with a glass tube of nearly the same
length as that used by Prof. Magnus, but have failed to do so.
The absorption of oxygen and air in his tube is 140 times, and
the absorption of hydrogen is 160 times what they show them-
selves to be in mine.
Whence these differences? They are plainly to be referred to
a source the same in kind as that which rendered an account of
the former ones; indeed I know not a more instructive example
of a single defect running through a long series of experiments
faithfully made, and so completely accounting for all the observed
anomalies. Prof. Magnus stops his tube with plates of glass
4 millimetres in thickness. Now Melloni has shown that 61
per cent. of the rays of a Locatelli lamp are absorbed by a plate
Prof. Tyndall on Recent Researches on Radiant Heat. 265 |
of glass 2°6 millimetres in thickness. It is therefore almost
certain that 70 per cent. of the entire heat emitted by the lamp
of Prof. Magnus were lodged in his first glass plate. A much
less quantity of the direct heat would be absorbed by his second
plate; but here the amount absorbed would be most effective as
a secondary source of heat, on account of the proximity of this
plate to the thermo-electric pile.
With the blackened tube, then, we had three sources of heat
acting directly or indirectly upon the pile—the lamp, the first
plate of glass, and the second plate. In reality, however, the
sources reduce themselves to two. For, glass bemg opake to
the radiation from glass, the heat emitted by the first plate was
expended in exalting the temperature of the second, close to
which the pile was placed. On admitting air at the ordinary
temperature into this tube, an effect similar in kind to that
which takes place in the other instrument of Prof. Magnus
must occur: the heated glass plates would be chilled, and they
would be chiiled more by the hydrogen than by the air, thus
giving us the exact results recorded by Prof. Magnus.
The same considerations applied to the unblackened tube,
explain perfectly the singular result obtained with it. On
theoretic grounds it is extremely difficult, if not impossible, to
conceive of such a change of quality as that above referred to.
But there appears to be no reason to call in its aid. Prof.
Magnus himself finds that the quantity of heat transmitted
through his unblackened tube is 26 times the quantity which
gets through his blackened one where the oblique radiation is
cut off. Im the case therefore of the naked tube, the flux of
- heat sent down by the heated glass plate adjacent to the lamp,
to its fellow at the other end, and likewise the heat sent directly
from the lamp to the same plate, are greatly superior to what
they are in the case of the blackened tube. The plate adjacent
to the pile becomes therefore more highly heated in the case of
the naked tube; and as its chilling is approximately propor-
tionate to the difference of temperature between it and the cold
air, the withdrawal of heat will be greatest when the tube is
unblackened within. While leaving myself open to correction,
I would offer this as the explanation of the extraordinary result
which Prof. Magnus has obtained. It is, I submit, not a case
of absorption, but of direct chilling by the cold air.
It is hardly necessary to say that similar remarks to those made
with reference to the blackened tube of Prof. Magnus apply to
the experiments of Dr. Franz. Dr. Franz, if I am correct,
never touched the absorption by air at all; his effects are
entirely due to chillmg by contact. The mistaking of chilling
for absorption causes him to find the same effect in a tube
Plul. Mag. 8. 4. Vol. 23. No. 154. April 1862. Lh
266 = On the Transformation of a certain Differential Kquation.
45 centimetres long as in a tube of 90 centimetres. He ranks
carbonic acid as low as air, and makes bromine-vapour a greater
absorbent than nitrous acid, whereas the absorption by the com-
pound gas is vastly greater than that by the elementary one.
The heat rendered latent by the evaporation of his bromine, aug-
mented the effect which in reality he was measurmg. In fact
all the differences between the German philosophers and myself
appear to be strictly accounted for by reference to a source of
error which the application of plates of rock-salt enabled me
from the outset to avoid *.
Royal Institution, i
March 1862.
XXXVI. Note on the Transformation of a certain Differential
Equation. By A. Cayzzry, Esq.t+
ape differential equation
Q OG cee
+67) 48 “ m*y =0,
if we put therein 10=2e7+1 (i= ./—] as usual), becomes
(1 +2*) en s +0 —4m?y=0.
In fact an integral of the second equation is ( V14+a24+ a)?” ;
this is
=( Vf (2x?+1)?—142a2+1)”;
or putting L6=22?+1, it is
—(V¥ —0?—1+476)”,
which is
= {1(//0+1+86)}”;
so that an integral of the transformed equation in @ is
=(V7@+1+80)”.
And writing im the second equation @ for z, and 4m for m, we
* I should be willing to pay a heavy price for a clear specimen of this
substance. Results of the very highest interest are, I believe, quite within
the reach of any experimenter who may be fortunate enough to possess a
suitable prism and one or two lenses of transparent rock-salt ; and I am
practically disabled at the present moment through my inability to procure
a moderate quantity of this precious material. A pair of plates, or even
one plate, of rock-salt, 3 inches in diameter and an inch thick, would also
be of the greatest use to me.
+ Communicated by the Author.
On the Regular inscribed Polygon of Twenty Sides. 267
see that the last-mentioned function, viz. (/@?+1+46)”, is an
integral of
d"y |g WY
OO eA Eee or mien:
(1+) a5 +67, my =O;
whence the transformed equation in @ must be this very eqna-
tion, that is, it must be the first equation. I have for shortness
used the particular integral (/1+2?+2)”"; but the reasoning
should have been applied, and it is in fact applicable, without
alteration, to the general integral
C(V1+a?+2)"4+C( 714+ 2?—2)”.
There is of course no difficulty in a direct verification. Thus,
starting from the first equation, or equation in @, the relation
10=22z?+1 gives
dy tidy ee plane h i a
dO 4adx’ dé?” 4adx\4adz/ ~~ — 16 z?\ dz? x dx/”’
1+@?= —427(1 42); :
so that the equation becomes
i Bho, edy NN ea? dy sila a
Aegis ede) de) de
Or multiplying by 4,
d?y ( 1+2? ao
BV iCe o at LEAT WC NEAT
Be) ae t @ i. v dz UL
that is,
ae d:
(1 +0°) 4 +2 —dmPy =0,
the second equation. But the first method shows the reason
why the two forms are thus connected together.
2 Stone Buildings, W.C.,
February 19, 1862.
XXXVII. Elementary Proof, that Eight Perimeters, of the Re-
gular inscribed Polygon of Twenty Sides, exceed Twenty-five
Diameters of the Circle. By Professor Sir Witt1amM Rowan
Hamizton, LL.D., &c.*
T was proved by Archimedes that 71 perimeters, of a regular
polygon of 96 sides inscribed im a circle, exceed 223 dia-
meters; whence follows easily the well-known theorem, that
eight circumferences of a circle exceed twenty-five diameters,
or that 8% > 25. Yet the following elementary proof, that eight
perimeters of the regular inscribed polygon of twenty sides are
* Communicated by the Author.
T2
268 On the Regular inscribed Polygon of Twenty Sides.
greater than twenty-five diameters, has not perhaps hitherto
appeared in any scientific* work or periodical; and if a page of
the Philosophical Magazine can be spared for its insertion, some
readers may find it interesting from its extreme simplicity. In
fact, for completely understanding it, no preparation is required
beyond the four first Books of Euclid, and the few first Rules
of Arithmetic, together with some rudimentary knowledge of
the connexion between arithmetic and geometry.
1. It follows from the Fourth Book of Euclid’s ‘ Elements,’
that the rectangle under the side of the regular decagon in-
scribed in a circle, and the same side increased by the radius,
is equal to the square of the radius. But the product of the
two numbers, 791 and 2071, whereof the latter is equal to
the former increased by 1280, is less than the square of 1280
(because 1638161 is less than 1638400). If then the radius be
divided into 1280 equal parts, the side of the inscribed decagon
must be greater than a line which consists of 791 such parts;
or briefly, if the radius be equal to 1280, the side of the decagon
exceeds 791.
2. When a diameter of a circle bisects a chord, the square of
the chord is equal, by the Third Book, to the rectangle under
the doubled segments of that diameter. But the product of the
two numbers, 125 and 4995, which together make up 5120, or
the double of the double of 1280, is less than the square of 791
(because 624375 is less than 625681). If then the radius be
still represented by 1280, and therefore the doubled diameter
by 5120, and if the bisected chord be a side of the regular deca-
gon, and therefore greater (by what has just been proved) than
791, the lesser segment of the diameter is greater than the line
represented by 125.
3. The rectangle under this doubled segment and the radius,
is equal to the square of the side of the regular inscribed poly-
gon of twenty sides. But the product of 125 and 1280 is equal
to the square of 400; and if the radius be still 1280, it has been
proved that the doubled segment exceeds 125; with this repre-
sentation of the radius, the side of the inscribed polygon of twenty
sides exceeds therefore the line represented by 400; and the
perimeter of that polygon is consequently greater than 8000.
4. Dividing then the numbers 1280 and 8000 by their
greatest common measure 3820, we find that if the radius be
now represented by the number 4, or the diameter by 8, the
perimeter of the polygon will be greater than the line repre-
* A sketch of the proof was published, at the request of a friend, im an
eminent literary journal last summer, but in a connexion not likely to
attract the attention of mathematical readers in general. At all events, it
pretends to no merit but that of brevity, and the simplicity of the principles
on which it rests.
On Land-tracts during the Secondary and Tertiary Periods. 269
sented by 25; or in other words, that eight perimeters of the
regular mseribed polygon of twenty sides (and by still stronger
reason, e2ght circumferences of the circle itself) exceed twenty-
five diameters.
Observatory, March 7, 1862.
XXXVIII. On the Form and Distribution of the Land-tracts du-
ring the Secondary and Tertiary periods respectively ; and on the
effects upon Animal Life which great changes in Geographical
Configuration have probably produced. By Sear.es V. Woop,
Jun.
{Continued from p. 171.]
Section 3.— The Changes in the Geographical Configuration which
resulted from Post-cretaceous Volcanic Action.
FE have numerous evidences that, since the close of the
secondary period, the volcanic energy has, with the
exception of the chain of the Cordillera, its continuation in the
Rocky Mountains, and the coast ranges of the latter, been exerted
in a diametrically opposite direction to that which I have attempted
to show prevailed throughout the secondary period, the tertiary
bands having been, with these exceptions, from east to west. I
have collected below the various tertiary geological systems and
anticlinals of which I am cognizant, and also the existing vol-
canic bands, omitting the Andes, with the average direction they
possess: the strictest accuracy in direction is not pretended, the
point of the compass being given which coincides nearest with
the general strike or direction of the chain or band.
The following are the systems or anticlinals whose direction is
due to post-cretaceous action. (The figures on the left hand
refer to the diagram.) |
MPC PAUSIETITE S$ < (Secia... oc olan ane o'> ave 4-e wide’ eseiele « E. to W.
ep eeenezuels and Prinidad’ oes. Sc ecle ss cc ee E. to W.
3. The Isles of Portland, Purbeck, and Wight, \ E. to W
NVC OF IKEHE crite salsa ds oc es 8 shore ; (
MC BESVECTICCS| /c100s tc aveleleiest oases eee ete e's s EK. to W.
me bifer ey teatic ISIES 1. ad ates vo alse cacs es oe W.S.W. to E.N.E.
SPUD AN Soro. let toc cols kc eee cease des W.S.W. to E.N.E.
ect Gite cet i Cy. ba sie Ns a N.W. to S.E.
8. The principal Alps, and the Noric Alps...... E.N.E. to W.S.W.
9. The Apennines, and the Julianand DinaricAlps. N.W. to S.E.
Persie aig AlNAnNiIA ., <2 .sc+ clade eeececionce N.W. to S.E.
ie) Phe Carpathians (Northern) .............. W.N.W. to E.S.E.
ba. he Carpathians (Southern) .............. W.S.W. to E.N.E.
BRIE Es allcati. notin ahr e ies Se cl cee ee oe E. to W.
14. The Caucasus and Crimea ................ W.N.W. to E.S.E.
Meer wentcnia and Ararat, .ecsc cs Se kee eweee se W.N.W. to E.S.E.
feereralicia and Cappadocia ............0...+- W. by S. to E. by N.
17. The Turco-Persian frontier...............: N.W. to S.E.
270 Mr. 8. V. Wood on the Form and Distribution of the
LOS y pris cn eat eee AIR ee eee Re oe E. by N. to W. by S.
20. FATA eee blastn ts:n Ldioivneiae Dyan W.N.W. to E.S.E.
24. The Salt-ranees PUNIAD ae. isin nis)’ sieyseuena W. by N. to E. by 5.
22. The Trappean range of Nerbudda.......... E. by N. to W. by 8.
23. The Lebanon and Anti-Lebanon .......... N. by E. to 8. by W.
SPA MOOISIOR ciel ew ardia ea h's,s sna ev eieieinl oie Seana N. to S.
The following are volcanic bands. (The letters on the left
hand refer to the diagram.)
a. The Aleutian Isles ...... siae caprayetstaval See een W. by S. to E. by N.
bz Phe Cananivs, (0s «tess une eee ae eet W. by S. to E. by N.
The band from Andaman to the Society Isles, divided as follows :—
[3 Andaman \£0 Jar sac. jk ios oie coin Bi alencts ereteeh aie N.W. to S.E.
d. Java to New Guimea! (if. i .ictvok fy iedeern se W. to E.
Le. New Britain to New Hebrides.......... N.W. by W.to S.E. by E.
f. The extinct band of South Australia and Vic-
toria (Australia), extending probably to New | E. to W.
LCM ACA oat tle eg k Thala dave y ays eee
g. Theband from the Aleutian Isles to Formosa, N.E.byE.toS.W.byW.
Including J Aas 75 « 0.05 amass oe cscs lseiele
h. The band from Formosa to the Moluccas... N.W.byN.toS.E.byS.*
The Andes, the Rocky Mountains, and the Pacific-coast ranges
of North America are omitted.
R
za
a
e]
=
Q
* The following authorities may be consulted in reference to the ages of
Land-tracts during the Secondary and Tertiary Periods. 271
It is remarkable how the general direction of all the tertiary
anticlinals, with two exceptions, coincides with the direction of
the existing volcanic bands (other than the Andes), the most im-
the above systems, anticlinals, and bands, the numbers followmg referring
to the corresponding numbers above :—
1b
Amor Lowbo
Oo Osi
Heneken, “On St. Domingo,” Quart. Journ. Geol. Soc. vol. ix. p. 115.
Cuba, Yucutan, and the chain of active voleanoes crossing Central
Mexico from E. to W. belong probably to this system.
. Wall, Quart. Journ. Geol. Soe. vol. xvi. p. 460.
. Weald: Hopkins, Trans. Geol. Soc. vol. vu. p. 1 et auctorum.
. Durocher, Comptes Rendus, 1851, p. 163. Noulet, im same, 1857; also
in Bull. vol. xv. p. 284. D’Archiac, Bull. vol. xiv. p. 507.
- La Marmora, “ On Majorca and Minorca.” Turin, 1834.
. Coquand, Comptes Rendus, 1847, vol. xxiv. p. 857. Nicaise, Bull.
vol. vill. p. 263. As to the coast-ranges forming the sub-Atlan region,
see the sections of Laurent’s paper “‘ On the Sahara,”’ Bull. vol. xiv.
p- 616. Consult also Pomel, Bull. vol. xii. p. 489; Ville, Bull.
vol. ix. p. 362.
. Spratt, Proc. Geol. Soc. vol. iv. p. 225.
. Auctorum. See, however, Murchison, Quart. Journ. Geol. Soe. vol. v.
p. 157.
- Cocchi, Bull. Soc. Géol. d. France, vol. xii. p. 226. Murchison, Quart.
10.
Journ. Geol. Soc. vol. v.p. 281. Ponzi, Bull. vol. x. p. 196.
Viquesnel, Mém. Géol. Soc. France, 1842, p. 35.
11 & 12. Boué, Mém. Géol. Soc. France, 1834, p. 224. Lilienbach, Mém.
13.
14.
15.
16.
LZ.
18.
13,
20.
21.
22,
23.
Géol. Soc. France, 1833, p. 224. Murchison, Quart. Journ. Geol. Soc.
vol. v. p. 259.
The Balkan region is coloured cretaceous in Murchison and Nicol’s
Geological Map of Europe, but I have not met with the authority.
See, however, Leonhard, Bull. vol. xu. (Old Series). Also Spratt,
Quart. Journ. Geol. Soc. p. 79.
For Caucasus, see Abich, Vergleichende geologische Grundziige der
Kaukasischen Armenischen und Nord-Persischen Gebirge, St. Peters-
burg, 1858. Also in Comptes Rendus, 1856, p. 227. For Crimea,
see De Verneuil, Mém. Géol. Soc. France, vol. i. (1838).
See Abich, as above.
Hamilton, Quart. Journ. Geol. Soc. vol. v. p. 369. Tehihatcheff,
Bull. Soc. Géol. d. France, vol. xi. p. 366.
Loftus, Quart. Journ. Geol. Soe. vol. xi. p. 247.
Raulin, Bull. vol. xii. p. 439.
Gaudry, Bull. vol. xi. p. 120.
Strachey, Quart. Journ. Geol. Soc. vol. vii. p. 292, vol. x. p. 249.
Vicary, Quart. Journ. Geol. Soc. vol. ix. p. 70.
Fleming, Quart. Journ. Geol. Soe. vol. ix. p. 192.
Hislop, Quart. Journ. Geol. Soe. vol. xi. p. 350. Sankey, Quart.
Journ. Geol. Soc. vol. x. p. 55. Calder and Coulthard, ‘ Asiatic
Researches,’ Calcutta, 1833, pp. 13 and 47.
Botta, Mém. Géol. Soc. France, 1833, p. 135.
24. Collomb, Bull. vol. xi. p. 63.
Ff Smyth, Quart. Journ. Geol. Soc. vol. xiv. p. 227. Woods, Quart. Journ.
Geol. Soc. vol. xvi. p. 253. Trans. Phil. Inst. Victoria, vol. i. p. 85. Heaphy,
Quart. Journ. Geol. Soe. vol. xvi. p. 242.
For the other volcanic bands, a, b, c, d, e, g, and h, see Mallet, Reports
of British Association, 1852 to 1858.
272 Mr. 8. V. Wood on the Form and Distribution of the
portant and marked of which may be considered as parts of one
large band, which extends from the Western Isles, with a vary-
ing breadth of from 10 to 20 degrees of latitude, through the
Mediterranean, Black, and Caspian Seas, and is continued through
Southern Asia, under the form of intense earthquake action, down
to the head of the Bay of Bengal, and thence in its most active form
through the Indian Archipelago to the centre of the South Pacific*.
The general conformity in direction of the great tertiary moun-
tain systems of Europe and Asia with that of this great volcanic
band forms a striking coincidence. The reports of geologists
upon most of the mountain systems of Europe and Asia show,
with considerable precision, the part which these systems have
played in the formation of the present Europeo-Asiatic continent.
I have in the introductory section alluded to the way in which
the elevatory forces have been exerted in foci, forming volcanic
bands and afterwards mountain chains, contorting violently the
strata within a limited area only, but desiccating over great areas
the pre-existing sea-bottom; thus it seems to have been with
the bed of the cretaceous ocean, at least in Europe and Asia.
Over the whole of Southern Europe and South-Western Asia
the sections published show, with the exception of the Carpa-
thians (where Sir R. Murchison has described the nummulitic
deposits as resting unconformably upon the secondary beds),
that the older tertiary and secondary formations, although thrown
into the greatest disorder in the mountain chains, in some by
older, but in most by middle and newer tertiary volcanic action,
have a general conformability to each other. This, coupled with
the well-known hiatus which exists between the fauna of the cre-
taceous and that of the older tertiary periods, justifies, | think,
the conclusion that over the whole of this area the bed of the cre-
taceous sea must have been desiccated by the effect of elevatory
forces having their foci separated by a wide interval, and the whole
sea-bed (in order to have preserved its horizontality up to the time
when it was again submerged to form the basin of the tertiary sea)
have been formed into a continent unmarked by any consider-
able irregularity of surface. Ifthe view advanced in the introdue-
tory section, as to the cause of the contiguity of the sea to voleanic
foci, be well founded, this undisturbed condition of the desiccated
bed of the cretaceous sea, coexisting with a gap in the geological
succession of very great duration, is what we should @ priori
expect to find, by reason that, the volcanic bands of the period
beimg remote from the area in question, an undisturbed perma-
nence of level was permitted; and this level being that of dry
land, we should find no formations until the area was again sub-
jected to the direct action of the volcanic bands, and with that
* See Mallet, ‘Reports of British Association,’ 1852 to 1858.
Land-tracts during the Secondary and Tertiary Periods. 273
to a return of the sea. We may to some extent trace the line
of voleanic band to which this elevation was due (or rather
in which it had its focus), along the northern border of the
tract. Thus the great chain of the Northern Carpathians,
although in convulsion during later tertiary periods, appears,
from the sections of Sir Roderick Murchison, to have been
upheaved, and the cretaceous strata to have acquired a con-
siderable inclination, prior to the formation of the nummulitic
deposits*. The Pyrenees also appeart to have undergone
their principal elevation prior to the newer cretaceous period.
Mr. Prestwich, again, has found reason to infer that the Weald
anticlinal had begun prior to the close of the upper creta-
ceous formation{. From these, and also from the system of
the Jura or Cote d’Or, which, coming into existence in the
early part of the cretaceous age§$, possessed a direction from N.E.
to S.W., or intermediate between those characteristic of the se-
condary and tertiary periods respectively, it appears that the
movements which elevated the old secondary sea-bed, and brought
into existence a continent which endured for a period long enough
to change the complexion of the higher orders of the animal
kingdom, had begun towards the close of the secondary period.
To what other volcanic bands the elevation of this continent was
due we have not at present the evidence to show; but the general
conformity, between the tertiary and cretaceous beds in Southern
Europe, to which I have adverted would point to these bands
beimg further to the south than any of the places hitherto ex-
amined.
We see that the Maestricht, and also some other deposits of
limited extent || which some geologists have referred to the new-
est cretaceous age, were formed in the contiguity of what appears
to me to have been the volcanic band from which the elevation of
the secondary sea-bed was proceeding; and their limited cha-
racter thus becomes intelligible, as they would only endure during
the comparatively brief period before the secondary sea-bed be-
came converted into a continental tract, when, the volcanic forces
to which that elevation was due becoming quiescent, no further
deposits took place until these forces again burst forth and pre-
vailed during the tertiary period over the areas occupied by the
* See the sections in Murchison, Quart. Journ. Geol. Soe. vol. v. p. 259.
t D’Archiac, Bull. vol. xiv. p. 507.
+ Quart. Journ. Geol. Soe. vol. vii. p. 257.
§ See Lory, Bull. vol. xi. p. 780°; Benoit, in vol. xv. p. 315.
|| The equivalent of the Maestricht is said by M. Coquand to occur in
the Charentes (Bull. vol. xiv. p. 571). The late Mr. Sharpe also referred
some sands at Farringdon to the same epoch (Quart. Journ. Geol. Soc.
vol. x. p. 176); but his views are disputed by others. See Davidson, Bull.
vol. xi. p. 180.
274 Mr. 8. V. Wood on the Form and Distribution of the
mountain systems of Southern and Central Europe and South-
Western Asia. The absence of deposits of a thickness sufficient to
withstand subsequent degradation during a period of elevation has
been urged by Mr. Darwin* ; andif true (as it may well be in the
sense of a general continental elevation, although not in that of
the gradual shoaling of such gulfs as those which received the
secondary deposits of France and England), we see in it an ex-
planation of the limited extent of the newest secondary (supra-
cretaceous) deposits, since it would only be on the skirts of the
continent formed out of the cretaceous sea-bed where these would
occur; and this skirt, except on its northern border, has not yet
been explored. The intra-cretaceous and tertiary deposits would,
I conceive, be taking place in the contiguity of any of the vol-
canic bands then in activity ; and we may still therefore look for
their discovery, unless they should now be beneath the ocean.
The Cordillera of the Andes, Mexico, California and Oregon,
places where, according to the views before discussed, the direc-
tion of the coast-line of America has remained since the secondary
period unaltered in its main features, and perhaps even Southern
India, offer probable sites for the occurrence of intra-cretaceous
and tertiary deposits f.
We have seen that the conformability between the newer
secondary and the tertiary formations, from the British Isles as
far east as India, shows that the tertiary sea over that area re-
turned mainly to the same bed as that occupied by the secondary
sea; it differed, however, essentially in one particular, viz. in
being shut in to the north by a barrier of land, no incon-
siderable portion of which was composed of elevated cretaceous
deposits: we find in the nummulitic deposits of Southern Europe,
Northern Africa, Southern and South-Western Asia, the evidence
of a vast gulf (interspersed with numerous islands) stretching
from the Bay of Bengal north-west through Hindostan and
Persia, across Asia Minor into Europe and North Africa,
including within it the present Mediterranean, Black, and
Caspian Seas; while, fringing the barrier of land which bounded
it on the north, we find the richly stocked marine deposits
of the English, Belgian, and French eocene basins generally
associated with estuarine and fluviatile beds of contemporaneous
aget. Fringing land composed of elevated Jurassic deposits,
* Origin of Species, pp. 300 and 327.
+ I entertain considerable confidence that some of the beds associated
with the great lignite formation of North-Western America, California, and
Vancouver will eventually prove to be of intra-cretaceous and tertiary date.
t The same association of fiuviatile and estuarme beds with the num-
mulitic deposit seems to exist wherever an insular tract of land occurred in
this gulf—as in the Pyrenees, where remains of eocene mammalia have been
Land-tracts during the Secondary and Tertiary Periods. 275
and which in India bounded this gulf on the south, we have the
nummulitic eocene beds of Cutch similarly connected with the
fluviatile deposits intercalated with trap which occupy a con-
siderable area in Western India. There seems to me every
reason to infer that the suggestion of M. d’Archiac, quoted by
Sir Roderick Murchison*, affords the true explanation of the
phenomena presented, viz. that the eocene formations of Western
Europe were but the littoral deposits of the great nummulitic
gulf}, and were formed by the sand and mud of rivers debouch-
ing into the gulf at the spots where these formations occur, the
_ deltas of which rivers have furnished the estuarine and fluviatile
beds which are associated with these deposits. The mollusca
of the eocene formations of England, France, and Belgium ap-
peart to have all their affinities with the existing mollusea of the
present Hastern seas (being those to which we trace the junction
of the nummulitic gulf), but exhibit a dissimilarity to the
mollusea of the eocene formations of America. M. Abich, in his
‘Paleontology of Asiatic Russia’ (Mém. de l’ Académie des
Sciences de St. Pétersbourg, 6™¢ série, vol. vii.), figures thirty-two
eocene species of mollusca, of which twenty-six are, he considers,
identical with English, French, and Belgian eocene forms, two
are given by him as indeterminate, and four only as new species,
being respectively 81:25, 6°25, and 12:5 per cent. on the whole
number of species described by him. These fossils, obtained
from beds reposing on nummulitic rock and overlain by middle
tertiary im the neighbourhood of the Sea of Aral, a district con-
tiguous to the southern extremity of the Oural region (which
formed the land fringing the sea these forms inhabited), lived at
a distance from the English, Belgian, and French basins of up-
wards of 2500 miles, and strongly confirm the inference (arising
fromthe outcrop across Russia of older strata uncovered by eocene)
of a continuous coast-line joining these distant places, lying as
found. Similar fluviatile and estuarine deposits will doubtless hereafter be
discovered associated with the eocene beds of the Aral Sea and Araxes.
The return of the sea after the long intra-cretaceous interval to parts of
its old secondary bed appears to have been very gradual, and the formation
of the great nummulitic deposit to have beeu preceded by local tertiary
_ formatious, mostly fluviatile and estuarine. This, at least, was the case
according to M. d’Archiac (An. Foss. de Inde, p.77); his remark, how-
ever, admits of many exceptions, as the nummulitic deposits frequently
repose immediately on the secondaries or other older rocks.
* Quart. Journ. Geol. Soc. vol. v. p. 301.
+ MM. Heéhert and Renesier also (Bull. vol. xi. p. 604) regard their upper
division of the nummulitic deposit of the Alps as the marine equivalent of
the upper eocene of the Paris basin, and probably also of the oldest mio-
cene (Mayence, Limbourg, Sables de Fontainebleau, &c.).
t See Introduction to Eocene Bivalves, p. 10; Palezeontographical Society’s
Velume for 1859.
276 = Mr. S. V. Wood on the Form and Distribution of the
they do under nearly the same latitude, this coast-line being what
I have termed the northern shore of the great nummulitie gulf.
It is worth observing, also, that such an identity of forms at so
great a distance is, so far as I know, unexampled during other
tertiary epochs (although it is conspicuous during the paleeozoic
period), and can hardly have existed, except by virtue of a simi-
larity of conditions over the whole area and of easy communica-
tion by coast-line. M. Abich also describes the older tertiaries
of the valley of the Araxes as containing a large proportion
of the species of the mollusca common to corresponding hori-
zons of the Paris basin, and, intermingled with them, many species
agreeing with mollusca from India described by M. d’Archiac*,
and containing also well-known forms of nummulites cha-
racteristic of the Pyrenean and other South-European num-
mulitic deposits. The proportion of the mollusca in the beds of
the Araxes valley common to the older tertiaries of England,
France, and Belgium is not so large as im the case of the beds ©
of the Aral-Sea region; but the intermixture of Indian species
much assists the proof of the continuous extension of the num-
mulitic gulf in the form I have described. The contiguity of
the Aral-Sea region to the northern coast-line of the gulf (which,
beginning perhaps to the north of the Indian beds described by
M. d’Archiac}, extended to the Aral region at the extremity of
the Oural chain, and thence to England) would account for the
somewhat larger per-centage there of the shells of the basins of
North-Western Europe. The beds of the Araxes valley, on the
other hand, appear to have occupied a position more towards the
centre of the gulf, in the vicinity of insular land (formed by the
paleozoic plateau of that region which is uncovered by eocene
deposits), but remote from the great coast-lines. The extra-
ordinary range of the mollusea of the older tertiary period over
the region filled by this sea tends, moreover, to show that the
sea-bed formed by the submergence of the post-cretaceous con-
tinent—a continent which I have suggested was a vast tract
uninterrupted by great mountains—was shallow over its whole
area, the tertiary mountain chains of Southern Europe and
South-Western Asia, which have since elevated portions of its
bed into land, and deepened other portions into the Caspian,
Black, and Mediterranean Seas, not having come into existence
until a later date.
While we have thus evidence of a great gulf or land-girt sea
stretching, at the dawn of the tertiary period, from the Bay of
Bengal in a north-westerly direction to the British Isles, frmged
* Animaua fossiles du terrain Nummulitique de ?’ Inde. Paris, 1853.
+ These beds are, Hala in Scinde, the Cashmere valley, and the range
of Subathoo (part of Himalayan chain).
Land-tracts during the Secondary and Tertiary Periods. 277
to the northward by a continuous shore, formed of deposits
which had been land since the close of the secondary period,
and closed from any connexion with the North American seas,
we have in the Vertebrata of the period most satisfactory evidence
of a continuous land-connexion between the American and the
Europeo-Asiatic continents. -Associated in the same bed at
Kyson in Suffolk, there have been found remains of the Macacus
(Eopithecus), an exclusively eastern genus of monkey, and the
Didelphis, an exclusively American form of marsupial. In the
fiuviatile deposit of Hordle in Hampshire, the remains of a type
of crocodile resembling the American form (the cayman) occur ;
at the not far distant locality of Bracklesham,in the marine
though slightly older portion of the same delta, the true Asiatic
gavial has been found; and in the London clay the true Eastern
form of crocodile. In the same fluviatile of Hordle there occurs
in the greatest abundance the remains of the peculiar freshwater
fish the Lepidosteus, now an exclusively American form; and
associated with these Vertebrata, a land-shell (Helia labyrinthica)
now existing only in North America; and the river in whose
deposits these forms occur, discharged into a sea containing
mollusca whose affinities, as I have shown, are entirely with the
East. Continuing eastward into Asia from the Kuropean termi-
nation of this Atlantic bridge, by following the line of secondary
formations, which extend through Northern Europe and Western
Asia uncovered by any eocene deposits (they having been already
traced as far east as the Aral Sea), we perceive the wide stretch
of land which at the dawn of the tertiary period connected the
Asiatic region with America. The dissimilarity between the
mollusca of the European and American eocene formations, to
which I have already adverted, militates against any hypothesis
of a coast-line joming the seas im which such formations were
respectively deposited; and this agrees with what might be im-
ferred from the indications afforded by the configuration of the
secondary strata which skirt the eocene basins of England, Bel-
gium, and France, whick is, that the latter countries formed the
head of the nummulitic gulf, the coast-line connecting England
with the shore of the American eocene sea being on the other
side of the land thus closing in that gulf.
The extension of the European continent westward at the
dawn of the tertiary period, in the manner I have attempted to
describe, that is, in the form of a tract cutting off the nummulitic
gulf from the Atlantic, is further shown by the circumstance of
the European and American fauna becoming more assimilated
when they occur in formations which were due to the sediment
of one common ocean, the Atlantic. Thus Sir Charles Lyell
278 Mr. 8. V. Wood on the Form and Distribution of the
long ago showed* the connexion of the American and European
miocene formations by the presence of several marine molluscous
forms i common. Now, the absence of any similar connexion
between the eocene marine mollusca of the two continents, while
so close a connexion exists between the terrestrial fauna of the
eocene of Europe with that now existing im America, seems
only intelligible upon the hypothesis of a land tract at once
joming the continents, but severing the seas. That this land-
connexion has been gradually disappearmg since the eocene
period, is shown by the agreement among naturalists that the
molluscous fauna of the shores of the Western Isles, the Madeiras,
and of Portugal, affords evidence of the extension of Western
Europe in this direction between the miocene and the pleistocene
epochs, forming a province to which they have given the name
of Lusitanian +.
The probability of the configuration, at the dawn of the tertiary
period, which I have described, receives support also from a con-
sideration of the climatal conditions which the fossils of that
period indicate.
It has not unfrequently been remarked, as inconsistent with
any theory of a gradual refrigeration of climate during geological
periods down to the pliocene, that the eocene fauna of Europe,
both vertebrate and invertebrate, should at so late a stage in
the geological succession, present at least as tropical a character
as that presented by the fauna of any preceding stage in our
latitudes. The explanation of this fact, standing out as it does
at variance with any law of gradual refrigeration, should, I think,
be sought im a consideration of the geographical configuration
of the period. It is, with reference to this subject, also worthy of
remark that we do not find this tropical eocene fauna extending
up into high latitudes, as has been the case with the fauna of
more ancient deposits, as the carboniferous of Spitzbergen and
Melville Island, and even some of the secondary formations,
whose fauna in our latitudes presents perhaps a less tropical ap-
pearance than does that of the eocene. In seeking the expla-
nation of this tropical character of the eocene fauna of Northern
Europe, we may refer to the existing conditions of such gulfs as
the Arabian Sea and Gulf of Persia, the latter of which repre-
sents on a very small scale what I conceive the nummulitic gulf
* Proc. Geol. Soc. vol. iv. p. 554.
+ See Forbes in ‘Memoirs of Geological Survey of United Kingdom,’
vol. 1. 1846, p. 406 & pl. 7, who indicates the land as far west as the me-
ridian of 30° W. See also Woodward, ‘ Rudimentary Treatise on Recent
and Fossil Shells,’ Weale, London, 1856, pp. 361, 385. See also this view,
of the extension of the miocene land into the Atlantic, adopted, from other
considerations, by De Verneuil and Collomb, Bull. vol. x. p. 77.
Land-tracts during the Secondary and Tertiary Periods. 279
to have been. Now, the sheres of these two seas or gulfs are
the hottest of those of any seas on the globe, although the half
of the former and the whole of the latter are extra-tropical. Let
us conceive the nummulitic gulf thus extending from its mouth
open to the tropical ocean at some point, how far east we have
not yet materials to decide, but beyond the region of the Aral
Sea, to its head in England and Belgium, and we may realize
the effect which would result from that configuration. Not only
would the tropical waters have free access and be closed by
land from the contact of cold currents from the north, but the
shores of this sea would be heated by the accumulation of land
surrounding the greater part of it**, while at places on its shore
the rivers which formed the deposits of the English and French
and other eocene formations had their deltas, the more open
portions of the sea furnishing the nummulitic deposits.
The view taken, that this formation of continent in the oppo-
site direction to that theretofore prevailing commenced in the
closing epoch of the secondary period contemporaneously with
the first outbursts of the east and west bands which have go-
verned the alignement during the post-cretaceous period (that is
to say, with the band of the Pyrenees), seems supported by the
greater approximation between the faunas of the eastern and
western extremities of the Huropeo-Asiatic continent which the
newer cretaceous beds afford over those of the older and of the
Jurassic deposits. The late Edward Forbes first remarked this
in the comparison of the fossils from the cretaceous deposits of
Verdachellam and Trinconopoly+, since which M. d’Archiac {
has found in the fossils of the uppermost cretaceous beds of
Bains de Rennes, in the Pyrenees, a few species closely resem-
bling forms described by Mr. Forbes from these Indian beds;
and M. Abich also gives several upper-cretaceous forms from the
Caucasus identical with, or closely resembling, species described
from the cretaceous beds of England and France.
The remarks of Mr. Forbes on the fossils from Southern India
are so germane to the views discussed in this section, and indeed
lend so much support to them, that I am tempted by the weight
always attached to the opinions of that deceased naturalist, to
subjom the following extract :—“ Considered in regard to the
* The northern shore I have attempted to describe ; the southern shore
would be the peninsula of Southern India, where nummulitie or other
marine eocene deposits do not occur, and probably Central Africa (which
I have, in Section 2, referred to as land probably formed at the commence-
ment of the secondary period), and that region, now sea, referred to in
Section 4, containing the islands of Mauritius, &c., in which birds of the
secondary continent have been preserved.
t+ Proc. Geol. Soe. vol. iv. p. 326.
{ Bull, vol. xi. p. 202; see also his remarks, p. 204.
280 Mr. 8. V. Wood on the Form and Distribution of the
distribution of animal life during the cretaceous era, this collec-
tion is of the highest interest. It shows that durmg two suc-
cessive stages of that era the climatal influence, as affecting
marine animals, did not vary in intensity in the Indian, Euro-
pean, and American regions, whilst the later of the two [ Verda-
chellam and Trinconopoly stage] had specific relations with the
seas of Europe which are absent from the earlier [Pondicherry
stage]. The cause of this remarkable fact is not to be sought
for in a more general distribution of animal life at one time than
at another, but rather in some great change in the distribution
of land and sea, and in a greater connexion of the Indian and
European seas during the epoch of the deposition of the upper
greensand than during that of the lower. To this cause must
also be attributed the peculiar tertiary aspect of the Indian col-
lections, depending upon the presence of a number of forms
usually regarded as characteristic of tertiary formations, such as
Cyprea, Oliva, Triton, Pyrula, Nerita, and numerous species of
Voluta, the inference from which, since not one of the species is
identical with any known tertiary form, should not be that the
deposits containing them are either tertiary or necessarily con-
nected with the tertiary, but that the genera in question com-
menced their existence earliest in the eastern seas.” By the
expression I have copied in italics, the author, I apprehend,
meant a greater connexion of the seas by a more continuous
shore line, affording facility for migration of mollusca ; and this,
in order to join these regions, would necessarily be in an easterly
and westerly direction. The origin of the characteristic eocene
molluscous forms in the east, and their subsequent development
westerly, thus suggested by Mr. Forbes, seems to me to lend
support to the view that I have taken, of the connexion of the
seas of Western Europe with those of Hastern Asia, in the form
of a gulf stretching from Eastern Asia as far at least as the most
westerly limits of Hurope, at the epoch when the sea again occu-
pied a part of the area which had been continent during the
intra-cretaceous and tertiary interval.
If at the commencement of the tertiary period we find the
evidences of a tropical climate extending northwards to the
52nd parallel, due to the peculiar geographical configuration of
the period, how excessive may we conceive the climate of the intra-
cretaceous and tertiary period to have been, when a vast level tract
of desiccated sea-bottom, uninterrupted by mountain chains of
any importance, extended through the whole region between the
tropic of Cancer and the parallel of 50° N., from England
on the west to the Bay of Bengal on the east, and (from the
evidence of the eocene land-fossils) appears to have been con-
tinued westward in a lower latitude to America. Whether this
Land-tracts during the Secondary and Tertiary Periods, 281
-hypertropical belt of continent was continued eastward beyond
the Aralian region, we have not any evidence to affirm; the
opening-up of Central Asia will alone disclose this, and until
_then the limit of this extension cannot be realized ; but it should
not be overlooked that the great region of Oceanica, which Mr.
Darwin has shown to consist of submerged mountain chains of
immense extent, and to be now in a state of elevation and depres-
sion in alternate bands, is traversed by that great volcanic band
to the operation of which has been due the formation of the
major part of the Europeo-Asiatic continent, that is, the part
which is composed of cretaceous and tertiary formations. It is
to the extreme climate and widely different conditions to which
this configuration must have given rise, that I venture to think
may be attributed those complete changes in animal life which
took place in the intra-cretaceous and tertiary interval. The effect
of a continent stretching east and west, and lying in low latitudes,
would operate not merely to exaggerate the terrestrial heat, and
produce those interferences with the trade-winds which cause
the monsoons and bring the alternations of extreme aridity and
extreme moisture, but to affect the marine conditions by arrest-
ing the interchange of the tropical with the polar waters,—an
example of the effects produced by such causes being now per-
ceptible in the condition of the southern border of the Asiatic
continent, and, to a less degree, in that of Africa, where the
Bight of Benin washes its southern shore.
We have seen that, as in the palzeozoic period, so in the se-
condary ; the complete changes in the direction of the volcanic
bands, which took place towards the termination of those periods
respectively, did not occur absolutely at their close, but rather
heralded it by occurring prior to the last of their epochs (as-
suming the Permian to be an epoch of the paleozoic period),
In the former case, the changes occurred between the carboni-
ferous and the Permian, and in the latter we have seen that the
volcanic bands from east to west had come into existence, in the
case of the Pyrenees, prior to the formation of the upper creta-
ceous deposits, while the system of the Jura (which seems to
have originated during the cretaceous epoch, from the occurrence
in it of detached portions of older cretaceous beds conformable
to the Jurassic) possessed a direction midway between those
opposite ones characteristic of the secondary and tertiary periods,
being from N.E.to S.W. Both in the palzeozoic and secondary
periods, therefore, the complete changes in the fauna which
marked their termination do not appear to have been immediate
upon the changes of the geographical alignement, but to have
required the lapse of an epoch for their fulfilment; and the com-
pleteness of that change is perhaps not less the indirect result
Phil. Mag. 8. 4, Vol. 23. No. 154, April 1862. U
4
282 Mr. W. H. Russell on Theorems in the Calculus of Symbols.
of the altered alignement, by the formation of continents where
seas had been, and the opening out of new seas for the habitation
of marine animals, thereby causing a gap in the geological records
so far as they have hitherto been discovered, than the direct
result of the changed conditions to which the inhabitants of
the seas, and even “hose of the lands, came to be subject on
account of the entire change in the alignement of the land over
the globe.
[To be continued. |
XXXIX. Theorems in the Calculus of Symbols.
By W. H. L. Russexy, Esq., A.B.*
bases followmg theorems in differentiation and integration
may be proved by means of the Calculus of Symbols. They
are a development of results which I gave in a Memoir published
in the Philosophical Transactions for the year 1861, and will,
I hope, be found interesting to mathematical readers. The
proof of these theorems will be suggested by the original
memoir.
2 1
amid oy ate an
at 1 a d _t ar) eam du
de da @ da as x" ” dee dx 2x dx
d”™u dis d i Wet r U
dx ada) gti
ee gcse Bali =) 5 u
ae ynte we 78 InP
(-rfS(S (= ve pees =e.
da”
=n(u $1) (dean n 2S (n+1). gs |e ate
2
m—1l n—2 nt+2n+3 1 5
oat {4 mi ak +1).—— 5) rt. Flaca Siete 2
the integral sign in the first member of the equation being
repeated (n+ 1) times.
* Communicated by the Author.
Mr. T. Tate on the Laws of Evaporation and Absorption. 283
, | de (dz pee)
—2) \2(3 ee {dea pnt
ca n+2 n+3 n+4 =
a tL GE TT 4 eee
hyp Pa ea 5 3 ae Gs dE «HUT osey
the ae sign in the first member an repeated (z+ 1) times.
(—2)" Reels le ou
ALU ] _ u
Ss PAT Pees ees ea 8
Le ] 7 ae
eperire SiGe) Jom On?
the integral sign in the first member ae repeated (n +1) times.
sei tal a ut oe (deat
£
ees n=l ale y (a 2 y=
Big
L v@
XL. Experimental Researches on the Laws of Evaporation and
Absorption. By Tuomas Tats, Esq.
[Continued from p. 135. ]
Mazimum absorption of water by different substances. Measure
of the porosity of different substances.
lice amount of water which a substance is capable of absorbing
depends upon the capacity of its pores, or the volume of its
interstices so far as they are permeable by water. In most
cases the volume of water which a substance absorbs is equal to
the volume of the air expelled. But this is not universally true ;
for I have found that water will filter through heavy sandstone
in opposition to an excess. of atmospheric pressure. In order
to saturate perfectly certam substances with water, they must bo
boiled in a vessel exhausted of air.
The capacity of different substances for absorbing and retain -
ing moisture is very various. The following substances being
2
284. Mr. T. Tate’s Experimental Researches on
thoroughly dried, I have found that ealico, linen, unsized paper,
and other substances of this kind absorb and retain about their
own weight of water; woollen cloth about twice its own weight ;
bath brick and fine sand about one-third their own weight;
plaster of Paris, after being set, about six-tenths; common deal,
six-tenths ; laurel-wood rather more than two-thirds; pine-wood
nearly six-sevenths; and bran, about three and three-quarters.
In order to determine the porosity of different substances, so
far as regards their capacities for absorbing water, we have the
following formule :— |
Wo—W
v= en x V; and v=(s,—s,)V;
where V= the volume of the body; v= the capacity of the
interstices of the body, or the volume of that portion of it pene-
trated by the water absorbed; w= the weight of the body in a
dry state, s, being its corresponding specific gravity; wo= its
weight when perfectly saturated with water, s, being its corre-
sponding specific gravity; and w,= the weight of the body in
water.
By means of these formule and the experimental data, I have
found the following results :—
For woollen cloth, v=2V; that is, the interstices are three-
fourths of the whole volume of the substance.
For bath brick, v=*V; that is, the interstices are two-fifths
of the whole volume of the substance.
For fine sand, v='47; that is, the interstices are nearly one-
half of the whole volume of the substance.
For deal, v=iV; for laurel-wood, v="45V; and for pine-
wood, v=3V. In these cases, however, a slight allowance must
be made for the expansion of the wood by the absorption.
Contraction and elongation of textile fabrics by the absorption of
moisture.
Under a constant stretching force, calico, linen, flax, and
unsized paper undergo contraction upon the absorption of
moisture, whilst certain woollen fabrics undergo elongation.
Thus strips of linen and calico were contracted about the ;1,th
part of their length, whilst strips of woollen cloth were elongated
nearly the same proportional part of their lengths by the absorp-
tion of moisture. ‘Threads of cotton and flax were contracted
about ;1,th*part of their lengths.
The strips as well as the threads were suspended from one
extremity, and had metal plates attached to their lower extremi-
ties, so as to give the material a uniform tension. The divisions
of the scale, measuring the lengths of the strips, were divided
the Laws of Evaporation and Absorption. 285
into tenths of an inch, so that with a vernier the contraction or
elongation, as the case might be, could be read off to hundredths
of an inch. After the strips had become dry, they nearly re-
turned to their original lengths.
A curious experiment.—Attach an oblong plate of metal to
one extremity of a cotton thread, and suspend it from a loop
formed in the other extremity: immerse the thread in a deep
glass jar filled with water; then the plate will revolve rapidly
in a direction contrary to the direction of the twist of the thread:
the rotation will go on for some time after the thread has been
taken out of the water. When the rotation has ceased, let the
plate be restrained from any further rotation; then after the
thread has become dry, remove the obstruction placed against
the plate, and it will again rotate in the same direction, and not,
as might have been expected, in a direction contrary to that in
which it had at first revolved. The cause of this rotation I appre-
hend to be as follows:—The moisture, by causing the thread to
contract, thereby tends to tighten the twist of the thread, and,
as a necessary consequence, the thread tends to revolve in a
direction contrary to that of the twist.
Spontaneous absorption of moisture from the atmosphere by dif-
ferent absorbents.
If an absorbent be thoroughly dried and then exposed to a
humid atmosphere at or near to the dew-point, it will gradually
absorb moisture from the air. The moisture thus absorbed by
some substances is something considerable. Woollen cloth
absorbs one-seventh of its own weight of moisture from air
whose temperature is about one degree above that of the dew-
point; bran about one-eighth of its weight; calico about one-
tenth; and soon. The amount of absorption increases as the
temperature of the air approaches that of the dew-point: the
maximum quantity of moisture absorbed takes place in an atmo-
sphere saturated with the vapour of water.
1. The rates of absorption by different absorbents presenting
equal surfaces are proportional to their respective maximum
quantities of absorption. Moreover, the moisture absorbed by ©
two equal surfaces of the same material, but of different thick-
nesses, 18 proportional to their respective weights.
Thus two equal surfaces of black cloth and flannel, weighing
respectively 400 graims and 300 grains, absorbed during the
same time of exposure 41 and 32 grains respectively, and their
maximum quantities of absorption were found to be 60 and 47
grains of moisture respectively. Here we have—ratio of
32 3.
weights = ='75; ratio of rates of absorption — Al
4.00
286 Mr. T. Tate’s Experimental Researches on
and ratio of maximum absorptions = = =°78. Again, two
equal surfaces of calico, but the one double the weight of the
other, absorbed during the same time of exposure to the air,
weights of moisture very nearly proportional to their respective
weights.
2. The weights of moisture absorbed by an absorbent exposed
to a humid atmosphere in equal successive intervals of time are
(nearly) in geometrical progression.
Thus, for example, during successive intervals of thirty minutes,
the weights of moisture absorbed by a piece of black cloth, pre-
senting a surface of 150 square inches to the air, were found to
be as follows :-—
Moisture absorbed,
In grains.
During the Ist interval 17-4
35 PA OG GN 13°5 = 17:4 2 nearly.
fp Ord) ts 10:0 = 17'4.x GPs,
ss Ath; 5; 70) =o AG ies
Absorption of moisture by sulphuric acid from an atmosphere
saturated with the vapour of water.
Equal measures of strong sulphuric acid diluted with different
proportions of water were introduced into a beaker 2? inches in
diameter, the liquid being half an inch from the edge of the glass ;
and the beaker with the acid was placed on a tray containing
water, and covered over with a large receiver about 1 foot in dia-
meter. The absorption by strong sulphuric acid, during twenty-
four hours, being first determimed, the strong acid was succes-
sively diluted with four equivalents of water, and the weights of
moisture absorbed in twenty-four hours by the respective liquids
were determined as follows :—
Corresponding weight
of water absorbed in Value of a from
Dilution of the acid. | twenty-four hours, the formula
In grains. a=44'8x ‘6k.
a
0 44°8 44°8
4HO 26°6 26'8
8HO 16:0 16-1
12HO 9-2 9:6
16HO 6:0 5:8
where p= Here it will be observed that, whilst the
dilution advances according to an arithmetical progression, the
the Laws of Evaporation and Absorption. 287
capacity for absorption deereases according to a geometrical pro-
gression.
It will be hereafter seen that a similar law applies to the solu-
tion of absorbent salts.
It was further determined that, the strength of the acid being
constant, the amount of absorption in equal times varies (approxi-
mately) Gnpersely as the depth of the liquid from the edge of the
vessel in which it is placed.
Other things being the same, the rate of absorption increases
with the temperature. It was also found that the rate of absorp-
tion, other things being the same, increases with the decrease of
the atmospheric pressure.
Absorption of moisture by solutions of chloride of sodium from
an atmosphere saturated with the vapour of water.
In this case 2824 grains of a saturated solution of the salt
were successively diluted with 1000 grains of water, the diameter
of the vessel exposed to the humid air of the receiver being 6
inches: thus the second solution contained 2824 grains of the
saturated, or first solution, with the addition of 1000 grains of
water; the third solution contained 3824 grains of the last solu-
tion, with the addition of 1000 grains of water; and so on to the
other solutions. The results of experiment were as follows :—
In twenty-four hours, the first, second, third, and fourth solu-
tions respectively absorbed 25, 15:4, 9:0, 6:0 and 4:1 grains of
moisture.
Now these results are approximately expressed by the formula
as=25 x ‘6k,
where K=+71,5 of the weight of the water added to the saturated
solution.
It will be seen that this law of absorption is similar to that
determined for sulphuric acid. It appears, therefore, that the
rate of absorption has a determinate atomic relation.
Spontaneous evaporation of moisture from different surfaces ex-
posed to the atmosphere.
It has been shown in one of the foregoing papers, that the
evaporation from absorbents saturated with moisture is for the
most part uniform, the temperature and hygrometric state of the
air being constant.
1. The rate of evaporation of moisture from damp porous sub-
stances, of the same material, is proportional to the extent of the
surface presented to the air, without regard to the relative thick-
nesses of the substances.
Thus two pieces of calico, presenting 150 square inches of
surface, but the one folded double whilst the other was single,
288 Mr. T. Tate’s Eaperimental Researches on
were saturated with moisture and suspended in a quiescent
atmosphere. After the lapse of two hours the single thickness
of calico had lost 41°6 grains of moisture by evaporation, whilst
the double thickness had lost 42 grains.
In this respect spontaneous evaporation differs entirely from
spontaneous absorption, which, as we have seen, is dependent
(within certain limits) upon the thickness or weight of the mate-
rial, and not upon the extent of its surface.
2. The rate of evaporation from different substances mainly
depends upon the roughness of, or inequalities on, their surfaces,
the evaporation going on most rapidly from the roughest or most
uneven surfaces; in fact, the best radiators of heat are the best
vaporizers of moisture.
Woollen cloth, calico, unsized paper, bran, and fine sand, of
equal surfaces, are very nearly the same as regards the rate at
which moisture is evaporated from them. Calico is a better
vaporizer than flannel, and very much better than water. The
mean result of a considerable number of experiments performed
in a quiescent atmosphere was, that the evaporation from the
surface of still water is nearly four-fifths of the evaporation from
an equal surface of calico.
3. The evaporation from equal surfaces composed of the same
material is the same, or very nearly the same, m a quiescent
atmosphere, whatever may be the inclination of the surfaces.
Equal pieces of woollen cloth, each contaming 25 square
inches, were cemented to thin tin plates, and after being satu-
rated with moisture and weighed, one plate was placed horizon- .
tally with its damp face upwards, another plate was placed upon
upright rods with its damp face downwards: in the same time.
the loss from evaporation in both cases was the same, or very
nearly the same.
Thus, at a summer temperature, when the air was somewhat
humid, the evaporation per hour from the damp surface placed
upwards was 4°78 grains, whilst the evaporation per hour from
the damp surface placed downwards was 4°71 grains; and when
the air was unusually dry, the evaporation from the former was
6°6 grains, and from the latter 6°5 grains.
Again, at a winter temperature, the evaporation per hour from
the former was 2°5 grains, whilst from the latter it was 2°46
grains.
The fact here enunciated is highly significant. It shows that
vapour is carried into the air from a damp surface for the most
part by the principle of diffusion, and not, as it is commonly
supposed, by the force of an ascensional current of vapour. If
the damp surface exposed to the air were higher in temperature
than the surrounding air, then we should most certainly have an
the Laws of Evaporation and Absorption. 289
ascensional current of vapour, which would facilitate the process
of evaporation; but this can only take place during continued
sunshine: in other cases the temperature of the damp surface
(owing to the cooling effect of evaporation) is from 1 to 6 de-
grees below that of the surrounding air; and under such circum-
stances, according to the results of these experiments, we can
have little or no ascensional current of vapour tending to pro-
mote the process of evaporation.
The temperature and hygrometric state of the air being con-
stant, the process of evaporation is very much accelerated by
aérial currents and by direct sunshine.
4. The rate of evaporation from a damp surface is very much
affected by the elevation at which the surface is placed above the
ground.
About half an hour before sunset, with a clear sky and a calm
air, the two tin plates, with their damp surfaces somewhat below
saturation, were placed as follows: one about an inch above the
grass, the other at an elevation of three feet, both damp surfaces
being placed upwards. In the course of two hours the former
had gained 7°5 grains of moisture by absorption, whilst the latter
had Jost 5 grains of moisture by evaporation. In another expe-
riment, the temperature of the air being higher, the former had
lost 12°7 grains by evaporation, whilst the latter had lost 21:2
grains by evaporation. Here the damp cloth at the surface of
the ground was cooled down with the grass by radiation, whilst
the upper cloth was nearly maintained at the temperature of the
air at that elevation.
5. The rate of evaporation is affected by the radiation of sur-
rounding bodies.
The plates, as described, were placed in the shade at the height
of six inches above the ground, with their damp surfaces up-
wards, the sky being clear, but one plate had a screen placed
over it. In the course of two hours the latter had lost 8 grains
by evaporation, whereas the former had lost only 3°5 grains;
that is, the evaporation from the surface with the screen was
about double that from the surface without the screen. On
another occasion the evaporation from the surface with the screen
over it was found to be 32°6 grains, whilst from the other surface
it was only 25 grains.
Hastings, February 16, 1862.
[To be continued. |
[ 290 ]
XLI. Liquid Diffusion applied to Analysis.
By Tuomas Grauam, F.R.S., Master of the Mint.
[Continued from p. 223. ]
3. Dialysis.
pes G from liquid diffusion in the water-jar, I may advert
first to the diffusion of crystalloids through a gelatimous or
colloid mass, the circumstances of the experiment being varied
as little as possible from those of jar diffusion.
Ten grammes of chloride of sodium and 2 grammes of the
Japanese gelatine, or gelose of Payen, were dissolved together in
so much hot water as to form 100 cub. centims. of fluid. Intro-
duced into the empty diffusion-jar and allowed to cool, this fluid
set into a firm jelly, occupying the lower part of the jar, and
containing of course 10 per cent. of chloride of sodium. Instead
of placing pure water over this jelly, it was covered by 700 cub.
centims. of a solution containing 2 per cent. of the same gelose,
cooled so far as to be on the point of gelatinizing,—the Jar at the
same time being placed in a cooling mixture, in order to expedite
that change. The jar with its contents was now left undisturbed
for eight days at the temperature 10°. After the lapse of this
time the jelly was removed from the jar in successive portions of
50 cub. centims. each from the top, and the proportion of chloride
of sodium in the various strata ascertained. The results were
very similar to those obtained in diffusing the same salt in a jar
of pure water. The diffusion in the gelose appeared more ad-
vanced in eight days than diffusion in water for seven days, as
will be seen by comparing the gelose experiment below with a
water experiment on chloride of sodium, which had been con-
ducted at nearly the same temperature (Table III.).
Taste XI.—Diffusion of a 10 per cent. solution of Chloride
of Sodium in the jelly of gelose, for eight days, at 10°.
No. of stratum. | Diffusate, in grammes.
1 015
2 015
3 026
4 035
5 082
6 130
7 212
8 350
9 "486
10 630
11 996
12 1-12
13 1°190
14 1:203
15 and 16 3°450
- Mr. T. Graham on Liquid Diffusion applied to Analysis. 291
_ Diffusion of a crystalloid thus appears to proceed through a firm
jelly with little or no abatement of velocity. With a coloured
crystalloid, such as bichromate of potash, the gradual elevation of
the salt to the top of the jar is beautifully illustrated. On the
other hand, the diffusion of a coloured colloid such as caramel,
through the jelly, appeared scarcely to have begun after eight
days had elapsed. The diffusion of a salt into the solid jelly
may be considered as cementation in its most active form.
Numerous experiments were made on the diffusion of crystal-
loids through various dialytic septa, such as gelatinous starch,
coagulated albumen, gum-tragacanth, besides animal mucus and
parchment-paper, which all tended to prove how little the dif-
fusive process was interfered with by the intervention of colloid
matter. Salts appeared to preserve their usual relative diffusi-
bility unchanged. The same partial separation of mixed salts
was observed as in the water-jar. With a mixture, for instance, of
equal parts of chlorides of potassium and sodium in the dialyser,
the first tenth part of the mixture which passed through was
found to consist of 59°17 per cent. of chloride of potassium and
40°85 per cent. of chloride of sodium. Double salts also, such
as alum, and the sulphate of copper and potash, which admit of
being resolved into pairs of unequally diffusive salts, were largely
decomposed upon the dialyser, as they are in the water-jar. The
effect of heat in promoting diffusion appeared, however, to be
- diminished in dialysis, at least with a parchment-paper septum.
Thus the diffusion from a 2 per cent. solution from chloride of
sodium in a constant period of three hours was,—
Li Ratio.
BAO ie tee, OOS erm.
ECON Sia os Os 9A sam. y OF
MeaO Sai. i. 1) O02 orm, B20
mG rie aie) WOLF orm.) 1:57,
The rate of diffusion in water alone, without the septum,
wonld have been doubled by an equal rise of temperature instead
of being increased one-third only as above.
Fig. 3.—Bulb Dialyser.
mye il
EE he.
The small glass bell-jar (figs.8, 4) formerly used as an osmometer,
292 Mr. T. Graham on Liquid Diffusion applied to Analysis.
Fig. 4.
om
UN
was conveniently applied to dialytic experi-
ments. Two sizes of the bulb were employed,
3°14 and 4-44 inches in diameter respec-
tively, and of which the dialytic septa pos-
sessed an area very nearly of ;,th and
shoth of a square metre (15°6 and 7°8
square inches). With 100 cub. centims. of Wi
fluid in the osmometer (the volume usually eg li
employed), the septum of the smaller instru- a |
ment was covered to a depth of about 20
millimetres (0°8 inch), and the septum of
the larger to a depth of 10 millimetres
(0'4 inch). The thinner the stratum, the
more exhaustive the diffusion in a given
time. It is generally unadvisable to cover the septum ieee
than 10 or 12 millimetres (half an inch), where a considerable
diffusion is desired within twenty-four hours. The following
practical observations may be found useful in applying the dialyser
to actual cases of analysis. They refer to the parchment-paper
septum, which is much the most convenient for use.
With a 2 per cent. solution of chloride of sodium, containing
2 grammes of the salt, and covering a septum of ‘nearly 0-01
square metre (15-6 square inches) in area, toa depth of 10 milli-
metres, the salt which diffused in five hours amounted to 0°75
gramme, aud in twenty-four hours to 1:657 gramme, leaving
behind 0-343 gramme, or 17°1 per cent. of the original salt.
The followimg experiments, made with the same osmometer and
solution, show the effect of reducing the volume of liquid placed
in the dialyser. The proportion of salt which diffused out mm
twenty-four hours was—
From 100 cub. centims. of solution 86 per cent.
From 50 cub. centims. of.solution 92 per cent.
From 25 cub. centims. of solution 96 per cent.
In all cases the volume of water outside into which the salt
escaped was ample, being from five to ten times as much as the
volume of fluid placed in the dialyser, and it was changed during
the continuance of the experiment. A much less volume of ex-
ternal water suffices, provided it is changed at intervals of a few
hours. The temperature was 10° to 12°. It will be observed
that these volumes correspond toa depth of liquid in the dialyser
of 0:4, 0:2, and 0-1 inch respectively.
The time of travelling through the thickness of the parchment-
paper itself may be observed, and is worthy of remark.
Of the quality of parchment-paper always used in these experi-
ments, as quare metre, when dry, weighed 67 grammes, and when
charged with water 108°6 grammes. ‘Taking the specific gravity
of cellulose at 1:46, that of the lighter woods, the parchment-paper
described will, in the humid state, have a thickness of 0°0877
Mr. T. Graham on Liquid Diffusion applied to Analysis. 293
millimetre, or —+, of a millimetre. Wet parchment-paper so
thin is highly translucent. Gelatinous starch, slightly coloured
with blue litmus, was applied by a brush to one side of the wet
parchment-paper. Immediately afterwards a drop of water,
containing z,)5)th part of hydrochloric acid, was applied on
the pomt of the finger to the other (the lower) side of the
paper. The time required by the acid to affect the litmus, in
five successive trials, was 6 seconds, 5°5 seconds, 6 seconds,
and 5 seconds. The mean is 5°7 seconds, which is therefore
the time required by hydrochloric acid, diluted already 1000
times, to travel a distance of 0:0877 of a millimetre, by the agency
of diffusion. The temperature was 15°.
With hydrochloric acid diluted twice as much as before (water
containing 0:0005 dry acid), the average time of passage was
10-4 seconds, or nearly double the preceding time.
Water containing ~,4,th of sulphuric acid (an acid less rapidly
diffused than hydrochloric acid) reddened the litmus in 9:1 se-
conds, and when doubly diluted, in 16°5 seconds.
These results are not affected, it is believed, by any sensible
diffusive movement on the part of the litmus. The diffusion of
that colouring matter, in a colloid medium, is so slow that it may
be entirely disregarded. The acid, therefore, is not met in its
way by the litmus, but really travels the entire distance expressed
by the thickness of the parchment-paper. The first experiments
related give a diffusive velocity, in water, to hydrochloric acid,
already diluted one thousand times, of 0°0154 millimetre per
second, and 0°924 millimetre in one minute.
The few following dialytic experiments may be recorded for the
sake of the practical points which they bring out. They were
made in the smaller osmometer, with 100 cub. centims. of a solution
containing 10 grammes of each of the various substances. The
area of the parchment-paper septum was 0:005 square metre, and
the depth of the stratum of fluid placed upon it 20 millimetres.
The substances diffused were all crystalloids, with the exception
of gum-arabic.
Tasie XIJ.—Dhialysis through Parchment-paper during
twenty-four hours, at 10° to 15°.
: ._ | Osmose, in si
Ten per cent. solutions. _ Diffusate, | Relative grammes Helative
in grammes. diffusate. osmose.
of water.
PARE ARADICU Soccedvencedrsivsrdacto cade 0029 004 5:0 263
SEAHEC MERU AT), 1, Usevseeesklacuetacesss 2°000 "266 17:0 894
MAC SUG AN es 6 ia abcdec asda su vate ctes’ « 1°607 "214 15°3 805
PRIMER dL vacet psec varneceneemscadte + 1°387 185 15-0 °789
PEIUMILUC cine cows sevaaatedoeavenactac sess 2°621 349 17°6 926
UMECHINE 27 3.055). etuteadae cat adee 3°300 440 17°6 926
BMP Yard caic'nc seve sdaseuqunemase tenses 3°570 476 7°6 400
Starch-sugar (second experiment) 2°130 "284 16°8 884
Giloride of sodium \./.:.......s00.s- 7°500 1 19°0 1
294 Mr. T. Graham on Liquid Diffusion applied to Analysis.
The experiments were all made through the same portion of
parchment-paper, and in the order of the Table—gum-arabic
first, and chloride of sodium last. After every experiment the
bulb was immersed in water for twenty-four hours, to purify the
septum, before it was again used. The diffusion of starch-sugar
was repeated early and late in the series of experiments, with
little change in the result, showing considerable uniformity in
the action of the parchment-paper,—the first diffusate of starch-
sugar being 2. grammes, and the second 2°13 grammes. Yet
the parchment-paper had been in contact with water or some
solution for a whole fortnight between the two observations
referred to.
A layer of animal mucus, taken from the stomach of the pig,
12 millimetres in thickness (10 grammes of humid mucus being
spread over 0-005 square metre of surface), was applied, between
two discs of calico, to the diffusion-bulb used above, the parch-
ment-paper being first removed.
Tasie XIII.—Dialysis through Animal Mucus during twenty-
five hours, at 10° to 15°.
Gim-arabiey accseevecsewases 023 "004 +29
Starch-Sugar ......0e0-.cecseee 1°821 360 + 7:6
Ganesugar ..s..v.c.vecvecens 1°753 347 + 4:6
IVC SUS AT: oveareeasacits dclcetels 1°328 262 + 71
Mannitemnanesccesatecadsccrcns: 1°895 375 + 5:0
PUCONOM Mr caccccacceaemesrascces 2°900 373 + 7:2
Starch-sugar ......scsraseeoses 1-764 *349 id
GIF CENNG! fi scdsecel see ee seves 2°554 °505 + 75
Chloride of sodium ......... 5°054 1 — 02
The relative diffusibilities of the different substances present
a considerable degree of similarity im the two Tables, and are
equally analogous to the diffusibilities of the same substances
observed in pure water. The intervention of a colloid septum
cannot be said to have impeded much the diffusion of any of these
substances except the colloid gum.
The dialysis through parchment-paper of several other organic
substances, both crystalloids and colloids, maybe brought together
in comparison with the chloride of sodium as a standard. The
larger osmometer bulb was used, and the parchment-paper was
now changed in each experiment. The substance in solution
amounted to 2 grammes, the depth of fluid in the dialyser to 10
millimetres (0:4 of an inch), and the surface of the septum to
0-01 square metre (15:6 square inches).
Mr. T. Graham on Liquid Diffusion applied to Analysis. 295
Taste XIV.—Dialysis through Parchment-paper during
twenty-four hours, at 12°.
Two per cent. solutions. Berge ober onal |
in grammes. diffusate.
Chloride of sodium ............000000 1°657 1
EN@EIPIACIC ¢. chekiceo< ec cku..secusccasadaa 1°690 1:020
PPMUMIOV cei c oes voccscecccccessesacvose 1°404 847
PRE MIE E occ ccs ecakecs cs sticaccedewelces 1°166 703
AMON ee ciscee esses ccaccccuciesessee ss *835 503
MGANIC“SHOUT, Schtivn'coiciivedeatsdssccne 783 “472
PEO AMNG) Ccscwsscecedscesnnestaseuve 517 “311
Extract of quercitron § ........sccsess 305 "184
Extract Of LOZ WOO. ..c.......220s "009 "005
Picric acid and theine were actually diffused from 1 per cent.
solutions, and the numbers observed are multiplied by 2. The
erystallizable principles, theine, salicine, and amygdaline, appear
greatly more diffusible than gallo-tannic acid, or than gum, as
has been already seen. Such inequality of rate is likely to
facilitate the separation of vegetable principles by the agency of
dialysis.
4. Preparation of Colloid Substances by Dialysis.
The purification of many colloid substances may be effected
with great advantage by placing them on the dialyser. Accom-
panying crystalloids are eliminated, and the colloid is left behind
in a state of purity. The purification of soluble colloids can
rarely be effected by any other known means, and dialysis is
evidently the appropriate mode of preparing such substances free
from crystalloids.
Soluble Silicic Acid.—A solution of silica is obtained by pouring
silicate of soda into diluted hydrochloric acid, the acid being
maintained in large excess. But in addition to hydrochloric acid,
such a solution contains chloride of sodium, a salt which causes
‘the silica to gelatinize when the solution is heated, and otherwise
modifies its properties. Now such soluble silica, placed for
twenty-four hours in a dialyser of parchment-paper, to the usual
depth of 10 millimetres, was found to lose in that time 5 per
cent. of its silicic acid, and 86 per cent. of its hydrochloric acid.
After four days on the dialyser, the liquid ceased to be disturbed
by nitrate of silver. All the chlorides were gone, with no further
loss of silica. In another experiment 112 grammes of silicate of
soda, 67:2 grammes of dry hydrochloric acid, and 1000 cub. cents.
296 Mr. T. Graham on Liquid Diffusion applied to Analysis.
of water were brought together, and the solution placed upon a
hoop dialyser, 10 inches in diameter. After four days the solu-
tion had increased to 1235 cub. centims. by the action of osmose,
colloid bodies being generally ghly osmotic. The solution
now gave no precipitate with nitrate of silver, and contained
60°5 grammes of silica, 6°7 grammes of that substance having
been lost. The solution contained 4 9 per .cent. of silicic
acid.
The pure solution of silicic acid so obtained may be boiled in
a flask, and considerably concentrated, without change ; but when
heated in an open vessel, a ring of insoluble silica is apt to form
round the margin of the liquid, and soon causes the whole to
gelatinize. The pure solution of hydrated silicic acid is limpid
and colourless, and not in the least degree viscous, even with 14
per cent. of silicic acid. The solution is the more durable the
longer it has been dialysed and the purer itis. But this solution
is not easily preserved beyond a few days, unless considerably
diluted. It soon appears slightly opalescent, and after a time
the whole becomes pectous somewhat rapidly, forming a solid jelly
transparent and colourless, or slightly opalescent, and no longer
soluble in water. This jelly undergoes a contraction after a fow
days, even in a close vessel, and pure water separates from it.
The coagulation of the silicic acid is effected ina few minutes by
a solution containing =4,>5th part of any alkaline or earthy
carbonate, but not by caustic ammonia, nor by neutral or acid
salts. Sulphuric, nitric, and acetic acids do not coagulate silicic
acid ; but a few bubbles of carbonic acid passed through the solu-
tion produce that effect after the lapse of a certain time, Alcohol
and sugar, in large quantity even, do not act as precipitants; but
neither do they protect silicic acid from the action of alkaline
carbonates, nor from the effect of time in pectizing the fluid colloid.
Hydrochloric acid gives stability to the solution: so does a small
addition of caustic potash or soda.
This pure water-glass is precipitated on the surface of a calca-
reous stone without penetrating, apparently from the coagulating
action of soluble lime-salts. The hydrated silicic acid then forms
a varnish, which is apt to scale off on drying. The solution of
hydrated silicic acid has an acid reaction, somewhat greater than
that of carbonic acid. It appears to be really tasteless (like most
colloids), although it occasions a disagreeable persistent sensation
in the mouth, after a time, probably from precipitation.
Soluble hydrated silicic acid, when dried in the air-pump re-
ceiver, at 15°, formed a transparent glassy mass of great lustre,
which was no longer soluble in water. It retained 21-99 per cent.
of water after being kept two days over sulphuric acid.
The colloidal solution of silicic acid is precipitated by certain
Mr. T. Graham on Liquid Diffusion applied to Analysis. 297
other soluble colloids, such as gelatine, alumina, and peroxide of
iron, but not by gum or caramel. As hydrated silicic acid, after
once gelatinizing, cannot be made soluble again by either water
or acids, it appears necessary to admit the existence of two allo-
tropic modifications of that substance, namely, soluble hydrated
silicic acid, and insoluble hydrated silicic acid, the flud and
pectous forms of this colloid.
The ordinary soluble silicate of soda is not at all colloidal, but
diffuses as readily through a septum as the sulphate of soda does.
Several crystalline hydrated silicates of soda are known (Fritzsche).
The amorphous silicic acid obtained by drying and calciming
the jelly, and the vitreous acid obtained by igneous fusion, have
both a specific gravity of about 2°2, according to H. Rose*, and
appear to be the same colloidal substance; while the specific
gravity of crystalloidal silicic acid (rock-crystal and quartz) is
about 2°6. ;
Soluble silicic acid forms a peculiar class of compounds, which,
like itself, are colloidal, and differ entirely from the ordinary sili-
cates. The new compounds are interesting from their analogy
to organic substances, and from appearing to contain an acid of
greatly higher atomic weight than ordinary silicic acid. Like
gallo-tannic acid, gummic acid, and the other organic colloidal
acids, silicic acid combines with gelatine—the last substance
appearing to possess basic properties. Stlicate of gelatine falls
as a flaky, white and opake precipitate when the solution of
silicic acid is gradually added to a solution of gelatine in excess.
The precipitate is insoluble in water, and is not decomposed by
washing. Silicate of gelatine prepared in the manner described,
contains 100 silicic acid to about 92 gelatine. Thisis a greater
proportion of gelatine than in the gallo-tannate of gelatine, and
requires for soluble silicic acid a higher equivalent than that of
gallo-tannic acid. In the humid state the gelatine of this com-
pound does not putrefy.
The acid reaction of 100 parts of soluble silicic acid is neu-
tralized by 1°85 part of oxide of potassium, and by corresponding
proportions of soda and ammonia. The colli-silicates or co-sili-
cates thus formed are soluble and more durable than fluid silicic
acid, but they are pectized by carbonic acid, or by an alkaline
carbonate, after standing for a few minutes. The co-silicate of
potash forms a transparent hydrated film on drying in vacuo,
which is not decomposed by water, and appears to require about
ten thousand parts of water to dissolve it. The silicate of soda
which Forchhammer obtained by boiling freshly precipitated
silicic acid with carbonate of soda, and collecting the precipitate
which falls on cooling, contains 2°74 per cent. of soda, and is
* Phil. Mag. S. 4. vol. xix. p. 32.
Phil. Mag. 8. 4. Vol. 23. No. 154, April 1862. Xx
298 Mr. T. Graham on Liquid Diffusion applied to Analysis.
represented by NaO +36S8i0? (Gmelin). This silicate is probably
a co-silicate of soda in the pectous condition. Soluble silicic
acid produces a gelatinous precipitate in lime-water, containing
6 per cent. and upwards of the basic earth. This and the other
insoluble earthy co-silicates appear not to be easily obtained in
a definite state. They gave out a more basic silicate to water on
washing. The composition of these salts and that also of the
co-silicate of gelatine were found to vary according as the mode
of preparation was modified. When a solution of gelatine was
poured into silicic acid in excess, the co-silicate of gelatine formed
gave, upon analysis, 100 silicic acid with 56 gelatine, or little
more than half the gelatine stated above as found in that com-
pound prepared with the mode of mixing the solutions reversed.
The gallo-tannate of gelatine is known to offer the same variability
in composition. : :
The gelatine used in the preceding experiments was isinglass
(colle de poisson) purified by solution in hydrochloric acid and
subsequent dialysis. As the acid escapes by diffusion, a jelly is
formed in the dialyser. This jelly is free from the earthy matter,
amounting to about 0-4 per cent., im isinglass, and is not liable
to putrefaction.
Cosilicic acid also precipitates both albuminic acid and pure
caseine.
Soluble Alumina.—We are indebted to Mr. Walter Crum for
the interesting discovery that alumina may be held in solution
by water alone in the absence of any acid. But two soluble
modifications of alumina appear to exist, alumina and metalu-
mina. The latter is Mr. Crum’s substance.
A solution of the neutral chloride of aluminium (Al? CI°),
placed on the dialyser, appears to diffuse away without decom-
position. But when an excess of hydrated alumina is previously
dissolved in the chloride, the latter salt is found to escape by dif-
fusion in a gradual manner, and the hydrated alumina, retaining
little or no acid, to remain behind ina soluble state. A solution
of alumina in chloride of aluminium, consisting at first of 52
parts of alumina to 48 of hydrochloric acid, after a dialysis of
six days, contained 66°5 per cent. of alumina; after eleven days
76°5 per cent.; after seventeen days 92°4 per cent. ; and after
twenty-five days the alumina appeared to be as nearly as possible
free from acid, as traces only of hydrochloric acid were indicated
by an acid solution of nitrate of silver. But in such experi-
ments the alumina often pectizes in the dialyser before the
hydrochloric acid has entirely escaped.
Acetate of alumina with an excess of alumina gave similar
results. The alumina remained fluid in the dialyser for twenty-
one days, and when it pectized was found to retain 34 per cent.
Mr. T. Graham on Liquid Diffusion applied to Analysis. 299
of acetie acid, which is in the proportion of 1 equivalent of acid
to 28°2 equivalents of alumina.
Soluble alumina is one of the most unstable of substances—a
circumstance which fully accounts for the difficulty of preparing
it in a state of purity. It is coagulated or pectized by portions,
so minute as to be scarcely appreciable, of sulphate of potash
and, I believe, by all other salts; and also by ammonia. A
solution containing 2 or 3 per cent. of alumina was coagulated
by a few drops of well-water, and could not be transferred from
one glass to another, unless the glass was repeatedly washed out
by distilled water, without gelatinizing. Acids in small quan-
tity also cause coagulation; but the precipitated alumina readily
dissolves in an excess of the acid. The colloids gum and cara-
mel also act as precipitants.
This alumina is a mordant, and possesses indeed all the pro-
perties of the base of alum and the ordinary aluminous salts,
A solution containing 6°5 per cent. of alumina may be boiled
without gelatinizing, but when concentrated to half its bulk it
suddenly coagulated. Soluble alumina gelatinizes when placed
upon red litmus-paper, and forms a faint blue ring about the
drop, showing a feeble alkaline reaction. Soluble alumina is
not precipitated by alcohol nor by sugar. No pure solution of
alumina, although dilute, remained fluid for more than a few
days.
‘Like hydrated. silicie acid, then, the colloid alumina may
exist either fluid or pectous, or it has a soluble and insoluble
form, the latter being the gelatinous alumina as precipitated by
bases. It is evident that the extraordinary coagulating action
of salts upon hydrated alumina must prevent the latter sub-
stance from ever appearing in a soluble state when liberated
from combination by means of a base.
Colloidal alumina possesses also, I believe, a high atomic weight,
like cosilicic acid. The chloride of aluminium with excess of alu-
mina referred to above appears to be, either im whole or in part, a
colloidal hydrochlorate of alumina, containing the latter sub-
stance with its large colloidal equivalent, and may be really
neutral in composition. The soluble basic persalts of iron, tin,
&c. are likewise all colloidal, and have no doubt a similar con-
stitution. Such colloidal salts are themselves slowly decomposed
on the dialyser, being resolved into the crystalloidal acid which
escapes and the colloidal oxide which remains behind.
Soluble Metalumina.—Mr. Crum first pointed out a singular
relation of acetic acid to alumina, which has never been explained.
Sulphate of alumina, when precipitated by acetate of lead or
baryta, gives a binacetate of alumina, with one equivalent of
free acetic acid—the neutral teracetate of alumina not appearing
X 2
3800 Mr. T. Graham on Liquid Diffusion applied to Analysis.
to exist. It was further observed that, by keeping a solution of
this binacetate in a close vessel at the boiling-point of water for
several days, nearly the whole acetic acid came to be liberated,
without any precipitation of alumina occurring at the same time.
Mr. Crum boiled off the free acetic acid, or the greater part of
it, and thus obtained his soluble alumina. The same result may
be arrived at by dialysing a solution of acetate of alumina that
has been altered by heat. In three days the acetic acid was
reduced on the dialyser to 11 per cent., giving 1 equiv. acetic
acid to 8 equivs. alumina; in six days to 7°17 per cent. acid; in
thirteen days to 2°8 per cent. acid, or 1 equiv. acid to 83 equivs.
alumina. The alumina exists in an allotropic condition, being
no longer a mordant, and forming, when precipitated, a jelly
that is not dissolved by an excess of acid. Metalumina resem-
bles alumina in being coagulated by minute proportions of acids,
bases, and of most salts. Mr. Crum found the solution of met-
alumina to require larger quantities of acetates, nitrates, and
chlorides to produce coagulation than of the former substances.
The solution of metalumina is tasteless, and entirely neutral to
test-paper, according to my own observation.
Tike alumina, the present colloid has therefore a fluid and a
pectous form—the liquid soluble metalumina, and the gelatinous
insoluble metalumina.
Soluble Peroxide of Iron.—A solution of hydrated peroxide of
iron may be obtained by a process exactly analogous to that for
soluble alumina. Perchloride of iron in solution is first saturated
with hydrated peroxide of iron, added by small quantities at a
time; or carbonate of ammonia may be added in a gradual man-
ner to perchloride of iron, so long as the precipitated oxide con-
tinues to be redissolved on stirrmg. These red solutions of iron
have lately been carefully investigated hy Mr. Ordway (Silliman’s
Journal, 3 ser. vol. xxxix. p. 197), by M. Béchamp (Annales de
Chimie, 3 sér. vol. lvii. p. 298), and by M. Scheurer-Kestner
(ib. vol. lv. p. 830). It is observed that the act of solution of
the hydrated peroxide by the chloride of iron is a gradual process,
demanding time. The quantity of oxide taken up will go on
increasing for a long time, if digestion in the cold is continued.
Mr. Ordway found chloride of iron to take up so much as 18
equivalents of peroxide of iron in the course of five months.
This slowness of action is highly characteristic of colloids.
Only monobasic acids, such as hydrochloric and nitric, serve for
preparing such solutions,—sulphuric and other polybasic acids
giving insoluble subsalts with excess of ferric oxide, or of any
other aluminous oxide. The red liquid so obtained is already a
coiloidal hydrochlorate of peroxide of iron, but requires to be
dialysed for a sufficient time. Such a compound possesses an
Mr. T. Graham on Liquid Diffusion applied to Analysis. 301
element of instability in the extremely unequal diffusibility of
its constitueuts. Beginning with perchloride of iron, containing
five or six equivalents of peroxide in solution, the whole solid
matter also amounting to 4 or 5 per cent. of the liquid, and the
latter forming a stratum of the usual depth of about half an
inch in the dialyser, it was found tnat hydrochloric acid diffused
out accompanied only by a small proportion of the iron. After
eight days, the deep-red solution in the dialyser contained
peroxide of iron and hydrochloric acid, in the proportion of 97°6
per cent. of the former to 2°4 per cent. of the latter. In nine-
teen days the hydrochloric acid was reduced to 1:5 per cent.,
which gives 1 equiv. of acid to 30°3 equivs. peroxide of iron.
The last solution was transferred to a phial, in which it remained
fluid for twenty days, and then spontaneously pectized.
The peracetate of iron, prepared by double decomposition, is
incapable of dissolving hydrated peroxide of iron, as is well
known, but still may be made a source of soluble peroxide, as
the salt referred to is itself decomposed to a great extent by dif-
fusion on the dialyser. About one-half of the iron was lost by
a diffusion of eighteen days, in a particular experiment, leaving
on the dialyser a red liquid, in which ninety-four parts of per-
oxide of iron were still associated with six parts of acetic acid.
Water containing about 1 per cent. of hydrated peroxide of
iron in solution has the dark-red colour of venous blood. The
solution may be concentrated by boiling to a certain point, and
then pectizes. The red solution is coagulated in the cold by
traces of sulphuric acid, alkalies, alkaline carbonates, sulphates
and neutral salts in general, but not by hydrochloric, nitric, and
acetic acids, nor by alcohol or sugar. The coagulum is a deep-
red-coloured jelly, resembling the clot of blood, but more trans-
parent. indeed the coagulation of this colloid is highly sug-
gestive of that of blood, from the feeble agencies which suffice to
effect the change in question, as well as from the appearance of
the product. The coagnlum formed by a precipitant, or, in the
course of time, without any addition having been made to the
solution of peroxide of iron, is no longer soluble in water, hot
or cold; but it yields readily to dilute acids. It is, in short,
the ordinary hydrated peroxide of iron. Here then, again, we
have a soluble and insoluble form of the same colloidal substance.
Native hematite, which presents itself in mammillary concretions,
is no doubt colloidal.
Soluble Metaperoaide of Iron.—The soluble peroxide of iron
of M. Péan de Saint-Gilles* appears to be the analogue of met-
alumina, It was also prepared by the prolonged action of
heat upon a pure solution of the acetate. The characteristic
* Comptes Rendus, 1855, p. 568.
802 Mr. T. Graham on Liquid Diffusion applied to Analysis.
properties of this substance, which indicate its allotropic nature,
are the orange-red colour and the opalescent appearance of its
solution. The metaperoxide of iron is entirely precipitated, of a
brown ochreous appearance, by a trace of sulphuric acid or of an
alkaline salt, and is insoluble in all cold acids, even when the
latter are concentrated. The solubility of metaperoxide of iron
in water appears to be more precarious, if possible, than that of
the colloid alumina. It would no doubt be more safely pre-
pared by diffusing away the acetic acid of the altered acetate of
iron, than it is by boiling off that acid, as the solution is said
to become precipitable by heat before the whole acetic acid is
expelled. :
Ferrocyamde of Copper.—Many of the insoluble ferrocyanides
are crystalline precipitates ; but the compound above named, and
the different varieties of prussian blue, appear to be strictly col-
loidal.
Certain anomalous properties long observed in these com-
pounds come thus to be explained. The ferrocyanide of copper
precipitated from ferrocyanide of potassium and sulphate of cop-
per, is a reddish-brown gelatinous precipitate, and carries down
a portion of the potash salt. It is obtained of greater purity,
like the other insoluble ferrocyanides, by the use of ferrocyanic
acid as the precipitant. Ferrocyanide of copper is then darker
in colour, and still more highly gelatinous. It is well known
that this substance appears as a transparent almost colourless
jelly when precipitated from strong solutions. This colloidal
matter assumes colour on the addition of water, im consequence
of further hydration, following in this respect the analogy of
the crystalloid salts of copper. The ferrocyanide of copper,
when once precipitated, may be washed without loss, and ex-
hibits no symptoms of solubility. But it has been remarked
that the same salt, when produced by mixing the precipitating
salts dissolved in not less than two or three thousand times their
weight of water, gives a wine-red solution with no precipitate.
This is the soluble condition of the colloid. When the red solu-
tion is placed in the dialyser, the salt of potash diffuses out and
the whole ferrocyanide of copper is retained behind in solution.
Precipitated ferrocyanide of copper is not dissolved by oxalic
acid, nor by oxalate of potash, but dissolves freely in about one-
fourth of its weight of neutral oxalate of ammonia. The ferro-
cyanide of copper must be washed beforehand, to ensure solu-
bility. A solution holding 3 or 4 per cent. of ferrocyanide of
copper is of a dark reddish-brown colour, intermediate in tint
between the acetate and meconate of iron. The solution is
transparent, but assumes a peculiar appearance of opacity when
seen by light reflected from its surface. ‘The same appearance
Mr. T. Graham on Liquid Diffusion applied to Analysis. 803
was observed by Péan de Saint-Gilles in his metaperoxide of
iron.
When a red solution, such as that described, was dialysed,
the oxalate of ammonia came away in a gradual manner; 30°6
per cent. of the oxalate of ammonia were found in the colourless
diffusate of the first twenty-four hours, 31 per cent. of the same
salt in the diffusate of the next three days, and 18°2 per cent.
in the diffusates of the following seven days, making altogether
79°8 per cent., or four-fifths, of the whole oxalate of ammonia
originally introduced. A small portion of the ammoniacal salt
is retained with force, as might be expected from a ferrocyanide.
Although the diffusate appeared colourless, it was found to con-
tain a little oxide of copper, namely, 0-041 gramme (of which
0:022 gramme diffused out in the first twenty-four hours), from
2 grammes of ferrocyanide of copper placed in the dialyser.
The liquid ferrocyanide of copper, both before and after bemg
dialysed, may be heated without change, but it is pectized by
foreign substances with extreme facility. This effect is pro-
duced by a minute addition of nitric, hydrochloric, and sul-
phuric acids in the cold, and of oxalic and tartaric acids with
the aid of a slight heat. It is remarkable that acetic acid does
not pectize the ferrocyanide of copper and many other colloids.
Sulphate of potash, sulphate of copper, and metallic salts gene-
rally appear to pectize the red liquid. The oxalate of ammonia,
if any is present, remains in solution.
Neutral Prussian Blue-—The blue precipitate from perchloride
of iron and ferrocyanide of potassium, or ferrocyanic acid, is a
bulky hydrate, which dries up into gummy masses, so far resem-
bling a colloid. The precipitate dissolves readily with the aid
of a gentle heat, in one-sixth of its weight of oxalic acid, giving
the well-known solution of prussian blue, used as an ink. Prussian
blue is equally soluble in the oxalate and binoxalate of potash.
When the solution of prussian blue in oxalic acid was placed on
the dialyser, no colouring matter came through, but 28 per cent.
of the oxalic acid diffused away in the first twenty-four hours,
accompanied by traces of peroxide of iron. The oxalic acid
appears to leave the colloidal solution very slowly and incom-
pletely, 8 per cent. diffusing away in the second twenty-four
hours, 11 per cent. in the next four days, and 2 per cent. in
the following six days. The colloidal solution of prussian blue
was pectized by small additions of sulphate of zinc and several
other metallic salts, but required larger quantities of the alkaline
salts for precipitation.
Ferrideyanide of Iron. —The blue precipitate from the ferrid-
cyanide of potassium and a protosalt of iron is soluble in oxalic
‘acid and the binoxalate of potash, but not in the neutral oxalates.
804 Mr. T. Graham on Liquid Diffusion applied to Analysis.
This blue liquid is quite incapable of passing through the dialyser,
and is equally colloidal with ordinary prussian blue. So also is
basic prussian blue prepared by the spontaneous oxidation of
precipitated ferrocyanide of protoxide of iron. This last colloid
might probably be purified with advantage upon the dialyser.
The ammonio-tartrate of iron, ammonio-citrate of iron, and
similar pharmaceutical preparations are chiefly colloidal matters.
Sucrate of Copper.—The deep-blue hquid obtained by adding
potash to a mixed solution of chloride of copper and sugar ap-
pears to contain a colloidal substance. Placed on a dialyser for
four days, the blue liquid became green, and no longer con-
tained either potassium or chlorine; it in fact consisted of oxide
of copper united with twice its weight of sugar. The external
liquid remained colourless, and gave no indication of copper
when tested with sulphuretted hydrogen. The colloidal solu-
tion of sucrate of copper was sensitive in the extreme to pec-
tizg agents. Salts and acids generally gave a bluish-green
precipitate ; even acetic acid had that effect. The precipitate,
or pectous sucrate, after being well-washed, consisted of oxide
of copper with about half its weight of sugar, and is therefore a
subsucrate. When the green liquid is heated strongly, it gives
a bluish-green precipitate, and does not allow the copper to be
readily reduced to the state of suboxide. The subsucrate of
copper possesses considerable vivacity of colour, and might be
used as a pigment. A solution of sucrate of copper absorbs
carbonic acid from the air with great avidity.
The sucrate of copper dries up into transparent films of an
emerald-green colour. These films are not altered in appearance
or dissolved in cold or boiling alcohol. In water they are re-
solved into sugar and the pectous subsucrate of copper.
Sucrate of Peroxide of Iron.—The perchloride of iron with an
addition of sugar is not precipitated by potash, provided the
temperature is not allowed to rise. The peroxide of iron com-
bined with the sugar is colloidal, and remains on the dialyser
without loss. At a certain stage, however, the sugar appears to
leave the peroxide of iron, and a gelatinous subsucrate of iron
pectizes. The subsucrate of iron thrown down from the soluble
sucrate by the addition of sulphate of potash consisted of about
22 parts of sugar to 78 parts of peroxide of iron.
Sucrate of Peroxide of Uranium.—A similar solution may be
obtained by adding potash to a mixture of the nitrate or chloride
of uranium with sugar, avoiding heat. The solution is of a deep
orange-yellow colour, and on the dialyser soon loses the whole
of its acid and alkali. This finid sucrate has considerable stabi-
lity, but is readily pectized by salts, like the sucrate of copper.
The subsucrate pectized has considerable solubility in pure water.
_Mr. T. Graham on Liquid Diffusion applied to Analysis. 305:
~ Sucrate of Lime.—The well-known solution of lime in sugar
forms a solid coagulum when heated. It is probably, at a high
temperature, entirely colloidal. The solution obtained on cool-
ing passes through the septum, but requires a much longer time
than a true crystalloid like the chloride of calcium.
The blue solution of tartrate of copper in caustic potash con-
tains a colloidal compound, which has not been fully examined.
Soluble Chromic Oxide.—The definite terchloride of chromium,
being a crystalloid, diffuses away entirely when placed in solu-
tion upon the dialyser. This salt dissolves, with time, a certain
portion of freshly-precipitated hydrated chromic oxide, and
becomes of a deeper green colour. Such a solution, after dia-
lysis for twenty-two days, contained 8 hydrochloric acid to 92
chromic oxide; and after thirty-days, 4°3 acid to 95:7 oxide, or
1 equiv. acid to 10°6 equivs. oxide. After thirty-eight days,
the solution gelatinized in part upon the dialyser, and then con-
tained 1°5 acid to 98°5 oxide, or 1 equiv. acid to 31°2 equivs.
chromic oxide. This last solution, which may be taken to repre-
sent soluble chromic oxide, is of a dark-green colour, and admits
of being heated, and also of being diluted with pure water with-
out change. It was gelatinized with the usual facility by traces
of salts and other reagents which affect colloid solutions, and
was then no longer soluble in water, even with the assistance of
heat. It appeared to be the green hydrated oxide of chromium
as that substance is usually known. A metachromic oxide may
possibly be obtained by heating and dialysing the acetate, but I
have not attempted to furm it.
Mr. Ordway succeeded in dissolving an excess of the hydrated
uranic oxide aud of glucina in the chloride of uranium and of
glucinum respectively. The dialysis of such solutions may be
reasonably expected to yield soluble uranic oxide and soluble
glucina.
It appears, then, that the hydrated peroxides of the aluminous
type, when free, are colloid bodies; that two species of each of
these hydrated oxides exist, of which alumina and metalumina
are the types—one derived from an unchanged salt, and the
other from the heated acetate of the base; further, that each of
these species has two forms—one soluble, and the other insoluble
or coagulated. This last species of duality should be well distin-
guished from the preceding allotropic variability of the same
peroxide. The possession of a soluble and an insoluble (fluid
and pectous) modification is not confined to hydrated silicic acid
and the aluminous oxides, but appears to be very general, if not
universal, among colloid substances. The double form is typified
in the fibrine of blood.
The precipitated and gelatinous peroaide of tin is largely
306 Col. Sir H. James and Capt. A. R. Clarke on Projections
soluble in the bichloride of the same metal. Such a solution,
when placed in the dialyser, allows the whole chlorine of the
salt and a portion of the tin to diffuse away. Peroxide of tin,
or stannic acid, remains behind, but not in a soluble state. It
forms in the dialyser a semitransparent gelatinous cake, which
after a few days is entirely free from chlorine. The original
solution, containing excess of stannic acid, was diluted to various
degrees, but was dialysed always with the same result. The
coagulum was insoluble in hot or cold water, but dissolved
readily in dilute acids. It was evidently the peroxide of tin
unaltered.
The metastannic acid, or nitric-acid peroxide of tin of Berzelius,
forms a solid compound with a small quantity of hydrochloric
acid. This compound is not dissolved by an excess of acid, but
is soluble in pure water. The solution placed in the dialyser is
readily decomposed, and leaves behind a semitransparent gela-
tinous mass of pure hydrated metastannic acid, insoluble both
in water and acids. There appears, then, to be no soluble form
of either hydrated stannic or metastannic acid, although both
are colloidal substances.
Precipitated tztanic acid was dissolved in hydrochloric acid and
submitted to dialysis. The hydrochloric acid readily diffused
away, leaving hydrated titanic acid, gelatinous and insoluble,
upon the dialyser. The proportion of titanic acid which escaped
from the dialyser and was lost amounted to 0-050 gramme out
of 2:5 grammes. Titanic acid thus resembles stannic acid in
not presenting itself in the form of a fluid colloid.
Metallic protoxides are not soluble in their neutral salts, and
therefore cannot be submitted to dialysis in the same conditions
as the preceding peroxides. It was observed, however, that
oxide of copper and oxide of zinc, when dissolved in ammonia,
are capable of diffusing through a colloidal septum, and are
therefore not colloids themselves. The water outside the dia-
lyser should be charged with ammonia in such an experiment.
[To be continued. ]
XLII. On Projections for Maps applying to a very large extent
of the Earth’s Surface. By Colonel Sir Henry Jamess, R.E.,
Director of the Ordnance Survey ; and Captain ALEXANDER R.
CiarkeE, R.EL* |
[ With a Plate. |
| Fe reading the “Explanation of a Projection by Balance of
Errors for Maps applying to a very large extent of the
Earth’s Surface, and comparison of this projection with other
* Communicated by the Authors. ;
or Maps applying to a-large extent of the Earth’s Surface. 307.
ips appryimng 9g
projections,” by G. B. Airy, Esq., Astronomer Royal, which
appeared in the Philosophical Magazine for December 1861,
and in examining the numerical results given in the Tables in
which the relative advantages of the Projection by Balance of
Errors, by Equal Radial Degrees, by Unchanged Areas, and in
the Stereographic (attributed to Hipparchus), and my Projection
of two-thirds of the sphere, I was struck with the fact that the
numbers. given as representing the Radial distances from the
centre of the Map, the Exaggeration of the projected areas, and
the Distortion of the form, did not show such advantages in
favour of the Projection by Balance of Errors as I was naturally
led to expect from the ingenious method employed by Mr. Airy
for obtaining them.
I therefore requested Captain Alexander R. Clarke, R.E., to go
through the mathematical process employed by Mr. Airy, and
examine the numerical results given in the Tables. I subjoin
the result of Captain Clarke’s examination ; and it will be observed
that, from a mistake inadvertently made in one of the constants;
the projection by Balance of Errors has greater advantages than
Mr. Airy has given it in his Tables.
The fundamental equation of this very beautiful method of
development is readily obtained in the following manner. Let
P be the point on the sphere which is to be the centre of the
map, and let Q be any other point on the sphere such that the
are PQ=@; if Q' be the representation of Q on the Development,
PQ’=r. Suppose a very small circle, radius w, described on
the sphere having its centre at Q, then the representation of
this circle in the map will be an ellipse having its mimor axis
in the line PQ! and its centre at Q’. The lengths of the semi-
axes will be
ont A)
Soe Sane
The differences between these quantities and that (w) shat
they represent are
dr r
(F -1), o( 5 -1);
and the sum of the squares of these errors is the measure of the
misrepresentation at Q'. The sum for the whole surface from
G=0 to 0=6 is a to
{4 ( 4(5- ha Bile
Sch | is to be a minimum.
308 Col. Sir H. James and Capt. A. R. Clarke on Projections
Putting r—@=y, and giving to y only a variation subject to
the condition dy=0 when 6=0, the equations of solution are
P, being the value of 2p sin @ when 6=8; hence
: dpe tt dy
2 ats
sin O92 + sin 8 cos 6 16
By =03 ot ae
—y=O0—sin6, . . (1)
from which
6 6 Bi is aie
y= —O—2 cots log coss + C tang +C cot 5, - (1)
B Boek i B
= 2h Ano eG det =a ee
O= cosec 5 log cos 3 + 5 © sec 5 5 © cosec 5:(2)
Now y must vanish with @; therefore C’=0, and, from (2),
= eae 2B
C= cot 5 log sec" 5
which completely determines r. At the centre of the map,
where 6=0,
dr Teng)
Cs orale
This quantity in the Astronomer Royal’s paper is inadvertently
made =1, and consequently the computed Tables, pp. 415, 416,
417, are incorrect, and the Development appears under disad-
vantage. ‘The limiting radius of the map is
R=2C tank.
This quantity does not increase indefinitely, but is a maximum
when B=126° 24! 53": for higher values of 8, R diminishes.
When B=120°, R=1-6007. When @=118° 30', which is the
limit of Sir H. James’s map, R=1°5760.
Let us now compare this Development with the Equal Radial
and Sir Henry James’s Projection. In order to do this, we must
suppose these to be drawn on such a scale that the limiting radius
shall be 1°5760, and then form the values of
dr 2 r 2
(5 -1) +(35 -1) .
The values of this quantity, which call U, are given in the fol-
lowing Table :—
for Maps applying to a large extent of the Earth’s Surface. 309
Balance of Errors. Sir H. James’s. Equal Fadial.
U. U sin 6. U. U siné. U. U sin @.
1) 1168 0000 "1182 0000 0836 0000 0
5 "1164 0101 1172 0102 0832 0072 5
10 °1149 °0200 1147 "0199 0819 70142 10
15 1126 0291 1106 0286 0799 "0207 15
20 1093 0374 "1050 0359 0771 0264 20
25 1052 "0444 0980 "0414 0737 0311 25
30 1002 0501 0897 "0448 0696 0348 30
35 0945 0542 0804 0461 0651 0373 35
40 0881 °0566 0704 0453 0603 0387 40
45 0812 0574 "0601 0425 0553 0391 45
50 (740 0567 0499 0382 0506 "0387 50
55 0667 0547 0404 0331 0464 0380 55
60 0598 0518 "0325 0281 0432 0374 60
63 0536 0486 0270 "0244 | -0418 0379 65
70 0491 0461 “0251 | .-0236 0430 "0104 70
75 0471 0455 0285 0275 *0479 "0463 75
80 0492 0485 "0391 "0385 0582 0573 80
85 0575 0573 "0597 0594 0759 0756 85
90 0752 0752 |. :0937 0937 1041 "1041 90
95 "1068 "1064 "1461 °1456 1469 71463 95
100 1593 "1569 2240 2206 *2099 ‘2067 | 100
105 *2442 2359 "3371 °3256 3013 °2910 | 105
110 3784 "3952 0002 "4700 4329 ‘4068 | 110
115 5904 5352 7350 6661 6223 5640 | 114
From these quantities we may infer the values of
B
{ Usn@.d0=M
0
for the different systems ; they are
Seabe James Se) aye « M=0°1718,.0r.as 1095
Kqual Radial. . . . = ==0°:1648, ,, 1047
Balance of Errors . . =O91569...° 00:0
By inspection of the Table it will be seen that from 0° to 45°
the Equal-Radial Projection has the advantage; from 50° to 80°
Sir H. James’s Projection has the advantage ; : from 80° upwards
the Balance of Errors has the advantage.
The first of these projections may, however, be greatly im-
proved. The general expression for the radius, ‘namely
14 ASG
~ A+ cos @’
involves two arbitrary quantities, and we may so dispose of them
as to render - integral M an absolute minimum ; that is,
fe k(h cos 0 +1)
eee. h-+ cos @ -1) 7 (eee (h+ cos 0 -1) "lind dé
310 Col. Sir H. James and Capt. A. R. Clarke on Projections
must be a minimum with respect to h and &, Effecting the in-
tegration, we get
M=/°H, +2k4H,+4sin? :
where the symbols H,, fe are
_ 14%? A(®—1) | (2-1)? (1—h)2
Srey, Ca ie Gere.
N h?—]
Bee) Ceca
nid N=A-+cosf. Now
dM
ay =O; «©. kHj)+H,=0;
dM _ sie) ae |
Git tee | ae a ee
A gi H, 2 dH, dH,
hence
‘ H,?
ag es aN ta
M=4sin A?
and # must be determined so that
2
Seam ig See 5
i a maximum.
This is most easily determined by calculating the values corre-
sponding to assumed values of A. We have the followimg :—
h. log H?,— log H).
Oo ae we el et OO ano
PSCr ee ss es UAT ao
1:37 0:4:20762
1:88 598 : - f . 0420747
1B) Hos ee Lot 420665
By a pees the maximum is found to be
h. log H*,— log Hy.
1:36763 2 8 oo 304207628
oe
ie = 2°634889 ;
‘and consequently
M=0:°16261;
and in this case the misrepresentation is to that in the Balance
of Errors as 103°6:100°0. The point of sight or of projection
for Maps applying to a large extent of the Earth’s Surface. 311
is here at the distance of 44 of the radius from the surface
instead of 4 the radius.
The expression then for 7 is
_ 166261 sin 6 |
"136763 + cos
When 8=113° 30!, this becomes R=1-'5737, which is very near
to the size of the Balance of Errors development, viz. R=1-5760.
The values of r are as follows :—
0 0:0000 60 0:7710
5 0°0613 65 0°8417
10 0°1227 70 0:9138
15 0°1844 75 0:9874
20 0:2464 80 1:0623
25 0:3090 85 1:1385
30 0:3722 90 1:2157 |
35 0-4361 95 1:2935
40 0:5009 100 1:3713
45 9-5666 105 1:4484
50 0:6335 110 1:5233
55 0:7016 115 15945
Ay HG.
I have had the projection by Balance of Errors and my pro-
jection of two-thirds of the surface of the sphere drawn of the
exact same size to facilitate the comparison of their relative
merits (Plate IV.) ; and I have drawn circles in their centres, that
the extent to which figures are distorted in form and exaggerated
in area may be seen, by comparing them with the elliptical figures
into which circles are projected towards the limits of the map*.
My projection of two-thirds of the surface of the sphere is
described in the Corps’ Papers of the Royal Engineers in 1858,
and in the Mittheilungen for the same year. It is a true geome-
trical or optical projection, in which the sphere is supposed to be
hollow, the plane of projection drawn parallel to and at the
distance of 23° 30! from the plane of any great circle, and the
point of sight or projection is at the distance of half the radius
from the surface of the sphere. Jn my published maps the plane
of projection is drawn parallel to the plane of the ecliptic.
Maps drawn on this projection have consequently a true
perspective effect, and all the circles are represented by true
elliptical arcs.
But in the projection, or, to speak more correctly, in the
* The diagrams (Plate IV.) have been reduced from larger diagrams, and
printed by photo-zincography at the Ordnance Survey Office, Southampton,
312. Prof. Tyndall on the Regelation of Snow-granules.
WYevelopment by Balance of Errors, for it neither has a point of
sight nor a plane of projection, we have no such effect, but, on
the contrary, we have in it some of the circular ares thrown into
lines of contrary flexure; and this I conceive is fatal to this
method of representing large portions of the earth’s surface.
For the projection of the surface of a hemisphere, the distance
of the point of sight which I have adopted is the best possible ;
for in it the distortion of form and the exaggeration of area—or,
as we may call these two defects of all projections, the misrepre-
sentation is a minimum; but for extending the projection from
90° to 113° 30’, Captain Clarke has shown that the distance of
the point of sight to ewe the least misrepresentation should have
been 44, instead of 42, in which case the misrepresentation would
have been 103°6 as compared to 100°0 in the projection by
Balance of Errors, the ratio in the projection as drawn by me
being 109°5 to 100-0.
In deciding to adopt half the radius as the distance for my
point of projection, I knew that this was not the best possible
point, but that it was so near to it that, for all practical pur-
poses and the simplicity of its definition, it was the best to
adopt; and it is the very best projection up to 90° from the
centre. For the same reason I adopted the limit of the tropics
for the position of the plane of projection, because this is very
definite, and near the limit which in prudence I could give to
the projection; and I have called it a projection of two-thirds
of the sphere, whilst in reality the surface represented 1s seven-
tenths of the whole surface.
A comparison of the two projections will satisfy any practical
person that, if the ratio of the misrepresentation in them is as
109°5 to 100:0, I should gain very little by making it in the
ratio of 103-6 to 100°0; in fact the eye would not detect the
difference.
I have prepared a map of the world and a map of the stars on
my projection, each ten feet in diameter, for the Great Exhibi-
tion of this year; and the public will have a full opportunity of
judging of its merits.
XLII. On the Regelation of Snow-granules.
By Joun Tynpaui, F.R.S*
i] THIS morning (March 21) noticed an extremely interesting
case of regelation. A layer of snow between 1 and 2 inches
in thickness had fallen on the glass roof of a small greenhouse,
into which a door opened from the mansion to which the green-
* Communicated by the Author.
Prof. Challis on the Principles of Theoretical Physics. 318
house was attached. Aur slightly warmed, acting on the glass
surface from underneath, melted the snow in immediate contact
with the glass, and the layer in consequence slid slowly down
the glass roof. The inclination of the roof was very gentle, and
the motion correspondingly gradual. When the layer overshot
the edge of the roof it did not drop off, but bent like a flexible
body, and hung down over the edge for several inches. The
continuity of the layer was broken into rectangular spaces by the
inclined longitudinal sashes of the roof, and from local circum-
stances one side of the roof was warmed a little more than the
other ; hence the subdivisions of the layer moved with different
velocities, and overhung the edge to different depths. The bent
and down-hanging layer of snow in some cases actually curled
up inwards.
Faraday has shown that when small fragments of ice float on
water, if two of them touch each other they instantly cement
themselves at the point of contact; and on causing a row of
fragments to touch, by laying hold of the terminal piece of the
row you can draw all the others after it. A similar cementing
must have taken place among the particles of snow now in
question, which were immersed in the water of liquefaction near
the surface of the glass. But Faraday has also shown that, when
two fragments of ice are thus united, a hinge-like motion sets in
when you try to separate the one from the other by a lateral push :
one fragment might in fact be caused to roll round another, like
a wheel, by incipient rupture and the re-establishment of rege-
lation. The power of motion thus experimentally demonstrated
rendered it an easy possibility for the snow in question to bend
itself in the manner observed. The lowermost granules, sub-
jected to pressure when the support of the roof bad been with-
drawn, rolled over each other without a destruction of continuity,
and thus enabled the snow layer to bend as if it were viscous. The
curling up was evidently due to a contraction of the inner surface
of the layer, produced, no doubt, by the accommodation of the
granules to each other as they slowly diminished in size.
Waverley Place, St. John’s Wood,
March 21, 1862.
XLIV. On the Principles of Theoretical Physics. By the Rev. J.
Cuatus, M.4., #.R.S., FLR.A.S., Plumian Professor of
Astronomy in the University of Cambridge *.
Shae great progress that is being made at the present. time
in experimental philosophy is remarkable in respect both
to the skill and ingenuity displayed in making the experiments,
* Communicated by the Author.
Phil. Mag. 8. 4. Vol. 23, No. 154, April 1862. Y
814 Prof. Challis on the Principles of Theoretical Physics.
and the success with which new facts are elicited and new laws
established. In consequence, perhaps, of the striking character
of these achievements, compared with the slow and uncertain
steps with which theoretical physics have of late advanced, the
idea seems to be gaining ground that theory may be dispensed
with, and that the domain of natural philosophy includes only
the discovery of facts and educing laws out of them. On this
point I beg to offer a few observations.
Natural philosophy, as the history of its progressive steps
seems clearly to point out, consists of two parts, related but di-
stinct—viz. the experimental and theoretical. The kind of rela-
tion existing between them may be illustrated by reference to
the history of physical astronomy. ‘The labours of Kepler are
exclusively in the province of experiment, or observation; those
of Newton in the province of theory. The former do not in-
volve the idea of force, while in the latter this idea is funda-
mental. By observations, carried on with wonderful patience
and perseverance, Kepler established three laws relating to the
motions of the planets about the sun. The knowledge of these
laws was not necessary for the discovery of the principle of
gravitation: Newton, in fact, did not use them for that purpose.
They were rather problems for solution, which Newton succeeded
in solving by differential calculation applied to the hypothesis of
a gravitating force varying according to the law of the inverse
square of the distance. It may, however, be doubted whether
the reasoning by which the solutions were effected would ever,
have been discovered if the problems had not been proposed.
But as soon as the proper calculation was employed and the
proper hypothesis made, a few steps of symbolic reasoning
sufficed for the demonstration of the laws which it cost Kepler
so many laborious years to arrive at by observation. From
Newton’s time, with the exception perhaps of some futile at-
tempts of Flamsteed, astronomical observation has not been
directed towards the investigation of laws, but has almost ex-
clusively-been employed in furnishing the data indispensable for
making theoretical calculations applicable to actual bodies and
actual instances of motion, and in giving the means of correcting
previous data by comparisons of observed with calculated celes-
tial positions. The general result of the combination of obser-
vation with theory is the demonstration of the law of gravity.
This law could not be shown to be a physical reality either by
observation alone, or by theory alone.
From this survey it would appear that in Kepler’s time astro-
nomical observation was in advance of theoretical calculation,
and was occupied with the investigation of laws because the
means of doing so by theory, to which such investigation pro-
Prof. Challis on the Principles of Theoretical Physics. 315
pérly belongs, was not yet discovered. Turning now to other
departments of physics—the phenomena of light, heat, electri-
city, galvanism, magnetism, and diamagnetism,—it may, in the
first place, be stated that with respect to all these theory is in a
condition analogous to that of physical astronomy in the time of
Kepler. Experiment has established the existence of a great
number of facts and laws, which are only so many problems
that wait for solution by some theoretical generalization. The
process for effecting such generalization must be of the same’
kind as that which has been so successful in physical astronomy:
Some hypothesis, or hypotheses, suggested by the antecedents
of physical science, must be thought of, and be made the basis
of appropriate calculation, in order that the truth of the hypo-'
theses may be tested by comparison of the results of the calcu-
lation with experimental facts.
I am not aware that any general physical theory, supported
by mathematical reasoning, and comprehensive of all the physi-
cal forces, has hitherto been proposed, excepting that of which
I have given an outline in communications made from time to
time to this Magazine. In the supplementary Number for last
June I have expressed the intention of gomg through a revision
of the proofs of certain propositions in hydrodynamics which are
essential to the general theory. Before, however, carrying out
this intention, 1 propose in this communication, in the first
place, to re-state the fundamental hypotheses of the theory, for
the purpose of showing that, in conformity with the principles
above laid down, they have regard to antecedent physical science,
and are proper for being the basis of mathematical calculation.
Then I shall endeavour to indicate in general terms the process
to be followed in order to found on these hypotheses a general
physical theory, and the requirements which such a theory must
satisfy. |
The hypotheses are of two distinc tkind—sone relating to the
agency by which the physical forces act, and the other to the
qualities of the ultimate constituents of material substances.
These two classes must be regarded separately, as they require
the application of different tests, and admit of different degrees
of verification.
The principal hypothesis of the first class is, that a very rare
and elastic fluid, called the ether, of uniform elasticity through-
out, pervades all space not occupied by the atoms of visible and
tangible substances, and that under all circumstances its pres-
sure is proportional to its density. The theory does not recog-
nize any active force which is not resident in this medium.
The conception of a medium of much greater tenuity and
- elasticity than the air is of very long standing, and was enter-
tamed especially by Descartes, who even applied it to account
pee
316. Prof. Challis on the Principles of Theoretical Physics.
for the transmission of light from one point of space to another.
And certainly this is a reasonable and a philosophical idea. For
let us consider what is the most general and patent fact in regard
to ight that we have to account for. Some impulse, or action,
originates at a position in space, for instance, at a star unnum-
bered millions of miles distant, and after a time is felt by a
spectator on the earth’s surface. The rate of transmission, it
has been ascertained, is nearly two hundred thousand miles in
one second. By what means, it may be asked, has the impulse
been transmitted from so distant a point at so rapid a rate? To
say that small particles of matter are violently driven off from
the star in all directions, must be pronounced to be a clumsy
explanation compared with that suggested by Descartes, espe-
cially as we now know, from our acquaintance with the pheno-
mena of sound, that a dynamical effect may be transmitted
through space with great velocity by an elastic medium, without
the transmission of matter. Ido not hesitate to say that this
antecedently known fact is ample justification of the hypothesis
that light is transmitted through space by an elastic medium
analogous in constitution to air. Yet this very reasonable hy-
pothesis meets with no favour from the mathematicians of the
present day. No one, as far as ] am aware, except myself,
has endeavoured to trace the consequences of it. Both experi-
mentalists and theorists have not hesitated to express their dis-
approval of it as a hypothesis. Let them argue against it as
much as, they please from the consequences to which it leads,
but to object antecedently to a hypothesis which is suggested
and made intelligible by ascertained facts, is, | maintain, wholly
contrary to right rules of philosophizing.
It is true that a medium of a different kind has been invented
to account for the transmission of light through space, and for
other of its phenomena. According to the assumed constitution
of this medium, it more resembles a solid than a fluid. It is,
however, not exactly ke any known body, a particular atomic
arrangement and constitution having been assigned to it expressly
to account for the polarization of light. The phenomena of
light are in this theory referred to the vibrations of discrete
atoms. I have from time to time given reasons for concluding
that there are phenomena of polarization which are incompatible
with such movements, and that this theory must consequently
be abandoned. My reasons remain unanswered. I seem, there-
fore, to have a right to ask that attention should be given to the
different course of reasoning which I have proposed, viz. that of
investigating mathematically the vibratory movements of a con-
tinuous elastic fluid, and referring to them the phenomena of
light. This course has required the discovery of new principles
Prof. Challis on the Principles of Theoretical Physics. 317
in the application of partial differential equations to the deter-
mination of fluid motion ; andI venture to assert that, till these
were known, the science of hydrodynamics was in so imperfect
a state that an undulatory theory of light was not possible.
There will appear to be the more reason for making the above
request when the nature of the task which I have, to a con-
siderable extent, accomplished is stated. It is known that there
are certain phenomena of light which are dependent only on
properties of the medium in which it is generated, and through
which it is transmitted. The followimg is a list of them:
(1) the uniformity of the rate of propagation; (2) the identity
of rate for rays of different intensity; (3) the difference of in- ©
tensity of different rays; (4) the variation of the intensity, ac-
cording to a certain law, with variation of distance from a centre ;
(5) the co-existence at the same instant of different portions of
light in the same portion of space; (6) the interference of diffe-
rent rays according to given circumstances; (7) the composite
character of light; (8) its colour; (9) results of compounding
colours ; (10) the different kinds of polarized light; (11) the
circumstances of the interference and non-interference of polar-
ized light. To account for all these facts, the single hypothesis
is made that the medium which is the vehicle of light is a
perfect fluid pressing proportionally to its density. Out of this
one hypothesis the explanations of all these different phenomena
are to be evolved by mathematics alone; and if any well-ascer-
tamed mathematical result be contradicted by any one of the
facts, the whole theory must be abandoned. Now the hydro-
dynamical propositions that I have spoken of, if my demonstra-
tions of them be true, do, in fact, give these explanations. Since,
however, the principles on which the demonstrations rest are in
some respects in advance of any previously proposed, additional
elucidation and confirmation may reasonably be required. It is
on this account that I intend, as already intimated, to revise
both the propositions and their demonstrations.
We have now to consider what hypotheses of the second
class—those relating to the qualities of the constituents of
bodies—may be allowable and sufficient for the foundation of a
general physical theory. First, it may be assumed that the
constitution of material substances is atomic, the adoption hypo-
thetically of this constitution being justified by the facts of
chemical combination and analysis. As the known inertia of
masses must be due to the inertia of the constituent parts, it
may also be assumed that the atoms are inert. It is necessary
to make a supposition respecting the forms of the atoms, other-
wise the mutual action between them and the ether cannot be
brought within the province of mathematical calculation. I have
318 Prof. Challis on the Principles of Theoretical Physics.
made the supposition that they are all spherical, but not without
regard to antecedently known facts, such as the following. The
properties of bodies in a fluid or gaseous state are in no respect
altered by any change of the relative positions of the parts—a
fact which would hardly be conceivable if the atoms had any
other than the spherical form, because in that case their mutual
actions would have relation to directions in space. Light 1s
found to traverse some substances without modification, or
change of velocity, on changing the direction of its passage
through them; and though this is not the case im other sub-
stances, yet as the latter are known to be crystalline, it is reason-
‘ able to attribute the circumstance to the arrangement of the
atoms, and not to deviations from the spherical form. Lastly, I
have adopted the Newtonian doctrine that inertia is an essential
quality, but not quantitative, and that consequently all atoms
have the same specific inertia. According to this and the preced-
ing hypothesis, atoms differ from each other only in magnitude.
The foregoing hypotheses relating to the ether and the qualities’
of atoms are the only ones that I have employed im laying the
foundation of a general mathematical theory of the physical
forces. This circumstance, while it may give an idea of the
difficulty of the undertaking, at the same time affords a presump-
tion that the hypotheses are true, it being extremely improbable,
if that were not the case, that in the varied and extensive appli-
cations that have been made of them, some obvious and fatal
contradiction would not have been encountered. The Newtonian
dictum, “hypotheses non fingo,” must be taken with reservation,
as itis not possible to frame a physical theory without hypotheses.
The theory of gravitation, for instance, rests on the hypothesis
of the law of the inverse square. But they ought, no doubt, to
be few and fundamental, and to be such as admit of being tested
by means of mathematical reasoning founded on them. The
multiplication of hypotheses, and making them pro re natd, are
sure signs of a failing theory.
It will be right here to draw a distinction as to kind and
degree between the verifications which the two classes of hypo-
theses admit of in the actual state of science. The verification
of the first class may be effected by comparing results deduced
from them by rigid mathematical reasoning directly with observed
phenomena. If, for instance, such deductions admit of being
brought into satisfactory comparison with the eleven different
kinds of phenomena of hght which I previously enumerated (as,
I beheve, may be done), there would be a strong presumption,
almost amounting to a proof, of the reality of the existence of
the ether, and of its being such as it was assumed to be. And
to arrive at this conclusion with so much of certainty as to allow -
Prof. Challis on the Principles of Theoretical Physics. 319°
of taking it for granted in prosecuting further researches, would
certainly be a great step in theoretical physics. The other class
of hypotheses do not admit of the same kind of verification,
because phenomena (such as are some of those of light) which
depend on the qualities of the constituents of bodies, require in
general for their direct theoretical explanation the knowledge
of the mutual action between the ether and the atoms, and the
number, magnitudes, and arrangements of the latter. But this
knowledge cannot be furnished in the present state of physical
science, and ought rather to be looked for as the final result of
physical inquiry pursued in different channels and by all avail-
able means.
Such being the account of the hypotheses of the proposed
physical theory, I proceed now to speak briefly and in general
terms of the course of reasoning required im their application to
different classes of phenomena, and the demands which they will
have to satisfy. First, let it be conceded that the before-men-
tioned explanations of phenomena of light have given strong
presumptive evidence of the existence of the xther, and of its
being such that variations of its pressure are proportional to
variations of its density. Next we must take mto account the
matter of fact that light-bearing rays are also heat-bearing, and
that consequently the ether must be the vehicle of the transmis-
sion both of light and of deat.. The explanation which the undu-
latory theory gives at once of this fact is, that in a ray there exist
conjointly transverse and direct vibrations, and that the former
expound light, and the latter heat. Again, as heat is known by
experience to act as a repulsive force, the zther which accounts
for other of its phenomena must account for this also. It must
be borne in mind that the ether was assumed to be a highly
elastic medium, and its dynamic action cannot therefore be over-
looked. In fact it is reasonable to attribute the sensation of
light to the dynamic effect of the ztherial vibrations on the ner-
vous system of the eye. But such vibrations, when we calculate
their effect only to the first power of the velocity, are found to
produce simply oscillations of small spherical bodies submitted
to their action, and not motions of translation. ‘T'o account for
the latter, it is necessary to proceed to the consideration of effects
due to the second power of the velocity. This I have attempted
to do, and to found a theory of the force of heat on a mathema-
tical investigation of the dynamic effect of pressures correspond-
ing to the square of the velocity in etherial vibrations. The
investigation showed that the result of such action on small
spherical bodies might under some circumstances be repulsion
from a centre, under others, attraction towards a centre. Thus
the theory was found to embrace the forces of aggregation which
320 Prof. Challis on the Principles of Theoretical Physics.
hold the constituent atoms of bodies in equilibrium. Between
these forces and the force of galvanism there is, as experiment
shows, a close relation, which the theory, if true, will account
for. But clearly it does account for a relation by merely sup-
posing that the two kinds of forces are modifications of the dy-
namical action of the same etherial medium. I may even go
further, and state, as a result to which my investigations point,
that while the forces of aggregation depend on the square of the
velocity in vibrations, galvanic force depends on the square of the
velocity in currents. Moreover, it is matter of experience that
galvanic, electric, magnetic, and diamagnetic forces have some
bond of connexion ; and obviously this circumstance also may be
referred to their being modes of action of the same medium. My
researches indicate, further, that these forces are all expounded
by the dynamic action of ztherial currents, and that they differ
from each other only in the conditions and circumstances under
which the currents are generated. Lastly, there is yet another
physical force, the relations of which to an etherial medium, and
to other modes of force, are not readily made out: I mean the
force of gravity. If, however, all the other forces are modifica-
tions of ztherial pressure, it is reasonable to suppose that this
one is of the same kind. I have ventured to reason on this sup-
position, and have attempted to deduce (I think with success)
the known laws of gravity from the dynamical action of etherial
waves of much larger magnitude than those which correspond to
molecular forces. It will be seen from these explanations that
very large demands are made on the hypothesis of a universal
zether, so large, indeed, that it seems impossible to account for
its meeting them in any degree excepting on the supposition that
it is a reality.
From the foregoing discussion, one general inference of an
important character may be drawn. If the principles of the
proposed theory be admitted, it will follow that, previous to the
theoretical explanation of a vast number of facts and laws which
modern experiments have discovered, it will be necessary to
investigate, by mathematical reasoning applied te the ether, the
modes of its action under given circumstances. To illustrate
this remark, I may refer to the problem of the generation and
permanence of the sun’s heat, and to that of the development of
the tails of comets, both of which have recently attracted the
attention of theorists. Now, as I conceive, neither of these
problems can be at all approached without the antecedent pos-
session of a mathematical theory of the force of heat, such as
that which I have deduced from the properties of an elastic
medium. If this course were pursued, it might perhaps be
found to be unnecessary to suppose that the sun’s heat is main-
Prof. Challis on the Principles of Theoretical Physics. 321.
tained by the impact of minute bodies whose existence even is
not ascertained; and to account for the elongation of comets’
tails, it might be equally unnecessary to invent pro hdc vice a
new kind of repulsive force emanating from the sun.
I take this opportunity of adverting to an assertion which has
been made and reiterated respecting the science of hydro-
dynamics, to the effect that, compared with other departments
of natural philosophy, it is of minor importance, and has pro-
duced “meagre” results. As this assertion is probably only
the expression of an opinion, entertamed by those who have
made it, respecting the course which physical research may
most profitably take, I claim the right in the interests of science
to state an opposite opinion, formed after having long made
hydrodynamics a special subject of inquiry, viz. that it 1s pre-
cisely the determination, by the application and solution of partial
differential equations, of the motion and pressure of fluids, which
is required for the theoretical explanation of the present large
accumulation of experimental facts, and that the discovery and
successful solution of the hydrodynamical problems proper for
this purpose hold the same place with respect to actual theore-
tical physics as the solution which Newton first effected of ap-
propriate dynamical problems held with respect to physical
astronomy.
I beg permission to close this communication by referring to
a fact of observation which appears to be a singular confirma-
tion of the new principles which | have applied m hydrodyna-
mical research. It will be unnecessary to indicate here the pro-
cess by which the velocity of sound has been determined on those
principles, as it is given at length in a communication to the
Philosophical Magazine for December 1852. For the present
purpose it will suffice to state that the velocity (a,) of the pro-
pagation of sound is there given by the equation
29a? 285
30 13)?
in which v is the maximum velocity of the propagated wave, and
h2
a,°=a? + - +1? (
Bok Ag? Rye A
the value of — 1s = Hence, substituting V for a 1+ —
it will readily be found that
2
a,=V. (a +1:0308 <3)
It thus appears, as a theoretical result, that the rate of propa-
gation depends in some degree on the loudness of the sound, the
louder being propagated with the greater velocity. JI was not
aware that such had been observed to be the fact, till my atten-
Re Notices respecting New Books.
tion was drawn to the experiments for the determination of the
velocity of sound made in the arctic regions under the superin-
tendence of Captain Parry, by the reference made tv them in
Mr. Karnshaw’s paper ‘On the Theory of Sound,” in the
Transactions of the Royal Society (Part I. 1860, p. 189). It is
stated that several times in the experiments made on February 9,
1822, the word of command to fire was heard after the report of
the gun; and though the same circumstance was not remarked
on other days, it is to be said that on that day the number of
experiments was greater than on any other, the distance was in-
termediate to what it was on most of the other days, and the air
was still and barometer low. Taking all circumstances into
account, the experiment seems to establish the fact of an actual
difference of rate of propagation in waves of different intensities.
Cambridge, March 21, 1862.
XLV. Notices respecting New Books.
A Manual of Chemistry, Descriptive and Theoretical. By W. On-
tinc, M.B., F.R.S. Part I. London: Longman and Co. 1861.
nppHE Unitary notation of Laurent and Gerhardt, although it has
made many disciples, does not as yet possess a complete lite-
rature of its own. It is true that there constantly appear, in Bri-
tish and foreign scientific journals, memoirs in which the unitary
formulze and an appropriate nomenclature are used. Yet although
this has been the case for several years, and many fresh converts
from among the most eminent chemists have joined the new sect,
the doctrines of Gerhardt, with the modifications and additions made
from subsequent experience, have not been embodied in a series of
text-books adapted for the instruction of the young student, nor of
works of reference for the more advanced. This is the more remark-
able since it seems almost customary for every professor of che-
mistry to write a manual of his science, which he can oblige his own.
pupils to buy, even if he is unable to persuade the scientific world
todoso. Nine out of every ten such works could well be spared: for
they resemble one another very closely; and even of some cf those
whose success was at first merited, later issues have retained old
fallacies and omitted newly-discovered facts ; for when will chemical
authors cease to talk of sulphuric and oxalic acids as monobasic, and
to introduce these bodies quite commonly into descriptions and equa-
tions as SO’ and C*O*? But we are in real want of one complete
set of treatises in which the various branches of chemical science
proper shall be treated systematically according to the new view ; and
we welcome the first instalment of Professor Odling’s contribution
to the series.
As necessary chemical works, we may suggest the following :—
1. A short, simple, introductory book explaining the scope and lan-
guage of chemistry, and describing fully the way of performing a
Notices respecting New Books. 323
few easy and instructive experiments; such a book as every student
might go through previously to attending lectures or entering the
laboratory. It might also be used as the elementary school-book of
chemistry. 2. A text-book of the most important chemical facts
and theories. 3. A complete dictionary or work of reference. 4. A
set of manuals of analysis, qualitative and quantitative. As to the
first of these works, we do not at present possess in the English
language a simple compact introduction to chemistry on the unitary
system ; but Prof. Odling has undertaken to supply the second book of
the series; for the third we must wait; while the commencement of
a set of analytical manuals was made more than three years ago, For
in November 1858 an important original work was published, which
Prof. Odling by a strange oversight neglects to notice, although he
mentions in his preface a much smaller handbook which was after-
wards issued, of no particular excellence, but owing any merit it
may possess to the German work of Prof. Will, on which it is based.
This adaptation by Mr. Conington attempts to embrace too much,
while it lacks the clearness and precision attained in the systematic
treatise of Messrs. Northcote and Church. The plan of the latter
volume seems to anticipate in some of its details the subsequent
work of Prof. Odling. re
The author, in the portion of his Manual now before us, devotes
thirty pages of Chapter I. to a brief outline of the generalities of the
science. These, however, are not treated with such fulness and
simplicity as to enable the beginner to read the present volume
without previous initiation into the general principles and termino-
logy of chemistry. For at the twentieth line of Chapter I. the stu-
dent is introduced precipitately to ‘‘ chlorous and basylous functions,”
and then told what is meant by this delightful expression in a couple
of sentences which imply previous acquaintance on the student’s
part with several chemical truths. ‘Thisreminds one of, Dr. Miller’s
plan of drawing the attention of the young student of organic che-.
mistry in the first place to glycyrrhizin, a substance whose constitu-
tion and relations are, it must be admitted, somewhat obscure.
In the paragraphs on Combination by Volume, Comparable Vo-
lumes, Equivalent Substitutions, and Molecular Types, many im-
portant principles are tersely explained; while the descriptions given
of Homologous, Isologous, and Heterologous series are illustrated by
well-selected examples. We may cite the two following sets of hete-
rologues, remarking en passant that Prof. Odling has shown, by an
experiment of his own, that it is possible actually to pass, by a pro-
cess of direct oxidation, from the first to the second member of the
hydrochloric acid series :—
HCl Hydrochloric acid. H?P _Phosphamine.
HClO Hypochlorous acid. H*® PO Phosphoric aldehyd.
HClO? = Chlorous acid. H* PO? Hypophosphorous acid.
HClO’ = Chloric acid. H* PO? Phosphorous acid,
HCl10* Perchloric acid. H? PO* Phosphoric acid,
-§§ 16-22 are devoted to the consideration of acids and salts. The
324 Notices respecting New Books.
author’s general formula for an acid (H,R,O,) can scarcely be
adapted to the non-oxygenized, binary, or hydrogen acids; for it
renders necessary the qualification that ‘“O, may range from 0.”
The basicity of acids is clearly explained by appropriate instances,
such as the following, drawn from the monobasic, bibusic, and tri-
basic acid of phosphorus :—
KH PO? H* PO? Hypophosphorous ) acids
KO HPO KE PO: H?PO* Phosphorous and
EPO Kk? HPO*K HPO H*®PO* Phosphoric salts.
As instances of derived acids, we have Na?CO?® and Na’ CS?,
(oxy)carbonate and sulphocarbonate of sodium: K* PO* and K* PO*S,
(oxy)phosphate and sulphoxyphosphate of potassium. ‘The relation
of anhydrides to acids is shown by the following scheme :—
Acids. Anhydrides.
SSeS —_—e
Penogic: .ccce 29H. 10% — HOS oF
Sulphuric.... H?SO* — H?O=S O°
Phosphoric,... . 20> PO*> —3 Hh? O/— 2" OF
Rilicic Hs occ H* Si0*— 2H?O = SiO?
‘ A class of curious bodies, the true relations of which have not -
been generally discerned, find suitable places in some of the series
given in the present volume. Among these substances the aldehydes
are most conspicuous. ‘They are usually found as chlorine-substi-
tution products of the normal aldehydes, and bear the same rela-
tions to their respective oxacids as common aldehyde bears to acetic
acid. In the following Table, the connexion between certain chlor-
aldehydes and their acids is traced :—
Chlor-aldehyds. Acids.
Nitries st he Cl NO?+ H’?O= HCl+H NO? (HO) NO?
Sulphuric .. Cl?SO? + 2H’?O = 2HC1+ H’SO* or { toys0
Phosphoric.. CPO + 38H*O=3HCl-+ H*PO* (HO)? PO
“Tt is observable that the conversion of normal aldehyds into
acids by oxidation may be represented as an exchange of hydrogen
H, for peroxide of hydrogen HO, analogous to the above-illustrated
exchange of chlorine for peroxide of hydrogen.”
The following illustrations of the four primary types put their
relations into a very clear light :—
Prot-equivalent Bi-equivalent Ter-equivalent Tetr-equivalent
radicles. radicles. radicles. radicles.
HCl—H=C!l'
Chlorine.
H?O0—H=HO’' |H?O—H*=0"
Eurhyzene. Oxygen.
H? N—H=H?N’ |H? N—H?= HN" H? N—-HW=N"”
Amidogen. Imidogen. Nitrogen.
H* N—H=H? C'|B* C — H?= H°C"|H* C— BH? =HC"”/H! C— H'=C"”
Methyl. Methylene. Formyl. Carbon.
a
Notices respecting New Books. 325
Professor Odling, with Laurent, Gerhardt, Kekulé, and others,
regarding double decomposition as the great type of chemical action,
enlarges the usual definition of it so as to include the direct union of
two elements, the substitution of one element for another, the break-
ing up of a compound into its elements, and the liberation of a single
element in the free state.
Compound radicals are regarded by our author as not necessarily
existent in bodies, but as molecular groupings capable of transference
from one body to another. Thus substances known to be mutually
related in derivation and behaviour are capable of being viewed as
related to one another in constitution also.
The general considerations conclude with an account of crystallo-
graphy, of the various states in which chemical substances occur,
and of atomic volume, atomic heat, and the diffusion of gases.
In the systematic description of the elements and their compounds,
hydrogen, as the great typical element, comes first, the other ele-
ments, beginning with the non-metallic, being considered in order
according to the gradually increasing complexity of their relations to
hydrogen. An excellent feature of the volume is here apparent,
namely, the strict order which is invariably followed in treating each
subject; but this feature becomes still more marked when our author
passes on to the consideration of the ‘‘monhydric elements.” He
gives us the requisite information about each element in the same
manner :—1. Distribution. 2. Preparation. 3. General Properties.
4. Relations. And at the end of each group of elements, such as
that which includes chlorine, bromine, iodine, and fluorine, we have
a useful summary of their general properties and relations. The
remainder of the volume is occupied by the dihydric and trihydric
elements and their compounds,-—the dihydric elements being oxygen,
sulphur, selenium, and tellurium: and the trihydric, nitrogen, phos-
phorus, arsenic, antimony, and bismuth. In the summary of the
nitrogen group, with which Part I. concludes, we have some notes
on ‘‘ Mixed Types,” and the following interesting contrast between
the parallel oxacid compounds to which chlorine, sulphur, and phos-
phorus respectively give origin :—
Monhydric. Dihydric. Trihydric.
HCl HS HP
HC1O Cl’SO Cl? PO
HC10° Cl’ SO? HPO?
HC1O* H? SO? Hee Os
HC1O* H? SO! He, PO*
under review. Prof. Odling has made but few and slight alterations
in the commonly received names of chemical compounds: the exam-
ples given below illustrate some of the more conspicuous changes :—
Chloronitrous gas .......... NOC, becomes nitrous chlor-aldehyd.
Terchloride of phosphorus .. Cl? P, becomes phosphorous chlor-aldehyd.
Oxychloride of phosphorus .. Cl’ PO, becomes phosphoric chlor-aldehyd.
Sulphochloride of phosphorus Cl’ PS, becomes’sulpho-phosphorie chlor-aldehyd.
Chlorosulphurous acid.,,... Cl?SO, becomes sulphurous chlor-aldehyd,
326 Royal Society :—
While the author feels no hesitation in calling Ayposulphite of
sodium thiosulphate, a change which will be scarcely relished by
photographers, he has scruples about altering sulphamide into sulpho-
diamide, saying (p. 228), ‘‘ sulphamide ought analogically to be called
sulphodiamide, and sulphimide sulphamide; but the use of these two
words to signify the compounds expressed above is too general to
allow of their alteration.” We confess that we have not heard or
seen much either of sulphamide or sulphimide ; but our chemical ex-
perience has been perhaps too limited. The free use, as an equiva
lent notation, of dashes attached to the symbols, is an important
feature of the work, and has already been employed with great ad-
vantage by Prof. Kekulé in his Lehrbuch der Organischen Chemie.
_ The volume before us is characterized by a force and precision of
style, and by a happy originality of view, which it would require
long quotations properly to illustrate, and which render the work a
valuable contribution to English chemical literature.
XLVI. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from p. 238.]
Apri 25, 1861.—Major-General Sabine, R.A., Treasurer and Vice-
President, in the Chair.
ae following communication was read :— :
“On the Synthesis of Succinic and Pyrotartaric Acids.” By
Maxwell Simpson, Esq., M.B.
Since my last communication to the Society*, I have succeeded
in obtaining the cyanide of ethylene in a state of purity by a slight
modification of the process 1 have already given. A detailed account
of it will be found in the paper which accompanies this abstract.
This is, I believe, the first example of a diatomic cyanide. It has
the following properties in addition to those I have already enume-
rated :—Below the temperature of 37° Cent. it is a crystalline
solid of a light-brown colour, above that temperature it is a fluid oil.
Its specific gravity at 45° Cent. is 1:023. It has an acrid dis-
agreeable taste. It is neutral to test-paper. It is decomposed by
potassium, cyanide of potassium being formed. Its solution in water
is not affected by nitrate of silver. Heated with nitric acid, it gives
succinic acid and nitrate of ammonia. Heated with muriatic acid, it
yields the same acid and muriate of ammonia. It forms an inter-
esting compound with nitrate of silver, which was obtained in the
following manner :—About three equivalents of crystallized nitrate
of silver were rubbed up in a mortar with one equivalent of pure
cyanide of ethylene and a considerable quantity of ether. The ether
was then poured off, and the residual salt dissolved in boiling alcohol.
On. cooling, the alcohol became a mass of brilliant pearly plates.
_ Submitted to analysis, these yielded results agreeing with the for-
* Phil. Mag. 8. 4. vol. xxii. p. 66.
On the Synthesis of Succinic and Pyrotartaric Acids. 327
mula C,H, Cy,+4(AgO, NO,). The crystals are soluble in water
and alcohol, insoluble in ether. When heated, they melt and explode
like gunpowder. They do not detonate on percussion. This com-
pound may possibly throw some light on the constitution of the
fulminates. ; :
I have also slightly modified the process I gave in my last note
for succinic acid. The modified process is very productive, and
yields the acid at once in a state of purity. From 1500 grains of
bromide of ethylene I obtained 480 grains of succinic acid, or nearly
33 per cent. It gave on analysis 40°54 instead of 40°67 per cent. of
carbon.
We are now enabled, thanks to the researches of Messrs. Perkin
and Duppa and of M. Kekulé*, to build up three highly complex
organic acids (succinic, paratartaric, and malic) from a simple hydro-
carbon ; and, what is more important, we are enabled to do this by
processes every stage of which is perfectly intelligible.
With the view of ascertaining whether or not the homologues of
Succinic acid could be obtained in a similar manner, I have endea-
voured to prepare pyrotartaric acid from the cyanide of propylene,
propylene being the radical of propylglycol.
Preparation of Cyanide of Propylene.—A mixture of one equi-
valent of bromide of propylene and two of cyanide of potassium, to-
gether with a considerable quantity of alcohol, was exposed to the
temperature of a water-bath for about sixteen hours. The alcohol
was then filtered and distilled. A liquid residue was thus obtained,
which was dissolved in ether. The body left on evaporating the
etherial solution was then submitted to distillation. Almost the
entire liquid passed over between 265° and 290° Cent. The fraction
distilling between 277° and 290° Cent. was collected apart and ana-
lysed. It gave 62:0 instead of 63:8 per cent. of carbon. This body
cannot be obtained purer by distillation under atmospheric pressure,
as it suffers partial decomposition during the process.
The properties of this cyanide very much resemble those of the
preceding. It differs, however, in its physical state, which is that
of #liquid at the ordinary temperature of the air. It is soluble in
water, alcohol, and ether. It has an acrid taste. It is neutral to
test-paper. It is decomposed by potassium, cyanide of potassium
being formed. Its solution in water does not precipitate nitrate of
silver. Heated with potash, it is resolved into an acid and ammonia.
Formation of Pyrotartariec Acid.—A mixture of one volume of
cyanide of propylene and about 14 volume of strong muriatic acid
was exposed in a sealed tube to the temperature of a water-bath
for a few hours. On cooling, the contents of the tube became a
mass of crystals. These were dried and dissolved in absolute
alcohol. ‘The residue obtained on evaporating the alcoholic solu-
tion was then twice crystallized from water, and finally digested
with ether. The body left on distilling off the ether is the acid in
* Quarterly Journal of the Chemical Society, July 1860; and Bulletin de la
Société Chimique de Paris du Aott, 1860, p. 208.
328 Royal Society :—
question. The numbers obtained on analysis agree very well with
the formula of pyrotartaric acid ; I got 44°6 instead of 45:4 per cent.
of carbon. It had also all the properties ascribed to this acid by
Pelouze and Arppe. The crystals were colourless, and very soluble
in water, alcohol, and ether. It had an agreeable acid taste. It
became semi-fluid at 100° Cent., and melted completely a few
degrees above that temperature. Long-continued ebullition in
a glass tube converted it into an oil, which was insoluble in cold
water, and no longer affected litmus-paper, but which gradually
dissolved in hot water, recovering at the same time its acid reaction.
The following equation will explain the reaction which gives birth
to this acid :
C, H, Cy, +2 H Cl+8 HO=C,, H,O0,+2(N H, Cl).
It is highly probable that there exists a series of isomeric acids
running parallel to these, which may be obtained by similar pro-
cesses from the diatomic radicals contained in the aldehydes. Thus
from cyanide of ethylidene (C,H,Cy,) we may hope to get an
isomer of succinic acid.
I propose to continue my researches in this direction, and to ex-
tend them to the cyanides of the triatomic radicals.
May 2.—Major-General Sabine, R.A., Treasurer and Vice-
President, in the Chair.
The following communication was read :—
“On Internal Radiation in Uniaxal Crystals.” By Balfour Stewart,
Esq., A.M.
The well-known theory of exchanges, which was proposed by the
late Prof. Prevost of Geneva, is built upon the fact that a substance
placed anywhere within an enclosure of a constant temperature will
ultimately attain the temperature of the enclosure.
In his theory M. Prevost supposes that a constant, mutual, and
equal interchange of radiant heat takes place between the body and
the enclosure which surrounds it, so that, receiving back precisely
that heat which it gives away, the former is enabled to remain at a
constant temperature.
With respect to this radiation, which is thus supposed to be con-
stantly taking place between substances at the same temperature, it
had until lately been conceived of as proceeding mainly, if not en-
tirely, from the surface of bodies—a very thin film or plate of any
substance being supposed to furnish the maximum amount of radia-
tion which that substance was capable of affording.
It lately occurred to the author of this paper, reasoning from the
theory of exchanges, that mere surface radiation is not sufficient to
account for the equilibrium of temperature which exists between a
body and the enclosure which surrounds it.
These theoretical conclusions have been amply verified by experi-
ment, and the subject has been discussed in a paper published in
the ‘ Transactions of the Royal Society of Edinburgh’ for the year
1858. As the chain of reasoning by which this fact is deduced
Mr. B. Stewart on Internal Radiation in Uniaxal Crystals. 829
theoretically from the law of exchanges, and the experimental evi-
dence upon which it rests, are both of a very simple nature, it has
been thought well to restate them here before proceeding further in
this investigation. : :
Let us imagine to ourselves an enclosure of lamp-black kept at a
constant temperature, and containing two pieces of polished rock-
salt similar to one another, except that the thickness of the one is
greater than that of the other.
Now it is evident that since the thick piece absorbs more of the
heat which falls upon it from the sides of the enclosure than the thin
piece, it must likewise radiate more in order that it may always re-
main at the same temperature. Here then we have the fact of in-
ternal radiation in the case of rock-salt deduced as a theoretical conse-
quence of the law of exchanges ; experimentally it is found that a thick
piece of rock-salt radiates very considerably more than a thin piece.
The fact of internal radiation being conceded, it is easy to see
that the amount of heat which a particle radiates must be indepen-
dent of its distance from the surface. For besides that this is the
simplest hypothesis, the absorption, and consequently the radiation
of two similar plates of rock-salt placed with their surfaces together,
ought to be the same as from a single plate of double the thickness ;
and experiment shows that this is the case.
It being therefore supposed that the internal radiation of a particle
is independent of its distance from the surface, let us imagine a row
of particles A, B, C, D in the midst of a substance of constant tem-
perature which extends indefinitely on all sides of them. There will
be a certain stream of radiant heat constantly flowing past any such
particle A to go in the direction AB.
Now, since the radiation is supposed to be the same for the different
particles A, B, C, D, it follows that the absorption of the stream of
heat by these particles must also be the same for each; and in order
that this may be the case, it is necessary that the stream which im-
pinges on one particle be the same in quantity and in quality as that
which impinges upon another. This consideration leads us to a me-
thod of viewing internal radiation, which is wholly independent of the
diathermanous or athermanous character of the body. For whatever
be the absorption of a particle for any description of heat, its radia-
tion must necessarily be precisely the same in order that the stream
of heat in passing the particle may be just as much recruited by its
radiation as it is reduced by its absorption ; in other words, we may
regard the substance through which the heat passes as perfectly
diathermanous.
We gain another advantage by this method of viewing the subject :
for, in the law which is expressed by saying that the absorption of a
particle is equal to its radiation, and that for every description of
heat, the word description is used to define and separate those rays
of heat which are absorbed in different proportions by the same sub-
stance. Therefore in any problem connected with this subject we
may suppose that a separate equilibrium holds for every such ray.
Now it is well known that rays of different wave-lengths are ab-
sorbed in different proportions by the same substance. We are
therefore entitled to suppose that a separate equilibrium holds for
Phil. Mag. 8. 4. Vol. 23. No. 154, Apri? 1862. Z
330 Royal Society.
each wave-length. The advantage of this is obvious in problems
which admit of the application of optical principles. But we may
go even further. For we know that in tourmaline, and in some other
crystals cut parallel to the optic axis, the ordinary ray is more ab-
sorbed than the extraordinary ; and the experiments of Prof. Kirch-
hoff and the author have shown that im tourmaline the ordinary ray
is also radiated in excess. It thus appears that, in the case of crystals,
we have not only a separate equilibrium for each wave-length, but
for each of the two rays into which the incident ray is divided.
The following method of comparing together two streams of radiant
heat has been adopted :—Consider a square unit of surface to be
placed in the midst of a solid of indefinite thickness on all sides, and
find the amount of radiant heat which passes across this square unit
of surface in unit of time in directions very nearly perpendicular to
the surface, and comprehending an exceedingly small solid angle d¢.
Call this heat_ Rdg, then R may be viewed as the intensity of the
radiation in this direction.
Let us now suppose that we have a uniaxal crystal of indefinite
thickness bounded by a plane surface, and that parallel to this sur-
face, and separated from it by a vacuum, we have a surface of lamp-
black, the whole being kept at a constant temperature.
Let us take a square unit of this surface, and consider the heat
from the lamp-black which falls upon it through an exceedingly
small solid angle in a direction not necessarily perpendicular to the
surface. Part of this heat will be refracted into the interior of the
erystal in two rays, the ordinary and the extraordinary. There will
be thus two separate bundles of refracted rays, the solid angle com-
prised by the individual rays of the one being different from that
comprised by the rays of the other; the inclination to the surface
also being different for each bundle.
Now, on the principle of a separate equilibrium for each ray, these
entering bundles of rays must respectively equal the rays of the same
kind which emerge from the crystal in the same directions.
Hence if we know the radiation of lamp-black, and the direction
in which the rays under consideration strike the surface of the crystal,
as also the angle which the latter makes with the optic axis, it is
conceivable that, by means of optical principles, jomed to the fact of
the equality between the entering and emerging bundles of rays, we
may be enabled ultimately to ascertain the internal radiation through
the crystal in different directions.
A little consideration, however, will show that this method of pro-
cedure presupposes a certain mutual adaptation to exist between the
optical principles employed and the theory of exchanges. For it is
evident that the expression for the internal radiation in any direction
may be obtained by operating upon terminal surfaces bearing every
possible inclination to the optic axis.
But the internal radiation, if the law of exchanges be true, is
clearly independent of the position of this surface, which is indeed
merely employed as an expedient. This is equivalent to saying that
the constants which define the position of the bounding surface must
ultimately disappear from the expression for the internal radiation.
The author then endeavours to show that such an adaptation does
Geological Society. 331
really exist, and that the expression for the internal radiation is in-
dependent of the position of the surface.
For the extraordinary ray, the internal radiation is found to be
ake ia
nee
where R is the radiation from lamp-black ;
dud
a pe
where » denotes the axial and m the equatorial radius of the
ellipsoid into which the extraordinary ray will have spread in the
erystal in the same time that zm vacuo it would have spread into a
sphere whose radius = unity ; and lastly, r denotes the radius of this
ellipsoid in the direction in which the internal radiation is measured.
The author concludes by remarking that the fundamental law,
which is intimately connected with the theory of exchanges, and
which renders an equilibrium of temperature possible in the case
_under consideration, seems to be the law of the equality between
action and reaction in the impact of elastic bodies.
He also considers that the law which is expressed by saying
‘That the absorption of a particle is equal to its radiation, and that
for every description of heat,’’ expresses another law of action and
reaction which holds when the motion which constitutes radiant heat
is not conveyed from particle to particle without loss, or when the
bodies under consideration are not perfectly elastic.
These two laws of action and reaction are viewed as supplement-
ing each other, so as to render that equilibrium of temperature which
is demanded by the theory of exchanges possible under all circum-
stances.
and for the ordinary, R,
GEOLOGICAL SOCIETY.
[Continued from p. 244.]
January 22, 1862.—Sir R. I. Murchison, V.P.G.S., in the Chair.
. The following communications were read :—
1. «‘On some Flint Arrow-heads (?) from near Baggy Point, North
Devon.” By N. Whitley, Esq.
Immediately beneath the surface-soil above the ‘‘ raised beaches ”
of North Devon and Cornwall the author has observed broken flints ;
and even at the Scilly Isles such flints are found. At Croyde Bay,
about halfway between Middle-Borough and Baggy Point, at the
mouth of a small transverse valley, Mr. Whitley found them in con-
siderable number, collecting about 200 specimens, of which about 10
per cent. of the splintered flints at this place have more or less of an
arrow-head form, but they pass by insensible gradations from what
appear to be perfect arrow-heads of human manufacture to such rough
splinters as are evidently the result of natural causes. Hence the
author suggested that great caution should be used in judging what
flints have been naturally, and what have been artificially shaped.
2. “ Onsome further Discoveries of Flint Implements in the Gravel
near Bedford.” By James Wyatt, Esq., F.G.S.
Since Mr. Prestwich described the occurrence of flint implements,
Z2
332 Geological Society :—
near Bedford (Geol. Soc. Journ. No. 67, p. 366) Mr. Wyatt, Mr. Nall;
the Rev. Mr. Hillier, and Mr. Berrill have added seven or eight to the
list, from the gravel-pits at Cardington, Harrowden, Biddenham, and
Kempston. Mr.J.G. Jeffreys, F.G.S., having examined Mr. Wyatt’s
further collections of Shells from the gravel-pits at Biddenham and
Harrowden, has determined seventeen other species besides those no-
ticedby Mr. Prestwich, and among these is Hydrobia marginata (from
the Biddenham pit), which has not been found alive in this country.
At Kempston, Mr. Wyatt has examined the sand beneath the gravel
(which is destitute of shells), and at 3 feet in the sand (19 feet from
the surface) he found Helix, Succinea, Bithynia, Pupa, Planorbis, &c.
with a flint implement. The upper gravel contained several flint flakes.
3. “On a Hyena-den at Wookey-Hole, near Wells, Somerset.”
By W. Boyd Dawkins, Esq., F.G.S.
In a ravine at the village of Wookey-Hole, on the southern flanks
of the Mendips, and two miles N.W. of Wells, the River Axe flows
out of the Wookey-Hole Cave by a canal cut in the rock. In cutting
this passage, ten years ago, a cave, filled with ossiferous loam, was’
exposed and about 12. feet of its entrance cut away. In 1859
the author and Mr. Williamson began to explore it by digging away
the red earth with which the cave was filled, and continued their
operations in 1860 and 1861. ‘They penetrated 34 feet into the
cave; and here it bifurcates into two branches, one vertical (which
was examined as far as practicable), and one to the right (left for
further research). A lateral branch on the left, not far from the en-
trance, was also examined. The cave is hollowed out of the Dolo-
mitic Conglomerate, from which have been derived the angular and
water-worn stones scattered in the ossiferous cave-earth. Its great-
est height is 9 feet, and the width 36 feet; it is contracted in the
middle, and narrow towards the bifurcation. Remains of Hyena spelea
(abundant), Canis Vulpes, C. Lupus, Ursus speleus, Equus (abun-
dant), Rhinoceros tichorhinus, Rh. leptorhinus (?), Bos primigenius,
Megaceros Hibernicus, C. Bucklandi, C. Guettardi, C. Tarandus (?),
C. Dama (?), and Elephas primigenius were met with; remains of
Felis spelea were found when the cave was first discovered. The
following evidences of man were found by Messrs. Dawkins and Wil-
liamson in the red earth of the cave—chipped flints, flint-splinters,
a spear-head of flint, chipped and shaped pieces of chert, and two bone
‘arrow-heads; and the author argues that the conditions of the cave
and its infilling prove that man was contemporaneous here with the
extinct animals in the pre-glacial period (of Phillips), and that the
cave was filled with its present contents slowly by the ordinary ope-
rations of nature, not by any violent cataclysm.
February 5, 1862.—Sir R. I. Murchison, V.P.G.S., in the Chair.
ie following communications were read :—
«On some Volcanic Phenomena lately susemved at Torre del
eee and Resina.”” By Signor Luigi Palmieri, Director of the Royal
Observatory on Vesuvius. In letters addressed to H.M. Consul at
Naples, and dated December 17th, 1861 and January 3rd, 1862.
The evolution of gases,—the outburst of springs of acidulous and
Mr. E. Hull on the Distribution of Sedimentary Strata. 3338
hot water,—and particularly the upheaval of the ground at Torre del
Greco to. a height of 1:12 métre above the sea-level, are mentioned
in this communication.
2. ‘On the Recent Eruption of Vesuvius.” By M. Pierre de
Tchihatcheff.
M. Tchihatcheff’s observations were made at Torre del Greco and
Naples from December 8th to 25th. Near Torre del Greco several
small craters (9-12) have been formed close to each other in an
E.N.E.—W.S.W. line, at a distance of about 600 metres E.S.E. of the
crater of 1794, and either on a prolongation of the old fissure or on
one parallel. The phenomena mentioned by Signor Palmieri were
also described by M. Tchihatcheff in detail.
3. “On Isodiametric Lines as means of representing the Dis-
tribution of Sedimentary (clay and sandy, Strata) as distinguished
from Calcareous Strata, with especial reference to the Carboniferous
Rocks of Britain.” By HE. Hull, Esq., B.A., F.G.S.
The author, in the first place, made a comparison of argillaceo-
arenaceous with calcareous deposits, as to their distribution, both in
modern and in ancient seas, and stated that he objected to calcareous
strata being regarded as sediments, in the strict sense of the word.
After noticing the distribution of sediments in the Caribbean Sea, he
referred to the relative distribution of limestones as compared with
shales and sandstones in the Oolitic formations (comparing those of
Yorkshire with those of Oxfordshire), in the Permian strata of Eng-
land, and in the Lower Carboniferous strata of Belgium and West-
phalia. After some observations on the nature of calcareous deposits,
and on the contemporaneity of certain groups of deposits, dependent
on the oscillatory movements of land and sea, the author described
his plan of showing on maps the relative thicknesses of the two classes
of strata under notice, by means of isodiametric or isometric lines.
Mr. Hull then proceeded to indicate the application of the isodia-
metric system of lines to the Carboniferous strata of the midland
counties and north of England; showing that there is a south-east-
erly attenuation of the argillo-arenaceous strata, and a north-westerly
attenuation of the calcareous strata. The existence, in the Carbo-
niferous Period, of a barrier of land crossing the British area, imme-
diately to the north of lat. 52°, was insisted upon; and, although
this barrier was probably broken through (in South Warwickshire)
in the latter portion of that period, yet it divided, in the author’s
opinion, the coal-area into a north and a south portion, the latter
having a very different set of directions in the attenuation of its
strata—the shales and sandstones thinning out eastward, the lime-
stones in the contrary direction.
In conclusion, the author stated that, in his opinion, the source of
the Carboniferous sediments was in the ancient North Atlantic Con-
tinent, for the existence of which Lyell, Godwin-Austen, and others
have argued; and he inferred that the shores of this Atlantis, com-
posed principally of granitoid or metamorphic rocks, were washed on
the west side by a current running 8. W., which drifted the sediment
in that direction, and on the other by a current running S.E., which
carried sediment oyer the submerged British area,
rr Seaa* |
XLVII. Intelligence and Miscellaneous Articles.
ON THE PROBABLE CAUSE OF ELECTRICAL STORMS.
BY DR. J. P. JOULE, F.R.S.
NHE very close correspondence between the theoreticalrate of cool-
ing in ascending, and the actual, indicates a rapid transmission
of the atmosphere from above to below, and vice versd, continually
going on. We may believe that during thunder-storms this inter-
change goes on with much greater than ordinary rapidity. Ata
considerable distance from the thunder-cloud, where the atmosphere
is free from cloud, the air descends, acquiring temperature according
to the law of convective equilibrium in dry air. The air then tra-
verses the ground towards the region where the storm is raging,
acquiring moisture as it proceeds, but probably without much dimi-
nution of temperature, on account of the heated ground making up
for the cold of evaporation. Arrived under the thunder-cloud, the
air rises, losing temperature, but at a diminished rate, owing to the
condensation of its vapour to form part of the immense cumulus
cloud which overcasts the sky on these occasions: The upward
current of air carries the cloud and incipient rain-drops upwards, but
presently, in consequence of the increased capacity of the mass from
the presence of a large quantity of water, the refrigeration of the air
in consequence of its dilatation will be so far diminished as to pre-
vent the condensation of fresh vapour, and ultimately to redissolve
the upper portion of the cloud. ‘This phenomenon, which has been
noticed by Rankine in the cylinder of the steam-engine, will account
for the defined outline of the upper edges of cumulus clouds. ‘The
upward current no doubt extends occasionally to regions below the
freezing temperature. If cloud be carried with it, snow or hail will
be formed, which, if sufficiently abundant, will pass through the ~
cloud and fall to the ground before it is melted. Now the dry cold
air in which the snow and hail are formed is a perfect insulator. Ice
has also been proved, by Achard of Berlin, to be a non-conductor and
an electric. Even water, in friction against an insulator, is known,
from the experiments of Armstrong explained by himself and Faraday,
to be able to produce powerful electric effects ; and this fact has been
suggested by Faraday to explain powerful electric effects in the atmo-
sphere. Sturgeon has noted the remarkable developmentof electricity
by hail-showers. Few heavy thunder-storms occur without the fall of
hail. Hail, whether in summer or winter, is almost, if not invariably,
accompained with lightning. In the presence of these facts it seems
not unreasonable to consider the formation of hail as essential to
great electrical storms, although, as has been pointed out by Prof.
Thomson, very considerable electrical effects might be expected from
the negatively charged air on the surface of the earth being drawn
up into columns, and although, as the same philosopher has observed,
every shower of rain gives the phenomena of a thunder-storm in
miniature. The physical action of insulators and electrics in mutual
friction must certainly produce very marked effects on the grand
seale of nature. If we suppose that the falling hail is electrified by
the air it meets, the electrification of the cloud into which the hail
Intelligence and Miscellaneous Articles. - 835
falls might thus be constantly increased until the balance between
it and the inductively electrified earth is restored by a flash of light-
ning. If the hail is negatively electrified by the dry air with which
it comes in contact, the latter will float off charged with positive
electricity, which mzy account for the normal positive condition of
the atmosphere in serene weather, as well as the electrification of
the upper strata evidenced by the aurora borealis. The friction of
wind has been supposed by Herschel to contribute to the intense
electrification of the cloud which overhangs volcanoes during erup-
tion.—From the Proceedings of the Literary and Philosophical Society
of Manchester, March 18, 1862.
ON THE INFLUENCE OF HEAT ON PHOSPHORESCENCE.
BY M. O. FIEBIG. :
The author has investigated the deportment of several phosphor-
escent bodies in reference to heat—whether phosphorescence could be
developed by heat alone, without the substance having been previously
submitted to the action of light. The sulphides of calcium, of barium,
and of strontium were prepared by the method of M. Becquerel, and
their phosphorescence confirmed. These substances, observed in
darkness, ceased to be luminous at the expiration of a certain time,
and were then subjected to the calorific action of a plate heated some-
thing below redness. Phosphorescence reappeared, but after a second
disappearance it could not be reproduced by the same method. A
fresh exposure of the substance to light rendered the substance again
phosphorescent.
An analogous experiment was made with a fragment of green
fluoride of calcium. According to M. Becquerel, this substance
becomes phosphorescent under the action of heat until it has lost
colour; but in this condition it has lost the property. A strong
elevation of temperature developed at first an intense violet light in
the fluoride of calcium ; after having been cooled it was again heated,
but to a less extent than at first; the fragment remained quite
dark, although it had retained its colour, which was seen by expo-
sing it to daylight. In a third case it was strongly heated until
decrepitation commenced; phosphorescence again appeared, and
when viewed by daylight it had lost its colour. Nevertheless,
heated afresh it again became luminous. These experiments show
that fluoride of calcium possesses the property of becoming phos-
phorescent under the action of heat after a previous insolation, and
that this property remains after the loss of colour.
M. Fiebig has also investigated the influence of heat upon the
phosphorescence of two liquids, zsculine and quinine. When a solu-
tion of the former is gradually heated, the blue tint at first becomes
deeper, and tends towards violet ; it then becomes paler, and at about
50 degrees it can scarcely be distinguished from the ordinary tint.
On continuing to heat it, the tint diminishes in intensity, becoming
of a pale green. In the case of a solution of quinine, the tint dimi-
nishes considerably in intensity when near the boiling-point. In
both liquids, cooling reproduces the ordinary colour.—Poggendorff’s
Annalen, October 1861.
336. Intelligence and Miscellaneous Articles.
RESISTANCE TO THE CONDUCTION OF HEAT.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
I am indebted to Professor Clausius of Zurich for having pointed
out an oversight in some tables of coefficients of resistance to the
conduction of heat which appeared some time ago in a work of
mine ‘On the Steam-engine and other Prime Movers.’ Those
coefficients were computed from data given by M. Peclet; but in
the computation the difference of the French and British units of
weight (the kilogramme and the pound) was neglected. _ I now beg
leave to send you the annexed Tables of the corrected values of those
coefiicients. Their meaning will be best understood by the aid of
the following formula. |
Conceive two media, whose temperatures, in degrees of Fahren-
heit, are respectively T’ (the higher), and T (the lower), to be sepa-
rated from each other by a layer of any given substance, whose
thickness, 7m znches, is denoted by a.
Let g denote the number of British units of heat (degrees of Fahr-
enheit) in a pound avoirdupois of water transmitted from the hotter
to the colder medium, per square foot of surface, per hour.
Then the resistance of the layer means the following quantity :—
T'—T l
hha jee
the first term being the internal resistance, and the second the super-
ficial resistance.
Values of the coefficient of internal resistance, p.
Gold, Platinum, Silver ...... ‘0016
Copper cyan noo me legs eee se OOKS
Dron yt cieyie te aus ee iadce seas pacer se) AL ey
LOCH teas ages ce BS aa ee eae °0045
ead We ere ober mereh we aay cae ‘0090
Marble cp: 3052 acenais asctets bee OG
BIC resus ets eta eae eae °1500
Values of A.
Water on both sides of the conducting layer. 8°8
Water on one side, air on the other :—
Polished metallic surfaces.......... 0:90
Dull metallictsurtaces en cee ee 1°58
Glass and varnished surfaces ...... isi
Surfaces coated with lampblack .... 1°74
Values of B.
Water on both sides of the conducting layer. 0°0580 —
Water on one side, air on the other :—
Polished metallic surfaces.......... 0:0028
Rough and non-metallic surfaces.... 0°0037
I am, Gentlemen,
Your most obedient Servant,
Glasgow, March 17, 1862. W. J. Macquorn RANKINE-
Vol. 28. PU LV.
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THE
LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
MAY 1862, ;
XLVILI. On some Apparatus for determining the Densities of
Gases and Vapours. By M. V. Reanavurt*,
[ With a Plate. ]
HE density of a gas or of a vapour at a temperature T and
under a pressure H, is the relation between the weight
P’ of a volume V of this gas or vapour, and the weight P of an
equal volume of atmospheric air at the same temperature T, and
under the same pressure H. If the gas or the vapour obeyed
exactly the same laws of expansion and elasticity as atmospheric
air, within the range of temperatures and pressures in which it
retains the aériform state, the density would be the same at all
temperatures and under all pressures; it would constitute a
specific character of the substance.
But experiment shows that this identity of laws does not
exist even for the most permanent gases, for those which have
not yet been liquefied. It shows further that the divergencies
of the laws of expansion and compressibility are greater for
vapours, and even that they often continue up to temperatures
much higher than that at which the vapour would assume the
liquid state under the same pressure. The density of a gas or
of a vapour, as just defined, is therefore not represented by a
constant number; it varies with the temperature and pressure,
and these variations are often very considerable.
It is necessary in physics to define two kinds of densities for
gases and vapours :—
1. The real densities, which vary with the temperature and
pressure; they ought to be determined by numerous experi-
ments, in which the temperatures and pressures are varied
within considerable limits. These densities are represented by
* Translated from the Annales de Chimie et de Physique, vol. Ixui. p, 45.
Phil. Mag. S. 4. Vol. 23. No. 155. May 1862. 2A
338 M.V. Regnault on some Apparatus for determining
a function of the temperature and of the pressure, the numerical
coefficients of which have been deduced from experiment; im
other terms, the density is one of the coordinates of a surface, of
which the two others represent the pressure and the temperature.
2. Theoretical or limit densities—These are what would be
found by operating on temperatures so high, and under pres-
sures so feeble, that the gas or vapour would follow exactly the
same laws of expansion and elasticity as atmospheric air under
an increase of temperature or a diminution of pressure to which
it is subjected. These mit densities obtain with all gases,
and with all vapours when they are subjected to an extreme
expansion, and if the temperature is sufficiently high. They
are the only ones which could be of use in studying the com-
position of a compound gas expressed in volume relatively to the
volumes of the simple gases of which it is formed..
Thus, when the densities of gases and vapours are determined
simply with reference to the constitution of bodies, the limit
density, or one nearly approaching it, ought to be sought. It
is hence desirable that the apparatus with which densities are
determined should be so constructed as to be easily used to
ascertain whether if, starting from the temperature and pressure
which prevailed in the apparatus during the experiment in
which a density is to be deduced, the gas or vapour follows the
same laws of expansion and elasticity as atmospheric air, for
small variations of temperature and pressure to which it is
subjected.
To satisfy these conditions in determining the density of a
gas, and of that of the vapours of bodies which only boil at very
high temperatures, I constructed some years ago the apparatus
represented in figs. 12, 18, 14, Plate I]. The receiver in which
the gas or vapour is measured consists of a tube A B, 3 or 4 centi-
metres in diameter, terminating below ina tube B ¢, 2 centimetres
in diameter, and above in a capillary tube AJ, provided with a
steel stopcock 7. The lower tube is hermetically fixed in an ap-
paratus of castiron, cdef. In the piece cde f there is a second
tubulure ef, in which the long open tube C D is fixed; cdef is
firmly screwed on an iron tripod M N PQ, which is furnished
with levelling-screws V, V. A strong plate of sheet iron, pqs,
the shape of which is seen in fig. 13, is fixed on ede f by means
of the screws u, uw and of red-lead cement. Lastly, a semi-
cylinder, ghz, of sheet lead, of which one side is a wrought-
iron frame, EF GH (fig. 12), is fixed on the sheet-iron plate
xa«ax by means of red-lead cement. The open face of the cy-
linder is closed by a pane of plate-glass, fixed by means of a
second iron frame exactly like the first, fastened down by screws
z, 2,2 (fig. 12). A plait of hemp, well stuffed with red lead, is
the Densities of Gases and Vapours. -. jad
interposed between the glass and the iron frames. This junc-
tion, which is made once for all, soon becomes hermetically
tight.
The experiment is conducted in the following manner.
The sheet-lead casing with its transparent glass is raised from
the sheet-iron base pq s after the screws 2, x, x have been taken
out. The tubes AB and CD are adjusted in their tubulures.
Fig. 14, which represents a magnified vertical section of the piece
edef, shows sufficiently the mode of adjustment. I will merely
say that the tube Be or the tube C D is coated with a plait of
hemp well stuffed with red-lead cement, and the plait is strongly
screwed on the annular spaces oo by means of the screws K, L,
The tubes AB, CD ought to be quite parallel. They are ad-
justed in a vertical position by moving the levelling-screws V, V.
I assume that the density of a gas is to be determined at
various temperatures and under different pressures.
The stopcock R being in the position 3 (fig. 8), mercury is
poured into the open tube C D, anda vacuum made by means of
the air-pump which is fixed to the stopcock 7. The vacuum is
made several times, dry air being admitted each time. The
object of this is to make the insides of the tube AB completely
dry. The stopcock R is then gently turned into the position 1
(fig. 8), while the vacuum is still produced in the tube AB;
the mercury from CD passes into the tube AB. The stop-
cock 7 is closed when the level of the mercury reaches the sum-
mit of the capillary tube Ad. The tube 4m is connected with
a bell-jar full of the gas whose density is to be determined, or
with the apparatus which disengages it in a state of purity;
the stopcock 7 is opened, and mercury allowed to flow out from
the tube A B by placing the stopcock R in the position 4 (fig. 8),
The stopcock r is closed, and the stopcock R placed in the posi-
tion 1 (fig. 8) as soon as enough gas has been introduced into
the tube AB; the quantity varies according to the conditions of
compression or of expansion under which the gas is to be studied.
The tubes AB and CD are divided into millimetres. Ina
preliminary experiment, the capacities of the tube AB corre-
sponding to the divisions traced on the tube have been determined
with great accuracy, by weighing the quantity of mercury which
fills these capacities, and successively allowing them to run out
by the stopcock R placed in the position 2 (fig.8). The casing
EFGH is now adjusted on the sheet iron pqs, and this case
is filled with water at the temperature at which the experiment is
to be made. This water is kept in continual motion by a stirrer,
and its temperature is maintained quite uniform. By allowing
mercury to flow out by the stopcock R, or by adding it to the tube
CD, the same quantity of gas may be successively put under the
| 2A2
840 M.V. Regnault on some Apparatus for determining
pressures H, H’', H", and the spaces V, V', V" noted which it
occupies in the tube AB. The lowest pressure under which this
apparatus could be worked would be that for which mercury
would stop at D in the tube C D, and the highest would be that
in which the mercury would stand at the top C of this tube.
These limits might be indefinitely increased by connecting C D
with a reservoir W, in which the air is either exhausted or com-
pressed. The elastic force of the air in this reservoir is measured
by a barometric pressure-gauge (fig. 15) when the air is expanded,
or with an ordinary manometer when it is compressed. The
mercury may also be kept at the saine level in both tubes A B
and C D.
These experiments may be repeated by raising the water in the
bath successively to gradually higher temperatures, and keeping
the temperature constant during each series of determinations.
There are thus all the elements necessary for knowing the law of
the compressibility of the gas for various temperatures.
The same experiments give all the data necessary for calcula-
ting the coefficient of expansion of gases under different pres-
sures. ‘The experiments may be made so as to determine the
real expansion of the gas, the latter being always under the same
pressure at different temperatures; or so as to measure the
change which the elastic force of the gas undergoes for variations
of temperature, its volume remaining the same.
To deduce from these experiments the density of a gas under
different pressures and at different temperatures, its weight must
be known. For this purpose different means may be employed,
according to the chemical properties of the gas. The most
general method consists in having a globe provided with a stop-
cock, which, by means of a capillary tube of platinum, silver, or
copper, can be exactly fitted on the prolongation 6m of the tube
AB. Vacuum having been produced in this globe, the gas con-
tained in the tube AB is passed into it, and the globe again
weighed by the method of compensating-weights. The increase
in the weight of the globe gives the weight of the gas. The gas
can frequently be absorbed directly by chemical agents—for
instance, carbonic acid, sulphurous acid, sulphuretted hydrogen,
ammonia, &c. In this case the tube dm is connected with an
apparatus containing the absorbing substance; the weight of the
gas is indicated by the increase in weight of the absorbing sub-
stance. Lastly, in many cases the weight of gas may be deter-
mined by chemical analysis: thus, for the carburetted hydrogens -
and the various gases of organic chemistry, the gas from the
tube AB is made to pass through an apparatus for organic
analysis.
The same apparatus can be readily used for vapours, The
the Densities of Gases and Vapours. 341
liquid to be determined almost exactly fills a glass bulb, closed
at the lamp, and the weight of which is known. The case
EFGH being detached, the screw ¢ (fig. 13) is loosened, and
the tube AB removed. The bulb is placed in the tube AB,
which is replaced in its original position and dried (as has been
already described, p. 339), by exhausting and allowing dry air to
enter. Lastly, the vacuum being continued, the stopcock R is
placed in the position 1 (fig 8); the mercury completely fills the
tube AB, and the stopcock r is closed when the mercury has
reached it. The bath is replaced and filled with water, and its
temperature raised by means of a lamp placed beneath it until
the liquid by its expansion breaks the bulb. The mercury
remains raised in the capillary tube Ad, and_hence neither the
liquid nor its vapour come in contact with the stopcock r.
The water in the bath is gradually raised to various tempera-
tures, and, by means of arrangements which I have already
described, the volume is measured which the vapour occupies at
different temperatures and under different pressures. The pres-
sures may be made to vary from the lowest limits up to eight or
ten atmospheres. We may thus determine at once, and within
very extensive limits,—
Ist. The laws of the compressibility of vapour at various tem-
peratures.
2nd. Its coefficient of expansion at various degrees of the ther-
mometric scale, the pressure remaining constant at different
temperatures, while the volume of the vapour alone varies, the
pressure varying within considerable limits.
ard. The increase of the elasticity of the vapour in conse-
quence of the increase of temperature, the volume remaining
constant, and the original pressure varying within considerable
limits.
4th. The real density of the vapour at different temperatures
and pressures.
Sth. The amit density of the vapour, which is that to which
the real density constantly epproximates when the pressure is
diminished and the temperature raised. |
The apparatus further gives the elastic forces of saturated
vapours for various temperatures; for it is merely necessary to
keep the pressure so that, while the temperatures gradually
increase, liquid remains condensed on the surface of the mercury,
though the vapour occupies part of the space of the tube A B.
Lastly, it may be used to measure the clastic forces of vapour,
either saturated or not, in air, or in other gases, at various tem-
peratures and pressures. For this purpose, the bulb having been
introduced into the tube A B, air or the gas (dry) is allowed to
enter by the stopcock 7, The elastic force and the volume of
342 M.V. Regnault on some Apparatus for determining
the gas alone are measured at a known temperature T. The
bulb is then ‘broken, and a series of experiments made under
varying temperature and pressure. From that, the elastic force
of saturated vapour in gases for all cases in which liquid remains
on the surface of the mercury, and the laws of the elasticity and
expansion of the mixture of gases and of vapour at different degrees
of saturation, may be deduced. Lastly, the elastic force of the
vapour in the gas may be determined at the moment at which
dew commences to be deposited in the tube AB. A large
number of examples of these determinations will be found in
vol. xxvi. of the Mémoires de Académie.
It often happens that the fragments of the broken bulb hinder
the exact reading of the level of the mercury in the tube AB.
This inconvenience is easily avoided by allowing the tube A B to
terminate in a narrower part L, slightly spheroidal (fig. 16).
The bulb is lowered to this cavity, and retamed there by a
small spiral of platmum; the remains of the bulb remain
then almost entirely on the spiral.
We shall readily understand the advantages which this method
presents over those hitherto used for determining vapours ; for
it furnishes at the same time a great number of other elements,
a knowledge of which is necessary in order to know what use
can be made of the density from the point of view of our chemical
theories. It might be feared that it was only applicable to very
volatile substances; for the temperature of the bath cannot
much exceed 100°, even when the vessel is filled with a saline
solution. But I must say that, for shghtly volatile substances,
which in general have high vapour-densities, it is especially
interesting to determine their vapour-densities under very feeble
pressures, because the limit density is thereby approximated to.
Now it is always possible to realize these favourable conditions
when the boiling-point does not exceed 200° under the ordinary
atmospheric pressure.
Apparatus for determining the Vapour-density of Substances which
boil at High Temperatures.
The very simple apparatus represented in figs. 10 and 11,
Plate II., may be used for a small number of imperfectly volatile
substances, the vapours of which do not readily alter in contact
with the air. ‘Two vessels, A, B, cast in iron of the same thick-
ness, terminate in small tubes which are closed by bullets placed
above. The capacities V and V' of the two flasks are gauged, by
ascertaining the weight of water which fills them. Mercury is
poured into one of them, A; and in the other is placed the sub-
stance whose vapour-density is to be determined. The apparatus
being thus arranged, is placed in a muffle heated to a high tem-
the Densities of Gases and Vapours. — 848
perature. The substances soon begin to boil, expel the air,
and escape by the tubes, which are very imperfectly closed by
the ball. When the apparatus is of the same temperature as the
mufile, it is withdrawn, and, after cooling, the weights of mercury
and of the substance respectively in the flasks A and B are
determined.
abet
P be the weight of mercury.
P’ that of the substance.
6 the density of mercury, compared with air under the pres-
sure and at the temperature which prevailed in the muffle
when the apparatus was withdrawn.
The density of vapour under the same conditions will be
!
v=35
_ In my Cours élémentaire de Chimie, 5th edit. vol. iv. p. 66, I
have given the arrangement of an apparatus analogous to that
which M. Mitscherlich has employed for substances boiling at
high temperatures; I simply endeavoured to obtain more equal
temperatures for the air-thermometer and the vapour-tube by
imparting a continual rotatory niotion to the system of the two
tubes in the muffle in which it is heated, and which has several
metallic envelopes. This apparatus can be simplified and made
more convenient now that the use of gas prevails in labora-
tories. It consists of three tubes of wrought iron closed at one
end, and resembling gun-barrels; they are 50 centims. in length,
and 20 millims. internal diameter. Fig 17 represents the longi-
tudinal section of one of these tubes; A B is the part which is
50 centims. in length. On each of two of these tubes is screwed
an additional piece BC of the same diameter, and on the second
tube anarrower tube,C D. On the third tube, which is intended
as a gas-thermometer, a sinule iron tube (fig. 18) B! C’ is screwed,
which is of almost capillary bore, and is terminated by a stopcock.
These three tubes, whose dimensions are quite similar, fit upon
the same iron bar II’, of which figs. 19 and 20 give a cross
section, I. Fig. 19 shows by a section how the three iron
tubes A are arranged in reference to the central bar I. The bar
is longer than the iron tubes; it is firmly fixed on two cast-iron
_ supports P P’ (fig. 21), arranged so that the bar is exactly on the
notch. ‘he three tubes are thus in a fixed position. This system
of the three tubes is surrounded by a cylinder EF of copper
or of sheet iron, which fits almost exactly, but so, however,
that the cylinder may be made to rotate rapidly about a hori-
zontal axis, II’. A sheet-iron disc abe (fig. 20), fitted on the
central bar 11, and almost exactly filling the cylinder E F, forms
344 On some Apparatus for determining the Densities of Gases.
the base of this cylinder, at a distance of a decimetre from the
end A of the tubes AB. The other end of the cylinder is open ;
it corresponds to about the middle of the tube CB. This cylin-
der may be made to move rapidly about its axis by means of a
rackwork, one of whose toothed wheels, F', is mounted at the
end of the cylinder EF. A gas-furnace, like those used for
organic analysis, serves to heat the cylinder to a strong red heat.
To make an experiment, the apparatus being arranged, a por-
tion of the substance whose vapour-density is to be determmed
is introduced into each of the similar iron tubes, and the screw
B put in its place. The air which fills the three tubes is first
eompletely expelled; for this purpose pure dry hydrogen is
allowed to enter by means of a capillary silver tube, which is
introduced by the tube CD, until its open end touches the
closed end A of the tube AB. When the air is expelled the
silver tube is withdrawn, and by means of an india-rubber tube,
C D, is connected with an apparatus which disengages hydrogen.
In fine, the three iron tubes, including that which serves as gas-
thermometer, remain during the rest of the experiment in con-
nexion with an apparatus for disengaging hydrogen under the
atmospheric pressure.
The gas-furnace is lighted, and its temperature raised as
rapidly as possible; the substances converted into vapour expel
the gas; the excess of vapour condenses in the half of the tube
BC which is not contained in the heated metallic eylinder EF.
In order to spread the heat uniformly over the three iron tubes,
the heated metallic cylinder which surrounds the fixed system
of tubes is continuously and rapidly turned.
The experiment is concluded by closing the stopcock of the
gas-thermometer, extinguishing the lamps, and cooling the
apparatus. The temperature of the gas-thermometer is deter-
mined by the method I have mentioned.
To ascertain the weight of vapour which filled the two other
tubes at the moment of maximum ‘temperature, the screws B
are unfastened, and the substance which is condensed in the
tube AB is determined by chemical methods.
The operation is much simpler when it is not attempted to
determine the temperature by a gas-thermometer, but simply to
seek the ratio of the density of the vapour of the substance to
that of mercurial vapour, the two vapours being under the same -
circumstances of temperature and of pressure. It is simply
necessary then to place mercury in one of the tubes A B, and to
weigh the mercury which remains in the space A B after the
experiment.
The volumes of the three tubés have been determined pre-
viously.
[ 345 ]
XLIX. Note on the Correction for the Length of the Needle in
Tangent-galvanometers. By G. Jounstone Stoney, M.A.,
F.R.S., Secretary to the Queen’s University in Ireland.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN, Dublin, April 7, 1862.
oe ZENGER, in the Supplement to the December
Number of the Philosophical Magazine, which has just
been published, couples my name in so pointed a manner with a
formula which he criticizes, that I am compelled, though wholly
averse from controversy, to ask you to be so goed as to insert
the following note in reply.
T am, @eneleinens
Yours faithfully,
G. JOHNSTONE SronE
Until I read Professor Zenger’s remarks*, I was under the
impression that the formula
Pe ian (1+ Py2sin%),
whichis a necessary result of the known laws of electro-magnetism,
had been, either in this or some equivalent form, long adopted
by physicists as the expression which furnishes the correction
arising from the length of the needle of a tangent-galvanometer
of the usual pattern, on the hypothesis that » (the ratio of the
distance between the poles of the needle to the diameter of the
circular current) is sufficiently small to sanction our neglecting
its fourth power.
Prof. Zenger does me too much honour in supposing me the
author of this formula. I do not know by whom it was origi-
nally investigated; but it had been, as I mentioned{ at the
commencement of the paper which he criticizes, known to, and
extended by, other writers before me. What I sought to con-
tribute to our knowledge of the subject was an examination from
which it appeared that no alteration of the formula becomes
necessary when the ordinary tangent-galvanometer is out of ad-
justment in that shght degree likely to occur in practice ; whereas
the simpler formula for Gaugain’s galvanometer requires, under
similar circumstances, corrections which it would be difficult to
apply.
* Philosophical Magazine, Supplement for December 1861, p. 529.
t Professor Zenger seems to misunderstand this symbol. ‘See his defj-
nition of A on the top of page 530.
~ Phil, Mag. February 1858, p. 135,
346 Mr. G. J. Stoney on the Correction for the
After quoting this formula, the Professor proceeds to deduce
one which he proposes to substitute for it; but as his funda-
mental assumption, p!/=p.f (6d), is at variance with the familiar
fact that the action of the element of a current on a magnet de-
pends on its inclination as well as its distance, it is not necessary
to scrutinize another hypothesis inconsistent with that just stated,
which he afterwards introduces*.
The formula thus obtained through a disregard of the laws
ascertained by Ampére, is supported by experiments which
appear equally independent of those due to Ohm. The internal
resistance of an electromotor was varied by immersing the plates
successively to different depths, and observations are recorded
with the assumption that the mtensity of the current changed in
the same ratio, although there does not seem to have been any
alteration made of the external resistance. I need not, then, con-
test other parts of the experiment, although I believe it would be
difficult to render the method by which the change of internal —
resistance was estimated practically trustworthy; nor need J
dwell on the peculiarity of testing the established formula, ez-
pressly limited to cases in which the needle is sufficiently short to
warrant our neglecting the fourth power of X, by making experi-
ments with a galvanometer the needle of which had, to use
Prof. Zenger’s description of it, an “ enormous length.”
Under all these circumstances, it can scarcely be matter of sur-
prise that no accordance was found between the observations and
the established formula: and we seem compelled to regard the
moderate agreement which was obtained between an erroneous
formula and faulty experiments as a coincidence without scien-
tific import. :
Although the topic is quite unconnected with Prof. Zenger’s
remarks, whom the error seems to have escaped, I may be
allowed to avail myself of this opportunity to correct a mistake
in my paper, to which Prof. Curtis of Queen’s College, Gal-
way, was so good as to direct my attention some months ago.
Having examined the corrections occasioned by a derangement
from its intended position of the magnetic centre of the needle,
regarded as the point round which the needle rotates, I endea-
voured?+, by a merely geometrical process, to include the error
which a separation between the pomt of suspension and the
magnetic centre would introduce. This was done under the mis-
* Professor Zenger’s equation,
S:S’=AN?; AN2
(see p. 530), is mathematically inconsistent with his former hypothesis. It
is equally inconsistent with Ampeére’s law. ;
+ Phil. Mag. February 1858, p. 138.
Length of the Needle in Tangent-galvanometers. 347
apprehension that the moment which arises is of a higher order
of small quantities than those included in the rest of the inves-
tigation, whereas it is of the same order. Accordingly another
term, with 6 for its coefficient, and therefore of the second order,
needs to be added to the general equation numbered (5) in
my paper. This term is easily calculated: but, without being at
the pains of going through the work, it is easy to see that it will
behave exactly as the other small terms which have been ineluded.
In fact the new term arises from the difference of the action of the
current on the two poles of the needle; and as this difference
would gradually decrease to ni if the centre of the needle
were moved from the position it occupies in Gaugain’s galvano-
meter into the position it has in the ordinary galvanometer, it is
plain @ priori that the most considerable term of the series ex-
pressing the moment (which is of the second order of small
quantities) vanishes as the needle approaches the latter posi-
tion.
Hence no term of the second order needs to be added to for-
mula (6), which has reference to the common galvanometer ; but
- a new term of that order should be added to formula (7), which
relates to Gaugain’s instrument,—thus leaving the conclusion at
which I arrived undisturbed, that, “though in Gaugain’s galva-
nometer we get rid of the trouble of applying a correction for
the length of the needle, it is necessary to attend carefully to
the position of the needle in its cradle, and to the horizontal
adjustments of the point of suspension, lest errors should creep
in of which it would be impossible to make any exact estimate ;”’
and that “in conducting investigations in which accuracy is a
point of much importance, the ordinary form of tangent-galva-
nometer is to be preferred.” (Phil. Mag. February 1858, p. 139.)
It may be well to add that the small moments arising from
the other defects of adjustment which could exist (such as a slight
lateral displacement of the.axis of rotation from the line joining
the poles, or a slight dipping of the needle, either when at the
meridian, or from the state of equipoise ceasing when it deviates
from the meridian) all yield to a precisely similar treatment,
and all corroborate the same conclusion.
This remark may be extended to the effects of small deviations
of the current-wire from the circular form, which therefore do
not ever sensibly disturb the law of the common tangent-galva-
nometer, but might be such as would render Gaugain’s instru-
ment inaccurate.
ee"
L. On the Position of Lievrite in the Mineral Series. By ¥. J.
Cuapman, Professor of Mineralogy and Geology in University
College, Toronto, Canada HWest*.
M UCH uncertainty still prevails regarding the true compo-
sition of Lievrite or Ilvaite. The earlier analyses of this
mineral, those of Vauquelin and Collet-Descotils, made the sub-
stance essentially a silicate of sesquioxide of iron and lime.
Stromeyer’s analysis, which followed those of the above-named
chemists, gave the iron, on the other hand, as protoxide. 16°33
Cae shh) Lae 4-11.
Although these values do not come out exactly equal, they
lead evidently to the common chrysolite formula 2(RQ), Si0°.
If we adopt, consequently, the assumption on which the above
calculation is based, the Lievrite falls naturally-into the minera-
logical group to which it undoubtedly belongs; whereas on the
other view, founded on the bare results of analysis, not only
does the atomic constitution of the mineral remain uncertain,
but its composition fails to harmonize with its physical characters
and conditions. The suggestion, therefore, embodied in this
brief notice may not be found altogether unworthy of considera-
tion by those engaged in the study of mineral analogies.
LI. On a Question in the Theory of Probabilities.
By A, Cayiry, Lsq.*
T is, I think, very desirable to further consider the question
in Probabilities proposed by Prof. Boole in the Cambridge
aud Dublin Mathematical Journal in the year 1851. The ques-
tion was originally stated as follows :—“ If an event E can only
happen as a consequence of some one or more of certain causes
A,, A,g...A,, and if generally c; denote the probability of the
cause A;, and p; the probability that if the cause A; exist the
event EH will happen, then, the series of values ¢,, Co... €ny
Pp Po+++Pn being given, required the probability of the event H.”
Considering only the causes A and B, the proposed question -
may be considered as being—
“Tf the event E can only happen as a consequence of one or
both of the causes A and B; and if & be the probability of the
existence of the cause A, p the probability that, the cause A ex-
isting, the event E will (whether or not as a consequence of A)
happen; and in like manner if 8 be the probability of the exist-
ence of the cause B, q the probability that, the cause B existing,
the event K will (whether or not as a consequence of B) happen :
required the probability of the event E.”
This, which is strictly equivalent to Prof. Boole’s mode of sta-
ting the question, may for convenience be called the Causation
statement. But his solution, presently to be spoken of, is rather
a solution of what may be termed the Concomitance statement of
* Communicated by the Author.
Theory of Probabilities. 353
the question: viz., if for shortness we use AE to denote the com-
pound event A and K, and so in other cases; and if we use also
A! to denote the non-occurrence of the event A, and so in other
eases (of course (AE)', which denotes the non-occurrence of the
event AE, must not be confounded with A/E’, which would de-
note the non-occurrence of each of the events A, E), then the
question is, “ Given
Prob. A‘BIE, = 0,
”? Av = a,
2 ee,
”? B a B,
» BE, = £9;
required the probability of E.””? To show that the two state-
ments are really distinct questions, it may be observed that when
A and B both exist, then, according to the causation statement,
they may one or each of them act efficiently, and HE may thus
happen as an effect of one of them only, or as an effect of each
of them; but, according to the concomitance statement, Ei can-
not be attributed rather to one of the events A, B, than to the
other of them, or to both of them.
The solution which I gave in the year 1854 (Phil. Mag.
vol. vil. p. 259) refers to the causation statement of the question,
and assumes the independence of the two causes*; and on this
assumption I believe it to be correct. And I remark, in passing,
that in the strictest sense of the word cause, all causes are ex v2
termini independent. ‘The solution was as follows:—Let wu be
the required probability ; A the probability that A acting, it will
act efficiently ; y the probability that B acting, it will act effici-
ently ; then we have
u=ra+yB—rpaP,
pHrx+ (1 —r) up,
q= # +(1—p)re;
and eliminating), » from these equations, we have the required
probability w.
As I did not further work out the solution, I omitted to state
the relations of inequality presupposed among the data «, 8, p, q,
or to show how the sign of the quadratic radical in the resulting
expression for wu was to be fixed. The omissions in question
were supplied by Dr. Dedekind, in his paper ‘‘ Bemerkungen zu
einer Aufgabe der Wahrscheinlichkeitsrechnung,” Credle, vol. 1.
* It is part of the assumption, that the causes do not combine to produce
the effect : viz. if they both act, the effect is not produced unless one of
them acts efficiently ; they may or may not each of them act efficiently. .
Phil. Mag. S. 4. Vol. 23. No. 155. May 1862. 2B
354° Mr. A. Cayley on a Question in the
p. 268, 1855. In fact, writing for shortness «! =1—«; &e., we.
have
u—ap = Balu,
u—Bg=2B)r ;
and thenee
B'+Bq—u=f'(1—an),
a! +-0q —u=al(1—By),
which gives
(a! —ap—u)(8! + Bg—u)=a'B'(1—u) ;
that is,
—u(a! + ap + B+ By—a'B!) + (a! + ap) (6! + Bq) —2'B'=0;
or, what is the same thing,
— @—u(l—-aB+apt+Bq)utelBq+aBlp+«Bpq=0;
and thence
u=3(l—eB+ap+Bq—p),
where
p’= (1-48 +ap+8q)?—4(aip + a!Bg + a8 pq),
which may also be written
p?=(a! —af! + ap —8q)?+ 4a! B'p!,
= (6'— Ba! —ap + Bg)? +48 B'al¢!
=(1 —a8 +ap—q)?—4e8'(p—Bq),
| =(1 —a8 —ap+ Bq)? —4a'B(q—ap) ;
and we then have
Balw=3(1—a8—ap+Bq—p),
Blak=3(1—aB +ap—Bq—p).
As probabilities, a Bp; a a all of them poe and less
than unity (so that a’, @', p’, g! are all positive) ; > U, A, &, Which
are also probabilities, must tee be positive, and less than
unity : and in order that this may be so, it is necessary and suf-
ficient that
P#By, gap,
and that p shall denote the positive square root of the above-
mentioned value of p?. The solution is therefore inapplicable,
unless the data are such that :
pth gap.
It may be added that, the values of X, w being known, the
solution gives the probabilities of all the compound events ABE
&e,: thus
‘Theory of Probabilities. : 855
Prob. A'B/E', = «'6',
ABE, = «Br,
ABE, = af'n,
» ABE, = a! Bu,
A'BE!, = a/Bu’;
» ABE, = «B(A+p—Ap),
ABE! = aBr py,
It will be remembered that
Prob. AUB veer),
Prof. Boole’s solution, which is inconsistent with the foregoing
one, is given in his well-known work, ‘ An Investigation of the
Laws of Thought,’ &c. Dublin, 1854, p. 321 ef seg. Although
given as a solution of the causation statement of the question, as
already remarked, it seems to be (and I think Prof. Boole would
say that it is) a solution of the concomitance statement of the
question. It is certaimly a most remarkable and suggestive one ;
I am strongly inclined to believe that it is correct; which of
course does not interfere with the correctness of my solution, if
the two really belong to distinct questions.
I reproduce Prof. Boole’s solution, without attempting to ex-
plain (indeed [ do not understand to my own satisfaction) the
logical principles upon which it is based. It is conducted by
means of the auxiliary quantities 2, y, s, ¢, which are quantities
replacing logical symbols originally repr esented by the same let-
ters. I will designate these quantities, without attempting to
explain the meaning of the term, as Boolian Probabilities, viz.
+ Boolian Prob. A = 2,
Bd AES == 5,
” Lhe eS Y;
ie BE = 7;
and, as before, z', &c. are used to denote 1—x, &c. The
required probability of EH is taken to be u.
The event A can, by the data of the question, only happen
in concomitance as follows : viz, the concomitant events are
Boolian Probs.
A. AK .B.BE asyt
A. AE. B! (BE)! Disiuts
AY (AR) (BE)! Sih
which may be analysed as follows: viz. if A and AE, then either
B and BE or B’ and (BE)'; but if A and (AE)’, then (B or B!
but of necessity) (BH)’. And this being so, the sum
asyt + xsy't! + as't!
2B2
356 Mr. A. Cayley on a Question in the
is assumed to be proportional to the given probability & of the
event A; viz. the ratio in question is equal to that of the corre-
sponding sum for all the possible events to unity.
The entire series of possible events is
Boolian Probs.
A.AE.B. BE xsyt
A. AE. B!.(BE) xsy't!
A',(AE).B . BE x'sly t
(AE)! .. (BE)! st,
which may be analysed as follows: viz. if AE and BE, then of
necessity A and B; if AK and (BE)’, then of necessity A and B’;
if (AE)! and BE, then of necessity A’ and B; but if (AB)! and
(BE)’, then at pleasure A and B or A and B’, or A! and B or A!
and B!: the sum proportional to unity therefore is
xsyt +asy't! + a'slyt+s't'.
Now in the same manner as with a, dealing with the remaining
given quantities ep, 8, Bq, and with the required quantity u, we
have
xsyt + asy't! + xs't! |
a
__ asyt+a's'yt+slyl! |
_ xsyt + asy't!
ep
__ asyt +alslyt - (L)
ie
__ asyt + xsy't! + alslyt + s't!
ae 1
__ asyt + axsy't! + a!slyt | |
Se ee
each of which is also }
— a'sty't!
~ A'BIE!
xsy't!
ABE
asly!t!
ABE!
ax's!yt
Theory of Probabilitics. 357
meee Sate
~~ A'BE!
_ axsyt
~ ABE
a axs'yt!
=) ABs
where, to avoid multiplication of symbols, I have used A’B/E,
&c. to denote the probabilities of the compound events A’B'E’,
&c. if these probabilities should be sought for.
We have thus five equations to determine x, y, s, t, u; these
equations give
ES ASU) See
u—ep u—Bq 1l—w
and
Ca Wy SG Nea tg SECU
atap—u B'+Bq—u ap+Bq-wu’
and we have thence
(u—ap) (u—q)(1—u) = (a! + ap—u)(6' + Bq—u) (ap +Ba—u).
Putting, for shortness,
ap=a,
bq=),
al +ap =f,
b'+ Bq=9,
a) ep Bg=
the equation in u 1s
—(u—1)(u—a)(u—b)
+ (u—f)(u—g(u—2) =0
viz. it is
w(1+a+b—f—g—h)—u(at+b+ab—fg—fh—gh) +ab—fgoh=0;
or, since h=a+4J, this is
w(1—f—9) —u(ab—fy + h(1—f—g)) +.ab—fyh=0,
which is easily transformed into
u?. (up! + Bq—1)
—u.{ (ap! + Bq! —1)(ap+B¢+1)+aB8(pq—p'g)}
+ a8 pq — (a! + ap)(8'+ Bq) (4p +89) =.
And we then have
ap! + Bq —1)(ep+ Bg +1) +48(pq—p'q') +o
2(ap' + Bq'—1) SOs
os
358 Mr. A. Cayley on a Question in the
where
o?= { (ap! + Bq! —1) (ap + Bq4+1)+48(pq—p'q')}?
—4(ap! + Bq! —1) (a8 pq—(a! + ap) (6! +8) (ap + B9)).
In order that u may represent the required probability, it is
necessary and sufficient that it shall be
Pig vl ara
a,
Theory of Probabilities. 361
respectively. But this is an immediate consequence of the given
values prob. A=a, prob. B=, and of the deduced equation
prob. AB=0.
2 Stone Buildings, W.C.,
March 18, 1862.
The foregoing paper was submitted to Prof. Boole, who, in a
letter dated March 26, 1862, writes :—
“The observations which have occurred to me after studying
your paper are the following.
Ist. “TI think that your solution is correct under conditions
partly expressed and partly imphed. The one to which you
direct attention is the assumed independence of the causes de-
noted by A and B. Now I am not sure that I can state pre-
cisely what the others are; but one at least appears to me to be
the assumed independence of the events of which the probabili-
ties according to your hypothesis are «A, Bu. Assuming the
independence of the causes as to happening, I do not think that
you are entitled on that ground to assume their independence as
to acting ; because, to confine our observations to common expe-
rience, we often notice that states of things apparently indepen-
dent as to their occurrence, may, when concurring, aid or hinder
each other in such a manner that the one may be more or less
likely to act ‘efficiently’ in the presence of the other than in
its absence. I use the language of your own hypothesis of effi-
cient action.
« 2ndly. When I say that I think your solution correct under
certain conditions, I ought to add that it appears to me that
such conditions ought to be stated as part of the original data,
and that they ought to be of such a kind that they can be esta-
blished by experience in the same way as the other data are.
For instance, if experience, as embodied in a sufficiently long
series of statistical records, establish that
Probe A—25) Prob: b= 8,
the very same experience may, by establishing also that
Prob. Aba:
whence in conjunction with the former it follows that
Prob. AB'=cf!', Prob. A’B=a'8, Prob. A'B!=a'f',
enable us to pronounce that A and B are in the long run, as to
happening or not happening, in the position of mutually inde-
pendent events.
‘© 3rdly. I think it may be shown to demonstration, from the
nature of the result, that the solution you have obtained does
not apply simply and generally to the problem under the single
362 Mr. A. Cayley ona Question in the
modification of the assumption that A and B are independent.
The completed data under this assumption are
Prob: A=e, Prob. B=; Prob. AB=ef;
Prob. AE=ap, Prob. BE=8zq.
You may deduce all these from your Table of probabilities of
‘compound events’ given in your paper. Now you may easily
satisfy yourself that the sole necessary and sufficient conditions
for the consistency of these data are the following :—
(1) ap'+BqSe8. )
(2) ap +Bq'S a8.
(3) wien aac -
" = 0:
But your solution requires the following conditions to be satisfied,
viz. 3
qg—p>0, p—&y> 0,
together with the system (3). Now (1) and (2) are expressible
in the form
B(q—ap)+ aBip' = 0,
| «(p—Bq) + Ba'g' = 0.
From which you will see that your conditions are narrower than
those which the data are really subject to. If your conditions
are satisfied, the data will be consistent; but the converse of this
proposition does not hold. |
“Athly. You remark that my solution of the problem, in which
the independence of A and B is not assumed, but in which the
probabilities are otherwise the same as in yours, is only appli-
cable when
al-tap=Bq, 6'+8q = ap;
but you do not appear to have noticed that these are actually
the conditions of consistency in the data. Unless these are satis-
fied, the data cannot possibly be furnished by experience.
“5Sthly. You remark that I have solved the problem under what
you call the ‘ concomitance’ statement, and not the ‘ causation’
statement. I think that every problem stated in the ‘causation’
form admits, if capable of scientific treatment, of reduction to the
‘concomitance’ form. I admit it would have been better, in
atating my problem, not to have employed the word ‘cause’ at
all. But the introduction of the hypothesis of the independence
of A and B does not affect the nature of the problem.
Theory of Probabilities. 363:
“6thly. The x, s, &c., about the interpretation of which you
inquire, are the probabilities of ideal events in an ideal pro-
blem connected by a formal relation with the real one. I
should fully concede that the auxiliary probabilities which are
employed in my method always refer to an ideal problem; but
it is one, the form of which, as given by the calculus of logic, is
not arbitrary. Nor does its connexion with the real problem
appear to me arbitrary. It involves an extension, but as it
seems to me, a perfectly scientific extension, of the principles of
the ordinary theory of probabilities. On this subject, however,
I have but little to add to what I have said, Transactions of
_ the Royal Society of Edinburgh, vol. xxi. part 4, ‘On the Ap-
plication of the Theory of Probabilities, &¢.’
“7thly. The problem, as stated by me, and then modified by
the simple introduction of the hypothesis of the independence of
A and B, must admit of solution by my method; and that solu-
tion ought to impose no restriction beyond the conditions of
possible experience noted in (M).
“J should be extremely glad if mathematicians would examine
the analytical questions connected with the application of my
method. There can, I think, after the partial proofs which I
have given, exist no doubt that the conditions of applicability of
the solutions: are always identical with the conditions of consist-
ency in the data, z. e. with what I have called, in the paper above
referred to, the conditions of possible experience. The proof of
the general proposition would involve the showing that a certain
functional determinant consists solely of positive terms, with
some connected theorems which appear to me to be of consider+
able analytical interest.
“8thly. I certainly think your paper deserving of publication.
If you think proper to add any or the whole of my remarks, you
can do so, with of course any comments of your own.”
I remark upon Prof. Boole’s observations :—
Ist. I do assume that the causes A and B are absolutely in-
dependent of, and uninfluenced by each other; viz. not only the
probability of A acting, but also the probability of its acting
efficiently, are each of them the same whether B does not act, or
acts inefficiently, or acts efficiently ; and the like for B.
2ndly. I do assume that the same experience which establishes
Prob. A=a, Prob. B=8,
would in the long run establish
Prob. AB=a8 ;
' if it does not, cadit questio, the causes are not independent.
364 On a Question in the Theory of Probabilities.
Srdly. I assume not only
Prob. A=, ‘Prob. B=, ‘Prob. AB=aB,
but also as Ist above stated; and I consider that, inasmuch as
the result of the investigation is to show that the conditions
g—ap a
+* os
Prof. Clausius on the Conduction of Heat by Gases. 419
- In answer to the objection that so great a mobility as I assume
ther molecules to possess must cause two gases which are in
contact with each other to mix very quickly, I have shown in a
former paper that the space moved through by each individual
molecule must be exceedingly small. Inreference to this, Joch-
mann says (p. 156), “ Even if we consider this as disposing of
the objection derived from the mixture of gases, it by no means.
disposes of the other, namely, that local variations in the tem-
perature of a gas would be impossible, but that a uniform mean
velocity must very soon be established throughout the mass.
Seeing that the irregular motions of the gaseous atoms cannot be
easily presented to the mind, let us make use of a simple analogy
im order to assure ourselves that the two points are essentially
different. Suppose a row of similar, perfectly elastic balls placed
_ at equal distances from one another in astraight line. Ifa certain
velocity be imparted to the first ball so as to cause it to strike the
second centrally, it is true that, the movement propagating itself
through the whole row, each ball will only alter its position as
much as the distance between two balls; but the velocity im-
parted to the first will propagate itself through the whole series
about as quickly as if the first ball had continued to move onward
without encountering any obstruction.”
Jochmann thus does not take the matter as it is into consi-
deration, but gets over the difficulty which the consideration of
it certainly does offer, by selecting as analogous a very much
simpler case. This case is, however, so entirely different from
the one it is supposed to represent, that no inference whatever
ean be drawn from the one respecting the other. If we wish to
arrive at really reliable conclusions concerning this and other
allied subjects, we must not be afraid of the somewhat trouble-
some consideration of the irregular motions. Of course this
does not preclude the use here and there of assumptions which
help us to avoid useless complication in calculations; but these
assumptions ought always to be of such a kind that we see clearly
that they cannot affect the result*,
The Philosophical Magazine for 1860 (vol. xix. p. 19, and
vol. xx. p. 21) contains an interesting memoir by Prof. Maxwell,
* Hoppe has also made the same objection, on essentially similar
grounds, in two papers, the last of which (Pogg. Ann. vol. cx. p. 598) is a
reply to a note published by myself. He says expressly, p. 603, ‘‘ The cases
in which two molecules that meet each other are unequal, or do not strike
centrally, can plainly cause no alteration in the general result.”” The word
plainly appears to me to be by no means in place here; on the contrary, I
believe that the maccuracy of the opinion which has been quoted will be
made clearly evident by what follows. I leave the reader to form his own
opinion of the other remarks occurring in Hoppe’s reply, for lam unwilling
to inflict upon the scientific public a mere dispute about words, :
F 2
420 Prof. Clausius on the Conduction of Heat by Gases.
entitled ‘ Illustrations of the Dynamical Theory of Gases,” in
which also the question of the conduction of heat is considered.
In this memoir, which is remarkable for the elegance of its mathe-
matical developments, the motion of small bodies is regarded
from very general points of view, and many valuable results are
arrived at in it; nevertheless I do not believe that its contents
are correct in every point. JI am more particularly of opinion
that the author has treated the conduction of heat too incom-
pletely ; and although his formula differs but little from that
which we shall deduce, important differences nevertheless occur
im respect to other matters, to which I shall refer in their proper
places, and which make it appear that the close agreement of the
ultimate formula is merely accidental.
The general importance of the phenomenon of the conduction
of heat, and the slight attempts that have hithertobeen made to
ascertain the real nature of the process upon which it depends,
induce me to think that I shall be justified in submitting this
process, and the entire condition of gaseous bodies by which it
is accompanied, to a closer mathematical treatment upon the
foundation of the hypothesis which I have hitherto advocated,
and in thus endeavouring to deduce the laws of the conduction
of heat by gases. I venture also at the same time to point out
that the principles which will be followed in this investigation
are capable of being applied, with certain modifications, to many
other cases where the problem is to determine the internal pro-
cesses going on in a quantity of gas, and that the developments
which follow may lay claim in this respect to a more general
significance than the problem treated in the first instanee.
I. Definition of the case to be considered.
§ 1. We will suppose a quantity of gas between two parallel
plane surfaces of infinite size, each of which is maintained at a
constant temperature. If the temperature of one surface is
higher than that of the other, a transference of heat from one
surface to the other will take place, through the medium of the
gas, by the continual passage of heat from the warmer surface
into the gas, its advance from one layer to the next within the
gas itself, and its being at last given up by the gas to the colder
surface. As it is our object to consider here only that movement
of heat which is caused by conduction, and not that which might
be occasioned by currents of gas produced by the warmer por-
tions being specifically lighter than the colder, we will suppose
the action of gravity entirely excluded: this is approximately
the case when the two surfaces are horizontal and the hotter is
above, for then no currents can arise,
Prof. Clausius on the Conduction of Heat by Gases. 421
If both surfaces are kept for a considerable time at constant
temperatures, a state of equilibrium is at length established in
the gas, of such a kind that the temperature remains invariable
at each point within it, but is different at different pomts—the
heat being so distributed that, in any plane parallel to the two
limiting surfaces, the temperature is the same at every point, but
that it continually decreases according to a definite law in the
direction from the warmer to the colder surface. A definite and
constant flow of heat through the gas then takes place.
It is this stationary condition of the gas that we have to con-
sider, and to endeavour to determine the amount of the flow of
heat which goes on owing to the conductive property of the
gas. .
§ 2. We will suppose a straight line drawn between the two
surfaces and perpendicular to them, and we will assume this as
the axis of abscissee: the temperature within the gas is then a
function of the abscissa x ; and if, in order to be able at once to
form a definite conception, we assume that the first surface, where
the abscissa has its smallest value, is the warmest, the tempera~
ture diminishes within the gas as the value of z increases. With
the density of the gas the case is reversed, for in a state of equi-
librium the density of the gas must be higher in proportion as
the temperature of the gas is lower; it is therefore a function of
z whose value increases with that of z.
We will assume at starting that the gaseous molecules fly
about irregularly in all directions, and accordingly strike and
rebound from each other, now in one place, now in another, and
also that the velocity of their motion is greater the higher the
temperature. Let us now suppose a plane cutting the space
filled with gas, and parallel to the surfaces by which this space
is bounded; then during a unit of time a great number of mole-
cules will pass from the negative to the positive side of this plane,
and vice versd. The molecules which pass from the negative to
the positive side have a greater average velocity than those which
pass from the positive to the negative side, since, according to
our assumption, the temperature is higher, and therefore the
moving velocity of the molecules greater, on the negative side of
the plane than on the positive side. The total vis viva which
trayerses the plane in a unit of time in the positive direction is
therefore greater than that which traverses it in the negative
direction; and if we strike out, as compensating each other,
equal quantities which traverse it in opposite directions, we still
obtain a certain excess Of vis viva traversing the plane in the
positive direction. Vis viva and heat being regarded as synony-
mous, the amount of vis viva thus passing through the plane
constitutes the heat-stream mentioned in the last section, which
422 Prof, Clausius on the Conduction of Heat by Gases.
we call conduction of heat, and which we have to consider in
the sequel*,
II. Behaviour of the molecules emitted from an infinitely thin
stratum.
§ 3. We will begin by considering somewhat more closely the
nature of the motions of the individual molecules.
We will suppose two parallel planes to be placed perpendicu-
larly to the axis of x and infinitely near to each other, so as to
enclose an infinitely thin stratum. Since molecules are continu-
ally flying through this stratum in all directions, it must some-
times happen that two molecules strike each other within it and
then rebound again. For the sake of shortness we will call these
molecules, which, after having lost their previous motions by the
impact, leave the stratum again with different motions, the mo-
lecules emitted from the stratum; and we will now fix our atten-
tion upon their motions.
These motions differ very much from each other ; and we must
distinguish between variations of two kinds, occasioned by two
mutually independent causes, and therefore susceptible of bemg
separately considered. The one kind consists of those irregular
variations which always prevail in the molecular motions called
heat, and which would therefore also occur if the gas were of
uniform temperature and density throughout. They arise from
various accidental inequalities accompanying the individual im-
pacts: we will designate them accidental variations. The other
kind of variations is caused by the circumstance of the gas not
having an equal temperature and density throughout. These
variations depend in a definite manner upon the laws which
govern the differences of temperature and density existing in
different parts of the gas: we will call them normal variations.
It is the latter which have especially to be considered in the
conduction of heat, and we will therefore direct our attention
first of all to them. |
* According to what is said above, we take account only, in considering
conduction, of the heat which is inherent in the molecules themselves, and
is communicated by one molecule to another solely by their impact. But
besides this, each molecule radiates heat, which is transmitted by the ether,
and is partially absorbed by other molecules on its way; so that there is
thus also a transmission of heat from one molecule to another. The com-
munication of heat in this way, in the case of bodies of such low radiating
and absorbing powers as the gases, can, however, scarcely be reckoned as
conduction, since the great distances which the rays of heat may traverse
without being absorbed gives it an entirely different character. In any case,
however, it is allowable to consider separately each of these two ways in
which heat moves; and we shall accordingly m the sequel always speak of
the conduction of heat in this sense.
4
Prof, Clausius on the Conduction of Heat by Gases. 428
_ The cause of their occurrence depends, in the case before us,
upon the fact that when two molecules, coming from different
sides, strike each other within the stratum, the molecule which
comes from the warmer side has in general a greater velocity
than the one which comes from the cooler side. The magnitude
of this difference is determined by the distances from the stratum
in question of the points at which the said molecules commenced
their motions; and since the distances through which the mole-
cules move between each two impacts are in general very small,
this difference must also be very small, so that we can regard the
mean value of this difference as a magnitude of the same order
with the mean excursions (Wegliinge) of the molecules. We
must now try to determine what influence this difference, exist-
ing before the impacts, exerts upon the motions after the impacts.
§ 4. The behaviour of two impinging molecules is not in every
respect the same as that of two elastic spheres; but we can never-
theless in many respects obtain a useful insight into the beha-
viour of molecules by starting from the consideration of elastic
spheres. The mutual action of two impinging elastic spheres is
very comprehensively treated by Maxwell in the memoir already
mentioned. I will here only quote a few principles, which may,
however, be considered as sufficiently well known Without my
doing so.
When two elastic spheres move with equal velocity in opposite
directions, and with their centres in the same straight line, so
that they strike each other centrally, they rebound from each other
in such a manner that each sphere moves back with the same
velocity in the direction of the point from which it came. But
if the spheres move, before the impact, still in opposite direc-
tions, but with their centres in two parallel straight lines stead
of in the same straight line, and so that the spheres consequently
impinge excentrically, they rebound again with equal velocities,
their centres again move in opposite directions in two parallel
straight lines; but the direction of these straight lines is not
the same as that of the straight lines in which the centres moved
before the impact. ‘The new direction depends upon the position
on the two surfaces of the point of contact ; and since the spheres
may strike each other on an infinite number of different points
of their surfaces, the rebound may also take place in an infinite
number of different directions; and it can be easily shown that
each possible direction in space is equally likely for the motions
of the spheres after the impact.
Let it now be assumed, as a general case, that the two equal
spheres move before the impact with any velocities whatever and
mm any directions whatever. We will decompose the motion of
each sphere into two components. We will take as the first coms
424 Prof. Clausius on the Conduction of Heat by Gases.
ponent the motion of the common centre‘of gravity of the two
spheres ; the second component must then be the motion of the
two spheres in question relatively to their common centre of gra-
vity. The former motion is equal and in the same direction for
both spheres ; the latter motion is equal and opposite for the
two spheres. The former is not altered by the impact ; the latter,
on the other hand, is altered exactly in the same way as it would
be if it existed alone and there were no common motion. In
relation to it, what has already been said of the case of two
spheres moving in parallel straight lines, and which assume
various directions after impact, according to the point at which
they strike each other, is applicable. It thus becomes evident
how far the motions after impact, of molecules which impinge
upon each other irregularly, are dependent upon their motions
before impact, and how far they are mdependent of them. The
motion of each sphere consists of two components, the first of which
is entirely determined, both as to magnitude and direction, by the
motions before impact, and the second of which has also a deter-
minate magnitude, but may have an infinite number of different
directions, every direction in space being equally probable with every
other*. :
§ 5. In applying this acti to the impacts which occur among
the molecules, we may assume that here also only that portion
of the motion possessed before impact by two impinging mole-
cules remains unchanged in magnitude and direction which is
common to both molecules, that a the motion of their common
centre of gr avity 5 ; while the direction of the second component
of their motions may be altered im so many ways that it may
with equal probability assume any direction in space whatever.
Let us now consider the whole number of molecules which
impinge upon each other in one unit of time within the infinitely
thin stratum spoken of in §¢3. The motions which they possess
before the impact have already been discussed in § 3: all possible
directions are represented among their motions; but the mole-
cules coming from the warmer side have in general somewhat
greater velocities than those which come from the colder side.
Since, according to our assumption, the temperature diminishes
as z increases, the warmer side is the negative side, that is, the
- one on which # has a smaller value than it has in the stratum:
hence the molecules which pass from the negative to the positive
* This result shows very plainly orhia at a great departure it is from the
real state of the case to regard, like J ochmann and Hoppe, in an approxi-
mate consideration of it, only central impact, since, instead of an infinite
number of different directions, there is thus obtaimed only one determinate
direction, and that one which is especially favourable to the transmission
of vis vivd.
Prof. Clausius on the Conduction of Heat by Gases. 425
side have in general greater velocities than those which pass from
the positive to the negative_side, so that, compounding the mo-
tions of all impinging molecules, we obtain a certain small mo-
mentum in the direction of positive z.
This common momentum remains unaltered by the impacts;
but at the same time a complete change occurs in the directions
of the motions, in so far that the molecules are impelled in all
directions without distinction. If therefore the motion were,
before the impacts, unequally distributed in the various direc-
tions (the number of molecules moving in certain directions
being greater than the number moving in other directions, or
their velocities beimg different), we must nevertheless assume
that all these inequalities would be equalized by the impacts ;
and that, excepting the general motion in the direction of posi-
tive z, no distinction between the different directions would
remain, but that all directions would be equally represented
among the new motions.
It thus becomes easy to give a definite representation of the
‘state of motion of the molecules emitted from the stratum, if,
instead of regarding the velocities of the separate molecules, we
content ourselves with knowing the mean velocity for each direc-
tion. First, let the molecules be conceived as moving equally in
all directions, so that an equal number of molecules, and all with
the same velocity, move in each direction, and then let a small
component motion in the direction of positive #, equal for all the
molecules, be conceived as added to all these motions. The
directions and velocities of the motions will be thereby somewhat
changed; and the system of motion so modified represents the
motions of the molecules emitted from the stratum*.
§ 6. We can define this system of motion mathematically as
follows.
Let the velocity possessed by all the molecules before the mo-
dification be A. The component velocity to be added to it in the
direction of positive # can, according to what has been said
above, be only a very small magnitude, of the same order as the
mean excursions of the molecules. Butas this latter is depend-
ent on the density of the gas, it is not the same at every point
of the quantity of gas under consideration ; and it will therefore
be convenient to substitute for this variable magnitude, in what
follows, one which has a determinate value for each gas. For
this purpose we will assume a certain condition as a normal con-
* In the memoir quoted above (Phil. Mag. S. 4. vol. xx.), Maxwell, in
determining the conduction of heat, has disregarded the circumstance that
the molecules emitted from a stratum have an excess of positive momentum,
but has tacitly assumed in his calculations that the molecules are emitted
équally in all directions.
426 Prof. Clausius on the Conduction of Heat by Gases.
dition for each gas—for instance, where the gas is exposed to the
pressure of one atmosphere, and its temperature throughout is
zero (the freezing-point). We will call the mean length of ex-
cursion which corresponds to this condition of the gas, the normal
mean length of excursion (normale mittlere Wegldnge), and we
will denote it by e«. We can then regard the component velocity
already mentioned as a magnitude “of the order of ¢, and can
accordingly denote it by pe.
We will now consider any molecule whateyer whose direction
forms the angle « with the axis of z, As in what follows we
have senerally only to consider the cosine of the angle which
the direction of any molecule forms with the axis of 2, we will
for the sake of shortness call it the cosine of the molecule, and
denote it by a single letter, which im the case before us shall be A.
If now the component velocity pe in the direction of positive 2
be imparted to the molecule, its velocity and its cosine will be
thereby changed, and we will denote the altered values which
take the places of A and X by U and w. We have then for the
determination of these two magnitudes the equations
Ups An pe 0) 8 02 a es
Ue AP eAApe + pe... 5 oo)
Substiteting for XA in the second equation the value Uu—pe
derived from the first equation, we get
U?= A? + 2uUpe—pe*.
By solving this equation we obtain two values for U, one posi-
tive and one negative, of which it is evident that we must take
the positive one: this is
U=ppet+ VA2—p1—pje2 . . (3)
enotae the particular value of U when p=0 by u, that 18,
ux V A?— pe, ER Ny ee
the last equation becomes
Upper Via pye; . ie
and developing this expression according to pe, we get the fol-
lowing equation, which conveniently represents the dependence
of the velocity U on the cosine p,
1p" a2 |
Usutppet ay bie fe golt. persis) ween
The magnitudes u and p which here occur may have different
values in different sirata, and are thus to be considered as func-
tions of z.
With reference to the distribution of the molecules among the
Prof, Clausius on the Conduction of Heat by Gases. 427
various directions of motion, it is easy to see that if the original
system of motion were such that an equal number of atoms moved
in each direction, this could no longer be the case in the modified
system of motion, but that more molecules must move in the
directions for which y is positive than in those for which p is
negative.
In order to be able to express this modification, let us begin
by considering the original system of motion, and let us deter-
mine the number of molecules whose directions form, with the
axis of,v, angles lying between « and da, the difference between
these values being infinitely small. For this purpose let us
imagine a spherical surface described with the radius 1; let the
point, where it is cut by a straight line drawn through the centre
in the direction of positive x, be the pole; and, with the pole for
centre, and the ares 2 and «+de for radii, let circles be drawn
upon the spherical surface: these two circles will then enclose
between them an infinitely narrow zone. The number of mole-
cules, whose directions form with the axis of x angles between «
and a-+da, will then be the same fraction of the entire number
of molecules that the area of the surface of the described zone is
of the entire area of the spherical surface, and will be represented
by
Qe sin « da ts 1 J ts
Aaah 18 4002. *s
But since ada=—dcosa=—d), we may also say that the
number of molecules whose cosine lies between X and dX is ex-
pressed as a fraction of the whole number by
tdn.
To find a corresponding expression for the number of mole-
cules in the modified system of motion whose cosine lies between
yw and 4—dy, we must modify the last expression by the addi-
tion of a factor which is dependent upon pw. Let this factor be
H, when the new expression becomes
4 Hdp.
The factor Hi may be determined as follows. Since the cosine
X is changed into pw by addition of the component velocity pe,
and, similarly, the cose X+dX into 4+dy, the same number
which, before the modification, expressed the molecules whose
cosine lay between > and A+dX, will, after the modification,
express those whose cosine lies between w and w~+du. We may
therefore put
4 Hdu=i dar,
whence dr
428 Prof. Clausius on the Conduction of Heat by Gases.
But by equation (1),
i tg a
a
and A, p, and e being independent of pu, we thus obtain
1 d(Up).
H=— Re satis (7)
Putting here for U the series given in (I.), and denoting the
fraction x by A, we obtain
H=A(1422 yet 54 wet...) Te i (sy
The factor / differs from 1 only by a quantity of the second
order in relation to e; and putting, according to equation (4),
the value “u?+ pe? for A, we have
Uu 1 lisa :
— Va pe pee 2 u? joy ——
The system of motion produced by adding the common com-
ponent velocity pe to the perfectly regular system, in which an
equal number of molecules move in every direction, is completely
defined by the equations (I.) and (I1.)
§ 7. The system of motion so defined corresponds to the
motions of the molecules emitted from a stratum, in case the
normal variations only are regarded. ‘To obtain the motions
which actually exist, the accidental variations spoken of in es 3
must also be taken into account. :
It is plainly impossible to do this by determining the motions
‘of each mdividual molecule; but the rules of probabilities enable
us to establish certain general principles for a large number of
molecules. Maxwell has thus deduced a formula purporting to
represent the manner in which the various existing velocities are
distributed among the molecules. It is not, however, necessary
for our present purpose to enter upon this; it is sufficient if it
be granted that the accidental variations occur to an equal extent
in all directions, and that therefore in a quantity of gas, whose
temperature and density are uniform throughout, the same num-
ber of molecules move in every direction, and that the mean
velocity in all directions is the same.
It is mdeed easy to see in this case that the accidental varia-
tions cannot in any degree contribute to cause more vis viva to
traverse a given plane in one direction than in the opposite
direction, since, whatever may be their individual effects, their
influence must ‘be the same in both directions. We may there-
fore entirely disregard the accidental variations in deducing the
Prof. Clausius on the Conduction of Heat by Gases. 429
general formula. They only come into account in the numerical
calculation, since for this—if the velocities and the magnitudes
dependent upon them, which are expressed in the formula by
particular letters, have in reality, various values—those mean
values which correctly represent the values that really occur
must be'calculated; and forthe calculation of these mean values,
the manner in which the values are distributed must be known. |
Reserving to ourselves to return again at the end to the latter
point, we propose to ourselves now to determine the condition of
the gas, and particularly the ws viva traversing a plane, starting
from the assumption that the magnitudes U and H, determined
by the equations (I.) and (II.), represent the real motions of the
molecules emitted from a stratum. ;
III. Behaviour of the molecules simuitaneously existing in an infi-
nitely thin stratum.
§ 8. We will suppose two planes placed perpendicularly upon
the axis of z, and with the abscisse # and «+dz, whereby we
obtain again, as in the foregoing section, an infinitely thin stra-
_ tum; but we will now consider, not the molecules emitted from
this stratum, but the molecules which exist in it stmultaneously.
If the gas had the same temperature and density throughout,
the motions would be such that an equal number of molecules
would move in all directions, and that the velocities would be
equal. But in the case before us, where the temperature and
density are functions of z, this uniformity does not occur.
To determine the velocities of the molecules, let us choose any
direction which makes with the axis of 2 an angle whose cosine
is , and let us consider the molecules which move in this direc-
tion. Before such a molecule enters our infinitely thin stratum
with the abscissa x, it has in general traversed a certain distance
since its last impact. Ifthis distance be called s, the abscissa of
the pot where the last impact occurred will be 2—ys; which
expression determines the velocity of the molecule, since, accord-
ing to the assumptions made above, the velocity with which a
molecule is impelled after an impact depends only upon the
abscissa of the point of impact, and upon the direction of its mo-
tion. We have above denoted the velocity as a function of x
and «, by U, and we may accordingly in this case, in which a
molecule is impelled from a point whose abscissa is « — ps, denote
its velocity by V, and write
dU Ld?U
VU St 5 oe ho 8 ore @ (9)
The distance s is not the same for all the molecules in our
stratum which have a determinate direction, so that their veloci-
430 Prof. Clausius on the Conduction of Heat by Gases.
ties are also somewhat unequal. We may hereafter denote the
arithmetical mean of a magnitude whose value, in the particular
cases which occur, is various, by making a horizontal stroke over
the symbol which represents the particular values of the magni-
tude, so that V shall represent the mean value of V, and s and s?
the mean values of s and s*. We may then write
=: dU 1d*U 4-
V=U— In ts Sei caer Be Aa a 50)
In this expression it is to be observed that the magnitude s?
is not equivalent to (s)?, but that it must be specially deter-
mined. Thence it also follows that the mean values of the
powers V?, V3, &c. are not quite equal to the corresponding
powers of the mean value V. We must, in fact, in order to ob-
tain this mean value, start from the equation (9), and, after
having squared it, cubed it, &c., then put the mean values for s,
hag &e. We thus obtain
ae dU d?U dU\2
Vat" 2U0~ s+ fue peal ade “5 |e ge ee }
3 2 Pa hae
eae as sp Bi +8u(5) kin °(11)
D dx |
pet daz dx?
V+= &e.
The differences between the magnitudes V*, V3, &., and the
magnitudes (V)?, (V)°, &c., which latter are obtained by squaring,
cubing, &c., equation (10), occur, as will be seen, first in
those terms which are of the second degree in relation to the
length of the excursion s; and as these excursions are, on the
average, very small quantities, the differences are also very small.
§ 9. It now becomes necessary to determine the values of s
and s* with greater exactness.
To this end, we will first examine the behaviour of these mag-
nitudes when the temperature and density of the given quantity
of gas are uniform throughout, and will afterwards superadd the
modification due to the inequality of temperature and density.
Considering, then, all the molecules which are contained at
any given time in a stratum of a gas whose temperature and
density are everywhere the same, we ask ourselves, how great
are the distances which the several molecules have traversed be-
tween their last impact and the moment at which we consider
them. The likelihood that a molecule has traversed a distance
lying between s and s+ds, between its last impact and the
moment fixed upon, is Just as great as the likelihood of its tra-
versing an equal distance between this moment and its next.
-Prof. Clausius on the Conduction of Heat by Gases. 431
impact; and the likelihood of the latter event can be easily
expressed. iit aL Lee ee
If, from a given moment of time, a large number of molecules
be supposed to move through the gas with an equal velocity, their
motion will cause each of them sooner or later to impinge upon
other molecules ; and if z denote the number of molecules which ©
traverse the distance s without striking against other molecules,
z must diminish according to a definite ratio as s increases. If
we say that the probability of one molecule striking another
» while traversing the infinitely small distance ds is ads, then of
the number z which have traversed the distance s without impe-
diment, the number zeds will be taken up during the next por-
tion of their course ds, and the decrement of z will hence be
represented by the equation |
| dz=—zads;
whence it follows that, putting Z for the initial value of z when
6==0
eae %:5
This value being substituted for z in the product zeds, gives the
expression |
— Le-“ads
for the number of molecules the length of whose excursions lies
between s and s+ds.
In order now to obtain the mean length of all the excursions,
it is only needful to multiply the last expression by s, then to
integrate from s=0 to s= o, and to divide the integral by the
whole number Z, This gives
al seus = SRE Ua Wupenaee Ti)
0
This expression applies primarily to the mean length of the
distances moved through by the molecules between the point of
time in question and their next impact ; but it can also be directly
used for the distances the molecules have moved through between
their last previous impact and the instant in question, for the
distances before any given point of time must, on the average,
be equal to the distances after it. |
|e gith fae : :
The same value, —, is also obtained if we investigate the mean
a
distances traversed between every two impacts during a given
time. For if, instead of considering the motions of all the mole-
cules between a given instant and their next impacts, we take a
large number of impacts as our starting-point, and then follow
the motions of the molecules until their next impacts, all the
432 Prof. Clausius on the Conduction of Heat by Gases.
foregoing conclusions remain applicable to this case also without
modification, and hence the value 2 given in (12) must also be
a
the mean value of these distances*.
The mean value of s? may be obtained in a way quite similar
to the above if s? be used as the multiplier before integration
instead of s, andthe rest of the operation be conducted as before.
We thus get
fitdalyre 2
s? =| ste-S ads = AE e e Py 6 e (13)
0
Hence it follows that the two mean values s and s® are related
to each other as expressed by the equation
SSS 2(8)2. es. bet, le |) ae
§ 10. We have now to investigate the modifications which
these mean values undergo if the gas has not a uniform tempe-
rature and density throughout, but if its temperature and den-
sity are functions of z.
All the foregoing considerations remain applicable to the mo-
lecules whose motions, being perpendicular to the axis of 2, do
not cause any alteration in the value of their abscissz. If, then,
in order to distinguish those particular values of the general
values which relate to this ‘case, we attach to the letters con-
cerned the index 0 (because in this case 4=0), we may write
= ez ZENO S75 % .
4 “0
The quantity = which represents the mean length of excursion
0
* Tt may perhaps appear surprising at first sight that the same value should
be found for the distances traversed between the last impacts and a given
moment of time, or between this moment and the next impacts, as for the
entire distance traversed in the gas from one impact to the next during a
given time. It must, however, be remembered that the mean value of all
the distances traversed in the gas between every two impacts during a given
time is not the same thing as the mean value which would be found by
taking into consideration the distances which all the molecules, which at
any given moment are simultaneously in one stratum, would traverse be-
tween their last previous and next following impacts. For the longer
distances would be of more frequent occurrence in the latter case than im
the former, since a molecule requires more time to move through a long
distance than to move through a short one; and the probability is therefore
greater that any given moment would occur during a longer than durmg a
shorter distance, whereas in the former case all the distances traversed in
the gas count equally. By making the calculation, it will be found. that
the latter supposition gives a mean value twice as great as the mean value
given by the former. The value of s, as determined above, is the half of
this greater mean value.
Prof. Clausius on the Conduction of Heat by Gases. 433
for this particular case, is a magnitude of the same order as the
normal mean length of excursion denoted by e€; and to indicate
this, we will put
1
Fata: e e ry 2 ® aa e e {15)
0
whence we have
S, = ce |
fi, > s e ® 2 5 e (16)
So eeet
The mean length of excursion is somewhat different for those
molecules which do not move perpendicularly to the axis of #; we
can express this by substituting, for the coefficients c and c* im
the foregoing equations, magnitudes dependent on the direction.
This dependence on the direction rests upon two circumstances,
each of which may be considered separately.
The first circumstance is this—that a different temperature
and density prevail at the points from which the molecules start,
and in the strata through which they have to pass before they
arrive at the stratum under consideration, from those which prevail
in that stratum. If the cosine of the angle formed by a given
direction of motion with the axis of x be denoted by yp, then the
distance of a molecule whose excursion is s, from our infinitely
thin stratum, is equal to us. The differences of temperature and
density existing at this distance can be represented, in the man-
ner already known, by series which progress according to whole
powers of ys. Now, since the modifications which the coeffi-
cients c and c* undergo owing to the differences of temperature
and density must correspond to these differences themselves, we
may conclude that the modified coefficients can be represented
by similar series, containing, however, the proper mean values,
instead of the particular values s, s?, &. We may accordingly
write
s=e(ctays+a'p?s?+...),
6? == 2e7(c?+bus+...).
By substituting for s and s? on the right uf these equations the
values which result from these same equations, we obtain series
which progress according to powers of we, and which, if we also
substitute simple symbols for the complicated coefficients of the
higher terms, may be written
ht. waged ae
s*=2e?(c? + Bue + eee 2
The second circumstance which has an influence on the mean
Phil, Mag. 8. 4. Vol. 23. No. 156, June 1862. 2G
434 Prof. Clausius on the Conduction of Heat by Gases.
length of excursion is, that the molecules do not move equally
in all directions within each individual stratum considered sepa-
rately, and that therefore the pr obability of one molecule striking
another during the element ds of its excursion varies at the same
plate with the various directions which ds may possess. In order
to bring this circumstance into calculation, let all the coefficients
ae Ki A', B be again replaced by magnitudes which are
dependent on the direction. Now we have already seen that
the magnitudes U and H, which determine the unequal motions
in various directions of the molecules emitted from any given
stratum, vary only slightly with the variations of 4,—so, indeed,
that they can be represented by series which progress according
to powers of we. It may be inferred hence that the coefficients,
as modified for these unequal motions, can likewise be repre-
sented by similar series; so that we may substitute for ¢
c+epetc pret ...,;
and so on for the other coefficients. By introducing these series
into the equations (17) and arranging the expression according
to we, we again obtain for s and s? series which progress accord-
ing to powers of ue, and which differ from the former series only
in the coefficients of the higher terms. If we denote these
coefficients by new letters, the ultimate expression which we
obtain by taking account of both circumstances, takes the form
s =e(e+ Cue + Clu2e? + Se a 7 See (18)
s* = 2¢7(c?+ Duet...)
It may be further remarked that, of the coefficients of these
series, only c will be used in the sequel ; the higher terms, where
they occur, are only added for the sake of greater completeness.
§ 11. These expressions for s and s? must now be introduced
into the equations (10) and (11) im § 8. If at the same time the
serles given in equation (I.) be substituted for U, we obtain for
V, V2, V°, &c. series which progress according to powers of se,
and. which, when a few new symbols are introduced, take the
following forms :—
Vi =ut+quetreweet ..., pers
v3 =u? +-Quque + (2ur+ qy?)wrer+ .6., (IIL)
Ve =u + wey +3 (u'r + ug,2)wre+..., (
Ge |
The teten 9; 4,7, aud r here introduced have the following
meanings :—
Prof. Clausius on the Conduction of Heat by Gases. 485
ea
du 2 ;
qe=e+e oa ] sinters =e (19)
belive .,..dp du eu | tas nde :
r =e ORE +O
§ 12. Having now determined the velocities of the molecules
which exist simultaneously i in a given stratum, it remains for us
to investigate the distribution of the motions of these molecules
among the various directions.
If the motions were directed equally towards all points, then,
for the same reasons as those discussed in § 6, in treating of the
molecules emitted from a stratum, the number of molecules
whose cosine lay between w and «+dy would be represented as
a fraction of the whole number present by 1du. In the case
before us, however, where the motions are not equally divided
among all the directions, but only among such directions as form
the same angle with the axis of z, we will denote the number of
molecules whose cosine lies between » and «+ dw as a fraction
of the whole number of molecules present by 41du, where I
signifies a function of ~. Now it is easy to convince ourselves,
by considerations similar to those contained in the foregomg
sections, that the function I must be capable of expression by a
series which progresses according to powers of me, and it may
therefore be written thus,
Rese omer pee. os ly es et et
where 2, g', 7’, &c. are magnitudes mdependent of p.
The magnitude 7 can be easily determined at once. If the
expression $Id be integrated from p=—1 to w= +], this
integration will include all the molecules present, and the value
of the integral must therefore be 1. Working this out by put-
ting for I the series just established, we get
l=i(1+ive+...),
and thence
a=1L—tyle? + eon @ ° ° ° ° e (20)
We will leave the other magnitudes gq’, 7’, &c., occurring in
equation (IV.), for the present undetermined, as an opportunity
will soon offer itself of determining them as far as is necessary.
[To be continued. ]
2G 2
[ 436 ]
LX. On the general Differential Equations of Hydrodynamics.
By Professor Cuauuis, F.R.S.*
¥. A Nees propositions in hydrodynamics, the proofs of which
I recently expressed the intention of bringing under
review, are contained for the most part in communications to
the Numbers of the Philosophical Magazine for January 1851,
March 1851, December 1852, and February 1853. In the
references that will be made to these communications, the
meanings of the symbols will be supposed to be known; and in
the present one the same symbols will be used, and in the same
significations. The article ‘‘On the Principles of Hydrody-
namics” in the Number for January 1851 contains definitions
of two fundamental properties of a perfect fluid, and the proofs
of six propositions founded on these properties, and on self-
evident principles. The first five of the propositions need not
be particularly dwelt upon, as the reasoning by which they are
established is not new, and has been generally accepted. Re-
specting the fundamental properties, viz. that the parts of a fluid
press mutually and against the surface of a solid, and that, if the
fluidity be perfect, the parts are separable by an infinitely thin
partition without assignable force, I will only remark that as
they are obvious and distinctive, and rest on experimental
evidence, they seem to be the most appropriate that can be
thought ‘of for the basis of imiitherhatical reasoning applied to
fluids. The proofs of Propositions I. and II. based upon them,
the‘one demonstrating the law of pressure in the case of equili-
brium, and the other the same law in case of motion, must be
considered to be as exact, on the hypothesis of perfect fluidity, as —
are those proofs of propositions in statics and dynamics which
rest on the hypothesis of the perfect rigidity of solids. Also
the law of pressure is as strictly proved for fluid in motion as
for fluid at rest.
2. Proposition VI., which has reference to a new general
differential equation, will require more particular consideration,
since it cannot be expected that such an equation will be ad-
mitted except upon ample evidence of the necessity for it, and
of its truth. I propose, therefore, to devote this communication
mainly to the discussion of the circumstances which render
necessary @ turd general hydrodynamical equation, and of the
process by which it may be investigated.
3. Before entermg upon this inquiry, it will be proper to
adduce the two commonly received hydrodynamical equations,
and to state briefly the principles on which they rest. The first
in order, the investigation of which is the solution of Prop. IV.,
* Communicated by the Author.
On the general Differential Equations of Hydrodynamics. 437
is deduced, by means of D’Alembert’s principle, from the general
hydrostatical equation obtained as the solution of Prop. III.,
just as questions relating to the motions of solids are solved as
statical questions by the intervention of the same principle.
The following is the analytical expression of this equation in its
most general form :
d deni d? d*z
fn v (x- 7 eet (v— SP )ay+ (z— oa). aaah
It is here to be remarked that this equation, as well as the
hydrostatical one on which it depends, was investigated with refer-
ence to a single elementary particle. But as the particle might
be any one whatever of the mass of fluid considered, we may at
once assert, with respect to the hydrostatical equation, that it
applies to the whole of the mass. The same assertion cannot be
made respecting the hydrodynamical equation (1), unless there
be fulfilled certain conditions arising out of the distinctive cha-
racter of the motion of fluids, according to which the particles
move inter se, and continually change their relative positions.
In fact, that equation has no application unless such motion be
consistent with the principle of constancy of mass. This prin-
ciple requires the investigation of a general equation, which
shall express that each given element changes form and position
by reason of the motion in a manner consistent with its remain-
ing of the same mass in successive instants. The result of the
investigation, which answers Prop. V., is the equation
dp . d.pu See ae ihe ee)
dt dx dy dz
This, in case the fluid be incompressible, becomes
du dv , dw __ 0
dat dy ee
4, Again, the movements of a fluid must be such as to satisfy
the geometrical condition that the directions of the motion in
each given element are normals toa continuous surface. It will
not perhaps be denied that, unless this condition be satisfied,
neither of the equations (1) and (2) has any application. But
the necessity of obtaining a general differential equation to express
the fulfilment of this condition has not been generally recognized.
I propose, therefore, before proceeding to the investigation of
such an equation, which, in fact, is the third general equation
mentioned above, to give some account of what has been done
with the other two, as this statement will serve to show the
necessity for the third. First, I remark that the two equations
have been applied to problems in which the motion is assumed
to be in directions tending to or from a fixed point or a fixed
438 Prof. Challis on the general Differential
plane. But clearly in these cases the condition that the lines of
motion are normals to continuous surfaces is satisfied, and the
principle above enunciated as the foundation of a third general
equation is consequently involved. For the solution of other
problems, the differential function udz + vdy + wdz is equated to
(dd), the differential with respect to coordinates of a new variable
dx
any problems have been attempted in which that supposition
has not been actually or virtually made. But whence arises the
necessity for a new variable, and what does the variable itself
signify ? Respecting the meaning of the variable, a very explicit
answer can be given. For since in the expression udz + vdy + wdz
the differentials dz, dy, dz are independent and arbitrary, we may
assume. them to be such that that expression is equal to zero. It
will then be seen that (dé) =0 is the differential equation of a
surface which is everywhere cut at right angles by the directions
of the lines of motion in the elements through which it passes.
It is evident that there will be an unlimited number of such
surfaces, the function ¢ being applicable at all times to all parts
of the fluid. Thus the introduction of this variable is really a
recognition of the principle that the lines of motion are subject -
to the above geometrical condition. The further step that I have
taken is to regard this principle as necessary and fundamental,
and to reason from it. According to this view, the substitution
of (dd) for udx +vdy +wdz would be a consequence of that prin-
ciple. The following considerations will, however, show that
this substitution is not sufficiently general, and would unduly
restrict the investigation of the laws of the motion of fluids. __
5. It is known from analytical geometrythat ude + vdy +wdz=0
would equally be the differential equation of a surface cutting at
right angles the directions of the motion, if u, v, and w, mstead
of being equal, were respectively propor tional to the partial
differential coefficients with respect to 2, y, and z of a function
of x, y, z, and ¢, that is, X and being both unknown func-
tions of #, y, z, and ¢, if
db, so that “u= ca ves oo and w= a8 IT am _ not aware that
and consequently
Mar) = uda + vdy + wdz.
It is admitted that the mght-hand side of the last equation is
not an exact differential in every case of the motion of fluids ;
so that, although by substituting (dd) for it a resulting differ-
ential equation involving only x, y, z, and ¢, with ¢ as the prin-
cipal variable, might be found, this equation would not possess.
Equations of Hydrodynamics. 439
the requisite degree of generality. All this reasoning points to
the conclusion that a third fundamental equation is necessary
for eliminating the unknown function A, and obtaining a result-
ing general differential equation in which the principal variable
is vr, and the other variables are x, y, z, and?¢. I proceed ee
the investigation of this third equation.
6. Preparatory to the investigation, it will be proper to tae
account of the following general. dynamical circumstance. The
accelerative forces which act on a given particle at any time are
the extraneous forces X, Y, Z, and the force due to the pressure
of the fluid, the components of which in the direction of the axes
of coordinates are LN Pap Now these forces are by hypo-
pdx’ pdy’ pdz’
thesis finite, and consequently the direction of the motion of a
given particle cannot alter per saltum, as it would require an
infinite accelerative force to produce this effect in an indefinitely
short time. Thus, although the course of a given particle cannot
generally be expressed by means of algebraic functions of con-
stant form, it must still be such that the tangents at any two
consecutive points do not make a finite angle with each other.
Hence also the direetions of the surfaces of displacement which
cut at right angles the lines of motion in a given element at two
successive instants do not change per saltum.
-7. This being premised, since the function yf is, by the fore-
going argument, applicable at all times to all parts of the fluid,
the equation
u v w
is a general differential equation applicable to all the surfaces of
displacement at all times. If therefore (dy) =O be taken to be
the differential equation of any one surface of displacement, the
coordinates of which are a, y, z at the time /, and if 7+6z,
y + dy, 2+6z, and ¢+ dt be substituted for these coordinates and
for ¢ respectively, that equation will still be satisfied if the new
values of the coordinates apply to another surface of displace-
ment at the time ¢+6¢. But from what is argued above respect-
ing successive surfaces of displacement of a given element, this
will be the case if
dv=udt, dy=vit, dsz=wot,
that is if 6x, dy, dz be the variations of the coordinates of any
given element in the indefinitely small time of. Now by the
substitution of the new values v is changed to
+ ote 7p wt obi wit,
440 Prof. Challis on the general Differential
which, by putting for w, v, and w their expressions above, becomes
aN aoa be
ae dat t dy? t a ah
Hence by the roel reasoning the differential of this quan-
tity with respect to space- -variables is equal to zero; that is,
ay (ye AY
(dy) oe (a. £5 +X dx? + dye? WPA 2m AP?
By the equations to the catenary we have
ste = (a 0)*, ow (1) si? + ce (a! +07, 5) AOR
P +e7= (h+6)*.... G-z))- -(1-"- 4 = Ne sel}
From these values of A and #’, by the help of (14) I I shall
obtain the value of c. That equation (14), by means of (1), (2),
(15), (12), (6), becomes
2 Z2. OF}
20 = log (1454 ae ie +(8 =1) log, ( (jo
Cc
12 2 oF
+ /(Q/ ey ne ai) rele (14 to):
Unstiffened Roadway in a Suspension Bridye. 449
The first term of this, after substituting for 4 and A! and ex-
panding,
=F0-"F 0-5 \-3 a4 14N+3(1—2=7( = ee
The second term
n9-02(0-2-*50-2))-0 vgn
(1 F542) +4(1-4-8340-)))}
The third term
=8(1—85%(1_ 6) seg fiew—(1- 854-8)
mn F pe tet
BoB (FM)
wp-w(t-£- 5-2) s0(1- 254-8))}
Let C be the value of c when @=1, or no train is on the
bridge; then
2) 20-2
Beret | 0°64] 1°57
CEL s nareccesoatescee cee ees
Horizontal distance of this 33 | 56
GEPTESSION, <2. se cccccene as
Greatest elevation of road- : ne
way beyond the train am 0°28) 0°97
Horizontal distance of this ,
lelevation from the left see 271 | 275
120 | 160
feet.| feet.| feet.| feet.| feet.| feet.| feet.| feet.
a ee ee
200 | 240 | 280 | 320 | 360 | 400
2°15) 2°24] 1:99) 1°54) 1°01] 0°53} 0°16) 0
73 | 86 | 97 | 105/113] 120} 127
1-73] 2:24] 2-42] 2-25] 1-78] 1°11] 0°39] 0
279 | 287| 297/309 | 324 | 342 | 367
Hence the greatest depression occurs nearly about the time
when the greatest elevation occurs, a little before it, that 1s,
when the train is nearly halfway over the span; the distance
between the lowest point of the roadway and the highest point
at that time, measured along the roadway, is about 200 feet,
or half the length of the span; and the greatest depression is
somewhat behind the middle point of-the train.
On the effect of the Iron Girder in checking the undulation of the
Roadway.
5. Suppose it possible that the undulation described and caleu-
lated in the last paragraph can take place in the roadway and
heave up the girder, as represented in the following diagram (fig.3).
More than half of the weight of the girder will be brought to
bear upon the point P where the girder touches the roadway
curve (which is the same as the curve into which the lowest ends
of the suspending rods are thrown), unless this curve 1s of no
greater curvature at P than that of the girder by its own weight.
The length of the girder to be used in the Hooghly Bridge is
Unstiffened Roadway in a Suspension Bridge. 453
400 feet, its weight 350 tons, and its deflection when suspended
at its two ends is 0°7 foot. It will have the same deflection as
this at its two ends if suspended im the middle. Moreover, if a
Vig, 3.
eee
b instead of 7 The result will be that the second blow
will occur just as the girder has sprung back to its original
position with a momentum equal to that which the first blow
gave to it, but in the upward direction; the second blow will
therefore be counteracted by this. The third blow will then
have its full effect; but being feebler than the first, will not
produce so great a depression as before; and the successive
results will be smaller and smaller.
The calculation in this paragraph is sufficient to show the
great importance of the rail over the bridge being entirely free
from every impediment or check of every kind, and the advan-
tage of having the girder unattached to the roadway.
J. H. Pratt,
Calcutta, March 12, 1862.
LXII. Some remarks on a Paper by Dr. A. Matthiessen, F.R.S.,
and C. Vogt, Ph.D., “ On the Influence of Traces of Foreign
Metals on the Electric Conducting Power of Mercury.” By
Ropert SaBinez, Esq.*
| ey the above paper, published in the March Number of the
Philosophical Magazine, Drs. Matthiessen and Vogt give
six Tables, with data and calculations of their tests, of the con-
ducting powers of amalgams of bismuth, lead, tin, zine, gold, and
silver, in different proportions.
Accompanying these Tables, however, no formula is given to
indicate how the numbers in the seventh columns, headed
“conducting powers calculated,” are obtained.
Having recently had occasion, in the laboratory of Dr.
Werner Siemens, at Berlin, to be occupied with inquiries on the
electrical resistances of amalgams, I was interested in going
* Communicated hy the Author.
458 Mr. R. Sabine on the Influence of Traces of Foreign Metals
carefully through the above paper, and have arrived at the
results which follow.
When, from the formula given by Dr. Siemens in his paper
“ Ueber Widerstandsmaasse und die Abhangigkeit des Leitungs-
widerstandes der Metalle von der Warme*,”
_ 100c (W—w)
f wsm
rv sp
we develope the value of the conducting power of the amalgam,
substitute volumes instead of weights divided by specific
gravities, and set C=the specific conducting power of mercury
instead of unity, we get the simple formula
v v
A=Bioo +e(1 oa)
in which A is the conducting power of the amalgam, and B that
of the dissolved metal.
With this formula (based on the supposition that the con-
ducting power of an amalgam is equal to the sum of the con-
ducting powers of two parallel wires of the metals composing
it) it would seem that Drs. Matthiessen and Vogt have also
reckoned the numbers given in their columns headed “ conduct-
ing power calculated ;”’ for, in so far as the first four Tables go,
the results agree perfectly with the formula. In the remaining
two Tables, however, Drs. Matthiessen and Vogt, for no assigned
cause, forsake the formula by which their former results were
calculated, and give us, in the “ conducting powers calculated ”
of gold and of silver amalgams, only a tenth part of the value of
the first member in the equation making up the value of A.
As the amount of this error (probably due to setting false
indices before the mantisse of their logarithms) is very con-
siderable, I give in four instances the corrected numbers.
Conducting power. Error
Amalgams,. y, |-_——__$____________________________|__ per
Observed. | Calculated. | Re-calculated, | cent.
v 0129 | 10-984 10:978 11-715 63
ee ee ee 4 1-280 | 11-566 11581 18-878 38'6
ee 0-007 | 10-913 10-913 10-944 03
| Pret te ete ¢ 4 0-700 | 11571 11-180 14-296 21°8
In his paper above referred to, Dr. Siemens expresses his
opinion that the conducting power of a fluid metallic mixture is
in proportion to the conducting powers of the two metals in
their fluid state at the same temperature.
Drs. Matthiessen and Vogt have taken into their calculations
of the conducting powers of their amalgams the conducting
* Poggendorff’s Annalen, vol. cxiii, p. 91.
on the Conducting Power of Mercury. . 459
powers of the various metals in their solid states in conjunction
with that of fluid mercury.
As it is important to know which. of these opinions is right, I
have calculated the conducting powers of the foreign metals from
all the tests in the given Tables, and set their means in column B
of the following
Table of Conducting Powers of Metals in Amalgam.
Conducting powers.
Table. Metal.
B (calculated). |. Matthiessen.
————
I .. | Bismuth 37°25 7°91
TL .,1 Lead.” 61°31 52-64
Pies lin. 75°16 78°51
PV. PP Hine 3) 92-99 184-06
Mins aes GOREN pe 4s 109°89 494-68
Wie. | Silver. 61-46 633°33
The comparisons are made with the gold-silver alloy of Dr.
Matthiessen, the conducting power of which, at 0° C, is taken
at 100.
The opinion of Dr. Siemens with regard to the conducting
powers of dissolved metals is therefore corroborated qualitatively
by these tests of the amalgams of gold, silver, tin, and zinc, the
conductibilities of which are all less in a melted than in a solid
state, but opposed by those of lead. The results of the tests
of bismuth-amalgam is also qualitatively corroborative of Dr.
Siemens’s opinion, as the conductibility of melted bismuth is
greater than that of mercury at the same temperature.
Dr. Siemens gave the calculated conductibility of fluid silver
at 15° C. (the temperature of the amalgams he tested) from
three different experiments, respectively 8°8, 9°3, and 7°8, com-
pared with the conductibility of mercury as unit. These num-
bers do not differ so materially from 5°64, the value given in
col. B reduced to the same standard, when we consider that the
conducting power of solid silver, according to Dr. Matthiessen,
is no less than 58-05, and according to Dr. Siemens 64°38.
The results of Dr. Siemens’s calculations of the conducting
power of fluid zinc at about 20° C., from three measurements
with zinc-amalgams given in the same paper, are 11°2, 12°7, and
11-2 respectively. Corresponding results from my calculation
of Drs. Matthiessen and Vogt’s experiments (col. B), reduced to
the same standard, is 8°5, while the conductibility of solid zine
is 16°9.
It is evident, therefore, that in no case are we entitled to take
the conductibility of metals in their solid states into our calcu-
lations of fluid amalgam resistances.
460 On the Conducting Power of Mercury.
It is not improbable that the metals combine with mercury
in atomic proportions, and, in this event, that the resulting
compounds are dissolved in the overplus of mercury.
‘Such a combination would undoubtedly modify the distances
of the compound atoms, and hence also the conductibility of the
mass. The conductibilities of tin, zinc, gold, and silver-amal-
gams from the tests in question show an expansion of the
molecules, those of lead and bismuth a contraction, supposing
that expansion of the molecules causes a decrement, and con-
traction an increment of conductibility.
In adopting the opinion of a chemical combination and sub-
sequent solution, the very conditions prohibit the adoption of a
common formula which shall express with exactitude, for every
metal, its amalgam conductibility, unless that formula embody
a term embracing the effect of the combination and solution on
the atoms and density of the resulting compound, although the
formula which combines the conductibilities of the metals in a
fluid state, without being absolutely correct, is near enough
with some metals, when the per-centage of foreign metal in the
amalgam is not too great. And a more exact knowledge of the
nature of the atoms and of the origin of electrical resistance is
necessary before such a formula can be constructed.
In these considerations I have supposed the methods em-
ployed by Drs. Matthiessen and Vogt, as well as their measure-
ments, to be correct.
It is doubtful, however, if the thermometer-tubes employed
were not necessarily of so small a bore that filtration of poorer
amalgam into the tube while thicker remained in the cups was
not facilitated. Thus the known proportions of the mixture
poured into the cups would not have given a correct idea of the
contents of the amalgam in the tube, and the conducting powers
of the richer amalgams would have appeared lower than they
really were.
It is also questionable if Drs. Matthiessen and Vogt have not
relied too much on the weights of the metals used in making up
the amalgams instead of analysing the latter after each test ; for
it is well known that amalgams of the easily oxidizable metals
change their proportions when in contact with the air by rapid
oxidation of the foreign metals.
I diminished these sources of error by employing tubes of, at
least, 2 millims. diameter, and by analysing the contents of each
tube after each test, disregarding entirely the contents of the cups,
which were made removeable.
94 Markgrafen Strasse, Berlin,
20th April, 1862.
[ 461 ]
LXIII. On Collyrite, and a native Carbonate of Alumina and
Lime. By J. H. Guapstonse, PA.D., F.R.S., and G.
GuapstoneE, F.C.S.*
T Hove, near Brighton, isan old quarry in the upper chalk
that presents some appearances of more than ordinary inter-
est. Among these are the faults which have traversed the strata
and broken the layers of flint, splittmg them in every direction,
and reducing them in some places almost to powder. Some of
these fissures are filled up with a mineral whiter than the sur-
rounding chalk, and perfectly distinct from it, which runs also
along the dislocated layers of flint, and frequently imbeds the
fragments.
This very white mineral occurs in rounded masses easily dis-
integrated in water. It is very soft, easily friable, with an earthy
fracture, of low specific gravity, porous, and slightly hygroscopic.
The external portions are frequently stained red with sesquioxide
of iron. When examined chemically, it was found to consist
mainly of hydrated silicate of alumina, perfectly decomposable
by strong hydrochloric acid. There was also a varying amount
of carbonic acid and of lime. The alumina was found to be free
from phosphoric acid; nor was it mixed with glucina, a small
quantity of which has been recently found so often to accompany
this earth. The mineral, when strongly heated, gave off both
the combined water and the carbonic acid.
For analysis the mineral was pounded and allowed to stand
over sulphuric acid in vacuo till freed from all hygroscopic
moisture. The determination of the different constituents was
made in the usual manner.
A very soft, pure-looking specimen gave the following pro-
portions :—
Silieie acid; . .. «. L449
PAUNUTLIA ats sledieeg lity hdc. ain Aisa
Carbonic acid . . . . O79
Lime SE VEER EY es, '. cu KO OU,
Water andloss . . . 986°39
100:00
The carbonic acid and lime, being in very nearly equivalent pro-
portions, may be assumed to have existed in combination ; and as
they form together only 1:68 per cent., they may be considered
as no constituent part of the aluminous mineral.
Excluding them, the results of analysis are as given below
* Communicated by the Authors.
462 Messrs. J. H. and G. Gladstone on Collyrite, and a
in the first column. The second column gives the theoretical
proportions calculated from the formula $i0%, 2Al?0?+9HO.
[t is perfectly clear that the silicic acid and the alumina are
in this ratio, but the amount of water is rather low for 9 equi-
valents.
A, II.
Silicic acid. . . . . 14°74 14°14,
Alumina.) (icc) Gate ae BEG 48:02
Wate wart or dutghietsaaie bl 37°84
100-00 100:00
The mineral agrees, both in’physical characters and in chemical
composition, with that which has been described under the name
of Collyrite, and to which the formula 8107, 2 Al?0?+ 10 HO
has been attributed; but our specimen appears to have been
purer, and to have given more accurate numbers for the disilicate
of alumina than those analysed by previous observers.
But no two portions analysed gave exactly the same composi-
tion. Some had a larger amount of carbonate of lime: thus a
piece which was considerably harder, and broke with a conchoidal
fracture, was found to contain between 5 and 6 per cent. of lime-
salt. Some had a much smaller amount of silica: thus a piece
which very easily fell to powder, and had the specific gravity of
1-99, gave about the following proportions :—
Silicie acide hi SAL
Adtuminal’< OC Saree 1 Oe BOs
Carbonate of ime . . . O6
Water and loss. . ..° 37." 3be5
But the most remarkable specimens were from another part
of the quarry. They had the same physical characters as those
already described; but quantitative analysis showed that they
contained more carbonic acid than was necessary to saturate the
lime, and that there was no other base present except the
alumina. Now as bicarbonate of lime is soluble in water, and
carbonate of alumina is unknown as a mineral species, and has
seldom, if ever, been procured even in the laboratory, it seemed
desirable not to depend on one analysis. A quantity of one
specimen was therefore pounded up and several determinations
were made of each constituent, and that by different processes,
the mean results of which are given in the first column of the
subjoined Table. Another specimen was reduced to powder,
and exposed over sulphuric acid zm vacuo for a whole month, by
native Carbonate of Alumina and Lime. 463
which it lost no carbonic acid, but apparently a little of its
combined water. It gave the analysis in the second column.
Other specimens yielded the numbers in columns III. and IV.
I. i Il. IV.
Silicic acid. . . 6°22 5°87 5°41 5°30
Alumma .. . 41:04 39°58 36°32 40°51
Carbonic acid. . 10°91 14°77 18°15 14°14
Ling 5 Sa aaeameny 624 11:22 11°62 9°18
Water Ly fs S816 |
Traces and loss . 1°30, 28°56 29°16 30°87
100:00 10000 10066 100-00
Now in each of these cases the carbonic acid is far more than
sufficient to neutralize the lime. Thus
7°37 parts lime neutralize 5°79 parts carb. acid, leaving 5°12
11°22 2 2» 29 8°81 9 29 ? y) 5°96
11°62 29 9 9 9°13 oP) 9 oe) ” 9°02
9°18 29 by) a hae E 7°20 oP) 9 9 9 6°94
In what way is this excess of carbonic acid combined? It never
exceeds in amount that which would be required to form bicar-
bonate, but in three instances it nearly approaches that quantity,
hence the lime might be conceived as existing as such; or it
might be carbonate of alumina; or a double carbonate of lime
and alumina; or collyrite in which part of the silicic acid is
replaced by carbonic acid. But each of these suppositions has
its difficulties. Bicarbonate of lime in a solid form is unknown ;
yet it is conceivable that alumina, by its remarkable power of
withdrawing other substances from solution, might have enabled
such a bicarbonate to exist in combination with itself. Of the
existence of any carbonate of alumina we have as yet no proof,
whether as a mineral or a production of the laboratory. A
double carbonate of lime and alumina was purely hypothetical.
The partial substitution of carbonic for silicic acid has not
hitherto been recognized, that we are aware of, in mineralogical
chemistry; and though the results of analysis of the first
and second specimens given above would accord very well
with that view, yet the third and fourth specimens show too
much silicic acid, unless mdeed we suppose that they were
derived from a collyrite much richer in silica than those hitherto
examined.
If in the above analyses we view the lime and carbonie acid
as wholly in combination, and reject them as adventitious, the
remaining mineral will have very nearly the same composition
464 Messrs. J. H. and G. Gladstone on Collyrite, and a
in the four specimens, and that composition will be that of the
previous specimen, minus half its silica, or Si0?, 4 Al? O8, 20HO.
a 1 Hil. IV. Theory.
7°8 8:0 78 73 pf
1:0 53°0 51-1 52°4 51°5
1:2
Alumina 5
Warr "ad 39°0 41°] 40°3 40°8
1000 100° 100° 1000 100:0
Silicie acid.
In order, however, to solve if possible the question of the
excess of carbonic acid, a portion of the fourth specimen was
finely powdered, diffused through water, and exposed toa stream
of carbonic acid; the gas dissolved out a little carbonate of
lime, which was precipitated and found to amount to 0°8 per
cent. Jt seemed incapable of dissolving out any more, leading
therefore to the conclusion that the amount of carbonate of
lime, existing as such in the mineral, is only a trace, and that
the remainder is in some form of combination with the alumina.
The powdered mineral, which had been acted on by a very large
amount of the gas, was afterwards analysed, and found to contain
very nearly all its original carbonic acid and lime.
Extending our inquiry we attempted to form an analogous
compound artificially, and at once obtained a double carbonate
of alumina and lime, in which the carbonic acid was to the lime
in the ratio of three to one, and another where the ratio was
similar to that in the mineral. |
Another fact which bears on the state of combination of this
excess of carbonic acid is the following :—If the mineral, after
having been dried zn vacuo, is exposed to a temperature of 100° C.,
it does not lose either water or carbonic acid; but if it be heated
more strongly, though not even to incipient redness, it parts
not only with the water and the excess of carbonic acid, but
also with a portion of that required to neutralize the lime,
and if to dull redness in a covered crucible, it parts with
nearly the whole of its carbonic acid; yet alittle remains which
cannot be driven off, even if the temperature be greatly raised.
Now it might be expected that simple carbonate of alumina or
a carbonated collyrite would be decomposed at a low heat, or
that bicarbonate of lime would be reduced to the common car-
bonate ; but the easy expulsion of the remaining carbonic acid is
not very compatible with either of these suppositions, and
appears rather to point to a double carbonate which yields up
all its carbonic acid more freely than carbonate of lime does.
The small quantity of undecomposable carbonate of lime left
may either have existed as such originally, or may have been
formed during the decomposition of the double salt.
native Carbonate of Alumina and Lime. 465
We are disposed, therefore, to regard this mineral as collyrite
mixed with a varying amount of a hydrated double carbonate of
alumina and lime. If it should bear a distinct name, it may be
termed Hovite, from the place where it was first recognized.
On looking over published analyses of silicates, it did not
appear that a “carbonate had often been found entering into the
composition of such minerals, yet there is a perfectly analogous
instance on a smaller scale. Allophane is another hydrated
silicate of alumina, and it occurs m a chalk-pit at Charlton,
also in the upper chalk, and under circumstances almost iden-
tical with those under which we found the collyrite at Hove.
In Mr. Dick’s analysis of this*, and in the analyses of four differ-
ent specimens by Mr. Northcote+, there was always found more
carbonic acid than was required to saturate the hme. In none
of these instances, however, did it exceed 1:31 per cent., and
Mr. Northcote propounded no other view than that it existed as
a bicarbonate.
On inquiring about the quarry at Charlton from which this
mineral was obtained, we were informed by Mr. Church that
the allophane was accompanied by a substance resembling our
collyrite. Some of this was obtained, and the two following
analyses were made of portions Haas rather different physical
characters.
_ The first was more compact and more vitreous in its fracture
than the specimens from Hove, and not so perfectly white. It
more closely resembled the specimens of collyrite in the British
Museum. On analysis it was found to be a silicate of alumina
soluble in acids, with a little carbonate of lime. On ooh toe he ee tee oes
Water cy, aia nineties, «oa oom
Carbonate of lime, and loss . . . 1°58
100-00
This is almost identical with one of the specimens from Hove. .
Altogether these hydrated silicates of alumina, many of which
have been analysed and described under the names of allophane
and collyrite, appear to form a series in which the silicic acid’
varies greatly in proportionate amount. They may be viewed
as a hydrated silicate of definite composition, combined with
indefinite amounts of the native hydrate of alumina, Al?O%,
3HO, Gibbsite. But what is this definite silicate? Collyrite,
2 (Al?0°) Si0?, 9HO plus 6(Al?0%, 3HO), would give numbers
almost identical with those of the last analysis recorded above ;
but collyrite itself might be viewed as allophane plus some
equivalents of hydrate of alumina, and Mr. Northcote views ©
allophane as a still higher silicate combined with different pro-
portions of the hydrate. All these formule might also be ex-
pressed as Dr. Odling’s ortho-silicate, Al* Si04, plus more or less
hydrate of alumina, plus more or less water ; but not one of these
methods of expression appears to possess any such preponderating
advantage as to lead to the conviction that it represents the
true composition of the mineral under its various phases.
LXIV. On the Allotropic States of Oxygen; and on Nitrification.
By Professor C. F. ScHONBEIN*.
| HAVE been busily occupied with my favourite study, and
have found out several new facts regarding the allotropic
states of oxygen, their changeability one into another, and nitri- .
fication, and I am inclined to believe that the results obtained
are not quite void of scientific interest.
After many fruitless attempts at isolating ozone from an
* ozonide”’, I have at last succeeded in performing that exploit ;
and have also found out simple tests for distinguishing with the
greatest ease ozone from its antipode, “antozone.” As to the
* Extracted from a Letter to Professor Faraday.
‘and on Nitrification: Mae) Zoe
production of ozone by purely chemical means, the whole secret
consists in dissolving pure manganate of potash in pure oil of |
vitriol and introducing into the green solution pure peroxide of
barium, when ozone mixed with common oxygen will make its
appearance, as you may easily perceive by your nose and other
tests. By means of the ozone so prepared, | have rapidly oxi-
dized silver at the temperature of —20° C., and by inhaling it
produced a capital “ catarrh.”
Regarding nitrification, the most important fact I have dis-
covered is the generation of nitrite of ammonia out of water and
nitrogen, 2. e. atmospheric air, which is certainly a most won-
derful and wholly unexpected thing. To state the fact im the
most general manner, it may be said that the salt mentioned is
always produced if water be evaporated in contact with atmo-
spheric ar. This may be shown in a variety of ways. Let, for
instance, a piece of clean lmen drenched with distilled water dry
in the open air, moisten it then with pure water, and you will
find that the liquid wrung out of the linen and acidulated with
dilute sulphuric acid (chemically pure) will strike a blue colour
with starch-paste contaiming iodide of potassium,—by the by,
the most delicate test for the nitrites. It is therefore a matter
of course that shirts, handkerchiefs, table-cloths, in fact all lien,
&c., must contain appreciable quantities of nitrite of ammonia;
and if the chemistry of England be not entirely different from
that of Switzerland, you will find the same thing at the Royal
Institution. The purest water, suffered to evaporate sponta-
neously in the open air, will after some time have taken up
enough nitrite of ammonia (continually being formed at the eva-
porating surface) to produce the nitrite reaction. If you make
use of water holding a little potash, or any other alkali, im solu-
tion, the same result will be obtained, 7. e. the nitrite of that
base will be formed (of course in small quantity). The most
convenient way of performing the experiment is to moisten a bit
of filtering-paper with a dilute solution of chemically pure pot-
ash, &c., and to suspend it for twenty-four hours in the open air.
On examining the paper it will be found to contain a perceptible
quantity of a nitrite, which by a longer exposure of course in-
creases. But you may still more rapidly convince yourself of the
correctness of my statements, if you heat pure water to a tempe-
rature of 50° or 60° C. in a porcelain basin, and suspend over
the evaporating surface bands of filtering-paper soaked with a
weak solution of potash, soda, or the carbonates of these bases,
Within a very short time (in ten minutes or so) there will be
enough of the nitrite accumulated in the paper to produce the
reactions of that salt. I enclose a bit of paper treated in that
way for a couple of hours, and by laying it upon a watch-glass
oo
468 On the Allotropic States of Oxygen; and on Nitrification.
and pouring over it acidulated starch-paste containing iodide of
potassium, you will perceive the effect produced. The fact which
I have ascertained, that the purest water mixed with a little che-
mically pure sulphuric acid or potash and kept for some time
evaporating in the open air at a temperature of 50° or 60° C.
(the loss of the liquid being now and then restored) contains, in
the first case, a perceptible quantity of ammonia, and, in the
second case, of nitrous acid, may now be easily accounted for.
You know that about eighteen months ago I found that, during
the slow combustion of phosphorus in moist atmospheric air,
very perceptible quantities of nitrite of ammonia are formed, and
drew from that fact the inference that the salt is engendered by
3 equivalents of water combining directly with 2 equivalents of
nitrogen. Now there is to me hardly any doubt that the pro-
duction of that nitrite is due to the evaporation of water taking
place about the phosphorus, whose temperature, in consequence
of its burning state, proves to be higher than that of the sur-
rounding medium, and the fact ailuded to must therefore be
considered only as a particular case of a general rule. The
same remark apples to the formation of nitrite of ammonia
which takes place durmg the rapid combustion of charcoal, &c.
in atmospheric air. Combustion, as such, has, I believe, nothing
to do with that formation. I must not omit to tell you that by
means of a large copper still, properly heated, and taking care
not to introduce too much water into the vessel at once, I can
prepare in a very short time several pints of water with which the
reactions of nitrite of ammonia may be produced in the most
striking manner. I hope before long to have an opportunity of
sending you some of this water.
I cannot finish my letter without saying a word or two about
nitrification in general, a fact hitherto so much enveloped in
obscurity. I think the matter is now clear enough. The evapo-
ration of water is continually going on in the atmosphere, and
along with it the generation of nitrite of ammonia. Now, this
salt being put in contact with the alkaline bases or their carbo-
nates, nitrites of potash and the other alkalies are formed, which
afterwards become gradually oxidized into nitrates. In our rainy
countries these salts are washed away almost as soon as formed,
and carried into the springs, rivers, &c.; and there is therefore
no accumulation of them as in the Hast Indies, &c.
That the formation of our nitrite out of water and nitrogen is
a fact highly important for vegetation need hardly be stated.
Indeed each plant, by continually evaporating water into the
atmosphere, becomes a generator of nitrite of ammonia, prepa-
ring, if uot all, at least part of its nitrogenous food, and the same
thing takes place in the ground on which it stands. Jam there-
On the Resolution of Equations of the Fifth Degree. 469
fore inclined to think that our friend Liebig is right in asserting.
that no plant wants any artificial supply of ammonia, or of mat-
ters producing that compound, there being enough of it offered
by natural means. Having communicated the results of my
researches on the subjects mentioned above to the Academy of
Munich, I hope they will soon be published.
[In relation to the peculiar circumstauces under which oxygen
and nitrogen combine, it may be worth while here to refer to the
results obtained by Dr. Bence Jones (Phil. Trans. 1851, p. 407,
&c.), where the direct union of these gases in all cases of com-
bustion in air is described. Sch6nbein’s results depend upon
evaporation.—M. F.]
LXV. Supplementary Remarks on M. Hermite’s Argument rela-
ting to the Algebraical Resolution of Equations of the Fifth
Degree. By G. B. JERRARD*,
- ‘ee art. 8 of my “ Remarks on M. Hermite’s Argument+,”
I stated that his conclusion was such as to indicate that
an error must somewhere have found its way into his calculus.
The reasons in support of my statement, which are there only
glanced at, I proceed to explain.
10. Putting his final result under the form
N
sy
it is clear that N may be regarded as an integral function of the
coefficients A,, Aj,..A;, and such as not to involve any radi-
cals except those characterized by the symbols ,/, ¢/ ; while D
may be supposed to be a rational as well as an integral function
of the coefficients in question.
11. Let now
N,
D,
N :
denote what ) becomes when we assign such values to A,,
A,,..As; that the equation in 2 shall be a solvible equation of
the fifth degree, the expressions for whose roots shall involve irre-
ducible radicals of the form 4/z, How can this case be explained ?
12. Here, you will say, ©,=0; so that we may obtain an
independent solution into which quintic radicals shall enter. A
* Communicated by the Author.
t+ See the Philosophical Magazine for last February.
470) Mr..A. Cayley on a Question in the Theory of Probabilities.
very little reflection, however, will convince us that the question
has a far wider scope than this answer would imply.
13. Doubtless S, ought to vanish ; in other words, ought
to be such as to become equal to zero for those particular values
of A,, Ag, ..A; which lead to a solvible case involving fifth roots.
If, then, © be so constituted as to apprise us of the existence of
all such solvible cases—as it unquestionably ought to do—it
must involve factors by the evanescence of which each expression
for S, shall vanish. Accordingly 2 must not be composed
merely of a succession of terms of the form 0 x A* B’ C’.. ES;
A, B, C,..E having the same meanings as Aj, Aj, Ag,.. A;
respectively. Now hia function S$), in which A, B, C,..E are.
all of them supposed to be arbitrary, cannot Pate ‘unleeen
opposition to what has been just stated—it be made up of
terms of the form 0 x A* B°C’..E*. I conclude therefore that
D ought to be different from zero.
14, Again, when I regard ‘ from another point of view as
the denominator of an expression indicative of an impossibility,
_I am forced to come to the conclusion that S ought to be equal
to zero.
15. Reflecting on the incongruous properties which are thus
seen to attach themselves to the function S, I am unable to
accept the result
N :
)
as free from error.
16. In mynext paper I purpose to meet some objections urged
by Mr. Cayley and Mr. Cockle against my proof, in the Philo-
sophical Magazine for May 1861, of the impossibility of establish-
ing a rational communication* between the function fife? fe fit
and its fifth power.
March 1862.
LXVI. Postscript to the Paper “On a Question in the Theory of
Probabihties” .1n the May Number. By A. Cayutny, Esq.
UNACCOUNTABLY did not recall to myself Mr. H. Wil-
braham’s paper “On the Theory of Chances developed in
Prof. Boole’s ‘Laws of Thought, ” Phil. Mag.vol.vil. pp.465-476
(1854), which contains a most valuable discussion of the ques-
* Tn addition, be it remembered, to the one ©
0",
which characterizes the case in question.
+ Communicated by the Author.
Mr. A. Cayley on a Question in the Theory of Probabilities. 471
tion. Using, as before, ABH, A'BE, &c. to denote the probabi-
lities of the compound events ABE, A’BE, &c., Mr. Wilbraham
in effect shows that in each of the two solutions the following
equations are (as they obviously should be) satisfied, viz.
ABE + ABE! + AB/E + AB'E’+ A'BE-+ A'BE! + ABE’ =1, >
eer Ady 1 ABR) AT ge ee
ABEPABY J... +ABELABE . 3. =, bq)
mepe . . SABE. OE (2 Tee aa
De er, ABM 27 0 teat) ee oghy)
but (besides these) that, on the one hand, Prof. Boole has the
relations
ABE ABE ABE! ABT
ABE ABP ABW ABE ¢ ©)
which equations are consequently implicit assumptions in his
theory, and which, with the equations (a), give his solution,
and that, on the other hand, I have the relations
ABE+ABH' — ABE +AB'H! ABE’ _ ABE!
A'BH+A'BH ~ A'BIE+A'BIE? ABE Apa OO)
which are consequently implicit assumptions of mine, and which,
with the equations (a), lead to my solution,—the signification of
these two equations being that the events A, B are treated as in-
‘dependent (1) in the case where it is not observed whether E
does or does not happen, (2) im the case where E does not
happen. °
The second of the equations (0) is the same as the second of
‘the equations (c). But it is not easy to explain the first of the
equations () ; indeed Mr. Wilbraham remarked that it appeared
to him not only arbitrary but emimently anomalous. The pecu-
liarity in its form is, that it does not, like the others, when ABE,
&c. are considered as products, reduce itself to an identity ; it
seems to be a conclusion which, in support of his theory, Prof.
Boole is bound to justify a posteriori.
Prof. R@yle wishes me to mention that he has succeeded in
‘obtaining a demonstration of the analytical theorem arising from
his theory, referred to in his “ Reply” in my paper.
2 Stone Buildings, W.C.,
May 7, 1862.
fF 472 0]
LXVII. Chemical Notices from Foreign Journals. By K. AvKIN-
son, Ph.D., F.C.S. |
[Continued from vol. xxii. p. 521.]
UBNER* has investigated several decompositions of chlo-
ride of acetyle. When this substance is enclosed in a sealed
tube with pentachloride of phosphorus and heated for some time
to 100°, and for a short time to 190°, an action takes place the
result of which is that the tube contains nothing but liquid. On
opening the tube, a stream of hydrochloric acid escapes ; and on
subsequently distilling the contents, a series of bodies is obtained,
the first of which is terchloride of phosphorus, followed by a little
oxychloride of phosphorus. The distillate which passed over at
about 118° consisted of chloride of trichloracetyle, €? Cl? 0 Cl, as
was proved by converting this substance into trichloracetic ether.
Besides this body, and the less highly chlormated compounds,
C? H?C10, Cl and C? HCl? 0, Cl, Hubner considers that the
bodies, G? H® Cl?, G? H? Cl*, €? HCl®, and C?CI°, are also pro-
bably formed.
Chloride of acetyle and cyanide of silver were enclosed together
in a glass tube, and heated for a couple of hours to 100° to com-
plete the reaction which was set up soon after the tube was sealed.
On subsequently opening the tube, an odour of acetamide and ~
hydrocyanic acid was perceived ; and on distilling the contents, a
body was obtained which was ultimately found to boil constantly
at 93°. The analysis of this compound proved that it was the
cyanide of acetyle, C? HP OE N. This body is lighter than water,
in which it dissolves with the formation of hydrocyanic and acetic
acids.
When this cyanide of acetyle is placed in contact with hy-
drate of potash or sodium in closed vessels, it is transformed
into an oil insoluble in water. Potash only acts when the mix-
ture is agitated, but then with such a disengagement of heat as
to require cooling down to prevent the evaporation of the cyanide
of acetyle. This oil, when washed with water, solidifies to a
divergent crystalline mass, especially when touched with a sharp
point. Singularly enough it has exactly the same composition
as the liquid cyanide of acetyle. It melts at 69° and boils at
170°; it remains liquid for some time at a moderate tempera-
ture, but then erystallizes m large plates. Boiled with potash
it disengages ammonia.
The author is still engaged with the investigation of these
compounds.
* Liebig’s Annalen, December 1861.
Chemical Notices :—Linnemann on Sulphocyanic Acid. 473
Sulphocyanic acid, Ss can be regarded as sulphuretted
hydrogen in which an equivalent of hydrogen is replaced by
cyanogen. Linnemann has prepared the corresponding anhy-
dride of sulphocyanic acid by the action of iodide of cyanogen
on the sulphocyanide of silver.
AgCyS + ICy = Agl + Cy?S
Sulphoeyanide Iodide of Iodide of Anhydrous sulpho-
of silver. cyanogen. _ silver. cyanic acid.
The reaction is exceedingly regular ; it takes place at a moderate
temperature, and is best effected when an etherial solution of
iodide of cyanogen is triturated at a gentle heat with the corre-
sponding quantity of the silver-salt. The product is treated
with bisulphide of carbon, by which the sulphide of cyanogen is
dissolved out, and, on cooling, is obtained in transparent rhombic
plates, or long thin lamine. It sublimes at 80° or 40°, and is
thereby obtained in small, highly refringent thin lamine. It is
heavier than bisulphide of carbon; it is dissolved by ether, alcohol,
and water, and readily crystallizes from the hot supersaturated
solution. It is decomposed by potash into cyanate and sulpho-
cyanide of potassium ; and with nascent hydrogen, sulphuretted
hydrogen, and sulphide of potassium it yields the same products,
namely hydrocyanic acid and sulphocyanic acid. It unites with
two molecules of ammonia to form a sulphide of cyanammonium
—a reaction quite analogous to that of sulphuretted hydrogen on
ammonia, which yields sulphide of ammonium. Thus,
Cy) _NH8Cy
GY bS+2NH= NH oF bs
H NHB
Hb S+2NH= Nis tt ts,
According to Lassaigne*, volatile chloride of cyanogen can be
obtained by the action of chlorine on an aqueous solution of
cyanide of potassium. A current of the gas is passed into a
solution of one part of cyanide of potassium contained in a room
flask which is kept cold with ice; in the cork of this flask is
fixed a tube leading to a U-tube placed in a mixture of ice and
salt: the greater part of the chloride of cyanogen condenses in
this tube to colourless crystals.
Bromide of cyanogen may be formed in an analogous manner
by adding bromine, which has been cooled to 0°, to a solution
of cyanide of potassium in water contained in a retort, which is
kept cold by means of ice. After a sufficient quantity of bro-
mine has been added, the retort is stoppered and gently warmed,
* Liebig’s Annalen (Supplement), December 1861.
AT4 ©... M. Wurtz on Props ylic Alcohol. WA tothe)
on which bromide of cyanogen is condensed in the neck in cubical
and acicular crystals.
Bunsen*, by means of the spectrum-analysis, has established
the presence of Uithion in two meteorites—one which fell at
Juvenas in France, in 1821, and the other at Parnella in South-
ern India, in 1857.
Lautemann has shown that, by the reducing action of hydriodic
acid, lactic acid may be reduced to propionic acid}. Propylic
elycol stands to propylic alcohol in the same relation as lactic
‘acid to propionic acid; and by the action of hydriodic acid on
propylic glycol, Wurtz} has shown that it is reduced to propylic
alcohol. When the former substance was heated in the water-
bath for some time with concentrated hydriodic acid, the mix-
ture became dark from the separation of iodine; and on subse-
quent neutralization and distillation, a heavy liquid was obtained
which proved to be iodide of propyle, €° H’I. This had been
formed in consequence of a double reaction—reduction of propylic
glycol to propylic alcohol, and change of the latter to iodide of
propyle in consequence of the further action of hydriodie acid.
Oye POPES" yp LO+H? 0421
Propylic glycol. Propylic alcohol.
cf
OT YO + HI =CH1+H0.
Propylic alcohol. Iodide of propyle.
This production:of propylic alcohol differs from the result ob-
tained by Lourengo, masmuch as the above reaction is one of
reduction, while Lourenco’s reaction is a case of 1 inverse substi-
tution.
Wurtz has also obtained iodide of butyle, by a precisely analo-
gous reaction with hydriodic acid and butylic glycol. Ethylic
alycol, as Simpson has shown§, is converted by ei acid
into iodide of ethylene.
Boutlerow|| has described the synthetic formation of a saccha-
rine substance. To a solution of dioxymethylene, lime-water was
cradually added, and this solution evaporated in the water-bath
and afterwards in vacuo, by which a syrupy residue was obtained
containing crystals of formiate of lime. By treating this residue
* Liebig’s Annalen, November 1861.
+ Phil. Mag. vol. xix. p. 384.
{.Ann. de Chim. et de Phys., vol. lxii, p. 124.
§ Phil. Mag. vol. xix. p. 73.
‘|, Liebig’s Annalen, December 186 Leo ii43f #
M. Boutlerow on Methylenitane. A75.
with alcohol a saccharine substance was dissolved out, which
Boutlerow calls methylenitane. It is uncrystallizable, and, heated.
on platinum-foil, emits the odour of burnt sugar. Its aqueous
solution is feebly acid, and reduces a solution of tartrate of copper ©
even in the cold. When heated with excess of butyric acid, it
forms an oily compound, which is somewhat viscous at ordinary
temperatures ; it is decomposed by baryta-water with formation
of butyrate of baryta. It was not possible to free it entirely
from an inorganic substance, probably formiate of baryta, and
the analyses were not very concordant. Boutlerow assumes pro-
visionally that its formula is G’ H'* 0°, and he thus expresses its
formation :—
4G? H*O? = G7 H40% + CH? 0?
Dioxymethylene. Methylenitane. Formic acid.
Boutlerow says, “It is the first example of the synthesis of a
substance of a saccharine character, and from the simplest com-
pounds of organic chemistry. Considermg the whole series of
changes through which ethylic alcohol passes, which can itself
be formed from the elements it contains, it may be said that the
first example of the complete synthesis of a saccharine substance
is here met with.”
The same chemist* has described a new mode of formmg
ethylene and its homologues. When iodideof methylene, C?H?1?,
was heated with copper and water in a closed tube, a gaseous
mixture was formed containing carbonic acid, marsh-gas, and
various hydrocarbons, about 85 per cent. of which were absorbed
by bromine with the formation of an oily liquid. This proved
to be a mixture of the bromides of the general formula €? H” Br’,
the a part of which consisted of bromide of SHEN EhS,
GC? H* Br?
Beilstein} has made a series of experiments on glyceric acid.
When an aqueous solution of this acid was mixed with iodide of
phosphorus a brisk reaction was set up, and hydriodic acid vapours
disengaged ; the mass in the retort, at first liquid, solidified on
cooling to a white crystalline mass, which on recrystallization
was found to consist of iodopropiunic acid, €? H° I 0%, the forma-
tion of which may be thus expressed :—
CHeOot+PP = HIS? + HI+P0%
Glyceric acid. Iodopropionie acid.
The group P 0”, which contains the elements of phosphorous and
phosphoric acids, probably takes up water, and decomposes into
these acids. lodopropionic acid crystallizes from a hot saturated
* Liebig’s Annalen, December 1861. _ + Ibid. November 1861.
A76 M. Caventou on Bromide of Ethyle.
aqueous solution in pearly lamin, and from a less concentrated
solution in large glassy erystals.. Its solution can be boiled
without change, but its salts are decomposed by this process.
When the silver-salt was treated in this way, it was decom-
posed with formation of iodide of silver. The mother-liquor |
from this yielded a substance which crystallized in fine needles,
was strongly acid, and evaporated without residue when heated
on platmum-foil. The analysis of this compound proved that
this was a substance having the same composition as lactic acid ;
but the investigation of the salts showed that it differed from
this acid. It is still under investigation.
Beilstein also endeavoured, but without success, to form a
bromolactic acid with a view to effecting its conversion into gly-
ceric acid, by a reaction analogous to that by which chloropro-
pionic acid is converted into lactic acid.
Caventou* has investigated some of the bromine substitution
products of bromide of ethyle. Bromide of ethyle was enclosed
in a sealed tube with excess of bromine and heated to about 170°.
By repeated fractional distillations of the product, two distinct
compounds were obtained: one, boiling at 110° to 112°, is mo-
nobrominated bromide of ethyle (CG? H* Br) Br, and is isomeric
with bromide of ethylene; the other, boiling at 187°, is
(GC? H? Br?) Br, and is not merely isomeric, but is identical
in properties with Wurtz’s brominated bromide of ethylene,
(CG? H? Br) Br?.. There is another compound of the formula
GC? H* Br?, bromide of ethylidene, obtained by the action of ter-
bromide of phosphorus on aldehyde. Unlike, however, its iso-
mers, bromide of ethylene and the body which Caventou has
described above, it cannot be distilled without undergomg de-
composition.
Caventou found that brominated bromide of ethyle is decom-
posed when heated with acetate of potassium for two days to
140°, forming bromide of potassium and acetate of glycol—an
instance of the transformation of alcohol into a glycol compound.
Zwenger and Dronke+ have discovered in the blossoms of the
Acacia a new glucoside. It is prepared by treating the evapo-
rated aqueous extract of the blossoms with alcohol; the new
body, which they call Robinine, separates out from the concen-
trated alcoholic solution in crystals, which are pressed, dissolved
in boiling water, and treated with neutral acetate of lead to
remove foreign substances. The solution is then freed from lead
by treatment with sulphuretted hydrogen; and, on the cooling
* Liebig’s Annalen, December 1861.
+ Liebig’s Annalen (Supplement), December 1861.
MM. Zwenger and Dronke on a new Glucoside. A77
of the liquid, robinine separates out in yellowish crystals, and is
purified by repeated recrystallizations from water.
It is a neutral substance, with a feeble astringent taste. Very
soluble in hot water, it is slightly soluble in alcohol, and inso-
luble in ether. It melts at 195°, and solidifies to an amorphous
mass. It is dissolved by alkaline solutions with a fine golden-
yellow colour. It readily reduces an alkaline solution of oxide
of copper, and also chloride of gold.
It is readily decomposed by boiling with dilute hydrochloric
acid, with the separation of quercetine, while the solution contains
sugar. Emulsine does not produce this change. This decom-
position reveals a connexion between this new glucoside and quer-
citrine; both of them yield quercetine by decomposition, but
differ in the nature of the saccharine substances which they con-
tainas a copulate. This is the first instance of the kind in which
such a difference occurs in the glucoside. Zwenger and Dronke
have prepared quercetine by the decomposition of quercitrine,
and found that this is quite identical with the body prepared
from robinine.
Robinine, dried at 100°, has the formula C°° H®° O%?; dried
in the air its formula is C°? H*! 0%, containing 11 equivalents
of water of crystallization. The formula of quercitrine was found
mee 118 ()*,
The decomposition of robinine is expressed by the following
equation :-—
C50 H20 022 + 4HO = C26 H! Ol? + 2(C!2 H!2 0!)
Robinine. Quercetine. Sugar.
and that of quercitrine thus :—
C23 H!8§ 024. 7HO=C% Hl? 0l2 4. Cl2 HBO}, x
Quercitrine. Quercetine. Sugar.
Quercitrine, in almost all its physical and chemical character-
istics, is different from robinme—more especially in its difficult
solubility in hot water, in its being precipitated by acetate of
lead, and in its crystalline form; and the only similarity is the
elimination of quercetine by both bodies when treated with acids.
The sugar from quercitrine forms yellowish crystals with a
sweet taste, reduces alkaline solution of sulphate of copper even
in the cold, and, mixed with yeast, passes into the spirituous
fermentation. By oxidation with nitric acid it yields oxalic acid
alone. ‘The robinine sugar, on the contrary, does not crystal-
lize; it however reduces oxide of copper in solution of potash
even in the cold, and, mixed with yeast, passes into the alcoholic
fermentation. Oxidized with nitric acid it yielded principally
picric acid, and was thus different from quercitrine sugar.
From the great analogy which a number of glucosides present,
478 Royal Society :—
in their products of decomposition, with robinine and quercitrine,
it is probable that they are either identical with these, or like
those analogous compounds of quercetine with different kinds of
sugar. The authors are engaged on investigations in this direction.
Berthelot* observed that m an alcoholic solution of ‘baryta
which had been kept in a loosely-corked vessel for several years,
there had been formed aldehyde resin, oxalic acid, and a small
quantity of a peculiar volatile acid soluble in water. As far as
this was investigated, its properties seemed to agree most closely
with those of acrylic acid, C® H* 0%,
The formation of this acid from alcohol is readily understood,
knowing that it is easily oxidized to acetic and formic acids, and
that it thus can be conceived as being formed from ordinary
aldehyde and formic acid,
C6 H4 O*= C4 H* 02+ C2 H? O4— H? 02,
just as cimnamice acid is formed from benzoic aldehyde and acetic
acid. 7
LXVIII. Proceedings of Learned Societies.
- ROYAL SOCIETY.
[Continued from p. 411.]
May 16,7—X\HE Crocnian Lecture-—‘“On the Relations between
1861. Muscular Irritability, Cadaveric Rigidity, and Putre-
faction.”’ By C. E. Brown-Séquard, M.D., F.R.S.
May 30.—“On the Elimination of Urea and Urinary Water in
their relation to the Period of the Day, Season, Exertion, Food,
and other influences acting on the Cycle of the Year.’ By Dr.
Edward Smith.
“On the Theory of the Polyedra.” By the Rev. T. P. Kirkman,
M.A., FR.S. &e. et
June 13.—Thomas Graham, Esq., Master of the Mint, Vice-
President, in the Chair.
The following communications were read :—
*< Notice of Recent Scientific Researches carried on Abroad.” By
the Foreign Secretary. ;
The following notice of his researches has been furnished to the
Foreign Secretary by M. Schrauf.
“On the Determination of the Optical Constants of Crystallized
Substances.’ (First and Second Series.) By Albert Schrauf
(Vienna. )
In the two hitherto published series of these investigations, the
data concernmg the refractive and dispersive powers of twenty cry-
stallized substances are communicated.
* Liebig’s Annalen (Supplement), June 1861.
Schrauf on the Optical Constants of Crystallized Substances. 479
‘Being persuaded that crystallo-physics, more than anyother
branch of physical science, is founded on quantitative calculation of
absolute exactitude, I contrived to obtain first incontestable facts
connected with the hitherto somewhat neglected phenomena of dis-
persion and refraction. Nearly 1000 substances have been crystallo-
graphically investigated, and about 200 have been made the object of
optical researches ; many of them, however, have remained unknown
as to their dispersive and reflective powers, which, representing the
quantitative and qualitative action of any substance on the pro-
pagation of light, are of absolute necessity for the construction of
any sound theory.
It becomes every day a greater necessity to obtain, within these
extensive dominions of human knowledge, a certain number of
general views, subservient to the explanation and systematic arrange-
ment of a great number of isolated facts, as only a small portion of
the present investigation has led to the establishment of general laws.
The great problem of crystallo-physics proposed for solution may be
expressed by the question, What is the causal connexion between che-
mical constitution and morphological and optical properties? The
phenomena of isomorphism, discovered by Prof. Mitscherlich, have
indeed thrown considerable light on the mutual relation of chemical
constitution and morphological properties; yet little, if anything, has
been done to arrive at the solution of the problem in its general form.
As latterly several doubts have been expressed as to the possible
existence of such a connexion, the purpose of my investigations shall
be not only (as expressed in their title) to fill up deficiencies in the
knowledge of facts, but also to propose several explanations indicating
the real existence of such a connexion, and the necessity of making
it an object of earnest research.
In the following paragraphs I intend only to mention some
theorems whose solution is already athieved. Another series of my
investigations, to be published subsequently, is to afford general
demonstrations and applications of consequences in strict connexion
with duly stated facts.
The most important of the theorems, as far as they may be simply
enunciated, are—
§ 1. The calculation, graphic representation, and derivation of all '
the ecrystallographical and physical properties of the rhombohedral
system are possible if three rectangular axes are assumed ; the axis ¢
coinciding with the principal rhombohedral axis, and the axes a and
6 with the diagonals of the prism of 60°.
§ 2. The following indices represent consequently the character-
istic equations for the s ymmetrical crystallographic systems :—
Rectangular Azes.
Tesseral Pees = Ps bs
Pyramidal me VS ey.
Rhombohedral —V3:1:1
Prismatic —— ae ae ae |
480 Royal Society :—
§ 3. The optical axes of elasticity, coinciding with the diagonal of
the prism of 60°, are nearly equal to each other, and (a and 6
being axes of elasticity and a and 0 crystallographical axes) if limit
a,
ps supposed to be = 3, then a=f.
§ 4. Whenever a prism of 60° is extant in the prismatic system,
the first median line (“ bissectrice de l’angle aigu’’) is perpendicular
to its diagonal*.
§ 5. Whenever a number of prisms of 60° are extant (110, 011,
101), the first median line stands perpendicular to the diagonals of
one of these prisms, and simultaneously to the plane of cleavage.
§ 6. The first median line is generally perpendicular to the dia-
gonal of prisms, whose limit may be expressed by simpler proportions,
as 12/2:V/3:V7524/7.
§ 7. The dispersion of the optical axes in the prismatic system is
dependent on the magnitude of the crystallographical axis, with
which the middle axis of elasticity is comcident.
(A) If the ecrystallographical axes (ds,, being a erystallographical
axis, with which coincides the second median line dg, with this the
medial axis of elasticity bemg coincident) are to each other as limit
of the square roots of odd numbers, then for
dg > dom 18S p>,
dg¢=1: 0°7725 706220:
ap=1°57586 pelo ¥p=1'55913
[for D] ap=1°58306 p= 1'56888 yp=1'56596
20. Asparagine. HO, C,H,N,O0,+2HO.
Prismatic. a:b: c=1-:0°8327 : 0°4737.
a,p=1'61392 Bg=157317 Yp= 1754380
a= 164221 = By=1°60194 —- yx = 156538
“Liquid Diffusion applied to Analysis.’ By Thomas Graham,
Esq., F.R.S., Master of the Mint. (This paper is printed in full in
the March, April, and May Numbers of this Magazine.)
“On some new Phenomena of Residuary Charge, and the Law of
Exploding Distance of Electrical Accumulation on Coated Glass.”
By Sir W. Snow Harris, F.R.S.
A main object of this paper is to prove that residuary charge in the
Leyden jar, subsequent to explosive discharge through an external
interrupted circuit, as in the case of discharge by a Lane’s electro-
meter, is not the result of a spreading of the charge upon the un-
coated part of the glass, or of penetration within its substance, but
arises from an undischarged portion of the accumulation left as it
were behind, and still existing in precisely the same way and under
the same conditions as the original charge.
Sir W. Harris on some new Phenomena of Residuary Charge. 485
The author introduces his subject with sundry observations on
Lane’s discharging electrometer, and the law of explosive discharge,
and adverts to the fact recorded by Nicholson in the Royal Society’s
Transactions for 1789, that ‘‘although in moderate charges the ex-
ploding distance appears exactly, or very nearly, proportionate to the
charge itself, yet for nigh intensity, the distance to which the charge
is carried exceeds that proportion:”’ this the author finds to be the
case generally, and quotes an experimental example showing the
amount of deviation from Lane’s law in that particular instance.
He further shows, that in order to obtain explosive discharges at the
increased distances agreeing with the calculated number of measures,
the distances must be slightly increased by certain small quantities.
The probable sources of these differences are now adverted to, and
the common objections to Lane’s discharging electrometer con-
sidered. A new and improved form of this instrument is figured and
described. One of its principal advantages is a means of changing
the exploding points of the discharging balls, which are moveable on
axial centres, so as to bring a new point of the circumference into
play, should abrasion or any other defect arise in the existing ex-
ploding point. The author endeavours to show that the apparent
irregularities so frequently observed in the striking distance of a
charged electrical jar, do not arise from any defect in the quantity
measure, or in the exploding electrometer when properly constructed,
but are altogether dependent on some peculiar conditions of electrical
accumulation on coated glass.
One remarkable peculiarity of the electrical jar, is a disposition to
retain a portion of the charge notwithstanding explosive discharge
has occurred through a discharging circuit; we do not discharge the
whole accumulation ; a portion is, as it were, left behind. The fact
itself is undisputed, but the cause or theoretical explanation does not
appear to have been very clearly comprehended.
The author here introduces some interesting quotations from
certain unpublished manuscripts of Mr. Cavendish, who investigated
so long since as the years 1771 and 1772, what he terms the
“charges of plate glass and other electrical substances coated in
the manner of Leyden phials.”’ Mr. Cavendish found his experi-
mental inquiries greatly embarrassed by the “ spreading of the elec-
tricity’ on the glass ; it is, he says, faster on some kinds of glass
than on others ; besides the slow and gradual spreading, he observed
an instantaneous spreading, visible in the dark, and extending to
about ‘07 of an inch beyond the edge of the coating upon glass °2
of an inch thick, and about *09 upon glass j-th of an inch thick.
Another source of inconvenience, observes Mr. Cavendish, arises from
a certain amount of penetration of the charge into the substance of
the glass itself, equal to about [ths of its thickness ; the space, he
says, within which the charge cannot penetrate is not above 1th of
the thickness, from which he concludes that the charge of a coated
electric will be different im cases in which this penetration of the
charge into the substance of the glass varies, and infers that different
electrics are susceptible of different degrees of charge. He examined
486 Royal Society :—
plates of glass of various kinds, as also of gum-lac, rosin, bees-wax,
&c., and found the capacity of these substances for electrical charge
different—phenomena recently explained by Faraday’s fine discovery
of Specific Inductive Capacity.
This last celebrated philosopher also recognizes the penetration or
infiltration of electrical charge within the substance of coated and
charged electrics, and attributes it to a certain amount of conducting
power in the electrical substance. All substances, he infers, are con-
ductors of electricity in a greater or less degree, and thus admit of
infiltration of charge through their substance. In the case of charged
electrics, the infiltrated electricity subsequently returns upon its path,
and hence residuary charge.
The author has no disposition to question the experimental results
arrived at by either of these eminent men, but is of opinion that they
apply to a different case of electrical force than that of secondary and
immediate discharge, supervening upon a primary discharge of an
electrical jar through an external explosive circuit, which he thinks
can neither be referred to any previous spreading of the charge upon
the glass, or to any penetration of it into its substance, or to return
action as described by Faraday. He has found that of 100 measures
of accumulated charge on a jar with imperfect conducting coatings,
no less than 75 measures, or three-fourths nearly of the whole accu-
mulation, has been left behind after explosive discharge. In a jar
coated with water full 14 measures out of 100, or about one-
seventh, was left undischarged. He thinks it difficult to reconcile
such an amount of residuary charge as this, with any spreading of
the electricity on the glass, or any possible amount of penetration
into its substance.
Although the deductions of Cavendish and Faraday may not be
found to apply as solutions of the interesting problem of residuary
charge, they still find their application in other cases, as in the case
of the facts noticed by Nicholson already detailed. The intensity of
explosive discharge may apparently become increased by a penetra-
tion of the exploding electricity into the air separating the balls of
the discharging electrometer, in which case the measured distances
of discharge, according to Cavendish, would, for given measured
quantities of electricity, continually decrease, and discharge at the
measured distances between the exploding balls would appear to
happen prematurely. It is now shown by reference to a Table of
experimental results, that at distances 1, 2, 3, 4, taken in tenths of
an inch, with quantities of measured charge also as 1, 2, 3, 4, the
actual distances of explosion are nearly as °1, °214, °325,°445. The
author hence infers that, supposing the penetration of the first
measures very small and not of much value, the penetration of the
succeeding measures may be taken as ‘014, ‘025, 045, that is -007,
0125, ‘0225 upon each of the opposed exploding points, taking the
surfaces of the exploding balls as curvilinear coatings to the inter-
vening air.
If any considerable spreading of the charge upon the uncoated
glass should arise, that, as remarked by Cavendish, would be equiva-
Sir W. Harris on some new Phenomena of Residuary Charge. 487
lent to an increase of the coating, and hence the tension due to a
given quantity of charge would be less. The effect would be greater
on the first measured quantity than on succeeding quantities; hence
for explosion at a first distance, an additional two or three measures
might be required, which, as the spread upon the glass became
satisfied, might not be requisite in the same proportion upon suc-
ceeding measured distances, in which case discharge would ensue
with a less number of measures than calculation determines according
to Lane’s law, making it appear as if, according to Nicholson, ‘“‘ the
intensity ran before the quantity.”
Both Franklin and Nicholson have taken a sound practical and
theoretical view of electrical accumulation on coated glass, which the
author conceives to depend on a play of opposite electrical forces,
either directly through the glass intermediate between the coatings,
or through the medium of an external circuit, or both. He con-
siders the terms “‘free’’ and ‘‘ compensated,” or “latent” electri-
city, perfectly admissible when correctly applied and limited by sound
definition. All the accumulated charge, up to the exploding point,
is evidently not sensible to the electrometer, and he thinks it con-
venient to distinguish between that portion of the charge of which
the electrometer directly says nothing, and that portion to which its
- indications are more immediately referable, more especially as these
two, or conjugate portions, have important relations to each other.
Thus a double measured charge has twice the amount of free charge ;
and the free charge, as estimated by attractive force, is as the square
of the accumulation. When the free charge explodes, the whole
accumulation, or nearly all, goes with it, at least in common cases of
metallic coated glass, and according to Nicholson carries it through
distances proportionate to the charge itself: the terms ‘‘free”’ and
“latent” electricity, or, as the French have it, ‘‘electricitédissimulée,”
may not be exact or admissible, if meant to imply a difference in kind
or mode of action of electrical force, but they are by no means
objectionable when denoting different amounts of the same force in
this or that direction.
In considering the nature of electrical accumulation on coated
electrics and the law of explosive discharge, we have to deal with a
simple question of physical force taken in the abstract, and not with
a theoretical electric fluid or fluids of high elasticity, subject to ex-
pansion or contraction, changes in thickness of stratum, tension,
density, and the like. The terms “‘tension” and “intensity,’’ so
commonly applied to designate degrees of electrical force, are con-
venient and not inappropriate terms when legitimately applied and
limited by definition. The term znéensity is well adapted to express
the attractive force of the charge in the direction of the electrometer,
and which, in continually zncreasing according to a known law, ter-
minatesinexplosion. The intensity or attractive force varies with the
square of the charge. The term “tension” is more especially appli-
cable to the constrained state of the dialectric particles sustaining the
induction necessary to the charge, and is equivalent to the reactive
force of the particles in an interrupted circuit of discharge to break
488 Royal Society :—
down or reverse the polarized state of the dialectric medium impeding
discharge, as between the exploding balls of the Lane’s discharger :
this is as the quantity of charge directly. In employing these terms,
the author has not the least view to any specific changes in the quality
or condition of the accumulated electricity, as relating to density,
elasticity, and such like. Whether the tension and intensity of a
charge, as evidenced by the electrometer, be great or little, he con-
ceives that the nature of the force and its mode of operation remains
the same. Viewing the process of electrical accumulation and dis-
charge in the Leyden jar as the result of certain powers or forces
operating either immediately through the glass or through an external
circuit, or both, we may readily imagine that at the critical point at
which the forces in the two directions become balanced, and at which
point the equilibrium of charge is, at it were, overset on the side of
the exterior circuit, then it is that residual charge ensues, either by a
momentary revulsion of force between the coatings in the direction of
the intervening glass, frequently causing fracture, or otherwise by a
retention of some of the charge in that direction at the instant of
explosion. Some instructive and important experiments by Mr. T.
Howldy are here quoted in support of this conclusion, from the
pages of the ‘ Philosophical Magazine’ for the year 1815. A ruptured
jar had the coatings removed from around the perforated part, so as to
admit of the jar receiving a given amount of charge. When explosive
discharge took place in the usual way, a spark was observed to pass at
the same instant between the coatings through the perforation in the
glass, evidently showing an exertion of force in that direction. This
spark is entirely independent of the discharge in the circuit, the
force of which remains the same as if no such perforation existed, as
Priestley and other electricians, and Mr. Howldy himself, have fully
demonstrated.
Considering the question of residual charge as bearing materially on
our views of the nature of electrical force, the author seeks to inves-
tigate, by new forms and kinds of experiment, the relation of the
residual quantity to the whole charge, whether accumulated on glass
coated with very perfect conductors such as the metals, or otherwise
with less perfect conductors, as water, or with imperfect conductors,
such as paper, linen and the like. The instruments employed are
now enumerated and commented on, and their experimental arrange-
ment figured and described. They consist of the electrical or Leyden
jar; Lane’s improved electrometer; the hydrostatic electrometer
as recently perfected; the thermo-electrometer; quantity or unit-
measure ; and battery charger and discharger. The following is the
course which the author pursued in his inquiries, through the medium
of these instruments.
The quantity of charge being given, its intensity is measured by
the hydrostatic electrometer in terms of attractive force at a constant
distance, suppose at distance 1 inch. This is first noted: the jar is
now discharged through its exploding distance by completing the
circuit through the Lane’s discharger. The hydrostatic electro-
meter, being now made perfectly neutral, is again brought into con-
Sir W. Harris on some new Phenomena of Residuary Charge. 489
nexion with the inner coating of the jar. The intensity or attractive
force of the residuary or remaining charge is now noted, but as this
force is necessarily small, it is taken with the attracting plates at a
diminished distance from °1 to °3 of an inch or more, as the case may
require, and subsequently reduced to the standard distance of one
inch, taking the force to vary, as demonstrable by the electrometer,
as = This being determined, the relative quantities of electricity
in the full charge and the residual charge will be as the square roots
of the respective attractive forces or intensities; the total force, as
also demonstrable by the instrument, being as the square of the ac-
cumulation. Let, for example, the quantity of charge communicated
to the jar be 100 measures, and the attractive force, or intensity at
distance one inch, be 144 degrees, and suppose intensity of residual
force at the same distance=‘08. In this case we have the simple
proportion 100 measures: « measures:: V7 144 : 708 :: 12: +283
and quantity of residual electricity Se 2°35 measures
nearly ; so that of the original 100 measures of charge communicated
to the jar, rather more than ;/,th remains undischarged in this case.
The author here offers some explanatory observations on the rela-
tive dimensions and extent of coating of the unit of measure and the
relative value of the measures quoted, and he thinks if electricians
would agree to recognize a standard instrument of this description, it
would be attended with very considerable advantage, as in the case of
other standard instruments. The unit of measure he employs ex-
poses about 9 square inches of coating ; it is about 4 inches long, °8
of an inch in diameter, and =},th of an inch thick; distance of ex-
ploding balls -05 of an inch. Similar observations were applied to
the thermo-electrometer, the ball of which is 4 inches in diameter,
and has a wire of platinum through it of °01 of an inch in diameter.
The dimensions of the attracting discs of the hydrostatic electrometer
are also noted, which in these experiments were 4 inches in diameter ;
the suspended disc weighs 82 grains. The discs are carefully gilded ;
5 degrees of the arc of measure represents a force of 1 grain, that is
to say, a weight of 1 grain added to either side moves the index
5 degrees of the scale. Having offered these preliminary remarks, the
author proceeds to the following experiments :—
Experiment 1.—Variable charges, amounting to 50, 100, 150
measures, were successively accumulated on different jars, exposing
from two to six square feet of coating, and the residual charges due to
each noted ; these were found to be as the total charge. Thus the
residual charge for 100 measures was in every case double that for
50 measures.
In a succeeding Table are noted—measured charge; exploding
distance ; intensity at distance 1 inch ; residual measures and thermo-
electric effect of discharge. It appears by this Table that residual
charge is as the total charge; exploding distances, as the quantity or
490 Royal Society : —
very nearly ; intensities and thermo-electric effect of discharge. as
square of the quantity or number of measure accumulated.
The author finds that for every metal-coated jar, whether large or
small, of thick or thin glass, exposing from 1°5 to 6 feet of coating,
the residual charge or quantity left undischarged, varies between the
limits of th and 5th of the total charge.
Experiment 2 investigates the effect of thickness of glass. Two
jars, exposing 2°5 square feet of coating, were employed, their .rela-
tive thickness being as 1: 2, that is, ,ths and 5$ths of an inch;
100 measures were accumulated and discharged at their respective
exploding distances. The following results appeared :—exploding
distance directly as thickness of glass ; intensity or attractive force in
direction of electrometer as square of the thickness ; residuary charge
in each case the same, being about =,th part of the total charge ; ther-
mo-electric effect of discharge very nearly the sdme ; so that whether
discharged from thick glass or thin, under intensities of very different
degrees the same quantity of electricity produces the same effect.
The intensities in this case were as 4: 1, yet the thermo-electric effect
did not differ more than one or two degrees, one being 12°, the other
13°. The author finds, by numerous experiments on a series of jars,
that the intensity indication has no influence on the force of discharge,
the quantity discharged being the same. Ima series of jars of dif-
ferent magnitudes, and in which the intensity of a given charge of
100 measures varied between the limits of 100 and 1000 degrees,
there did not appear a difference of more than a few degrees amongst
the whole; the effects varied between 8 and 11 degrees. Some little
difference will generally arise in favour of electricity accumulated on a
small area of coated glass ; in consequence of the greater facility of dis-
charge the accumulation has greater freedom of operation through the
external circuit, as is shown by its greater effect on the electrometer.
A celebrated electrician, the late Mr. Brooke of Norwich, in a con-
ference with Cuthbertson about the year 1800, stated that a Leyden
jar coated with strips of metal ths of an inch wide, leaving intervals
of the same width between the strips, was equally efficient as a full
coating in the ordinary way. ‘Two equal and similar jars, about
1 foot in diameter and 19 inches high, were prepared accordingly ;
ene fully coated to about 4 square feet, the other coated in strips
to about 3°5 square feet. The author, although doubting this state-
ment in all its generality, still considered an investigation of it, more
especially coming from such men as Brooke and Cuthbertson, desi-
rable, and as being calculated to throw further light on the pheno-
mena of the Leyden jar.
A few preliminary experiments seemed to accord with Mr.
Brooke’s view ; the exploding distance of the two jars with a given
charge did not appear extremely different. The accumulated elec-
tricity spread upon the glass between the strips of metal, and thus
enabled the partially coated jar to receive a larger accumulation, upon
the principle stated by Cavendish, than was really due to its extent
of actual coating. Mr. Brooke, in the then state of practical electri-
city, might have been therefore easily led to imagine that a partial
Sir W. Harris on some new Phenomena of Residuary Charge. 491
coating such as he describes was sufficient. It is, however, shown
in this paper that the cases of the two jars are widely different. As
the spread of the electricity becomes satisfied, a less charge is re-
quired for explosion, and the tension of a given quantity increases.
The followmg are the results of experiments with 100 measures
similar to the preceding :—
Full coating.
Exploding distance ...... 15 Intensity 100° at 1 inch.
Residual measures ...... 2°45 Therm. electric effect 8°.
Partial coating.
Mean exploding distance... °25 Intensity 160°.
Residual measures ...... 4:97 Therm. electric effect 3°5.
It is evident the two forms of coating are not equally efficient, the
heating effect of discharge not being half as great in the partially
coated jar, whilst the residual charge is twice as great. The experiment
so far shows the spread of electricity on the uncoated glass to be a
source of absorption of charge to a greater or less extent, and goes
far to confirm the views of Mr. Cavendish, relative to the spreading
of electricity on glass.
The phenomena of metal-coated jars having been so far examined,
a similar course of experiment is followed with jars coated with less
perfect conductors, commencing with water coatings. For this pur-
pose a jar exposing nearly 5 square feet of coating was prepared with
metal coating, and the results of a charge of 100 measures determined
and noted as before ; the metal coating being removed, the same jar
had an equal extent of water applied to its opposite surface coating.
The method of effecting this is described. The author states that it
was so perfect as to shield the experiment from all interference of
vapour from the water surface, so that the jar completely retained
the charge without any dissipation, and in no sense differed in this
respect from a metal-coated jar.
The results of this experiment are not a little remarkable. The
exploding distance of the 100 measures, whether with the metal or
with the water coating, did not materially differ, except in apparent
force, being for the metal °22, for the water -2. The exploding
spark from the water coating, instead of the sharp ringing sound
attendant on the exploding spark from the metal coating, is weak and
subdued, and is often like the sound of fired damp gunpowder. The
intensity or attractive force is also in each case alike, or very nearly ;
being for the metal coating 144°, for the water 142°. The residuary
charges differed considerably, being for the-metal coating about 2°25
measures, or about -/=th part of the total charge; for the water
coating 14°5 measures, or about the 1th of the total charge. The
residuary charge with a water coating is more than six times as great as
with a metal coating. The thermo-electric effect with the metal
coating was 10°, with the water coating nothing ; 200 measures, or
double the charge, had no effect on the thermo-electrometer.
In this experiment it does not appear requisite that both the
coatings should be water; one coating may be metal, as in the first
492 Geological Society :—
forms of the electrical jar. The author could not, at least, discover
any material difference in the results, and concludes that if the first
forms of the electrical jar with an internal coating of water had been
continued, we should have had but small experience of the effects of
artificial electrical discharge on metallic wires.
Imperfect conducting substances employed as coatings to the elec-
trical jar have very similar but very exaggerated effects. With coat-
ings of paper we have a striking example of retention of charge. A
jar exposing 5°5 feet of coated glass, first coated with metal and sub-
sequently with paper, gave the following results under a charge of
100 measures.
Exploding distances, as in the former case, nearly the same, being
"23 and *25; attractive forces or intensity also nearly the same,
being 158° and 160°; residual measures with the metal coating 2°5
measures, or about the th of the total charge; with paper coating, in
some experiments 80 measures, or about ;5,ths of the total charge, so
that the residual charges with metal and paper are as 1 : 32. Thermo-
electric effect for metal coating 8°, for paper coating nothing. It
appears from these and similar experiments, that the interposition of
imperfect conductors between the coating and the glass of the Leyden
jar must necessarily impair its efficiency, and change its electrical
indications, especially when of any considerable thickness. Three
turns of common linen interposed between the outer coating and the
glass reduced the force of discharge from 11° to 6°, nearly one-half,
whilst the residuary or retention of charge is considerably increased :
this question, as bearing in some degree on the retention of charge by
the electric cable, may not be undeserving of further investigation.
GEOLOGICAL SOCIETY.
{Continued from p. 414.]
March 19, 1862.—Prof. A. C. Ramsay, President, in the Chair.
The following communications were read :—
1. ‘On the Sandstones, and their associated deposits, in the
Valley of the Eden, the Cumberland Plain, and the South-east of
Dumfriesshire.” By Prof. R. Harkness, F.R.S., F.G.S.
Having defined the area occupied by these sandstones, breccias,
clays, and flagstones; and referred to the published memoirs in which
some notices of these deposits have been given by Buckland, Sedg-
wick, Phillips, and Binney, the author described, Ist, a section near
Kirkby-Stephen, across the vale of the Eden, where two breccias,
separated by sandy clay-beds, underlie sandstones of considerable
thickness ; 2ndly, a section across Eden Vale from Great Ormside
to Roman Fell, in which the breccias, associated with sandstones,
form a mass 2000 feet thick, and are succeeded by thin sandstones,
shales (with fossils), and thin limestone, altogether about 160 feet,
and next by sandstones 700 feet thick. This is the typical section ;
the fossiliferous shales are regarded by Prof. Harkness as equivalent
to the Permian Marl-slate of Durham; they contain (at Hilton Beck)
remains of Conifere, Neuropteris, Sphenopteris, Weissites (?), Cau-
lerpites selaginoides (?), Cupressites Ullmani (?), Voltzia Phillipsii (?),
Mr. A. Geikie on the Central Valley of Scotland. 493
Cyathocrinus ramosus, and Terebratula elongata. The breccias and
sandstone beneath, previously recognized as Permian, are here re-
ferred to the Rothliegende; and the sandstones above are regarded
as belonging to the Trias. Detailed descriptions of the sandstones
and breccias in the country between Great Ormside and Penrith
were then given, and the gypseous character of the clays at Long
Martin and Townsend noticed. In the section across the vale of
the Eden from the west of Penrith to Hartside Fell, the Permian
breccias, sandstone, and flags are nearly 5000 feet thick, but the
clay series is poorly represented. North of Penrith the flagstones
bear foot-marks (at Brownrigg) like those of Corncockle Muir.
Mr. Harkness next described several sections of these Permian
rocks in the western Westmoreland; and traced them to the other
side of the Solway Firth, in Dumfriesshire (as described in former
papers). Some remarks on the relations of the Permian beds of
Cumberland and Westmoreland with those of St. Bee’s Head, near
Whitehaven, and those of Annandale and Nithdale, concluded the
paper.
2. “On the Date of the Last Elevation of the Central Valley of
Scotland.” By Archibald Geikie, F.R.S.E., F.G.S.
After alluding to the position and nature of the raised beach
which, at the height of from 20 to 30 feet above the present high-
water-mark, fringes the coast-line of Scotland, the author proceeded
to describe the works of art which had been found in it. From their
occurrence in beds of elevated silt and sand, containing layers of
marine shells, it was evident that’ the change of level had been
effected since the commencement of the human period. ‘The cha-
racter of the remains likewise proved that the elevation could not be
assigned to so ancient a time as the Stone Period of the archeologist.
The canoes which had from time to time been exhumed from the
upraised deposits of the Clyde at Glasgow clearly showed that, at
the time when at least the more finished of them were in use, the
natives of this part of Scotland were acquainted with the use of
bronze, if not of iron. The remains found in the corresponding beds
of the Forth estuary likewise indicated that there had been an up-
heaval long after the earlier races had settled in the country, and that
the movement was subsequent to the employment of iron. From
the Firth of Tay similar evidence was adduced to indicate an up-
heaval possibly as recent as the time of the Roman occupation. The
author then cited several antiquaries who from a consideration of
the present position of the Roman remains in Scotland had inferred
a considerable change in the aspect of the coast-line since the
earlier centuries of the Christian era. He pointed out also several
circumstances in relation to these Roman relics, which tended to
show a change of level, and he referred to the discovery of Roman
pottery in a point of the raised beach at Leith. ‘The conclusion to
which the evidence led him was that since the first century of our
era the central parts of Scotland, from the Clyde to the Forth and
the Tay, had risen to a height of from 20 to 25 feet above their pre-
sent level.
[. 494. ]
LXIX. Intelligence and Miscellaneous Articles.
NOTE ON THE ELECTRICITY DEVELOPED DURING EVAPORATION
AND DURING EFFERVESCENCE FROM CHEMICAL ACTION. BY
PROFESSOR TAIT AND J. A. WANKLYN, ESQ.
NE of Professor W. Thomson’s divided-ring electrometers having
been recently procured for the Natural Philosophy collection in
the University, we have made use of it in repeating and extending the
experiments of Volta, Pouillet, and others, on the electricity pro-
duced during the evaporation of various bodies. In some cases our
results agree with those already known, but im others we find effects
differing totally in kind or degree from the accepted ones; and with
some substances we find occasionally contradictory indications among
our own results.
The electrometer is in every respect a far superior instrument to
the gold-leaf electroscope, which (sometimes with the addition of a
condenser) was used by former experimenters, and enables us to give
our results in a form easily reducible to absolute measure. The
charge of the instrument was such that, when the half-rings were
respectively connected with the zinc and platinum of a single Grove’s
cell, the deflection observed amounted to about 5°8 scale divisions.
This was found to be the most useful charge for the bulk of our expe-
riments, but it was easily increased. twenty or thirtyfold when we
sought to verify any very delicate indications.
Our apparatus consisted of a platinum dish, placed on an insula-
ting stand, and connected with the insulated half-ring. A lamp
could be placed on the stand so as to heat the dish; and while this
was going on, the indications of the electrometer gave us the atmo-
spheric charge. The experiments were all conducted when the latter
was very small; so that, although the sputtering of the fluids dropped
on the hot plate may have prevented us from observing some slight
effects, the large deflections we observed in many instances can have
nothing to do with the electric state of the air of the room. Witha
different disposition, which enabled us to use a Bunsen lamp to heat
the dish, we obtained the atmospheric potential by burning a little
ether or alcohol on the dish itself when the lamp was removed.
We agree generally with previous experimenters, that during the
continuance of the spheroidal state there is little, if any, perceptible
disengagement of electricity. We also agree with the statement that
the main effect is produced while the fizzing sound that accompanies
the loss of the spheroidal state is heard, and that during the conti-
nuance of the mechanical action to which that sound is due the
indications of the electrometer ir general steadily increase. That
the greater part of the electricity produced is due to friction is proved
by the fact that when fluids are forcibly squirted upon the hot dish
the electrical indications are very much increased, and that a con-
cave surface gives far more powerful deflections than a convex one
at the same temperature. The sputtering or violent boiling which
succeeds the fizzing state shows little, if any, disengagement of
electricity. The principal interest of the results which we have
obtained is in the cases of iodine, bromine, and various other
Intelligence and Miscellaneous Articles. 495
bodies which do not seem to have been before examined. We have
as yet met with no discordance in our own results as far as simple
bodies are concerned.
In giving the following numbers, we have not attempted any cor-
rection for the loss of electricity which is caused by the high tempe-
rature of the platinum dish.
Mean Electric Effects given by a few substances during the continuance
of the fizzing sound which immediately follows the disappearance of
the Spheroidal State, 5°8 representing the Electromotive Force of a
single Grove’s Element.
OTS Sr + 400
Iodine. ~ coca SNe rth 9Os
Beanida a ethyle wales aggtt. de + but very small indeed, if any.
Iodide of methyle .......... In many experiments strong +, but
in three cases pretty strong —
Benzole ...:.. eae. es.2 a Noveftect.
Valerianic ether............ No effect.
Common ether ............ - Very slight and dubious effects.
Wipers f2055:23::---)- — if plate very hot, + if colder.
3 Jc 0 1S re — 200
PMP OMBE MO sss 554) Se )0'9 2's — 10
RCI Fete 8/2) 12's pe y-ce § 2s =) 75
Chloride of sulphur ........ — 100
Water (distilled), containing
only a trace of carbonic acid,
which was too small to be de-
tected by lime-water
Solutions in water of—
Carbonate of potash strong) — 310
Caustic soda (strong) ... — 40
Caustic soda (dilute)...... “aaa rd T
Caustic potash beompushon
strength) Ae Te "}+ an Poe
Nitric acid (strong) ...... a5
Nitric acid (1 in 4 ‘of water) — 35
Hydrochloric acid (strong) — 160
Hydrochloric acid (weak)... —
Sulphuric acid (strong).... + 15
Strong solution of NaCl .... 400
Strong solution of KI........ — 8&0
Strong solution of CuO, SO3.. —1000?
Sdlation of double oxalate of Vv “fi ff
chromium and potash... gy ae erect.
Fe? Cl, solution moderate, --. Negative effect.
Acetic acid(monohydrate).. + 3
Acetic anhydride eat oe
* This sample was in fine crystals. Far higher effects (also positive)
were obtained from it in powder.
+ This is a very difficult substance to experiment upon.
496 Intelligence and Miscellaneous Articles.
The sulphate-of-copper solution is by far the most remarkable
that we have tried. ‘The smallest globule, on leaving the spheroidal
state, gave intense effects, sending the lamp-image entirely off the
scale.
We have also commenced a set of experiments with a view to test
the electricity developed during the brisk disengagement of a gas by
chemical action, which was discovered eighty years ago by Volta. In
some of these experiments it was observed that when the gases were
disengaged with considerable effervescence, and in a mass of large
bubbles foaming over the platinum crucible in which the experiment
was conducted, the bursting of each bubble was attended by a simul-
taneous increase of deflection in the electrometer. These experiments
are as yet exceedingly imperfect, but they seem, like the preceding,
to indicate friction as a main cause of the observed results. The
effects on the electrometer are by no means so uniform, either as to
kind or quantity of electricity, as those given by evaporation.
Electricity developed during Effervescence.
7; (Ns | C) eye ie — 750
Zn+NO5HO...... + 175. Inanother trial —120.
Nin? Ole. oo sn | hoe — 150
CaO, CO2+HCl.......... Trifling effects.
WaOSSO2--FHCl: 6. ey At first a small negative deflection,
finally + 50.
NaCl+S0:HO...... + 10
—From the Proceedings of the Royal Society of Edinburgh, February
1862. Eber ebare Bs
POSTSCRIPT TO PAPER “ON eae ASTRONOMICAL
EPOCHS.’
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
In my paper ‘‘On Chinese Astronomical Epochs” which you pub-
lished in your Number for January last, I substituted in a formula the
English measure of 12 inches for the foot, whereas I ought to have
used 10 only, the French measure. In consequence of this, the 0°25
at the top of p. 3 ought to be changedinto 0°30. ‘The effect of this
is that the range of time within which the Chinese observations may
have been made is 45 centuries, instead of 371; and therefore the
uncertainty arising from the ill-defined termination of the shadow of
the gnomon is still greater thanI make it in that paper. I shall be
much obliged by your inserting this letter in your next Number after
receiving it.
_I take this opportunity of asking you to make two more correc-
tions; viz.
Page 3, last line but one, for Nos. 4 and 5 read Nos. 5 and 6.
— 6, line 12 from the bottom, for Nos. 2 and 4 read No. 4.
I am, Gentlemen,
: Yours faithfully,
Calcutta, April 1, 1862. J. H, Prarr.
THE
LONDON, EDINBURGH anv DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
SUPPLEMENT To VOL. XXIII. FOURTH SERIES.
LXX. An Account of Observations on Solar Radiation.
By Joun James Waterston, Esq.*
[With a Plate. |
$1. ir March of last year I submitted to the Society some
computations with reference to the sun’s heat, and
suggesting a mode of deducing the potential temperature of its
radiating surface. This last summer I have endeavoured to put
this method to the proof by a series of observations on solar
radiation, supplemented with experiments on the rate of cooling
of thermometers in air and zn vacuo with different kinds of radia-
ting surfaces,—also by another series, applymg the method of
deducing the potential temperature of a radiating surface to pre-
dicate the temperature of one that is maintained at a constant
known temperature.
The success of these last mentioned, so far as they have as
yet been carried, encourages me to lay before the Society the
observations on solar radiation, with an account of the method
employed to obtain the results, and of the mode of reducing
them to a vacuum.
§ 2. It will be remarked, on inspecting the Chart in which
the observations are projected +, that a simple law of atmospheric
absorption is indicated, which, if confirmed by other similar
observations in different climates, would perhaps lead to more
exact ideas of the influence of the atmosphere on the sun’s rays.
Unfortunately the best part of the summer had passed before I
could begin to observe, and there was almost constant interrup-
_ tion with clouds and unsettled weather. In a tropical station,
* From the Monthly Notices of the Royal Astronomical Society with
Notes; communicated by the Author.
t This chart is omitted, and another substituted (fig. 3, Plate V.), show-.
ing the observations of August 21, also of August 6 and July 28, projected
in the same way to a larger scale. Each observation is represented bya
point, the coordinates of which are the reciprocal of the radiation and secant
of apparent zenith distance of the sun’s centre.
Phil. Mag. 8S. 4. No. 157. Suppl. Vol, 238, 2 L
498 Mr. J. J. Waterston on Solar Radiation.
where the sun rules in a cloudless sky, the presumed law might
soon be put to the test, and the heating-power of the sun’s rays
before entering the atmosphere ascertained with precision.
Having determined this for the earth’s mean distance from the
sun, its value for any other planetary distance may be deduced
by the law of the inverse square.
§ 3. When a thermometer is exposed to the sun with its bulb
blackened, it is presumed to absorb all the heat that impinges
on a plane surface equal to the transverse section of the bulb ;
it rises and is maintained at a certaim temperature; and when
this balanced condition is attained, we can with certainty assert
that the amount that issues from the bulb is precisely equal to
the quantity that enters. The elevation of its temperature above
surrounding bodies due to the sun’s radiant power (which is
denoted by the symbol r) would be an exact measure of that
power if no heat issued from it except by radiation, and if the
rate at which heat was emitted from it creased exactly im pro-
portion to7. Now I find that if the bulb of a thermometer is
enclosed in a vacuum, the walls of which are brass coated with
lampblack, the rate at which it cools is exactly proportional to
the value of r, and this rate has exactly the same value whether
the glass bulb is uncoated or coated with lampblack*. When
enclosed in air, the rate of cooling increases faster than r. The
mode of measuring the rate in both cases, and of reducing the
values of r observed in air to what they would be in a vacuum,
are described at the end of this paper.
§ 4. The instrument employed was designed so that the
thermometer exposed to the sun’s rays should radiate against an
enclosing metallic surface coated with lampblack, and so that
the temperature of that surface should always be known.
Fig. 1, Plate V., with the description that accompanies it,
gives the details. The rays of the sun were admitted, to strike
upon the bulb of the thermometer X, through a hole but little
larger than its diameter, and were entirely screened off the brass
tube, against the blackened inner surface of which the radiation
of the bulb took place. The thickness of the sides of the brass
tube was 4 inch; and the thermometer Y, that indicated its
temperature, was lodged in a hole cut in the upper side. The
* This unexpected result is confirmed by repeated observations. While
the emitting-power of a mercurial thermometer is thus the same, coated
or uncoated, the absorbing-power of the uncoated surface is only six-tenths |
of the same coated with lampblack. This apparent anomaly is no doubt
caused by the incident rays of heat, after passmg through the glass, bemg
reflected from the surface of the mercury, because I find that, with spirit-
thermometers (in which the spirit is largely impregnated with red vegetable
matter), the uncoated reservoir absorbs radiant heat exactly the same as
when coated with lampblack.
Mr. J. J. Waterston on Solar Radiation. 499
eireumference of the bulb touched the brass, and its upper side
was enclosed with cork, while the lower was exposed to the air
within the tube, but was untouched by the rays of the sun that
passed through. The internal diameter of the tube was 0°9 inch,
and length 6 inches. The bulb of the solar thermometer was
0-42 mch in diameter, spherical in shape, and fixed in the centre,
as shown in the figure. Its shadow was an easy guide in moving
the tube in altitude and azimuth to keep pace with the sun. It
is difficult, if not impossible, to demonstrate that the thermo-
meter Y shows the exact temperature of the inner surface of the
tube. It was subjected to three tests.
1. The instrument being out of the sun’s rays, and X and ¥
showing the same temperature, it was removed to a place where
the atmospheric temperature was 10 degrees lower. Both thermo-
meters descended, and showed a difference equal to about one-
tenth the amount they had to fall to arrive at the atmospheric
temperature, Y being so much in advance of X.
2. A bat’s-wing flame of gas was brought within 3 inches
fronting the middle of the tube; both X and Y rose together,
keeping pace exactly.
3. While taking observations, the heat absorbed by X from
the sun, and again emitted from it and transferred to the tube,
gradually raised its temperature until a maximum was obtained.
Now, comparing X and Y while both are rising, and after having
obtained their maximum, a difference of 0°°3 was remarked; and
this difference, no doubt, affected isolated observations when this
maximum was not attained in consequence of interruption by
clouds passing, when it was usual to heat the solar thermometer
artificially to near the stationary point, in order to save time,
the great inconvenience of the apparatus in this climate bemg
the slowness with which 7 obtained its final value. An arrange-
ment with a differential air-thermometer would, no doubt, be
preferable in this respect, but the absolute value of the degrees
indicated does not seem capable of being exactly determined *.
The thermometers were carefully graduated and compared by
myself, and the divisions between two fixed points, 60° and 100°
(which included all the observed temperatures), were drawn
as nearly equal as a good ivory scale and magnifying lens would
admit. The length of a degree on the scale of Y was about
05 inch, and upon X *067 inch : with practised eye it was easy
to read off the temperature to ,j,th of a degree with lens;
but such accuracy was unattainable for other reasons, and chiefly
* Another mode, which is perhaps the least liable to uncertainty, is to
have the surface against which the sun-thermometer radiates maintained at
212° by surrounding it with the steam from boiling water: only one thermo-
meter would be required in this arrangement.
od
500 Mr. J. J. Waterston on Solar Radiation.
a sensible difference was caused by the varying amount of the
stem that was under the influence of the sun’s rays as it moved.
§ 5. The observations taken on the morning of the 21st of
August, continuously during 24 hours of uninterrupted sunshine,
were graphically equalized, the curve drawn, and ordinates mea-
sured off at every 20 minutes. This was the only opportunity
that occurred of continuous observation between such favourable
limits of altitude as to indicate the direction of a line with some
precision.
§ 6. In the Table of observations given in the Appendix*, the
date and apparent time are given im the first two columns. The
timepiece was regulated daily by the one o’clock signal-gun. The
third column contains the values of 7, the observed difference
between thermometers X and Y. The film of tale that was
interposed between the sun and X was found to reflect “ths of
the incident rays. This ratio was determined by observations
taken with the film off during calm weather. The value of r
without the film to 7 with the film on was as 1°18 to 1°00, the
sun’s power not sensibly varying during the interval. This pro-
portion was mamtained at low values of 7, and even when the
source of radiation was a gas-flame. The fourth column contains
the observed values of r increased in this ratio. The fifth
column contains the corrections required to reduce the values in
the third toa vacuum. The correction is taken from a scale
that was constructed by means of an empirical formula derived
from observations on the cooling of X, as detailed in the Appen-
dix. The sixth column is the final value of 7 as it would appear
in a naked vacuum, that is, a vacuum without any interposed
transparent solid between the sun and the bulb of the thermo-
meter. The numbers in this column represent the quantity of
heat-force supplied from the sun to the bulb of the thermometer
in a constant element of time, or the quantity that emanates from
the bulb in a unit of time.
§ 7. The experiments on the cooling of the thermometer X
in a vacuum show that, from r=80° to r=15°, the time of cool-
ing was 294 beats of a time-piece, of which 774 were equal to
60 seconds; also from r=15° to 7 =74° the time was the same,
and generally from r=2m to r=m the elapsed time is the con-
stant 294, which thus represents the logarithm of 2 in the loga-
rithmic curve of which the ordinates are 7, and the abscissze the
time of cooling, z. ‘The equation of the curve being
7
wv yay
0
* The observations commenced on July 28, and continued for one
month, at times when the sky was sufficiently free of clouds. A selection
froma this Table is given at the end of this paper.
Mr. J. J. Waterston on Solar Radiation. 501
in which c log 2=294, or to reduce to seconds,
60
c log 2=294 x 77
and c=7561. Let ¢;—¢,=d¢, then log - == , ; = in which
Q
f=hyp. log of 10; hence
c or rs
—>—== of log — =2°51636]. e
ae [log = ]
From this we may compute the quantity of heat supplied toa
unit of surface by the sun ina unit of time corresponding to any
value of r, As an example, suppose 7=10° and d¢=1 second,
then 6r= = =0°:030453, or 3°°0453 in 100 seconds, is the
rate at which the sun communicates heat to a thermometer whose
bulb is a sphere 0°42 inch in diameter, when r=10°.
Suppose the glass of the bulb to be 5th of an inch thick,
there would be -0108 cubic inch glass and ‘0287 cubic inch
mercury heated 3°°045 in 100 seconds. If r=20°, the same
heating would take place in 50 seconds, and so on.
To reduce this to thickness of ice melted in 1 minute, we have
Specific heat of mercury *033, and of glass *177.
Specific gravity of mercury 13°5, and of glass 2'9,
0108 cubic inch glass equal in weight to °0313 cubie inch water.
*0287 cubic inch mercury equal in weight to ‘387 cubic inch water.
“0108 cubic inch glass raised 3°°045 takes as much heat as ‘0313 cubic
inch water raised 0°°54.
*0287 cubic inch mercury raised 37045 takes as much heat as °387 cubic
inch water raised 0°'101.
°0313 cubic inch water raised 0°54 takes as much heat as is required to
raise 1 cubic inch 0°0169.
*387 cubic inch water raised 0°101 takes as much heat as is required to
raise 1 cubic inch 0°'0391,
The entire bulb of the thermometer thus raised 3°°045 is thus
equal to | cubic inch of water raised ‘0169 -+ ‘0391 =0°:056.
Now the transverse section of bulb is 0°188 square inch; and
since specific gravity of ice is 0°93, and it requires 140° to melt
ice, we have 140 x 0°728 x 0:93 x 7~=3'045 ; hence x=0-00312
inch, the thickness of ice melted by the sun in 100 scconds,
when r=10°. This is equivalent to 0:001872 inch in 1 minute.
502 Mr. J. J. Waterston on Solar Radiation.
With »=20° the thickness would be double this amount, and so
on. Thus the presumed extra atmospheric value of 7 being 67°
gives 0°0124 inch thickness melted per minute.
From June to December the amount may be expected to vary
tsth, corresponding to alteration of sun’s distance. In Her-
schel’s ‘Meteorology’ the probable thickness is stated to be
0109 inch.
§ 8. If the law indicated by straight lines on the chart is true,
it would require extremely accurate observations to give the extra
atmospheric constant of solar radiation with precision*. From a
single observation made in Bombay some years ago, I am disposed
to believe it may exceed 67° considerably.
§ 9. The mode of approaching the law of absorption is as fol-
lows :—Project the values of 7 as ordinates to the secants of
zenith distances as abscisse: the resulting curve is evidently
hyperbolic in character. If it is the conic hyperbola, the reci-
procals of the ordinates laid off to the same abscissze should
range in a straight line. The obvious plan is therefore to lay
off the reciprocals of 7 im this way, and see how far their range
agrees with the straight; and if it differs, the character of the
divergence might lead us to the true function that expresses
the natural law, if it was not very complicated, and if the
condition of the atmosphere did not vary so rapidly as to
obscure it.
The observations, though taken under unfavourable conditions,
favour the simple hyperbolay.
§ 10. It will be remarked, on inspecting the Chart, that the
value of 7 at the same altitude of the sun diminishes with the
declination as the season advances. If continuous observations
were possible for a few hours each day, when the altitude of the
sun ranged between 15° and 45°, we might expect to see the
projection of the equalized observations range each day in a
different line; but these lines ought all to converge on nearly
the same point in the ordinate at the zero of the secant scale,
if the law holds good.
* That is in this climate, where r is comparatively small, and the trend
of consecutive observations slopes from a part of the chart, where the scale
of r is large, to where it is small. In a tropical station, such as Bombay,
where even during the winter months the value of r for the same altitude
-is double what it is at our summer solstice, the trend must incline much
less to the axis, and consequently errors of observation will be but slightly
magnified in the value given to R, the extra atmospheric value of r.
ft The equation of which is 7 cosec altitude =k a constant, hence cosec
altitude a = and thus the reciprocals of r laid off as ordinates to the secants
of zenith distances may be expected to range in a straight line. See Chart,
fig 3.
Mr. J. J. Waterston on Solar Radiation. 503.
Let N, fig. 5, be the position of the
observer, Z his zenith, and NS the direc- Pe
tion of the sun. Draw parallel lines &
ab, ed, &e.; now ac: bd :: rad.: sec. fe
sun’s zenith distance ; so that the thick-
ness of each stratum varies as the
secant; and if the physical condition
of the stratum do not alter between
two observations*, we may take the
secant as the representative of the
collective thickness of the absorbing
medium traversed by the sun’s rays,
except at such low altitudes when the curvature of the earth
as well as refraction may be expected to introduce uncer-
tainty. The minimum value of the secant is radius; but we
may imagine the sun’s rays to pass through a similarly con-
stituted atmosphere in which the thickness of the same layers
proportionally diminishes from unity or radius to zero. The
reciprocal of 7 diminishes for values below radius at the same
rate as for values above radius, attains at zero the extra atmo-
spheric limit, which, in all climates and seasons, ought to be
determined by the inverse square of our planet’s distance from
the sun in its orbit, and should not vary beyond 3th of its
mean value.
* But the very absorption of the sun’s rays must promote change in
-physical condition. Is the law for a constant physical condition thereby
masked? JI believe that during an interval of one or two hours it is not
sensibly disturbed, for the following reason: the absorption of the sun’s
heat by the aqueous particles in the atmosphere would tend to dimmish
their number, and thus augment r beyond the value assigned by the law
for the condition constant. The later of the observations taken in the
forenoon of August 21, projected in fig. 3, may thus be suspected to give
too high values for 7; and ifso, the lower points on the left-hand side would
require to be removed higher up, and the trend of the poimts continued
towards the vertical axis would intersect it at a poimt which would give a
value to R less than 67°. But this is impossible, because in India r exceeds
this amount. The trend must therefore be the other way; and as the
scale of r diminishes rapidly downwards, and as R is certainly a constant
quantity in all climates, a very slight depression of the trend (the dotted line
in fig. 3), such as may be due to fault of observation, would intersect
the axis at a pomt giving a sufficiently probable value of R. In short, R
is a fixed point im the axis towards which the projected points of a conse-
cutive series of observations, wherever taken, must trend, whether by straight
or curve, if the physical condition of the atmosphere is undisturbed. The
line of the consecutive series of the 21st is straight, and points, within
‘moderate limits of inaccuracy, to a probable value of R. On the other
hand, if the effect of the sun’s rays was to diminish the diathermity of the
atmosphere, and the observations were quite accurate, the points would be
conformable, and indicate a disturbance of physical condition.
504 Mr. J. J. Waterston on Solar Radiation.
Let mm, m, be the secants at which the radiation is 79, 7, we
. ° . My— mM
have, according to the projection 71 =k, a constant quan-
na Tea
tity so long as the physical condition of the atmosphere remains
constant; and to find R, the extra atmospheric value of 7, we
have
Mg— mM, if a. ay as
fe Pe adiucgis teed :
Hence m= Sen and ae Since R is constant, we may
put ~ =e, so that r= — This expresses the presumed law
of absorption or interception.
The essential nature of this law is seen by studymg the pro-
portionate differential of r,
kém —dr_ dm r —Or 5
—or= (me? ant Sine =Odm- 5 hence Sm OP
Thus the sun’s rays, in passing through a constant element
of the thickness of the atmospheric medium, loses a proportionate
amount of its power that is not constant, but that diminishes in
the simple ratio of that power.
As an example, suppose with 7=380°, the value diminishes 1°
im passing through 1 mile; it would only lose 4° in passing
through the same mile if r=15°, and 54,th of a degree if r=1°.
We might thus expect, when the atmosphere is clear, it does not
intercept any sensible proportion of the heat radiated from the
earth’s surface into space.
§ 11. Compare the value of 7 with one sun and with two;
the supply from each, supposed equal, doubles the value of 7,
which, measured at the extremities of the mile nearest and
furthest from them, shows that for the same element of the
thickness of the medium the proportionate decrement of 7 is
constant. Let # represent the angular space occupied by the
sun’s disk, and ¢ the potential temperature of its radiating sur-
face, then Za represents the supply of heat by radiation from it
upon a unit surface, and is measured by 7; so that if at becomes
2at, r becomes 2r. Now the factor 2 may have reference to a,
the magnitude of the sun’s disk ;"or it may have reference to ¢,
its temperature. The fluctuating value of 7 from change of
altitude or climate represents a fluctuating potential value of at;
but « being constant, the change is similar to what would take
place above the atmosphere by a change in ¢alone. At different
parts of the earth’s orbit the value of « changes; so that with
Mr. J. J. Waterston on Solar Radiation, 505
¢ constant and @ variable the proportionate absorption represented
by ov is a constant quantity; but so far as 7 depends on ¢,
the value = increases with ¢, and the causal relation may be
expressed as follows :—
The heat-pulse travels, carrying with it an intensity that it
borrows from the temperature of its source, and encounters a
deflecting or absorbing power in passing through a constant
element of the atmospheric medium that is exactly proportional
to that intensity.
It would be simpler if the resistance was uniform—if the
proportion of force absorbed was constant; but the observations
do not admit of the possibility of this. The curve traced out
by the coordinates, 7 and secant zenith distance, would in that
case be no longer the conic hyperbola, but the logarithmic
curve*.
§ 12. At 6 o’clock in the evening of the 31st of July, while
making an observation, an extensive shower of thin rain took
place overhead and westward towards the sun, without sensibly
obscuring its light or affecting its image when examined through
a telescope: the value of 7 descended immediately from 15° to
13°. The single observation I took in India, compared with
those taken at the same altitude in this country, indicates
that the value of r is there fully double what it is here, while
the quantity of vapour held in suspension estimated from the
dew-point is certainly greater. It would seem probable, there-
fore, that the absorbing power of the atmosphere depends on the
watery particles contained in it, not upon the aqueous vapour
dissolved in it.
§ 18. Referring to the method of computing the sun’s po-
tential temperature, described in the ‘ Proceedings’ of the Society
for March 1860, and employing the same rule with R, the extra
atmospheric value of r equal to 70° at earth’s mean distance,
we arrive at 12,880,000° as the potential temperature of its
radiating surfacey.
If we expose the flame of a bat’s-wing jet to one ball of a
differential thermometer, the effect is the same whether the
broad side or the narrow side of the flame is presented, as I
have found on trial. Now the potential temperature being
equal to the product of r by the reciprocal of the angular space
occupied by the flame, it is in the one case about five times
* And the points on the Chart ranging in a curve convex towards the
axis, and leading by its trend to an inadmissibly low value of R.
+ Bya typographical error, z, the potential temperature of the radiating
surface of the sun, was represented to be 918,000° instead of 9,180,000°,
506 Mr. J. J. Waterston on Solar Radiation.
greater than in the other. In the same way we might compute
the potential temperature of an angular space occupied. by many
thousand flames placed one behind the other, extending in a line
from the observer, and probably we should find it cumulative in
the ratio of the number of flames.
From observations I have made on gas-flames with the radia-
tion-meter, fig. 1, it would seem to require about 4000 bat’s-
wing flames ranged behind each other to give a potential equal
to that of the sun. :
If the upper radiating matter of the sun is in any degree
transparent or permeable to radiation from lower strata, it is
obvious that the actual temperature may thus be much below
the potential. |
26 Royal Crescent, Edinburgh,
November 25, 1861.
EXPLANATION OF THE FIGURES IN PLATE VY.
Fig. 1. T U BE is a square tube of brass, mounted with motion in
altitude upon an upright, R, fixed into a round slab of lead. The inner
surface of this tube is blackened, and at each end, at J and c, a film of
transparent tale was stuck on to prevent the wind from moving the air
within the tube.
HD, DH a double screen made of cardboard and cork, coated on both
sides with tinfoil, and fitted to slip on the extremity of the tube presented
towards the sun.
m, the hole in the centre of screen, about 5th inch greater diameter
than the bulb of the solar thermometer, X.
The tale film 7 was also coated with tinfoil, except the central circle.
_X, the thermometer in sun with spherical bulb fixed im a cork that fitted —
the hole L, L in top of brass tube.
Y, the thermometer in the shade fixed in the hole N, N, with cork and
soft wax as shown.
Z, a thermometer applied to outer surface of tube.
Fig. 2 is a transverse section of vacuum-bath, employed to ascertain the
rate of cooling of the solar thermometer X in air and im vacuo.
It consists of a cylmdrical vessel of brass, coated internally with lamp-
black; the lid Lis ground to the upper edge of the cylinder, and in its
centre is a stuffing-box, S, with Indian-rubber collar, through which the
stem of the thermometer is passed, as shown in the figure; C is a stopcock,
~upon which N, the nozzle of a flexible tube communicating with an air-
pump, is ground air-tight. H is a wooden handle for removing the appa-
ratus to and from the water-bath without touching the metal.
Fig. 3 is a Chart of the observations taken in July 28, August 6 and 2].
Each observation is represented by a pot, the ordinate of which is the
reciprocal of the radiation potential, and the abscissa of which is the secant
of the apparent zenith distance of the sun’s centre.
Fig. 43s a duplex scale, showing the correction to be applied to the radia~-
tion potential as observed in air to what it would be if i vacuo. It con-
forms to the observations on cooling in air and in vacuo given in the Ap-
pendix, and was computed from the empirical formula therein described.
The correction in degrees and tenths is found on the right-hand side of
the line opposite the value of ra entered on the left-hand side. It has to
be added to rz.
Mr. J. J. Waterston on Solar Radiation. 507
Appendix, describing the Method employed to discover the Influence
of the Air in the Cooling of the Sun-thermometer X, and of
ascertaining the Correction required to be applied to Observa-
tions of r, so as to reduce them to a vacuum.
The apparatus employed was the vacuum-bath represented in
fig. 2. Plate V. (see explanation of figures). With a plentiful
supply of lard to the stuffing-box and ground surfaces, a good
vacuum could be maintained in it for a day unimpaired.
The time was measured by the beats of a clock: to register
the number of these at each degree as the mercury of the ther-
mometer descended, a scale of equal parts was prepared extend-
ing to 1000, and with distinguishing marks at each 5, 10, 50,
and 100. Then with a penell i in the right hand over the scale,
and a magnifying glass in the left over the scale of the thermo-
meter, I counted the beats; and when the mercury came to the
line of a degree, made a mark on the scale of equal parts oppo-
site the number of beats, and at the same time continued to
count on; e. g. if 57 was the number when the mercury came to
a line, a pencil-mark was made at 57 on the scale of equal parts,
and the counting went on, 58, 59, &c., until the mercury came
to the next line.
Thus not a beat was lost from beginning to end, and the accu-
racy was only limited by the accuracy of the divisions on the
scale of the thermometer. Indeed, this method is a severe test
to the equality of the divisions, because the reciprocal of the
differences in the number of the beats for each degree, if laid
off as ordinates to the total number of beats, ought to range ina
straight line, and any saw-like irregularities indicate maccuracy
in the divisions of the scale of the thermometer. To heat the
bulb of the thermometer, a funnel was placed over the small
flame of a Bunsen; then holding the plate (having the thermo-
meter fixed in its place) by means of the stopcock, the bulb was
brought over the top of the funnel until the mercury had risen
to near the top of the scale. The plate was then quickly placed
on the cylinder, communication made with the air-pump, and
the air exhausted from the cylinder by twenty strokes, the
capacity of the pump being about one-third that of the cylin-
drical vessel or yacuum-bath. The vessel thus exhausted was
placed in a water-bath, the temperature of which was ascertained
at the beginning and end, the difference seldom amounting to
one-tenth of a degree.
The following Table exhibits two series of observations on the
cooling of the ‘sun-thermometer X in the vacuum, and in air,
taken while the water-bath remained steady at 48°. This basal
temperature being. at an exact degree, enables the rate of cool-
508 Mr. J. J. Waterston on Solar Radiation.
ing to be studied easily without fractional parts or interpola-
tion :—
Temp. |Beatsin| ,, | Beats | Temp. | Beatsin| ,., Beats
d2¢ vacuum, in air. X., | vacuum. in air.
90 42 0 Once) hone
85 0 aie 36 65 323 17 270
4 12 36 4 348 16 291
3 24 a 3 347 15 312
2 36 34 2 406 14 336
| 48 33 1 437 13 360
80 604 | 32 738 60 470 12 385
9 73 a 9 510 ll 414
8 86 30 8 549 10 448
7 1004 | 29 7 594 9 484
6 115 28 6 643 8 527
75 130% | 27 129 55 704 A 576
4 1453 | 26 4 765 6 630
3 161 25 3 843 5 695
2 179% | 24 2 sak 4 780
1 197 23 1 ore 3
70 214 22 191 50 a 2
9 235 21 9 eats 1
8 255 20 48 more 0
7 276 19
6 298 18
|
a a ae
Thus, 53 being the last observation of the vacuum-ccoling,
corresponds with 7=5°; then
oO
At r= 5 we have a6 beats Ditrerence 294
‘ 7% i as oe 2 He 294 Mean Difference 291:7
as 33 99
Tr = 40 9? has 32 99 ” 287
Again, beginning with r=7°,
Oo
Atr= 7 we have 704 beats :
r= 14 apg AUG Difference Be Mean Difference 2944
7 = 28 ” 115 ” i
And beginning with r=9°,
oO
Atr= 9 we have 594 beats :
r=18 a Ea ss Difference st Mean Difference 291
r = 36 ” 12 9 mF
The numbers in the column of differences ought to be the
same if the law of cooling in a vacuum is perfectly true, if the
vacuum is complete, and if the graduation of the thermometer
is correct. ‘The difference between them is so snrall that the
result must, I think, be deemed satisfactory.
Mr. J. J. Waterston on Solar Radiation. 509
Let us study the same differences with the cooling in air :-—
[o)
Atr= 5 we have 695 beats ‘
r=10 Ty. (ine 1st Difference al 2nd Difference 19
T = 20 ” 220 ” we 206 ” 22
r= 40 se TAs og ”
= 7 we have 5/6 beats
r= 14 ons B 1 adler
r = 28 Pomme) Jara
y= 9 we have 484 beats
y=18 ,, 254
8G Th Ase 8 ”
lst Difference 240
‘i O17 2nd Difference 23
Ist Difference 230
210 2nd Difference 20
Thus it appears that in air the cooling takes place in a ratio
greater than 7, the first difference of the times diminishing and
the second difference slightly increasing between 247 and 210.
The limitmg value of the first difference must be 294 when
7=0, and 294 minus the first difference increases nearly as JP.
An empirical formula constructed in conformity with this ratio
cannot differ much from the observations*.
Let A represent Ist difference, and g a constant,
A=294—g Vr
and
294.— 247 294.—210
= Wa a= li 162 eer as = &c. (nearly).
* That is, within the above limits of the value of r; but since it makes
Au=0 when r=294, it is not to be trusted in the upper part of the scale.
Another empirical formula of better promise may be constructed on the
hypothesis that the second difference is constant. If we lay off the first
difference as ordinate to the mean proportional between the values of r to
which it belongs, the curve traced out would be the logarithmic curve if
the second difference were constant. Now it has every appearance of being
so. The mean of the four is 21, the extremes being 19 and 23, and the
irregularities are evidently casual. The equation derived from this is
Aa=211 + io53 (log 20 —log rz), the second difference being assumed 20.
The following Table is computed from this value of Ag :—
fa tp=Tv. rTatp=rv.
5-407 — oF 50+27-4= 77°4
10+ 2°5=12'5 604+35°4= 95:4
15+ 46=19°6 70+4+43'9=113'9
20+- 7':1=27°'1 §0+53°2=133'2
30+13 =43°0 904-63 °2=153'2
40+19°'8=59'8 100+ 73°6=173°6
The influence of the air in conveying away heat thus increases in a much
higher proportion than r. Further experiments are required to test this
at the higher parts of the scale, also to determine whether the ratio of
Ta to ry is not affected by the size of the spherical reservoir. The actual
time of cooling must augment with the diameter of the sphere, but the
ratio of the times in air and in vacuo is probably not affected by the dia-
meter.
510 Mr. J. J. Waterston on Solar Radiation.
A represents the logarithm of 2; so that, ¢ being a constant,
we have log 2 7% In the curve that represents the cooling
in air, we may assume a small are of it to coincide with a true
logarithmic curve, or the curve of cooling in a vacuum, and we
have to find the value of 7, the ordinate of the true logarithmic
curve at the given point.
The logarithmic curve is defined by the equation
A r}
Let
T= (7,—0°1).
To find the value of 7, corresponding toa given 7, (7, vacuum,
7, air), we require to compute the value of ¢,—), employing
Ag=294—g Vr in the equation
Ua | eas li
log 2° (r,—0°'1)
then, with this value of ¢;—/), and with A,=294, find the value
of 7, in the equation
=h—lo;
vat Ts
i—fh= log 2 ° ee (aoa
The direct equation is
A, {log r,—log (rz —0°'1) } =A. {log 7, —log(7,—0°1) }
and
Aa
A,
= 7 22 Zin nae Vr
7 rin aga ta lem qeep a
Hence 7, may be ascertained by inspecting the differences of
a table of logarithms; and it was from these that the Scale,
fiz. 4, Plate V., was constructed for reducing the values of r
taken in air to what they would be if taken in a vacuum, where
the emission of heat was by radiation alone.
The cooling of the sun-thermometer in air when fixed in its
place in the tube, as in fig. 1, was found to be exactly the same
as when fixed in the cylinder, fig. 2, unexhausted.
A chemical thermometer with cylindrical reservoir was tried
in the vacuum-bath, and the cooling was found to take place
exactly in the logarithmic curve. It is difficult to adjust the
yacuum-bath in time to observe a high value of 7, but good
observations were obtained from 7=190° downwards; so there
is little doubt that the law of cooling by radiation is general and
independent of the shape of the cooling body. — I purpose extend-
Mr. J. J. Waterston on Solar Radiation. 511
ig these observations with different surfaces. One result is
interesting as showing the perfect reciprocity of the radiation,
viz. a gilt bulb radiatmg agamst a blackened metallic surface
loses heat at the same rate as a blackened bulb against a bright
metallic surface, the rate being slower than when both are
blackened.
Observations on Solar Radiation.
= mn so ¢ O
2 aes Z 3 Sa .\f6.|5 ake Eg
Sg2gs |2.|28|(sesiesel es |s2s| a8
HEweY [ok] Sel8o 8 S58! 28 Bus] SSS
ePeoagd |e°}| -S12238\988l S00 |zo3| ee8 Remarks,
BAB SA |S |Sn/BBFIagFl Ss jas°| gs%
maser Solaris) (ambi es ae a
ro. | ra De Py 2 vi
1861. hm ° ° ° ° 1
July 28.| 4 25 p.m 17°5 |20°6 |+7°4 | 28°0 |°0357 |28 49} 2°075
4 36 16°5 |19°5| 6°8 | 26°3 |-0380 27 19} 2-183
4 56 15°5 |18°3| 6°2| 24-5 |-0408 |24 30} 2-411
5 26 14°0|16°5} 5°2|21°7 |-0461 |20 19} 2°880
6 18 13°2}15°5 | 4-7 | 20-2 |-0495 113 11} 4°385
Aug.6.|8 7am 16:2 |19°1} 6°6| 25-7 |0389 |31 17) 1°926
G8 18°0 |21°2| 7:7) 28-9 |°0346 |42 21] 1-484
9 32 18°3 |21°6} 8°0/| 29°6 |-0338 |45 12] 1-409
13. | 7 27 p.m. 2°2| 2°6| O'3| 2:9 3448 | 0 53 Sunset
16. | 5 16 a.m. 44| 5-2| 0-8| 6-0 |-1667| 5 29|10-465 |Sun rises per-
9 39 14°6 |17°2| 5°6| 22-8 |-0439 |39 51] 1-561 | fectly clear of
1 15°0 17:7 | 5°8| 23-5 |-0425 |46 20) 1-382 | clouds.
20. | 6 21 16 p.m 6°6| 7°7 |-+1°4| 9°1 1099} 7 21) 7-817) }
6 23 16 6°5| 76] 1:4] 9:0 1111] 7 4] 8-128
6 24 31 64) 7°5| 1:4] 8-9 |-1124| 6 55} 8-304
6 26 16 6-1) 7-2} 13) 8:5 |:1177| 6 41) 8-592) | Consecutive
6 27 16 60) 71) 1:2} 8:3 |-1205| 6 33} 8°767| + series not
6 28 36 61) 7-2) 13] 85 11177] 6 22) 9-018 equalized.
6 31 0 beg) Gee JE) 67:8; (1282 Gy 2) 9-54 |
6 37 16 4°8/ 5°7| 08) 65 |-1538| 5 12/11-034| |
osos “O 4°7| 5°6| 0°38) 6:4 |°1562) 4 59/11-512) J
21. | 7 20 a.m 9°8 11°76) 2°9)14°5 |-0690 |19 0) 3:071/)
7 40 10°7 |12°6| 3:3) 15-9 |-0629 |21 45} 2-698] | Consecutive
8 0 11°6|13°7| 3°8|17°5 |°0571 |24 29) 2-413 series gra-
8 20 12°3.14°5| 4-2|18*7 |-0525 |27 9} 2-191] | phically
8 40 13°0 15°3 4°6 | 19°9 |-0502 |29 45] 2-015 ' projected
9 0 13°5 |15°9| 4-9 | 20°8 |-0481 /32 14) 1°874 and equal-
9 20 13°8 16°2| 5:0} 21°2 |:0472 |34 37] 1°760 | ized.
9 40 14°1,16°6| 5°3/21°9 |-0457 |36 50} 1-668} J
[The observations taken on seven other days between July
28 and August 28 are here omitted. ]
[ 512 ]
LXXI. On the Conduction of Heat by Gases. ByR. Crausivs.
[Concluded from p. 435.]
IV. Behaviour of the Molecules which traverse a given Plane in
a Unit of Time.
§ 13. WE will direct our attention to any plane situated
perpendicularly to the axis of x, and to the mole-
cules which traverse this plane. Let us take, for instance, the
plane whose abscissa is 2, and which is therefore the first limit-
ing plane of the infinitely thin stratum that we have been con-
sidering in § § 8 e¢ seg.; we can then draw, from the behaviour
of the molecules existing simultaneously in the stratum, definite
conclusions as to the behaviour of those which traverse our plane
during a given time.
Let us suppose a part of the plane, equal in size to a unit of
surface, to be divided off from the rest. The cubic capacity of
the portion of the stratum corresponding to this extent of surface
will then be represented by dz, if dx is the thickness of the
stratum; and we will denote the number of molecules which
exist simultaneously in this space by Ndz, where N is a very
large number dependent upon the density of the gas at the place
in question. These Ndz molecules move in all possible direc-
tions, and the number of them whose cosine lies between w and
p2+dwis, according to § 12, the fraction }Idy of the entire num-
ber, and is therefore perfectly represented by the product,
LNIdedu.
Tn order from this expression, which refers to the molecules
simultaneously existing in the stratum, to deduce the number of
molecules which traverse the stratum in a unit of time, and
which therefore must also traverse the plane in question, we
must take into consideration the time which each molecule
requires in order to traverse the stratum from one limiting
plane to the other. For a molecule with the cosme p, the
distance to be traversed from one plane to the other is, disre-
garding its sign, equal to ma ; and the time required to tra-
: eS cose
verse this distance is equal to —, if V denotes the velocity. We
will assume provisionally that all molecules whose cosine hes
between » and »+dy have the same velocity, and therefore
require the same time for traversing the stratum; the number
of molecules which exist simultaneously in the stratum will then
bear the same proportion to the number which traverse the
stratum in a unit of time as this small space of time bears to a
Prof. Clausius on the Conduction of Heat by Gases. 513
unit of time; we must therefore divide the former number by
the small time in order to obtain the latter.
To apply this to the case before us, we must divide the mag-
nitude 4 NIdzdu by * and we thus obtain for the number of
molecules which traverse our unit of surface during a unit of time,
in such directions that their cosines lie between w and z+ dp, the
expression ANIVpudu.
It must, however, be further remarked that the difference of
sign in this expression, resulting from the circumstance that the
cosine 4 may be either positive or negative, corresponds to an
essential difference in the manner of traversing the stratum. If
# is positive, the molecules pass through the plane from the
negative to the positive side; if w is negative, they traverse in
the contrary direction.
§ 14. Before extending the expression just arrived at, which
refers only to an infinitely small interval of the cosme y, and pre-
supposes equal velocities, we will first deduce two other corre-
sponding expressions,
If we denote by m the mass of a molecule moving with the
velocity V, its momentum is mV, and the product mVy repre-
sents that component of the momentum which falls in the direc-
tion of z, so that a positive value of this product corresponds to
the case in which the component falls in the direction of positive 2.
We will accordingly call the product shortly the positive momen-
tum of the molecule. Hence the collective positive momentum
of the above mentioned }NIVydy molecules which traverse our
plane will be represented by
imNIV?u7du.
Further, the wis viva of a molecule whose mass is m, and whose
velocity is V, will be represented by JmV*. If, in addition to
the motion of translation with the velocity V, the constituents of
the molecule have also a rotatory or a vibratory motion, the col-
lective vis viva exceeds that product. I have spoken of these
additional motions, which may occur independently of the motion
of translation, in my memoir “Qn the kind of Motion which
we call Heat” (Phil. Mag. August 1857, p. 108), and have
pointed out. that, for a given kind of molecules, a constant rela-
tion must on an average prevail between the various simulta-
neously occurring motions, in such sort that the vis viva of the
motion of translation forms a constant aliquot part of the total
vis viva. We willaccordingly denote the mean value of the total
vis viva of a molecule by }émV?, where & is a factor whose value
* In my earlier paper, quoted in the text, I have shown how this factor
may be calculated by aid of the two specific heats. Jor such simple gases
Phil. Mag. S. 4, No. 157. Suppl, Vol. 23. 2M
514 Prof. Clausius on the Conduction of Heat by Gases.
is constant for each individual kind of gas*. In accordance
herewith, we obtain for the vis viva of the }NIVyudu mole
cules which traverse our plane the expression -
| tkmNIV udp. | .
§ 15. In order now so to transform the expressions arrived at
in the last three sections that they may also remain applicable
when the velocities of the individual molecules are not equal, we
only require to substitute for the values V, V*, and V° the mean
values V, V*, and V°. In order further to extend the expression,
which at present has reference only to an infinitely small interval
of the cosine yw, to all the molecules which traverse the plane, we
must also integrate it from w= —1tow=+1. In addition, we
will, for the sake of uniformity, multiply the first expression also
by m, so that, instead of the number, it may denote the mass of
the molecules. If, then, for the sake of shortness, we mtroduce
the following signs, E the mass, F the positive momentum, and
G the vis viva, which pass in the positive direction through the
superficial unit of our plane in a unit of time, we obtain the fol-
lowing equations :— |
2
1 “Vy se tee EY
B= 5mN | 18.2, i , ie W ,
] toy oe
G= jminn | * LV3 udp. 4 |
The last of these three quantities represents the conduction of
heat which occurs in the gas; it is therefore the determination
of this quantity which will be principally treated of in what fol-
lows. ‘The two other quantities must also be taken into consi-
deration, because, as we shall immediately see, they aid in the.
determination of this one.
By substituting in the three equations the series given in (III).
and (IV.) for V, V?, V°, and I, and performing the integration,
we get ;
E=imN(qg+uq')e+ Xe,
B= dmN+X,e, a
= tkmNu?(3q +uq')e+ X,¢°.
as exhibit no irregularity in regard to their volume, and for compound gases
which are formed without condensation, the value of this factor is approxi-
1 ae
mately 9.3/5 = 1584. For gases whose formation is attended with dimi-
nution of yolume it is larger.
Prof. Clausius on the Conduction of Heat by Gases. 515
The terms Xe?, X,¢*, and X,e?, in which the factors X, X,, and
X, denote functions of z which are left undetermined, are only
added in order to indicate of what degree are the terms which
would be obtained by carrying out the calculation still further.
It will be seen that in all three equations the second term is two
degrees higher than the first ; and if we content ourselves with:
such an approximation in our results that we neglect magnitudes
of the order e? in comparison: with unity, which we may do
without hesitation, seeing that ¢is avery small quantity, we may
entirely disregard thése additional indeterminate terms in the
developments which follow. i.
. On considering the degree of the first and important term, it
may perhaps ‘appear surprising that the magnitude F is of no
degree in respect of «, whereas E and G are of the first degree.
This, however, becomes intelligible when we remember that the
momentum behaves differently in regard to its sign from the
mass or vis viva. _The momentum of a molecule which traverses
the plane in the negative direction is in itself negative; but as
it must again receive a negative sign in consequence of its
passage in the negative direction, it thereby becomes positive
again; so that the positive and negative passages are not in this
case, as in the other two, to be subtracted from, but added to,
each other.
§ 16. In reference to the magnitudes H, F, and G, the assump-
tion that the gas is in a state of rest enables us to deduce at once
the following propositions :—
1. The mass of gas which traverses the plane must be equal to 0.
For, since the whole quantity of gas is contaied between two
fixed surfaces, if any gas passed through an intermediate plane
in either direction, the density must increase at one side of the
plane and diminish ‘at the other, which would be in contradiction
of the presupposed conditions.
2. The positive momentum which traverses our plane in a unit
of time must be independent of the situation of the plane, and there-
fore constant in regardtox. For if we suppose a stratum bounded
by any two parallel planes, the momentum which enters the stra-
tum through one plane must be equal to the momentum which
/ passes out ‘of it through the other, for otherwise the momentum
present in the stratum must vary; this, however, would be
m contradiction of the stationary state which is one of our
conditions.
3. The vis viva which traverses the plane in a unit of time must
be constant in regard to x, for the same reason as that given in
the case of the positive momentum.
We can therefore establish the following three equations of
condition :—
2M2
516 Prof. Clausius on the Conduction of Heat by Gases.
=
F = constant quantity, La catiee Uae
G= constant quantity,
which we will now apply to the expressions already Ree, at
for HK, F, and G.
The first equation gives, if we neglect the term Xe°,
q+ugq'=0,
which determines the ratio between the coefficients g and gq’,
namely,
= ar 2. e ° ° ® © e (22)
Hence equation (IV.) takes the following form, if we at the same
time introduce into it the value of 2 given in (20):—
T=1—fpetr(W—Het+... ee ay
_The second of the foregoing equations (VI.), neglecting X,¢?,
Sives Nu?== const. ss 6. s gece
N determines the density of the gas at the point in question,
and u? is proportional to its absolute temperature; whence it
follows that the product of the density into the absolute tempe-
rature, or, what comes to the same thing, that the pressure must
be the same throughout the whole mass “of gas—a result which
might also have been assumed as self-evident at starting.
Finally, touching the magnitude G. On applying to the last
of the equations (VI. ) the equation (22), and neglecting the
term X,¢%, it becomes
GalkmNutge. . . . . « (VIL)
But since, accordmg to what precedes, Nw? is a constant quan-
tity, and k, m, and ¢ are essentially constants, it follows that, if
G is to be, as in fact it must be, constant,
g=constant quantity. . « ss s.(2u)
In order to determine the conduction of heat without consi-
dering the magnitude e, which I have discussed in my former
paper, it now only remains to determine this one constant quan-
tity g.
V. Relation between the molecules existing simultaneously in a
given stratum and those emitted from the same stratum.
§ 17. In order to find how many molecules are emitted from
a stratum, we must know how great is the likelihood that a mole-
cule, while traversing the stratum, will strike against another
Prof. Clausius on the Conduction of Heat by Gases. 517
molecule ; for it is the molecules which strike each other, and,
after the rebound, leave the stratum with altered directions and
velocities, which we have agreed to call the molecules emitted
jrom the stratum.
We will call the probability of one molecule striking another
while traversing the infinitely small space ds, as we have done
in § 9, ads; and our business is now to make a closer approxi-
mation to the value of a.
In my former memoir* I have determined the value of & for
the case of a molecule moving in a space containing very. many
other molecules in a state of rest, and there I found
_ 7
ere r3 3
where p is the radius of the sphere of action of a molecule, in
the sense indicated in the paper quoted, and 2X is the interval
which would exist between every pair of neighbouring molecules
if, instead of the irregular distribution of them which occurs in
reality, the molecules had a regular cubical arrangement (that
is, if the entire space were divided up into small cubical spaces,
and the centres of the molecules were at the corners of the
cubes). Instead of the magnitude A, we may likewise introduce
N, the number of the molecules existing in a unit of space.
There must indeed be as many molecules in a unit of space
as there are such cubical spaces with the side X contained in it ;
1 sae
hence we have N= xe whereby the last equation is transformed
into a=p°N. Battlin tac Rel (25)
This expression for « admits of being easily modified so as to be
likewise applicable to the case in which the other molecules are
in motion instead of being at rest.
If we denote the likelihood that there is of the molecule under
consideration striking another during the element of time dt, by
adt, and regard ds as the space traversed during the time dé,
we get
OCR GAS eh) 2) Mihi feo pins! 426)
ds
or, putting v in place of WP
that is to say, the velocity of the
molecule in question,
ee gg a tic, inti oa Leet)
Substituting here for « its value as deduced in (25), we have
asp Nve + 6 2) 6) ess (28)
* Phil. Mag. S. 4, vol. xvii. p. 87.
518 Prof. Clausius on the Conduction of Heat by Gases.
If we now suppose that, instead of being at rest, the other
molecules are all moving with a common velocity in a given
direction, the likelihood of the molecule in question striking
another during the time df will plainly be represented by the
same formula, if we substitute, for the absolute velocity, v, of this
molecule, its velocity relatively to the other molecules. Let V
be the common velocity of the other molecules, ¢ the angle
which the direction of their motion makes with the direction
of the molecule under consideration, and R the relative velo-
city ; then . a
R= VV?+1?—2Vvcos¢, . . - « -(29)
and with this value we can put |
a=rpeNR.:
~ Finally, let us suppose that the other molecules move, not all
in the same direction, but in various directions, and with velo-
cities which are not necessarily equal to each other; in this case
the velocities of our molecule, relatively to the several other
molecules, will be various, and we must use in the equation the
mean value of the relative velocities. Denoting this mean value
by R*, the equation for a becomes
} a=mpNR, . . act)
and thence we obtain as a result of (27), the following equation
for a :— ig:
= ee (52)
' §18: We have now to determine the mean relative velocity of
a given molecule moving in our stratum, as compared with all
the other molecules simultaneously existing therein.
The velocity of the given molecule relatively to another given
molecule, whose direction forms the angle ¢ with its own direc-
tion, and whose velocity is V, is determined by equation (29).
If we now consider all the molecules which are moving in the
same direction, their velocities, as we have already seen in § 8, ©
are not.exactly equal to each other; and hence the velocities of
the given molecule relatively to them are also somewhat unequal.
We will accordingly, in the first place, intreduce a mean relative:
velocity, denoted by R, for each separate direction.
In order to be able to present in a tangible form the conside-
rations which further régard the various directions in which the
movements take place, we will, as before, imagine a spherical
surface described, with the radius 1, and regard the various direc-
* The reason for putting here two horizontal strokes over the letter R,
instead of only one, as in former cases, will become evident immediately.
Prof. Clausius on the Conduction of Heat by Gases. 519
tions as being drawn from its centre, so that every point on the:
surface of the sphere represents a direction. If the molecules:
moved equally in all directions, the number whose directions
would fall within an element de of the spherical surface would:
have the same ratio to the whole number of molecules as the
size of that element to the surface of the entire sphere; hence it
would be represented, as a fraction of the whole number of
molecules present, by 2 - In the present case, in which the
molecules do not move equally in all directions, this expression
must undergo a modification, and one of-such a kind that,
according to the notation adopted i in § 12, the number of mole-
cules whose directions fall within the superficial element dw will.
be represented, as a fraction of the entire number of molecules,
by i
= R ene the mean. velocity of the given molecule rela-
tively to those molecules whose directions fall within the element
do, and B its mean. velocity relatively to all the molecules pre-,
sent, the following equation will serve to determine the latter
quantity : =
BS We ER. ote ee | (33)
The integration must here be extended to the whole spherical
surface; and this integral we will now proceed to develope.
§ 19. According to equation (29);
ih VV24+02—2V0 cos q,
to which we will give the followmg slightly modified form:
( } . . WAS HVA oe / son (V—v)?
ti V2VWA/1— cos 6 + ST Paee Wa aie (34)
The velocity V of any molecule existing in the stratum differs,
as we have already seen, only so slightly from the velocity u of
the molecules which move perpendicularly to the axis of 2, that
the difference is a magnitude of the same order ase. If we now
assume that the velocity of the given molecule denoted by v like-
wise only differs from w by a magnitude of the same order, the
difference ek must also be a magnitude of the order of €; and
(Yo);
hence the term Vo”? which occurs in the last root, must be
a magnitude of the order of «%. By integrating this term no-
thing but another term of the same order can be obtained :
520° Prof. Clausits on the Conduction of Heat by Gases.
accordingly, if we neglect terms of the second or higher degrees:
in the expression sought for for RK, we may disregard the quan-
Tis la\e |
tity eee , whereby the calculation becomes very much sim-
plified.
The equation for R then becomes
R= V2V1—cosdVVo. . . » « (35)
But, by equation (9),
V=U— ay Stieee3
= Tg MSH oss
so that, by developing the foregoing equation according to s as
far as the term of the first degree, it is transformed into
1 dU.)
20 dz}
And substituting for s in this expression the mean value s, we
obtain instead of R the mean value R: thus
7 OT camera atta oo 1idU -\
R= V2 VI wg VVo(1— 3 ES os): - (36)
R= V2 V1—cosg VUo(1—
In place of U and s we will now put the values given for them
in (1) and (18), which, neglecting terms of the second and
higher degrees, are as follows :—
U=u-+ppe,
S$ =Ce;
at. the same time we will put
V==U fb 5, e ° e ° e e e (37)
where 6 may denote any magnitude of the order of «. Then we
get
oS yao Lege Yc =) ]
ie VEVI= cos | ut 53+ 5(p C7) HE | 3
or, substituting q for poet, as we have done already in (19),
R= V2V71—cosd(ut+3o+3que). + - + + (88)
This expression must be multiplied by I, which is represented,
according to (VII.), disregarding the higher terms, by 1— fe.
Prof, Clausius on the Conduction of Heat by Gases. 521
Thus we have
Me 4/2 1 —cosdlu-t 28—lgpe)®, <<. 789)
which product must be introduced into (33) and the integration
then carried out.
_ For this purpose we require to know what ratio cos ¢ bears to
the cosine denoted by w. We have used wu to stand for the
cosine of the angle formed by the moving direction of any molecule
whatever with the axis of z, and ¢@ to stand for the angle con-
tained between the direction of this molecule and that of the given
molecule. Further, let the angle which the moving direction of
the given molecule forms with the axis of x be », and the angle
between two planes passing through the moving direction of the
given molecule, and containing respectively the angles ¢ and 7,
bey. Then
p=cosyncosd+sinnsngdcosy. . . . (40)
The superficial element dw may at the same time be represented
by sin ddddyy. The equation (33) thus becomes
R= YA aay sin d Y1—cos d6[u+6
— Agq(cos 7 cos gé+sinnsndcosyje], . . (41)
where the integration according to yr must be carried out from
0 to 27, and that according to ¢ from 0 to z.
By performing this integration we get
R=4(u+i8+pyqc0sn.6)t. « . - (IX)
20. We must introduce this expression for R into the equa-
tions (31) and (82), in order to obtain the values of a and a.
* [Thus in the original: probably a misprint for
x . | =a Peal i Re}
IR=V2V1— cos p| Y+ 35- sque) — | WW Te08g (+3 9~g0r0) | Zue,
—G. C. F.]
+ For the sake of greater clearness, I have omitted in the above calcu-
lations all terms contaiming any power of «¢ higher than the first. I will,
however, here give the result of the more extended calculation in which
terms containing the second power of. are also included; namely,
= 4 1 1 162 1 Oe
axe sy ee re ie! acta
R=3{"+5 acon alsa Wee i
1 : 1 1,2 ] 2 LE ¢_ 1 Apa *) €?
tea] — 642-4202 +6rut 5 r u*+ & ea te ru cost [FI
522 Prof. Clausius on the Conduction of Heat by'Gases.
Thereby, substituting also u+6 for v, we get
4 Lea |
= 570°N(u+ 55+ yp9 cone), - = ts (42)
i sale! ( Lo ea €
= 5 7p N 1=5—+ poy cos: ). ~ « (48) |
The unknown quantity p can still be eliminated from these
expressions. For assuming, as a particular case, that the given
molecule, as well as all the other molecules present, has the
velocity u, we have 5=0 and g=0; whence it results that
asp! 2N. ° ; e e | e e (44),
Further, according to § 9, the fraction ; represents the mean
length of excursion between any two anaes whence we obtain
for the mean length of excursion the following expression :—
ary ee :
4 arp?N *
In order to render the signification of this expression ‘still more
special, so that it may represent the normal mean length of excur-
sion, which we have denoted by e, we only require to substitute
for N, which signifies the number of molecules contained in a
unit of volume, the particular value which corresponds to the
normal condition of the gas. Distinguishing this value by No,
we obtain |
ie aul
Ted: PepUN es ee a)
Bliminating p® fromthe above expressions by means of the
equation, they become
(45)
T= x Aut =O-+ TT A 1%
N EO Ue eye
Nala + soe)
_ We see from these expressions that the quantities a and a are
dependent on the velocity and direction of motion of the given’
molecule, and further, since N and wu are functions of 2, that.
they are dependent upon the position of the par ticular stratum
in which we consider the motion fF.
OL ==
a (XL)
* J have already given this value for the mean length of excursion, in
the case in which all the velocities are equal, in my former paper (Pogg.
Ann. vol. exv. p. 249), but without the details of calculation.
+ Maxwell has not in his calculations sufficiently attended to the de-
pendence of the quantity # on various circumstances, inasmuch as he treats
Prof, Clausius on the Conduction of Heat by Gases: 523
By help of these expressions it will now be 2h) to make ee
calculations necessary for our purpose.
§ 21. We will try to determine how many mulnenles ntti
each other. with eur infinitely thin stratum during a unit of time,
and how great is the collective momentum of these molecules.
The probability that one molecule moving within the stratum
will meet another during the element of time dé, will be repre-
sented by adt, if we put “for cos 7 and 6,in the expression for a,
the values corresponding to the direction and velocity of the
molecule in question. If, therefore, we want to determine the
number of molecules, out of a given large number of molecules,
which will-strike each other during the time dt, we only need to
multiply the whole number of molecules by alt, employing the
mean value of a, if it is not the same for all the molecules. Con-
sidering now the molecules simultaneously existing m a portion
of our stratum corresponding to a superficial unit, let us direct’
our attention, in the first imstance, to those whose cosine lies
between w and w+du. The number of these is $NIdudx; and
multiplying this expression by adt, where a denotes the mean
value of a for these molecules, the product 4Nladudxdi repre-
sents, according to what has been said above, the number of
them which will strike each other during the time dt. Inte-
grating the last expression according to w from—1 to +1, we
obtain the total number of molecules whick will strike one another
within the stratum during the time dé. We now only require
to divide this expression ‘by dt, in order to obtain the total,
number of molecules which will strike one another within the
stratum during a unit of time. Calling this pumber Mdz, we
have ta
aes ey 2? gepeariae
m= yn{ Tadeo ee) ee)
—|
The quantity I, which occurs here, we already know to be
=]— 4 pe. To obtain the:value of a, we must -put p for cos 77
in equation (X.), and V—u for 8, since V denotes the velocity
df a molecule. - But as all the molecules for which the cosine be
has the same value have not the same velocity, we must make’
use of the mean value V in order to obtain the mean value a.
According to (IIL.), V=u+que+.,., and, disregarding higher
the motions of the molecules emitted from an infinitely thin stratum as
though the value of « were the same for all and invariable. It accidentally
happens that the effect of this oversight is in the opposite direction to
that mentioned at § 5; so that the two Y partially compensate each a at’
least so far as regards the calculation of the conduction of heat,
524 Prof. Clausius on the Conduction of Heat by Gases.
powers of e, we thus obtain for the mean value of 6 the quantity
gue. Introducing this value in equation (X.), we obtain
—- N 3 |
aS wig t Rabel pel ie. emo eS
and accordingly equation (46) becomes
LN? (Hy 8
M= 55) (u—Sque) dus
and performing the integration, we get
M => e € 2 e ° 2 e e (48)
The total positive momentum .of the molecules which strike
each other within the stratum during a unit of time may be
arrived at in a corresponding manner. The positive momentum
of a molecule whose velocity is V and whose cosine is p, is muV,
and. hence we have to make use of the product myVa, instead of
the quantity a; but here again we have to determine the mean
value of Va, just as previously we had to determine the mean
value of a. The expression for the momentum sought is there-
fore
1 ee
5 item { TVapdp.
-1
If, as before, we substitute their values for I and Va in this
expression, it becomes i
1 IN? Gy oo )
5 dam Ral (x + 5 UqKE pd,
whence we get, by performing the integration,
Lee
Bo UNG
for which, by applying equation (48), we may also write
1damM qe.
§ 22. This last expression may serve us for the determination
of the constant quantity gq.
The molecules which impinge within the stratum are also those
which, after impact, are emitted from the stratum, and the col-
lective momentum which these molecules possessed before im-
pinging must remain the same afterwards. Now the positive
momentum of the molecules emitted from the stratum can be
easily expressed according to the method of representation pre-
viously adopted. For we have seen that the motions of these
molecules may be expressed by assuming at first motions taking
Prof. Clausius on the Conduction of Heat by Gases. 525
place equally in all directions, and then supposing a small addi-
tional component velocity in the direction of positive 2, which we
represented by pe, to be imparted to all the molecules. It fol-
lows thence that, if Md denotes the number of molecules emitted
im a unit of timc, their collective positive momentum will be
expressed by
damMpe.
- Comparing this expression with that previously arrived at, we
ave 7
drmMpe=idzemM ge,
and hence
PE) Pn Pain eae Seem rene 2 2,)
Having obtained this result, let us return to equation (19),
which is as follows :—
du
7=p—¢7,
and by means of the foregoing equation may be transformed into
5 du
/ reer haere << ae ° e ° e e (50)
The magnitude c which here occurs may be deduced from what
has gone before in the following manner. According to equa-
tion (15), .
1 —
my =e,
where ¢, denotes the particular value possessed by @ in the case
of those molecules which move perpendicularly to the axis of z,—
a value which is obtained by putting 6 and cos7 equal to O in
equation (XI.), namely,
4,= ——:
eouNige |
This value, introduced into the foregoing equation, gives us
N
0
‘ cC=-~=—. ° . ° e 2 e 2 e 5]
> (51)
ao ak, ihe daaagaeraa
* If the calculations are worked out further than they have been above,
by taking account, that is, throughout of the next higher power of e¢, it will
be found that the expressions deduced above, for the number and momentum
of the molecules which impinge within the stratum, have such a degree of
accuracy that only a quantity of the order of ¢’, as compared with unity, has
been disregarded throughout.
526 Prof, Clausius on the Conduction of Heat by Gases.
The determination of the coefficient ge gives at the same time,
as a consequence of equation (22), also the value of g’. The series
in equations (III.) and (IV.), which express the kind of motion
of the molecules existing simultaneously in a stratum, are there-
fore known as far as is necessary for our purpose; that is, m7
each series, besides the term which is independent of ¢, that one,
which contains its first power is known*. | ,
VI: Final Conclusions.
§ 23. Having in the preceding. pages ascertained the value
of the necessary coéfficients, we may now proceed to draw con-,
clusions from the equations that have been established, as to the
condition of the ‘gas and the’ conduction of heat taking place
within it. b ine.
In § 16 we found that g must be a constant quantity; and
if, instead of g, we put its value, we may accordingly write
ld
| N dz
The same section further teaches us that
= constant.
Nu?= const. ;
and by multiplying these two equations, we have
et const. 9-2 . oer
But, since the quantity u is proportional to the absolute tempe-
rature T, we may put :
u= const. VT,
and hence the last equation becomes
aT |
Vv TT =oonst.. » - . + - (58)
By integrating this equation, an equation of the following form:
* In the terms of the second degree we meet with the quantities q,, r,
and r', which can be determined in the same way as g by carrying out the
calculations further. Without here dwelling upon this extension of the
calculations, which presents no difficulty whatever in regard to principle, I
will merely quote the values of these quantities which are so arrived at:
Hamely, » = +4.
4]
peal aa
Jt op 2 2
31 g?
"=~ 50
pl ce 266 g
Prof, Clausius on the Conduction of Heat he Gases. 527
Is obtained, :
P= Cr4HC ey a eg a (54)
where C and C, are constants.
The quantity of gas enclosed betweeen two surfaces of given
temperatures does not, therefore, as might perhaps be supposed
at first glance, assume such a condition that the temperature is
a linear function of the abscissa; but the alteration of tempera-
fare from one limiting surface to the other takes place according
oa somewhat more complicated law, inasmuch as the poe
T= is represented by a linear function of the abscissa.
When the constants C and C, in equation (54) are deter-
mined -by-aid of the given temperatures of the limiting sur-
faces, the temperature can be calculated for every other point of
the gas. And since, further, the product of temperature into
density must remain constant within the gas if the density be
given for any one point, it can be calculated from the tempera-
ture for every other point. Accordingly, the condition of the
gas is fully known so far as regards temperature, density, and
pressure.
§ 24. By introducing into equation (VIIT.) the value that has
been found for g, we obtain the following equation for G, the
conduction of heat within the gas:
5 du
G=- Ta kmNoue sz e*. we ak By
_ * Maxwell (Phil. Mag. S. 4. vol. xx. p. 32) gives the following expres-
sion for the vis viva which passes in the positive direction through a super-
ficial unit of a plane perpendicular to the axis of z during a unit of time, |
oan 2 TAY
G=— Ea (GkmeNul ), ah pike!
where 7 denotes the mean length of excursion of the molecules which cor-
responds to the density of the gas at the place under consideration. Sub;
stituting for / its value
we have
gee hd. C kN, we )=—) | Nut €
dn
This expression differs from that given above only by containing } in place
of ;;. But if we trace the way in which Maxwell arrives at equation (A),
we shall find that this near accordance of his result with mine is only
apparent.
Denoting the mass of gas which passes in a positive direction through
the unit of surface during a unit of time by E, Maxwell establishes the
528 — Prof. Clausius on the Conduction of Heat by Gases.
For the sake of greater convenience we will still somewhat
alter the form of this equation. If we denote the velocity of the
molecules in the normal condition of the gas by up, and the ab-
solute temperature by T,, we have | |
uz *T
uy Ty
and thence
Uo
nny vpVt. . pao
The foregoing equation thus becomes
5 kmN,u,%e T dT
ga S tnNoute, /T a1
2A a 73 Dp | Relies (56)
If we assume the freezing-point as the temperature of the gas in
its normal condition, Tp=273 nearly, and T=273-+42, where ¢
following equation (Joc. cit. p. 23),
ld
——— — e 2 e e e e ° es s B
E 3 Gp (mNul) (B)
Then, in order to obtain the vis viva which traverses the plane instead of
the mass, he simply substitutes in this equation the vs viva of a molecule,
zkmu*, for the mass of a molecnle m, and so obtains equation (A). If we
now consider equation (B) more closely, and substitute there also its value
N
NS for /, we get
ld 1 du:
E=— = — (mN,we)=— = mN, —e.
Sag an
This equation proclaims that, if the temperature of the gas varies in the
du
direction of z so that 7 has an appreciable value, a progressive move-
ment of the mass in the direction of 2 must take place, masmuch as more
molectiles pass through the plane in one direction than in the other. Itis
therefore contradictory of the supposition which we must make when we
speak of the conduction of heat; for we understand by conduction of heat
a progressive movement of the heat without a progressive movement of the
mass.
Independently, therefore, of the question whether equation (B) is ad-
missible or not, we are forced to one of the following conclusions : im esta-
blishing his equations, Maxwell either had in view a state of things quite
different from what we presuppose in speaking of conduction of heat;
namely, such a state that the gas has a progressive movement in a parti-
cular direction, in which case his equation (A) does not express what we
understand by conduction of heat, and what is expressed by my equation
(XIII.), but a@ motion of heat accompanied, and partly occasioned, by a
motion of mass; or else he really imtended to represent the condition in
which 2 movement of heat takes place unaccompanied by a movement of
mass, in which case the equation (B) is wrong, and the equation (A) de-
duced from it is only approximately correct because two errors haye par-
tially neutralized each other.
Prof. Clausius on the Conduction of Heat by Gases. 529
denotes the temperature reckoned from the freezing-point. If
we further represent the coefficient of expansion of the perma-
nent gases, namely 73° by a, as is usually done, we can write
5 kmN, Up? € dt
AOA a ae V1i+at—. ,
Lastly, if we introduce here the symbol K with the value
G= (XIV.)
_ 5 kmNgu,?
js 34 973? (XV.)
our equation reads
ee |,
G@= = K' V/1 at = ek NON EMU (XVI.)
§ 25. The factor K contains only magnitudes which relate to
the normal condition of the gas, and is therefore only a constant
dependent on the nature of the gas under consideration. Accord-
ingly, the form of the last equation enables us at once to draw
two general conclusions.
; dt as
First. For a given value of ey the conduction of heat increases
with the temperature which the gas has at the place under consi-
deration. This increase takes place in the same ratio as the
imerease in the velocity of sound by rise of temperature, namely,
proportionally to the quantity /1+ at.
Secondly. The conduction of heat is not affected by the pressure
to which the gas is exposed. This is explained by the circum-
stance that, although the number of molecules which can convey
the heat is greater in a gas which is rendered more dense by in-
creased pressure, the distances traversed by the individual mole-
cules are smaller. This latter conclusion might lead to absur-
dity if it were assumed to be applicable to the gas under every
conceivable condition of compression or expansion. It must,
however, be borne in mind that there are obvious limits to the
application of it to conditions of the gas which depart very much
from the mean condition: on the one hand, the gas must not be
so much compressed as to produce a too great departure from
the laws of permanent gases which have been taken as the foun-
dation for the whole course of reasoning; and on the other
hand, it must not be so much expanded that the mean length of
excursion of the molecules becomes so great that its higher
powers cannot be disregarded.
§ 26. It will be necessary, for the numerical calculation of the
above formula, to return once more to the point mentioned in
§ 7, namely, the accidental variations of the velocity of the mole-
Phil. Mag. S. 4. No. 157. Suppl. Vol. 23. 2N
530 ~— Prof. Clausius on the Conduction of Heat by Gases.
cules which occur even when the temperature and density of the
gas is uniform throughout.
Accordingly we must not attribute to the quantity wu (which
occurs in the formule for the motions of the molecules, and repre-
sents their velocity for the case where no variations of tempera-
ture and density occur) a fixed value applicable in the case of all
the molecules, but different values which vary in many ways from
one molecule to another. The same thing holds also for other
magnitudes which are dependent on the velocity of the mole-
cules,—e. g. for the length of excursion s, which we meet with in
$$ 8 et seg., and whose value must be on the average somewhat
greater in the case of molecules whose velocity is greater, than in
the case of those that have a less velocity. We have then now to
find mean values for these quantities, so far as they occur in the
formule, which must be determined in such a way that by their
employment the values of the formule remain the same as those
which would be obtained by taking into calculation the actual
velocity of each molecule. .
In order to be able rightly to calculate these mean values, we
must know the law which regulates the various velocities which
occur. As I have already stated above, such a law was esta-
blished by Maxwell, and it might perhaps be employed for
calculating the mean values*. I prefer, however, not to discuss
this subject here, as a few remarks concerning this law would be
required which would lead us too far at present; and I feel the
more justified in leaving this point, since the numerical value of
eis so imperfectly known that the aceurate numerical calculation
of a formula in which it occurs is not possible. I will therefore
content myself, in the calculation of the conduction of heat, with
* T must here remark that this calculation would not be quite so simple
as might perhaps appear at first sight. For a pomt must be attended to
which has already been remarked upon in a similar connexion above,
namely, that the mean value of a power of uw is not the same thing as the
corresponding power of the mean value of wu; and the same thing is true
for other quantities which depend upon w, or for products into which such
quantities enter. The consideration of the following series of expressions,
for example (a horizontal] stroke being used, as before, to denote the mean
values),
Unt2
w, (we, ar+(1—a)(up, Gao &e-
plainly shows that if all the values of w which occur in them were equal,
they would take the common form u?; whereas if the value of wu is not
everywhere the same, they are not equivalent to each other. _ If, therefore,
in any formula which is deduced upon the supposition of uw having always
the same value, u? should occur, we cannot be at once certain which of the
mean values indicated above ought to be taken, but, in order to decide,
we must trace the whole development of the formula.
Prof. Clausius on the Conduction of Heat by Gases. 531
employing in the above formula, which is deduced without con-
sidering the accidental variations, a mean value for the velocity
which is easily arrived at, and which, though not strictly accu-
rate, may still be regarded as sufficiently so, considering the
uncertainty which still prevails in regard to the value of e.
§ 27. We will employ that mean value of w which gives the
same vis viva as the velocities which actually occur. This value
may be obtained by taking the arithmetical mean of the squares
of the velocities, and extracting therefrom the square root.
In this case the product 44Ngmu,? has a simple meaning. It
represents, namely, the vis viva, or, in other words, the quan-
tity of heat contained in a unit of volume of the gas in its nor-
mal condition. Ify stands for the specific heat of a unit of
volume of the gas, the volume being kept constant, yT, will
represent this quantity of heat; or if the freezing-point be
taken as the normal temperature T,, it will be represented
approximately by y.273; whereby equation (XV.) becomes
= UGE Ss ecm oe Oe)
and if y be expressed in common heat-units, the conduction of
heat is also expressed in common heat-units by employing this
formula. The magnitude uw, may be deduced as follows from
the formula which | formerly* established for the moving velo-
city of the molecules,
__ 485”
U. _— —— .
0 5)
Vo
where o denotes the specific gravity of the gas in question com-
pared with atmospheric air. The foregoing equation is thus
transformed into
(58)
Ree ee one Mn ONAL Ti
Vo
For the simple permanent gases, and such compound gases
as suffer no contraction on the combination of their elements,
the specific heat y is the same as for atmospheric air; and if a
cubic metre, which contains 1°2982 kilog. atmospheric air in the
normal condition, be taken as our unit of volume,
y=0°1686 . 1:°2982=0°21803. . . . (59)
By employing this value, we get for the gases mentioned
Bee Fa ysl swod +S ULI)
Vo
Hence for the three simple permanent gases and for atmospheric
air, which must be treated as a simple gas im relation to the
* Phil. Mag. S. 4. vol. xvii. p. 124.
2N2
532 Prof. Clausius on the Conduction of Heat by Gases.
conduction of heat, we obtain the following values for K ; namely,
For atmospheric ar . . . 44°06.6¢
Horiosyeen’ fs ee ekg LO) 4€
Hor mtrormen oo. (ve bieiaatetd Ween
Por’ hydrogen’. ogee
The complete numerical determination of these values requires
that the factor « should be known. A direct theoretical calcu-
lation of this quantity, according to the principles developed
above, is not possible, because for this it is necessary to know
the radius of the sphere of action p. We must therefore make
use of other data for the determination of e«. Maxwell has caleu-
lated the mean length of excursion of the molecules from the
result of experiments on the friction of air in motion and on the
diffusion of gases, and in both cases has arrived at figures which
do not differ much from
iL ay (HA 1
400,000 English inch, or 16,000,000 metre.
Without giving any opinion here as to the degree of confidence
which may be placed in this number, [ am nevertheless of opinion
that we may employ it to give us an approximate idea of the
kind of magnitudes with which we have to do. Putting this
value into the above equation, we get for atmospheric air
44 Nagios
16,000,000 ~— 4,,000,000°
This quantity denotes the quantity of heat, expressed in com-
mon heat-units, which would traverse a plane of one square
he (60)
Rae ie
metre during one second, if dg Were equal to —1; that is, if
d.
the temperature decreased in the direction of the axis of abscissze
near the point under consideration in such wise that, if a similar
decrease took place throughout a greater length, the tempera-
ture would diminish 1° C. in the length of 1 metre.
§ 28. In order to compare this conducting-power for heat
with that of the metals, we may make use of a result observed
by Peclet, who found, by measurement of the quantity of heat
which passed through a plate of lead, that, if a large mass of
lead were placed under such circumstances that a diminution of
temperature of 1° C. took place in a thickness of 1 metre, a
quantity of heat equal to 14 heat-units would then pass through
a surface of 1 metre square in one hour*. To compare this
number with that found for air, we must multiply the latter
by the number of seconds contained in an hour, it having been
* Traité de la Chaleur, vol.i. p. 391.
Prof. Clausius on the Conduction of Heat by Gases. 533
calculated for 1 second; we thus get
TEx 2000) Ps
4,000,000 100
This calculation leads therefore to a conducting-power for heat
which is 1400 times smaller than that of lead*.
If this number can but lay claim to a small degree of accu-
racy, so that it can only be regarded as an approximation to the
truth, we may at least regard it as proved that the conducting-
power of gases for heat, which can be theoretically deduced from
the hypotheses respecting the molecular motions of gases which
lie at the foundation of this memoir, is much less than that of
the metals—a result which entirely accords with observation.
The objection that this hypothesis involved so rapid a distribu-
tion of heat that local differences of temperature within the gas
are impossible, is accordingly completely without foundation.
We may even quote, as a fresh argument im favour of this hypo-
thesis, the very phenomenon which has been urged with such
particular emphasis against it.
§ 29. The expressions which have been found for K admit,
further, of an approximate comparison with each other of the
various gases in respect of their conducting-power for heat.
In the expression (X VII.) the specific gravity o is sufficiently
well known ; and the specific heat y can be approximately calcu-
lated from the experiments of Regnault. If we consider apart
the simple gases and such compound gases as possess the same
volume as their constituents before combination, we may, as has
been said, assume that y is the same for all; and the expression
for K thus assumes the form (XVIII.), which contains nothing
but the fraction in addition to the numerical factor.
/ Oo
The quantity «, the mean length of excursion of the mole-
cules, is not necessarily equal for different gases, and we do not
know what proportion the lengths of excursion im various gases
hold to each other. Nevertheless there is no obvious reason to
* Maxwell arrived at quite a different result, namely, that atmospheric
air conducts ten million times worse than copper. This was, however,
caused only by the occurrence of two oversights in his numerical calcula-
tions. In the first place, mstead of Peclet’s numbers, which express the
conducting-power of the metals in French measures, he employs numbers
calculated from them by Ranke (Manual of the Steam-engine, p. 259)
in order to express the conducting-power in English measures. These num-
bers, however, are not quite correct; they still require to be multiplied by
0°4536, the ratio of the English pound to the kilogramme, in order to
make them correspond with Peclet’s numbers. Maxwell has further em-
ployed the numbers which relate to one hour as the unt of time as though
they were calculated for one second.
534 Mr. W. Baker on the Metallurgy of Lead.
assume that it is shorter for light gases than for heavy gases ; for
it is inversely proportional to the radius of the sphere of action,
and it would be difficult to assign a greater sphere of action to
the lighter than to the heavier molecules. If, accordingly, ¢ is
not smaller for the lighter gases, the fraction ce , and therefore
8 8 reaps
the conducting-power for heat, must be greater in this case than
in the case of the heavier gases.
This result accords perfectly with the results of observation
hitherto obtaimed, and especially with those of the beautiful
investigations by Magnus, in which he avoided the currents of
gas which, in the experiments of Dulong and Petit, existed at
the same time as the conduction of heat properly so called. From
these experiments we see very plainly that the lightest gas
(hydrogen) conducts considerably better than the other gases.
§ 30. We may sum up as follows the conclusions at which
we have arrived. ;
1. Gases conduct heat considerably worse than the metals. An
approximate calculation based upon the mean length of excur-
sion of the molecules, as deduced by Maxwell, gives, for the con-
ducting-power of atmospheric air near the freezing-point, a num-
ber which is 1400 times smaller than that which represents the
conducting-power of lead.
2. The conducting-power for heat depends on the tempera-
ture of the gas, and increases in the same ratio as the velocity
of sound.
3. The conducting-power for heat is, within certain limits,
independent of the pressure to which the gas is subjected.
4. light gases conduct heat better than heavy gases. Hydro-
gen must therefore conduct heat considerably better than any
other gas.
Zurich, October 1861.
LXXII. Contributions to the Metallurgy of Lead. By Wii11aM
Baker, Associate of the Government School of Mines, F.C.S.* —
i was shown, ina paper published in the ‘ Chemical Gazette,’
October ‘1, 1556, that Pattinson’s process of concentrating
silver in lead by crystallization accomplished at the same time a
separation of copper, the latter beimg found in the larger pro-
portion in the fluid lead which had been drained from the ery-
stals. It was supposed therefore that this method offered a
valuable means of preparmg an inferior quality of lead for those
purposes in the arts for which a metal of the greatest purity
attainable is required.
* Communicated by the Autuor.
Mr. W. Baker on the Metallurgy of Lead. 530
It might seem to the uninitiated that the lead then operated
upon was already sufficiently pure for all practical purposes, the
quantity of copper it contained amounting to only 0:0154 per
cent., or 5 oz. 0 dwt. 14 grs. per ton. Neglecting the small
quantities of iron, sulphur, and silver, we will confine our atten-
tion to the copper, which is the most objectionable impurity
that has to be removed.
For a long time certain “brands” of lead have been preferred
to all others for such purposes as making white lead and glass-
maker’s red lead. We may instance the lead made from the
Snailbeach Mines in Shropshire, which has enjoyed a repu-
tation for making good red lead for glass-makers. The best
selected lead of the Northumberland district has been also much
sought after by the manufacturers of white lead. Happily we
are now emancipating ourselves from the fashion of ascribing
peculiarities in the smelted metal to the “nature of the ore.”
This term is perhaps useful enough in the mouth of the practical
smelter when explaining how the charge is worked in the fur-
nace, but in all cases it may be translated into more precise
language by a due methodical and scientific imquiry. As the
most remains to be known about iron of all the common metals,
it is exceedingly probable the “nature of the ore” will have for
some time to come to account for the nature of the pigs intro-
duced.
A very small quantity of oxide of copper in the red lead is
found to impart a bluish shade to flint-glass. In some cases it
can hardly be pronounced blue, but at least the glass is wanting
in the pure watery lustre which is the perfection of “cristal.”
It is almost incredible that so small a proportion as 3 oz. per
ton, or 0:009 per cent., should impart an undesirable tint ; yet
the evidence upon this pomt is conclusive. Some facts in refer-
ence to white-lead-making will, however, quite corroborate this
statement. In making carbonate of lead by the method of fer-
menting tanners’ bark and acetic-acid vapour, the corroded or
converted lead often presents a delicate pink tint. Close obser-
‘ yation has shown me that this is invariably connected with the
presence of copper. Where the air has had more free access, the
pink colour disappears, or is replaced by a far more delicate blue,
indicating the passage from suboxide of copper (Cu? O) to prot-
oxide of copper (CuO). Finally, pure lead specially prepared,
which gave repeatedly pure-white corrosions on receiving the
addition of a very small proportion of copper, exhibited the cha-
racteristic pink tint when again submitted to the action of the
corrosive vapours. Providing the lead is otherwise pure, a pro-
portion of only 24 ozs. per ton, or 0:0071 per cent. of copper, is
sufficient to produce a delicate but decided pink hue. Should
536 Mr. W. Baker on the Metallurgy of Lead.
antimony or sulphur be present, the colour is somewhat masked
and a dull-coloured white lead is produced. That the presence
of iron has nothing whatever to do with this appearance, is mani-
fest from the fact that the lead containing only an mappreciable
trace of copper which gave pure white corrosions, contained quite
as much iron as the specimens which afforded pmk corrosions.
Proceeding upon the results given above, Derbyshire lead,
which, when properly smelted, contains from 2 ozs. to 5 ozs. of
copper per ton, was crystallized three or four times and pro-
duced remarkably pure lead. Numerous analyses have con-
firmed the fact that, in dealing with a metal contamimeg up to
5 ozs. or perhaps 7 ozs. per ton, the copper is always concen-
trated along with the silver. Buta most remarkable fact was
discovered upon applying this method of purification to lead
containing above 10 ozs. of copper per ton.
Five tons of lead, contammg 0°0774 per cent. of copper, or
25 ozs. per ton, were submitted to Pattinson’s process. At the
fourth operation the following was the distribution of copper in
the charge :—
Crystals . . . . . . 0°0574 per cent. copper
Fluid lead drained from 0:0526 : f
the crystals
At the sixth crystallization,—
Crystals). 62s 1) 9.00642 per cent coppen
Phorddleads:.” 340.2. 03 00570 3 3
proving that no concentration of copper in the fluid portion had
taken place. The lead, which was otherwise soft and fit for all
ordinary purposes, such as rolling into sheets and making pipes,
possessed a surface unmistakeably different from that of the
purest lead, the most marked difference being a somewhat irre-
gular depression or crumpling in a line along the direction of
the length of the mould. Other experiments with lead contain-
ing various proportions of copper have showed that when the
quantity is above a certain limit, which can only be more accu- .
rately defined when a larger number of analyses have been made,
the crystallization process cannot be economically employed.
It still remains, however, a useful adjunct to refining-opera-
tions, when the lead operated upon has been smelted from ore
carefully selected to exclude the more coppery kinds. Lead-
smelters, besides, might do much for the purity of lead if their
charges were worked in such a manner as that, with good ore, by
keeping the temperature as low as possible, even at the sacrifice
of the yield of metal, most of the copper would go into the slags.
These would yield equally good common lead; and the repu-
M. V. Regnault on an Air- Thermometer. 537
tation of the smelter would be so much increased by the higher
degree of purity of the selected lead. It is to be feared that, in
the attempt to get the utmost out of the ores at the “ first”
operation, they have often deteriorated from the quality of metal
produced in former times.
LXXIII. On an Air-Thermometer used as a Pyrometer in mea-
suring Hiyh Temperatures. By M. V. Reenavur*.
[| With a Plate. |
j | ae pyrometers which from time to time have been proposed
for the measurement of high temperatures in industrial
furnaces, have not hitherto received any important application.
Those which depend upon the expansion or on the increase in elastic
force of air confined in a closed vessel, are apparatus both difficult
and expensive to construct, and can only be used by observers
well practised in delicate manipulations.
The pyrometers whose indications are based on the apparent
expansions of two metals, or on that of a metal as compared with
a rod of baked clay or porcelain, which is supposed to be unalter-
able, could in no case be used other than as pyroscopes, to see if
the same furnace has been raised to the same temperature in suc-
cessive operations. But it is difficult to graduate these instru-
ments, and even to compare them with a normal instrument so
as to be able to transform their indications into degrees of our
thermometric scale. Lastly, the same instrument undergoes,
when exposed to high temperatures, permanent alterations which
affect the scale and prevent any comparison of its indications.
Wedgewood’s pyrometer, which depends on the contractions
which the same clay undergoes at different temperatures, can also
only be used as a pyroscope; but it is still more defective in
principle. The contraction which the same clay undergoes for
the same increase of temperature depends on the degree of com-
pression to which it has been exposed in the crude state, on the
more or less rapid increase of temperature, on the more or less
prolonged action of heat.
I proposed in 1846 (Mémoires de TP Académie des Sciences,
vol. xxi. p. 267) an apparatus easy of manipulation, by which the
temperature of any part of a furnace may at any given moment
be obtained with sufficient accuracy. The apparatus consists of
a kind of flask A, fig. 5, Plate II., either cylindrical or spherical,
of from } to 1 litre in capacity, and which may be either of cast
or wrought iron, of platinum or of porcelain; the mouth a is
closed by a plate cd containing an aperture o. From 15 to 20
* Translated from the Annales de Chimie et de Physique, September 1861.
538 M. V. Regnault on an Air- Thermometer
grms. of mercury are added to this flask, which is then placed in
the furnace in the part the temperature of which is to be known.
The mercury soon boils, its vapour expels the air, which escapes
by the orifice o ; the excess of mercurial vapour emerges by the
same issue. When the apparatus has acquired the temperature
of the furnace, the plate cd is taken out in order to close the
orifice 0, the flask is withdrawn and made to cool rapidly. The
mercury which remains in the flask is weighed; it is removed by
the addition of water and agitation. The mercury can be weighed
directly ; or if it contains impurities, it is dissolved in acid and
estimated as precipitate.
The neck may also have the form of fig. 6. The tubulure
then terminates in a hollow conical part, and im its orifice is a
ball B of the same material as the flask. This does not close it
hermetically, but it prevents the currents of air of the furnace
from disturbing the mercurial vapour in the interior of the flask.
Let
V be the capacity in cubic centimetres of the flask at O° as
given by the weight of water which fills the flask ;
k be the coefficient of cubical expansion of the substance of
which it is made;
H be the height of the barometer at the moment at which it
is withdrawn from the furnace ;
A the difference between the pressure in the interior of the
furnace and of the surrounding atmosphere. This differ-
ence may often be neglected, but it can readily be deter-
mined by means of a water manometer.
H, the height H—A reduced to 0°;
6 the theoretical density of mercurial vapour compared with
that of air under the same circumstances of temperature
and pressure ; that is, the density of this vapour taken at
temperatures starting from which it no longer changes ;
in other terms, higher than that, starting from which, mer-
curial vapour and air follow the same laws of expansibility
and compression. Itis, moreover, clear that it is only above
this temperature that the pyrometer can give exact tempe-
ratures.
p the weight of the mercury which remains in the flask at the
end of the experiment.
The weight of mercurial vapour which fills the flask at the
maximum temperature « is
Vv l+ka Hy
9
ery .0°0012982. 8 a0;
we have then
V. ae 0:0012932. 5 lo =p,
ltaz 760
used as a Pyrometer in measuring High Temperatures. 589
from which
ee te OM ute Pw DP
tae V.0'0012982.5 H”~ -H’
M being a quantity which is constant for the same flask.
From which 1s obtained
pqupl:
ii if Ma
Mat —k
a= 0:00367.
The method here described may be used in many cases, but it
requires that the introduction and removal of the apparatus from
the furnace takes place without detriment to the operation. I
have devised another apparatus, which has the advantage over
this of always remaining in one place, and of serving as often as
necessary to measure the variable temperatures of the same fur-
nace. I proposed to employ it in determining the temperatures
at which enamels and the different kinds of painting on porcelain
are baked at the Imperial Manufactory of Sévres.
The apparatus consists of a tube, AB, fig. 7, of wrought
iron, the length of which varies according to the extent of the
space whose mean temperature is to be determined. Its internal
diameter varies from 2 to 5 centimetres; it is more when the
tube is somewhat long. This tube is closed at both ends by
iron discs which are screwed and braced, each of which is pro-
vided with an iron capillary tube ab, cd passing through the
side KH! of the furnace. To construct these tubes, a very soft
and frequently reheated soft iron cylinder, perforated by a lon-
gitudinal aperture 3 or 4 millims. in diameter, is drawn out in
the drawing-frame. Hach of these capillary tubes terminates
outside the furnace in a three-way stopcock, RR’. By means of
the stopcock R, the large tube A B can be successively connected
with either of the two tubulures e and f/. By the stopcock R!
the same tube communicates with either of the tubulures g, h.
The metallic tubulure / is soldered to the end of a copper tube
C, filled with oxide of copper.
When the temperature of the furnaces is to be determined at
a given moment, the stopeocks R and R’ are placed in the posi-
tions represented by fig. 7; by means of a caoutchouc tube, the
tubulure fis connected with an apparatus which furnishes a
constant supply of dried and purified hydrogen; the hydrogen
expels the air of the tube AB through the tubulure g, which
remains open. The disengagement of hydrogen is continued
until the air is completely expelled: any oxide which might
540 M. V. Regnault on an Atr- Thermometer.
exist on the inner side of the tube AB will be reduced to the
metallic state.
The stopcock R is then turned into the position 2 (fig. 8), the
hydrogen-apparatus is detached from the tubulure f, and the
tubulure e is connected with an apparatus which disengages,
when convenient, dry air with a velocity which can be regulated.
This apparatus, represented by fig. 9, consists of a tubulated
flask V, into which water passes from a higher reservoir X,
through a leaden tube a8, provided with a stopcock 7, by which
the flow of water can be regulated. The air of the flask V traverses
a tube cd, filled with pumice saturated with strong sulphuric
acid. When the stopcock 7" is closed, the air in the flask V is
under a higher pressure than that of the atmosphere, for it sup-
ports in addition the pressure of the column of water ad.
Thus, when the temperature of the furnace is to be determined,
the tube A B is filled with hydrogen under the pressure of the
atmosphere H, and at the unknown temperature z. Further, the
copper tube C, filled with oxide of copper, is heated to redness by
a row of gas-burners; lastly, its second tubulure, 7, communicates
with a U-tube, filled with pumice saturated with sulphuric acid,
and which has been previously weighed. The stopcock R is in
the position 2 (fig. 8), and the stopcock R/ in the position 3
(fig. 8). The stopcock R’ is opened for a moment to expel the
hydrogen of the tubulure ef; R’ is then placed in the position 1
(fig. 8), finally im the position 3 (fig. 8). The stopcock 7! of the
air-vessel is then carefully opened (fig. 9); dry air passes
slowly into the large tube AB; expels from it the hydrogen,
which partially burns, and drives the remainder over the hot
oxide of copper, where it burns completely; the water arising
from this combustion condenses in the sulphuric acid tube 8.
The current of air is continued until the hydrogen and aqueous
vapour are completely expelled from the tube AB. The
reduced oxide of copper reoxidizes in this current of air.
Let |
V be the capacity of the apparatus at 0° in cubic centimetres.
6 the density of hydrogen as compared with air.
a the coefficient of expansion of this gas.
k the coefficient of cubical expansion of the metal of which
the tube A B is made.
P the weight of water collected in the tube S.
We shall have
1+ke LoD es Aral
Va re §.0:0012982. 60 =P ii9-50
In a preliminary experiment, made in the same apparatus
before the tube A B had been arranged in the furnace, A B was
On the Oxidation of Gaseous Hydrocarbon-compounds. 341
surrounded by melting ice; and, working exactly in the manner
described above, a + geen was nale of the weight P’
of water furnished by the hydrogen which filled the appar atus at
0°, and under the pressure H!. ”'There was obtained thus :
He 203, 250
Vi Oi - 00012982 = = T1250"
Dividing the first of these equations by the second, we get
ee P H’
ltar ee
!
pi is given by experiment with melting ice; it remains the same
for all determinations of high temperatures ; I represent it by M ;
I have then
Pe eee oH
ie ae ee
Th : y
whence i-M =
mae
M PI a—k
The determination of a temperature by this method requires
very little time, and the apparatus is ready for the next experi-
ment. There is therefore every facility for studying the ascend-
ing or descending course of the temperature of furnaces.
o—
LXXIV. On the Oxidation of Gaseous Hydrocarbon-compounds
contained in the Atmosphere. By H. Karsren*.
N Y experiments on the oxidation of organic substances con-
taining carbon, published in Pogcendorff’s Annalen,
vol. cix. p. 346, proved that these bodies combine, at the ordi-
nary temperature, with the oxygen of the air to form carbonic
acid and water, and that the presence of nitrogenous substances,
which chemists have been hitherto accustomed to think requisite
in order to set up the process of decay, is of no consequence,
since even pure carbon is oxidized to carbonic acid by exposure
to the air at the common temperature, just as it is at higher
temperatures, only more slowly.
These experiments further showed that organic hydrocarbon-
compounds are also oxidized under water, with formation of
earbonic acid, if air has sufficient access to them, more rapidly
than in the dry state. When under these circumstances the
access of air is insufficient, they rot, that is, they yield, besides
* Translated by G. C. Foster, B.A., from Poggendorff’s Annalen,
for 1862.
542 M. H. Karsten on the Oxidation of Gaseous
carbonic acid, gaseous hydrocarbons and other volatile products,
as yet for the most part only imperfectly known. When oxygen
is completely excluded, they remain unchanged under water *.
After the completion of my former investigation, it still re-
mained to determine the manner in which the gaseous hydro-
carbons produced by the process of putrefaction, and the other
gaseous and solid organic bodies (odorous substances, &c.) which
are also present in the air, behave when they are diffused through
the atmosphere—a problem of the greatest importance in relation
to the vital process of the animal organism.
The results of my former experiments rendered it probable
that these hydrocarbons would be acted on by contact with free
oxygen in the same way as others, but it still seemed desirable
to confirm this supposition by experiment.
Two methods presented themselves for the attainment of this
object, which, as supplementary to each other, required both to
be carried out.
In the first place, atmospheric air which still contains volatile
hydrocarbons, when passed through a series of vessels filled alter-
nately with air and with lime-water, must give up carbonic acid
to the lime-water until all the hydrocarbons contained in it are
oxidized ; and. the quantity of carbonic acid deposited in the first
vessel must be greater than the quantity deposited in those which
follow, if the intervening spaces filled with air are of equal size.
In the second place, if atmospheric air laden with hydro-
carbons is heated to redness, it must deposit carbonic acid only
in the first vessel containing lime-water or potash, and, when
thus freed from carbonic acid, it ought not to deposit anything
in the succeeding vessels. Experiments had already been made
according to the first of these two methods by Messrs. C. W.
Eliot and Frank H. Storer; but as these chemists had in view
the solution of another problem, and as I did not know whe-
ther in their experiments, which were carried out very carefully
in other respects, the contact of the air operated upon with the
organic substances, such as cork and caoutchouc, used for con-
necting the various parts of the apparatus was avoided (a
circumstance which must necessarily have affected the result), I
repeated the experiments myself. 7
In doing so I made use of a series of vessels similar to one
another, one of which is represented in the accompanying figure,
connected together in such a way that the air in passing through
* During the course of the experiments here published, the evolution
of carburetted hydrogen and carbonic oxide gases by living plants was
observed by Boussingault (Compt. Rend. Nov. 1861); and the presence of
a large quantity of solid organic matter in the air, which remains suspended
when the air is in motion, was pointed out by Pasteur (Annales de Chimie
et de Physique, 3rd series, vol. Ixiv. p. 24, January 1862).
Hydrocarbon-compounds contained in the Atmosphere. 548
them never came in contact with organic matter. This was
effected by covering the corks a with a layer of mercury of suffi-
cient thickness.
The mercury was introduced through the drawn-out point of
the tube 4, by means of another tube drawn out to a still longer
and finer point, and serving as a funnel.
Before fillmg the apparatus with lme-water the air contained
in it was replaced by air free from carbonic acid, and in like
manner the tubes 0, which serve to connect the different vessels
containing lme-water, were filled with air deprived of carbonic
acid immediately after being placed on the corks and before the
mereury was poured in. After the troduction of the mercury,
air free from carbonic acid was again passed into them, in order
to displace any common air which might have got in during the
pouring in of the mercury, and they were then immediately
closed by quickly melting off the drawn-out points.
In order to exclude any possibility of the leakage inwards of
common air at any accidental orifice, the air experimented upon
was not drawn, but pressed, through the apparatus*.
* The whole apparatus was, moreover, found to be perfectly air-tight
before beginning the experiment, and no leakage arose during the course
of it.
544 M. H. Karsten on the Oxidation of Gaseous
In the first experiment, that of leading through the apparatus
atmospheric air which had not been heated to redness, the
supposition with which I started required that a certain amount
of carbonate of lime should be deposited in each vessel, but
especially in the first, and, further, that the vessel following a
large tube of 200 cubic centims. capacity, which was substituted
for one of the small tubes 6, should contain more carbonate of
hme at the end of the experiment than the vessel immediately
preceding it.
120 litres of air were pressed through the apparatus, a single
bubble at a time, so slowly that about 5 litres went through in
twelve hours.
The air used in the experiment was freed from carbonic acid
by being passed through three vessels containing hydrate of
potash before it came in contact with the lime-water.
As I have already pointed out*, the white opake precipitate
of carbonate of lime does not form (especially in the cold) on the
sides of the glass tube where it dips into the lime-water, if only
a very small quantity of carbonic acid is contained in the gas
which bubbles through the liquid, but only crystals of hydrated
carbonate of lime, which collect at the bottom and against the
sides of the glass bulbs together with a little gelatinous-looking
hydrate of lime. And since the air employed in this case was
very strongly dried by being previously passed through a con-
centrated solution of potash, it carried away water from the
saturated solution of caustic lime, and so occasioned the pre-
cipitation of a certain quantity of hydrate of lime.
When 60 litres of air had been passed through the apparatus,
the first tube of the lime-water-vessel immediately followmg the -
large tube filled with air showed already the well-known deposit
of carbonate of lime, whereas all the other tubes in the apparatus
remained free from it even at the end of the experiment. This
vessel also contained a larger quantity of crystallized carbonate
of lime than the others, in which, however, were distinct (though
not weighable) traces of it, recognizable by the evolution of gas
bubbles when a few drops of hydrochloric acid were brought in
contact with it after the lime-water had been removed by a
stream of air free from carbonic acid.
The result of this one experiment is not alone sufficient to
prove the accuracy of the supposition that a continual oxidation
of compounds of carbon and hydrogen goes on in the atmosphere.
It might be urged that the potash solution was not sufficient to
keep back the whole of the carbonic acid already existing m the
air, or even that it is altogether impossible to free air completely
from carbonic acid by means of lime-water or of solution of
* Poggendorff’s Annalen, vol. cix. p. 349.
Hydrocarbon-compounds contained in the Atmosphere. 545
potash. The latter opinion has in fact been maintained by very
able chemists, for example, by Messrs. Eliot and Storer ; and it
was with a view of proving the accuracy of it that they under-
took the experiments which they have published in the ‘ Pro-
ceedings of the American Academy of Arts and Sciences’ for
September 1860.
As has been already stated, these chemists do not appear to
have observed the precautions necessary for keeping the air from
contact with organic matter during its passage through the
apparatus, so that the result of their experiments 1s affected by
a twofold source of error*. The first of these sources of error
was avoided in my experiments by disposing the apparatus in
the manner already described. The presence of the second was
demonstrated by my second experiment, which consisted in
passing the air, before allowing it to enter the apparatus where
it was washed with potash and lime-water, through a red-hot
platinum tube, 1 metre long and 15 centimetres wide, filled
with oxide of copper, so as to convert any volatile compounds of
carbon and hydrogen which might be contained in it into car-
bonic acid and water.
In this experiment, as in the first, the heated air to be experi-
mented upon was passed through three bulb-apparatus, such as
that shown in the figure, containing potash before it came in
contact with the lime-water. The quantity of air passed through
the apparatus was also, as before, 120 litres, and the rate of
passage about 5 litres in twelve hours.
At the end of this experiment all the vessels containing lime-
water were found to be perfectly unchanged, except that the
quantity of liquid in them was somewhat smaller, and hence a
little gelatimous hydrate of lime was deposited in them, but no
* During the passage of atmospheric air through a caoutchouc tube, the
formation of carbonic acid by the oxidation of the caoutchouc takes place
to a very considerable extent. I placed at the end of the apparatus above
described a piece of so-called vulcanized india-rubber tubimg, | foot in length,
and of the diameter of a raven’s quill, which was connected with a bulb-
apparatus filled with lime-water, wherein the air, which entered the india-
rubber tube free from carbonic acid, was again washed. At the conclusion
of the experiment above described, the whole surface of the bulb-apparatus,
with which the lime-water came in contact, was covered with crystals of
carbonate of lime. In order to form an approximate idea of the quantity
of carbonic acid formed in the caoutchouc tube, I allowed a very slow
stream of air, deprived of carbonic acid, to flow during fourteen weeks
through a caoutchouc tube 3°2 metres in length, and 4°7 millimetres
internal diameter, the air as it issued being made to pass through a weighed
quantity of solution of potash, and then through a weighed chloride-of-
calcium tube as described in Poggendortf’s Annalen, vol. cix. p. 349. At
the end of the experiment the potash apparatus and chloride-of-calcium
tube had together increased in weight by 0°1166 gramme.
Phil, Mag. 8. 4. No. 157. Suppl. Vol. 28. 20
546 M, A. de la Rive on the Aurore Boreales,
crystals. On moistening them with hydrochloric acid, with the
precautions already indicated, the closest observation could not
detect any evolution of gas ; evidently no formation of carbonate
of lime had taken place.
This experiment proves, in the first place, that a solution of
hydrate of potash is sufficient to absorb completely the carbonic
acid contained in the air; and secondly, that air which has been
carefully and sufficiently heated to redness, and then passed
through caustic potash, is and remains free from carbonic acid ;
while, on the other hand, air that has not been heated to redness,
when passed through the same apparatus and through the same
quantity of potash, still yields to potash a distinctly perceptible
quantity of carbonic acid, which must therefore have been formed
during the passage of the air through the apparatus.
In conclusion, I cannot omit publicly acknowledging my
obligation to Dr. Finkener for the willing aid he afforded me in
putting together, in Prof. H. Rose’s laboratory, the complicated
apparatus required for these experiments.
LXXV. Further Researches on the Aurore Boreales, and the Phe-
nomena which attend them. By M. A. DE La Rive*,
# Pte object which I have in view in this new investigation is
to show that the theory which I have advanced of the phe-
nomenon of aurore boreales is remarkably confirmed by observa-
tions made during the last few years,—especially by those of Mr.
Walker on the currents exhibited by telegraphic wires, notwith-
standing that this learned observer has deduced from them con-
clusions unfavourable to this theory.
I will in the first place call attention to two fundamental points
which have been confirmed by observation, and which may now
be regarded as definitively established in science.
The first of these points is the coincidence of the occurrence
of aurore boreales and aurore australes; it has been established
by numerous observations made in the two hemispheres, parti-
cularly at Hobart Town in the southern hemisphere, and at Chris-
tiania in the northern.
The second important point, likewise definitively established
in science, is that the phenomenon of aurora borealis and aus-
tralis is an atmospheric phenomenon. Father Secchi and several
other distinguished scientific men were of this opinion, which
had already been expressed by Arago, and the truth of which I
have endeavoured to demonstrate in my former researches, and
is confirmed by recent investigations.
* Extract, communicated by the Author, of a memoir read before la
Société de Physique et d’Histoire Naturelle de Genéve on the 6th of Fe-
bruary, 1862, ~~ m
and the Phenomena which attend them. 547
Not insisting here on the discussion and study of these inves-
tigations, from which it results that the aurora is an electro-
atmospheric phenomenon, [| will simply call attention to the fact
that it is satisfactorily accounted for by admitting, in conformity
with the data furnished by direct observation, that, the waters of
the ocean being continually charged with positive electricity, the
vapours which arise from them act as a conductor of this electri-
city as far as the upper strata of the atmosphere, where, carried
towards the polar regions by the trade-winds, they form as it
were a positive envelope to the earth, which itself remains charged
with negative electricity. But the earth and the highly rarefied
air of the elevated atmospheric regions being perfect conductors,
they may be regarded as forming the two conducting-plates of a
condenser, of which the insulating stratum is the inferior por-
tion of the atmosphere. The two antagonistic electricities must
then necessarily be condensed by their mutual influence in those
portions of the atmosphere and of the earth to which they are
the nearest, consequently in the regions near the poles, and there
neutralize themselves in the form of discharges more or less fre-
quent as soon as their tension reaches the limit which it cannot
‘exceed. These discharges should take place almost simulta-
neously at the two poles, since the earth being a perfect con-
ductor, the electric tension should be nearly the same at each;
there can only be differences in the intensity of the discharges
in one region and the other, and from one instant to another in
the same region, since the resistance of the stratum of air which
separates the two electricities must constantly vary from sundry
causes. It is evident, too, that the neutralization of the opposite
electricities would not be effected instantaneously, but, consider-
ing the low conducting-power of the medium through which it
takes place, by successive discharges more or less continuous and
variable in intensity.
These principles admitted, I endeavoured to produce artifi-
cially in all its details, and under all the attendant circumstances,
the phenomenon of the aurora. I have already published the
results which I obtained some time since respecting the influence
of strong electro-magnets on luminous electric discharges in
highly rarefied air—an influence which explains that of terrestrial
magnetism on the aurora, The magnetic and electric pheno-
mena which attend their appearance may likewise be produced
artificially. The first, as is well known, consist of an augmenta-
tion of westerly deflection, followed and occasionally preceded by
a much weaker and much less durable easterly deflection. The
second, the electric phenomena, manifest themselves by the pre-
sence of currents, frequently very intense, in the telegraphic
wires. Accurate observations made by Mr, Walker in England,
| 202
548 M. A. de la Rive on the Aurore Boreales,
and by Mr. Loomis in America, show that these currents vary
every moment during the appearance of an aurora, not only in
intensity, but also in direction, flowing sometimes from N. to
S., sometimes from S. to N. But bearing in mind that the
currents developed in the telegraphic wires are currents derived
from large sheets of metal implanted in moist earth, it will be
seen that, the plates bemg speedily polarized under the che-
mical action of the current passing through them, they must
develope im the wire which unites them an opposite current as
soon as that whence they derived their polarization ceases or
simply diminishes in intensity. In fact it has been universally
remarked that the light of aurorze exhibits a very variable inten-
sity and continual oscillations. Moreover, the discharges which
take place simultaneously at the two terrestrial poles, and which
constitute the aurorz boreales and australes, must, by the mflu-
ence of variable and local circumstances, be alternately stronger
at one pole than at the other, and even momentarily cease at one
pole whilst in action at the other.
The phenomenon occurs thus: the negative electricity with
which the earth is charged, arriving at a certain degree of tension,
discharges itself in the atmosphere of the polar regions, where it
meets the positive accumulated there by the trade-winds. There
result on the earth two currents directed from the poles to the
equator, the direction being that of the positive electricity ; there
is especially a current directed from the N. to the 8. in the
northern hemisphere. But if the discharge takes place at one
pole only, the south pole for instance, there 1s in the northern
hemisphere, instead of a current directed from the N. to the S.,
a current directed from the S. to the N., but weaker. It results
from this that the deflection of the magnetic needle, which under
the influence of the first current was west in the northern hemi-
sphere, in conformity with laws of electrodynamics, becomes
east; hence also the currents exhibited by the electric wires
are directed from the S. to the N. instead of from the N. to the
S. This cause, added to the secondary polarity which the plates
had acquired in transmitting the current directed from the N. to
the S., must produce a current almost as strong as the latter.
But in reality it is only rarely that the discharges cease at one
pole to take place exclusively at the other ; it is rather in differ-
ence of intensity that these variations manifest themselves: the
‘same results, however, ensue both as regards the magnetic needle
and the telegraphic wires, only they are less pronounced, and
accompanied by numerous oscillations.
I have succeeded in verifying by experiment all these results ;
I have especially convinced myself, by passing the discharge of a
Ruhmkorff apparatus, which has traversed highly rarefied air in
and the Phenomena which attend them. 549
order to produce the appearance of the aurora, through a slightly
saline solution, and by producing, by means of two copper plates
immersed in this solution, a derived current, that these plates
acquire secondary polarities which give rise to an inverse current
almost as strong as the derived, compensating by its duration
what it may lack in intensity. As regards the magnetic dis-
turbances, they are very easy to reproduce by suspending above
and very near a surface of mercury placed in the circuit of the
same discharge a sewing-needle, the lightest obtainable, very
strongly magnetized: the extent and direction of its deviations
show that it obeys all the variations of intensity and of direction
of the discharge.
The better to realize this reproduction of the natural pheno-
menon in its entirety and in detail, I have had an apparatus con-
structed composed of a wooden sphere of from 80 to 35 centime-
tres in diameter, which represents the earth. At each extremity of
one of the diameters of this sphere is fixed a cylinder of soft iron of
from 3 to 4 centimetres in diameter, and from 5 to6long. The
two cylinders repose each, in the portion nearest to the sphere,
on a rod of soft iron to which they are solidly united by strong
screws; the two rods being vertical, serve as a support to the
cylinders and to the sphere, which has thus a horizontal axis
terminated by two soft-iron cylinders, which may be magnetized
by placing the two vertical supports respectively on the two poles
of an electro-magnet, or by surrounding them with a coil tra-
versed by a strong current. An excellent representation is thus
obtained of the earth with the two magnetic poles.
The cylinders of soft iron covered with a non-conducting
coating, except at their extremity, are each surrounded with a
wide glass tube of which they occupy the axis, ending in the
middle of this axis. The tubes have a diameter of about 10
centimetres, and a length of about 15; they are hermetically
closed by two metailic disks, of which one is traversed by the
soft-iron cylinder, and the other bears, by means of two metal
branches covered with a non-conducting varnish, a ring, of
which the diameter is a trifle less than that of the tube, and of
which the centre coincides with the end of the soft-iron cylinder,
whilst its plane is perpendicular to the axis of the cylinder, and
consequently to that of the tube. The ring itself presents a
bright metallic surface, and its outer edge is about half a centi-
metre from the inner surface of the glass tube. Stopcocks
fastened to the disks which close the tubes externally, admit of
producing a vacuum, or of introducing at pleasure gases or
vapours in greater or smaller quantities.
When operating with this apparatus, two broad bands of
blotting-paper are placed on the wooden sphere, one of which
550 M. A. de la Rive on the Aurore Boreales,
entirely surrounds its equator, and the other, which crosses the
first, extends from one pole to the other in such a manner that
its extremities are respectively in contact with the iron cylinders.
On the last-mentioned band, small plates of copper, of from 1
to 2 centimetres square, are placed, on both sides of the equa-
torial band ; these are to be fixed on by small screws of the same
metal, which penetrate the wood of the sphere, and to be placed
equidistant from each other on the same meridian.
568
Suspension bridge, on the undulation
of an unstiffened roadway ima, 445,
Symbols, theorems in the calculus of,
| ‘aon.
Tait (Prof.) on the electricity deve-
loped durmg evaporation, 494.
Tangent-galyanometers, on the cor-
rection for the length of the needle
in, 345.
Tate (T.) on the laws of evaporation
and absorption, 126, 283.
Temperatures, on a new method of
measuring high, 537.
Thomson (Prof. J.) on regelation, 407.
(Prof. W.) on the possible age
of the sun’s heat, 158.
Tomlinson (C.) on the cohesion-
figures of liquids, 186.
Tungsten, on the specific heat of, 116.
Tyndall (J.) on recent researches on
radiant heat, 252; on the regela-
tion of snow-granules, 312.
INDEX.
Tyrite, on the composition of, 563.
Urine, on sugar in, 179.
Van Breda (Prof.) on Ampére’s expe-
riment on the repulsion of a recti-
' lmear electrical current on itself,
140, 365.
Vapours, on some apparatus for de-
termining the densities of, 337.
Vogt (Dr.C.)on the influence of traces
of foreign metals on the electric con-
ducting power of mercury, 171.
Wagite, on the composition of, 160.
Wanklyn (J. A.) on the electricity |
developed during evaporation, 494,
Waterston (J. J.) on solar radiation,
497.
Wood (Searles V.) on the form and
distribution of the land-tracts du-
ring the secondary and tertiary
periods, 161, 269, 382.
Wurtz (M.) on propylic alcohol, 474.
Zwenger (Dr.) on robinine, 476.
END OF THE TWENTY-THIRD VOLUME.
PRINTED BY TAYLOR AND FRANCIS,
RED LION COURT, FLEET STREET.
ALERE
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