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THE
LONDON, EDINBURGH, and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

CONDUCTED BY

SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & E. &c.
SIR ROBERT KANE, M.D., F.R.S., M.R.I.A.
WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S.
JOHN TYNDALL, F.R.S. &c.

" Nee aranearum sane textus ideo melior quia ex se fila gignunt, nee noster
vilior quia ex alienis libamus ut apes." Just. Lips. Polil. lib. i. cap. 1. Not.

VOL. XX.— FOURTH SERIES.
JULY— DECEMBER, 1860.

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.

*f Meditations est perscrutari occulta; contcmplationis est admirari

perspicua Admiratio geuerat quacstionem, quicstio investigationem,

investigatio inventionem." — Hugo de S. Victore.

— " Cur spirent venti, cur terra dehiscat,
Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Phoebus ferrugine condat,
Quid toties diros cogat tlagrare cometas ;
Quid pariat nubes, veniant cur fulmina ccelo,
Quo micet igne Iris, superos quis conciat orbes
Tarn vario motu."

J. B. Pinelli ad Mazonium.

CONTENTS OF VOL. XX,

(FOURTH SERIES.)

NUMBER CXXX.— JULY 1860.

Page

Prof. Kirchhoff on the Relation between the Radiating and

Absorbing Powers of different Bodies for Light and Heat . . 1
Mr. J. C. Maxwell's Illustrations of the Dynamical Theory of
Gases :—

Part it. On the Process of Diffusion of two or more kinds
Of moving particles among one another ............ 21

Part III. On the Collision of Perfectly Elastic Bodies of any

Form i i 33

The Rev. S. Earnshaw on a new Theoretical Determination of

the Velocity of Sound (continued) . . .......... 37

Dr. Atkinson's Chemical Notices from Foreign Journals . . . i 41
Mr. C. J. Burnett on several Forms of Actinometer. (With a

Plate.) iDiiuvMntttiiii 50

Notices respecting New Books : —

Mr. J. B. Smith's Arithmetic in Theory and Practice for

advanced Pupils. Part the First i n 61

Mr. J. R. Lunn : Of Motion. An Elementary Treatise . ■. 62
Dr. Boole's Treatise on the Calculus of Finite Differences. 62
Archdeacon Pratt's Treatise on Attractions, Laplace's
Functions, and the Figure of the Earth .......... , » 62

Proceedings of the Royal Society : —

Dr. Matthiessen on the Electric Conducting Power of Alloys. 63
Rear-Admiral FitzRoy on the Storms of October 25-26 and

November 1, 1859 ....;.*;.. 64

Dr. Hofmann on the Diatomic Ammonias i. 66

Mr. T. Hopkins on the Forces that produce the great Cur-
rents of the Air and of the Ocean i.inunt.it 74

Mr. J. P. Gassiot on the Interruption of the Voltaic Dis-
charge in vacuo by Magnetic Force ;....;;*;. ^4

Proceedings of the Royal Institution : —

Mr. W. Odling on Acids and Salts 78

Proceedings of the Geological Society:-—

Mr. J. Pilbrow on a Well- section at Bury Cross, near

Gosport 84

Mr. J. Prestwich on the presence of the London Clay in

Norfolk 84

Mr. T. R. Jones and W. K. Parker on some Foraminifera
from the Upper Triassic Clays of Chellaston, near Derby 85

IV CONTENTS OP VOL. XX. — FOURTH SERIES.

Page
The Rev. W. S. Symonds on the Physical Relations of the

Reptiliferous Sandstone near Elgin 85

Baron Anca de Mangalaviti on the Discovery of two Bone-
caves in Northern Sicily 86

Chemical Analysis of two Mineral Products formed by Subli-
mation in the Eruption of Vesuvius in 1858, by M. Cappa. . 87
On the Fluozirconates, and on the Formula of Zirconia, by
C. Marignac 87

NUMBER CXXXI.— AUGUST.

Professors Kirchhoff and Bunsen's Chemical Analysis by Spec-
trum-observations. (With a Plate.) 89

Messrs. A. H. Church and E. Owen on the Bases produced by
the Destructive Distillation of Peat 110

M. G. R. Dahlander on a New Species of Figures of Equili-
brium for Revolving Fluids, the particles of which attract
one another according to Newton's Theory 119

M. G. R. Dahlander on a Theorem relating to the Attraction
of the Ellipse 125

Mr. W. R. Grove on the Transmission of Electrolysis across
Glass 126

Prof. Breithaupt's Preliminary Notice on Thirteen Systems of
Crystallization in the Mineral Kingdom, and their Optical
Characters 129

Dr. Atkinson's Chemical Notices from Foreign Journals .... 139

Mr. B. Stewart : Note regarding Mr. Ponton's Paper " On cer-
tain Laws of Chromatic Dispersion " 143

Mr. J. Cockle's Sketch of a Theory of Transcendental Roots. 145

Proceedings of the Royal Society : —

Mr. G. Gore on the Movements of Liquid Metals and
Electrolytes in the Voltaic Circuit 149

Proceedings of the Geological Society : —

Mr. G. P. Wall on the Geology of part of Venezuela and of
Trinidad 164

On the Formation of Ice at the bottom of Water, by M. Engel-
hardt 166

On a remarkable Ice shower, by Captain Blakiston, R.A 168

NUMBER CXXXII.- SEPTEMBER.

Mr. B. Stewart on the Radiative Powers of Bodies with regard
to the Dark or Heat-producing Rays of the Spectrum 169

Prof. Swan's Note on Professors Kirchhoff and Bunsen's Paper
" On Chemical Analysis by Spectrum-observations." 173

M. C. Sainte-Claire Deville's Considerations in reference to M.
Rose's Memoir on the different conditions of Silicic Acid . . 175

CONTENTS OF VOL. XX.— FOURTH SERIES. V

Page
The Rev. S. Earnshaw on a new Theoretical Determination of

the Velocity of Sound 186

Mr. J. Spiller's Photographic Observations of the Solar Eclipse,

July 18, 1860 192

Archdeacon Pratt on the Thickness of the Crust of the Earth. 194
Dr. Atkinson's Chemical Notices from Foreign Journals. ...... 196

Mr. J. J. Sylvester on Poncelet's approximate linear Valuation

of Surd Forms 203

Proceedings of the Royal Society : —

Mr. J. P. Gassiot on Vacua as indicated by the Mercurial

Siphon-gauge and the Electrical Discharge 223

Dr. A. H. Hassallon the frequent occurrence of Phosphate

of Lime, in the crystalline form, in Human Urine .... 224
Dr. Harley on the Saccharine Function of the Liver .... 224
Drs. De la Rue and Miiller on the Resin of the Ficus

rubiginosa, and a new Homologue of Benzylic Alcohol. . 225
Mr. P. Griess on a new Method of Substitution ; and on
the formation of Iodobenzoic, Iodotoluylic, and Iodo-

anisic Acids 226

Mr. B. Stewart on an Instrument combining in one a

Maximum and Minimum Mercurial Thermometer .... 227
Messrs. Crace-Calvert and Lowe on the Expansion of

Metals and Alloys 230

Prof. W. Thomson on the Measurement of the Electro-
static Force produced by a Daniell's Battery 233

Proceedings of the Geological Society : —

M. E. Lartet on the co-existence of Man with certain

Extinct Quadrupeds 239

Mr. W. P. Jervis on certain Rocks of Miocene and Eocene

age in Tuscany 240

Dr. Falconer on the Ossiferous Caves of the Peninsula of

Gower in Glamorganshire 241

On the Periodicity of the Solar Spots, and induced Meteorolo-
gical Disturbances, by Robert P. Greg, Esq 246

On the Phenomena of Heat which in certain cases accompanies

the Vibratory Motion of Bodies, by M. Le Roux 247

On the Density of Ice, by M. L. Dufour 248

NUMBER CXXXIII.— OCTOBER.

Dr. Gladstone on the Electric Light of Mercury. (With a
Plate.) 249

Mr. M. Ponton's Further Researches regarding the Laws of
Chromatic Dispersion 253

Mr. T. Tate on a new Self-registering Mercury Barometer.
(With a Plate.) 263

Mr. R. P. Greg on the Periodicity of the Solar Spots 271

M. Regnault on the Elastic Force of Vapours 275

M CONtffiNTS OP VOL. XX. — FOURTH SERIES.

Page

Prof. Challis on a Theory of the Force of Electricity . ; . i 280

Dr. Atkinson's Chemical Notices from Foreign Journals .... 290
Mr. T. Tate on the Construction of a new Air-thermometer , . 298
Mr. D. Campbell on the presence of Arsenic and Antimony in

the sources and beds of Streams and Rivers 304

Mr. J. J. Sylvester: Meditation on the Idea of Poncelet's

Theorem. .' i 307

Proceedings of the Royal Society : —

Prof. W. Thomson on the Measurement of the Electro-
motive Force required to produce a Spark in Air between

parallel metal plates at different distances 316

On the difference in size of Medals of different Metals obtained
by Stamping, and by Casting in the same Mould, by Ht. W.

Dove 327

On Atmospheric Electricity, by M. Volpicelli 327

On a Magnetic Phenomenon, by M. Ruhmkorff 328

NUMBER CXXXIV.— NOVEMBER.

M. F. August on a new Species of Stereoscopic Phenomenon.

(With a Plate.) i ; . . . 329

Mr. A. Cayley on a Problem of Double Partitions 337

Mr. A. Cayley on a System of Algebraic Equations 341

M. R. Schneider on the Volumetric Determination of Antimony. 342
The Rev. It. Carmichael's Illustrations of Symmetrical Integra-
tion 348

Prof. Dove on the Dichrooscope. (With a Plate.) 352

Prof. W. Thomson's Notes on Atmospheric Electricity 360

Mr. T. Tate's Experimental Researches on the Laws of Ab-
sorption of Liquids by Porous Substances. (With a Plate.) 364

Mr. J. Cockle's Note on Transcendental Roots 369

MM. A. and F. Dupre : Spectrum-analysis of London Waters. 373
Dr. Atkinson's Chemical Notices from Foreign Journals .... 374
Proceedings of the Royal Society : —

Sir David Brewster and Dr. Gladstone on the Lines of

the Solar Spectrum * 385

Dr. Crace Calvert on some New Volatile Alkaloids given

off during Putrefaction 387

Prof. Matteucci on the Electrical Phenomena which accom-
pany Muscular Contraction 388

Dr. RadclifFe on the Muscular Movements resulting from

the action of a Galvanic Current upon Nerve * ; . 390

Proceedings of the Geological Society : —

M. E. Lartet on some Arrow-heads and other Instruments
found with Horns of Cervus megaceros in a Cavern in

Languedoc ...;.;..:. 400

Mr. T. F. Jamieson on the occurrence of Crag Shells
beneath the Boulder- clay in Aberdeenshire 401

CONTENTS OF VOL. XX. — FOURTH SERIES. Vll

Page
Prof. Owen on some small fossil Vertebra from near Frome,

Somersetshire 401

On the Law of the Propagation of Electricity in Imperfect Con-
ductors, by J. M. Gaugain 401

Wood's Fusible Metal 403

Description of an Apparatus for generating Hydrogen, Carbonic

Acid, and Sulphuretted Hydrogen, by G. Gore, Esq 405

On New Forms of Actinometers, by C. J. Burnett, Esq 406

On Arsenic in Coal, by Dr. R. A. Smith 4Q8

NUMBER CXXXV.— DECEMBER.

Mr. D. Vaughan on the Form of Satellites revolving at small

distances from their Primaries 409

Mr. A. Cayley on the Cubic Centres of a Line with respect to

Three Lines and a Line . 418

Mr. D. Forbes on Darwinite, a new Mineral Species from Chile. 423
M. G. R. Dahlander on the Form assumed by a Fluid Shell re-
volving freely within a Hollow Spheroid 426

Prof. Challis on a Theory of Galvanic Force 431

Dr. P. L. Rijke on the Inductive Spark 441

Mr. C. W. Merrifield on Approximation to the Integrals of Irra-
tional Functions by means of Rational Substitutions 446

M. H. Ste. -Claire Deville on the Decomposition of Bodies by
Heat, and on Dissociation. ........................... 448

Prof. W. Beetz on the Molecular Changes produced by Mag-
netization 458

Proceedings of the Royal Society : —

Major-General Sabine on the Solar-diurnal Variation of

the Magnetic Declination at Pekin . . , 469

Mr. T. Wharton Jones on the Focal Power of Eyes for

Horizontal and Vertical Rays 480

Proceedings of the Geological Society : —

The Rev. O. Fisher on the Denudation of Soft Strata . . 483
Dr. Dawson on an undescribed Fossil Fern from the Lower

Coal-measures of Nova Scotia 485

Mr. C. Rickman on the Sections of Strata exposed in the
Excavations for the South High-level Sewer at Dulwich. 486
On the Relation between the Direction of the Vibration of Light

and the Plane of Polarization, by Friedrich Eisenlohr 486

On the Specific and Latent Heat of Naphthaline, by M. Alluard. 488

NUMBER CXXXVI.— SUPPLEMENT.

Prof. Sylvester on the Pressure of Earth on Revetment Walls 489
Mr. T. Tate's Experimental Researches on the Laws of Absorp-
tion of Liquids by Porous Substances 500

Vlll CONTENTS OF VOL. XX. — FOURTH SERIES.

Pap

Prof. Magnus on the Conduction of Heat by Gases 510

Mr. A. Cayley on a Relation between two Ternary Cubic Forms. 512
Dr. Atkinson's Chemical Notices from Foreign Journals .... 515
M. Fessel on the Sensitiveness of the Human Ear to the Pitch of

Musical Notes 523

Prof. Sylvester's Notes to the Meditation onPoncelet's Theorem. 525
Notices respecting New Books : — Mr. E. J. Kouth's Elementary

Treatise on the Dynamics of a System of Rigid Bodies .... 533
Proceedings of the Royal Society : —

Mr. B. Stewart on the Light radiated by heated Bodies. . 534
Mr. J. P. Gassiot on the Luminous Discharge of Voltaic

Batteries, when examined in Carbonic Acid Vacua. . . . 540
Dr. T. Andrews and Mr. P. G. Tait on the Volumetric
Relations of Ozone, and the Action of the Electrical Dis-
charge on Oxygen and other Gases 549

Mr. J. P. Gassiot on the Application of Electrical Dis-
charges from the Induction Coil to the purposes of Illu-
mination 550

On the alleged practice of Arsenic-eating in Styria, by Dr. H.

E. Roscoe 550

On the Density of mixtures of Alcohol and Water, by M. von

Baumhauer 552

On the Thermal Effects of Fluids in Motion, by Dr. Joule and

Prof. W. Thomson 552

On the Temperature of Water in the Spheroidal State, by C.

Marignac 553

Index , 555

ERRATA.

Page 361, line 18 from bottom, a full point after the word electricity, dele
if, and put A for a.

— 362, line 13 from top, for cloudy read cloudless.

— 363, line 1 9 from bottom, for out a window read out of a window.

PLATES.
Frontispiece to the Volume — Portrait of Richard Taylor, F.L.S.

I. Illustrative of Mr. C. J. Burnett's Paper on several Forms of Actino-

metcr.

II. Illustrative of Professors Kirchhoff and Bunsen's Paper on Chemical

Analysis by Spectrum-observations.

III. Illustrative of Dr. J. II. Gladstone's Paper on the Electric Light of

Mercury, and Mr. T. Tate's Paper on a new Self-registering Mer-
cury Barometer.

IV. Illustrative of M. F. August's Paper on a new Species of Stereo-

scopic Phenomenon, Prof. Dove's Paper on the Dichrooscope,
and Mr. T. Tate's Paper on the Laws of Absorption of Liquids
by Porous Substances.

THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE,

[FOURTH SERIES.]

JULY 1860.

I. On the Relation between the Radiating and Absorbing Powers
of different Bodies for Light and Heat. By G. Kirch hoff*.

A BODY placed within a covering whose temperature is the
same as its own, is unaffected by radiation, and must
therefore absorb as many rays as it emits. Henee it has long
been concluded that, at the same temperature, the ratio between
the radiating and absorbing powers of all bodies is the same, —
it being, however, assumed that bodies only emit rays of one
kind. This law has been verified experimentally, especially by
MM. de la Provostaye and Desains, in many cases in which the
homogeneousness of the emitted rays could at least be so far
assumed, inasmuch as they were all invisible. Whether the same
law holds good when bodies emit rays of different kinds (which,
strictly speaking, is always the case), has never hitherto been de-
termined theoretically or by experiment. I have, however, now
found that the law in question extends to this case also, provided
that by the radiating power the intensity of one species of emitted
rays be understood, and that the absorbing power be estimated
with reference to rays of the same kind. Taken in this way, the
ratio of the radiating and absorbing powers of all bodies at the
same temperature is the same. I shall first give the theoretical
proof of this principle, and then develope certain remarkable
consequences that immediately follow therefrom, which partly
explain phenomena already known, and partly suggest new ones.
All bodies emit rays, the quality and intensity of which
depend on the nature and temperature of the bodies themselves.
In addition to these, however, there may, under certain circum-
stances, be rays of other kinds, — as, for example, when a body

* Translated bv Mr. F. Guthrie from Poggendorff's Annalen, vol. cix.
p. 275.

Phil. Mag. S. 4, Vol. 20. No. 130. July 1860. B

2 Prof. Kirchhoff on the Relation between the Radiating and

is sufficiently charged with electricity, or when it is phospho-
rescent or fluorescent. Such cases are, however, here excluded.

When a body encounters rays from without, it absorbs a por-
tion of them and converts it into heat. But, besides this species
of absorption, there may, under certain circumstances, be others,
as, for example, when a body is phosphorescent or fluorescent.
It is, however, here assumed that all absorbed rays are converted
into heat.

§ 1. Before the body C (fig. 1), imagine two screens, S„
S?, to be placed, containing openings 1 and 2, Yig. 1.

whose dimensions must be regarded as infi- s» * .

nitely small in comparison with their distance

apart, and each of which has a middle point.

Through these two openings a pencil proceeds

from the body C. Of this pencil let that part

be considered which consists of waves, the ~~Z^Z

length of which lies between X and X -f dk, and Qy

let this be divided into two component parts

polarized in the perpendicular planes a and b passing through

the axis of the pencil. Let the intensity of the part polarized in

a be Ec?\ : E is then the radiating power of the body.

Conversely, a pencil of rays polarized in plane a, and having
waves of the length X, falls on the body C through the openings
2 and 1. Of this, part is absorbed by the body, the rest being
partly reflected and partly transmitted. Let the ratio of the
absorbed to the incident rays be called A ; then A will represent
the power of absorption of the body.

The magnitudes E and A depend on the nature and tempera-
ture of C, on the position and form of the openings 1 and 2, on
the magnitude X, and on the position of the plane a. It will be
shown that the ratio of E to A is independent of the nature of
the body ; it will thence necessarily follow that it cannot be
affected by the position of the plane a, and its independence of
the position and form of the openings 1 and 2 will thence be
easily deduced, so that it only remains to be determined how far
it depends on the temperature of C and the wave-length X.

The proof I am about to give of the law above stated, rests on
the supposition that bodies can be imagined which, for infinitely
small thicknesses, completely absorb all incident rays, and neither
reflect nor transmit any. I shall call such bodies perfectly black,
or, more briefly, black bodies. It is necessary in the first place
to investigate the radiating power of bodies of this description.

§ 2. Let C be a black body. Let its radiating power (gene-
rally indicated by E) be called e. It will be shown that e
remains the same when C is replaced by any other black body of
the same temperature.

Fig. 2.

Absorbing Powers of different Bodies for Light and Heat. 3

Imagine the body C enclosed in a black covering, of which the
screen Sj forms a part. Let the second screen, S2, be black
also, and let the two be united all round by black walls (fig. 2).
Let the opening 2 be in the first place closed by
a black surface, which I shall call surface 2, and
let the whole system be kept at a constant tem-
perature by being completely enclosed in a co-
vering impermeable to heat, as, for example, in
a perfectly reflecting surface. Then, since the
temperature of the body C remains constant,
the intensity of the incident rays (which, ac-
cording to hypothesis, it entirely absorbs) must
be equal to that of the emitted rays. Now imagine surface 2
to be removed and replaced by a portion of a perfectly reflecting
spherical mirror having its centre in the middle point of open-
ing 1. The equilibrium of the temperature of the system will
be undisturbed, and the equality of the intensities of the emitted
and incident rays must therefore still subsist. As, however, the
body C emits the same rays as before, it follows that the inten-
sity of the rays that impinge on it must be the same in both
cases. By the removal of surface 2, those rays are withdrawn
from the body which proceeded from that surface through open-
ing 1. In the place of the rays so withdrawn, the mirror applied
at 2 reflects back on the body the rays which proceeded from it
through the openings 1 and 2*. Whence it may be concluded
that the intensity of the pencil which proceeds from the body
C through the openings 1 and 2, is equal to the intensity of the
pencil which at the same temperature proceeds from surface 2
through opening 1. But this is independent 'of the form and
constitution of the body C. The alleged law is therefore proved
when all the rays of the pencils compared have the same wave"
length X, and are polarized in the same plane a. llegard, how-
ever, to the possible diversity of these rays renders somewhat
more complex considerations necessary.

§ 3. In the arrangement represented in fig. 2,
imagine a small plate P (fig. 3) placed between
openings 1 and 2, which in the visible rays
displays the colours of thin plates, and which,
partly on account of its extreme thinness, and
partly on account of its material constitution,
neither absorbs nor emits any perceptible quan-
tity of rays. Let this plate be so placed that
it cuts the pencil passing between 1 and 2 at the

* The effect of the diffraction of the rays by the edges of opening 1 is
here neglected. This is allowable if openings 1 and 2, though infinitely
small in comparison with their distance apart, be considered as very great
in comparison with the length of a wave.

Fig. 3.

JP

1 3»
k

«, 1

O

4 Prof. Kirchhoff on the Relation between the Radiating and

angle of polarization, the plane of incidence being a. Let the wall
which unites S, and S2 be so situated that the image cast by plate
P of opening 2 lies in it ; and in the place and of the form of this
image imagine an opening, which I shall call opening 3. Let
opening 2 be closed by a black surface of the same temperature
as the rest of the system, and let opening 3 be closed, in the
first place by a similar surface (which I shall call surface 3), and
secondly, by a perfect concave mirror, having its centre in the
image which the plate P casts of opening 1. In both cases the
equilibrium of temperature remains undisturbed, and for reasons
similar to those mentioned in the last section ; it thence follows
that the sum of the intensity of the rays withdrawn from the
body by the removal of surface 3, is equal to the sum of the
intensities of the rays incident on the body in consequence of the
application of the mirror. Let a black screen S3, of the tempe-
rature of the rest of the system, be so placed that no rays ema-
nating from opening 3 can reach the body directly. The first
sum is then the intensity of the rays which proceed from sur-
face 3, are reflected by plate P, and pass through the opening 1 ;
let this be indicated by Q. The second sum consists of two
parts : one depending on the body C, which is

dXer*,

where r indicates a magnitude depending on the constitution of
plate P, and independent of \ ; the second part consisting of
rays which have proceeded from some portion of the black wall
uniting S! and S2, have penetrated plate P, and have been
reflected, first by the mirror, and then by P. This portion I
shall indicate by R. It is unnecessary further to determine the
value of R, it being sufficient to observe that R, like Q, is inde-
pendent of the nature of C. Between these magnitudes, then,
there subsists the following equation :

f

*/\er2 + R=Q.

If, now, the body C be replaced by some other black body of the
same temperature, e! indicating for this body what e does for the
other, then

{™d>Jr* + R=Q.

Whence

i

d\(e-e,)r* = Q.
Now let the index of refraction of plate P be supposed to be

Absorbing Powers of different Bodies for Light and Heat 5

infinitely near unity. From the theory of the colours of thin
plates, it follows that

r=p sm^;

where p indicates a magnitude proportional to the thickness of
the plate, and independent of \, and p a magnitude independent
of the thickness of the plate. The former equation then becomes

d\{e-e>)p*sm4£- = 0.

And since this equation holds good whatever be the thickness of
plate P, that is, whatever be the value of p, it may be deduced
that whatever X may be,

6-^ = 0.

In order to prove this, in the above equation for sin4^ substitute

itSValue i(cos4f-4co82f+3),

and differentiate twice with respect to p} we then have

\*ik —^ p2 (cos 4| - cos 2|) = 0.

o

Let - = a and (e-el)p<2=fa. Then

A

1 dot fa (cos 2/?a— cosjoa) =0.

And since when <f>a is any function of a,

I da (j>a cos 2pa = ^\ da$( ^J cos pa,

as will be seen if ^ be substituted for a, the above equation may
be written as follows:

\ dcV i — 2/«)cos^«=0.

Multiply this equation by dp cos xp, where x is any magnitude
whatever, and integrate from p = 0 to p = x . Then by Fourier's
formula, that

1

4» cos px I da$(a) cos pa = -^ </>\,

o */o

6 Prof. Kirchhoff on the Relation between the Radiating and

From which it follows, either th'at fa is nothing for every value
of a, or that it is infinitely great when a vanishes. But when a
vanishes, X becomes infinite. Recollecting then the meaning of
/a, and recollecting also that p is a proper fraction, and that
neither e nor e1 can become infinite when X increases without
limit, the second alternative cannot be admitted, and therefore
for every value of X we must have

e^e1.

§ 4. If the pencil which proceeds from the black body C
through the openings 1 and 2 consisted partly of rays polarized
in* a plane, the plane of polarization of the polarized portion must
rotate when the body itself rotates about the axis of the pencil.
Such a rotation must therefore affect the value of e. But since,
by the above equation, no such effect can be admitted, it follows
that no part of the pencil can be so polarized. It can also be
shown that no part of the pencil can be circularly polarized. "We
shall not give the proof of this here. Without this it will be
admitted that black bodies can be imagined so constituted that
there is no more reason why they should emit rays circularly
polarized in one direction more than the other. All the black
bodies hereafter mentioned are supposed to be of this kind, viz.
that they emit no polarized rays whatever.

§ 5. The magnitude indicated by e depends, not only on the
temperature and length of the wave, but also on the form and
relative position of the openings ] and 2. Let wx and w;2 be
the projections of these openings on the planes which cut the
pencil at right angles to its axis, and let s be the distance of the
openings apart ; then

e—i ,

where I is a function of the length of the wave and the tempe-
rature only.

§ 6. As the form of the body C is arbitrary, we may substi-
tute for it a surface which exactly fills the opening 1, and which
we shall call surface 1. The screen S, may then be imagined to
be removed. The screen S2 may also be removed, if the pencil
to which e relates be defined as that which proceeds from sur-
face 1 and is incident on surface 2, which exactly fills the
opening 2.

§ 7. A consequence that immediately follows from the equa-

Absorbing Powers of different Bodies for Light and Heat. 7

tion last obtained, and which will afterwards be made use of, is
that openings 1 and 2 may be interchanged.

§ 8. We shall now establish a law which may be regarded as
a generalization of that announced in the last section.

Between the two black surfaces 1 and 2 of equal temperature,
imagine a body placed which may refract, reflect, and absorb
the rays which pass between them in any way whatever. Several
pencils may reach surface 2 from surface 1 ; of these let one be
chosen, and let that part of it be taken when it leaves 1, which
consists of waves of length between X and X-\- d\ and let this be
divided into two component parts polarized at right angles to
each other in the planes ax and bv Let that part of the first
component which reaches 2 be itself divided into two parts,
whose planes of polarization are the perpendicular but otherwise
arbitrary planes «2, 62. Let the intensity of the part polarized
in #2 be KdX. Of the pencil which pursues the same path, but
in the opposite direction, viz. from 2 to 1, consider at 2 the part
which consists of the waves whose length lies between X and
X + dX, and let it again be divided into two parts polarized in
the planes aq and b2, and let the portion of the first component
part that reaches 1 be also divided into two components polarized
in ax and bv Let the intensity of the part polarized in ax be K'dX.
Then K=K'.

The truth of this proposition shall, in the first place, be esta-
blished on the hypothesis, first, that the rays suffer no diminu-
tion of intensity on their path, that is, that the refractions and
reflexions to which they may be subjected cause no loss, and
that there is no absorption; and secondly, that the rays that
proceed from 1 polarized in av impinge on 2 polarized in «2, and
conversely.

Through the middle point of 1 let a plane be placed perpen-
dicular to the axis of the incident and emerging pencil, and in
this plane let a system of rectangular coordinates be taken, of
which the middle point of 1 is the origin. Let xv yx be the coor-
dinates of some point in this plane (fig. 4). At the distance of
unity from this plane let another plane be taken pjg 4

parallel to the first, and containing a system of
coordinates parallel to the first system, having
its origin in the axis of the pencil. Let #3, y3
be the coordinates of a point in this plane. Simi-
larly, let a plane be taken passing through the
middle point of 2, perpendicular to the axis of
the incident and emerging pencil, and in this
plane let a system of rectangular coordinates be
taken having the middle point of 2 for its origin.
Let a?2, i/2 be the coordinates of a point in this

8 Prof. Kirchhoff on the Relation between the Radiating and

plane. Lastly, at the distance of unity from the last plane, and
parallel to it, let a fourth plane be taken, containing a system of
rectangular coordinates parallel to those in the third plane, and
having the axis of the pencil for its origin. Let x4) y4 be the co-
ordinates of any point in this plane.

From the point xxyx a ray is supposed to proceed to the point
xflq. Let the time it takes to pass from one point to the other
be called T. Then T is some function of xxyv #„y2, which we will
suppose to be known. If the points x3y3, x4y4 lie in the path of
the ray, and if for the sake of brevity the velocity of the ray in
vacuo be taken as unity, then the time required to pass from
x9y3 to x4y4 will be

=T- Vn-^-^ + y,-^2

- Vl+a?2-ff4V + y2-y4l8-
If the points x^y^ x4y4 were given, and the points xxylt x2y2
were required, they might be found from the condition that the
above expression is a minimum. Supposing, therefore, that the
eight coordinates, xv yv x2, y2, x3, y3, x4, y4i are very small, the
condition that the four points of which they are the coordinates
shall all lie in the path of the same ray is expressed by the fol-

ing equations

: —

ST

ST

x3=

=*r

ST

#4 =

= X<2-

"&Z-2

ST

^3=

syr

"V

&•■

= 2/2"

~w*

Now let xxyx be a point in the projection of surface 1 on the
plane xxyu and let dxx dyx be the element of this projection which
contains the point xxyXi and which must be considered as infi-
nitely small as compared with the surfaces 1 and 2. Let x3y3
be a point in a ray which proceeds from 1 to 2, dx3dy3 the su-
perficial element containing the point x3y3> and of the same order
of magnitude as dxx dyx. The intensity of the rays whose waves
are of the length already mentioned, and which are polarized in
the given plane, and proceed from xxyx through #3yg, is then,
according to § 5,

d\\ dxx dy} dx3 dy3.

Now according to the hypothesis we have assumed, the pencil
arrives at 2 with its intensity undiminished, and forms an ele-
ment of the magnitude indicated by Kd\. Whence for K we
must have the integral

taken between the proper limits.

The integration according to x3 and y3 must be between the

3 /

-M

Absorbing Powers of different Bodies for Light and Heat. 9

values which those magnitudes have according to the equations
above obtained, while xx and yl are constant, and #2?/2 have all
the different values which answer to the different points of the
projection of surface 2 on the plane #2y2 ; the integrals accord-
ing to xxyx must then be taken over the projection of surface 1.
The double integral,

§§dx3dy3,

so limited is

mCttgk

or applying the equations for x3 and y3,

32T 3*T S*T a*T \

$xx $x* ' 9jf , fy2 &r, %, ' fy2 Ss, / 2 ^'

where the integrals are to be taken over the projection of sur-
face 2. Whence

where the integrals are to be taken over the projections of sur-
faces 1 and 2.

If the magnitude K' be treated in the same way, it being remem-
bered that a ray takes the same time to pass between two points
down the same path in either direction, the same expression will
be found for K' as for K. The proposition to be proved is thus
demonstrated, subject to the limitation already mentioned. This
limitation may, however, be got rid of by means of an observa-
tion made by Helmholtz in his f Physical Optics/ p. 169. Helm-
holtz here says (with somewhat different notation), " A ray of
light proceeding from point 1 arrives at point 2 after suffering
any number of refractions, reflexions, &c. At point 1 let any
two perpendicular planes alt 6, be taken in the direction of the
ray ; and let the vibrations of the ray be divided into two parts,
one in each of these planes. Take similar planes a2, \ in the
ray at point 2 ; then the following proposition may be demon-
strated. If when the quantity i of light polarized in the plane
ax proceeds from 1 in the direction of the given ray, the part k
thereof of light polarized in «2 arrives at 2, then, conversely,
if the quantity i of light polarized in «2 proceeds from 2, the
same quantity k of light polarized in a2 will arrive at 1*."

* This proposition of Helmholtz ceases to hold good, as he himself
observes, when the plane of polarization of the ray suffers any alteration
such as that produced by magnetism, according to Faraday's discovery. In
what follows, therefore, the effect of magnetic force must be excluded.
Helmholtz limits his proposition also by the supposition that light suffers

10 Prof. Kirchhoff on the Relation between the Radiating and

k
Applying this proposition, and representing by 7 the ratio -,

in whichever direction the ray passes between the points xlyl
and xqyv an expression is obtained for K and K' which only
differs from that above obtained by the occurrence of 7 as a
factor under the integral sign.

The equality of K and K' therefore still subsists, even when 7
has different values in the rays into which any one of the com-
pared pencils may be considered as divided ; it is, for example,
unaffected if any part of the pencil be intercepted by a screen.

§ 9. The following proposition may also be proved of the
same pencils as were compared in the last section. Of the
pencil which proceeds from 1 to 2, consider at 2 that part which
consists of waves whose length lies between \ and XdX, and let
it be divided into two components polarized in «2 and bT Let
the intensity of the first of these components be E.d\. Of the
pencil that proceeds from 2 to 1, consider at 2 the part consist-
ing of waves whose length lies between \ and \ + d\, and divide
this into two parts polarized in a2 and £2. Let the intensity of
that portion of the first part which arrives at 1 be R'd\. Then
must

H = H'.

The proof of this proposition is as follows : — Let K and K/
have the same meaning as in the previous section, L and L'
being the magnitudes that K and K' become when planes a} and
£, are interchanged. Then L=L', just as K=K', and also

H = K + L;

for rays polarized perpendicularly to each other, provided they
are parts of a non-polarized ray, do not interfere when they are
brought back to a common plane of polarization ; and, according
to § 4, surface 1 emits none but non-polarized rays.
Lastly, we must have

H'=K' + L',

because two rays, whose planes of polarization are perpendicular,
do not interfere. From these equations it follows that H = H7.

§ 10. Let fig. 2 have the same meaning as in § 3 ; only let the
body C be no longer black, but a body of any kind. Let open-
ing 2 be closed by surface 2 ; then a pencil proceeding from this
surface through opening 1 reaches C, and is there partly absorbed
and partly dispersed in various directions by reflexion and refrac-
tion. Of this pencil between 1 and 2 let that part be considered

no change of refrangibility such as occurs in fluorescence ; this limitation,
however, ceases to be necessary if, in the application of the proposition,
only rays of a given length of wave are regarded.

Absorbing Powers of different Bodies for Light and Heat. 1 1

which consists of waves whose length lies between X and X + d\t
and let it be divided into two components polarized in a and its
perpendicular. Let that part of the first component which is
not absorbed by C, and which therefore reaches the black cover-
ing in which the body C is enclosed, be M!d\. Of the rays that
proceed from the covering and are incident on C, a certain por-
tion reach surface 2 through opening 1. The body C thus ori-
ginates a pencil of rays which is incident on surface 2 through
opening 1 . Of this pencil consider that part which consists of
waves whose length lies between X and \ + d\, and let this be
divided into two parts polarized in plane a and its perpendicular.
Let the intensity of the first component be M.d\, Then is

M = M'.

This follows from the proposition established in the last sec-
tion, by applying that proposition to all the pencils which sur-
face 2 and all the elements of the black covering exchange with
each other through the medium of the body C, and then sum-
ming the equations so obtained.

§ 11. Let the arrangement represented in fig. 3, and described
in § 3, be again taken, C, however, being no longer a black body,
but one of any kind. In both the cases described in that section
the equilibrium of temperature must still subsist, and therefore
the vis viva that is withdrawn from the body by the removal of the
surface 3, will be equal to the vis viva it receives by the applica-
tion of the concave mirror. Let the letters used in § 3 have the
same meaning as in that section, and let E and A have the sig-
nification given them in § 1. Then the vis viva withdrawn from
the body C by the removal of surface 3 is, according to § 7,

roo
d\erA.

■I

The vis viva which the body receives by means of the concave
mirror consists of three parts : — The first due to the rays emitted
by C itself; this is

1

= 1 d\Er2A.

The second due to the rays which, having proceeded from the
part of the black covering opposite the mirror, have passed
through the plate P, and have been reflected, first by the mirror,
and then again by P. This, according to § 9, is

= 1 d\er{l-?')A.

The third and last part is due to the rays which have fallen on C

12 Prof. Kirckhoff on the Relation between the Radiating and

from various parts of the black covering, have been thence re-
flected or refracted through opening 1 towards surface 2, have
been reflected by the plate P, and again by the mirror at 3, and,
lastly, again reflected by P through opening 1. If M then have
the meaning given it in § 10, this last part

4

d\Mr*A.

It may appear doubtful whether the above expressions for the
first and third of these portions are correct when C is in such a
position that a finite portion of the pencil proceeding from 2
through opening 1, and incident on C, is by C reflected back
towards 2. Such cases are therefore for the present excluded.

According to § 10, M = M', and by definition M'=<?(1— A).
The third part is therefore

= r°d\*(l-A)r2A,
whence we have the equation

rf\(E-Ae)Ar2=0.

I

And from considerations identical with those mentioned in § 3
with reference to a similar equation, the conclusion may be drawn,
that for every value of \

E

A = e;
or, putting for e its value as obtained in § 5,

The proposition we undertook to prove is therefore established,
subject to the condition that no finite part of the pencil that
proceeds from surface 2 through opening 1, and is incident on
the body C, is reflected back by C to surface 2. That the pro-
position is true without this limitation, is obvious when we
consider that, if the condition in question be not fulfilled, it is
only necessary that the body C should be turned through an
infinitely small angle in order to satisfy it, and that such a change
of position can only cause an infinitely small change in the values
of A and E.

The magnitude indicated by I is, as remarked in § 5, a func-
tion of the temperature and the wave-length. The determina-
tion of this function is a problem of the highest importance ;
and though difficulties stand in the way of our effecting this
by experiment, there is nevertheless a well-grounded hope of

Absorbing Powers of different Bodies for Light and Heat, 13

ultimate success, since the form of the function in question is no
doubt simple, as is the case with all functions hitherto discovered
that do not depend on the properties of individual bodies.
Whenever this problem is solved, the full fertility of the law
above demonstrated will be apparent ; even at present, however,
important consequences may be deduced from it.

§ 12. If a body (a platinum wire, for example) be gradually
heated up to a certain temperature, it only emits rays consisting
of waves longer than those of the visible rays. Beyond that
point, waves of the length of the extreme red begin to appear ;
and as the temperature rises, shorter and shorter waves are added ;
so that, for every temperature, rays of a corresponding length of
wave are originated, while the intensity of the rays of greater
wave-length is increased. If the law we have established be
applied to this case, it will be seen that the function I, for waves
of any given length, must vanish for all temperatures below that
answering to the wave-length in question, and that, for tempera-
tures above this, it must increase with the temperature.

Whence, applying the same proposition to other bodies, it
follows that all bodies, when their temperature is gradually
raised, begin to emit waves of the same length at the same
temperature, and therefore become red-hot at the same tempera-
ture, emit yellow rays at the same temperature, &c* The
intensity of rays consisting of waves of a given length, which
different bodies emit at the same temperature, may, however, be
very different, since it is proportional to the power of absorption
of the body for waves of that particular length. At the same
temperature, accordingly, metal glows more brightly than glass,
and glass more brightly than a gas. A body that remains per-
fectly transparent at the highest temperature never becomes red-
hot. In a platinum ring of about 5 millims. diameter, I placed a
small portion of phosphate of soda, and heated it in the dull
flame of Bunsen's lamp. The salt melted, formed a fluid lens,
and remained perfectly transparent ; it, however, emitted no light,
while the platinum ring, with which it was in contact, glowed
brilliantly.

§ 13. For the same temperatnre the magnitude I is a con-
tinuous function of the wave-length, except for such values of the
latter as render I evanescent. The truth of this assertion may
be concluded from the continuity of the spectrum of a red-hot
platinum-wire, provided it be admitted that the power of absorp-
tion of such a body is a continuous function of the length of the
waves of the incident rays. It may also be affirmed, with the
highest degree of probability, that while the temperature remains

* Draper, Phil. Mag. vol. xxx. p. 345; Berl. Ber. 1847.

14 Prof. Kirchhoff on the Relation between the Radiating and

constant the function I can have no strongly marked maxima
and minima for waves of different lengths. Hence it follows that
if the spectrum of a red-hot body presents discontinuities or
strongly marked maxima or minima, the power of absorption of
that body, regarded as a function of the length of the waves, must
present similar discontinuities or strongly marked maxima and
minima. Spectra with strongly marked maxima may be ob-
tained by placing various salts in the flame of a Bunsen's lamp.
Chloride of lithium affords interesting results in this respect. If
a bead of this salt be melted in a platinum ring and placed in the
mantle of the gas-flame, the spectrum of the flame (when
unaffected by the presence of other salts and not too brilliant) is
a single bright red line of light, formed of waves whose length is
about the arithmetic mean of the lengths of the waves corre-
sponding to the lines B and C of Fraunhofer. For waves of this
length the radiating power of the flame is very considerable,
while for waves of lengths corresponding to the other visible
colours it is imperceptible. Accordingly, the power of absorption
of the lithium-flame must be great for waves of this length, but
very small for those constituting the other visible rays. If, there-
fore, a continuous spectrum be formed by suitable means and a
lithium-flame be placed between the source of light and the slit
of the apparatus, the spectrum is only affected in the place of
the lithium line, its brightness being increased in that part by
the radiation of the flame, while on the other hand it is diminished
by its power of absorption for waves of that particular length.
Suppose the absorptive power to be J. This would be the case,
according to the law we have demonstrated, if the brightness of
the line which constitutes the spectrum of the lithium-flame
were Jth of that of the corresponding line of the spectrum pro-
duced by a black body of the same temperature. The lithium-
flame would then be without effect on the spectrum produced
by any other source of light, provided the intensity of its
own spectrum were Jth of that of the corresponding line of the
spectrum produced in its absence. If the source of light were
proportionately brighter than this, the joint effect of it and the
lithium-flame would be to produce a comparatively dull line on
a bright ground ; and conversely, if the source of light were pro-
portionately duller, a bright line on a dull ground would become
visible. In the first case the apparent dullness of the line would
be greater in proportion to the brightness of the radiating body
behind the lithium-flame ; for in proportion as the light of the
former was increased, so would that of the latter become less
observable. For the particular value of the absorptive power
mentioned, the brightness of the lithium line can, however, never
be less than f ths of that of the surrounding parts of the spectrum.

Absorbing Powers of different Bodies for Light and Heat. 15

But this limit may be decreased by increasing the thickness of
the lithium-flame, and its consequent absorptive power.

A small bead of chloride of lithium, placed in the flame of a
Bunsen's lamp, imparts to the latter so considerable an absorptive
power for waves of the particular length mentioned, that if the
rays of the sun be suffered to fall on the slit of the apparatus
that forms the spectrum through such a flame, the corresponding
part of the spectrum appears like a fine black line.

The spectra produced when other salts are placed in the flame
are for the most part less simple than the lithium spectrum,
and seldom exhibit such brilliant lines. All of them, however,
are capable of being reversed by similar means. If flames of
sufficient thickness be employed and light of suitable intensity
be passed through them, the bright lines of the spectra may all
be converted into lines of shade. The only exception would be
in the case of a flame the light of which was partly produced by
some immediate chemical action, or in case of a fluorescent flame.
Experiment must decide whether such flames exist.

If the source of light employed is an incandescent body, the
intensity of the light it emits depends on its temperature, — the
intensity, for the same temperature, being greatest when the body
is perfectly black. If this condition be fulfilled in the case of
two sources of light, and if their temperature be the same, the
spectrum of the one will be unaffected by the interposition of the
other. The more remote source of light can therefore only
reverse the spectrum of the other when it possesses a higher
temperature, and the reversed spectrum will be more distinct the
greater the excess of the temperature of the former source of light
over that of the latter.

Besides the spectrum of the lithium-flame, I have succeeded in
' reversing that of the common salt-flame. This spectrum consists,
as is well known, of two very brilliant yellow lines close together,
the wave-length of which corresponds to Fraunhofer's double
line D. If the rays of a Drummond light be passed through a
salt-flame of not too high a temperature, the bright lines of the
salt-spectrum become dark, and occupy the place of Fraunhofer's
lines D, presenting in every respect the same appearance as those
lines*.

§ 14. The wave-lengths which correspond to maxima of the
radiating and absorbing powers are, as will be fully explained in
another place, altogether independent of the temperature ; and

* More. recently Prof. Bunsen and I have likewise reversed the brighter
lines of the spectra of potassium, calcium, strontium, and barium, by explo-
ding before the slit of the spectral instrument mixtures of milk-sugar and
chlorates of the respective metals during the passage of the sun's ravs. —
May 9, 1860.

16 Prof. Kirchhoff on the Relation between the Radiating and

moreover, in the case of salts which produce flames having such
maxima, it is the metal that determines the nature of the spectrum.
Imagine a body of very high temperature, in whose spectrum the
double line D does not appear, surrounded by a gaseous atmo-
sphere of somewhat lower temperature. If sodium be present in
the latter, the spectrum of the whole system so constituted will
contain the double line D . From the occurrence of these lines, the
presence of sodium in the atmosphere may therefore be concluded.
Now the sun is undoubtedly a body of this description*; and
therefore, from the occurrence of the lines D in the solar spectrum,
the presence of sodium in the sun's atmosphere may be concluded.
An objection may perhaps be urged against the justice of this
conclusion. " The cause of the line D is," it may be said, " to
be sought for in the atmosphere of the earth." This objection
may, however, be disposed of on the following grounds : —

(1) The necessary quantity of sodium in the gaseous form
can hardly be present in our atmosphere, and the gaseous form
is necessary to produce the effect in question.

(2) If the line D depended on our atmosphere, it would
become more strongly marked when the sun approached the
horizon. I have, however, never observed any such change in
the distinctness of these lines, though in the case of some of the
neighbouring lines, such changes are very conspicuous.

(3) If the line D were not caused by the physical constitu-
tion of the sun itself, it would exist in the spectra of all the
fixed stars of sufficient brightness ; but according to Fraunhofer
and Brewster, it is wanting in the spectra of some of the fixed
stars though present in others.

The precise coincidence of the sodium lines with the D lines of
Fraunhofer may be most satisfactorily proved by suffering the
sun's rays to fall on the slit of the apparatus through a sodium-
flame. The effect of the flame is exhibited in the increased
distinctness, darkness, and breadth of the lines D. At the first
glance it may appear somewhat strange that the sodium in a
small flame should perceptibly increase the effect of the sodium
present in the immense mass of the sun's atmosphere. Our
surprise at this will, however, be diminished when we consider
that the brightness of the lines D of the solar spectrum is deter-
mined by the temperature of the solar atmosphere, and especially
of its outer portion, and that the temperature of this is certainly
much greater than that of a gas-lamp. If a sodium-flame be
imagined whose thickness may be regarded as infinite with
respect to its power of absorbing the rays that correspond to the

* Whether the central mass of the sun, from which the light principally
proceeds, is solid, liquid, or gaseous, may, as far as we are here concerned,
be regarded as an open question.

Absorbing Powers of different Bodies for Light and Heat. 1 7

lines D, and if rays from some other source of light be supposed
to pass through this flame, and then to be separated into a
spectrum, the brightness of the part of the spectrum corre-
sponding to the lines D depends on the radiation of the flame
alone. If, then, another sodium-flame of the same temperature
be interposed, the spectrum remains unaltered ; but if the flame
interposed be of lower temperature, the lines must become duller.
The effect on the solar spectrum of a gas-flame containing sodium
is in this way accounted for, if it be admitted that the tempera-
ture of such a flame is lower than that of the outermost envelope
of the sun's atmosphere ; and this must certainly be the case,
since the external portion of the sun's atmosphere cannot have
a lower temperature than that of the focus of a powerful concave
mirror directed towards the sun.

What has been stated concerning sodium is equally true of
every other substance which, when placed in a flame of any sort,
produces bright lines in its spectrum. If these lines coincide
with the dark lines of the solar spectrum, the presence in the
sun's atmosphere of the substances which produce them must
be concluded, provided always that the lines in question cannot
have their origin in the atmosphere of the earth. In this way
means are afforded of determining the chemical constitution of the
sun's atmosphere; and the same method even promises some
information concerning the constitution of the brighter fixed
stars*.

§ 15. From the proposition demonstrated in the first part of
this essay, it follows that a body that absorbs more rays polarized
in one plane than in another, must emit proportionately more
rays of the first description than of the latter. Whence, as is
known to be the case, a red-hot opake body with a smooth
surface must emit rays in directions oblique to this surface partly
polarized perpendicularly to the plane passing through the ray
and normal to the surface ; for of the incident rays polarized
perpendicularly to the plane of incidence, the body reflects less
and absorbs more than of the rays whose plane of polarization
is the plane of incidence. By means of this principle the state
of polarization of the emitted rays can easily be determined when
the law of reflexion of the incident rays is known.

A tourmaline plate split perpendicularly to its optic axis
absorbs at ordinary temperatures more of the perpendicularly

* In two communications laid before the Berlin Academy of Sciences
on the 27th of October and the 15th of December, 1859, some statements
are to be found concerning the physical constitution of the sun's atmo-
sphere which are not introduced here. In the second of those communica-
tions also the proposition that forms the principal subject of this essay is
proved in another way, but with less generality.

Phil Mag. S. 4. Vol. 20. No. 130. July 1860. C

18 Prof. Kirchhoff on the Relation between the Radiating and

incident rays whose plane of polarization is parallel to the axis
of the plat i', than of those whose plane of polarization is per-
pendicular to that axis. If it be granted that the tourmaline
retains this property when red-hot, then rays emitted in a direc-
tion perpendicular to its surface must be partly polarized in a
plane passing through the optic axis, and therefore perpen-
dicular to what is called the plane of polarization of the tourma-
line. I have experimentally tested this striking deduction from
the law here demonstrated, and have confirmed its truth. The
tourmaline plates employed bore a considerable heat in a Bunsen's
lamp for some time without suffering any permanent alteration,
except that they appeared on cooling to have become a little
cloudy at the edges. They retained the property of transmitting
polarized light even when red-hot, though to a considerably less
degree than at a lower temperature. This appeared on observing
through a doubly-refracting prism, a red-hot platinum wire
placed behind a tourmaline plate. The two images of the wire
so produced were of unequal intensity, though the difference
between them was much less than when observed through a plate
of the ordinary temperature. To the doubly-refracting prism
was then given that position in which the difference of the
intensities of the two images was a maximum ; if now it was the
upper image of the wire that was the brightest, then on removing
the wire and observing the plate alone, it was found that the
upper image of the plate was unmistakeably though not strikingly
duller than the other. The two images appeared exactly like
two equal red-hot bodies, of which the upper possessed a lower
temperature than the other.

§ 16. Place must be found for one more deduction from the law
here established. If a space be entirely surrounded by bodies
of the same temperature, so that no rays can penetrate through
them, every pencil in the interior of the space must be so
constituted, in regard to its quality and intensity, as if it had
proceeded from a perfectly black body of the same temperature,
and must therefore be independent of the form and nature of the
bodies, being determined by the temperature alone The truth
of this is obvious when we reflect that a pencil having the same
position but the opposite direction to that chosen, is completely
absorbed by the successive reflexions it undergoes from body to
body. In the interior therefore of an opake red-hot body of
any temperature, the illumination is always the same, whatever
be the constitution of the body in other respects.

It may be observed, by the way, that the proposition demon-
strated in this section does not cease to hold good even if some
of the bodies are fluorescent. A fluorescent body may be defined
as one whose radiating power depends on the rays incident on it

Absorbing Powers of different Bodies for Light and Heat. 19

E

for the time being. The equation -r=e cannot generally be

true of such a body ; but it is true if the body is enclosed in a
black covering of the same temperature as itself, since the same
considerations that led to the equation in question on the hypo-
thesis that the body C was not fluorescent, avail in this case even
if the body C be supposed to be fluorescent. To be convinced
of this, it is only necessary to consider that if the magnitude E
could have two different values in the two arrangements of the
system represented in fig. 3, the difference of these values could
only be an infinitely small quantity.
Heidelberg, January 1860.

Postscript*.

1 . Since the appearance of the above paper in PoggendorfFs
Annalen, I have received information of a prior communication
closely related to mine. The communication in question is by
Mr. Balfour Stewart, and appeared in the Transactions of the
Royal Society of Edinburgh, vol. xxii. 1858. Mr. Stewart has
made the interesting observation that a plate of rock-salt is
much less diathermic for rays emitted by a mass of the same
substance heated to 100° C, than for rays emitted by any other
black body of the same temperature. From this circumstance
he draws certain conclusions, and is led to a result similar to
that which I have established concerning the connexion between
the powers of absorption and emission. The principle enun-
ciated by Mr. Stewart is, however, less distinctly expressed, less
general, and not altogether so strictly proved as mine. It is as
follows : — " The absorption of a plate equals its radiation, and
that for every description of heat."

2. The fact that the bright lines of the spectra of sodium- and
lithium-flames may be reversed, was first published by me in a
communication to the Berlin Academy, October 27, 1859. This
communication is noticed by M. Verdet in the February Number
of the Ann. de Chim. et de Phys. of the following year, and is
translated by Prof. Stokes in the March Number of the Philo-
sophical Magazine. The latter gentleman calls attention to a
similar observation made by M. Leon Foucault eleven years ago,
and which was unknown to me, as it seems to have been to
most physicists. This observation was to the effect that the
electric arch between charcoal points behaves, with respect to the
emission and absorption of rays of refrangibility answering to
Fraunhofer's line D, precisely as the sodium-flame does accord-
ing to my experiments. The communication made on this sub-

* Communicated by the Author.
C2

20 On the Radiating and Absorbing Powers of different Bodies.

iect by M. Foucault to the Soc. Philom. in 1849 is reproduced
oy M. Verdet, from the Journal de Vlnstitut, in the April Num-
ber of the Ann. de Chim. et de Phys.

M. Foucault* s observation appears to be regarded as essentially
the same as mine ; and for this reason I take the liberty of draw-
ing attention to the difference between the two. The observa-
tion of M. Foucault relates to the electric arch between charcoal
points, a phenomenon attended by circumstances which are in
many respects extremely enigmatical. My observation relates
to ordinary flames into which vapours of certain chemical sub-
stances have been introduced. By the aid of my observation,
the other may be accounted for on the ground of the presence of
sodium in the charcoal, and indeed might even have been fore-
seen. M. Foucault' s observation does not afford any explana-
tion of mine, and could not have led to its anticipation. My
observation leads necessarily to the law which I have announced
with reference to the relation between the powers of absorption
and emission; it explains the existence of Fraunhofer's lines,
and leads the way to the chemical analysis of the atmosphere of
the sun and the fixed stars. All this M. Foucault* s observation
did not and could not accomplish, since it related to a too com-
plicated phenomenon, and since there was no means of deter-
mining how much of the result was due to electricity, and how
much to the presence of sodium. If I had been earlier acquainted
with this observation, I should not have neglected to introduce
some notice of it into my communication, but I should never-
theless have considered myself justified in representing my ob-
servation as essentially new.

3. Since the above communication was printed in Poggen-
dorfFs Annalen, I have learned in the course of a written corre-
spondence with Professor Thomson, that the idea was some years
ago thrown out, if not published, that it might be possible, by
comparing the spectra of various chemical flames with that of the
sun and fixed stars, in the manner I have described, to become
acquainted with the chemical constitution of the latter bodies
(an idea now demonstrated to be correct by the observations
and theoretical considerations above set forth). Prof. Thomson
writes : —

" Professor Stokes mentioned to me at Cambridge some time
ago, probably about ten years, that Professor Miller had made
an experiment testing to a very high degree of accuracy the
agreement of the double dark line D of the solar spectrum with
the double bright line constituting the spectrum of the spirit-
lamp burning with salt. I remarked that there must be some
physical connexion between two agencies presenting so marked
a characteristic in common. He assented, and said he believed

On the Diffusion of Moving Particles among one another. 21

a mechanical explanation of the cause was to be had on some
such principles as the following : — Vapour of sodium must pos-
sess by its molecular structure a tendency to vibrate in the
periods corresponding to the degrees of refrangibility of the double
line D. Hence the presence of sodium in a source of light must
tend to originate light of that quality. On the other hand,
vapour of sodium in an atmosphere round a source, must have a
great tendency to retain in itself, i. e. to absorb and to have its
temperature raised by light from the source, of the precise qua-
lity in question. In the atmosphere around the sun, therefore,
there must be present vapour of sodium, which, according to the
mechanical explanation thus suggested, being particularly opake
for light of that quality, prevents such of it as is emitted from
the sun from penetrating to any considerable distance through
the surrounding atmosphere. The test of this theory must be
had in ascertaining whether or not vapour of sodium has the
special absorbing power anticipated. I have the impression that
some Frenchman did make this out by experiment, but I can
find no reference on the point.

" I am not sure whether Professor Stokes's suggestion of a me-
chanical theory has ever appeared in print. I have given it in
my lectures regularly for many years, always pointing out along
with it that solar and stellar chemistry were to be studied by
investigating terrestrial substances giving bright lines in the
spectra of artificial flames corresponding to the dark lines of the
solar and stellar spectra."

II. Illustrations of the Dynamical Theory of Gases. By J. C.
Maxwell, M.^., Professor of Natural Philosophy inMarischal
College and University of Aberdeen.

[Concluded from vol. xix. p, 32.]

Part II. On the Process of Diffusion of two or more kinds of
moving particles among one another.

WE have shown, in the first part of this paper, that the
motions of a system of many small elastic particles are
of two kinds : one, a general motion of translation of the whole
system, which may be called the motion in mass ; and the other
a motion of agitation, or molecular motion, in virtue of which
velocities in all directions are distributed among the particles
according to a certain law. In the cases we are considering, the
collisions are so frequent that the law of distribution of the mole-
cular velocities, if disturbed in any way, will be re-established in
an inappreciably short time; so that the motion will always con-

Prof. Maxwell on the Process of Diffusion of two or

mm of this definite motion of agitation, combined with the general
motion of translation.

When two gases are in communication, streams of the two
gases might run freely in opposite directions, if it were not for
the collisions which take place between the particles. The rate
at which they actually interpenetrate each other must be investi-
gated. The diffusion is due partly to the spreading of the par-
ticles by the molecular agitation, and partly to the actual motion
of the two opposite currents in mass, produced by the pressure
behind, and resisted by the collisions of the opposite stream.
When the densities are equal, the diffusions due to these two
causes respectively are as 2 to 3.

Prop. XIV. In a system of particles whose density, velocity,
fyc. are functions of x, to find the quantity of matter transferred
across the plane of yz, due to the motion of agitation alone.

If the number of particles, their velocity, or their length of
path is greater on one side of this plane than on the other, then
more particles will cross the plane in one direction than in the
other; and there will be a transference of matter across the
plane, the amount of which may be calculated.

Let there be taken a stratum whose thick-
ness is doc, and area unity, at a distance x from
the origin. The number of collisions taking
place in this stratum in unit of time will be

Njdx.

The proportion of these which reach a distance between nl and
(n-\-dn)l before they strike another particle is

e~ndn.

The proportion of these which pass through the plane yz is

nl+x

2nl
and nl— x

when x is between — nl and 0,
when x is between 0 and -f nl ;

2nl

the sign being negative in the latter case, because the particles
cross the plane in the negative direction. The mass of each
particle is M ; so that the quantity of matter which is projected
from the stratum dx, crosses the plane yz in a positive direction,
and strikes other particles at distances between w/and (n + dn)l is

2yt/r ' dxe~*dn, (26)

where x must be between ±nl, and the upper or lower sign is
to' be taken according as x is positive or negative.

more kinds of Moving Particles among one another. 23

In integrating this expression, we must remember that N, v,
and / are functions of x, not vanishing with x, and of which the
variations are very small between the limits x = — nl and
x= -f nl.

As we may have occasion to perform similar integrations, we
may state here, to save trouble, that if U and r are functions of
x not vanishing with x, whose variations are very small between
the limits x— +r and x= — r,

+ Vxmdx=-?-,4-(Vrm+2)' • • • (27)
~ m + 2 ax v ' v '

When m is an odd number, the upper sign only is to be con-
sidered ; when m is even or zero, the upper sign is to be taken
with positive values of x, and the lower with negative values*
Applying this to the case before us,

t+nlMNvxdx . d ,Z*-*r or,

I

1

i

+~2r^=:~'^(MNmZ)*

We have now to integrate

i

■~^(MNviye-»dn,

n being taken from 0 to oo. We thus find for the quantity of
matter transferred across unit of area by the motion of agitation
in unit of time,

«=-i£(pf). (28)

where p=MN is the density, v the mean velocity of agitation,
and / the mean length of path.

Prop. XV. The quantity transferred, in consequence of a mean
motion of translation V, would obviously be

Q= V (29)

Prop. XVI. To find the resultant dynamical effect of all the
collisions which take place in a given stratum.

Suppose the density and velocity of the particles to be func-
tions of xy then more particles will be thrown into the given
stratum from that side on whicli the density is greatest ; and
those particles which have greatest velocity will have the great-
est effect, so that the stratum will not be generally in equilibrium,
and the dynamical measure of the force exerted on the stratum
will be the resultant momentum of all the particles which lodge
in it during unit of time. We shall first take the case in which

d.r,

24 Prof. Maxwell on the Process of Diffusion of two or

there is no mean motion of translation, and then consider the
effect of such motion separately.

Let a stratum whose thickness is a (a small
quantity compared with /), and area unity,
be taken at the origin, perpendicular to the
axis of x ; and let another stratum, of thick-
ness dx, and area unity, be taken at a distance
x from the first.

If M, be the mass of a particle, N the number in unit of
volume, v the velocity of agitation, / the mean length of path,
then the number of collisions which take place in the stratum
dx is

- *$*.

The proportion of these which reach a distance between nl and
(n-f fl?n)/is

e~ndn.

The proportion of these which have the extremities of their paths
in the stratum a is

The velocity of these particles, resolved in the direction of x, is

vx
~"n~V

and the mass is M ; so that multiplying all these terms together,
we get

2n*/3 6~ (30)

for the momentum of the particles fulfilling the above conditions.
To get the whole momentum, we must first integrate with
respect to x from #= — nl to x= +nl, remembering that / may
be a function of x, and is a very small quantity. The result is

d /NMiA -

Tx\-^-rmdn'

Integrating with respect to n from n=0 to n= oo, the result is

-"di\—)=ttXp • • • • (31

as the whole resultant force on the stratum a arising from these

NMv2
collisions. Now — jr- =p by Prop. XII., and therefore we

(33)

more kinds of Moving Particles among one another. 25
may write the equation

* -!=x<» • <32)

the ordinary hydrodynamical equation.

Prop. XVII. To find the resultant effect of the collisions upon
each of several different systems of particles mixed together.

Let M„ M2, &c. be the masses of the different kinds of par-
ticles, Nu N2, &c. the number of each kind in unit of volume,
»i, u2, &c. their velocities of agitation, /„ /9 their mean paths,
PuPv &c. the pressures due to each system of particles; then

-r=A/31-f B/>2+ &c.

-j-=fy1+Dft+ &c.

The number of collisions of the first kind of particles with each
other in unit of time will be

Hlv1Apv

The number of collisions between particles of the first and second
kinds will be

N^jB/Dg, or ffg&gCpi, because v13B=v23C.

The number of collisions between particles of the second kind
will be N2%Djo2, and so on, if there are more kinds of particles.

Let us now consider a thin stratum of the mixture whose
volume is unity.

The resultant momentum of the particles of the first kind
which lodge in it during unit of time is

* dx' '

The proportion of these which strike particles of the first kind is

APl lv

The whole momentum of these remains among the particles of
the first kind. The proportion which strike particles of the
second kind is

The momentum of these is divided between the striking particles

M

in the ratio of their masses ; so that g — K-=- of the whole goes

1VX| -j" 1VJ.2

M

to particles of the first kind, and M 2M to particles of the

second kind.

26 Prof. Maxwell on the Process of Diffusion of two or
The effect of these collisions is therefore to produce a force

on particles of the first system, and

on particles of the second system.

The effect of the collisions of those particles of the second
system which strike into the stratum, is to produce a force

- ite^^ + H;

on the first system, and

on the second.

The whole effect of these collisions is therefore to produce a
resultant force

on the first system,

on the second, and so on.

Prop. XVIII. To find the mechanical effect of a difference in
the mean velocity of translation of two systems of moving particles.

Let Vj, V2 be the mean velocities of translation of the two

M M

systems respectively, then A } * (Vt — Vj) is the mean mo-
mentum lost by a particle of the first, and gained by a particle
of the second at collision. The number of such collisions in unit
of volume is

Nj B/32 vv or N2 Cpi v9 ;

therefore the whole effect of the collisions is to produce a force

^N'^'lT+M,^'-^ • • • <36>
on the first system, and an equal and opposite force

= +NaCPlBs5»-4(V1-V9) . . . (37)

on unit of volume of the second system.

more kinds of Moving Particles among one another. 27

Prop. XIX. To find the law of diffusion in the case of two gases
diffusing into each other through a plug made of a porous material ',
as in the case of the experiments of Graham.

The pressure on each side of the plug being equal, it was
found by Graham that the quantities of the gases which passed
in opposite directions through the plug in the same time were
directly as the square roots of their specific gravities.

We may suppose the action of the porous material to be similar
to that of a number of particles fixed in space, and obstructing
the motion of the particles of the moving systems. If L, is the
mean distance a particle of the first kind would have to go before
striking a fixed particle, and L2 the distance for a particle of the
second kind, then the mean paths of particles of each kind will
be given by the equations

l=APl + B^+i -L=Cp1+Dp2+i-. . (38)

The mechanical effect upon the plug of the pressures of the gases
on each side, and of the percolation of the gases through it, may
be found by Props. XVII. and XVIII. to be

1^ * L2 dx L, dx L2 ' ' W

and this must be zero, if the pressures are equal on each side of
the plug. Now if Qw Q2 be the quantities transferred through
the plug by the mean motion of translation, Q, ^pjfj = MjN,Vj ;
and since by Graham's law

Q2~ " V Ms" ~V

we shall have

MlN1v,Vl = — M2N2v2V2= U suppose ;

and since the pressures on the two sides are equal, ■— = — ■—,

and the only way in which the equation of equilibrium of the
plug can generally subsist is when Lj = L2 and lx — l^ This
implies that A=C and B = D. Now we know that v13B=v23C

A

Let K=3— o, then we shall have
v?

A=C=4KV, B=D = |Ki;23, . . . (40)

and

y- = y- ^Kfa^+tW^+jj. > • • (41)

The diffusion is due partly to the motion of translation, and
partly to that of agitation. Let us find the part due to the
motion of translation.

28 Prof. Maxwell on the Process of Diffusion of two or

The equation of motion of one of the gases through the plug
is found by adding the forces due to pressures to those due to
resistances, and equating these to the moving force, which in
the case of slow motions may be neglected altogether. The
result for the first is

Making use of the simplifications we have just discovered, this
becomes

whence

dp Kljvfyi + Vfpj . r44x

dx v^+v*' ' "'

whence the rate of diffusion due to the motion of translation
may be found; for

Q,= 2,andQ,--J (45)

To find the diffusion due to the motion of agitation, we must
find the value of qv

L d px

vY dx 1 + KL(i?j px -f- Vet p2'

*.=-^iO+KL^.+^> • ■ (46)

Similarly,

^=+il(l+KLp'(^+ft)> • • (47)

The whole diffusions are Q1 + qx and Q*-hf* The values of qx
and q2 have a term not following Graham's law of the square
roots of the specific gravities, but following the law of equal
volumes. The closer the material of the plug, the less will this
term affect the result.

Our assumptions that the porous plug acts like a system of
fixed particles, and that Graham's law is fulfilled more accurately
the more compact the material of the plug, are scarcely suffi-
ciently well verified for the foundation of a theory of gases; and

more kinds of Moving Particles among one another. 29

even if we admit the original assumption that they are systems
of moving elastic particles, we have not very good evidence as
yet for the relation among the quantities A, B, C, and D.

Prop. XX. To find the rate of diffusion between two vessels
connected by a tube.

When diffusion takes place through a large opening, such as
a tube connecting two vessels, the question is simplified by the
absence of the porous diffusion plug ; and since the pressure is
constant throughout the apparatus, the volumes of the two gases
passing opposite ways through the tube at the same time must
be equal. Now the quantity of gas which passes through the
tube is due partly to the motion of agitation as in Prop. XIV.,
and partly to the mean motion of translation as in Prop. XV.

Let us suppose the
volumes of the two ves-
sels to be a and b, and
the length of the tube f a

between them c, and its
transverse section s. Let
a be filled with the first
gas, and b with the second
at the commencement of

the experiment, and let the pressure throughout the apparatus
be P.

Let a volume y of the first gas pass from a to b, and a volume
y1 of the second pass from b to a ; then if pl and p^ represent
the pressures in a due to the first and second kinds of gas, and
p\ and p'% the same in the vessel b,

' P. . (48)

Pl~ a W

i Vi

-« ' ft!?

y-Y

br'

y2=

b-y'
b

Since there is

still i

equilibrium,

i+y«»

which gives

2/=2/f and pl+p2=Y=p'1+pt<i. . . . (49)

dv Axi

The rate of diffusion will be + -^ for the one gas, and — -~ for

the other, measured in volume of gas at pressure P.
Now the rate of diffusion of the first gas will be

di~s P =* P

(50)

30 Prof. Maxwell on the Process of Diffusion of two or
and that of the second,

-§f=# ^-p C")

We have also the equation, derived from Props. XVI. and XVII.,

*j (Ap/,(M, + M2) +BMM,- Cp,Z2M,)

+ Bp,p9t.1Ms(V,-V8)=0 (53)

From these three equations we can eliminate V, and V„ and
find -j- in terms of p and -j-, so that we may write

!=/(-!•) «

Since the capacity of the tube is small compared with that of

the vessels, we may consider -j- constant through the whole

length of the tube. We may then solve the differential equation
in p and x\ and then making p=pv when x=0, and p—p\
when x=c, and substituting for px and p\ their values in terms
of y, we shall have a differential equation in y and t, which being
solved, will give the amount of gas diffused in a given time.

The solution of these equations would be difficult unless we
assume relations among the quantities A, B, C, D, which are
not yet sufficiently established in the case of gases of different
density. Let us suppose that in a particular case the two gases
have the same density, and that the four quantities A, B, C, D
are all equal.

The volume diffused, owing to the motion of agitation of the
particles, is then

7 P dxVL>

and that due to the motion of translation, or the interpenetration
of the two gases in opposite streams, is

s dp kl

The values of v are distributed according to the law of Prop. IV.,
so that the mean value of v is — =, and that of - is ... , that
of k being \a*. The diffusions due to these two causes are

y= ^(1-eWir ^<"

more kinds of Moving Particles among one anothev. 31
therefore in the ratio of 2 to 3, and their sum is

dV ± /M si dp ...

If we suppose -£ constant throughout the tube, or, in other
words, if we regard the motion as steady for a short time, then
-j- will be constant and equal to * l~^1 j or substituting from
(48), _

whence

/2k si

a + b

By choosing pairs of gases of equal density, and ascertaining
the amount of diffusion in a given time, we might determine the
value of / in this expression. The diffusion of nitrogen into
carbonic oxide or of deutoxide of nitrogen into carbonic acid,
would be suitable cases for experiment. The only existing ex-
periment which approximately fulfils the conditions is one by
Graham, quoted by Herapath from Brande's Quarterly Journal
of Science, vol. xviii. p. 76,

A tube 9 inches long and 0*9 inch diameter, communicated
with the atmosphere by a tube 2 inches long and 0*12 inch dia-
meter; 152 parts of olefiant gas being placed in the tube, the
quantity remaining after four hours was 99 parts.

In this case there is not much difference of specific gravity

between the gases, and we have «=9 x (0*9)2-r cubic inches,
£= qo, c=2 inches, and 5=(0*12)2^- square inches;

^Vhl^lO.l.H^); . (57)
•\ /=000000256 inch = -J- inch. . . . (58)

Prop. XXI. 2 o find the amount of energy which crosses unit of
area in unit of time when the velocity of agitation is greater on
one side of the area than on the other.

The energy of a single particle is composed of two parts, — the
vis viva of the centre of gravity, and the vis viva of the various
motions of rotation round that centre, or, if the particle be
capable of internal motions, the vis viva of these. We shall sup-
pose that the whole vis viva bears a constant proportion to that

32 Prof. Maxwell on the Process of Diffusion of t too or
due to the motion of the centre of gravity, or

where ft is a coefficient, the experimental value of which is 1*634.
Substituting E for M in Prop. XIV., we get for the transference
of energy across unit of area in unit of time,

hi- — ^(j/9M»W),

where J is the mechanical equivalent of heat in foot-pounds, and
q is the transfer of heat in thermal units.

Now MN=p, and /= -r-, so that MN/= -r- ;

T , fiv* dv /K .

Also, if T is the absolute temperature,

T dx~v dx'
/.%=-f/^lg, (60)

where p must be measured in dynamical units of force.

Let J = 772 foot-pounds, />=2116 pounds to square foot,
l=^~ inch, v = 1505 feet per second, T=522 or 62° Fahren-
heit; then

T'— T

9=ioooS (61)

where g is the flow of heat in thermal units per square foot of
area; and T', and T are the temperatures at the two sides of
a stratum of air x inches thick.

In Prof. Rankine's work on the Steam-engine, p. 259, values
of the thermal resistance, or the reciprocal of the conductivity,
are given for various substances as computed from a Table of
conductivities deduced by M. Peclet from experiments by M.
Despretz: —

Gold, Platinum, Silver. . 00036'

Copper 00040

Iron 00096

Lead 00198

Brick 03306

Air by our calculation . . . 40000

It appears, therefore, that the resistance of a stratum of air
to the conduction of heat is about 10,000,000 times greater than

more kinds of Moving Particles among one another. 33

that of a stratum of copper of equal thickness. It would be almost
impossible to establish the value of the conductivity of a gas by
direct experiment, as the heat radiated from the sides of the vessel
would be far greater than the heat conducted through the air,
even if currents could be entirely prevented.

Part III. On the Collision of Perfectly Elastic Bodies of any
Form.

When two perfectly smooth spheres strike each other, the
force which acts between them always passes through their cen-
tres of gravity ; and therefore their motions of rotation, if they
have any, are not affected by the collision, and do not enter into
our calculations. But; when the bodies are not spherical, the
force of compact will not, in general, be in the line joining
their centres of gravity ; and therefore the force of impact will
depend both on the motion of the centres and the motions of
rotation before impact, and it will affect both these motions after
impact.

In this way the velocities of the centres and the velocities of

rotation will act and react on each other, so that finally there

will be some relation established between them ; and since the

rotations of the particles about their three axes are quantities

related to each other in the same way as the three velocities of

their centres, the reasoning of Prop. IV. will apply to rotation

as well as velocity, and both will be distributed according to the

law

rfN AT 1 _'*
— =N — jh.t «2.
ax u Vit

Also, by Prop. V., if x be the average velocity of one set of par-
ticles, and y that of another, then the average value of the sum
or difference of the velocities is

\/x* + y*;
from which it is easy to see that, if in each individual case
u — ax-\-by + cz,

where x, y, z are independent quantities distributed according to
the law above stated, then the average values of these quantities
will be connected by the equation

Prop. XXII. Two 'perfectly elastic bodies of any form strike
each other : given their motions before impact, and the line of im-
pact, to find their motions after impact,

Phil. Mag. S. 4. Vol. 20. No. 130. July 1860. D

34 Prof. Maxwell on the Collision of

Let M, and M2 be the centres
of gravity of the two bodies. M, Xt,
Mj Y„ and M, Z, the principal axes
of the first; and M2X2, M2, Y2J
and M2Z2 those of the second.
Let I be the point of impact, and
H , 1 R , the line of impact.

Let the coordinates of I with
respect to Mj be xx yx zv and with
respect to M2 let them be x2 y2 z2.

Let the direction-cosines of the line of impact R, I It2 be

lxmlni with respect to M„ and Z2m2w2 with respect to M2.

Let Mj and M2 be the masses, and Aj^Bj C, and A2B2 C2 the
moments of inertia of the bodies about their principal axes.

Let the velocities of the centres of gravity, resolved in the
direction of the principal axes of each body, be

Ui V, W, and U2 V2 W2 before impact,
and

U'j V^ W\ and U'2 V2 W2 after impact.

Let the angular velocities round the same axes be

Pi 9i ri and Pz 02 ra before impact,
and

P'\ tfi ^i an(* P!2 Q1* ^2 a^ter impact.

Let R be the impulsive force between the bodies, measured by
the momentum it produces in each.

Then, for the velocities of the centres of gravity, we have the
following equations :

U'.-U. + g, U'2=U2-g*, .... '(62)

1 2

with two other pairs of equations in V and W. The equations
for the angular velocities are

T» T»

yi=Pi + j- to**i~'A& p'^p*- a" (yf1*-**™*)' (63)

with two other pairs of equations for q and r.

The condition of perfect elasticity is that the whole vis viva
shall be the same after impact as before, which gives the equation

M,(U'?-U?) + M2(U'?-U^+A1(P'?-^) + A2(y2-^)+&c.=0.

The terms relating to the axis of x are here given ; those relating
to y and z may be easily written down.

Substituting the values of these terms, as given by equations

Perfectly Elastic Bodies of any Form. 35

(6.2) and (63), and dividing by R, we find

Wi + UJ -/2(U'2+ U2) + (yini -z^) (p\ fj$

— {y^2 — Z2m2) {P*2 +P2) + &C. = 0 (65)

Now if vl be the velocity of the striking-point of the first body
before impact, resolved along the line of impact,

vi = W + (ft»i —*\mi)Pi + &c- ■>
and if we pnt pa for the velocity of the other striking-point
resolved along the same line, and v\ and v'2 the same quantities
after impact, we may write equation (65),

vl+v'l-v2-v'2 = 0, ..... (66)
or

Vl — V9-v'2-v'l) (67)

which shows that the velocity of separation of the striking-points
resolved in the line of impact is equal to that of approach.

Substituting the values of the accented quantities in equa-
tion (65) by means of equations (63) and (64), and transposing
terms in R, we find

2{V1l1—\J2l2+pl{ylnl-zlml)~p2(y2n2-z2m2)} + &c.

= -E{£ + £ + (y'Vm'r + {y^TinhY + &c- (68)
IM, M2 A, A2 v '

the other terms being related to y and z as these are to x. From
this equation we may find the value of R; and by substi-
tuting this in equations (63), (64), we may obtain the values of
all the velocities after impact.

We may, for example, find the value of V*[ from the equation

TV JZi2 j_ l* , (l/ini-^m,)2 (y2n2-z2m2y -, \%

^I-m^m^ — tt — + — A2 +&C7T

+ 2V2l2—2pl(yln1—zlm1)+2p2{y2n2 — z2m2)-- &c.

Prop. XXIII. To find the relations between the average velocities
of translation and rotation after many collisions among many bodies.

Taking equation (69), which applies to an individual collision,
we see that V\ is expressed as a linear function of Up y^PvPa
&c, all of which are quantities of which the values are distributed
among the different particles according to the law of Prop. IV.
It follows from Prop. V., that if we square every term of the
equation, we shall have a new equation between the average
values of the different quantities. It is plain that, as soon as the
required relations have been established, they will remain the

D2

36 On the Collision of Perfectly Elastic Bodies of any Form.

same after collision, so that we may put U1'2=Ul2 in the equa-
tion of averages. The equation between the average values may
then be written

(M.U.'-M^^g+tM.U.'-A.p,')^"1^""0'
+ (M.U,*- A,j»«) fo"2-*^' + fa. =0.

A2

Now since there are collisions in every possible way, so that the
values of /, m, n, &c. and SB, y} z, &c. arc infinitely varied, this
equation cannot subsist unless

M1U1a=M2U22=A1jol2=A2^22=&c.

The final state, therefore, of any number of systems of moving
particles of any form is that in which the average vis viva of
translation along each of the three axes is the same in all the
systems, and equal to the average vis viva of rotation about each
of the three principal axes of each particle.

Adding the vires vivce with respect to the other axes, we find
that the whole vis viva of translation is equal to that of rotation
in each system of particles, and is also the same for different
systems, as was proved in Prop. VI.

This result (which is true, however nearly the bodies approach
the spherical form, provided the motion of rotation is at all
affected by the collisions) seems decisive against the unqualified
acceptation of the hypothesis that gases are such systems of hard
elastic particles. For the ascertained fact that y, the ratio of the
specific heat at constant pressure to that at constant volume, is
equal to 1*408, requires that the ratio of .the whole vis viva to
the vis viva of translation should be

whereas, according to our hypothesis, /3=2.

We have now followed the mathematical theory of the col-
lisions of hard elastic particles through various cases, in which
there seems to be an analogy with the phenomena of gases. We
have deduced, as others have done already, the relations of pres-
sure, temperature, and density of a single gas. We have also
proved that when two different gases act freely on each other
(that is, when at the same temperature), the mass of the single
particles of each is inversely proportional to the square of the
molecular velocity; and therefore, at equal temperature and
pressure, the number of particles in unit of volume is the same.

We then offered an explanation of the internal friction of

On the Velocity of the Sound of Thunder. 37

gases, and deduced from experiments a value of the mean length
of path of a particle between successive collisions.

We have applied the theory to the law of diffusion of gases,
and, from an experiment on olefiant gas, we have deduced a
value of the length of path not very different from that deduced
from experiments on friction.

Using this value of the length of path between collisions, we
found that the resistance of air to the conduction of heat is
10,000,000 that of copper, a result in accordance with experience.

Finally, by establishing a necessary relation between the mo-
tions of translation and rotation of all particles not spherical, we
proved that a system of such particles could not possibly satisfy
the known relation between the two specific heats of all gases.

III. On a New Theoretical Determination of the Velocity of
Sound. By the Rev. S. Earnshaw, M.A., Sheffield.
[Continued from vol. xix. p. 455.]
On the Velocity of the Sound of Thunder.

I INHERE yet remains to be considered a case of sound-velocity
A to which the investigations of Newton and the suggestion
of Laplace are totally inadequate, which nevertheless is naturally
suggested, by what has been done in the preceding articles, as
necessary to complete the theory of sound-velocity : I allude to
the propagation of the sound of a clap of thunder. The con-
sideration of this case will strengthen the evidence of the sound-
ness of the preceding investigations.

Before it was announced by myself at the Meeting of the
British Association at Leeds in 1858, that according to theory
violent sounds are propagated more rapidly than gentle sounds,
I believe the fact was not suspected by philosophers. I was led
to this result by a careful discussion of the integral of the
well-known equation of motion of an elastic fluid in a horizontal
tube. I was, however, not able to bring forward any instance
of the fact having been observed, except a single one, recorded
in one of Parry's Voyages to the North. The records of
experimentalists agreed in stating, on the contrary, that all sounds
travel at the same rate. Since that time the subject has rested.
A few weeks ago, however, my attention was recalled to it by the
receipt of a memoir printed in the Bulletins de VAcademie Royale
de Belgique, kindly forwarded to me by its author, Professor
Ch. Montigny of Antwerp, which has satisfied me that, in the
case of a thunder-clap, sound is sometimes propagated with a
velocity far greater than I had ever imagined, and that the
problem of the propagation of sound is yet far from having been
fully solved.

88 The Rev. S. Earnshaw on the Velocity

In the spring of 1851, when I was living in the small village
of Conisborough about five miles from Doncaster, there occurred,
one Sunday evening about 5 o'clock, a thunder-storm which lasted
about half an hour. It was not different from other thunder-
storms, except that it was terminated by a flash of lightning of
great vividness, which was instantly (i. e. without any appreciable
interval between) followed by an awful crash, that seemed as if
by atmospheric concussion alone it would crush the cottages to
ruins. Every one in the village, as I found afterwards, had felt
at the moment of the crash, as I felt myself, that the electric
fluid had certainly fallen somewhere in the village. Indeed it
seemed impossible for any one to think otherwise than that his
neighbour's cottage had been struck, and his own had had a
narrow escape. But, to the surprise of everybody, it turned out
that no damage had been done in the village, but that that flash
of lightning had killed three sheep, knocked down a cow, and
injured the milkmaid who happened to be milking the cow, at a
distance of more than a mile from the village. I was at that
time under a physician's orders not to think about anything,
but I remember thinking that it was very singular the lightning
should fall at such a distance, when I should have expected it,
from the received theory of sound, to fall in the village. Professor
Montigny's memoir records similar, and yet more striking
instances, which have come to his knowledge or been observed
by himself. In one of them the report of a thunder-clap reached
him after an interval of 2 seconds, which according to theory
should have occupied more than 15 seconds. As he well
remarks, the difference in this instance is too great to be accounted
for by the agency of wind, or errors of observation; besides
which, his observation was confirmed by an independent ob-
server, the cure of a parish a few miles off, who observed the
same flash and estimated the interval that elapsed before the
report reached him at 2 seconds, though according to theory it
should have been nearly 15 seconds, the two observers and the
point struck by the electric fluid being nearly equidistant from
one another. Other cases, less striking perhaps, but quite
agreeing with this, are recorded in the memoir ; and after reading
them and remembering my own experience, I cannot but consider
this a subject worthy of the attention of observers. And if it
shall seem good to them to record their observations in cases
where, from some noticeable peculiarity, the point struck by a
particular flash can be identified, I strongly suspect it will soon
be established as a law of nature, that the sound of a thunder-clap
is propagated with far greater rapidity than ordinary sounds.
We shall presently see what light theory throws upon this point.

9. The velocity of sound has been determined in the last

of the Sound of Thunder. 39

article by the assumption of the musical type of the sound-wave.
The result shows that all audible musicalsounds are transmitted
with the same velocity : and, as the equation of motion in art. 3
is linear, it follows that every sound which can be considered as
a combination of musical sounds, will be transmitted with the
same velocity : and as in general any ordinary function of t can
be expanded in the form A' cos (k! t + a!) + A" cos (k'1 1 + a11) + . . . . ,
it follows that all ordinary sounds are made up of musical sounds
and transmitted with the same velocity.

10. From this it will be seen that we may consider the equation

as the definition of the elements of what I have denominated a
gentle or ordinary sound. The convenience of analysis requires
that, in treating the differential equation of art. 3, we should be
able to express Jftxr in the form of xr multiplied into a constant,
or to substitute a constant for the symbol D}; and hence it is
obvious there remains yet to be considered the form

In other words, it remains that we should consider the exponential
type xr — Arekt} which we shall consider to be the type of ele-
mentary violent sounds.

By the substitution of this form in the equation of art. 3 we
obtain

k2Ar=mf{h) . (Ar_!-2Ar+ Ar+1) + &c,

which being a linear equation of finite differences, we find for
its solution

A^Crf'+C'a-*, (lf)

the quantity a being such as to satisfy the equation

k*=mf(h) . (u-d-^ + mffih) . (a2-a-2)2+ ... . (2')

the form of which indicates that, for every value of k, there is a
possible value of a— ex.'1, and therefore of a. The case of
a— a-1 = 0 is excluded because it makes £=0, and destroys the
previous assumption of the exponential type. I assume there-
fore the value of a— a-1 to be the measure of the degree of vio-
lence of the genesis of any proposed wave.
The above leads to the equation

x = Ceft*+2rlogea + C'€w-2rloge<x

the two terms of which indicate the possible coexistence, at the
same point, of two violent waves travelling in opposite directions.
We shall therefore only retain the latter term,

xr=A€kt-2rl°s<«, (5')

as the representative of a progressive wave of the violent type.

40 On ike I 'd»iity of the Sound of Thunder.

From this equation wc determine, as before, the velocity of a
violent sound to be •

•-nr^vr^-' {/'(A).(«-»-')9+/'(2A)-(«9-«-a)2+-}i, (7')

Z loge a 2 loge a
■ result which may be written in the form

i i 2 /« + «-' V L 1 Z^+l + a-V,
1 + 2n*~2~~V + 32\ 3 / +•••

V~2loi^

l+29 + g2

V being the velocity, before determined in art. 8, for all gentle
sounds. That the full meaning of this equation may be obvious,
it is necessary to remember that

21oge« ""1+TT273'+1.2.3.4.5+,,* * {)

11. It is manifest, from inspection of the last two equations,
that when « = 1 or a— a-1=0, thenr = V. This case therefore
connects (or, rather, stands between as the limit of both) the
gentle and the violent sounds. But for every value of a greater
than unity, we perceive that v must necessarily be greater than
V, which is the limiting velocity of gentle sounds, for both the
factors of the right-hand term of equation (8) are greater than
unity.

12. In art. 8 we found an expression for the velocity of
transmission of ordinary sounds which was independent of the
pitch. But equation (8) we perceive involves a— a-1, the degree
of violence belonging to each wave : and hence it is not true of
violent sounds that they all travel with the same velocity. The
elements of a compound violent sound will also not keep together
unless the value of a be the same in all, or vary continuously
from one element to another. In the latter case the sound will,
by the unequal motion of its elements, have a tendency to
lengthen ; and if a do not vary continuously, the sound will soon
be heard, not as one clap, but as a series of minor claps, or as a
rattle.

13. It is seen from observing the forms of equations (8) and (9),

that such a value can be found for a as shall make the ratio ^

as large as we please. It would appear therefore that there is no
other limit to the velocity with which a violent sound is trans-
missible through the atmosphere, than that which the possibility
of supplying a sufficient degree of force in its genesis may impose.

(8)

M. Lourenco on Glycol Compounds. 41

Hence it is probable that there is no sound which is propagated
faster than a thunder-clap, the genesis of which by the electric
discharge being extremely violent and almost instantaneous, and
accompanied by a large development of heat.

If the theory here advanced be true, the report of fire-arms
should travel faster than the human voice ; and the crash of
thunder faster than the report of a cannon.

It will be admitted, I think, that the expression for the
velocity in equation (8) is capable of furnishing any required
amount of velocity. The difficulty of putting it to the test of expe-
riment lies in our utter inability to say, in any proposed case, what
is the value of a. All that it seems possible to do is to observe
v, and thence calculate a by the equation referred to ; and then
to judge, by the comparison of different observations, whether
the calculated values of a — a-1 seem to agree with the observed
violence of the electric discharges.

Sheffield, June 11, 1860.

[To be continued.]

IV. Chemical Notices from Foreign Journals. By E. Atkin-
son, Ph.D., F.C.S.y Teacher of Physical Science in Cheltenham
College.

[Continued from vol. xix. p. 390. J

LOURENCO* has prepared several of the compound ethers
of glycol. The ethers with a single acid radical are formed
according to the reaction

h*}°2+h}°= b U2 + H20,

Glycol. Monobasic " J

acid.

in which R is an acid radical. The preparation is effected by
heating equivalent quantities of the substances together in a

€2H4" 1
sealed tube. In this manner the monoacetate C2H30 >92,

e2H4" 1 H J

the monobutyrate G4H7OV02; and the monovalerianate

C2H4" I H J

G5H90 ^O2 have been obtained. The monoacetate prepared

H J
by this method corresponded in properties with that obtained by
another process f. The monobutyrate and monovalerianate are

* Bulletin de la Societe Chimique, p. 90.
f Phil. Mag. vol. xvi. p. 433.

42 M. Lourenco on Glycol Compounds.

colourless, oily liquids, insoluble in water, but readily soluble in
alcohol and in ether, and with odours resembling their corre-
sponding acids. They boil respectively at 220° and 240° C.

The ethers with two acid radicals of the same kind are formed
by heating glycol with excess of the acid in question. Divale-

rianate of glycol, ,p5 ti9 qx, >02, is an oily liquid insoluble in

water, and boiling at 255°.

The mixed ethers are prepared by treating with another acid
the ethers with a single acid radical. Thus :

€«H4
R
H

€2H41

>0* + gl*0= R to2+H20.

In this manner Lourenco has prepared acetobutyric acid, already

€2H4 1
obtained by Simpson*, and acetovalerianic acid, €2H89>92.

€6H90j
This latter is a colourless, oily, neutral liquid, soluble in ether
and in alcohol, and boiling at 230° C.

These ethers distil without decomposition. When treated with
water, they experience a decomposition analogous to that of the
ethers of alcohol and glycerine, being resolved into an acid and
glycol, or an intermediate compound. Thus neutral acetate of
glycol, when treated with water, is resolved into free acid and
monoacetate of glycol ; and monoacetate of glycol, when treated
with water, is decomposed into free acetic acid and glycol.

By the action of chloride of acetyle or butyryle on glycol, the

C2 H4 i C2JT4 t *

chloroacetine of glycol, e2H30[02,andchlorbutyrine,^4H70}0,

CI CI

are obtained. The two phases of the action may be thus ex-
pressed : —

G2^|o2-f2C2H3OCl==^g39|o+C2H402+HCl.

G1ycoL aceVe0 C1 Aceticacid-

Chloracetine.

€2S^02 + €2H402 + HCl=g^34A"lo-f2H29.

ni n. J Acetic acid. b n * 1

Glycol. CI

Chloracetine.

The reaction of a chloride of an acid radical on a glycol with

one acid radical gives rise to the formation of an ether with two

radicals and a chlorhydrine and water. By treating monoacetate

* Phil. Mag. vol. xix. p. /0.

2

M. Lourenco on Glycol Compounds. 43

of glycol with chloride of acetyle, Lourenco has thus obtained
chloracetine and acetate of glycol ; and by treating monoacetate
of glycol with chloride of butyryle, he has obtained acetobutyrate
of glycol and chloracetine. The former reaction is thus ex-
pressed : —

(S|oJG-)+?SoS-|g:o).}0'+Sg:o}e+H.a

V J / acetyle. Acetate of CI

Monoacetate of J glycol. Chloracetine.

glycol.

The same chemist has investigated* the action of bibasic acids
on glycol. He heated together succinic acid and glycol in a
sealed tube to 90° for some hours. An action resulted which,
as Lourenco anticipated, was in accordance with the equation

e2H4

2|o2+^H4gY}o2=€4H402 lo3+H90.

Glycol. Succinic acid. ^ , ,-'

The contents of the tube, after the operation, consisted of a
colourless, oily, homogeneous liquid. It was dissolved in alcohol,
and a large quantity of ether added, by which some succinic acid
was precipitated. After removing this, the alcohol and ether
were expelled at the temperature of the water-bath, and the
residue then maintained for some time at 200° in order to get
rid of any excess of glycol. The analysis of the residual liquid
gave for it the formula G6 H10 O5. This body has a composition
analogous to that of diethylenic alcohol f. It may be viewed as
this compound in which an atom of the diatomic radical succi-
nyle replaces an atom of the diatomic ethylene, and it may hence
be called succinoethylenic acid. Thus

£2 JJ4" *\ £2 JJ4" 1\

£2H4" lo3 G4H402" >®3>

H2 J H2 J

Diethylenic alcohol. Succinoethylenic acid.

g2h4 -)

This acid is accordingly bibasic. The silver salt, G4H402 >03,

. As2J

is obtained by the double decomposition of succinoethylenate of
ammonia and nitrate of silver as a gelatinous curdy precipitate.
When succinoethylenic acid is heated to 300° it loses water, and
leaves, on cooling, a crystalline mass which melts at about 90° C.

* Bulletin de la Societe Chimique, p, 123.
t Phil. Mag. vol. xix. p. 124.

44 M. Bauer on Oxide ofAmylene.

It melts in boiling water to a thick oil, which is insoluble in
water, and may thus be freed from succinic acid. It is dissolved
by boiling alcohol, from which it separates, on cooling, in small
crystals. It decomposes by distillation. Analysis gave for it

the composition €6H894=^4 „4 q2h rO2. It is neutral suc-
cinate of glycol, and is the first well-defined example in which a
diatomic radical is substituted for the two atoms of replaceable
hydrogen of a diatomic compound.

Bauer has obtained * oxide of amylene, the compound cor-
responding to Wurtz's oxide of ethylene f. The preparation of
this body is very troublesome, owing to the difficulty of pre-
paring bromide of amylene, and, therefrom, amylglycol. To
prepare bromide of amylene, amylene is placed in a long-necked
globe, surrounded by a freezing mixture, and a calculated
quantity of bromine gradually added. When the action is com-
plete, the liquid is shaken with dilute potash, then washed with
water, dried, and allowed to stand over chloride of calcium. It
boils at 170° to 175°, but decomposes at that temperature. For
the preparation of amylglycol, it is sufficient to keep it at 160°
for some time. Bauer observed that this liquid contained some
hydride of amyle,G6 H12, and some brominated amylene, €5 H9 Br,
but both these pass off almost entirely below 100°.

Bauer found, as has been observed by the writer of these
notices, that acetate of potass cannot be used advantageously in
the preparation of amylglycol. The action of bromide of
amylene on acetate of silver is slow, but complete. It is effected
by making acetate of silver into a paste with glacial acetic acid,
gradually adding the bromide of amylene, and after the first
action is over, heating the whole to 100° for a few days. It is
then distilled, the portion above 140° being collected separately.
When this is treated with potash and distilled, amylglycol is
obtained.

When hydrochloric acid gas is passed into amylglycol, the
liquid becomes coloured, and the further action of the gas
converts it into a black viscous mass, which decomposes on di-
stillation. Aqueous hydrochloric acid acts with great energy on
amylglycol at ordinary temperatures, forming several chlori-
nated compounds, among which is hydrochloric amylglycol,

Q6JJ10 1

>9. Efforts made to separate this body in the pure state

CI
writ fruitless.

* Bulletin de la Sociiti Chimique, p. 148.

t Phil. Mag. vol. xvii. p. 427 ; vol. xix. p. 122.

M. Kolbe on the Constitution of Organic Compounds. 45

Oxide of ethylene was prepared by Wurtz by the action of
potash on hydrochloric glycol ; for the preparation of oxide of
amylene, Bauer treated amylglycol with diluted hydrochloric
acid, and then mixed the crude product thus obtained, which
consisted mainly of hydrochloric amylglycol, with potash, and
distilled the mixture. The distillate consisted of water with a
layer of an oily liquid. This was removed, dried, and repeatedly
rectified. It boiled at 95°, but could not be freed from traces of
a chlorinated compound. The analyses and determination of
the vapour density left no doubt that it was oxide of amylene,
e5H,o0, corresponding to oxide of ethylene, G2H40. Its
formation may be thus expressed : —

2(G5H11C19) + K2O=2KCl + 2€5H10e + H2O.

Hydrochloric Chloride of Oxide of

amylglycol. potassium. amylene.

Oxide of amylene boils at about 95°, and has the spec. grav.
08244 ; it burns steadily with a yellow flame. It has an agree-
able etherial odour, and a bitter taste. It is insoluble in water,
but dissolves in alcohol, in ether, in amylglycol, and in acids.
Heated with acetic acid, it is converted into acetate of amyl-
glycol.

In a series of recent communications, Kolbe has developed
certain views of the constitution of several of the principal series
of organic compounds. These views are supported by a wide
variety of illustrations from organic chemistry ; and several in-
teresting investigations have been undertaken by Kolbe and his
pupils in order to test their validity. Without going too much
into detail it is impossible to give the grounds on which these
views are based ; but the investigations to which they have given
rise will probably be intelligible from the following statement.

Organic compounds he considers to be derived from inorganic
compounds, and usually resulting from them by simple processes
of substitution. Carbonic acid plays the most important part
among those inorganic compounds which serve as starting points
for organic bodies. Liebig had already pointed out (in 1847)
that many important compounds, alcohol, sugar, formic acid,
stood in close relation to carbonic acid, and were derivable from
it by the substitution of hydrogen for oxygen. It must be con-
sidered certain that starch, sugar, gum, the vegetable acids, &c,
which are found in plants where the decomposition of carbonic
acid takes place, are formed, at any rate indirectly, from this
carbonic acid. This idea of the connexion between these bodies
and carbonic acid is rendered antecedently probable by the
relations of these formulae, and by their mode of occurrence ;
and it has been made more probable since it has been found

46 M. Kolbe on the Constitution of the Fatty Acids.

possible to replace directly the oxygen in carbonic acid by
hydrogen and bodies allied to it, and so give rise to the forma-
tion, not indeed of sugar, but of bodies immediately derived from
it. In Wanklyn's discovery of the transformation of carbonic
acid into propionic acid and into acetic acid, the view that the
fatty acids, the alcohols, acetones, aldehydes, &c, are simple
derivatives of carbonic acid, finds its chief support.
Kolbe writes the formula of anhydrous carbonic acid

C204=C202,02,

in which two atoms of oxygen are supposed to exist outside the
radical carbonyle. If in carbonic acid one of the four oxygen
atoms is replaced by hydrogen, formic acid results ; and if three
atoms of oxygen are replaced by three atoms of hydrogen,
methylic alcohol is produced. A comparison of the formulae
shows these relations ; and it is to be remarked that when a
positive element replaces a negative, Kolbe writes it on the left
of the primary radical.

2 HO, (C2 O2) O2 HO, H (C2 O2) O2 HO, (H3 C2) O.

Carbonic acid. Formic acid. Methylic alcohol.

By the replacement of one of its atoms of oxygen, the bibasic
carbonic acid is changed into the monobasic formic acid.
Similarly, by the replacement of an atom of oxygen by
methyle, ethyle, butyle, &c, we obtain the corresponding
acids HO, C2 H3 (C2 O2) 0, acetic acid ; HO, (C4 H5) (C2 O2) 0,
propionic acid ; HO, C8 H9 (C2 O2) 0, valerianic acid. In an
analogous manner, Kolbe derives from bibasic sulphuric acid,
the monobasic methylsulphuric acid and phenylsulphuric acid.

2 HO, (S2 O4) O2 Sulphuric acid.

HO, C2 H* (S2 O4) 0 Methylsulphuric acid.

HO, C12 H5 (S2 O4) 0 Phenylsulphuric acid.
If in carbonic acid an atom of oxygen is replaced by an atom of
hydrogen, acetic acid results ; if a second atom of oxygen is re-
placed by a radical, we get the formula of an acetone.
HO, C2 H3 (C2 O2) 0 Acetic acid.

£j^3J(C202) Acetone.

If, in carbonic acid after an atom of oxygen has been replaced by
methyle, the second be replaced by chlorine, chloride of acetyle
results ; and if the second, third, and fourth atoms of oxygen
be successively replaced by hydrogen, we have the compounds

C* ifl c* °9' aldebyde > H0> c* h2}C2> °' alcoho1 ; °2 H31 C*

hydride of ethyle.

M. Kolbe on Isethionic Acid. 47

Glycocol, and its homologues alanine, leucine, &c, are derived
from the corresponding acids, acetic, propionic, and valerianic,
when an atom of amidogen replaces an atom of hydrogen. They
hence receive the name amidoacetic, amidopropionic, amido-
valerianic acids. In like manner Kolbe considers lactic acid to
be derived from carbonic acid by the replacement of an atom of
oxygen by an atom of peroxide of ethyle, or, as he calls it,
oxyethyle ; or it may also be regarded as propionic acid, in which
an atom of hydrogen in the replacing radical is replaced by per-
oxide of hydrogen. Kolbe gives to it the name oxypropionic
acid. The homologues glycolic and leucic acids have, of course,
a similar constitution. Their relations will be best apparent from
a comparison of their formulae.

HO, C9 H3 (C2 O2) 0 HO, C4 H5 (C2 02)0.

Acetic acid. Propionic acid.

HO

C2 Sh*} <C* °2)° H°' °4 NH2} C* °2> °«

Amidoacetic acid Amidopropionic acid

(glycocol). (alanine).

' ^ HO*} (C* °2)0 H°' ^ NH«} C* °*> °-

Oxyacetic acid Oxypropionic acid

(tact

(glycolic acid). (lactic acid).

The recent experiments on the conversion of lactic acid into
propionic acid* and into alanine, support these relations.

In a similar manner Kolbe derives a series of bodies from an-
hydrous sulphuric acid, the formula of which he writes (S204), O2,
that of the hydrated acid being 2 HO, (S2 O4) O2. Just as acetic
acid is methylcarbonic acid, so sulphomethylic acid is methylsul-
phuric acid.

HO, C2 H3 (C2 02) 0 HO, C2 H3 (S2 O4) O.

Methylcarbonic acid Methylsulphuric acid,

(acetic acid).

Isethionic acid stands in the same relation to sulphovinic acid
as lactic acid to carbovinic acid. And as lactic acid is carbonic
acid in which an atom of peroxide of ethyle replaces an atom of
extra-radical oxygen, so isethionic acid is derived from sulphuric
acid by the substitution of an atom of oxygen for an atom of
extra-radical oxygen. Kolbe adduces, in support of these views,
some experiments which he has made with isethionic acid. When
isethionate of potash is distilled with pentachloride of phosphorus,

p4 TT41

a compound, ™ > (S2 O4) CI, corresponding to chloride of lac-
* Phil. Mag. vol. xix. p. 384.

48 M. Kolbe on the Constitution of Bibasic Acids.

tyle is formed*, from which he has further obtained chloroethyl-
sulphuric and amidocthylsulphuric acids, and sulphovinic acid.
Amidoethylsulphuric acid is identical with taurine. The rela-
tions of these bodies to each other, and to the corresponding
terms derived from carbonic acid, are thus seen : —

(C202)02 S204,02.

Carbonic acid. Sulphuric acid.

HO, C4 H5 (C2 O2) 0 HO, C4 H5 (S2 04)0.

Propionic acid. Ethylsulphuric acid.

°4 ci4} (C2 °2) C1 °4 ci4} (S2 °4' CL

Chloride of chloropropionyle New chloride,

(chlorolactyle).

H°' °4 S4H«} (CS °5)' ° H0' °4 NH»} <* °4' ?•

Amidopropionic acid Amidoethylsulphuric acid

(alanine). (taurine).

H0, °4 HO2} (C2 °2) ° H0, ^ HO2} (S' °4J °*

Oxypropionic acid Oxyethylsulphuric acid

(lactic acid). (isethionic acid.)

Kolbe extends these views to explain the constitution of some

bibasic acids which stand in close relation to those of the acetic

acid series. He derives these acids from the compound group,

C2 O2 ^1
a double atom of carbonic acid, p2n2 r^4, When two of the

extra-radical atoms of oxygen are replaced by a diatomic radical
(for example, ethylene and homologous or corresponding carbo-
hydrogens), we obtain acids of the succinic series, and the analo-
gous acids, pthalic acid, &c. Thus :

Succinic acid . . 2HO (C4 H4)" (J£[£W

Suberic acid . . 2HO(Cl2H12)''(£2£2W.

Sebacicacid . . 2HO (Ci6H,6)"/^q1)o«.

Pthalic acid . . 2HO (C12 H4)" (££ °*\ O2.

Insolinic acid . . 2110 (C14 H6)" (££o«)oa.

Now, malic and tartaric acids differ from succinic acid by con-
taining respectively two and four atoms of oxygen more than

• Phil. Mng. vol. xviii. p. 285*

MM. Schmidt and Dessaignes on Tartaric Acid. 49

that acid. Kolbe considers that they bear to succinic acid a
relation analogous to that which he considers lactic and glyceric
acids to bear to propionic acid. That is, malic acid is oxysuc-
cinic acid, and tartaric acid is dioxysuccinic acid, as is seen from
the formulae —

HO, C4 H5 (C2 O2) 0 2HO, C4 ^*(% ™W.

Propionic acid. . . \ . , /

Succinic acid.

HO, C*|^ (©■ 0*) 0 2HO, C< H^J (g 0^Q2

Oxypropionic acid Oxysuccinic acid

(lactic acid). (malic acid).

C4H3 "1 H2 "1

HO, HO2 I (C2 O2) 0 2 HO, C4 HO2 I ( £2 £ \ O2.
H02J HO2 J VL u /

Dioxypropionic acid Dioxysuccinic acid

(glyceric acid). (tartaric acid).

Schmidt has, from this point of view, made a series of experi-
ments* on the action of reducing agents on malic and tartaric
acids ; and he has found that they may be converted into suc-
cinic acid by the use of the reducing agent, hydriodic acid, by
which Lautemannf effected the transformation of lactic acid into
propionic acid. The change was found especially easy with
malic acid. When a concentrated aqueous solution of hydriodic
acid was saturated with malic acid, and the mixture heated in a
sealed tube for some hours to a temperature of 130°, a large
quantity of iodine along with some brown crystals separated.
The latter were succinic acid coloured with iodine. They were
readily purified, and gave correct numbers on analysis. The
change is thus expressed : —

C8H60io + 2HI = C8H608 + 2HO + 2I.

Malic acid. Hydriodic Succinic
acid. acid.

The transformation of tartaric into succinic acid took place
with greater difficulty. It also was effected by saturating a con-
centrated aqueous solution of tartaric acid with hydriodic acid
gas, and heating the mixture in a sealed tube to a temperature
of 120°. The contents of the tube were then boiled in a retort,
with frequent additions of water, until the iodine and hydriodic
acid were removed, then evaporated to dryness, and treated with
ether to remove the last traces of iodine, and finally, the succinic
acid repeatedly crystallized from ether to free it from an admix-

* Liebig's Annolm, April 1860.
f Phil. Mag. vol. xix. p. 384.
Phil Mag. S. 4. Vol. 20. No. 130. July 1860. E

50 Mr. C. J. Burnett on several Forms of Actinometer.
ture of undecomposed tartaric acid. The change is thus ex-

C8H6012 + 4HI = C8H608+4HO+4I.

Tartaric acid. Hydriodic Succinic
acid. acid.

Dessaignes, in a letter* to the Secretary of the Academie des
Sciences, announces that he has effected the transformation of
tartaric acid into succinic acid by treating the former acid with
iodide of phosphorus. Dessaignes' view of the relations of these
acids does not differ from those of Kolbe. The paper in which f
the latter chemist developed his views, and in which he announced
that Schmidt was occupied with the above experiments, appears
to have been unknown to Dessaignes.

These experiments of Schmidt and of Dessaignes acquire an
additional interest at the present time, when Perkins and DuppaJ,
by an experiment the reverse of that of Schmidt, have converted
succinic acid into tartaric acid. This has been done by means
of bibromosuccinic acid. When the silver salt of this acid is
boiled with water, it decomposes, forming bromide of silver and
tartaric acid. Thus :

C8H2Br2Ag208+4HO = C8H6012 + 2AgBr.

Bibromosuccinate Tartaric Bromide

of silver. acid. of silver.

The reaction is thus exactly analogous to that by which chlor-
acetic acid is converted into glycolic acid.

V. On several Forms of Actinometer. By C. J. Burnett, Esq.§

[With a Plate.!

To the Editors of the Philosophical Magazine and Journal.

21 Ainslie Place, Edinburgh,
Gentlemen, April 13, 1860.

APROPOS of the description of a "new actinometer" by
Dr. Woods, which, as I find in its republication in the
Photographic Journal of January 16, appeared first in your
Magazine, I would call your attention to an old actinometer of
mine, a rough sketch of which appeared in the Liverpool Photo-
graphic Journal of December 15, 1858. Without any insinuation

* Comptes Rendus, April 1860.

t Liebig's Annalen, March 1860.

X Chemical Society, April 19.

§ Communicated by Sir D. Brewster, K.H., F.R.S. &c.

Mr. C. J. Burnett on several Forms of Actinometer, 51

of plagiarism against Dr. Woods, it appears right that you and
your readers should know that the measurement of actinism by
the gas evolved is not altogether so novel an idea as Dr. Woods
imagines. By reference to my old sketch alluded to, you will
find that not only the principle of measurement by gas-evolution,
but more also of what Dr. Woods brings before the public as
novel, has been anticipated ; and had my sketch not been a very
hurried one, abridged hurriedly from my old notes of 1855, it
would have contained various other particulars which are, I
believe, even yet new to the public, — and among others the fol-
lowing modifications, &c, which may perhaps be of interest.
I remain, Gentlemen,

Your obedient Servant,

C. J. Burnett.

A column of oil, spirit, or other lighter liquid may be made
{entirely or partially) to replace the mercury, the employment of
this lighter liquid enabling us to use an erect register-tube with-
out having the result so seriously interfered with by the pressure in
it, as is the case where such a very heavy register-fluid as mercury
is employed. The interference of the pressure of a column, and
especially one varying in weight according to its varying height,
gives rise, be it noted, to two inconveniences : first, the render-
ing of equal distances on the register-scale not true measures of
the quantity of gas evolved, and of its pressure ; and secondly, to a
smaller and constantly decreasing sensitiveness of the instrument,
owing to the smaller distance which the column, of the heavier
liquids especially, is pushed forward as its height and pressure
increases. There is an objection to water as a registry-liquid,
that it absorbs and transmits a large portion of the carbonic acid,
which neither oil, mercury, nor even, 1 think, spirit does. The
employment of the sensitive fluid itself for an index, as suggested
and employed by Dr. Woods, is manifestly still more objection-
able, from the chemical action in this case going on in the register-
tube as well as in the reservoir.

The oil or other liquid should be coloured, say dark red, to
make the results more legible, or to facilitate the photographic
registry of them, where that is wished to be carried on.

Using either the heavy or the lighter liquids, the apparatus,
as figured formerly in one of its most simple states, may be with
advantage modified in very many ways : e. g. Plate I. fig. 1 repre-
sents an apparatus in which the registry-liquid is contained in a
second bottle or reservoir, A being the reservoir* containing the

* No attempt at correct proportion is made in these rough figures,
which are only intended to show the principle of action. Thin glass, to
intercept little light, would be advisable. N.B. The sensitiveness of the

E 2

52 Mr. C. J. Burnett on several Forms of Actinometer,

gas-evolving or sensitive liquid, with, at the top, two openings,
one for a cork or stopper, and the other for the tube C which con-
veys the gas to the second reservoir B, but which does not de-
scend beyond the top of either reservoir. B is, as we have
already stated, the second reservoir ; and from the bottom of it
starts the register-tube D, which may either be continued directly
upwards, or slantingly, to diminish so far the pressure of the
liquid, or may be carried along horizontally, so as to diminish it
still further or eliminate it entirely, as in fig. 2, — the tube
with the scale of degrees thus resembling so far the common
register-thermometer (and if it should be necessary to prevent
the liquids flowing onwards, though I hardly think it will when
the tube is fine enough, we may have a short plug or cylinder
close to the surface of the liquid, just as in the thermometer
alluded to).

Fig. 3 represents a plan (which will be found to answer well
enough without resorting to an additional reservoir and its accom-
paniment, just described) to prevent the mixture of the register-
liquid with the sensitive liquid ; and which is quite necessary
where oil is the fluid used for the former, as otherwise it would
come to the top of the sensitive liquid, instead of lying at the
bottom in contact with, and ready to be forced up, the register-
tube, as a heavier fluid might do. In fig. 3 the scale is most
conveniently attached to, and the registry made by, the side of
the tube next the reservoir; and the superfluous register-liquid,
as it is driven onwards, may then be allowed to flow out at the end
of the tube, which may be turned down so as to prevent its accu-
mulating in a column above, and acting by its pressure ; to get
rid of which source of error and of diminished sensitiveness, we
may mention (adhering still to the same general system of registry
by production of gas) two other plans. They are, first, the sub-
stitution (in an upright or other tube) of a solid, closely-fitting
cylindrical piston * for the varying column of the register-liquid
(the piston having, it may be, a little oil or other liquid above it
to show that there is no leakage of gas). Such a piston (or we
may call it a cylindrical plug, as it does not necessarily have any
rod attached to it), being constant and uniform in its height and
resistance, will, if well fitted and running smoothly, give a uni-
form resistance, and consequently be an accurate index of the
amount of gas liberated. If in a glass tube, it will (even with

apparatus is in proportion to the size of the sensitive reservoir and the bulk
of its liquid exposed to sunshine. A good plan of facilitating the regular
rising of the liberated carbonic acid, is to put a little sand or broken glass
(of a given weight) into the sensitive liquid before solarization.

* Say of some very light material, as pith, cork, gutta-percha, india-
rubber, to diminish resistance to the pressure of gas, especially when the
tube is upright.

Mr. C. J. Burnett on several Forms of Actinometer. 53

the film of oil above it) be as convenient for photographic registry
as the column of liquid was ; and if in a metal one, photographic
(or other) registry might be carried out by the intervention of a
piston-rod and other easily contrived apparatus attached, or by
attaching an upright glass tube with a column of liquid, to the
top of the metal one ; and such a column of liquid, being not
fluctuating in height like those in our earlier-described forms,
but of one constant height, will give a correct register, as far as
absence of unequal pressure goes. (This suggestion of a metal
tube with a glass one over it, is made in case it should be found
difficult to fit the glass tube sufficiently well to the piston.)

The second plan is the making our register (photographic, or
simply visible) dependent on the loss of weight experienced by
the gas-evolving liquid, the vessel containing the sensitive liquid
being either balanced by a delicate spring, or by a system of
leverage, on some plan allied to the steel-yard principle; or
else, and probably better, the vessel containing the sensitive
liquid is made to float at a fixed height (when charged) in
or above the surface of water or other liquid in a suitably- shaped
vessel, and the loss of weight, and consequently the amount of
actinic influence exerted, is measured by the height to which,
or rapidity with which, it rises after exposure or during exposure
to light. This form of apparatus has a considerable resemblance
to some of the hydrometers. The apparatus may of course be
arranged either so as to leave the sensitive-liquid-containing
vessel below, or so as to keep it above the liquid. Above should
have the advantage in the sensitiveness of the apparatus, by not
losing so much light by absorption; while under has the ad-
vantage of enabling us to have our thermometer in the water
close beside it, and so either to register the temperature, if we
wish, on the same sheet of paper on which the actinism is regis-
tered, or else to maintain the temperature of the sensitive liquid
uniform* by letting a constant flow of cold water pass through
the water vessel ; or rather, to prevent shakings and disturbance
of the registry, we may have the sensitive (-liquid) vessel, with
its connexions, protected from disturbance by the motion of the
current of cold water by an immediately surrounding glass vessel
or thin tube. The immersion of the sensitive vessel would also
be convenient, as enabling us to make many interesting obser-
vations connected with resistance offered to actinic rays, or mo-
difying effects produced on them, either by variously coloured, or
by colourless, liquids of various compositions, as solutions of

* A set of observations with the sensitive vessel at different temperatures
would be in many ways likely to lead to interesting results, and could pro-
bably be easily managed by regulating the heat of the current passed round
the sensitive vessel.

54 Mr. C. J. Burnett on several Forms of Actinometer.

vegetable and mineral salts, &c., fluorescent and non-fluorescent,
variously polarizing and non-polarizing, &c. Such observations
might also probably give interesting results as connected with
substances of one composition, but differing allotropically. Using
various liquids in this way, we should, however, of course require
to make allowance for the effects of differing specific gravities,
either in reading or in translating the observations, or otherwise*.

As to the precise form of this apparatus and mode of register-
ing, whether photographic or other, the principles once explained,
it would be occupying space to perhaps no great purpose to
enter into pretty obvious details and variations. If the sensitive-
liquid reservoir, if below the water (or the float attached to it, if
above), has attached to it a descending rod which fits into, and is
held perpendicular by, a ring or rings, and if another rod attached
to the float or sensitive-liquid vessel above the water is similarly
kept in its upright position by similar rings, it is obvious that
the upper rod affords very convenient means of registry, either
by having the scale on itself, with a marker pointing to it attached
to the side of the outer vessel or other fixed object, or by making
it cany the marker (in this case a shifting one) and making the
scale attached to the outer vessel (or otherwise) fixed and steady.
As to the adaptation of photographic self-registry on sheets or
slips of sensitive paper, I need hardly say that the upper rod is
capable of performing here exactly the same part which the
column of mercury, oil, or other register-liquid performs in the
earlier-described apparatus.

With regard to all the apparatus described, it would be in
most cases, especially where used for protracted observation,
advisable to have them kept in one angle, as regards the sun, by
some sort of heliostat. It might, however, be found practicable
in consecutive, independent, and even perhaps in continuous
observations, to avoid the necessity of this by having the sen-
sitive vessel, or that part of it which is exposed to the rays, of a
globular form, so as to make their incidence similar at all hours.
In this case, however, it must be observed that the part exposed
to the rays must be filled with liquid ; otherwise, however simi-
larly they might fall on the surface of the glass, we should still
have them impinging at varying angles on the plane upper sur-
face of the contained sensitive liquid. Where the weight and
floatation-system is employed, this plan is not quite so conve-

* We might avoid this, or the necessity for other scales, simply by adding
to, or deducting from, the weight of the sensitive fluid and its reservoir till
it floats or sinks to the same depth in the liquid to be experimented on as
it does in water. This will be conveniently managed by having a little cup
attachable to some part of the floating apparatus, into which we may put
more or less sand, removing or adding it till the apparatus floats at the
proper line marked on or by it.

Mr. C. J. Burnett on several Forms of Actinometer. 55

nient j but if we estimate the weight in any other way, the dif-
ficulty disappears.

With regard to all these modes of registry by gas-evolution
now described, there are two material deficiencies, at all events as
applied to continuous self-registry. The first is the constant
diminution of sensitiveness of the apparatus, consequent on the
diminishing quantity of the decomposable salt or salts left in the
liquid ; and this (though the inconvenience might possibly be to
some extent diminished by using a very large quantity of solu-
tion with only a small portion of it exposed to the light, and
arranged so as to secure a circulation of liquid, or by having a
supply of a concentrated solution of the salt or salts gradually
admitted, and there are also other possible contrivances), toge-
ther with the uncertainties about the influence of absorbed light
at the beginning of, and after withdrawal from, solarization,
about absorbed gas at the beginning of solarization, and about
so-called catalytic influence, or the impulse which changing par-
ticles give to others, renders it necessary to speak cautiously
about the value of at least continuous observations with one and
the same portion of liquid, till careful experiment has shown
what sort of results are attainable.

As to repeated observations with successive and fresh portions
of liquid, we can of course feel much more confident of valuable
results, — photographic or other self-registry, if desired here, how-
ever, necessitating the recourse to rather more complex apparatus.

In my old paper, the salts recommended for forming the sen-
sitive solution were those of ferric and uranic oxide, — the binoxa-
late, ammonio-oxalate, and soda-oxalate of ferric oxide, and the
binoxalate of uranic oxide being especially suitable. For conve-
nience, I tried also the mixture of some of the more generally
accessible salts, as uranic nitrate, or iron-alum, with oxalic acid or
binoxalates*. Some of my other experiments were with solu-
tions of chromic acid, or bichromate of ammonia, soda, or potash,
along with oxalic acid, or one of its acid or neutral salts. Citric,
tartaric, and other vegetable acids were tried instead of oxalic,
but they seemed in many cases to be much acted on even in the
dark. Solutions of brown oxide of manganese in tartaric, citric,
and, still far more, in oxalic salts were liable to the same objection,
as well as to that of uncertainty as to strength. A solution of
permanganate of potash along with one of these vegetable acids
or of its salts (or ammoniacal saltsf ?), however, seems not alto-
gether so unpromising {.

* The presence of an excess of oxalic or other acid is perhaps useful,
t Nitrogen being liberated.

t Solutions of ferric salts containing citric, tartaric, or other vegetable
acids, rendered alkaline by ammonia, and with the iron held in solution,

56 Mr. C. J. Burnett on several Forms of Actinometer.

We now come to the paper actinometer ; which offers the very
great advantage that the sensitive substance and the registering
material are one and the same. Nothing, in fact, can well be
simpler than the apparatus. The sensitive paper, ruled with lines
to correspond with the seconds and minutes and hours, hours,
days, and weeks, weeks and months, or whatever other intervals
are to be observed, is made by clockwork to pass (either firmly
fixed and revolving on one roller of large diameter, or otherwise)
behind a hole or slit which admits the light, the intensity of
which will be of course registered by the differing degree to
which the different parts of the paper are affected by it*.

The main difficulties attending this system of actinometry are,
1st, the difficulty of securing uniform sensitiveness in the same, and
still more in different samples of paper, even when similarly sen-
sitized ; 2nd, corresponding uncertainties in development, where
development-processes are used ; 3rd, the difficulty of keeping
paper unaltered in its sensitive condition, and this both before
and after the solarization (as we may wish to develope several
sheets at once, to be sure that the developer acts alike on them) ;
and 4th, the difficulty of different papers being differently acted
on by the fixing solutions. Still all these difficulties may to a
great extent be got over by care and proper contrivances in the
selecting, sensitizing, drying, and development of papers, cutting
off parts near the edge, and using for each observation, not one
single slip, but several, say two or three, cut either from differ-
ent sheets or different parts of the same sheet, or, if from origi-
nally contiguous parts, with the sides (not the surfaces of the
paper) of one of them reversed, so that the original right-hand
of the one slip, or its top part, corresponds to, and is, when in the
actinometer ,in contact with, or juxtaposition to, what was originally
the left-hand side of the other slip, or the lower part of it, if they
were cut from top to bottom of the sensitive sheet.

As to the third source of difficulty attending this variety of
actinometer (for in the others, where the paper is only the regis-
tering machine, the exact depth of tint produced is of no moment,
the direction or curve of its line being all that is required), there
would appear to be modes of sensitizing the silver papers which
give a much better paper as regards keeping than others. It

showed little action. The addition of a neutral chromate, however, made
them much more sensitive ; and after this addition they were found capable
of yielding very sensitive photographic papers, giving good impressions,
capable also of further development by silver-salts, metal -cyanogen salts, &c.
* To eliminate possible action of actinism held in solution by the air or
other actions of the air, it might be well to compare the record of the in-
strument when the paper in the solarization-slit is open to the air, with the
action when it is protected by a thin scale of glass. This comparison might
possibly lead to very interesting results.

Mr. C.J. Burnett on several Forms of Actinometer. 57

may be generally observed that, using the ordinary style of papers,
the best plan, where the paper is intended for a long observation,
is not to use development, and not to make it too highly sensi-
tive, also to sensitize it as if it were a very weak paper for the
ordinary positive printing. Where, however, it is intended for
registry of seconds or minutes, we must use a more highly sen-
sitive printing-paper, or have recourse to an after-development of
it ; and it is here also, when we wish to have sets of successive
observations made from slips cut from one sensitive sheet (to en-
sure uniform value of colour), that our difficulty is felt.

Suppose we have two, three, or four slips, each one repre-
senting, say, a different hour with the variations during it*.
Here there may be no very great difficulty in one way, as sup-
posing the hours successive, there is hardly time for the paper to
go far wrong ; but suppose they are successive days instead, we
see the relative value of the periods on each day, but are at a
loss to estimate their value compared with another day. The
simplest plan which suggests itself is to check the value of the
hour observations by day observations, of the day observations by
week observations, and so on, — the observations of the longer
periods being made, as they conveniently can be, on much weaker
and consequently much better-keeping paper; and these dif-
ferent sets of observations will enable us to eliminate not
only errors produced by the sensitive paper going wrong by
keeping, but original differences in the quality of the papers
before sensitizing, as well as in the chemicals, and, what with all
care is most difficult to avoid, in the manipulation and in the
weather.

As to the fourth difficulty (that connected with the inequality
in fixing), with all care and study of time, and keeping the liquid
in motion, it is a serious one ; for, though we may secure pretty
uniform action by these precautions and by study of strength
and temperature in the case of one piece of paper, yet in the
case of comparisons between different papers we must trust a
good deal to the system of mutual checks (as of day papers or
hour papers, &c), as is to be explained.

Another plan, however, is, to be satisfied with a less perfect
fixing, which will do well enough to engrave from, or copy in
China ink, or to print from by a negative process, or to make a
negative from in the camera.

For some of our registers by the Papyro- actinometer, the
gradually and uniformly progressive motion behind the solariza-
tion-slit may be the best ; but for others a motion by jerks,

* Or, as formerly described, we may and should have two or more slips
(say reversed, as described, for each hour) ; but we have left this out for
simplicity in the explanation.

58 Mr. C. J. Burnett on several Forms of Actinometer.

with still intervals between, might be preferable ; and this latter
plan would give us, in different registers, the average of each
second in the minute, each minute in the hour, hour in the day,
day in the week or month, and so on, — the average or mean, as
compared with other days on the same week's or month's regis-
try-slip, giving us at once the true value of the depth of tint in
the whole and every part of that day's own separate registry,
and so giving it a real utility which, taken by itself and without
being thus brought to the test, it could never have had ; and (on
the same principle) so on with week-, month-, and, it may be,
year-register papers. It must be allowed, with all their recom-
mendations, that it would be desirable to get papers which would
keep better than the ordinary silver ones, and which would
suffer less in fixing.

As long ago as 1857* I called attention to the probable
value, both for actinometry and for all other self-acting scien-
tific registry by time, of papers prepared with the salts of
ferric and uranic oxides. I had then, as I remarked, found
them to retain their properties unimpaired for between one and
two years, and I have since found them good when four years
old. This ought to save a good deal of labour, by enabling us
to prepare at once and keep ready a large stock of them. I am
not, however, prepared to state what their relative advantages as
compared with silver papers are, as regards keeping after
solarization and before development. The development is, I
think, more uniform in its results than that of the silver papers,
being performed with nitrate of silver alone. The time of keep-
ing without a material change after solarization (or the amount
of change) would require to be more minutely examined before I
could speak veiy positively as to the advantage of their applica-
tion to the papyro-actinometer ; but for the paper-registry of
the gas-evolving actinometers, whether gauged by floating or
by fluid columns, as well as for self-registry of thermometers,
barometers, anemometers, &c, there can be, I think, little room
to doubt that these papers will be found particularly convenient.

It is perhaps hardly necessary to remark that one clock, or other
moving power, may of course be made to move all the different
time-registries we have recommended, each one at its own proper
rate.

A very convenient arrangement for a set of paper-slips would
be to have one a continuously moving slip ; the second one
moving by sudden jerks, taking place every minute or every five
minutes, and so giving the average of, say each minute or five
minutes ; the third a similarly jerked slip, giving the average
or mean for each hour ; and the fourth (say a week- or month-
* Even in 1855 I alluded to the possibility of their availability.

Mr. C. J. Burnett on several Forms of Actinometer. 59

long slip) giving the average or mean for each day of twelve or
twenty -four hours*.

In conclusion, I would call attention to the great importance
of carrying on a system of actinic registry coupled with simul-
taneous observations of other kinds, including ozone observations
(though I believe there is much uncertainty as yet attached to
the latter f), (1) in various latitudes, and with reference to the

* Divisions by tens instead of twelve, might in some respects be pre-
ferable, and sets of slips might conveniently, for several reasons, be all of
one length ; among other advantages of this uniformity, we could use the
same papers for all. An interesting set of observations would be on the
actinisms before and after sunset, and on the effects of moonlight (and,
query, starlight ?) ; but then we should require either to observe the effect of
longish periods, or to employ very sensitive papers, or daguerreotype, or
else to concentrate the rays on the solarization-slit by a powerful lens.
As to the probable superiority of either mode of estimating actinism, i. e.
by the amount of its action on sensitive paper, or by that on sensitive
liquids (or, it may be, on gases, such as carbonic oxide, and chlorine, &c),
their relative advantages will probably be found to vary considerably ac-
cording to varying circumstances. For a continuous observation there are
certainly (unless we use more complicated apparatus) some apparent ad-
vantages attending the estimation by sensitive paper alone ; and in many
cases it might be found possible to preserve a tolerably accurate record of
the relative depths of tint produced (without the trouble and risk attendant
on keeping, hypo-fixing, and printing from the impressed papers), by pro-
viding ourselves with a scale of permanently tinted paper, ivory, or other
material representing a great variety of depth of tint gradually increasing
from one end of the scale to the other, and each depth of tint being marked
with a number, 1, 2, 3, 4, &c. We should only (after some slight and tem-
porary fixing process, sufficient to prevent rapid action of light during com-
parison) require to shift each part of the actinized paper along the scale till
we came to a part corresponding to it in depth of tint, and then record the
number (1, 2, 3, or others) which represents it. There is, however, a diffi-
culty attending this plan — that the colour of the actinized paper may turn
out to be different from that of the tints on our scale, so that it may not
be found easy to say what is the depth of tint corresponding. This diffi-
culty, however, might be met or obviated in various ways. 1. By having
several similar scales of different colours, such colours being the same as
those which our sensitive paper is found liable to assume. 2. By employing
such photographic papers, &c. (developments if necessary), whether argen-
tine, ferric, uranic, chromic, or others, as are least liable to vary in colour,
either when used on different occasions or on one occasion in the one slip,
according to strength of actinism. 3. By making even our one scale vary
to a certain extent in the nature of the colour, as well as in depth of it, if
the difficulty just alluded to in connexion with this should still be found
troublesome. My impression, however, is that there are photographic
papers which will be found to colour so uniformly as to render this varia-
tion on our scale unnecessary.

t How, for instance, can we distinguish between the effects of loosely
absorbed actinism and ozone ? and how are we sure that the actions of the
tests themselves may not produce it, and more rapidly in certain states of
the air than in others ?

GO Mr. C. J. Burnett on several Forms of Actinometer.

corresponding latitude in the two hemispheres ; (2) in countries
in the same latitude but differing in climate, e. g. in America and
in Europe, and generally on the opposite sides of continents,
and on sea contrasted with land j at sea in the trade- wind belt
and in the variables, &c. ; in our own country, on the west
coast as contrasted with the east ; on the sea coast, and inland ;
amidst vegetable life, and away from it, and the latter especially as
connected with the disease known as " hay fever/' possibly pro-
duced by the abundance of ozone or some imponderable, or wave-
power, disengaged by vegetation during what we may call the
phytolysis* of carbonic acid — the supposition of such injurious
effect, on persons exceptionally constituted, of allotropic oxygen
or some unrecognized wave-power or imponderable or other
agent disengaged or produced by vegetation being no way in-
consistent with the belief that this same liberation or production
is, in general, importantly or essentially conducive to the puri-
fication and salubrity both of our own atmosphere and of that
watery one in which organic impurities would have a still greater
tendency to accumulate; (3) at different elevations in the same
latitude and country, either on mountains or, occasionally, in
balloons.

Such observations would be likely f to help us to a somewhat
less utterly hazy idea than what we have as to what constitutes
climate, and what is the nature of its action on vegetable, and
what on animal life. Why does a plant or animal thrive in one
country and languish or die in another, where there are not
sufficient differences of soil, moisture, or temperature to account
for the difference between life and death, luxuriance or lan-
guishing ?

* Phytactinolysis would be unnecessarily clumsy, and actinolysis I
would reserve for the numerous cases where actinism acts without the pre-
sence or aid of vegetable or other life.

t There are many other considerations, however (as to probable actions
of soil, &c. on the air), to be taken into account. Is the very remarkable
and well-ascertained difference in sanitary properties between the air of the
Egyptian valley and that of the immediately adjoining portions of the desert
in any degree owing to this, or to the effect of vegetation ? It would seem,
also, in the absence of any other probable cause yet given, deserving of
investigation whether the remarkable properties of the well-known desert
simoom may not be owing to allotropic action, to wave-powers, or impon-
derables connected either with chemical actions, or with friction between
the sand and the air at certain temperatures : and why may not other in-
fluential powers as well as heat, light, and electricity be disengaged by
the friction of bodies? and why may not the necessary accompaniments
and circumstances be as peculiar as they often are with relative electricity ?

[ 61 j

VI. Notices respecting New Books.

Arithmetic in Theory and Practice for advanced Pupils. Part the
First. By J. Brook Smith, M.A. London: Macmillan and
Co. 1860.

ALTHOUGH Mr. Smith's arithmetic can scarcely be said to meet
any urgent demand, inasmuch as we already possess several ex-
cellent works of the same kind, it deserves to take its place amongst the
small number of sound educational works. The first part, the only one
yet published, contains a lucid and correct exposition of the prin-
ciples of numeration, addition, subtraction, multiplication, and divi-
sion, of the theories of the greatest common measure and least
common multiple, and of some of the more elementary properties
of numbers with respect to their divisibility.

In such a treatise we do not, of course, expect to find new matter ;
our demands are limited to a few necessary qualities, such as clear-
ness, precision, conciseness, good arrangement of the several parts,
and at least so much originality in the general treatment of the sub-
ject as is necessary to support the book's claim to a separate existence.
With respect to the two first of these qualities, this treatise has far more
than average merits; in the third quality it does not excel so much,
for the numerous theorems scattered throughout the book might, we
think, have been better " welded " together. In point of arrange-
ment there is much merit and some originality, a greater space than
usual having been devoted to the very useful and interesting sub-
jects of the criteria of the divisibility of numbers and of their decom-
position into prime factors.

With respect to general treatment, one of the author's chief objects
has been to render his demonstrations purely arithmetical. To do
so he has been induced to discard all symbols and to conduct his proofs
by means of particular numbers, striving always to make the general
law apparent in the particular example. In so'me cases, and for
young pupils especially, this method has its advantages, but in
other cases it is clumsy and open to suspicion. Mr. Smith appears
to have mistaken a little the true character of an arithmetical, as
distinguished from an algebraical proof ; he must admit that symbols
may be introduced without interfering in the least with the purity or
the strictly arithmetical character of the reasoning. Thus used,
symbols are merely representatives of the subjects (numbers) dis-
cussed ; no material diminution in the length of the proof is produced
by their introduction, but the latter gains in elegance, in generality,
and sometimes even in simplicity. Some of the author's proofs might,
we think, have been improved in this manner.

Mr. Smith professes to write for advanced pupils, but in all pro-
bability his work will find the greatest number of readers amongst
junior masters, the advanced pupils of our schools being in general
too much occupied in breaking new ground to be able to return and
inquire so closely into the principles upon which the very rudiments
of their science is based. To the junior master, however, this re-
examination is absolutely indispensable : he has to launch the young
intellect entrusted to his care into the wide ocean of mathematics,

62 Notices respecting New Books,

where at the very outset there are numerous shoals and reefs to be
carefully avoided, and the success of the voyage depends greatly upon
the manner in which it is commenced. To junior masters and pupil-
teachers, therefore, Mr. Smith's book will be both acceptable and
valuable : alone it will by no means fit them for their duties, but as
a guide in the preparation of their own lessons it may be of great
utility.

Of Motion. An Elementary Treatise by John Robert Lunn, M.A.,
Fellow and Lady Sadleir's Lecturer of St. John's College. Cam-
bridge: Deighton, Bell and Co. 1859.

Mr. Lunn, in his Preface, says, — " My object in the following
pages has been to put forth the principles of the science of motion
in their true geometrical form, postponing the consideration of
force (the properties of which are presumed to have been fully inves-
tigated in statics) until the reader may be able to separate in his
mind the geometrical ideas from the mechanical. To the fact that
these ideas are not kept separate at the outset, I apprehend that the
want of clearness in the student's mind about the real investigation
that does take place in any case may be attributed."

We very much doubt whether the difficulties encountered by those
who are commencing the study of dynamics are — to any great ex-
tent— assignable to the cause here alleged. Nor do we understand
how " the properties of force " can be " presumed to have been fully
investigated in statics," — seeing that in " statics " only some of the
properties of force, and those the least important, are investigated.
Nevertheless we doubt not that Mr. Lunn's mode of treating the
subject will be useful to some readers, whilst his numerous problems
and their solutions will certainly be so to all.

A Treatise on the Calculus of Finite Differences. By George Boole,
D.C.L., Professor of Mathematics in the Queens University,
Ireland. Cambridge : Macmillan and Co. 1860.
A Treatise on Attractions, Laplace's Functions, and the Figure of the
Earth. By John H. Pratt, M.A., Archdeacon of Calcutta. Cam-
bridge : Macmillan and Co. 1860.

The name and character of Professor Boole are too well known
to our mathematical readers to render it necessary for us to do more
than announce this new work of his ■ On the Calculus of Finite
Differences.' As an original book by one of the first mathematicians
of the age, it is out of all comparison with the mere second-hand
compilations which have hitherto been alone accessible to the
student. We heartily wish that our elementary books on mathe-
matics were more frequently written by men of the rank of Prof.
Boole, instead of being left to mere book-makers.

The work of Archdeacon Pratt " is in part a republication of those
portions of" his " work on ■ Mechanical Philosophy ' which treat of
Attractions, Laplace's Functions, and the Figure of the Earth ; " but
very greatly enlarged and improved. The reader will find new and
interesting matter, both in the purely analytical portion and in the
physical applications. " It has been my endeavour," says the author,
" to put the well-known difficulty in Laplace's analysis, arising from

Royal Society, 63

the use of a discontinuous function, in the clearest light, that the
student may understand both what it is and how it is overcome.
.... I have also introduced some propositions on the geodetic
method of determining the Figure of the Earth, suggested by an
acquaintance with the circumstances of the Great Trigonometrical
Survey of India, and by the volume of the Ordnance Survey of
Great Britain and Ireland recently published by Lieut. -Colonel
James, R.E., Superintendent of the Ordnance Survey." The re-
searches of Mr. Hopkins and Professors Hennessy and Haughton
are also referred to. . As a specimen of some of the calculations in
this volume, interesting to the general reader, we may cite the
following: — "The increase in height of the sea-level at Karachi
above that at Cape Comorin, arising from the drawing of the waters
northwards by the Himmalayas, and in consequence of the deficiency
of attraction of the ocean =643 feet."

VII. Proceedings of Learned Societies.

ROYAL SOCIETY.
[Continued from vol. xix. p. 467.]
December 22, 1859. — Sir Benjamin C. Brodie, Bart., President,
in the Chair.

THE following communications were read : —
" On the Electric Conducting Power of Alloys." By A. Mat-
thiessen, Ph.D.

In this paper I have given the determinations of the electric con-
ducting power of upwards of 200 alloys, and have found that the
metals employed may be divided into two classes, viz. —

A. Those metals which, when alloyed with each other, conduct
electricity in the ratio of their relative volumes.

B. Those metals which, when alloyed with one of class A, or with
each other, do not conduct electricity in the ratio of their relative
volumes, but always less.

The alloys may be divided into three groups ; viz. —

1 . Those made of the metals of class A with each other.

2. Those made of the metals of class A with those of class B.

3. Those made of the metals of class B with each other.

From the experiments described in the paper I have tried to deduce
the nature of alloys, and have arrived at the following conclusions : —

A. That most alloys are only a solution of one metal in the other ;
for, —

1. On looking at the curves belonging to the different groups, we
see that each group of alloys has a curve of a distinct and separate form.
Thus for the first we have nearly straight lines ; for the second, the
conducting power decreases always rapidly on the side of the metal
belonging to class B, and then turning, goes almost in a straight
line to the metal belonging to class A ; for the third group we find a
rapid decrement on both sides of the curve, and the turning-points
united by almost a straight line.

2. On examining that part of the curve where the rapid decrement

64 Royal Society : —

takes place, we find that with the lead and tin alloys it generally
requires twice as many volumes of the former as of the latter to
reduce a metal of class B to a certain conducting power.

3. That the turning-points of these curves are not chemical com-
binations we may assume from the fact that they only contain very
small per-centages of the one metal.

4. That the alloys at the turning-points have their calculated
specific gravities.

5. From the similarity of the curves of the conducting power of
alloys, where we may assume we have only a solution of one metal
in the other, we may always draw approximatively the curve of the
alloys of any two metals if we know to which class they belong.

B. That some alloys are chemical combinations ; for —

1. At the turning-points of the curve we generally find contraction
or expansion.

2. We have no regular form of curve, so that we cannot a priori
approximatively draw it.

3. At the turning-points of the curve, the alloy retains large per-
centages of each metal.

4. The appearance (crystalline form, &c.) of the alloys at these
points is different from each other.

C. That some alloys are only mechanical mixtures ; for example,
bismuth-zinc, lead-zinc, some silver- copper alloys, &c.

The question now arises, To what is the rapid decrement of the
conducting power of the metals belonging to class B, when alloyed
with other metals, due 1

The only answer I can at present give to this question is, that
most of their other physical properties are altered in a like manner ;
for where we find no marked change in most of the physical pro-
perties, as in group I, and in the second group on the one side of
the curve, then we have nearly their calculated conducting powers.

In the Appendix I have given some determinations of the con-
ducting power of pure gold, which I find has a higher value than
that generally quoted.

In conclusion, I may take this opportunity of thanking Dr. M.
Holzmann for the excellent manner in which he has carried out the
greater part of the experiments.

" On an extended Form of the Index Symbol in the Calculus of
Operations." By William Spottiswoode, Esq., M.A., F.R.S.

" Problem on the Divisibility of Numbers." By Francis Ele-
fanti, Esq.

" On the Structure of the Chorda Dorsalis of the Plagiostomes and
some other fishes, and on the relation of its proper Sheath to the
development of the Vertebrae." By Professor Albert Kolliker.

" Remarks on the late Storms of October 25-26 and November 1,
1859." By Rear- Admiral FitzRoy, F.R.S.

As many of our Society must doubtless be interested in the nature
and character of that storm in which the * Royal Charter ' went to

Rear- Admiral FitzRoy on the Storms of Oct. and Nov. 1859. 65

pieces on Anglesea Island, and as abundant information has been
obtained from Lighthouses, Observatories, and numerous private
observers, I would take this earliest opportunity of stating that the
combined results of observations prove the storm of October 25th
and 26th to have been a complete horizontal cyclone.

Travelling bodily northward, the area of its sweep being scarcely
300 miles in diameter, its influence affected only the breadth of our
own Islands (exclusive of the west of Ireland) and the coast of France.

While the central portion was advancing northward, not uniformly
but at an average rate of about twenty miles an hour, the actual
velocity of the wind — circling (as against watch-hands) around a
small central " lull " — was from forty to nearly eighty miles an hour.

At places north-westward of its centre, the wind appeared to
"back" or "retrograde," shifting from east through north-east,
and north to north-west ; while at places eastward of its central
passage, the apparent change, or veering, was from east, through
south-east, south, south-west, and west.

Our Channel squadron, not far from the Eddystone, experienced
a rapid, indeed almost a sudden shift of the wind from south-east to
north-west, being at the time in, or near, the central lull ; while, so
near as at Guernsey, the wind veered round by south, regularly,
without any lull. This sudden shift off the Eddystone occurred at
about three (or soon after), and at nearly half-past five it took place
near Reigate, westward of which the central lull passed.

From this south-eastern part of England, the central portion of
the storm moved northward and eastward. Places on the east and
north coasts of Scotland had strong easterly or northerly gales a
day nearly later than the middle of England. When the ' Royal
Charter ' was wrecked, Aberdeen and Banffshire were not disturbed
by wind ; but when it blew hardest, from east to north, on that
exposed coast, the storm had abated or almost ceased in the Channel
and on the south coast of Ireland.

Further details would be ill-timed now, but they will be given in
a paper to the Royal Society, as soon as additional observations
from the Continent, and from ships at sea, have been collected and
duly combined with other records.

The storm of the 31st, and 1st of November, was similar in
character ; but its central part passed just to the west of Ireland's
south-west coast, and thence north-eastward.

Of both these gales the barometer and thermometer, besides other
things, gave ample warning ; and telegraphic notice might have been
given in sufficient time from the southern ports to those of the
eastern and northern coasts of our Islands.

As it is the north-west half of the cyclone (from north-east to
south-west, true) which is influenced chiefly by the cold, dry, heavy,
and positively electrified polar atmospheric current, and the south-
west half that shows effects of equatorial streams of air — warm,
moist, light, and negatively electrified ; — places over which one part
of a cyclone passes are affected differently from others which are
traversed by another part of the very same meteor, or atmospheric

Phil. Mag. S. 4. Vol. 20. No. 130. July 1860. . F

66 Royal Society : —

eddy, the eddy itself being caused by the meeting of very extensive
bodies of air, moving in nearly, but not exactly opposite directions,
one of which gradually overpowers, or combines with the other, after
the rotation.

On the polar half of the cyclone, continually supplied from that
side, the visible effect is a drying up and clearing of the air, with a
rising barometer and falling thermometer ; while on the equatorial
side, overpowering quantities of warm moist air — rushing from
comparatively inexhaustible tropical supplies — push towards the
north-east as long as their impetus lasts (however originated), and
are successively chilled, dried, and intermingled with the always
resisting, though at first recoiling, polar current. After such
struggles these two currents unite in a varying intermediate state
and direction, one or other prevailing gradually.

Very plain and practical conclusions are deducible from these
considerations : —

One, and the most important, is that in a gale which seems likely
to be near the central part of a storm, that should be (of course)
avoided by a ship which has sea room : a seaman, facing the wind,
knows that the centre is on his right hand in the northern hemisphere,
on his left in the southern ; he therefore is informed how to steer.

Another valuable result is that telegraphic communication can
give notice of a storm's approach, to places then some hundred miles
distant, and not otherwise forewarned.

Jan. 12, 1860. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.

The following communications were read : —

" Notes of Researches on the Poly ammonias.'' — No. VII. On
the Diatomic Ammonias. By A. W. Hofmann, LL.D., F.R.S.

In continuing my inquiries into the nature of the organic bases,
I was led in the commencement of the year 1858 to repeat some
experiments on the action of dibromide of ethylene upon ammonia,
which M. Cloez* had published in 1853. The repetition of these ex-
periments compelled me to contest not only the formulae of M. Cloez,
but also the general interpretation which he had given to his results.

I have not hesitated to communicate my conclusions to the Royal
Society-)*.

M. Cloez J shortly afterwards discussed my observations, and
pointed out the arguments which induced him to maintain his
formulae and his interpretations.

I have not replied to these remarks. M. Cloez having stated in
the same note that he was still engaged with his experiments and
that his inquiry was nearly completed, I discontinued my experi-
ments on the action of dibromide of ethylene upon ammonia, fully
persuaded that the chemist, to whom we are indebted for the first
observation of this reaction, in continuing his experiments would
arrive at the same results which I had myself obtained.

In discontinuing the discussion with M. Cloez, I was not freed
from the obligation of proving the general thesis of my note, viz.
* L'Institut, 1853, p. 213. f Phil. Mag. vol. xvi. p. 309.

\ Comptes Rendus, xlvi. p. 255.

Dr. Hofmann on the Diatomic Ammonias. 67

the formation of diatomic bases by the action of diatomic bromides
on ammonia. I have given the proof in several communications*
addressed during the last two years to the Royal Society, and
especially in a notef describing some new derivatives of phenylamine
and ethylamine published during last summer. The formation of
these bodies, their analysis and their transformations, have, I believe,
settled the question at issue in a satisfactory manner.

These researches have been the subject of some remarks on the
part of M. Cloez|, from which it appears that this chemist has
interpreted my silence as a tacit admission of defeat ; he rejects the
formulae which I have given for the diatomic derivatives of phenyl-
amine and ethylamine, and blames me for having continued my
researches on the diatomic bases without having previously replied
to his observations.

Under these circumstances I have been compelled to resume the
investigation of the action of dibromide of ethylene upon ammonia,
and to reply, after nearly two years have elapsed without M. Cloez's
paper having been published, to the series of objections which this
chemist has raised against the theory of the diatomic bases.

Since this continuation of my experiments throws considerable
light upon this new class of compounds, I beg leave to submit them
to the judgment of the Royal Society.

In order to render more intelligible the line of argument which
M. Cloez has brought forward against the diatomic notions, it will
be useful to recapitulate in two words the subject of our controversy.

M. Cloez admits that in the action of dibromide of ethylene upon
ammonia, the molecule of ethylene splits into radicals belonging to
three distinct groups, viz. the formic, acetic, and propionic series ;
these radicals acting upon one molecule of ammonia, in which each
of them replaces one equivalent of hydrogen, give rise to the forma-
tion of three primary monamines, viz. Formenamine, Acetenamine,
and Propenamine.

According to the view which I defend, the molecule of ethylene
remains intact in the reaction, acting upon two molecules of ammonia
in which 2, 4, or 6 equivalents of hydrogen are replaced respectively
by 1, 2, or 3 diatomic molecules of ethylene; the dibromide of
ethylene gives rise to the formation of three diamines belonging to
the same family, a primary, a secondary, and a tertiary diamine.

Expressed in formulae the two views may thus be represented : —

Formula of M. Cloez. „

Formenamine C2 H3 N= H \ N.

H J
C4H3]
Acetenamine C4 H5 N= H \ N.

H J

Propenamine C6 H7 N= H \ N.

H J
* Phil. Mag. vol. xvii. pp. 66, 133 ; xviii. p. 148. f Ibid. vol. xix. p. 232.
% L'Institut, 1859, p. 233.

F2

68 Royal Society : —

Formula of Dr. Ilofmann.

(C.H,)"
Ethylene-diamine .... C4 H8 N2= H2 [► Na.

(C H V
Diethylene-diamine .. C8 H10Na=(C4H4)'' j-

(C H V
Triethylene-diamine . . C12 H12 N2= (C4 H*)" }> N2.

(C4H4)"

It was by careful examination of the physical properties of the
bases under consideration, and more especially by the absence of
simple equations capable of explaining the formation of the first and
of the thirdjterms of the series, that I had first been led to doubt the
correctness of M. Cloez' s formulae ; but I would not have expressed
this doubt, if, on repeating the analysis of the first base, of formen-
amine, the slightest doubt on the subject had remained in my mind.
I did not at the time investigate the two other bases, and I limited
myself to stating that the constitution of these bodies would probably
be found analogous to that which I had experimentally established
for the first term of the series.

Let us now examine the objections which M. Cloez has brought
forward against my argument. "According to the hypothesis of
M. Hofmann," says he, " the action of ammonia on the chlorinated
and brominated hydrocarbons cannot give rise to the formation of
chloride or bromide of ammonium ; the reaction consists simply in a
combination of the two substances, without the separation of a third
compound : it is a case of sytnmorphosis or addition,

(C4 H4) C12 + 2H3 N=(C4 H4)H4 N2, 2HC1.
Experiment proves, however, that the reaction involves the elimi-
nation of hydrochloric acid and the fixation of the elements of
amidogen : apomorphosis and symmorphosis are accomplished side
by side, as indicated by the following equation: —

C4 H4 C12 + 2H3 N=(C4 H3)H2 N, HC1 + H3 N, HC1."

M. Cloez would be perfectly right if during the reaction no other
base were formed except the first one. But he forgets altogether
that in the process under examination — exactly as in the mutual
reaction between bromide of ethyle and ammonia — several other bases
of more advanced substitution are produced. The equations which
I give for the formation of these bodies likewise involve the elimi-
nation of bromide of ammonium, and in fact of considerable quantities
of this compound.

2(C4 H4)" Br2 + 4H3 N=(C4 H4)2" H2 N2, 2HBr+2(H3 N, HBr).
3(C4 H4)" Br2 + 6H3 N=(C4 H4)3" N2, 2 HBr+4 (H3 N, HBr).
The bromide of ammonium then, which separates in considerable
quantity in the action of dibromide of ethylene upon ammonia, be-
longs to the second and third portions of the reaction ; it has nothing
whatever to do with the formation of the first base. M. Cloez, as I

Dr. Hofmann on the Diatomic Ammonias. 69

have pointed out, does not admit the simple equation which I have
given for the formation of this body ; he denies that it is simply
formed by the union of the two compounds reacting upon each
other. According to his opinion it is produced in a secondary re-
action, occasioned by the intervention of heat. My experiments do
not confirm this opinion. A mixture of dibromide of ethylene and
alcoholic ammonia allowed to stand for some time at the ordinary
temperature, deposited a quantity of crystals, from which I was en-
abled to extract, without distillation, simply by successive crystal-
lizations, absolutely pure salt of ethylene-diamine, as proved by the
analysis of the bromide, the chloride, and the platinum-salt.

In discussing the numbers which I have obtained in analysing the
hydrate and the hydroehlorate of the first base, M. Cloez quotes the
results on which he founds his own formula. A glance at these
figures will show unmistakeably that they agree much better with
my formula than with the one which he defends. The following
are the analytical details of our analyses, together with the theo-
retical values required by each formula : —

Formula of

Analysis of

Formula of

Analysis of

M. Cloez.

M. Cloez.

Dr. Hofmann.

Dr. Hofmann,

Carbon . .

..31*58

31-12

30-76

30-67

Hydrogen

. . 10-52

12-77

12-82

12-97

Every experimentalist has incontestably the first right of inter-
preting his analytical results ; knowing, as he does, his methods, he
will do it generally much better than any other person. In the case
before us, however, I believe very few chemists would have inter-
preted the results of analysis as M. Cloez has done. As far as I
am concerned, I would always prefer to admit having lost 0-2 per
cent, of hydrogen, to calculating a formula requiring 2*25 per cent,
of hydrogen less than had been obtained by experiment. I would
prefer this especially in analysing a substance like ethylene-diamine,
attracting carbonic acid with the utmost avidity — a trace of which
would very appreciably lower the experimental hydrogen — and con-
taining so high a percentage of hydrogen, that the presence even
of a small quantity of water would produce a somewhat similar
effect.

The results which M. Cloez has obtained in the analysis of the
hydroehlorate are not less in favour of my views. He finds 1*28 per
cent, of hydrogen more than required by his formula, whilst ad-
mitting my theory, he would not have lost more than 0*13 per
cent.

I have since examined several other salts of ethylene-diamine, and
the results fully confirm the conclusions drawn from my former
analyses. It would be useless to quote these additional experiments,
but I will mention the characteristic numbers furnished by the ana-
lysis of the anhydrous base, since the diminution of the equivalent
exhibits in a more striking manner the differences between the
theoretical values of the two formulae. Ethylene- diamine retains the
water with the greatest energy, and it is in fact only by protracted

70 Royal Society : —

contact with metallic sodium that it is possible to obtain this body
in the anhydrous condition. I give the numbers obtained by com-
bustion, side by side with the theoretical values of the two formulae :

Formula of

Formula of

M. Cloez,

Dr. Hofmann,

Analysis

C,H3N.

C4H8N2.

..41-37

4000

40-13

. . 10-34

13*33

13-31

Carbon .
Hydrogen

These numbers require no commentary.

It is not, however, in the results of analysis that M. Cloez finds
the chief support of his views ; he quotes an observation which at the
first glance appears fatal to the diatomic notions.

" But there is" continues M. Cloez, " a capital fact (un fait
capital) which completely settles the question at issue : this is the
vapour-density of the free base."

This density has been found by experiment to be 1*42.

" The theoretical density calculated for my formula, referred to
4 volumes, is 1*315 ; the modified formula of M. Hofmann, likewise
referred to 4 volumes, gives the theoretical density of 2*699.

" These results appear to me decisive, and I do not hesitate to
maintain the formula of the new series of bases, of which I first
pointed out the formation "

I entirely agree with M. Cloez as to the importance of the deter-
mination of the vapour-densities, but I certainly arrive at a very
different interpretation of his result.

In repeating the experiment of this able chemist, I have arrived,
as might have been expected, at exactly the same number. But this
number refers to the hydrated base, and it is easily seen that the
hydrated molecule, when in the state of vapour, must occupy 8
volumes. In calculating the theoretical density corresponding to
the diatomic formula when referred to 8 volumes, we arrive at the
number 1*35, which coincides in fact with the number obtained by
experiment.

It is obvious that under the influence of heat the hydrated base
splits into anhydrous base (4 volumes) and water (4 volumes),

e4H10N2O2 = C4H8N2+2HO,

and that, instead of taking the vapour-density of the intact hydrated
molecule, M. Cloez has determined the density of a mixture of an-
hydrous base and water, which on cooling combined again, repro-
ducing the hydrated compound. And here I must recall the observa-
tions of several chemists, especially those of M. Bineau, of M.
Kekule", and of M. H. Saint- Claire Deville, each of whom has had
the opportunity of explaining the anomalous vapour-densities in the
transitory decomposition of the compounds submitted to experiment ;
and I would quote particularly a note by Professor Kopp*, in which
this distinguished physicist has treated the question of anomalous
vapour- densities in a general manner.

In the case before us, there is a very simple experiment, calculated
* Ann. der Chem. und Pharm. cv. 390.

Dr. Hofinann on the Diatomic Ammonias. 71

to remove all hypothesis from the above explanation, — the determina-
tion of the vapour-density of the anhydrous base.

The experiment made with a substance the purity of which had
previously been proved by analysis, led to the number 2*00, which
indeed absolutely coincides with the theoretical density of the
diatomic formula C4 H8N2 referred to 4 volumes. This theoretical
density is 2*07, whilst the formula of M. Cloez, likewise referred to
4 volumes, requires the theoretical density of 1*00.

The molecule of ethylene-diamine (formenamine) then, like those
of all other well-examined organic compounds, corresponds to 4«
volumes of vapour ; and the vapour-density of the base, far from
militating against the molecular value which I assign to this body,
furnishes on the contrary an additional and incontestable argument
in its favour.

The preceding remarks are, I hope, sufficient to establish the
formulae of the diatomic ammonias upon a solid basis. I will there-
fore only briefly allude to some results which I have obtained in
studying the products of decomposition of ethylene- diamine, and
which are not less characteristic. Submitted to the action of nitrous
acid, this base is decomposed with evolution of nitrogen ; in the first
stage of the reaction an indifferent crystalline body is produced, and
the final result of the process is a large quantity of pure oxalic acid.
The nitrogen evolved during the transformation is accompanied by a
very volatile liquid, the odour of which is somewhat similar to that
of aldehyde. At the time when I made these experiments I really
believed the liquid to be aldehyde, but since I failed in obtaining the
crvstalline compound with ammonia and in transforming it into acetic
acid, I abstained from mentioning this reaction in my note to the
Royal Society. I have now scarcely a doubt that the volatile liquid
was the oxide of ethylene, isomeric with aldehyde, since discovered
by M. Wurtz. The transformation would be

C4H8N2 + 2N03=4N + C4H402+4HO.

In preparing the ethylene-diamine for my experiments, I obtained
as a secondary product a small quantity of the second base, which
M. Cloez has described as acetenamine, and for which I now propose
the term diethylene-diamine. This base has exactly the same per-
centage composition, whether viewed as a diamine or considered as
the monatomic acetenamine of M. Cloez. The analysis of the base
itself, and of some of its salts, fully confirms the results obtained by
that chemist. But this base is no primary monamine.; it does not
contain the radical acetyle, C4 H3, as supposed by M. Cloez ; it is a
secondary diamine containing two molecules of ethylene. Aceten-
amine, as conceived by M. Cloez, should be formed by the action of
chloride, bromide, and iodide of vinyle (C4H3C1, C4H3Br, C4H3I)
upon ammonia. These reactions do not furnish a trace of the base
in question. But there is a more conclusive proof of the diatomic
nature of this body, the evidence of which will not be contested by
M. Cloez, — this is the determination of the vapour-density. Experi-
ment gave the number 27. The diatomic formula, C8 ~~

72 Royal Society : —

to 4 volumes of vapour, requires 2*9. According to the monatomic
view, a vapour-density of 1*45 should have been found.

The preceding experiments, although fixing in a satisfactory
manner the composition and the equivalents of the two diammonias,
do not unveil their molecular constitution — their degree of substi-
tution.

I have endeavoured to solve this problem by submitting them to
the action of iodide of ethyle, a process which I first used for simi-
lar purposes, and which has since become of general application.
This process, moreover, could not fail to furnish a final decision
between the two theories.

In considering with M. Cloez the two bases as primary monamines
belonging respectively to the formic and to the acetic groups,

C2H] C4H3]

H N . H N,

H J H J

it is evident that each of them must be capable of absorbing success-
ively 1, 2, or 3 equivalents of ethyle, and of yielding three ethylated
bases, two volatile, and one fixed. On the contrary, if the bases were
products of the successive substitution of the same molecule for the
hydrogen of two equivalents of ammonia, if they were respectively a
primary and a secondary diamine,

(C4HJ"1 (C.H,)'

i.HJ"l (C4Ht)"l

H, lN2> (C4H4)"In2,

H2 Ha J

the first of the two must likewise give rise to the formation of three
bases, whilst the second one would produce only two.

Experiment has verified this latter anticipation. In submitting
ethylene-diamine to the alternate action of iodide of ethyle and oxide
of silver, I have succeeded in obtaining two volatile ethylated bases,
and a third one, which is fixed. These compounds are well defined ;
their composition was established by the analysis of their iodides or
their platinum-salts. Represented as salts, these bases contain —

Saltofethylene-diammonium [(C4H4)" H6N2]"Ia.

Salt of diethylated ethylene-diammonium . . [(C4 HJ" (C4 H6)2 H4 N J" Ia.

Salt of tetrethylated ethylene-diammonium [(C4 HJ" (C4 H5)4 H2 NJ" I,.

Salt of hexethylated ethylene-diammonium [(C4 H4)" (C4 H5)6 N J" I2

On repeating the same experiments with diethylene-diamine, per-
fectly analogous phenomena were observed, but the reaction yielded
only one volatile base, which was immediately converted into a fixed
base. Analysed in a similar manner, and represented as salts, these
bases exhibit the following composition :—

Salt of diethylene-diammonium [(C4 H4)"2 H4 Nj" I2.

Salt of diethylated diethylene-diammonium [(C4 H4)"2 (C4 H5)2 H2 N J" I2.

Salt of tetrethylated diethylene-diammonium [(C4 H J"2 (C4 H5)4 N J" Ia.

Dr. Hofmann on the Diatomic Ammonias.

73

The same result is accomplished, but in a shorter and more elegant
manner, by substituting iodide of methyle for its ethylated homologue.
Already, at an earlier period, I have shown that iodide of methyle has
a remarkable tendency to yield the last product of substitution.
Thus, on treating iodide of methyle with ammonia, the iodide of
tetramethylammonium is alone obtained, together with a very large
proportion of iodide of ammonium. The action of iodide of methyle
with the ethylenated bases is perfectly analogous. The last product
of substitution is formed at once in notable quantity, and may be
purified by a simple crystallization. I have obtained in this manner,
without being embarrassed by the intermediate compounds, the iodide
of hexm ethylated ethylene-diammonium and of tetramethylated
diethylene-diammonium .

These results require no further explanation.

In the present state of science we rely upon a certain number of
considerations which guide us in the construction of a chemical
formula. These are, — the study of the origin of a body ; analysis ;
observation of the physical properties, and especially of the boiling-
point ; the determination of the vapour-density ; and lastly, the exa-
mination of its metamorphoses. I have endeavoured to look at the
question under discussion from these several points of view ; experi-
ment has given invariably the same reply.

It follows from this controversy that the diatomic alcohols imitate
the monatomic alcohols in their deportment with ammonia. Ethyl-
alcohol produces, as is well known, three ethylated ammonias, the
molecules of which occupy 4 volumes of vapour.

ojfc.i

Ethylamine H VN =4 volumes.
H

c4h;

Diethylamine C4H
H
C4H

Triethylamine C4 H

cX

-N=4 volumes.

►N = 4 volumes.

Ethylene-diamine

In a similar manner we find that glycol, the diatomic alcohol of
ethylene, the discovery of which we owe to the remarkable labours of
M. Wurtz, gives rise to three diatomic bases, corresponding to 2
molecules of ammonia, and representing likewise 4 volumes of vapour.

(CtH4)»-

H2

H2

(<W

Diethylene-diamine (C4 H4)"

H2

(c h yr

Triethylene-diamine (€* H4)"
(C4HJ"_
The two first terms of this series are the bases which M. Cloez

-N2=4 volumes.

•N2=4 volumes.

»NQ=4 volumes.

74 Royal Society : —

discovered about six years ago, but the true nature of which he failed
to recognize. To complete the series, it remains only to examine
the third volatile base and the oxide of tetrethylene-diammonium.

The observations which I have the honour of submitting to the
Royal Society coincide in every point with the first note upon this
subject which I presented nearly two years ago. I have simply
carried out somewhat more in detail the sketch traced in my former
communication.

In conclusion I may state a fact which has also been observed
by M. Cloez, viz. that the action of dibromide of ethylene upon
ammonia gives rise to the formation of bases not directly belonging
to the series which we have discussed. In searching for the method
of purifying the ethylene bases, I have been obliged to examine also
the terms of the other group ; but since these substances do not
necessarily belong to this part of the inquiry, I omit for the present
to enter more fully iuto their examination.

" On the Forces that produce the great Currents of the Air and of
the Ocean." By Thomas Hopkins, Esq.

In this paper the writer pointed out the fact that we have at
present no satisfactory evidence in books of what are the immediate
causes of the great currents of the air and of the ocean ; and he
maintained that the liberated heat of condensing vapour is the cause
of these currents. He then proceeded to show that all the great
winds terminate in comparative vacua created in particular localities
where much vapour has been condensed ; and contended that such
vacua enable and cause heavier air to press and flow towards the
parts which have been rendered light, — to re-establish the equilibrium
of atmospheric pressure, — thus making heat the disturbing power
in the aerial ocean, and leaving gravitation to act to restore an
equilibrium. The great primary currents of the ocean were also
described, and they were shown to be so situated as to be under the
influence of the principal winds, which, in their passage over the
waters, press on them, and force them forward as currents. These
currents were maintained to be of a velocity, extent, and depth
proportioned to the strength and continuity of the wind, showing
that the pressure of the air on the water, whilst moving over it, is
capable of producing the movement which takes place. When, how-
ever, water is put into motion, it may be obstructed by land, and
turned from its direct course, and in that way be made to form
secondary currents. But it was contended that heat of vapour, set
free in the atmosphere, is the force which disturbs the equilibrium
of pressure, and either directly or indirectly produces all the great
continuous movements that take place both in the atmosphere and
the ocean.

Jan. 19. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communication was read : —
" On the Interruption of the Voltaic Discharge in Vacuo by Mag-
netic Force.,, By J. P. Gassiot, Esq., F.R.S.

The late Professor Daniell, in his Fifth Letter on Voltaic Combina-

Mr. J. P. Gassiot on the Voltaic Discharge in Vacuo. 75

tions (Phil. Trans. 1839, part 1), describes some experiments madewith
seventy series of his constant battery, and states (page 93) " that the
arc of flame between the electrodes was found to be attracted and
repelled by the poles of a magnet, according as one or the other pole
was held over or below it, as was first ascertained by Sir H. Davy ;
and the repulsion was at times so great as to extinguish the flame."

In the Philosophical Magazine of July 1858, Mr. Grove has de-
scribed an experiment made by him with one of my vacuum-tubes,
2 feet 9 inches long, in which he ascertained that the discharge of a
Ruhmkorff's induction coil could be stopped by bringing a magnet
near the positive terminal wire, but that this effect was not obtained
when the magnet was made to approach the negative. The mercurial
vacuum-tube in which Mr. Grove observed this phenomenon was
unfortunately shortly afterwards broken ; and although Mr. Grove
and myself have repeatedly endeavoured to obtain the same result in
similar and in other vacuum-tubes (and since that period I have ex-
perimented with upwards of two hundred), all our efforts have been
hitherto unsuccessful.

The experiments I am now about to describe were made with two
carbonic acid vacuum-tubes, the vacua being obtained in the same
manner as described by me in the Philosophical Transactions, part 1,
1859*.

A, h>the annexed figure, represents a glass tubular vessel (No. 146),
24 inches long and 6 inches diameter in its wide part ; at one end,
attached to the platinum wire («), is a concave copper plate 4 inches
diameter, at the other end is a brass wire attached to the platinum
wire (b). B represents a glass tube (196) 5 inches long (in its wide
part), in which two small balls of gas-retort coke are attached to the
platinum wires a' and bf, and are placed about 3 inches apart, all the
platinum wires being hermetically sealed in the glass. In A the
potash is placed in the vessel between the electrodes ; in B it is
placed in the further part of the tube, beyond one of the wires.

Battery.

* The carbon-balls do not in these experiments affect the results described, as
1 have obtained the same in a tube of the same dimension with brass wires.

76 Royal Society : —

An electro-magnet is placed at C, and is constructed so as to allow
the two helices to be separated ; and by these means the larger vessel
can, if required, be placed between them, and any portion of the
luminous discharge may be thus exposed to any part of the magnetic
field.

"When the terminals of an excited induction coil are attached to
the wires of either of the above vacuum-tubes A or B, luminous
discharges are obtained, the negative wire ball or plate being
covered with a luminous cloud-like glow extending towards the
positive ; but the stratifications are not developed, except by the
magnet, and these become more clearly defined as the magnet is
caused to approach, or as the power is increased, when they are de-
flected according to the direction of the discharge, or of the polarity
of the magnet. But with the induction coil, no matter how I re-
duced the intensity of the discharge, or varied that of the electro-
magnet, in no instance could I produce in these, or in any of my
vacuum-tubes, a similar result to that which Mr. Grove obtained in
the vacuum-tube so unfortunately broken ; the experiment evidently
requires a certain balance of power between the electric discharge
and that of the magnet, and this I had hitherto been unsuccessful
in obtaining.

I next experimented with my water-battery (Phil. Trans. 1844,
and Proceedings, 26 May, 1859), which I have recently had carefully
cleaned and recharged with rain-water ; the luminous discharge in
both the vacua A and B was obtained with less than 1 000 series,
and this discharge, as well as that from the full series of the battery of
3520 cells, was under certain conditions, hereafter described, entirely
destroyed or interrupted by the power of the magnet.

At first the interruption or break in the luminous discharge ap-
peared to be caused by the sudden action of the magnet, as if it were
merely momentarily blown out, for the discharge recovered itself
while it remained under the influence of the magnet — the luminous
discharge under this condition gradually reappearing stratified and
strongly deflected j but I subsequently ascertained that, by carefully
adjusting the intensity of the battery discharge, and the force or power
of the electro-magnet, this recovery in the discharge could be en-
tirely prevented.

On approaching the vacuum A towards the electro-magnet, the
luminous discharge from the battery assumed the same form as that
from the induction coil ; but when the vacuum was placed between
the helices, so as to permit the armatures or poles of the magnet
to touch one or each side of the glass vessel at about its centre, the
discharge disappeared ; as soon as the magnet was removed, or the
vacuum-tube withdrawn from its influence, the luminous discharge
was reproduced.

To test whether a complete disruption of the electrical current
had taken place, two gold-leaf electroscopes were attached, one to the
zinc and the other to the copper terminal of the water-battery ; the
leaves diverged with considerable energy ; connection was then made
from the electroscopes to the wires of the vacuum-tube ; the luminous

Mr. J. P. Gassiot on the Voltaic Discharge in Vacuo. 77

discharge became visible, and the leaves of both electroscopes par-
tially collapsed ; the vacuum-tube was then placed as before, between
the armatures of the electro-magnet, and immediately the magnet
was excited, the luminous discharge disappeared, and the leaves of
the electroscopes diverged to their original maximum extent, thus
proving the disruption to be complete.

If the smaller tube B is placed across both poles of the magnet,
the luminous discharge at its centre assumes the appearance of being
nearly separated into two parts, each part showing a tendency to
rotate round the pole of the magnet on which it is placed, the one
in an opposite direction to the other. I endeavoured to obtain a
disruption of the battery discharge when in this state, and possibly
with a more powerful electro-magnet this experiment would succeed ;
but although I reduced the intensity of the battery discharge and
increased the power of my electro-magnet, I could not in this manner
obtain an actual discontinuity of the battery discharge ; but when the
same vacuum-tube was placed in a longitudinal or equatorial position
between the poles, or even approached them within three or four
inches in that direction, an immediate interruption of the dis-
charge took place.

When both vacuum-tubes are placed in the battery circuit, the
interruption can be shown in a very striking manner : the general
arrangement of the apparatus represented in the figure shows how
this experiment is made. A is fixed on a wooden support. One
wire (b) is attached to the copper terminal of the battery, the other
wire (a) being connected to one of the wires in B, which is held by
the hand, the other wire (6') being connected with the zinc terminal
of the battery, gold-leaf electroscopes being placed as before. In
this manner all the apparatus is fixed except B, which being held by
the hand, and the connecting wires being flexible, can be placed in
any required position.

As long as the vacuums are at a sufficient distance from the
action of the magnet, the luminous discharge is visible in both, and
the leaves of the electroscopes partially collapse ; but immediately the
discharge in B is placed in the position described in the previous
experiment, between the poles of the magnet, the discharges in both
vacua instantly disappear, and the leaves of the electroscopes di-
verge to their original maximum.

The actual position of what is termed the magnetical field, around
and between the poles of a magnet, has been generally delineated by
means of iron filings placed between the poles on a sheet of paper.
Assuming the lines in which these particles arrange themselves to
represent the direction of the power of the magnet, or the magnetic
field, they also explain the actual position through which the vacuum-
tube should be placed to obtain the preceding result, and in this
manner to show by experiment that a voltaic discharge which has
sufficient intensity to pass through a space of upwards of 6 inches in
attenuated carbonic acid gas is not only interrupted, but absolutely
and entirely arrested by magnetic force.

Postscript. — In repeating the experiments with Dr. Tyndall in my

78 Royal Institution : —

laboratory, the disruption of the luminous discharge in vacuo from
400 cells of the nitric-acid battery was obtained : some most beautiful
and striking results were obtained from the same battery on the
16th inst., on repeating the experiment in the Theatre of the
Royal Institution, with its large electro-magnet, Dr. Faraday and
Dr. Tyndall being present.

The large receiver (14G) was placed between the poles of the
electro-magnet, the lines of force going through it ; electrodes
equatorial. The stratified discharge was extinguished. Subsequently,
through the sinking of the battery, or some other cause, the stra-
tifications disappeared, and the luminous glow which filled the entire
tube remained. On now exciting the magnet with a battery of ten
cells, effulgent strata were drawn out from the positive pole, and
passing along the upper or under surface of the receiver, according
to the direction of the current. On making the circuit of the magnet,
and breaking it immediately, the luminous strata rushed from the
positive and then retreated, cloud following cloud with a deliberate
motion, and appearing as if swallowed by the positive electrode.

The amount of electricity which passed appeared materially in-
creased on exciting the magnet ; once the discharge was so intense
as to fuse half an inch of the positive terminal.

After this had occurred, the discharge no longer passed as before
when the terminals of the battery were connected with it ; but on
connecting the positive end of the battery with the gas-pipes of the
building, the discharge passed.

The discharge could also be extinguished by the magnet ; and
the time necessary to accomplish this, furnished a beautiful indication
of the gradual rise and reduction in the power of the electro-
magnet.

ROYAL INSTITUTION OF GREAT BRITAIN.

March 30, I860.—" On Acids and Salts." By William Odling,
Esq., M.B.,F.R.S.

It is natural to inquire whether the doctrines of series and substi-
tutions, which are essential for the association of organic products,
may not throw some additional light upon the simpler compounds of
mineral chemistry, when viewed as unitary molecules ; and particu-
larly upon the relations and properties of the mineral acids and their
salts, which have hitherto constituted the strongholds of the electro-
chemical, or binary, theory of combination.

The doctrine of series affirms that chemical compounds may be
arranged in series, the successive members of each of which differ
from one another in composition by a common increment, and are
associated with one another by a certain relation of properties, the
exact nature of the relation varying with the nature of the increment.

The doctrine of substitutions affirms that, in very many chemical
compounds, one or more atoms may be displaced by some other
atoms or groupings, and that the new bodies, resulting from this
displacement, correspond in constitution with the normal bodies

Dr. Odling on Acids and Salts. 79

from which they Were derived. The doctrine of substitutions affords
great assistance to the doctrine of series ; for when, as frequently
happens, a gap exists in any series, that gap can almost always be
filled up by a substitution-representative of the missing body.

(o.) There are four acid compounds of hydrogen, two volumes of
each of which contain one volume of hydrogen, namely :
HF Fluorhydric acid.
HC1 Chlorhydric acid.
HBr Bromhydric acid.
HI Iodhydric acid.
When two volumes of chlorhydric acid, for instance, are acted upon
by a red-hot iron wire, the chlorine is absorbed by the iron, and one
volume of hydrogen gas liberated. The two volumes of chlorhydric
acid yield one volume of hydrogen, or the original bulk of gas is
reduced to one-half by the absorption of its chlorine. The above
four acids may be looked upon as substitution-representatives, one
of another.

Chlorhydric acid yields the following series of oxides, convertible
into each other by mutual metamorphosis :—

HC1 Chlorhydric acid.

HCIO Hypochlorous acid.

HCIO2 Chlorous acid.

HCIO3 Chloric acid.

HCIO4 Perchloric acid.
When chlorhydric acid, HC1, is oxidated by permanganic acid, hypo-
chlorous acid, HCIO, is produced ; and, conversely, chlorhydric acid
may be reproduced by the deoxidation of hypochlorous acid. Hypo-
chlorous acid, when heated, breaks up into chloric acid, HCIO3, and
other products. When chloric acid is deoxidated by nitrous acid, it
becomes chlorous acid, HCIO2 ; and when oxidated at the positive
pole of a galvanic battery, it becomes perchloric acid, HCIO4. Here
then is a series of associated acids, expressed as unitary molecules, by
the simplest possible formulas, and arranged in a series, the successive
members of which differ from one another in composition by an incre-
ment of one atom, or volume, of oxygen.

(/3.) There are four other binary compounds of hydrogen, two
volumes of each of which, however, contain two volumes of hydro-
gen, namely : —

H20 Water.

H2S Sulphydric acid.

H2Se Selenhydric acid.

H2T Tellurhydric acid.
A given volume of any one of these gases or vapours contains exactly
twice the quantity of hydrogen that the same volume of any one of
the first class of gases contains. When two volumes of sulphydric
acid, for instance, are acted upon by a red-hot iron wire, the sulphur
is absorbed by the iron, and two volumes of hydrogen gas are liberated.
The two volumes of sulphydric acid yield two volumes of hydrogen,
or the abstraction of the sulphur produces no alteration in the bulk
of gas. The bihydric character of water, moreover, is well shown

80 Royal Institution : —

by the experiment of its electrolytic decomposition, in which two
volumes of hydrogen are produced for every one volume of oxygen.
In the sulphur series of oxygen acids we have two gaps, which,
however, can be filled up by the chloro -representatives of the missing
bodies, thus :

Ha,S Sulphydric acid. C13S.

HaSO Wanting. ClaSO.

HaSOa Wanting. Cl^SO2.

H2S03 Sulphurous acid.

HaS04 Sulphuric acid.

The compounds ClaSO and CI2 SO2 are obtainable from the chloro-
representative of sulphydric acid, CI2 S, by successive oxidation. The
first product actually afforded by the oxidation of sulphydric acid is
sulphurous acid, H2S03, which is produced by the combustion of
sulphydric acid in air or oxygen. Conversely, sulphydric acid may be
obtained by deoxidating sulphurous acid with nascent hydrogen.
Sulphuric acid, H2S04, results from the oxidation of sulphurous
acid, and by deoxidation can reproduce that body, as in the ordinary
process for the preparation of sulphurous acid. Here then, includ-
ing the chloro-representatives, is a second series of acids associated
with one another by a common increment of composition, and by
mutual metamorphosis.

Sulphuric acid, H2SO\ is the representative on the sulphur series, of
perchloric acid, HC104, on the chlorine series. Each contains one
atom of the radical which gives the special character to the acid, in the
one case chlorine, in the other sulphur. Each contains also four
atoms, or volumes, of oxygen ; but whereas perchloric acid contains
only one atom, or volume, of hydrogen, sulphuric acid contains two
atoms, or two volumes. And this difference in composition leads to a
marked difference in the properties of the two acids. Perchloric
acid, HC10\ has only one atom of hydrogen that can be replaced.
Hence it forms only one description of salt, such, for instance, as
perchlorate of potassium, KC104, and only one description of ether,
such, for instance, as perchloric ether, EtCIO4. But sulphuric acid has
two hydrogen atoms that can be replaced. Hence it can form acid
salts, neutral salts, double salts, acid ethers, neutral ethers, double
ethers, and saline ethers, as shown in the Table.

H2S04 Sulphuric acid.

KHSO4 Acid sulphate of potassium.

K2 SO4 Neutral sulphate of potassium.

KNiSO4 Potassio-sulphate of nickel.

EtHSO4 Ethylo-sulphuric acid.

Et2S04 Neutral sulphate of ethyle.

EtMeSO4 Ethylo-sulphate of methyle.

EtK SO4 Ethylo-sulphate of potassium.

This property of forming acid and double salts, and acid and
double ethers, &c, indicates a fundamental difference in character be-
tween sulphuric and perchloric acids, a difference that is satisfactorily
represented by the difference in their formulae as here written down,

Dr. Odling on Acids and Salts, 81

HCIO4, and H2S04. Bibasic characters are manifested as decidedly
by the sulphurous and sulphydric acids.

(y.) There are four other binary compounds of hydrogen, two
volumes of each of which, however, contain three volumes of hydro-
gen, namely : H3 N Ammonia.

H3P Phosphamine.
H3As Arsenamine.
H3Sb Stibamine.
When the two volumes of phosphamine, for instance, are acted upon
by a red hot iron- wire, the phosphorus is absorbed by the iron, and
three volumes of hydrogen gas are liberated. Two volumes of chlorhy-
dric acid yield one volume of hydrogen ; two volumes of sulphydric
acid yield two volumes of hydrogen, while two volumes of phos-
phamine yield three volumes of hydrogen ; and this is a most import-
ant distinction between the three classes of hydrides to which these
hree gases respectively belong. Again, two volumes of gaseous
ammonia, when decomposed by the Ruhmkorff spark, become con-
verted into three volumes of hydrogen and one volume of nitrogen ;
or the original bulk of the ammonia becomes doubled.

In the phosphorus series of oxygen acids there is but one gap, and
this can be filled up by the chlorine- or the ethyl-representative of
the missing body.

H3P Phosphamine. C13P Et3P

H3PO Wanting. Cl3PO Et3PO

H3P02 Hypophosphorous acid.

H3P03 Phosphorous acid.

H3P04 Phosphoric acid.
Brodie has ascertained that oxychloride of phosphorus, Cl3PO, may
be obtained directly by passing oxygen gas through boiling terchloride
of phosphorus, or trichloro- phosphamine, CI3 P. The union of tri-
ethylphosphine, Et3 P, with oxygen, to form the oxide of tri-ethylphos-
phine,Et3PO, constituted one of Hofmann's earliest experiments on the
phosphorus bases. Proceeding to the actual oxides of phosphamine, it
is doubtful whether hypophosphorus acid, H3P02, has been obtained by
the oxidation of phosphamine ; but, on the other hand, phosphamine
is readily obtainable by deoxidating hypophosphorous acid with
nascent hydrogen ; while by oxidating hypophosphorous acid, phos-
phorous and phosphoric acids are successively produced. Phosphorous
acid, H3P03, results from the slow oxidation, and phosphoric, acid,
H3P04, from the rapid oxidation of phosphamine. Conversely, phos-
phamine may be obtained by the deoxidation of each of the two last-
mentioned acids. Here again, then, is a series of naturally associated
and mutually convertible bodies, represented by the simplest possible
formulae, by formulae which do not express any speculative view
whatever, but merely indicate the indisputable fact that these bodies,
or their representatives, differ from one another in composition, by
the successive increments of one, two, three, and four oxygen atoms.
Phosphoric acid, H3 PO4, is the representative in the phosphorus
series, of sulphuric acid, H2 SO4, in the sulphur series, and of per-
chloric acid, HCIO4, in the chlorine series ; but whereas perchloric
Phil. Mag. S. 4. Vol. 20. No. 130. July 1860. G

82

Royal Institution :•

acid contains only one atom of hydrogen, and can form only one class
of salts and ethers ; whereas sulphuric acid contains only two atoms
of hydrogen, and can form only two classes of salts and ethers ;
phosphoric acid contains three atoms of hydrogen, and can form
three classes of salts and ethers. One-third, two-thirds, or three-
thirds of its hydrogen may be displaced by a metal or basic radical,
or the hydrogen may be partly or wholly displaced by two or three dif-
ferent metals, or by two or three different radicals, or by a mixture of
metals and radicals, thus :— EtKCuPO4, or H (NH4) NaPO4, &c.

(S.) There is yet another primary hydride to be considered,
namely, that of silicon, the siliciuretted hydrogen of Wohler. The
composition of this body has not been ascertained. It has been
ascertained, however, that the substance from which it is obtained
by the action of chlorhydric acid, is a silicide of magnesium,
represented by the formula Mg4 Si, whence the formula of siliciu-
retted hydrogen is assumed to be H4 Si, analogous to that of marsh-
gas, H4 C, a conclusion strongly confirmed by the composition of
chloride of silicon, which is undoubtedly CI4 Si, that is, a chloro-
representative of siliciuretted hydrogen Each primary hydride,
hitherto considered, has yielded a remarkably stable acid, formed
by the addition of four atoms of oxygen to the hydride ; and hydride
of silicon ought to behave in the same manner, thus : —

Chlorhydric acid .... H CI H CIO4 Perchloric acid.

Sulphydric acid . . . . H2 S H2 S O4 Sulphuric acid.

Phosphamine H3 P H3 P O4 Phosphoric acid.

Hydride of silicon . . H4Si H4Si04 Silicic acid.
Now whether or not H4 SiO4 is the correct formula for silicic acid,
it is certain that the great majority of simple and well-defined sili-
cates may be referred to that type, as. illustrated in the Table*
Orthosilicates.

Et4Si04

Li4 SiO4

Naa H2 SiO4

Ca4Si04

Mg4 SiO4

CaaMgaSi04

Zn4 SiO4

Gl4 SiO4

Ce4 SiO4

Fe4 SiO4

Fe2Mn2Si04

Cu2H2Si04

Al2 Ca SiO4

Al2 Mn SiO4

Silicic ether.
Silicate of lithium.
Silicate of sodium.
Silicate of calcium.
Olivine, Chrysolite.
Batrachite.
Zinc glance.
The next Table illustrates the general relations of the perchloric
salts and ethers to their sulphuric, phosphoric, and silicic analogues.
The existence of the silicated compounds corresponding to the
formulae in italics, has not yet been established.
Acids, Salts, and Ethers.
fNaCIO4
EtCIO4

Phenakite.

Cerite.

Fay elite.

Knebelite.

Dioptase.

Anorthite.

Karpholite.

HC1

HC10<

HaS

HaS04

H'P

HsP04

H4Si

H4Si04

Naa SO4

NaHSO4

Eta SO4

Et H S O4

Na3P04

Na2HP04

NaH2P04

Et8 PO4

Et2 HPO4

Et H2 P»04

Na4Si04

Na'HSiO*

Na2H2Si04

NaH'SiO4

Et4 SiO4

Bt'HSiO4

EeWSiO1

EtWSiO*

Dr. Odling on Acids and Salts. 83

Considering the relations of ammonia and phosphuretted hydrogen,
H3 N and H3 P respectively, and the relations of marsh-gas and sili-
ciuretted hydrogen, H4 C and H1 Si respectively, there should exist
nitrates and carbonates having the general formulae M3 NO4 and
M4C04 respectively, corresponding to ordinary phosphates and
silicates having the general formula? Ms PO4 and M4 SiO4 respec-
tively. It is observable, however, that in addition to ordinary
phosphates and silicates, there are other phosphates and silicates,
known respectively as metaphosphates and metasilicates, which differ
from the ordinary salts by the loss of an atom of base, and that it is
these metasalts to which ordinary nitrates and carbonates correspond,
thus : —

Phosphate M8 P04-Ma 0 = MP03 Metaphosphate.

MNO3 Nitrate.
Silicate M4Si04-iMa 0 = M2Si03 Metasilicate.

M2C03 Carbonate.

But chemists are acquainted with a considerable number of car-
bonates and nitrates, which may be called orthocarbonates and ortho-
nitrates respectively, that do correspond in their formulae with
ordinary silicates and phosphates, as shown in the Table.

Orthocarbonates.

Ca4 CO4 Dicarbonate of calcium.

Zn4 CO4 Dicarbonate of zinc.

Mg3H CO4 Dicarbonate of magnesium,

Pb4 CO4 Dicarbonate of lead .

Pb3HC04 White lead.

Cu4C04 Mysorine.

Cu8HC04 Azurite.

Bi'" H CO4 Dicarbonate of bismuth .

Orthonitrates .
Pb3H NO
Pb3NO

;i lead.

Hg'HNO4/0^™^'

Bi'"JN04 of bismuth.
The succeeding Tables present lists of the principal ter-oxygen
and tetra-oxygen mineral acids. Some of these acids are known
only through the medium of their metal- and ethyl-representatives.

Ter- Oxygen Acids.

Chloric H CI O8

Bromic H BrO3

Iodic H I O3

Nitric HNO3

Metaphosphoric H P O3

Sulphurous . . Ha S O3

Selenious .... HaSe03

Tellurous .... HaT 0s

Carbonic .... HaC O3

Metasilicic. ... Ha Si 0'

G2

Tetra- Oxygen Acids.
Perchloric .... H CI O4
Periodic ....HI O4
Permanganic . . H Mn204
Sulphuric .... H8S O4
Selenic .... Ha Se O4
Telluric . . . . Ha T O4

Oxalic HaCa O4

Molybdic .... HaMo204
Vanadic .... Ha Va O4
Tungstic .... H2W2 O4

84 . Geological Society :•

Tables (continued).

Ter -Oxygen

Acids.

Tetra- Oxygen Acids.

Titanic ....

HaTi O3

Chromic ....

H3 Cra O4

St aim ir ....

HaSn03

Manganic. . . .

HaMn204

Vanadoua ....

Ha Va O3

Ferric

HaFea O4

Phosphorous . .

H3P O9

Orthonitric . .

H3N O4

Arsenious ....

H3As03

Phosphoric . .

H3 P O4

Antimonous . .

H8 Sb O3

Arsenic ....

H3As O4

Bismuthous . .

H3Bi O3

Antimonic . .

H3Sb Ol

Boracic ....

H3B O3

Orthocarbonic

H4C 0'

Aluminous . .

H8 Ala O3

Silicic

H4Si O4

Hence the formula H* R^ 0* will represent the general type for
an acid, where H* represents the atoms of hydrogen, which, save in
carbon compounds, are found to vary only from 1 to 4 ; where
Ry represents the acid radical, that is the chlorine, or sulphur, or
phosphorus, or carbon, &c. which gives the special character to the
acid, and which, save in carbon compounds, is usually confined to 1
or 2 elementary atoms; and where O* represents the atoms of
oxygen, which generally range from 0 to 4, but occasionally extend
to higher numbers. ,

GEOLOGICAL SOCIETY.
[Continued from vol. xix. p. 408.]
April 18, 1 860.— General Portlock, Vice-President, in the Chair.
The following communications were read : —

1. " On a Well-section at Bury Cross, near Gosport." By James
Pilbrow, Esq. In a letter to the Assistant-Secretary.

This well, which was dug to a depth of 110, and bored 221 feet
deeper, appears not to have penetrated the Bracklesham series of
sands and clays, many of the characteristic fossils of which, obtained
from the well, were exhibited by Mr. Pilbrow, together with speci-
mens of the beds perforated. The yield of water in this well is very
copious, certainly equal to 500,000 gallons at about 70 feet from
the surface. When not pumped, the water rises to about 9 feet from
the surface.

2. " On the presence of the London Clay in Norfolk, as proved
by a boring at Yarmouth/' By J. Prestwich, Esq., F.G.S.

In 1840 Sir E. Lacon and Co. commenced a well, for the supply
of water to their brewery, and had a shaft dug to the depth of 22
feet, and then a boring made to the depth of 597 feet, entering the
Chalk, but stopped by massive flints. The work was unsuccessful ;
but the specimens of the strata were carefully preserved : Mr.
Prestwich and Mr. Hose lately examined them, and the following
is Mr. Prestwich's opinion of the strata that they represent: —
Blown sand and shingle, about 50 feet ; recent estuarine deposits
(with Ostrca edulis, Cardium edule, Corbula Nucleus, Tellina Bal-
thica, T. planuta, Cyprina Islandica, Pecten operculars, Mytilus, and
Balanus), 120 feet ; London Clay, 310 feet ; Woolwich and Reading
series, 46 feet; Chalk, 57 feet.

This section is interesting as being illustrative of the estuary and

Mr. T. R. Jones on some Foraminifera from Chellaston. 85

its filling up, and of the extension of London Clay and Lower Ter-
tiary deposits to a more northerly point than had previously been
ascertained.

3. "On some Foraminifera from the Upper Triassic Clays of
Chellaston, near Derby." By T. Rupert Jones, Esq., F.G.S., and
W. K. Parker, Esq., M. Micr. Soc.

Bluish-grey specimens of the mottled clay from the pits at Chel-
laston, 3 miles south of Derby, whence the alabaster is obtained,
yielded abundance of minute Foraminifera, a few Entomostraca
(Cy there), some Otolites, and spines and plates of small Echinoderms,
together with fine siliceous sand and pyritous granules. Of the
Foraminifera nearly one-half consist of a small variety of Rotalia
repanda, namely R. elegans, D'Orb. The next most numerous
group are the Nodosarince, including varieties of Nodosaria, Denta-
Una, Marginulina, Vaginulina, Planularia, Frondicularia, Flabellina,
and Cristellaria. The genus next in numerical force is Nubecularia.
Polymorphina, Bulimina, and Lituola are represented by a few indi-
viduals.

The authors stated that nearly all the varieties of the Nodosarince
found at Chellaston are present in the Lias, in the clays of the
Oolites, in the Gault, Chalk- marl, Chalk, some Tertiary deposits,
and in some of the muds of the western Mediterranean and other
seas ; and the species of the other genera have also persisted to the
present day. One of the Triassic forms was described as a new
variety under the name of Planularia pauperata. It is found also in
the Oolite and in the recent seas. The authors also entered at some
length into the history of the genus Nubecularia, and described a
new elongated variety under the name of N. Tibia. After describing
the distribution of Foraminifera in many of the Mesozoic strata, and
pointing out that Nodosarice, Textularitf, Rotalice, and some other
Foraminifera occur in the palaeozoic rocks, Messrs. Jones and Parker
observed that altogether we have here some remarkable instances of
the persistency of life-types among the lower animals. " Though the
specific relationship of the palaeozoic Foraminifera require further
elucidation, we feel certain that the six genera represented in the
Upper Keuper Clay of Chellaston by at least 30 varieties stand
really in the place of ancestral representatives of certain existing
Foraminifera, — that they put on their several subspecific features in
accordance with the conditions of their place of growth, just as their
posterity now do, and that, although we have in this instance met
with only the minute forms of a 700 fathoms mud-bottom, yet else-
where the contemporaneous fuller development of these specific types
may be found by careful search in other and more shallow-water
deposits of the Triassic period."

May 2, I860.— L. Horner, Esq., President, in the Chair.

The following communications were read : —

1. "On the Physical Relations of the Reptiliferous Sandstone
near Elgin." By the Rev. W. S. Symonds, F.G.S.

Referring to Sir R. Murchison's sections of the Elgin district,
published in the Quart. Journ. Geol. Soc. No. 59, pp. 424 and 428,

86 Geological Society.

which show a conformable sequence of strata from the Old Red
Sandstone of Foths to the yellow sandstone and cornstone of Lossie-
mouth and Burgh Head, the author first stated that the siliceous
marly rocks, or so-called " cornstones " of Glassgreen, Linksfield,
Spynie, Inverugie, and Lossiemouth are in reality very dissimilar to
the cornstones of Foths and Cothall ; and he then pointed out the
improbability of the so-called cornstone of Glassgreen continuing to
dip north- westwardly under the sandstone of the Quarry- wood Ridge,
especially as near Linksfield it is, at different spots, seen to dip away
from that ridge. Evidence also of a break in the strata at the Bishop
Mill quarries was brought forward to show that the sandstone beneath
this " cornstone " (presumed to be the Reptiliferous sandstone) is
probably faulted against the lower or Holoptychian sandstone, which
latter towards Spynie was shown to be surmounted by the Repti-
liferous sandstone, and this last conformably by a marly siliceous
rock or so-called " cornstone."

Beyond Spynie Loch, northward, the author supposed that another
fault had again brought up the sandstone with Stagonolepis and
Hyperodapedon at Lossiemouth. Beyond this a cornstone-like rock
is again seen to cover the sandstone.

The author then referred to the probable Liassic and Triassic cha-
racter of the shales at Linksfield, and dwelt upon the suggestion
that had been offered as to the probability of the layer of boulder-
clay beneath the shales having been due to the mass of shales being
a portion of a cliff in the glacial period, and having then slipped
from a higher level. Regarding these shales as having been removed
merely by a slip from their original site, and as conformably over-
lying the calcareo- siliceous rock and sandstone beneath, Mr. Sy-
monds expressed his belief that this sandstone, faulted against the
Holoptychian sandstone at Quarry-wood, must be the Reptiliferous
sandstone and of Triassic age. Lastly he remarked that the pebble-
beds and sandstone, track-marked and rippled, of Burgh Head are
far more like the Triassic conglomerates of England than like the
Old Red rocks of Cothall and Foths.

2. " Notice of the Discovery of two Bone-caves in Northern
Sicily." By Baron Anca de Mangalaviti. In a letter to Dr. Fal-
coner, F.G.S.

One of the caves discovered by Baron Anca is at Monte Gallo, at
the western extremity of the Bay of Palermo, the other near the
village of Acque Dolci, at the foot of Monte San Fratello. These
caves, especially the last, are very rich in bones, and contain large
quantities of remains of Carnivora, including jaw-bones with molars
and canines. Bones belonging to animals of the following genera
have been met with : — Hippopotamus, Elephas, Equus, Bos, Cervus,
Canis, Ursus, Ht/cena, Felis, and some smaller Carnivores.

In these caves Baron Anca has found also a large quantity of flint
implements, but only where remains of Cervus are abundant. Copro-
lites also, both of Carnivores and Herbivores, were met with.

The author has also met with teeth of Carnivora in the Grotta
dell' Olivella.

[ 87 ]
VIII. Intelligence and Miscellaneous Articles.

CHEMICAL ANALYSIS OF TWO MINERAL PRODUCTS FORMED BY
SUBLIMATION IN THE ERUPTION OF VESUVIUS IN 1858. BY
M. CAPPA.

HPHESE two products, which by their physical properties appear to
■*■ be cotannite, are of a yellow colour and not lustrous. The two
specimens were marked A and B, and the results obtained were : —

A . Chlorine ; sulphuric, and traces of silicic acids ; lead in large
quantity ; copper, and a small quantity of sodium.

B. Chlorine, copper, and lead.

A, from its physical and chemical properties, might be considered
as oxychloride of lead mixed with small quantities of chlorides of
copper and sodium, along with traces of sulphates and silicates. The
compounds PbO, Pb CI, and '2 PbO, PbCl are well known. A seems
to belong to the former species, — a supposition which appears more
probable when it is remembered that oxychloride of lead is commer-
cially obtained by treating oxide of lead with chloride of sodium and
water. The hydrated body thus obtained becomes yellow by calci-
nation. Probably the lead placed under the same circumstances in
the presence of chloride of sodium and aqueous vapour, has given
rise to the above compound.

B appears to be oxychloride of lead with a small quantity of chlo-
ride of copper. — Comptes Rendus, May 21, 1860.

ON THE FLUOZIRCONATES, AND ON THE FORMULA OF ZIRCONIA.
BY C. MARIGNAC.

The formula for zirconia generally adopted, Zra03, was proposed
by Berzelius, who was led to it by a comparison of the composition
of two compounds which fluoride of zirconium forms with fluoride
of potassium. The formula ZrO, assumed by some chemists, is quite
indefensible. Neither it nor the formula ZrQ 0s are in harmony
with the properties of the body.

Recently Deville and Troost's researches* on the vapour-density
of chloride of zirconium have led to the formula Zr CI"2. Zirconia,
on this hypothesis, would be a binoxide allied to titanic, stannic,
and silicic acids. The similarity of zirconium to silicium was pointed
out by Berzelius, and he was only prevented from placing them
together by the necessity of classifying the elements into metals and
metalloids. The resemblance, too, of titanic acid and zirconia is so
great, that it is almost impossible to separate them by analysis.

Marignac has undertaken a comparative study of the fluozirconates
with a view of throwing light on the question. The material for
the research was obtained by treating zirconia with hydrofluorate of
fluoride of potassium at a red heat. A mixture of fluosilicate and
fluozirconate of potash is obtained, from which the latter salt is
readily obtained pure.

Fluoride of zirconium forms double salts with a great number of
t Phil. Mag. vol. xv. p. 459.

88 Intelligence and Miscellaneous Articles.

metallic fluorides ; but it appears to officiate less powerfully as an
acid than fluoride of silicon does. They are all decomposed by
prolonged contact with the air.

The relation between the fluorine of the basic fluoride and that of
the fluoride of zirconium is either —

1 1:4

II 2:4

III 3:4

IV 4:4

presenting a perfectly regular series, which precludes the possibility
of assuming three atoms of fluorine in fluoride of zirconium.

The most stable of these compounds, as well as the most common,
is the second. It may be taken as the type of the normal fluozir-
conate, M Fl, Zr Fl2.

There is one crystallized compound which does not belong to the
above series. It has the abnormal relation 5 : 8, which leads to the
formula 5 Na Fl, 4 Zr Fl2. However singular this formula may appear,
it is preferable to the more complicated one, 15NaFl, 8Zr2Fl3,
which the old formula of zirconia would require.

From the constitution of these salts, numerous instances of iso-
morphism between them and the fluosilicates, fluotitanate3, and
fluostannates might be expected. Such, however, is not the case.
There is isomorphism only in the case of the zinc and nickel
salts, which cannot be distinguished by their forms from the fluosili-
cates, &c.

The following is a list of the fluozirconates of which the crystal-
line forms have been determined. They are arranged in isomor-
phous groups : —

KFl,ZrFl2) *^J\ u -a i ■

NH4F1 ZrFl9 I Right rhomboidal prism.

3KFl,2ZrFlM „ , . , ,

3NH«Fl,2ZrFl2j '••• Regular octahedron.

KF1, 2ZrFl2 + 2Aql rkkr , ^, .
5 Na Fl 4 Zr Fl2 j ' 0bll(lue rhomboidal prism .

MgFl,ZrFl2 + 5Aq\ tA

MnFl,ZrFl*+5Aq/ ' ia*

ZnFl,ZrFl2 + 6Aql ...

NiFI,ZrFl2+6Aqj ' Rhombohedron.

K Fl, Ni Fl, 2Zr Fl2 + 8Aq. . Oblique rhomboidal prism.

2MnFl,ZrFl2 + 6Aq\ T,

2CdFl,ZrFl2 + 6AqJ * ld*

2ZnFl,ZrFl2+12Aq"l
2NiFl, ZrFl«+ 12 Aq } Id.

2CuFl, 2ZrFl2-f 12AqJ

3CuFl, 2ZrFl2 + 16Aq. . Id.

Comptes Rendus, May 21, 1860.

THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

♦

[FOURTH SERIES.]
AUGUST 1860.

IX. Chemical Analysis by Spectrum-observations.
By Professors Kirchhoff and Bunsen*.

[With a Plate.]

IT is well known that certain substances possess the property of
imparting definite colours to flames in which they are heated.
When the coloured light thus produced is analysed by a prism,
spectra exhibiting differently coloured bands or lines of light
are seen. Upon the occurrence of these lines of light an en-
tirely new method of qualitative chemical analysis can be based —
a method which greatly enlarges the scope of chemical reactions,
and points to the solution of problems hitherto unapproachable.
In the present paper we shall confine ourselves to the application
of this method to the detection of the metals of the alkalies and
alkaline earths, and to the illustration of the value of the
method in a series of examples.

The bright lines in the flame-spectrum are seen most plainly
when the temperature of the flame is highest, and its illu-
minating power least. The laboratory-lamp described by one
of usf, in which a mixture of air and gas burns, gives a flame
of extremely high temperature and very slight luminosity, and
is therefore especially well adapted for experiments upon the
bright lines produced in the way described.

Plate II. represents the spectra given by a colourless flame in
which chemically pure salts of potassium, sodium, lithium,
strontium, calcium, barium are allowed to volatilize. The solar
spectrum is added for the sake of comparison.

The potassium compound employed was obtained by igniting

* Communicated by Professor H. E. Roscoe.
t Poggendorff's Annalen, vol. c. p. 85 ; Phil. Trans. 1857, p. 377-
Phil Mag. S. 4. Vol. 20. No. 131. Aug. 1860. H

90 Professors Kirchhoff and Bunsen on Chemical

chlorate of potassium which had been previously recrystallized
six or eight times. The chloride of sodium was prepared by
neutralizing pure carbonate of sodium with hydrochloric acid
and crystallizing the salt several times. The salt of lithium was
purified by precipitation fourteen times with carbonate of am-
monium. The purest specimen of marble which could be
obtained, dissolved in hydrochloric acid, was the source of the
calcium salt. From this solution the carbonate of calcium was
thrown down in two portions by fractional precipitation with
carbonate of ammonium, the latter half of the calcium salt being
converted into the nitrate. The salt thus obtained was dissolved
in absolute alcohol, and after evaporation of the alcohol, converted
into the chloride by precipitation with carbonate of ammonium
and solution in hydrochloric acid.

In order to obtain pure chloride of barium, the commercial
salt was boiled out repeatedly with nearly absolute alcohol.
The residual salt freed from alcohol was dissolved in water, and
thrown down by fractional precipitation in two portions, of
which the second only was dissolved in hydrochloric acid, and
the salt still further purified by repeated crystallizations.

The pure chloride of strontium was prepared by crystallizing
the commercial salt several times from alcohol, and by fractional
precipitation of the salt with carbonate of ammonium, the second
portion being dissolved in nitric acid, and the nitrate freed from
the last traces of calcium salt by boiling with alcohol. The
product thus purified was lastly thrown down with carbonate of
ammonium, and the precipitate dissolved in hydrochloric acid.
All these various purifications were conducted as much as pos-
sible in platinum vessels.

The apparatus which we have usually employed for our
spectrum-observations is represented in the annexed woodcut.
A consists of a box blackened on the inside, the bottom of
which has the form of a trapezium, and rests on three feet ; the
two inclined sides of the box, which are placed at an angle of
about 58° from each other, carry the two small telescopes B and C.
The ocular lenses of the first telescope are removed, and in their
place is inserted a plate, in which a slit made by two brass knife-
edges is so arranged that it coincides with the focus of the
object-glass. The gas-lamp D stands before the slit in a position
such that the mantle of the flame is in a straight line with the
axis of the telescope B. Somewhat lower than the point at
which the axis of the tube produced meets the mantle, the end
of a fine platinum wire bent round to a hook is placed in the
flame. The platinum wire is supported in this position by a
small holder, E, and on to the hook is melted a globule of the
dried chloride which it is required to examine. Between the

Analysis by Spectrum-observations.

91

object-glasses of the telescopes B and C is placed a hollow
prism, F, filled with bisulphide of carbon, and having a refracting
angle of 60°. The prism rests upon a brass plate moveable
about a vertical axis. The axis carries on its lower part the
mirror G, and above that the arm H, which serves as a handle

for turning the prism and mirror. A small telescope placed
some way off is directed towards the mirror, and through this
telescope an image of a horizontal scale, fixed at some distance
from the mirror, is observed. By turning the prism round, every
colour of the spectrum may be made to move past the vertical
wire of the telescope C, and any required position in the spec-
trum thus brought to coincide with this vertical line. Each
particular portion of the spectrum thus corresponds to a certain
point on the scale. If the luminosity of the spectrum is very
small, the wire of the telescope C may be illuminated by means
of a lens, which throws a portion of the rays from a lamp through
a small opening in the side of the tube of the telescope C.

We have compared the spectra represented on the Plate, which
we have obtained from the pure chlorides, with those produced
when the bromides, iodides, hydrated oxides, sulphates and
carbonates of the several metals are brought into the following
flames : —

Into the flame of sulphur.

„ „ bisulphide of carbon.

„ „ aqueous alcohol.

Into the non-luminous flame of coal-gas.

Into the flame of carbonic oxide.
„ „ hydrogen.

Into the oxyhydrogen flame.

As the result of these somewhat lengthy experiments, the
details of which we here omit, it appears that the alteration of

H2

92 Professors Kirchhoff and Bun sen on Chemical

the bodies with which the metals employed were combined, the
variety in the nature of the chemical processes occurring in the
several flames, and the wide differences of temperature which
these flames exhibit, produce no effect upon the position of the
bright lines in the spectrum which are characteristic of each metal.
The following considerations show how much the temperature
of these various flames differ. An approximation to the tempe-
rature of a flame is obtained by help of the equation

._Zgw

in which t signifies the required temperature of the flame, g the
weight of one constituent of substance burning in oxygen, w the
heat of combustion of this constituent, p the weight, and s the
specific heat of one of the products of combustion. The heat
of combustion of the following bodies may be taken as —

Sulphur 2240 C.

Bisulphide of carbon . . 3400

Hydrogen 34462

Marsh-gas 13063

Elayle 11640

Ditetryle 11529

Carbonic oxide .... 2403

The specific heats under constant pressure were found by
Regnault to be —

Sulphurous acid = 0*1553
Carbonic acid =0*2164
Nitrogen =0*2440

Aqueous vapour =0*4750

Hence the temperatures of the flames are found to be —

The sulphur flame 1820 C.

The bisulphide of carbon flame . . 2195

The coal-gas flame* 2350

The carbonic oxide flame f .... 3042

The hydrogen flame in air % . . . 3259

The oxyhydrogen flame § .... 8061

It was found that the same metallic compound, placed in one
of these flames, gives a more intense spectrum the higher the
temperature of the flame. In the same flame, those of the com-
pounds of a metal give the brightest spectra which are most
volatile.

* Ann. Chem. Pharm. vol. cxi. p. 258.

t Bimsen's ' Gasometry,' p. 242. J Ibid. § Ibid.

Analysis by Spectrum-observations. 93

In order to prove still more conclusively that each of the
above-mentioned metals always produces the same bright lines
in the spectrum, we have compared the spectra represented in
the Plate with those produced when the electric spark passes
between electrodes made of these metals.

Small pieces of sodium, potassium, lithium, strontium, and
calcium were fastened to fine platinum wires and melted two
by two into glass tubes, so that the pieces of metal were sepa-
rated by about 1 to 2 millims., and the platinum wires were
melted through the sides of the glass tubes. Each of these
tubes was placed in front of the spectrum-instrument, and
by means of a RuhmkorfPs induction apparatus, sparks were
allowed to pass between the pieces of metal inside the tube ;
the spectrum thus produced was then compared with that given
by a gas-flame in which the chloride of the metal was brought.
The flame was placed behind the glass tube. By alternately
bringing the induction apparatus into and out of action, it was
easy, without measuring, to convince ourselves that in the
brilliant spectrum of the electric spark, the bright lines of the
flame-spectrum were present in their right position. Besides
these lines, other bright ones appeared in the electric-spark
spectrum ; some of these were produced by foreign metals present
in the electrodes, others arose from nitrogen, which filled the
tubes after the oxygen had combined with a portion of the
electrodes*.

From these facts it appears certain that the appearance of
the bright lines represented in the spectra on the Plate may be
regarded as absolute proof of the presence of the particular
metal. They serve as reactions by means of which these bodies
may be recognized with more certainty, greater quickness, and
in far smaller quantities than can be done by help of any other
known analytical method.

The spectra drawn on the Plate represent those seen when
the slit was of such a width that only the most conspicuous of
the lines of the solar spectrum were visible, the magnifying
power of the telescope C being a fourfold one, and the light of a
moderate degree of intensity. These circumstances seem to us
to be the most advantageous when it is required to make a
chemical analysis by means of spectrum-observations. The

* On employing on one occasion with strontium-electrodes a tube filled
with hydrogen instead of nitrogen, the stream of sparks changed rapidly
into a continuous arc of light, whilst a grey pellicle covered the inside of
the tube. The tube was opened under rock-oil, when it was found that it
was empty, the hydrogen having disappeared. This gas appears, at the
enormous temperature of the electric spark, to have decomposed the oxide
of strontium which was not completely removed from the metal.

94 Professors Kirchhoff and Bunsen on Chemical

appearance of the spectrum can under other conditions vary
considerably. If the purity of the spectrum be increased, many
of those lines which appeared before as single ones are split up
into several ; thus the sodium line is divided into two separate
lines. If the intensity of the light, on the other hand, be in-
creased, new lines appear in several of the spectra represented in
the Plate, and the relation of the brightness of the old ones becomes
altered. In general an indistinct line becomes brighter upon
increasing the illumination, more rapidly than does a brighter
line, but not to such an extent that the indistinct line ever
overtakes in intensity the brighter one. A good example of
this is seen in the two lithium lines. We have only observed
one exception to this rule, namely in the line Ba rj, which by
light of small intensity is scarcely visible, whilst Ba 7 appears
plainly, but by light of greater intensity becomes more visible
than the latter. This fact appears to us of importance, and
we intend on a future occasion to examine this point in detail.

We now proceed to describe the peculiarities of the several
spectra, the exact acquaintance with which is of practical im-
portance, and to point out the advantages which this new method
of chemical analysis possesses over the older processes.

Sodium.

The spectrum-reaction of sodium is the most delicate of all.
The yellow line Na a, the only one which appears in the sodium
spectrum, is coincident with Fraunhofer's dark line D, and is
remarkable for its exactly defined form, and for its extraordinary
degree of brightness. If the temperature of the flame be very
high, and the quantity of the substance employed very large,
traces of a continuous spectrum are seen in the immediate
neighbourhood of the line. In this case too, the weaker lines
produced by other bodies, when near the sodium line, are
discerned with difficulty, and are often first seen when the
sodium reaction has almost subsided.

The reaction is most visible in the sodium salts of oxygen,
chlorine, iodine, bromine, sulphuric acid, and carbonic acid.
But even in the silicates, borates, phosphates, and other non-
volatile salts, the reaction is always evident.

Swan* has already remarked upon the small quantity of
sodium necessary to produce the yellow line.

The following experiment shows that the chemist possesses
no reaction which in the slightest degree will bear comparison,
as regards delicacy, with this spectrum-analytical determination
of sodium. In a far corner of our experiment room, the capacity

* Trans. Roy. Soc. Edinb. vol. xxi. Part III. p. 411.

Analysis by Spectrum-observations. 95

of which was about 60 cubic metres, we burnt a mixture of 3
milligrammes of chlorate of sodium with milk-sugar, whilst the
non-luminous colourless flame of the lamp was observed through
the slit of the telescope. Within a few minutes the flame, which
gradually became pale yellow, gave a distinct sodium line, which,
after lasting for ten minutes, entirely disappeared. From the
weight of sodium salt burnt, and the capacity of the room,
it is easy to calculate that in one part by weight of air there is
suspended less than 20 ~ 000 of a part of soda-smoke. As the
reaction can be observed with all possible comfort in one second,
and as in this time the quantity of air which is heated to
ignition by the flame is found, from the rate of issue and from
the composition of the gases of the flame, to be only about 50
cub. cent, or 0*0647 grm. of air, containing less than 200o0000 of
sodium salt, it follows that the eye is able to detect with the
greatest ease quantities of sodium salt less than 8 00* 000 of a
milligramme in weight. With a reaction so delicate, it is easy
to understand why a sodium reaction is almost always noticed
in ignited atmospheric air. More than two-thirds of the earth's
surface is covered with a solution of chloride of sodium, fine
particles of which are continually being carried into the air by
the action of the waves. These particles of sea-water cast thus
into the atmosphere, evaporate, leaving almost iu conceivably
small residues, which, floating about, are almost always present
in the air, and are rendered evident to our eyesight in the
sunbeam. These minute particles perhaps serve to supply the
smaller organized bodies with the salts which larger animals
and plants obtain from the ground ; in another point of view,
however, the presence of this chloride of sodium in the air is of
interest. If, as is scarcely doubtful at the present time, the
explanation of the spread of contagious disease is to be sought
for in some peculiar contact-action, it is possible that the pre-
sence of so antiseptic a substance as chloride of sodium, even in
almost infinitely small quantities, may not be without influence
upon such occurrences in the atmosphere. By means of daily
and long-continued spectrum-observations, it would be easy to
discover whether the alteration of intensity in the line Na a
produced by the sodium in the air, have any connexion with the
appearance and direction of march of an endemic disease.

The unexampled delicacy of the sodium reaction explains also
the well-observed fact, that all bodies after a lengthened exposure
to air show the sodium line when brought into a flame, and that
it is only possible in a few salts to get rid of the last traces of
the line Naa, even after repeated crystallization from water
which had only been in contact with platinum. A thin platinum

96 Professors Kirchhoff and Bunsen on Chemical

wire, freed from every trace of sodium salt by ignition, shows the
reaction most visibly on allowing it to stand for a few hours in
the air. In the same way the dust which settles from the air
in a room, shows the bright line Na a : to render this evident
it is only necessary to knock a dusty book, for instance, at a
distance of some feet from the flame, when a wonderfully bright
flash of the yellow band is seen.

Lithium.

The luminous ignited vapour of the lithium compounds gives
two sharply defined lines, the one a very weak yellow line, Li /3,
and the other a bright red line, Li a. This reaction exceeds in
certainty and delicacy all methods hitherto known in analytical
chemistry. It is, however, not quite so sensitive as the sodium
reaction, only, perhaps, because the eye is more adapted to
distinguish yellow than red rays. When 9 milligrammes of
carbonate of lithium mixed with excess of milk-sugar was burnt,
the reaction was visible in a room of 60 cubic metre capacity.
Hence, according to the method already explained, we find that
the eye is capable of distinguishing with absolute certainty a
quantity of carbonate of lithium less than 10 ~ 000 of a milli-
gramme in weight : 0'05 grm. of carbonate of lithium salt, burnt
in the same room, was sufficient to enable the ignited air to show
the red line Li a for an hour after the combustion had taken
place.

The compounds of lithium with oxygen, iodine, bromine, and
chlorine are the most suitable for this peculiar reaction ; still
the carbonate, sulphate, and even the phosphate give almost as
distinct a reaction. Minerals containing lithium, such as tri-
phylline, triphane, petalite, lepidolite, require only to be held in
the flame in order to obtain the bright line Li a in the most
satisfactory manner. In this way the presence of lithium in
many felspars can be directly detected, as, for instance, in the
orthoclase from Baveno. The line is only seen for a few mo-
ments, directly after the mineral is brought into the flame. In
the same way the mica from Altenberg and Penig was found to
contain lithium, whereas micas from Miask, Ashaffenburg,
Modum, Bengal, Pennsylvania, &c, were found to be free from
this metal. In natural silicates which contain only small traces
of lithium, this metal is not observed so readily. The examina-
tion is then best conducted as follows : — A small portion of the
substance is digested and evaporated with hydrofluoric acid or
fluoride of ammonium, the residue moistened with sulphuric acid
and heated, the dry mass being dissolved in absolute alcohol.
The alcoholic extract is then evaporated, the dry mass again dis-
solved in alcohol, and the extract allowed to evaporate on a shal-

Analysis by Spectrum-observations. 97

low glass dish. The solid pellicle which remains is scraped off
with a fine knife, and brought into the flame upon the thin
platinum wire. For one experiment, TV of a milligramme is in
general quite a sufficient quantity. Other compounds besides
the silicates, in which small traces of lithium require to be de-
tected, are transformed into sulphates by evaporation with sul-
phuric acid or otherwise, and then treated in the manner de-
scribed.

In this way we arrive at the unexpected conclusion that lithium
is most widely distributed throughout nature, occurring in
almost all bodies. Lithium was easily detected in 40 cubic
centimetres of the water of the Atlantic Ocean, collected in 41°
41' N. latitude, and 39° 14' W. longitude. Ashes of marine
plants (kelp), driven by the Gulf-stream on the Scotch coasts,
contain evident traces of this metal. All the orthoclase and
quartz from the granite of the Odenwald which we have examined
contain lithium. A very pure spring water from the granite in
Schlierbach, on the west side of the valley of the Neckar, was
found to contain lithium, whereas the water from the red sand-
stone which supplies the Heidelberg laboratory was shown to
contain none of this metal. Mineral waters, in a litre of which
lithium could hardly be detected according to the ordinary
methods of analysis, gave plainly the line Li a, even if only a
drop of the water on a platinum wire was brought into the flame*.
All the ashes of plants growing in the Odenwald on a granite
soil, as well as Russian and other potashes, contain lithium. Even
in the ashes of tobacco, vine leaves, of the wood of the vine,
and of grapes f, as well as in the ashes of the crops grown
in the Rhine-plain near Waghausel, Deidesheim, and Heidelberg,
on a non-granitic soil, was lithium found. The milk of the
animals fed upon these crops also contains this widely diffused
metal J.

It is scarcely necessary to say that a mixture of volatile sodium
and lithium salts gives the reaction of lithium alongside that
of sodium with a precision and distinctness which are hardly
perceptibly diminished. The red lines of the former substance
are still plainly seen when the bead contains l01o6 part of lithium
salt, and when to the naked eye the yellow soda-flame appears
untinged by the slightest trace of red. In consequence of the

* When liquids have to be brought into the flame, it is best to bend the
end of the platinum wire, of the thickness of a horsehair, to a small ring,
and to beat this ring flat. If a drop of liquid be brought into this ring,
enough adheres to the wire for one experiment.

t In the manufactories of tartaric acid, the mother-liquors contain so
much lithium salts that considerable quantities can thus be prepared.

X Dr. Folwarczny has been able to detect lithium in the ash of human
blood and muscular tissue by help of the line Li a.

98 Professors Kirchhoff and Bunsen on Chemical

somewhat greater volatility of the lithium salt, the sodium
reaction lasts longer than that of the other metal. In those
cases, therefore, in which small quantities of lithium have to be
detected in presence of large quantities of sodium salt, the bead
must be brought into the flame whilst the observer is looking
through the telescope. The lithium lines are often only seen
during a few moments amongst the first products of the volati-
lization.

In the production of lithium salts on the large scale, in the
proper choice of a raw material, and in the arrangement of
suitable methods of separation, this spectrum-analysis affords
most valuable aid. Thus it is only necessary to place a drop
of mother-liquor from any mineral spring in the flame and to
observe the spectrum produced, in order to show that in many of
these waste products a rich and hitherto unheeded source of
lithium salts exists. In the same way during the course of the
preparation any loss of lithium in the collateral products and
residues can be easily traced, and thus more convenient and
economical methods of preparation may be found to replace
those at present employed*.

Potassium.

The volatile potassium compounds give, when placed in the
flame, a widely extended continuous spectrum, which contains
only two characteristic lines, namely, one line, Ka a, in the
outermost red approaching the ultra-red rays, exactly coinciding
with the dark line A of the solar spectrum, and a second line,
Ka /3, situated far in the violet rays towards the other end of
the spectrum, and also identical with a particular dark line
observed by Fraunhofer. A very indistinct line coincWing
with Fraunhofer's line B, which, however, is only seen when
the light is very intense, is not by any means so characteristic.
The violet line is somewhat pale, but can be used almost as
well as the red line for the detection of potassium. Owing to
the position of these two lines, both situated near the limit at
which our eyes cease to be sensitive to the rays, this reaction
for potassium is not so delicate as the reaction for the two
metals already mentioned. The reaction became visible in the
air of our room when 1 gramme of chlorate of potassium
mixed with milk-sugar was burnt. In this way, therefore, the

* We obtained by such an improved method from two jars (about 4
litres) of a mother-liquor from a mineral spring, which by evaporation with
sulphuric acid gave l**2of residue, half an ounce of carbonate of lithion of
the purity of the commercial, the cost of which is about 140 florins the
pound. A great number of other mineral-spring mother-liquors which we
examined showed a similar richness in compounds of lithium.

Analysis by Spectrum-observations. 99

eye requires the presence of l0100 of a milligramme of chlorate
of potassium in order to detect the presence of potassium.

Caustic potash, and all compounds of potassium with vola-
tile acids, give the reaction without exception. Potash sili-
cates, and other non-volatile salts, on the other hand, only
produce the reaction when the metal is present in very large
quantities. It is only necessary, however, to melt the substance
with a bead of carbonate of sodium, in order to detect potassium
even when present in a very small quantity. The presence of
the sodium does not in the least interfere with the reaction, and
scarcely diminishes its delicacy. Orthoclase, sanidine, and
adularia may in this way be easily distinguished from albite,
oligoclase, Labradorite, and anorthite. In order to detect the
smallest traces of potassium salt, the silicate requires only to be
slightly ignited with a large excess of fluoride of ammonium on
a platinum capsule, after which the residue is brought into the
flame on a platinum wire. In this way it is found that almost
every silicate contains potash. Salts of lithium diminish or
influence the reaction as little as soda salts. Thus we need
only to hold the end of a burnt cigar in the flame before the
slit, in order at once to see the yellow line of sodium and the
two red lines of potassium and lithium, this latter metal being
scarcely ever absent in tobacco ash.

Strontium.

The spectra produced by the alkaline earths are by no means
so simple as those produced by the alkalies. That of strontium
is especially characterized by the absence of green bands. Eight
lines in the strontium-spectrum are remarkable, namely, six red,
one orange, and one blue line. The orange line, Sr«, which
appears close by the sodium line towards the red end of the spec-
trum, the two red lines, Sr /9 and Sr 7, and lastly, the blue line,
SrS, are the most important strontium bands, both as regards their
position and their intensity. For the purpose of examining the
intensity of the reaction, we quickly heated an aqueous solution
of chloride of strontium, of a known degree of concentration,
in a platinum dish over a large flame until the water was evapo-
rated and the basin became red-hot. The salt then began to
decrepitate, and was thrown in microscopic particles out of the
dish in the form of a white cloud carried up into the air. On
weighing the residual quantity of salt, it was found that in this
way 0*077 grm. of chloride of strontium had been mixed in the
form of a fine dust with the air of the room, weighing 77000
grms. As soon as the air in the room was perfectly mixed, by
rapidly moving an open umbrella, the characteristic lines of the
strontium- spectrum were beautifully seen. According to this

100 Professors Kirchhoff and Bunsen on Chemical

experiment, a quantity of strontium may be thus detected equal
to the j^^0 part of a milligramme in weight.

The chlorine and the other haloid salts of strontium give the
best reaction. The hydrated oxide and the carbonate of stron-
tium give the action less vividly, the sulphate less distinctly,
whilst the compounds of strontium with the non-volatile acids
give either a very slight reaction or else none at all. Hence it
is well first to bring the bead of substance alone into the flame,
and then again after moistening with hydrochloric acid. If it
be supposed that sulphuric acid is present in the bead, it must
be held in the reducing part of the flame before it is moistened
with hydrochloric acid, for the purpose of changing the sulphate
into the sulphide, which is decomposed by hydrochloric acid. In
order to detect strontium when combined with silicic, phospho-
ric, boracic, and other non-volatile acids, the following course of
procedure gives the best results. Instead of fusing with carbo-
nate of sodium in a platinum crucible, a conical spiral of plati-
num wire is employed ; this spiral is heated to whiteness in
the flame, and dipped whilst hot into finely powdered dried
carbonate of sodium, which properly should contain so much
water that a sufficient quantity adheres to the wire when it is
once dipped into the salt. The fusion takes place in this spiral
much more quickly than in a platinum crucible, as the mass of
platinum requiring heating is small, and the flame comes into
direct contact with the salt. As soon as the finely powdered
mineral has been brought into the fused soda by means of a
small platinum spatula, and the mass retained above the fusion
point for a few minutes, the cooled mass has only to be turned
upside down, and knocked on the porcelain plate of the lamp
in order to obtain the salt in one coherent bead. The fused
mass is covered by a piece of writing-paper, and then broken by
pressing it with the blade of a steel spatula until the whole is in
the state of a fine powder. The powder is collected to one spot
on the edge of the plate, and carefully covered with hot water,
which is allowed to flow backwards and forwards over it, so that,
after decanting and rewashing the powder several times, all the
soluble salts are extracted without losing any of the residue. If
a solution of chloride of sodium be employed instead of water,
the operation may be conducted still more rapidly. The inso-
luble salt contains the strontium as carbonate ; and one or two
tenths of a milligramme of the substance, brought on to the
wire and moistened with hydrochloric acid, is sufficient to pro-
duce the most intense reaction. It is thus possible, without help
of platinum crucible, mortar, evaporating basin, or funnel and
filter, to fuse, powder, digest, and wash out the substance in the
space of a few minutes.

Analysis by Spectrum-observations. 101

The reactions of potassium and sodium are not influenced by
the presence of strontium. Lithium also can be easily detected
in presence of strontium when the proportion of the former
metal is not very small. The lithium line Li a appears as an
intensely red sharply defined band upon a less distinct red
ground of the broad strontium band Sr yS.

Calcium.

The spectrum produced by calcium is immediately distin-
guished from the four spectra already considered by the very
characteristic bright green line Ca /3. A second no less charac-
teristic feature in the calcium spectrum is the intensely bright
orange line Ca u, lying considerably nearer to the red end of
the spectrum than either the sodium line Na a, or the orange
band of strontium Sr a. By burning a mixture consisting of
chloride of calcium, chlorate of potassium, and milk-sugar, a white
cloud is obtained which gives the reaction with as great a degree
of delicacy as strontium salts do under similar circumstances.
In this way we found that 10 000 000 of a milligramme in weight
of chloride of calcium can be detected with certainty. Only the
volatile compounds of calcium give this reaction ; the more vola-
tile the salt the more distinct and delicate does the reaction be-
come. The chloride, bromide, and iodide of calcium are in this
respect the best compounds. Sulphate of calcium produces the
spectrum, after it has become basic, very brightly and continu-
ously. In the same way the reaction of the carbonate becomes
more distinctly visible after the acid has been expelled.

Compounds of calcium with the non-volatile acids remain in-
active in the flame; but if they are attacked by hydrochloric
acid, the reaction may be easily obtained as follows : — A few
milligrammes of finely powdered substance are brought on to
the moistened flat platinum ring in the moderately hot portion
of the flame, so that the powder is fritted, but not melted on to
the wire ; if a drop of hydrochloric acid be now allowed to fall
into the ring so that the greater part of the acid remains hang-
ing on to the wire, and if then the wire be brought into the
hottest part of the flame, the drop evaporates in the spheroidal
state without ebullition. The spectrum of the flame must be ob-
served during this operation ; and it will be noticed that at the
moment when the last particles of liquid evaporate, a bright
calcium spectrum appears. If the quantities of the metal pre-
sent are very small, the characteristic lines are only seen for a
moment; if larger quantities are contained, the phenomenon
lasts for a longer time.

Only in the silicates which are decomposed by hydrochloric
acid can the calcium be thus found. In those minerals which

102 Professors Kirchhoff and Bunsen on Chemical

are not attacked by that acid, the following method may be best
employed for the detection of calcium. A few milligrammes of
the substance under examination, in a state of fine division, are
brought upon a flat platinum lid, together with about a gramme
of fluoride of ammonium, and the mixture is gently ignited until
all the fluoride is volatilized. The slight crust of salt remaining
is moistened with a few drops of sulphuric acid, and the excess
of acid removed by heat. If about a milligramme of the resi-
dual sulphates be scraped together with a knife, and brought
into the flame, the characteristic spectra of potassium, sodium,
and lithium, supposing these three metals to be present, are
first obtained either simultaneously or consecutively. If calcium
and strontium be also present, the corresponding spectra gene-
rally appear somewhat later, after the potassium, sodium, and
lithium have been volatilized. When only traces of strontium
and calcium are present, the reaction is not always seen ; it be-
comes, however, immediately apparent on holding the bead for a
few moments in the reducing flame and, after moistening it
with hydrochloric acid, again bringing it into the flame.

These easy experiments, such as either heating the specimen
alone, or after moistening with hydrochloric acid, or after treat-
ing the powder with fluoride of ammonium, either alone or in
presence of sulphuric or hydrochloric acid, provide the minera-
logist and geologist with a series of most simple methods of
recognizing the components of the smallest fragment of many
substances (such, for instance, as the double silicates containing
lime) with a certainty which is attained in an ordinary analysis
only by a large expenditure of time and material. The follow-
ing examples will illustrate this statement.

1. A drop of sea- water heated on the platinum wire shows at
first a strong sodium reaction ; and after volatilization of the
chloride of sodium, a weak calcium spectrum is observed, which
on moistening the wire with hydrochloric acid becomes at once
very distinct. If a few decigrammes of the residual salts ob-
tained by the evaporation of sea-water be treated in the manner
described under lithium with sulphuric acid and alcohol, the
potassium and lithium reactions are obtained. The presence of
strontium in sea-water can be best detected in the boiler-crust
from sea-going steamers. The filtered hydrochloric acid solution
of such a crust leaves, on evaporation and subsequent treatment
with a small quantity of alcohol, a residue slightly yellow-
coloured from basic iron salt, which is deposited after some
days, and can then be collected on a small filter and washed
with alcohol. The filter, burnt on a fine platinum wire and held
in the flame, gives, besides the calcium lines, an intensely bright
strontium spectrum.

Analysis by Spectrum-observations, 103

2. Mineral waters often exhibit the reactions of potassium,
sodium, lithium, calcium, and strontium by mere heating. If,
for example, a drop of the Diirkheim or Kreuznach waters be
brought into the flame, the lines Na «, Li a, Ca a, and Ca /3
are at once seen. If, instead of using the water itself, a drop of
the mother-liquor is taken, these bands appear most vividly.
As soon as the chlorides of sodium and lithium have been to a
certain extent volatilized, and the chloride of calcium has become
more basic, the characteristic lines of the strontium spectrum
begin to show themselves, and continue to increase in distinct-
ness, until at last they come out in all their true brightness. In
this case, therefore, by the mere observation of a single drop
undergoing vaporization, the complete analysis of a mixture
containing five constituents is performed in a few seconds.

3. The ash of a cigar moistened with hydrochloric acid, and
held in the flame, shows at once the bands Na a, Ka a, Li a,
Ca a, Ca 0.

4. A piece of hard potash-glass combustion tubing gave, both
with and without hydrochloric acid, the lines Na a and Ka a ;
treated with fluoride of ammonium and sulphuric acid, the bands
Ca a, Ca /3, and traces of Li a were rendered visible.

5. Orthoclase from Baveno gives, either alone or when treated
with hydrochloric acid only, the line Na a with traces of Li a
and Ka a. ; with fluoride of ammonium and sulphuric acid, the
bright lines Na a and Ka a, and a somewhat less distinct Li a,
are seen. After volatilization of the bodies thus detected, the
bead moistened with hydrochloric acid gives a scarcely distin-
guishable flash of the lines Ca « and Ca /3. The residue on the
platinum wire, when moistened with cobalt solution and heated,
gives the blue colour so characteristic of alumina. If the well-
known reaction of silicic acid be likewise employed, we may
conclude from this examination, made in the course of a very few
minutes, that the orthoclase from Baveno contains silicic acid,
alumina, potash with traces of soda, lime, and lithia ; and also
that no trace of baryta or strontia is present.

6. Adularia from St. Gothard comported itself in a similar
manner, with the exception that the calcium reaction was indi-
stinctly seen, whilst that of lithium was altogether wanting.

7. Labradorite from St. Paul gives the sodium line Na a, but
no calcium spectrum. On moistening the fragment with hydro-
chloric acid, the lines Ca a and Ca /3 appear very distinct ; with
the fluoride of ammonium test, a weak potassium reaction is ob-
tained, and also faint indications of lithium.

8. Labradorite from the Corsican diorite gave similar reac-
tions, except that no lithium was found.

9. Mosanderite from Brevig, and Tscheffkinite from the

104 Professors Kirchhoff and Bunsen on Chemical

Ilmengebirge, showed, when treated alone, the sodium reaction ;
on the addition of hydrochloric acid, the lines Ca a and Ca $
appeared.

10. Melinophane from Lamoe gave the line Na a when placed
alone in the flame ; with hydrochloric acid the lines Ca a, Ca ft
and Li a became visible.

11. Scheelite and sphene give, on treatment with hydrochloric
acid, a very intense calcium reaction.

12. When small quantities of strontium are present together
with calcium, the line Sr 8 may be most conveniently employed
for the detection of this metal. In this way the presence of
small quantities of strontium can be easily detected in very many
sedimentary limestones. The lines Na a, Li a, Ka a, especially
Li a, are observed as soon as the limestone is brought into the
flame. Converted by hydrochloric acid into chlorides, and
brought in this form into the flame, these minerals give the
same bands ; and not unfrequently the line Sr 8 is also distinctly
seen. This latter appears, however, only for a short time, and
is in general best seen when the calcium spectrum begins to fade.

In this way the lines Na a, Li a, Ka a, Ca a, Ca ft and Sr 8
were found in the spectra of the following limestones : —

Limestone from the Silurian at Kugelbad near Prague.
Muschelkalk from Rohrbach near Heidelberg. Limestone from
the Lias at Malsch in Baden. Chalk from England.

The following limestones gave the lines Na a, Li a, Ka a, Ca a,
Ca ft but not the blue strontium band Sr 8 : —

Marble from the granite near Auerbach *. Limestone from the
Devonian at Gerolstein in the Eifel. Carboniferous limestone
from Plauitz in Saxony. Dolomite from Nordhausen in the Harz.
Jura kalk from Streitberg in Franconia.

From these few experiments it is evident that a more extended
series of exact spectrum analyses, respecting the amount of stron-
tium, lithium, sodium, and potassium which the various limestone
formations contain, must prove of the greatest geological im-
portance, both as regards the order of their formation and their
local distribution, and may possibly lead to the establishment of
some unexpected conclusions respecting the nature of the oceans
from which these limestones were originally deposited.

Barium.
The barium spectrum is the most complicated of the spectra
of the alkalies and alkaline earths. It is at once distinguished

* According to the method already described, a quantity of nitrate of
strontium was obtained from 20 grms. of this marble such as to give a com-
plete and vivid strontium spectrum. We have not examined the other
limestones in the same way.

Analysis by Spectrum-observations. 105

from all the others by the green lines Ba a and Ba /3 (which are
by far the most distinct) appearing the first and continuing
during the whole of the reaction. Ba 7 is not quite so distinct,
but is still a well-marked and peculiar line. As the barium spec-
trum is considerably more extended than those of the other
metals, the reaction is not observed to so great a degree of
delicacy ; still 0*3 grm. of chlorate of barium burnt with milk-
sugar gave a distinct band of Ba a which lasted for some time,
when the air of the room was well mixed by moving an open
umbrella about. Hence we may calculate, in the same manner
as was done in the sodium experiment, that about y^ws °^ a m*Ui-
gramme of barium salt maybe detected with the greatest certainty.

The chloride, bromide, iodide, and fluoride of barium, as also
the hydrated oxide, the sulphate, and carbonate, show the reac-
tion best. It may be obtained by simply heating any of these
salts in the flame.

Silicates containing barium, which are decomposed by hydro-
chloric acid, also give the reaction if a drop of hydrochloric acid
be added to them before they are brought into the flame. Baryta-
harmotome, treated in this way, gives the lines Ca ex. and Ca /3,
together with the bands Ba a and Ba /?.

Compounds of barium with fixed acids, giving no reaction
either when alone or after addition of hydrochloric acid, should
be fused with carbonate of sodium, as described under strontium,
and the carbonate of barium thus obtained examined. If
barium and strontium occur in small quantities together with
large amounts of calcium, the carbonates obtained by fusion are
dissolved in nitric acid, and the dried salt extracted with alcohol.
The residue contains only barium and strontium, both of which
can almost always be detected. When we wish to test for small
traces of strontium or barium, the residual nitrates are converted
into chlorides by ignition with sal-ammoniac, and the chloride of
strontium is extracted by alcohol. Unless one or more of the
bodies to be detected is present in very small quantities, the
methods of separation just described are quite unnecessary, as is
seen from the following experiment : —

A mixture of the chlorides of potassium, sodium, lithium,
calcium, strontium, and barium, containing at the most T^- of a
milligramme of each of these salts, was brought into the flame,
and the spectra produced were observed. At first the bright
yellow sodium line Na a appeared, with a background formed by
a nearly continuous pale spectrum. As soon as this line began
to fade, the exactly defined bright red line of lithium Li « was
seen ; and still further removed from the sodium line the faint
red potassium line Ka a was noticed, whilst the two barium lines,
Ba Uj Ba 0, with their peculiar form, became visible in the proper

Phil Mag, S. 4. Vol. 20. No. 131. Aug. 1860. I

106 Professors Kirchhoff and Bun sen on Chemical

position. As the potassium, sodium, lithium, and barium salts
volatilized, their spectra became fainter and fainter, and their
peculiar bands one after the other vanished, until, after the lapse
of a few minutes, the lines Ca «, Ca /8, Sr a, Sr /3, Sr 7, and Sr S
became gradually visible, and, like a dissolving view, at last
attained their characteristic distinctness, colouring, and position,
and then, after some time, became pale and disappeared entirely.
The absence of any one or of several of these bodies is at once
indicated by the non-appearance of the corresponding bright lines.

Those who become acquainted with the various spectra by
repeated observation, do not need to have before them an exact
measurement of the single lines in order to be able to detect the
presence of the various constituents ; the colour, relative position,
peculiar form, variety of shade and brightness of the bands are
quite characteristic enough to ensure exact results, even in the
hands of persons unaccustomed to such work. These special
distinctions may be compared with the differences of outward ap-
pearance presented by the various precipitates which we employ
for detecting substances in the wet way. Just as it holds good as a
character of a precipitate that it is gelatinous, pulverulent, floccu-
lent, granular, or crystalline, so the lines of the spectrum exhibit
their peculiar aspects, some appearing sharply defined at their
edges, others blended off either at one or both sides, either similarly
or dissimilarly, or some, again, appearing broader, others narrower;
and just as in ordinary analysis we only make use of those precipi-
tates which are produced with the smallest possible quantity of the
substance supposed to be present, so in analysis with the spectrum,
we employ only those lines which are produced by the smallest
possible quantity of substance and require a moderately high
temperature. In these respects both analytical methods stand on
an equal footing ; but analysis with the spectrum possesses a great
advantage over all other methods, inasmuch as the characteristic
differences of colour of the lines serve as the distinguishing
feature of the system. Most of the precipitates which are valu-
able as reactions are colourless ; and the tint of those which are
coloured varies very considerably according to the state of divi-
sion and mechanical arrangement of the particles. The presence
of even the smallest quantity of impurity is often sufficient
entirely to destroy the characteristic colour of a precipitate ; so
that no reliance can be placed upon nice distinctions of colour as
an ordinary chemical test. In spectrum-analysis, on the con-
trary, the coloured bands are unaffected by such alteration of
physical conditions, or by the presence of other bodies. The
positions which the lines occupy in the spectrum give rise to

Analysis' by Spectrum-observations, 107

chemical properties as unalterable as the combining weights
themselves,, and which can therefore be estimated with an almost
astronomical precision. The fact, however, which gives to this
method of spectrum- analysis an extraordinary importance is, that
the chemical reactions of matter thus reach a degree of delicacy
which is almost inconceivable. By an application of this method
to geological inquiries concerning the distribution and arrange-
ment of the components of the various formations, the most
valuable results may be expected ; even the few random experi-
ments already mentioned have led to the unexpected conclusion,
that not only potassium and sodium, but also lithium and stron-
tium must be added to the list of bodies occurring, only indeed
in small quantities, but most widely spread, throughout the
matter composing the solid body of our planet.

The method of spectrum-analysis may also play a no less im-
portant part as a means of detecting new elementary substances ;
for if bodies should exist in nature so sparingly diffused that the
analytical methods hitherto applicable have not succeeded in
detecting, or separating them, it is very possible that their
presence may be revealed by a simple examination of the spectra
produced by their flames. We have had opportunity of satis-
fying ourselves that in reality such unknown elements exist. We
believe that, relying upon unmistakeable results of the spectrum-
analysis, we are already justified in positively stating that, besides
potassium, sodium, and lithium, the group of the alkaline metals
contains a fourth member, which gives a spectrum as simple
and characteristic as that of lithium — a metal which in our ap-
paratus gives only two lines, namely a faint blue one, almost
coincident with the strontium line Sr S, and a second blue one
lying a little further towards the violet end of the spectrum, and
rivalling the lithium line in brightness and distinctness of out-
line.

The method of spectrum-analysis not only offers, as we flatter
ourselves we have shown, a mode of detecting with the greatest
simplicity the presence of the smallest traces of certain elements
in terrestrial matter, but it also opens out the investigation of
an entirely untrodden field, stretching far beyond the limits of
the earth, or even of our solar system. For, in order to examine
the composition of luminous gas, we require, according to this
method, only to see it ; and it is evident that the same mode of
analysis must be applicable to the atmospheres of the sun and
of the brighter fixed stars. A modification must, however, be
introduced in respect to the light which these heavenly bodies
themselves emit. In a memoir published by one of us*, "On

* Kirchhoff, Poggendorff's Annalen, vol. cix. p. 275 ; and Phil. Mag.
S.4, vol. xx. p. 1.

1%

108 Professors Kirchhoff and Bunscn on Chemical

the Relation between the Coefficients of Emission and Absorp-
tion of Bodies for Heat and Light/' it was proved from theo-
retical considerations that the spectrum of an incandescent gas
becomes reversed (that is, that the bright lines become changed
into dark ones) when a source of light of sufficient intensity,
giving a continuous spectrum, is placed behind the luminous
gas. From this we may conclude that the solar spectrum, with
its dark lines, is nothing else than the reverse of the spectrum
which the sun's atmosphere alone would produce. Hence, in
order to effect the chemical analysis of the solar atmosphere, all
that we require is to discover those substances which, when
brought into the flame, produce bright lines coinciding with the
dark ones of the solar spectrum.

In the paper above referred to, the following experimental
facts are given in confirmation of the preceding theoretical con-
clusion.

The bright red line produced in the spectrum of a gas-flame
by the presence of a bead of chloride of lithium, is changed into
a'dark one when direct sunlight is allowed to pass through the
flame. When the bead of lithium is replaced by one of chloride
of sodium, the dark double line D (coincident with the yellow
sodium line) appears with uncommon distinctness.

The dark double line D also appears when the rays of a Drum-
mond's light are passed through the flame of aqueous alcohol
into which chloride of sodium is thrown*.

It appeared of interest to obtain still further confirmation of
this important theoretical conclusion ; the following experiments
answered this purpose : —

We ignited a thick platinum wire in the flame, and then by
means of an electric current, heated it to a temperature approach-
ing its melting-point. The wire gave a bright spectrum, in
which no trace of either dark or bright lines was seen. A flame
of weak aqueous alcohol, in which common salt was dissolved,
on being brought between the wire and the slit of the apparatus,
gave the dark line D most distinctly.

In the Philosophical Magazine for March 1860, Prof. Stokes calls atten-
tion to the fact that in the year 1849 Foucault made an observation very
similar to the above. In the examination of the spectrum produced by the
electric arc between carbon points, Foucault noticed that bright lines occur
where the double line D of the solar spectrum is found, and that this dark
line D is produced or made more intense when the rays of the sun, or those
from one of the incandescent carbon poles, are passed through the luminous
arc. The observation mentioned in the text affords an explanation of this
interesting phenomenon observed by Foucault eleven years ago, proving
that it is not occasioned by the properties of the electric light, which in
many respects is still so enigmatical, but that it arises from a compound
of sodium contained in the pole, and converted into incandescent gas by
the current.

Analysis by Spectrum-observations. 109

The dark line D can be produced in the spectrum of a platinum
wire heated in a flame, by holding between flame and spectrum
a test-tube containing some sodium amalgam which is heated to
boiling. This experiment is important, because it shows that
sodium vapour at a temperature much below that at which it
becomes luminous, exerts its absorptive power at exactly the same
point of the spectrum as it does art the highest temperatures
which we can produce, or at the temperatures existing in the
solar atmosphere.

We have succeeded in reversing the bright lines in the spectra
of Ka, Sr, Ca, Ba, by employing sunlight and mixtures of the
chlorates of these metals with milk-sugar. A small iron trough
was fixed in front of the slit of our apparatus, in which the mix-
ture was placed ; the direct sunlight was then allowed to fall
along the whole length of the trough, and the mixture ignited
with a heated wire. The telescope C, with the wires cutting
each other at an acute angle, was placed so that the point of in-
tersection of the wires coincided with the bright line of the
flame-spectrum which was to be examined. The observer con-
centrated his attention upon this point, to judge whether, at the
moment of burning the mixture, a dark line showed itself pass-
ing through the point of intersection of the cross wires. In this
way it was easy, when the right proportions for the mixtures
were found, to show that the lines Ba «, Ba /3, as well as the
line Ka /3, were reversed. The last of these lines coincides with
one of the most distinct dark lines in the solar spectrum, though
not marked by Fraunhofer, which, however, appears much more
plainly than it is generally seen at the moment the potash salt
burns. In order to prove that the strontium lines can be re-
versed, the chlorate of strontium must be most carefully dried,
as the slightest trace of moisture produces a positive strontium
spectrum, owing to the small particles of salt being thrown
about in the flame, and thus diminishing the power of the solar
rays.

We have, in the present memoir, contented ourselves with
such an examination of the spectra of the metals of the alkalies
and alkaline earths as was necessary for the analysis of terrestrial
matter. We reserve for a future communication the further
applications of the spectrum-analytical method to terrestrial
matter, and to the analysis of the atmospheres of the stars.

[ no ]

X. On the Bases produced by the Destructive Distillation of Peat.
By Arthur H. Church and Edward Owen *.

THE crude material which furnished the bases described in
the present communication was obtained by the destruc-
tive distillation of Irish peat. The operation was performed in
a blast-furnace, according to the patent of Mr. Rees Reece, the
carbonaceous residues of former operations constituting the fuel
employed. The distillation was conducted at the lowest possible
temperature, avoiding thereby any undue carbonization of the
turf prior to the formation and liberation of its volatile products.
Close to the nozzle or tuyere of the blast, the heat, it is true, is
intense ; but the carbonic acid there produced passing up the
furnace through a zone of carbon, is reduced in temperature
and converted into carbonic oxide, while this gas ascending higher
carries off the tarry products of the turf at a temperature of
some 200° C. only. The bases upon which we have been ex-
perimenting were contained in the distillate of a tar thus pro-
duced in the destructive distillation of peat in an atmosphere of
carbonic oxide and marsh-gas at the lowest possible temperature.
According to the researches of Kane and Sullivan, the tarry pro-
ducts from the various kinds of peat differ but very inconsider-
ably in their ultimate composition.

The process adopted in order to extract the bases from the
peat distillate was essentially the 3ame as that employed by
Hofmann, and described by him in his papers on the organic
bases contained in coal-gas naphtha. The oil, about 400
gallons, being the product from the distillation of 100 tons of
peat, was shaken with hydrochloric acid, the solution drawn off,
and this operation repeated until no more bases were thus ex-
tracted. The pyrrol and other impurities in the acid solution
were then removed by long-continued ebullition, and evaporation
to a small bulk. The liquid was then filtered, introduced into
a still, and supersaturated with lime. The bases that came over
on distillation were again combined with hydrochloric acid, and
separated anew by distillation with excess of potash. They were
then thoroughly dried with caustic potash, and submitted to re-
peated fractional distillations. The ammonia (the quantity of
which yielded by peat is comparatively trifling) and any very
volatile bases present had been previously eliminated in the ori-
ginal distillation of the peat, and occurred in the watery fluid
which accompanied the oils.

The following sketch, which represents very roughly the
amount of base which came over in the 8th rectification at in-
tervals of 5° C, or in some cases of 10°, may serve to give some
* Communicated by the Authors.

On the Bases produced by the Destructive Distillation of Peat. Ill

idea of the proportionate quantities of the various bases present,
for it was found that these proportions were not very materially
altered even after the tenth rectification.

I I

98

175

195

275

Between 500 and 600 distillations were performed during the
course of the present investigation, and the expenditure of
material, time, and labour has been very large. We could have
wished to offer an exhaustive account of the complex basic fluid
which we have worked upon ; the entire absence of any previous
knowledge of the bases produced by the destructive distillation
of peat must be our excuse for the imperfections of the present
memoir.

A. few tentative experiments were first made as to the nature
and composition of the basic oils by means of their platinum
salts. But our attention was soon mainly directed to the most
volatile fraction collected between 95° and 97°, and the boiling-
point of which was almost constant at 97°. This liquid was in
reality separated by an interval of 23° from the next higher
fraction, while any more volatile bases that might originally
have been present in the distilled oil had been lost in the
various operations to which it had been subjected. To this body,
which subsequent examination proved to be a pure base, we
have assigned the name cespitine. We proceed to detail our
analyses and experiments, and to give some account of the pro-
perties of the new base and its derivatives.

Cespitine.

The fraction 95° to 100° of the 8th rectification was dried

thoroughly with caustic potash and redistilled, — the portion

coming over between 95° and 97°, which constituted T9oths of

the whole, being employed for experiment. A considerable

112 Messrs. A. H. Church and E. Owen on the Bases

quantity was dissolved in water, hydrochloric acid added, and
then bichloride of platinum ; sufficient water to redissolve the
orange-yellow crystalline precipitate first formed was then
poured in and the mixture set aside to crystallize. Several crops
of magnificent orange-red shuttle-shaped crystals were suc-
cessively obtained, and these, after washing with alcohol and
ether, gave the following results on analysis : —

I. 0*325 grm. gave 0*2432 grm. carbonic acid and 0*1414
grm. water.

II. 0*2705 grm. gave 0*201 grm. carbonic acid and 0*119
grm. water.

III. 0*3008 grm. gave 0*101 grm. platinum.

IV. 0*409 grm. gave 0*1378 grm. platinum.

V. 0*1925 grm. gave 0*0648 grm. platinum and 0*283 grm.
chloride of silver.

These numbers correspond to the following per-centages : —

Experiment. Theory,

I. II. III. IV. V. Cl0H14NCl,PtCl2.

Carbon 20*41 20*26 20*43

Hydrogen 4*83 4*89 4*77

Nitrogen . . . . . . . . . . 4*77

Chlorine 36*36 36*29

Platinum .. .. 33*57 33*69 33*66 33*74*

10000
The platinum salt analysed had therefore the composition of
that of amylamine ; our reasons for thinking it isomeric but not
identical with that substance, will be found below. We place
but little reliance upon any distinctions based upon the physical
characteristics only of the two salts, such characteristics being
singularly variable in the case of many platinum salts. A few
brilliant yellow spangles finally separated from the mother-liquor
of the cespitine platinum compound, and gave the following
result when burnt : —

0*1786 grm. gave 0*0618 grm. platinum.
This corresponds to 34*60 per cent, of platinum, and agrees
with the per-centage of platinum in the pyridine double salt —
34*68.

Our earliest determinations of platinum in the platinum salt
of the fraction 95° — 100°, gave the following numbers : —
I. 0*3121 grm. yielded 0*101 grm. platinum = 33*29 p. c.

II. 0*4235 grm. yielded 0*1418 grm. platinum = 33*29 p. c.
On recrystallizing the remaining salt and igniting, the follow-
ing results were obtained : —

III. 0*3115 grm. gave 0*1055 grm. platinum = 33*86 p. c.

IV. 0*3173 grm. gave 0J085 grm. platinum = 34*19 p. c.
* 99 is the equivalent of platinum adopted in this memoir.

produced by the Destructive Distillation of Peat. 113

These numbers agree pretty closely with those required by
the theory, C10 H14 N CI, Pt CI2, while the excess of platinum
obtained in analyses III. and IV., made with a salt recrystallized
by the aid of heat, is probably to be explained by the result of
an experiment in which we have proved that the cespitine pla-
tinum salt yields a platinized derivative when boiled with water.
Before proceeding to describe this new substance, we give the
results furnished by an analysis of the pure base cespitine.
0*237 grm. gave 0*598 grm. carbonic acid and 0*32 grm. water.
Experiment. Theory, C10 H13 N.

Carbon 68-81 68*96

Hydrogen 15*00 14*95

Nitrogen . . 16*09

10000
The platinum salt of cespitine, which is but slightly soluble
in cold water, dissolves readily in boiling water ; and the solu-
tion, if kept in steady ebullition for half an hour, deposits bril-
liant pale yellow scales, the supernatant liquid becoming colour-
less.

During this transformation hydrochloric acid is evolved in
considerable quantity, and may be readily detected at the mouth
of the vessel. The reaction proceeds as follows : —

C,0H14NCl,PtCl2=C10H13PtNCl2 + HCl,
and is perfectly analogous to the change produced in the pla-
tinum salts of pyridine and picoline by ebullition with water,
although it is effected with much greater ease, and its produc-
tion is not preceded by that of a double compound containing
one equivalent of the original united with one of the changed
salt.

The composition of the new crystals was ascertained by the
analysis given below: —

I. 0*3715 grm. gave 0*316 grm. carbonic acid and 0*2085
grm. water.

II. 0*42 grm. gave 0*1605 grm. platinum.
III. 0*2595 grm. gave 0*099 grm platinum.
IV. 0*2018 grm. gave 0*077 grm. platinum.

Experiment. Theory,

I. II. III. IV. (C10H13)'"PtNCl2.

Carbon 23*20 . . . . . . 23*34

Hydrogen 6*23 5*06

Platinum .. 38*21 38*11 38*16 38*52

Nitrogen . . . . . . . . 5*45

Chlorine 27*63

100*00
An attempt to prepare the bichloride of plato-cespityl-ammo-

114 Messrs. A. H. Church and E. Owen on the Bases

nium, for so we provisionally name the salt just described, by
the direct union of cespitinc and bichloride of platinum, led to
no definite result. The bichloride of plato-cespityl-ammonium
is not altered by continued ebullition, but may be crystallized
from boiling water.

The metamorphosis of the platinum salt of cespitinc pointed
to an essential difference between that base and amylamine ; and
this difference is the more remarkable, since the true amylamine
has been detected by Greville Williams and by Anderson among
the products of the destructive distillation of several organic
substances. An experiment was made, however, in order to
establish this distinction more conclusively. One volume of pure
cespitinc was digested in a sealed tube at 120° C. for several
days with 8 or 10 volumes of iodide of ethyle. On opening the
tube no escape of hydriodic acid gas occurred, but on shaking
up its contents with water, and evaporating the aqueous solution,
a syrup was obtained which did not show the least tendency to
crystallize even in vacuo over sulphuric acid ; the iodide of ethyl-
amyl-ammonium is easily crystallizable. On the addition of
oxide of silver to this syrup after it had been diluted with water,
an alkaline and caustic liquid was obtained, but no volatile base
separated ; had the cespitine been in reality amylamine, ethyl-
amylamine should have been formed, together with other bases
containing more ethyle. But no such substitution had taken
place ; the cespitine, being a nitryle base containing no hydro-
gen thus replaceable, had merely combined with 1 equiv. of iodide
of ethyle to form a salt. The alkaline solution of the ethyle
derivative was now neutralized with hydrochloric acid, and pre-
cipitated with bichloride of platinum ; a buff-coloured curdy
precipitate was formed, which, when washed and then recrystal-
lized from warm water, yielded very voluminous micaceous plates
of a straw colour. These crystals were almost insoluble in cold
water. The following determinations proved them to be the
platinum salt of ethyl-cespityl-ammonium : —

I. 0*4295 grm. gave 0*132 grm. platinum.

II. 0*338 grm. gave 0*1037 grm. platinum.

III. 0*5078 grm. gave 0*1555 grm. platinum.

Experiment. Theory,

I. II. III. (C10H13)"',C4H5,NCl,PtCla.

Platinum 30*73 30*69 30*62 30*79

When cespitine is acted on by iodide of amyle, a yellow un-
crystallizable gummy mass is obtained, the iodide of amyl-
cespityl-ammonium (C^H^^C10!!11^ Cl,PtCl2, very dif-
ferent from the isomeric body, the crystalline iodide of diamyl-
ammonium, produced by the action of iodide of amyle on

produced by the Destructive Distillation of Peat t, 115

amylamine. And when this iodide was acted upon by oxide of
silver, and the hydrate thus produced combined with hydro-
chloric acid, an excessively soluble chloride was obtained, which
did not exhibit a trace of crystallization when evaporated to dry-
ness, and had in fact no character in common with that of the
highly crystalline and difficultly soluble chloride of diamyl-
ammonium.

Cespitine is isomeric not only with amylamine, but also with
diethylmethylamine and dimethylpropylamine ; and since it has
been found to contain no replaceable hydrogen, it seemed pro-
bable that it might be one of the nitryles just mentioned. But
cespitine is entirely unacted upon by nitrous acid, not a trace of
any alcohol being produced, and the original base being recover-
able by distillation with potash. In our ignorance of the true
constitution of cespitine we have supposed it to contain the tri-
atomic radical (C10H13)'", although the unusually large propor-
tion of hydrogen casts a doubt upon such a view. All our ex-
periments with cespitine lead us to believe that it bears the
same relation to the true amylamine as picoline does to aniline.

Cespitine is a colourless oil, less fluid than water, and miscible
in all proportions with that liquid. It is nearly insoluble in a
saturated solution of caustic potash. It boils at about 95°, the
boiling-point of amylamine its isomer. It is lighter than water ;
its odour is powerful, and although slightly unpleasant, much
less so than amylamine. It precipitates many metallic solutions ;
with sulphate of copper it gives a green precipitate, soluble in
excess of the base with a pale green colour. With chloride of
mercury a beautiful pearly substance is deposited in iridescent
scales. The platinum double salt has been already described :
the gold salt is a pale yellow crystalline powder. The cadmium
double salt is very soluble, but it may be obtained in long colour-
less prisms by mixing strong solutions of hydrochlorate of ces-
pitine and chloride of cadmium, and then evaporating the liquid
over sulphuric acid.

Pyridine.

It will be seen from our further examination of the bases from
peat, that they are identical in composition with pyridine and its
homologues. And since we have not thought it necessary to
describe them minutely, we may here state that their properties,
physical and chemical, correspond closely with those of pyridine,
picoline, &c, as recorded by Anderson.

The boiling-point assigned to pyridine is 116°- 5. The few
drops of base which distilled near this point, coming over in the
8th rectification between 110° ai\d 120°, were converted into the
hydrochlorate,, and precipitated with an insufficient quantity of

116 Messrs. A. H. Church and E. Owen on the Bases

bichloride of platinum : this first crop of platinum salt gave the
following result when burnt : —

0*495 grm. gave 0*1708 grm. platinum.
Reducing this number to a per-centage, we have

Experiment. Theory— Pyridine.
Platinum 3450 34*68.

The filtrate from the pyridine salt yielded another crop of
crystals on the addition of more bichloride of platinum; the
amount was, however, insufficient for an analysis.

The pyridine platinum salt yielded pale yellow flocks of the
bichloride of plato-pyridyl-ammonium after having been boiled
with water for forty-eight hours.

Picoline.

Between 130° and 140°, rather more than 70 grammes were
obtained in the 9th rectification ; picoline is said to boil at 135°.
This fraction proved to be pure picoline. Converted into a plati-
num salt, —

I. 0*5824 grm. gave 0*1922 grm. platinum = 33*01 p. c.

Between 140° and 145° 100 grammes distilled over, and, like
the preceding fraction, were pure picoline. Three successive
crops of the platinum salt fractionally precipitated, gave the
following numbers : —

II. 0*3755 grm. gave 0*1238 grm. platinum =32*97 p. c.

III. 0*441 grm. gave 0*1455 grm. platinum = 32*98 p. c.

IV. 0*278 grm. gave 0*0916 grm. platinum = 32*95 p. c.
The platinum salts of the next fraction gave slightly different

numbers, indicating a mixture of picoline and lutidine. The oil
had been collected between 145° and 150°, and amounted to not
less than 60 grammes.

V. 0*292 grm. gave 0*0958 grm. platinum = 32*81 p. c.

VI. 0*3056 grm. gave 0*1008 grm. platinum = 32*98 p. c.

VII. 0*5002 grm. gave 0*1615 grm. platinum = 32*29 p. c.

VIII. 0*51 grm. gave 01632 grm. platinum = 3200 p. c.

IX. 0*3372 grm. gave 0*109 grm. platinum = 32*03 p. c.

X. 0*4816 grm. gave 0*1516 grm. platinum = 31*47 p. c.

The following is a comparison of the ten preceding experi-
mental pcr-centages of platinum, with the theoretical per-centages
required by picoline and lutidine : —

Experiment. Theory.

I. II. III. IV. V. VI. VII. VIII. IX. X. Picoline. Lutidine.
33-01 32-97 32-98 32*95 32-81 32-98 32-29 32-00 32-03 31-47 33-06 31-58

The quantity of pure picoline at our disposal has induced us
to experiment further upon it, in order to obtain some insight
into its true constitution. By the action of the bichloride or

produced by the Destructive Distillation of Peat. 117

the bibromide of ethylene upon picoline, we have obtained salts
of an ammonium which is remarkable for the beauty of many of
its compounds. The reaction, which takes place readily when
the materials enclosed in a sealed tube are heated to the boiling-
point of picoline, proceeds thus : —

2[(C12 H7)"'N] + (C4 H4)" Cl2= (C12 IF)'"2 (C4 H4)" N2 CI2.

Two equivalents of picoline have thus been united into one
molecule by means of the diatomic group ethylene : at the
same time hydrochlorate of picoline and other compounds appear
to be formed, but only in small quantity. The details con-
cerning several new derivatives of the pyridine bases are reserved
for another communication.

Lutidine.

The fraction 150° to 155° was not examined. The fraction
155° to 160° amounted to 60 grammes, and consisted of pure
lutidine, the boiling-point of which is 154°. The following deter-
minations of metal in the platinuui salt agree well with the
theory : —

I. 0-0728 grm. gave 0-0228 grm. platinum = 31-33 p. c.

II. 0*605 grm. gave 0*19 grm. platinum = 31 -40 p. c.

A portion of the base which distilled over in the 8th rectifica-
tion between 160° and 165°, gave a platinum salt which on
ignition furnished the following numbers : it had been recrystal-
lized from alcohol, and was a very beautiful salt : —

III. -5062 grm. gave 0-1585 grm. platinum = 31 -31 p. c.

IV. *506 grm. gave 0-1585 grm. platinum =31*32 p. c.
These platinum salts, which were of a deep orange colour and

highly crystalline, occurring in very regularly flattened square
tables, corresponded almost exactly with the lutidine platinum
salt as described by Anderson, but seemed to be rather less solu-
ble in cold water.

Translated into per-centages, the four preceding analyses give
the following results : —

I.

Experiment.
II. III.

IV.

Theory.
Lutidine.

31-33

31-4 31-31

31-32

31-58

Platinum

The fraction 165° — 170° gave indication of the presence of the
next higher homologue of lutidine when the platinum salts frac-
tionally precipitated were ignited.

V. 0334 grm. gave 0*1052 grm. platinum = 31 -52 p. c.
VI. 0-4345 grm. gave 0*1346 grm. platinum = 30*97 p. c.
VII. 0-291 grm. gave 0*0884 grm. platinum = 30-37 p. c.
The per-centage of platinum in the last of these salts is almost

118 On the Bases produced by the Destructive Distillation of Peat,

exactly the same as that in the salt of collidine which contains
30-23 per cent, platinum.

Collidine.

The fraction 170° — 175° was a mixture of lutidine and collidine,
while the liquids that distilled between 175°— 180°, 180°— 185°,
185° — 190 were nearly pure collidine, which is stated to boil at
180°. The three annexed determinations were made with the
platinum salts obtained from these three fractions.

I. 0*4162 grm. gave 0*1256 grm. platinum =30* 17 p. c.

II. 0-383 grm. gave 0*1153 grm. platinum = 30- 10 p. c.

III. 0*354 grm. gave 0*107 grm. platinum = 30*22 p. c.

Experiment. Theory.

I. II. III. Collidine.

30-17 30*10 30-22 30-23

The largest quantity of collidine distilled over between 180° and
186° ; altogether about 200 grammes were collected. The entire
absence of aniline from the peat bases was proved by several
careful qualitative experiments • while the platinum determina-
tion made with the salt of the 180° — 185° fraction (III. above)
gave a per-centage differing from that of the aniline salt by as
much as 2*84 per cent. In this fraction, aniline, the boiling-
point of which is 182°, should have been found had it been
present.

The examination of the fractions above 190° and up to 210°
has not led to any very definite result. Not only are the oils above
this point difficult of combustion, but they are not capable of
furnishing crystalline salts. Concentrated hydrochloric solutions
of the various fractions which came over in the 10th rectification
between 190° and 215°, gave no precipitate with a strong solu-
tion of bichloride of platinum, even after the addition of alcohol
and ether; nor could any double compound be prepared, either
with the chloride of uranyleor of cadmium. The compounds pro-
duced with sulphuric and oxalic acid are colourless gummy masses.
But all the fractions give with chloride of gold a bright yellow pre-
cipitate, which quickly collects at the bottom of the vessel as a
brownish-yellow exceedingly heavy oil. This oil is slightly soluble
in water, and perfectly soluble in a mixture of alcohol and ether.
Two specimens of this gold salt were prepared and the gold
determined. The first determination was made with a salt ob-
tained from the fraction boiling between 202° and 205°, which
after washing with water was dried in vacuo over sulphuric acid
until constant, for otherwise gold was reduced at a very slight
elevation of temperature. The second determination was made
with a salt similarly prepared from the fraction 205° — 208°, but

On New Figures of Equilibrium for Revolving Fluids. 119

it had been dissolved in a mixture of alcohol and ether. These
fractions were those of the 10th rectification.
I. 0-2404 grm. gave 0*0928 grm. gold.

II. 0-5296 grm. gave 0-2038 grm. gold.

Translated into per-centages, these numbers correspond with
the proportion of gold required by a gold salt of parvoline
(C18 II13 N) containing four equivalents of water ; —

Experiment. Theory.

I. II. C18H14NCl,AuCP+4Aq.

38-60 38-46 38-55

The unpromising character of the salts of these fractions has,
however, deterred us from making further experiments with
them.

Between 210° and 230° the quantity of distillate was but
small, and we have as yet gained no insight into its constitution.
From 230° to 280° or 290° several grammes of a thick brown-
ish oil came over ; these fractions yielded crystalline platinum
salts; it is very probable that they contain chinoline and its
higher homologues, lepidine and cryptidine, bases discovered by
Greville Williams among the products obtained by the destruc-
tive distillation of cinchonine.

The following formulae are those of the new compounds
described in the present memoir. —

Cespitine

Chloride of cespityl-ammonium
Platinum salt of cespityl-ammonium
Bichloride of plato-cespityl-ammonium
Chloride of amyl- cespityl-ammonium
Chloride of ethyl- cespityl-ammonium
Hydrate of ethyl-cespityl-ammonium

(O10H13)'"N.

(C">H18)"'HNC1.

(C10H13)r"HNCl,PtC12.

(CiOHi3)"fPtNCl2.

(C»0H13)'"C10H»Na.

(C10H13)'"C4H5NC1.

(CioHi3y"c4H5NQ,HQ.

Platinum salt of ethyl-cespityl-ammonium . (C10 H13) '" C4 H5 N CI, Pt CP.
Bichloride of ethylene- dipicolyl-diammonium (C12 H7) '"2 } -«-3 ni2

(C4H4)" j^ 01-

XI. On a New Species of Figures of Equilibrium for Revolving
Fluids, the particles of which attract one another according to
Newton's Theory. By G. R. Dahlander*.

SUPPOSE a hollow ellipsoid of rotation to revolve round its
figure-axis with a constant velocity. Let it be bounded
within by another ellipsoid of rotation, concentric with the first
one and having the same axis. Around the inner walls there is
a fluid, which does not, however, fill up the whole of the hollow
ellipsoid, but forms within a cavity round the centre. By attrac-
tion and centrifugal force the fluid can, under certain circum-
stances, form a figure of equilibrium, which we will now consider.
Let the axis of rotation be the z axis of a rectangular coordinate
* Communicated by the Author.

120 M. G. R. Dahlander on a New Species of Figures

system, whose origin is in the centre of the ellipsoid. It has
now to be shown that an ellipsoid of rotation can form the limit-
ing surface for the cavity within the fluid, supposing the pres-
sure is not directed against the cavity ; or if such is the case,
that it is counterbalanced by the pressure of a body of gas
enclosed in the cavity, whose density is, however, so small that
the attraction exerted by the gas on the fluid may be neglected.
Let X, Y, Z denote the three components parallel with the co-
ordinate axes of the attraction which the ellipsoid and the fluid
exercise on a particle of the fluid having the coordinates x, y, z.
The attraction of the mass of the hollow ellipsoid on the point
x, yt z is equal to that of a solid ellipsoid, diminished by that
which another solid ellipsoid equal to the hollow part would
exert on the point. Let the components of attraction of the
former ellipsoid be

— Mx, —My, — Ns,

and those of the latter

-Mx, -Wy, -Wz.

The attraction of the fluid, which is supposed to be bounded by
the two spheroids, is equal to that which an ellipsoid of massive
fluid would exercise, diminished by that of an ellipsoid with the
same density corresponding to the inner cavity. Let the com-
ponents of the former attraction be

-M'fc, -M"y, -N"*,
and those of the latter

-W'x, -M"fy, -N'"*.
Then we get

X=(-M+M'~M'' + M'>n

Y=(-M + M'-M'' + M''')y, I . . (1)

Z=r(-N + N'-N" + N'yJ

The differential equation of the surfaces de niveau will there-
fore be

(-M + M-M" + M'"){xdx + ydy) + (-N + W-W + W")zdz

+ w\xdx + ydy)=0} (2)

where w is the constant angular velocity.

M, M', M", N, N', N" are independent of x} y, z; but M";
and N"; are generally dependent upon them. When the in-
nermost bounding surface is alone considered, even M'" and W"
become independent of x, y, z. If this surface be a spheroid,
it will be possible to express its equation in the form

t±t+ zl -1 ... (3)

a2 +a*(l+\"2)-1 K)

of Equilibrium for Revolving Fluids. 121

Differentiating this equation, we get

aedx + ydy+ 1+^//a = ° (4)

In order that the equations (2) and (4) may both exist at the
same time, it is necessary that

The equation (5) shows the relation that must exist between
the several quantities in order that the inner bounding sur-
face may form a spheroid, whereby it is supposed, as before
mentioned, that the pressure on the surface is either counter-
balanced by the pressure of a body of gas, or is =0 in conse-
quence of attraction and centrifugal force. The general exami-
nation of the circumstances which occur in this case is par-
ticularly complicated, as the equation (2) cannot be integrated ;
we shall therefore confine ourselves to the single case in which
an integration can be effected, when the inner bounding surface
of the fluid becomes a sphere, and both the outer spheroids are
oblong.

Let p denote the density of the solid part of the ellipsoid, and
p' that of the fluid ; / the attraction between two unit masses at
the unit of distance ; and let X and V have the same significa-
tion for the two outer spheroids as \" has in the equation (3).
Further, let r be the radius of the spherical cavity. Then

M=27rPrl+x*[WT+x>-i. (\+vT+i\?) %

M'=27r/)/^^~2[xVlTx^-/. (V + x/T+V*)],

N^W/^^f^v+yiT^-^^^

3 x/{x2 + y* + z2)3
Phil. Mag. S. 4. Vol. 20. No. 131. Aug. 1860.

(6

122 M. G. H. Dahlander on a New Species of Figures

If we now take ^ — n.=E, S = m. we find the differential
27rP'f ft

equation for the surfaces de niveau to be
{-"nrIVl:^-'' (X + VI+J?)] + (m-l)^l+^[x'v/iTxr'

^■{-^[MHv/IW,-^]

+s7TO+^}^=0 (7)

But for the surface de niveau which forms the inner bound-
ing surface \/a;2 + y'2 + z'2=r'2, and we have therefore for it

"Ti^rJ +2(m-1) ^W^[1' (v+v/TTxS)

-vm<]+i}M <8>

But for the corresponding values of x, y, z we have the relation

xdx + ydy + zdz=0 (9)

By comparing the equations (8) and (9), therefore, wc get

+ 3(OT-]Vr^Mv+v/CT) (10)

This relation must exist between the several quantities in
order that the inner bounding surface may be a sphere. If we
now take

+2(„-i)*^+*'[,. (V+^n.x«)--7IE5-J=r, (ii)

of Equilibrium for Revolving Fluids. 123

the differential equation for the surfaces de niveau in general,
according to equation (7), will be

(p+ h(x*+f+z*?){3cd3C+ydy+zdz)=0- • (l2)

This shows that the surfaces de niveau become all spherical.
If p denote the pressure on a point of the fluid with the coordi-
nates Xj y} zt we have

z$y = (p+ l(v/^+*y) (**+yfr+«fe)- (13)

If the radius of the spherical surfaces of niveau is supposed to
be n, whereof xdx + ydy + zdz=ndn, this equation will be

dp -r, 7 2r3 7

which, when integrated, gives

p _Yn* 2r*

2V2/~ 2 3rc

If we now suppose that the equilibrium is only sustained by
the attraction and the centrifugal force acting on the particles,
the pressure on the inner surface of the fluid must be =0. If
we^ determine the arbitrary constant by this condition, we get,
lastly,

In order to examine the circumstances under which equilibrium
can be sustained by attraction and centrifugal force, we shall sup-
pose an infinitely small canal in the fluid with a constant sec-
tional area going from the exterior surface of the fluid to its
inner surface. We may suppose this canal to be separated from
the other fluid by an infinitely thin tube ; and if now the acting
forces tend to conduct the fluid in the canal towards the cavity,
no equilibrium is possible under the supposed circumstances.
But if, on the contrary, the resultant of these forces, taken with
regard to all the particles of fluid that are in the canal, tends to
conduct the fluid towards the solid ellipsoid, equilibrium may
exist if at the same time the forces acting on the particles upon
the inner surface are also directed towards the solid ellipsoid.
As now the surfaces de niveau are spherical, it is sufficient to
examine a canal going in the direction of the axis of revolution.
If the forces acting on the particles in this canal are directed
outward, this must be still more the case with the other canals.

If now c denote half the major axis of the inner spheroid,

K3

f

124 On Figures of Equilibrium for Revolving Fluids,

these conditions are expressed by

/ 2 r*\

VP+3?M20> * • ' .• • (15)
which, after integration gives

!#*&**&? <16)

If this condition is fulfilled, it is clear that the force which acts
upon a particle on the inner surface of the fluid, must also be
directed outward from the cavity.

Let us now, lastly, consider the special case when ?w=l, i. e.
when the density of the hollow spheroid is equal to that of the
fluid. The equation (11) gives then

P=-2

1+X2

X3

[mx+v/i+x*)-7!=]. - tm

If the smaller semiaxis of the inner spheroid be equal to the

r 1

radius of the surface of the sphere, we set - = . . and the

condition (16) is then expressed by

+ 5OTS0 "8>

The equation of condition (10) will in that case be

E=^_3vTO*MW_2)_ . . (19)

When \ is given, we can define by (18) the greatest value of
X' which is compatible with the conditions of equilibrium. The
equation (19) then gives the corresponding value of E. If, for
instance, \=0, then

|=-|, X<=0, E = 0;

if \=1, then
P

= -0-2464, X'=0-699, E = 0-2608;
if\=2*5, then

| = -0-22169, V = 1732, E= 0-628.

Every value of \' smaller than those here calculated must, there-
fore, also satisfy the conditions of equilibrium.
Gothenburgh, June 12, 1860.

r 125 ]

XII. On a Theorem relating to the Attraction of the Ellipse.
By G. R. Dahlander*.

CERTAIN investigations relative to the attraction of the
ellipse have led me to a theorem analogous to Ivory's well-
known theorem concerning the attraction of the ellipsoid, which
I will here communicate, as, so far as I am aware, it has never
before been remarked.

It is supposed that from every element of the surface of the
ellipse emanates an attracting force proportional to the area of
the element, and varying according to a function P(r) of the
distance of the element from the attracted point, which is sup-
posed to be in the plane of the ellipse.

Let the equation of the ellipse be -^ + 4* — 1, and let A* and

Ky denote the components of attraction parallel to the x and
y axes, and let ct and ft be the coordinates of the attracted
point. Then

| \Zb'2-7J2

A*=/aI dy\ dx^—-~F(r),

in which expression jjl is a constant quantity, and

The result of the integration according to x can be expressed in
the form

a*=/u,I Ar(#ri)*~$CrJ)>

ct — x
where <f>(r) = 1 dx F(r), and f\ and r2 denote the values of r

corresponding to the values ^ x/tf—y'2 and — ^ \/b*—y2 of x.

If these limiting values of x be denoted by xx and — xv it fol-
lows that

r,= i/(i-.a?|)«+(0_y)a and r2= • (a + *!>•+ ^-.y)*.

xJi y12
If we now consider another ellipse, -^ -f ju ~1} confocal with

the former, and passing through the point (a, (3), we find in the
same way that the attraction which it exercises on the point
(a', /3') has a component parallel to the x axis,

A^jV^R,)-^)),

* Communicated by the Author.

126 Mr. W. R. Grove on the Transmission of

when

tt'

o/j denoting the expression jj \/b,%—yli.

In order to compare Ax and A'* with each other, we can trans-
form the variables within the integral signs. If we take
jc^asinp, and y = bcosp, we obtain

A*=fi jo dp ' siuyu" ^r^ ~^r^y

Mx=^dp . sin p . (^(R,) -0(R2)).

Supposing that the point (a', /3') is in the periphery of the
first ellipse, and that its coordinates are denned by the analogies
a:ot' = a' :a and /3 : 0 — b1 : b, whereby (a, 0) and (a', /3') become
so-called corresponding points, we get

V-^aW^ + ^-l),

when we substitute in the expressions for R, and r, the values
ofa?,,^^ andy'p observing at the same time that a'2 — a*=zV*—b%9
because the ellipses are confocal. But as the coordinates of the

point (a', ft') must satisfy the equation -2 + 72=1, we have

a'2 jS2

-5 + ^2 — 1=0, and consequently Rj^r,, In like manner it

can be shown that R2=r2. The expressions within the integral
signs in the values of the components of attraction are, conse-
quently, equal, and we may thence conclude that

Ax:A'x=b:b'.

Iu the same way we obtain

Av:My=a\a!.

Gothenburgh, June 12, 1860.

XIII. On the Transmission of Electrolysis across Glass.
By W. R. Gkove, Q.C., FM.S*.

IF glass or an equally non-conducting substance be interposed
between electrodes in an electrolyte, so that there be no liquid
communication around the edges of the glass, it is hardly neces-

* Communicated by the Author, having been read at the Chemical Section
of the British Association, June 28, 1860.

Electrolysis across Glass. 127

sary to say that, according to received opinions and experiments,
no current passes and no electricity takes place. I was led by
some theoretic considerations to think that this rule might not
be without an exception ; and the following experiment realized
my views.

A Florence flask, well cleaned and dried, was filled two-thirds
full of distilled water with a few drops of sulphuric acid added
to it, and placed in an outer vessel containing similar acidulated
water which reached to the same height as the liquid in the
interior. A platinum wire was passed through a glass tube, one
end of which was hermetically sealed to the platinum, but so as
to allow a small portion of the wire (about 2u^n °f an mcn) to
project J the other end of the wire was passed through a cork, and
the cork fitted to the mouth of the flask ; when the cork was
introduced, the projecting end of the platinum wire was three-
quarters of an inch below the surface of the interior liquid ; a
similar coated wire was dipped into the outer liquid, and this
and the wire which passed through the cork were brought
respectively into connexion with the extremities of the secondary
coil of a Ruhmkorff apparatus. Upon the latter being excited
by the battery, a stream of minute bubbles arose from both the
platinum points, proving clearly that electrolysis took place not-
withstanding the interposition of the glass. The portions of the
flask above the liquid, both outside and inside, were perfectly dry,
so that there could have been no communication of the current
over the surface of the glass. This was further proved by re-
moving the outer wire a short distance from the surface of the
water, when sparks passed nearly equal in length to those which
took place between wires from the terminals. As the outer wire
was further removed, keeping it near the glass, the sparks passed
along the surface of the latter for a short distance ; and as it was
further removed they ceased, thus showing conclusively that
there was no passage of electricity over the upper and unwetted
surface of the glass.

With distilled water unacidulated I could observe no effect of
electrolysis.

With acidulated water and the same arrangement I could detect
no signs of electrolysis when, instead of the UuhmkorfF coil, an
intensity nitric acid battery of thirty cells was employed.

In the first experiment the evolution of gas gradually dimi-
nished, and ceased after about twenty minutes' experiment ; but
upon intercepting communication with the battery for ten
minutes and then reconnecting it, the evolution took place again ;
or a recurrence of electrolysis could be produced by reversing
the direction of the current.

When the flask, after twenty minutes' experiment, was removed

128 On the TYansmission of Electrolysis across Glass,

from the outer vessel and tapped, minute bubbles rose from the
interior surface. When a tolerably thick test- tube was used
instead of the Florence flask, a very slight effect of electrolysis
could be detected ; and when the outer wire was removed to a
short distance from the surface, sparks passed, but not of half the
length of those with the Florence flask. When, however, a
large phial of somewhat greater contents- than the Florence flask
was used, the effects were the same as with the latter, showing,
as I expected, that surface is an important element in the success
of the experiment.

There seems little doubt from the above experiments that the
electrolysis was effected by induction across the thin glass of the
Florence flask ; and its cessation after a time, and recurrence after
interruption of the current, would seem to indicate something
like a state of charge or polarization of the surface of the glass.

Whether the bubbles which arose from the interior surface of
the glass were the effect of electrolytic action or mere air-bubbles,
cannot be affirmed with certainty; but as there was distinct
evolution from the platinum wires, the corresponding elements
must have been either dissolved, evolved, or deposited somewhere,
and the most probable place of evolution would be the surface of
the glass. If this be so, the glass would act in effect just as an
interposed plate of inoxidable metal, though the one acts by in-
duction, the other by conduction.

The oxygen and hydrogen may, however, be spread over the
surface of the glass without evolution in the form of gas ; and
when the glass is, so to speak, coated by the elements, decom-
position would cease.

The quantity of gas in the above experiment was too small
for analysis; and in all probability, could it have been examined,
some mixed gas would have been found to have been eliminated
from each electrode. When, however, there is a small interrup-
tion in the secondary circuit of RuhmkorfFs coil, producing a
rapid succession of sparks, I have found that between electrodes
in the same circuit true polar decomposition takes place, and a
galvanometer is steadily deflected according to the direction of
the current, while without such interruption the movements of
its needle are most irregular. I therefore repeated the experi-
ment of interposed glass with an interruption in the circuit, and
found that electrolysis took place as before; and in this case I
have little doubt was true polar decomposition.

Although I failed with thirty cells of the nitric acid battery,
I should fully expect that a battery of very high intensity, such
as the 500 cells nitric acid, or the water battery of Mr. Gassiot,
would produce effects of electrolysis across glass without the use
of the coil.

C 129 ]

XIV. Preliminary Notice on Thirteen Systems of Crystallization
in the Mineral Kingdom, and their Optical Characters. By
Professor Breithaupt, of Freiberg, Councillor of Mines*.

I^HE important discovery made by Councillor Jenzsch, that
tourmaline had two optical axes (PoggendorfFs Annalen,
vol. cviii. p. 645), certainly delighted no one more than myself.
Soon after reading that account it occurred to me that the same
character must be found in those crystals of apatite and idocrase
in which I had more than ten years since observed the asymme-
trical condition of the pyramidal planes with respect to the base.
Reich found the two optical axes beautifully distinct in a
fine crystal of apatite from Ehrenfriedersdorf, Pollachites
haplotypicus (see my ' Mineralogy, vol. ii. p. 277), having at
one pole a smooth basal plane, and at the other a good cleavage
plane. I estimate the angle that the two axes make at 6 degrees
at the least.

The same applies,[though in a less degree, to|the apatite from
Schwarzenstein in the Zillerthal in Tyrol, which, however, T have
not measured ; perhaps in this case the axes are only 2 degrees
apart.

The apatite from St. Gothard, Pollachites galacticus, which
I had measured, was polished, and I then found that it presented
the same characters as the one from Schwarzenstein.

M. Lingke, the optician to the University, was kind enough
to cut and polish for me two plates of the green idocrase from
Piedmont (Idocrasius calaminus, B. M. p. 652) ; and I found two
axes in this also very plainly evinced.

When I had obtained these results, I received a letter from
M. Jenzsch, saying that he also had found two optical axes in
apatite and idocrase.

Col. von Kokscharoff has tried to set aside my measurements
of the idocrase. He believes that I used imperfect crystals for
these trials ; but he is wrong ; my measurements were not only
most carefully made but repeated very often, and I selected
the best crystals, viz. those from Piedmont, and I found the
inclination to the base as follows : —

One plane = 152 55

Two neighbouring planes . . . = 142 50
And the fourth, opposite the first . = 142 47

Col. von Kokscharoff says he found the angle only =142° 46f
in all four planes.

* Translated from the Berg- und Hiittenmannische Zeitung, by William
Hustler, Esq., and communicated by Professor W. H. Miller, F.R.S. &c.

130 Prof. Breithaupt on Thirteen Systems of

These differences are certainly the smallest and most difficult
which I have had to determine, especially when the crystals pre-
sent only one termination, and where perimetrical measurements
are impossible.

It would have been more than wonderful, if one had wished
for such a difference of angles, to have found them, especially
in so many crystals, all of which had their symmetry destroyed in
one and the same way; and this was certainly more than I either
expected or sought for. Nevertheless I see no reason why some
crystals of idocrase, which I have not examined, may not be
found having their planes symmetrically arranged ; but those
individuals found by me to be asymmetrical, when transparent,
have most certainlv, without exception, two optical axes. This
much is certain, that tetragonal and hexagonal substances, whose
pyramidal and rhombohedral planes are arranged in an absolutely
symmetrical order, cannot have two optical axes.

I discovered the peculiarities of idocrase in quite a different
manner from that in which Col. von Kokscharoff did those of
clinochlore ; for I investigated these bodies without a previously
formed opinion, and it was many years afterwards that the two
optical axes of idocrase were made known. On the contrary,
Col. von Kokscharoff first found in clinochlore with hexagonal
base that the terminal planes were in symmetrical order; and
after he had discovered that this mineral had two optical axes, he
found by new measurements that, with the same hexagonal
base, the terminal planes were asymmetrical and differed consi-
derably from his former measurements. This second trial may,
however, be considered very satisfactory. He will now see the
wrong he did me in doubting the correctness of my measure-
ments of idocrase, and also that the symmetrical construction
of the pyramidal planes of those minerals which have two optical
axes can no longer be reckoned on.

I have also examined many zircons in an unprejudiced manner,
and found varying angles in different specimens ; but the planes
of a pyramid always had equal inclination to their polar edges, and
again other equal inclinations to the planes of the prism. Clino-
chlore has been too rashly set down as hemirhombic ; and if the
hexagonal prism were found on it tomorrow, it would be again
proclaimed to be hexagonal, which it most certainly is and must
be. It resembles the above-mentioned apatites, in which, it is
true, a difference in the angles of only 15 minutes is shown.
It is evident that the figure of the base, or the angle of the
prism, must in asymmetrical substances determine the system of
crystallization to which they belong. The absence of the planes of
the prism is not necessarily of importance; nobody, as far as I
know, has observed the prism in tungstate of lime (Scheelite).

Crystallization in the Mineral Kingdom, 1 31

It may be asserted that not only clinochlore, but also the
other micas (the Aster ites, ' B. M/ p. 375) which have been
believed to possess one optical axis, but which have indeed two
weakly developed axes, and may therefore be said to have nearly
one axis, belong to the hexagonal system. And now my mea-
surements of the tourmalines, so long doubted, will be recognized
as correct. I may here remark that the angles I gave as belong-
ing to the red tourmaline from Siberia, may require some correc-
tion, owing to the crystals examined not being well fitted for
the purpose. But for the other tourmalines I had always good,
sometimes first-rate crystals to operate on ; moreover, occasionally
differences of more than 30 minutes appeared in the inclination
of the rhombohedral planes. Why have not these measurements
been repeated by others, that they might be confirmed or rejected?
Why has the incorrect assumption been retained, that the pri-
mary form of all tourmalines is a symmetrical rhombohedron ?
Measurements are possible with a hand goniometer to a quarter
of a degree when the crystals are good. Truly, next to want of
truth, indolence is the greatest foe to the advance of science.

The essential crystallographical varieties extend still further.
Many years ago I observed that the four planes of a crystal
of anatase had at one pole a fourfold inclination towards the
tetragonal base ; a learned friend at that time induced me to
believe that I had supposed a plane to be the basal one, which
was in fact only very obtusely pyramidal. Unfortunately I gave
in — and ceased my measurements too soon, for I had found im-
portant differences. I have since lost the notes I took at that
time. The mighty architect of the universe can have forgotten
no law in the construction of the " crystal world " which would
tend to the completeness and harmony of the whole.

I have often repeated these observations, and can now say
with certainty that we find in anatase a fourfold inclination of
the pyramidal planes to the base, which differ 34 minutes alto-
gether, and form a tetraplohedron. These observations, how-
ever, are not yet terminated, and must be often repeated to
ensure perfect accuracy. On this account anatase also must
have two optical axes. Unfortunately a crystal of anatase which
I sent to be cut and polished, in order to test this fact, broke
during the operation. Further, I believe I may say from care-
fully conducted investigation, that the tungstates of lime (Pyra-
midites hystaticus and Pyramidites macrotypicus, c Breithaupt's
Mineralogy/ pp. 266, 268) have also an asymmetrical arrange-
ment of their pyramidal planes, and will be found to have two
optical axes. The following hexagonal minerals, from the
analogy of careful observations, must be asymmetrical, and
those which are transparent have two optical axes.

132 Prof. Breithaupt on Thirteen Systems of

First, dioptase ; and I must say at once that its primary form
will be found to consist of two-thirds of a rhombohedron and
one-third of a rhombohedron : I estimated this myself some time
ago, but only measured the angles of one set of polar edges.
Haydenite ought to have the same character. It is classed as a
chabasite, and so it appears to be at the first glance ; but accord-
ing to Levy, the inclination of its rhombohedral planes to the
polar edges differs by some degrees. It is very probable that it
is hexagonal, and that it has a rhombohedral-like "diplohedron"
or "triplohedron" for its primary form. The late M. Schuler
measured this mineral in Freiberg, and found that the polar edges
had three angles. Schuler wished to publish this fact, but I do
not believe that he did so.

Perhaps other chabasites are asymmetrical and have two
optical axes. It is very probable that an asymmetrical arrange-
ment of the primary pyramidal planes exists in magnetic pyrites.
I have no other ground for believing this, than the fact of its
magnetic character.

The Museum at Freiberg is indebted to M. Muller for a
large crystal of magnetic pyrites from Norway ; it is a prism
more than an inch long, and has a basal plane an inch broad.
This crystal has a most distinct magnetic axis, which does not, as
I expected, run parallel to the principal axis, but is nearly or
quite horizontal, and is indeed perpendicular, or nearly so, to
two parallel planes of the prism. It may be proved hereafter
that the magnetic and crystallographical axes harmonize. When
we know better the optical characters of the various species into
which idocrase, tourmaline, apatite, titanites and other mine-
rals, according to my views, ought to be crystallographically
divided, the angles which the two optical axes form will assist
in determining and arranging them. Of the apatites which I
have been able to measure exactly, Pollachites galacticus and
Pollachites haplotypicus differ greatly.

Tesseral minerals also show particular laws. It is known that
I found quite constant deviations in melanite, sp. gr. = 3*777
(Granatus melanites, B. M., p. 637), and in almandine (Grana-
tus almandinus, B. M., p. 644), sp. gr. = 4*119; so that the
icositetrahedron (the leucite form) is not a simple figure, but a
combination of an obtuse tetragonal and an acute ditetragonal py-
ramid. According to the measurements, the inclination of sixteen
principal edges gave the same angle = 131° 48' ; the same edges,
reckoned according to the formula \ J, would give 131° 48' 36''';
but the eight remaining edges, on two angles composed of four
edges, lying diametrically opposite to each other, and, again, equal
among themselves, gave the angle = 131° 54', or a deviation of 6
minutes. The tetragonal pyramid is thus much more obtuse

Crystallization in the Mineral Kingdom. 133

than it would be if it represented the derivation from \ J (viz.
by 6') . This obtuser pyramid, which I designate as P, is the espe-
cial primary form, while D, the rhombic dodecahedron, remains
as the general primary form of the garnets. I found a greater
difference in the inclination of the grossular garnet (Granatus
grossularis, B. M., p. 635), but, owing to the want of a perfect
crystal, I could not properly estimate the variation.

I may ask, who has ever taken the trouble to centre and
measure a garnet crystal twenty-four times along the principal
edges ? Has not the labour of centring and measuring the
crystals of tourmaline three times according to their polar edges
been avoided ?

Now that my measurements have so clearly proved those
newly discovered optical appearances which are above described, I
conclude that the tesseral symmetry of the garnet crystals above
described is also destroyed, and that as a tetragonal axis appears
to be the principal one, it must also be an optical axis, I gave
utterance to these views with the greatest confidence at the sit-
ting of the Freiberg Mining Union on the 17th of January last.

As melanite is opake, I tried no experiments on it ; but as
M. Reich and I were examining some polished garnets on the
22nd of January in Werner's Museum, I was fortunate enough
to find a specimen which showed one optical axis perfectly and
beautifully. This specimen had a sp. gr. = 4*152 (nearly that
of the crystals that were measured). We convinced ourselves,
however, that there are red garnets which have no optical axis,
— for example, that garnet which has the sp. gr. = 4*20 to 4*27,
and which, according to Prof. Rammelsberg, is so rich in prot-
oxide of manganese.

The beautiful hyacinth-red garnet from the granite druses
of the island of Elba belongs to this class, and has the same
optical character. This, the heaviest of the garnets, must be
separated from almandine, and called Granatus manganosus:
one must not be astonished that species of essentially different
character appear in one genus of an old system of crystallization.
We have only to remember the felspars, where adularia and peg-
matolite are monoclinohedric, and tetartine, Labrador, and peri-
cline are triclinohedric. Who would have believed that at least
one of the well-known topaz family is hemihedral ? and yet it is
so. I am much indebted to Dr. Krantz for sending me trans-
parent garnets from Piedmont and the East Indies. I found
one optical axis in Hessonite from Ala in Piedmont.

It now remained to determine whether the optical coincided
with the tetragonal axis in those garnets which possessed one
optical axis. For this purpose I had a cube cut by M. Lingke
out of a crystal of Hessonite, having its planes parallel respect-

134 Prof. Breithaupt on Thirteen Systems of

ively to the three planes mutually at right angles to each other, in
which lie the twenty-four edges of the crystals before mentioned ;
and I found that one optical axis was plainly visible, in a direc-
tion perpendicular to a hexahedral plane. The cutting of the
crystal was not quite perfect, and therefore the point of inter-
section was not very clear; but the double refraction was un-
questionable. I am now having a similar cube cut out of a cry-
stal of almandine.

It has long been known that I discovered a particular law in
the crystallization of iron pyrites and cobalt-glance, by which
the pentagonal dodecahedron may be disjoined and formed into
a combination of two rhombohedrons, while the hexahedron and
octahedron retain their peculiarities. Naturally all forms with
two- and threefold edges must behave in the same way, and be
capable of being disjoined and formed into figures with one axis.
I never found even two of those truncations, which are placed
obliquely on the edges of the cube, to have a like inclination to
the hexahedral planes.

The crystals of iron pyrites used in these investigations were
from Kongsberg in Norway (with calc-spar), from Traversella,
from Schemnitz in Hungary (in druses with galena, and blende),
and from Mautern in Styria. The difference in the inclination
of the planes of a supposed pentagonal dodecahedron is only
4 minutes, as shown in the above-mentioned crystals j but in
the cobalt-glance from Skutterud in Norway, and from Tuna-
berg in Sweden, it is above 8 minutes. These facts have up to
this time been ignored in mineralogical treatises, but have never
been contradicted.

M. Websky, a pupil of mine, has confirmed them ; he found
a difference of from 5 to 10 minutes, and presented his ob-
servations to me, which I take this opportunity of acknow-
ledging.

The behaviour of the last-named minerals so far resembles the
garnets, that if you place the crystal so as to have the axis of an
acute rhombohedron perpendicular, it will be exactly represented

by the formula ^r-, while the obtuse rhombohedron is still more

obtuse than it would be if represented by this formula. These
pyrites have also one of the four hexagonal axes as the principal
axis. The hexahedron will remain as the general primary form
of this genus, which I call Marcasites, and to which all the
pyrites belong which crystallize in the tesseral form. But the
obtuse rhombohedron designated for the future as B, will be an
especial primary form for those species which do not possess a
pentagonal dodecahedron, but which are formed by the combina-
tion of two rhombohedrons.

Crystallization in the Mineral Kingdom. 135

It may happen, and I think it is probable, that pentago-
nal dodecahedrons may exist in other species, perhaps in Gers-
dorffite, and I fully expect it will be found in Hauerite, which,
however, does not belong to that genus. In this case an espe-
cial primary form does not exist.

If iron pyrites and cobaltine could be rendered transparent,
they would be found to have one optical axis that coincides with
their hexagonal axis.

I am here reminded that Sir David Brewster recognized bo-
racite forty-one years ago, as having one optical axis which co-
incided with a hexagonal one.

It appears very likely that the form of boracite, which has up
to this time been regarded as a trigonal dodecahedron, may not
be a simple form, but a combination of figures with one axis.
I stated at the above-mentioned meeting of the 17th of January,
that this was my belief; and the measurements which have been
made since that time on some pretty clear crystals, have proved
that I was right.

At first the cube, the pentagonal dodecahedron, and the tetra-
hedron gave their proper angles ; but I afterwards found that
though three of the planes on the three-edged angles gave the
proper inclination towards the hexahedral planes for the trigonal

dodecahedron, and exactly represented the formula ~, the

fourth differed materially.

The first three gave the angle 144° 44', reckoned according

I j

to the formula **~; it ought to have been 144° 44' 8"; but the
is

fourth gave 144° 17', a difference of 27 minutes : the crystals
presented no difficulty to the measurer.

These figures, therefore, when placed upright on their hexa-
gonal axis, resolve themselves into an acute hemimorphous sca-
lenohedron, and into an obtuse hemimorphous rhombohedron,
which we will designate as R ; this last form is again more ob-

xj
tuse than if it had been deduced from the formula ^-. The

figures of the hemimorphous scalenohedron, and of the trigonal
prism (the last reminds one of the same form in tourmaline),
are placed in such a manner round the three hexagonal poles as
the formula requires, and form A,-*f °f the planes belonging
to a deltoid icositetrahedron. The hemimorphous R, on the
other hand, gives A=^ of the planes of another deltoid icosite-
trahedron. The figures must in this case be held in the same
way as they were before examined ; and the hexahedron or the
rhombohedron of the rhombic dodecahedron can now be taken as

136 Prof. Breithaupt on Thirteen Systems of

the general primary form, and the II as the especial primary
form.

The crystallographer must in future take a hexagonal axis as
the principal one in boracite, as well as in the above-mentioned
pyrites. The value of the form R is easily calculated ; from the
angles it contains, it appears that the inclination of the planes
to the principal axis is 70° 59'. If, then, we use the formula

*p = 1 to express the principal axis of such a rhombohedron, we

obtain, from \\ of the planes and the angle they form with the
chief axis, the angle 70° 58' 10" ; the other angle we found
= 144° 1 7', which, according to calculation, = 144° 1 7' 2". If we
deduce R from the rhombohedron of the rhombic dodecahedron,
we get the coefficient f#, and from the cube -&$.

Further, the inclination of the planes to the polar edges of R
is found to be 147° 12' 46" ;

if calculated after ^, = 146° 26' 33" ;

46' 13", which is an important de-
viation, and could easily be found with the hand-goniometer on
a crystal the size of the tip of one's finger.

It is on account of this R that boracite has one optical and
one crystallographical axis ; and thus, owing to prejudiced opi-
nions, boracite has been considered isometrical for forty-one
years.

If we wish to carry our comparisons between the tesseral sy-
stem and the symmetrical tetragonal and hexagonal systems
further, we find some of the minor divisions wanting. The
tetragonal garnets represent the holohedral division of the tetra-
gonal systems.

May not a mineral be found also of a tetragonal character
which has hitherto been called semitesseral ? It seems very pro-
bable to me that among those minerals which I have called
Clinoedrites, viz. Kupferblende, Tennantite, Fahlerz, Schwarzerz,
and crystallized Weisgiiltigerz (from Freiberg), some species may
be found having other symmetrical forms than those which they
are generally supposed to possess. Pharmakosiderite, helvin and
eulytine must have their two-edged forms investigated; and then,
I fancy, the missing links will be found. Further, were it pos-
sible to construct two hexagonal pyramids out of that tetrakis-
hexahedron ^ J (which is the holohedral form of the pentagonal
dodecahedron), when placed upright on a hexagonal axis (and
this might be occasioned by the necessary difference in the
angles), then an analogy would be established between the hex-
agonalized tesseral system and the holohedral division of the
symmetrical hexagonal system. Perowskite, and perhaps fluor-

Crystallization in the Mineral Kingdom. 137

spar, should be examined for this purpose. Is it not possible
that different species of this mineral may be discovered, when we
reflect that specimens from more than a hundred localities may
be found in collections ? I have found the sp. gr. to vary from
3-017 to 3*324. Is it not possible that a fluor-spar might be
discovered having one optical axis ? Who can boast of having
undertaken optical or crystallographical researches on this mine-
ral ? If we estimate the number of the systems of crystallization
by the important mathematical differences which we have here
described, and which are in part only slightly marked, in the
same way that the old rhombic system has been divided into four
systems, we must form thirteen systems of crystallization, which
are divided into four groups after the old ones : —

1st Group. Tesseral System.

A. Isometrical tesseral, without optical axis. Spinelle.

B. Anisometrical tesseral, with one optical axis.

1. Tetragonalized tesseral. Some of the garnets.

2. Hexagonalized tesseral. Boracite, iron pyrites, cobaltine.

2nd Group. Tetragonal System.

A. Symmetrical tetragonal, one optical axis. Zircon, rutile.

B. Asymmetrical tetragonal, two optical axes.

1. Monasymmetrical tetragonal. Idocrase.

2. Diasymmetrical tetragonal. Anatase.

3rd Group. Hexagonal System.

A. Symmetrical hexagonal, with one optical axis. Carbonates

of lime, &c, quartz, beryl.

B. Asymmetrical hexagonal, two optical axes.

1. Monasymmetrical hexagonal. Some apatites, clinochlore,

and other micas, Turmalinus amphibolicus, Turmalinus
ferrosus (B. M. pp. 704, 706).

2. Diasymmetrical hexagonal. Turmalinus hystaticus, Tur*

malinus dichromaticus, Turmalinus medius, Turmalinus
calaminus (B. M. pp. 698, 700, 703, 704).

4th Group. Heterogonal t} or Rhombic System,

A. Holoprismatic.

1. Symmetrical heterogonal. Anhydrite, Arragonite, cymo-

phane.

2. Monasymmetrical heterogonal. Sulphate of iron, blue

carbonate of copper, epidote, pyroxene, amphibole.

B. Hemiprismatic.

1. Diasymmetrical heterogonal. Adularia, pegmatolite.

2. Triasymmetrical heterogonal. Pericline, microcline, tetar-

tine, axinite.
Phil Mag, S. 4. Vol. 20. No. 131. Aug. 1860. L

138 On New Systems of Crystallization in the Mineral Kingdom.

In each of these four groups the determining forms are con-
tinued as before.

In the first, the cube, octahedron (with the tetrahedron) and
the rhombic dodecahedron.

In the second, the basal pinacoid and the two prisms differ-
ing 30° from each other.

In the fourth, the pinacoids of the base and of the macro- and
brachy-diagonals.

Moreover, I take each base as being horizontal and each
prism as vertical.

The asymmetrical forms are arranged according to the length
of their various axes.

Other circumstances, which are well enough understood, must
be taken into account for the further division of one-axed forms.

All this and much more will shortly appear in a forthcoming
work.

Especial notice will be taken of the analogy between the cry-
stallographical, optical, electrical, and magnetic phenomena ; and
Councillor Reich has kindly promised a valuable paper on the
last-mentioned subject.

Six new systems of crystallization ft. e. the sections B of the
first three groups) are thus to be added to those already known ;
and by this means all the systems are brought nearer to each
other. No doubtful conclusions have been formed, for they are
all founded on ascertained facts. A person must have some
self-confidence who has used scientific means for assisting him
in his researches for more than forty years, and who during that
period has measured between 12,000 and 13,000 angles with the
reflective goniometer, and has also determined the specific gra-
vity in more than 4000 instances, and who has often had to deal
with inferior specimens.

These new systems will perhaps have to contend with a good
deal of opposition; but I am convinced that their correctness
will be established by investigation.

Feb. 16th, 1860.
I have been enabled this day to examine a plate of dioptase
one millimetre thick, cut from a transparent crystal perpendicular
to the principal axis, with Amici's polarizing microscope, which
has already been productive of so much benefit ; and to my great
satisfaction the plate showed two optical axes in a beautiful
manner. I estimate the angle formed by the two optical axes
at 4°. Thus the rhombohedron cannot be the primary form
of dioptase ; it must be either a rhombohedron-like diplohedron,
or triplohedron. I hope by measurements to determine this
satisfactorily.

Chemical Notices : — M. Schmidt on some New Acids* 139

The same analogy which led me to suppose that dioptase had
two optical axes, has also reference to the tungstates of lime,
Pyramidites hystaticus and Pyramidites macrotypicus (B. M.
pp. 266 to 260); and I most certainly believe that the asymme-
trical condition of their planes will be discovered ; and if trans-
parent crystals can be obtained, they will be found to have two
optical axes.

The translator has had a letter from Professor Breithaupt,
wishing him to add the following remarks to this paper.

" The tungstates of lime show two optical axes beautifully. I
have measured Hessonite and found the variation to be 12 mi-
nutes, while in almandine and melanite it was only 6 minutes.

" Further, mellite or honeystone shows two optical axes, and
is also very decidedly asymmetrical in the same way as idocrase,
though with a greater difference in its augles.

" Finally, I have found a calc-spar or carbonate of lime with
one optical axis and of asymmetrical form."

XV. Chemical Notices from Foreign Journals, By E. Atkin-
son, Ph.D., F. C.S.j Teacher of Physical Science in Cheltenham
College.

[Continued from p. 50. J

ACCORDING to Laurent, sulphanilidic acid is obtained by
the reducing action of sulphide of ammonium on nitrosul-
phophenylic acid ; and this acid is identical with the acid obtained
by the action of anhydrous sulphuric acid on aniline. Kolbe is of
opinion, on the contrary, that they are only isomeric, and that
the same relation obtains between them as between the isomeric
carbanilic and benzamic acids. Thus :

H0'C12NH2}C2°2'° H0' (C12H}N)C202>a

Amidobenzoic acid Carbanilic acid,

(benzamic acid).

H0' C'2 NK*}S* °4' ° H0' (°2 H5}N) S* °*» °-

Amidophenylsulphuric acid. Sulphanilic acid.

These formula? show that amidobenzoic acid and amidosulpho-
phenylic acids are respectively derived from carbonic acid, and
sulphuric acid by the substitution of an atom of oxygen by the

group amidized phenyle, t^tj2 f ; while in carbanilic and

sulphanilic acids this atom of oxygen is replaced by phenylamide,

C12H51 .

jj r N, that is, amide in which an atom of hydrogen is re-
placed by phenyle.

L2

140

M. Schmidt on some New Acids.

Schmidt*, in a preliminary notice, states that experiments he
has made show that these acids are not identical. At the same
time he describes the action of nitrous acid on sulphanilic acid.
By this action a new body is formed which crystallizes in needle-
shaped crystals. It has the formula C12 H4 N2 S2 O6, and may
be regarded as phenylsulphuric acid in the phenyle of which
two atoms of hydrogen are replaced by two atoms of nitrogen :

C12H31
thus, HO, -^2 f S2 O4, 0. Schmidt names it diazosulpho-

phenylic acid. It has acid properties, but is very unstable. When

its aqueous solution is heated to 60°, a decomposition ensues

accompanied by a copious disengagement of pure nitrogen. The

acid liquid now contains a new acid, oxyphenylsulphuric acid.

Cl2H4 "1
HO, TTQ2 >S2 O4, 0, which is phenylsulphuric acid in which

an atom of hydrogen in the phenyle is replaced by peroxide of
hydrogen. The formation may be thus expressed : —
Ci2H4N2S206 + 3H0 m C12H6S208 + 2N.

Diazophenylsulphuric
acid.

Oxyphenylsulphuric
acid.

Oxyphenylsulphuric acid corresponds to oxybenzoic acid, and
diazosulphophenylic acid to diazobenzoic acid, the remarkable
body obtained by Griessf by the action of nitrous acid on alco-
holic solution of benzamic acid. Schmidt considers that in all
cases in which amidized acids, such as amidoacetic acid, are con-
verted into oxyacids, intermediate bodies, of which diazobenzoic
acid is a representative, are first formed. Hence we might anti-
cipate that between glycocol and glycolic acid, and between ala-
nine and leucic acid, intermediate bodies corresponding to diazo-
benzoic acid will be found to exist. A comparison of the for-
mulae will show these relations more clearly.

HO'C'8JJ4H9}c202,0 HO,C««J£j.C,10«,0 HO.CwJJj.JcW.O.

Amidobenzoic acid.

HO'Th*>o*o

Amidoacetic acid
(glycocol).

HO,C4H4

Diazobenzoic acid.

■}

ctie
KOl

NH.}c«o»,o

Amidopropionic acid
(alanine).

HO,C2H2

N2

|c2o2,o

Intermediate body.

HO,C4H3

H31
£2|C202,0

Intermediate body.

Oxvbenzoic acid.

Oxyacetic acid
(glycocol).

H0,C4H4 1

HO2 J L u 'u*

Oxypropionic acid
(lactic acid).

* Liebig's Annalen, October 1859.
t Phil. Mag. vol. xvii. p. 371.

M. Wohler on Cocaine* 141

In Peru and in other South American countries the coca leaf
(Erythroxylon coca) has long been extensively used as a narcotic.
As to its effects, accounts differ much. According to Von
Tschudi *, its use in moderate quantities is that of a beneficial
stimulant, and enables persons taking it to do without food for a
long time, and to bear great fatigue. But its immoderate employ-
ment produces effects analogous to those caused by excessive
use of opium. The peculiar physiological effects have been
ascribed to the presence of a narcotic principle, the existence of
which, however, has not been established.

The plant (a supply of which was obtained through the Aus-
trian surveying frigate 'Novara') has been investigated by
Wohler f assisted by Niemann, who have established the ex-
istence in it of a peculiar crystallized organic base, to which the
name cocaine has been given. The investigation is not com-
pleted ; the formula is not fixed, nor has the chief point been
settled, whether the peculiar physiological effects are attributable
to this base. To obtain the base, the leaves were digested with
alcohol containing some sulphuric acid, the solution pressed and
mixed with hydrate of lime, by which a wax and part of the
chlorophyll were precipitated. The filtered alkaline solution
was neutralized with sulphuric acid, and the alcohol distilled off
in the water-bath. The addition of water to the residue caused
the precipitation of a semifluid mass which contained the re-
mainder of the chlorophyll. The supernatant liquid contained
sulphate of cocaine, from which the base was precipitated on the
addition of carbonate of soda. By treating this precipitate with
pther, the cocaine was dissolved out, and remained on evapora-
tion of the ether as a yellowish mass, which afterwards crystal-
lizes. By repeated treatment with alcohol it is obtained pure
and colourless.

Cocaine crystallizes in small, white, colourless and inodorous
prisms. It is little soluble in water, more so in alcohol and in
ether. It has a bitter taste, and exerts a peculiar action on the
tongue ; the parts touched appear quite without feeling. It
melts at 98°, and solidifies crystalline. At a higher temperature
it decomposes with formation of ammoniacal compounds. Co-
caine is strongly alkaline; it completely neutralizes acids, but the
salts remain amorphous for some time before crystallizing.

Cocaine most resembles atropine ; but it appears to differ in
composition, and in some properties. The gold salts of both
bases are precipitated from their cold hydrochloric acid solutions
on the addition of chloride of gold as amorphous masses, and
from their heated solutions in crystalline laminae. But the

* Johnson's Chemistry of Common Life, chap. xx.
t Gbttinger Nachrichten, No. 10, 1860.

142 M. Fremy on the Colouring Matter of Leaves.

cocaine compound is distinguished by giving off benzoic acid
when it is distilled — a fact in which will probably be found the
key to its composition. Unlike atropine, cocaine does not act
on the pupil.

Fremy has published* an important investigation on the
green colouring matter of leaves. He has found that it consists
of a blue and yellow principle, which he has succeeded in isolating.

The colouring matter is contained in the green oil which is
extracted by alcohol from leaves. This oil may provisionally be
termed chlorophyll, but it contains several other substances
which render the separation of the colouring matter difficult.
The blue and yellow colouring principle have a different affinity
for hydrate of alumina. When a strong alcoholic solution of
chlorophyll was digested with hydrate of alumina, no alteration
took place ; but by adding a small quantity of water, a dark-
green, almost blue precipitate was obtained, and the alcohol solu-
tion was of a yellow colour. When a considerable quantity of
water was added, the precipitate had a colour like that of the
ordinary colouring matter. Although this experiment effected
some separation of the two colouring matters, the separation
could not be carried further by its means.

Fremy next tried the action of different neutral solvents on
the combination of alumina with the green colouring matter.
He found that some, such as bisulphide of carbon, dissolved in
preference the combination of yellow colouring matter and alu-
mina ; others, such as ether, alcohol, turpentine, dissolved out
the green matter. By employing successively these different
solvents, after the use of bisulphide of carbon, he succeeded in
obtaining lakes of different shades, but was not able to carry
the separation further.

The usual reducing agents, which change other colours, do
not affect chlorophyll. But by the action of bases this body is
converted into a yellow colour, which forms with alumina a
beautiful yellow lake, soluble in neutral solvents, such as ether,
alcohol, bisulphide of carbon. By acting on the solution of this
body with acids, especially hydrochloric acid, it was transformed
into the original green. Now, assuming that the green thus
formed was composed of blue and yellow colouring matters, the
point was to separate these two bodies at the moment of their
formation. This must be done by the simultaneous use of sol-
vents which act differently on the two colouring matters. Such
a solvent is a mixture of hydrochloric acid and ether ; and it was
used as follows : —

Two parts of ether and one part of hydrochloric acid, diluted

* Comptes Rendus, February 27, 1860.

Mr. B. Stewart on certain Laws of Chromatic Dispersion. 143

with a little water, were shaken in a stoppered bottle for some
time, so as to saturate the ether with hydrochloric acid. When
the solution formed by the decolorization of the chlorophyll by
bases was shaken with this solution, a remarkable change took
place; the ether retained the yellow matter, and the hydro-
chloric acid the blue colouring principle. The two colours were
thus isolated ; but if now alcohol in excess was added, which dis-
solves both the yellow and green colouring matters and their
solvents, the solution became of the original green tint.

To the yellow matter soluble in ether, Fremy gives the name
phylloxanthine, and to the blue colouring matter the name phyllo-
cyanine. To the other yellow body which results from the change
of phyllocyanine, he gives the name phylloxantheine.

The blue and yellow colouring matters may be obtained
directly from chlorophyll by adding the ether and acid mixture
directly to the alcoholic extract of the leaves. The green first
becomes brown and is then resolved into phyllocyanine, which
dissolves in the acid, and phylloxanthine, which dissolves in the
ether. This interesting experiment may also be made directly
with the leaves.

Fremy found that the yellow colouring matter formed in the
young shoots is the same as that resulting from the decom-
position of chlorophyll. It may be extracted by alcohol, and
partially resolved into yellow and a little blue colour by means
of hydrochloric acid and ether. Leaves which become yellow
in autumn, then only contain phylloxanthine.

XVI. Note regarding Mr. Ponton's Paper, " On certain Laws
of Chromatic Dispersion." By Balfour Stewart.

To the Editors of the Philosophical Magazine and Journal.

Gentlemen,

HAVING perused a paper " On certain Laws of Chromatic
Dispersion" which appeared in your Journal of last March
as a communication from Mr. Ponton, I feel the following diffi-
culty in recognizing as additions to our knowledge certain laws
which this author claims to have discovered.

To adopt Mr. Ponton's notation, let U be the length in free
aether of the undulation corresponding to one of Fraunhofer's
seven fixed lines, and let u denote the wave-length of the same
line within a given medium after refraction. Then the relation
between U and u may be expressed by the equation

€(u-t-a±cc) = Vj

where the quantities e and a are constant for the same medium
and temperature, being the same for all undulations ; while, on

144 Mr. B. Stewart on certain Laws of Chromatic Dispersion,

the other hand, the quantity a: is peculiar to each wave, the
medium and temperature remaining the same.

Adopting, therefore, the above equation, and applying it to
the seven lines B, C, D, E, F, G, H, we obtain, in Mr. Ponton's
notation, the following seven equations : —

e(b + a±b*)=B,

e{c + a±cx)=C,

&c. &c. &c.

e(A+a±k) = H.

In these, by c, &c, B, C, &c. are supposed to be determined
by observation. We have thus remaining as unknown quanti-
ties e, 0, bX) cXi &c. (nine in all), which require to be determined.

In order to accomplish this, it is necessary to make two addi-
tional assumptions. These assumptions are quite arbitrary, and
have no relation to physical science.

The first of these is made by Mr. Ponton in page 167, where
he assumes as true the following equation :

(SB + 2C + D)-(F + 2G + 3H) _
(3*+2c+rf) - (f+2g + M) ~6'

An inspection of the seven equations given above will show
that this assumption implies that the following equality subsists :

± 3k ± 2cx ± 4= ± 3k ± %g* ±U

This equation, which is the immediate consequence of Mr.
Ponton's first assumption, he seems to regard as the general
expression for a law of nature, which he denominates the semel-
bis-ter law (see page ] 72). The second assumption is also made
in page 167.

Calling B + C+D + E+F + G + H = S,

b+ c +d+e +f+c/+ h=s}
it is assumed that

S-€S =

7e

An inspection of the same seven equations will show that this
assumption implies that

bx + cx + dx + ex+fx+gx+hx=0.

This consequence of his second assumption appears also to be
recognized by Mr. Ponton as a law of nature in page 168, where
it is said, " In every case the motive energy gained by the one
set of waves is exactly balanced by the loss sustained by the
others ; so that the sums of the positive and negative extrusions
being each denoted by X, these two quantities are always equal.

Mr. J. Cockle on a Theory of Transcendental Roots. 145

♦ . . . This, which may be called ' the law of equal transference/
is first to be recognized ; and it is found to prevail in all media,
whether regular or peculiar/'

It thus appears that Mr. Ponton regards "the law of equal
transference " and u the semel-bis-ter law 9> as laws of nature ;
whereas I am unable to view them as anything else than the
immediate results of two arbitrary assumptions which it was
necessary for Mr. Ponton to make before he could determine
nine unknown quantities by seven equations.
I am, Gentlemen,

Yours sincerely,
KfcW Observatory, BALFOUR STEWART.

June 1860.

XVIT. Sketch of a Theory of Transcendental Roots.
By James Cockle, M.A., F.R.A.S., F.C.P.S. %c.*

IN these and otherf pages I have, I believe, proved the hope-
lessness of solving a quintic by means of an Abelian sextic ;
at all events I have given formulae which afford a ready test of
any supposed solution. Solubility by radicals is, indeed, a cha-
racteristic of equations of the lower degrees, and of certain forms
of those of the higher ; but the conclusions of Abel and Sir Wil-
liam Rowan Hamilton indicate that it is not a property of equa-
tions in general. And if we would study the general problem
of solution, we must introduce functions which are not in general
algebraic, though in special cases they may be susceptible of
algebraical expression. The introduction of such functions is
facilitated by results with which Cardan, Tschirnhausen, and
Mr. Jerrard have enriched science, and which manifest the pos-
sibility of reducing to the form

xn— nz+(n— 1)# = 0

any general equation of a degree lower than the sixth. The
possibility of this transformation entails, save in the case of
quadratics, that of the transformation

wn— nacc + an=0

within the same limits. The non-symmetric and the symmetric
forms alike disclose that the roots are functions of a single para-
meter ; and, inasmuch as these forms are substantially as general

* Communicated by the Author.

t See my "Notes on the Higher Algebra" in the current (June 1860)
Number of the ' Quarterly Journal of Pure and Applied Mathematics/ In
a paper " On the Resolution of Quintics," which appears in the same
Number, I have given some additional development to formulae discussed
in this Journal.

146 Mr. J. Cockle on a Theory of Transcendental Roots.

as the general equation, the roots of the latter are also functions
of a single parameter, and that equation admits of the applica-
tion of the processes which follow without any preliminary trans-
formation. Retaining the above forms for the sake of brevity,
let either of them indifferently be represented by

and either of their systems of roots by

<l>la9 <l>2a> • • • <\>tfl>

no assumption whatever being made as to </>, except its funda-
mental property of satisfying the condition

f<t>a=0

identically. The next step is to treat this equation by the cal-
culus of functions, or rather (since the discoveries of M. Hermite
and of M. Kronecker have shown that the roots of a quintic are
expressible in terms of elliptic integrals) by the differential cal-
culus, which, where the roots are obtainable in terms of integrals,
ought to enable us to obtain them. In consequence of its iden-
tical nature, the successive derived equations

df<f>a &fil>a

da m%h da* -U' ' * ' '

are satisfied identically. Replace <f>a by x in each of these rela-
tions, and seek the form of </>. For the quadratic we have

x2— 2# + «=0,

0 dx dx
da da

and the elimination of x leads to

1 C da j

= — , : x=* 1 — + const.,

2Vl-<z J2</l-a

= 1— a/1 — a = <t>a,

the ordinary solution. But here the radical flows from the in-
tegral expression. Again, for the cubic we have

xsSx + 2a=0,

whence

dx
da

Mr. J. Cockle on a Theory of Transcendental Roots. 147
and, by the elimination of a;,

^-i)(333+9£+3=°-

Multiplying this result into vl~«2, and making

-^^■i=?>

it becomes

f3-3f + 2\/l-«2=0,

which is of the same form as the given cubic. Hence, since

sc = (j)a,
therefore

and

dx _ fys/l—a9,
da~" &Sl — a*'

of which a corrected integral is

n . /27T+ sin-1 «\
# = 2sm( 5 ),

which expresses the mean root of the cubic. And if we call

#1 = 2sml — ^ — ) =9i«,

0 . /27r+sm~1a\ ,
%o=2 — )~9<2.a>

F«=*!Hfl\ 3

#3= 2 sin y g J = cj>3a,

we have

~da~~~~~ Zs/\=d?

dfycfi _ <£2 v 1 — a2
~da~"~~~ 3^1"^?'

d(j>3a _ ^x/l — «2.
and the mean root alone satisfies all the conditions of the pro-

148 Mr. J. Cockle on a Theory of Transcendental Roots.

cess. Thus far I have used the non-symmetric form ; but inas-
much as the symmetric one leads to

# = <£<(, a=^<f>x = ^xf)aJ

we have, in </>2a = a, a relation which further limits the form of (f>.
Whichever form we employ, the first derived equation may be
depressed to the second degree in #, and for the latter we find

_ ,dx dx ; _ , -

xn~ ! -j a -r: x + an~l =0,

da da

or, reducing,

In treating of equations which involve more than one para*
meter, we must employ the differential equations

and however numerous be the symbols in the equation

flv,w,...y,z) = 0,

we shall, provided that relation be symmetric, in the end be led
to relations of the form

z=^y, y=^z=y*y.

I mention this because it may be found desirable to study
some canonical forms other than those pointed out by Mr.
Jerrard. When a is greater than unity, logarithmic may replace
the above circular functions, and, when the parameters are inde-
pendent, the 8 of the calculus of variations may replace d, and
we shall have the identical equalities

#(«,i,..)=o, 8/^(a,*,..)=o, sy<K«,A,..)=o,...

I noticed the auxiliary condition ^a — a in a footnote at p. 133
of this Journal for February 1846 (S. 3. vol. xxviii.). Subsi-
diary conditions are necessary, even in the foregoing discussion
of a cubic, for suggesting or completely ascertaining the form of
<f) ; and it will be observed that

dx . . <//C+sin-1«\

where C is a constant.

4 Pump Court, Temple, London,
June 30, 1860.

[ 149 ]
XVIII. Proceedings of Learned Societies,

ROYAL SOCIETY.

[Continued from p. 78.]

Jan. 12, 1860. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.

npHE following communications were read : —

-*- " On the Movements of Liquid Metals and Electrolytes in the

Voltaic Circuit." By George Gore, Esq.

1 . It has long been known that when a globule or layer of pure
and clear mercury is placed upon a smooth non-metallic surface, a
watch-glass for example, and covered to a small depth with a watery
electrolyte, sulphuric acid in particular, and two terminal platinum
wires from a voltaic battery are dipped into the electrolyte, one on
each side of the globule, the mercury makes a movement towards
the negative wire, and a rapid and continuous stream of the super-
natant liquid flows from the negative to the positive electrode over
the surface of the mercury, and back again by the sides of the con-
taining vessel. Also that when a small drop of a watery electrolyte,
especially sulphuric acid, is placed upon the surface of pure and dry
mercury, the latter connected with the negative pole of a battery,
and a platinum wire from the other pole momentarily immersed in
the electrolyte, the drop of liquid is suddenly repelled and spreads
over the surface of the mercury.

2. These phenomena have been examined by Herschel*, Erman,
H. Davy, Runge, Pfaff, and others f, and some of the results have
been recorded in the 1st volume of 'Gmelin's Handbook of Che-
mistry,' page 486 (published by the Cavendish Society) ; but no
definite cause of the movements seems to have been discovered.
Herschel has, however, shown that the continuous movement of the
supernatant liquid is unaffected by the approach of strong magnets,
and that it is influenced by the chemical nature of the electrolyte ;
also that its direction is notably influenced by the presence of vari-
ous metallic impurities in the mercury.

3. Being desirous of ascertaining the conditions under which the
movements are produced, the relations of the phenomena to ordinary
and recognized actions, and the more immediate cause or causes of the
movements, Ihave undertaken the following experimental investigation.

4. In describing the experiments I shall have frequent occasion to
speak of the continuous flow of the electrolyte, and of the sudden re-
pulsion of drops of liquid already mentioned, and shall therefore
speak of the former as the continuous action or movement, and of the
latter as the sudden or momentary one. Also in speaking of the conti-
nuous motion, I shall call it positive flow or movement when the super-
natant liquid proceeds from the positive wire towards the negative
one, and negative flow, &c. when it passes in the opposite direction.

5. The usual method of manipulation I have adopted has been to

* " On certain Motions produced in Fluid Conductors when transmitting the
Electric Current," Phil. Trans. 1824.

t Draper has recorded some experiments of a similar kind. — Philosophical
Magazine, S. 3. vol. xxvi. p. 185.

150 Royal Society : —

take a watch-glass of about 2 inches diameter and place in it by means
of a small gutta-percha spoon capable of containing from 20 to 50
grains of mercury, a globule of that metal of about 30 grains weight,
adding sufficient of the electrolyte to just cover or nearly cover the
globule of metal, and sifting a few particles of finely powdered char-
coal or asphaltum upon the surface of the liquid, to facilitate obser-
vation of the movements ; next, using a Smee's battery of 22 pairs
of plates 4 inches deep and 2£ inches wide with terminal platinum
wires, charged with one measure of oil of vitriol and 1 5 measures of
water, I place the end of the negative wire in the liquid about ^th of
an inch from the mercury, and then carefully immerse the end of the
positive wire in the liquid on the opposite side of the globule, at a
greater distance from the mercury than the negative wire in the case
of an alkaline solution, and at a less distance in the case of an acid
one, in order to prevent the mercury from touching the electrodes
by its movement and thus vitiating the first and purest result. A
polished oval space 2 inches long, Jths of an inch wide, and -|ths of
an inch deep, with a curved bottom, formed in a thick plate of glass
and substituted for the watch-glass, did not admit of such satisfactory
freedom of motion. In*doubtful cases of movement, a small porcelain
boat, such as is used in organic chemical analysis, was sometimes
employed instead of the watch-glass ; and in certain special experi-
ments a V-tube was employed. In nearly all cases the mercury gra-
dually became impure, and therefore fresh mercury was taken for
each experiment.

A. Conditions of the Movements.

6. Two substances are always required in these experiments, with
one alone the movements never occur.

7. To determine whether both the substances must be in a liquid
Btate: — 1st. A portion of mercury in a watch-glass was connected
with the negative pole of a battery and covered with a flat piece of
platinum foil ; a drop of solution of sulphate of potash was placed
.upon the foil and the end of the positive wire dipped into it. No move-
ment, either sudden or continuous, of the solution or mercury took
place. On substituting for the foil a circular piece of filtering paper
varnished all round its edge and covered with several drops of the
solution of sulphate of potash, the sudden repulsions were produced
readily, but were much less powerful than when the liquid was placed
alone upon the mercury. 2nd. Two circular clean spaces, | an inch
wide, were scraped with a knife upon a horizontal plate of zinc ; one
of them was amalgamated with mercury and left covered with a very
shallow layer of that metal, the other was also amalgamated, but the
excess of mercury was wiped off; each of the spots was now covered
with a shallow layer of a weak solution of sulphate of alumina, the
zinc plate connected with the negative plate of the battery, and the
end of the positive platinum wire dipped in succession into the super-
natant portions of liquid ; the solution above the thin layer of liquid
mercury was powerfully repelled on making the contact, whilst that
upon the other spot was unaffected. Similar results were obtained

On the Movements of Liquid Metals in the Voltaic Circuit. 151

with a solution of caustic potash, also with a plate of tin. 3rd.
A portion of Newton's fusible alloy was melted under a layer -J-th of
an inch deep of a solution of chloride of zinc, and the ends of the
platinum wires from the battery immersed in the supernatant liquid
until the alloy cooled and solidified ; the zinc solution flowed from
the negative towards the positive wire as long as the surface of the
alloy remained in the liquid state, and ceased to flow immediately the
surface of the metal solidified. Also a drop of a strong solution of
caustic potash placed upon the melted fusible alloy, the latter con-
nected with the negative pole and the former with the positive pole,
exhibited the usual momentary repulsions as long as the surface of
the alloy remained fluid. I therefore conclude that both the substances
must he in a liquid state.

8. To ascertain whether both the substances must be conductors
of electricity : — 1 st. I formed melted globules of phosphorus in warm
oil of vitriol, also in a hot mixture of one measure of distilled water
and two measures of oil of vitriol, and immersed the wires in the usual
manner, but no motion of the liquid occurred. 2nd. No movements
were obtained with a globule of bromine under warm oil of vitriol ; a
large globule of bromine was placed in a porcelain boat, and dilute sul-
phuric acid added until the bromine was partly covered ; the wires
were then applied, but no movements took place. Also the addition
of sulphur and of selenium to the bromine did not ensure a different
effect. 3rd. With a large globule of selenium under fused chloride
of zinc no motion was obtained. 4th. I made similar experiments
with globules of chloroform, also of bisulphide of carbon in dilute sul-
phuric acid, but obtained no movements. 5th. No movements took
place with globules of chloroform in a solution of caustic potash or of
sulphate of alumina.

9. To determine whether one of the substances must be metallic : —
1st. A definite layer of oil of vitriol was placed beneath a layer of
distilled water weakly acidulated with sulphuric acid, and the terminal
wires immersed in the upper liquid ; no movements occurred at the
boundary line of the two liquids. 2nd. A dense solution of cyanide
of potassium was placed in a small glass beaker, a few particles of
charcoal were sifted upon its surface, and a layer of aqueous ammonia
\ an inch deep carefully poured upon it. A vertical diaphragm of
thin sheet gutta percha was then fixed so as completely to divide the
upper liquid into two equal parts ; the vessel was placed in a strong
light, and two horizontal platinum wire electrodes from 66 pairs of
freshly -charged Smee's batteries immersed -J-th of an inch deep in the
liquid ammonia on each side of the diaphragm. A copious current of
electricity circulated, but no movements of the liquids at their mutual
boundary line could be detected. A small globule of mercury placed
in the lower liquid at once produced evident signs of motion. One
of the substances must therefore be a metallic conductor of electricity.

10. To ascertain whether the capability of producing these move-
ments was a general property of metals and alloys when in the liquid
state : — 1st. Bismuth was fused beneath a layer of chloride of zinc ;
tin was also melted under a similar layer, and the terminal wires im-

152 Royal Society : —

mersed in the supernatant liquid ; a steady negative flow occurred in
each case. 2nd. Cadmium was similarly treated under fused cyanide
of potassium, and a positive flow obtained. 3rd. Cadmium, lead,
Britannia-metal, and fusible metal were melted separately, small pieces
of cyanide of potassium placed upon them and melted, the metal con-
nected with the negative platiuum wire, and the positive wire dipped
into the melted cyanide; positive repulsions took place with each
metal on making contact. I conclude from these experiments that
the power of rotating under the influence of an electrolytic current is
a general property of metals and alloys when in a liquid state.

1 1 . That the mass or body of the metal is not essential to the
production of the movements, is evident from the fact that the move-
ments have been readily obtained with thin layers of mercury upon
amalgamated zinc (7) and copper plates.

12. I have endeavoured to obtain the movements without the
presence of an electrolyte, by passing an electric current through a
small globule of zinc fused upon the surface of bismuth, but the
ready mingling of the melted metals, and their rapid oxidation, pre-
vented a reliable experiment being made.

13. It has already been shown, in the instances of fused salts upon
melted metals (10), that the presence of water is not a necessary
condition of the phenomena.

14. The power of producing the movements is a general property
of electrolytes as well as of liquid metals ; I have experimentally
found it in the following classes of substances : — organic and in-
organic acids ; water ; aqueous solutions of caustic alkalies* ; alkaline
carbonates, bicarbonates, borates, hypophosphites, phosphates, sul-
phides, hyposulphites, sulphites, sulphates, bisulphates, iodides, bro-
mides, chlorides, chlorates, nitrates, and silicates ; salts of alkaline
earths and of alumina ; salts of tungsten, molybdenum, chromium,
uranium, manganese, arsenic, and of the malleable heavy metals ; also
with fused salts, aqueous solutions of organic salts, and solutions of
salts in alcohol. The salts of tungsten, molybdenum, chromium,
uranium, and manganese, generally gave the weakest and most
variable results ; whilst sulphuric acid and solutions of alkaline
cyanides yielded very strong and definite movements. In feeble
cases of motion the globule of mercury should be placed in a narrow
porcelain boat, and a strong solution of the substance added until
the metal is only covered at its sides with the liquid ; and for still
greater sensitiveness, the experiment of placing a drop of the liquid
upon the surface of the mercury should be adopted.

15. The mass or body of the liquid is not essential to the move-
ments ; mere films of solution adhering to the under surface of a
circular disc of brass, brought into contact with mercury under the
influence of a voltaic current, exhibited the phenomenon readily.

* Herschel found no movements with solutions of caustic alkalies ( Vide Gmelin's
Handbook, vol. i. page 490) ; I have readily obtained them with pure mercury in
solutions of pure alkalies by using strong solutions and a powerful electric current,
and placing only a small quantity of the liquid above the mercury so as to pro-
duce the maximum of effect. Alkaline solutions in general act much more feebly
than acids.

On the Movements of Liquid Metals in the Voltaic Circuit. 153

16. To ascertain whether the current of electricity must pass from
the electrolyte into the metal, or vice versa : — 1st. A layer of mercury
was placed in a narrow glass heaker, upon it a shallow layer of chlo-
roform, and above this, in one instance a dilute solution of sulphate
of alumina ; and in the other instance a solution of caustic potash,
and the wires from the battery dipped into the upper liquid ; no
movements at either of the contiguous surfaces occurred. 2nd.
Similar experiments were made, substituting in one case a definite
layer of oil of vitriol with a very dilute solution of sulphuric acid
above it, and in the other case a dense solution of chloride of zinc
with a very dilute solution of the same salt above it, for the chloro-
form and its supernatant liquid ; in each case only feeble movements
in the usual direction at the surface of the mercury occurred ; the
weakness of the movements was probably a consequence of the in-
creased distance of the electrodes from the mercury. 3rd. The lower
part of a V-tube of half an inch bore was just filled with mercury,
and a small quantity of solution of cyanide of potassium poured into
each leg ; on dipping the polar wires, one into the solution of each
leg, the saline liquid rapidly flowed from the positive to the negative
leg until it was \\ inch high in that limb. From these experiments
I infer that the electric current must pass from the electrolyte into
the metal, or vice versa, and that the continuous movements are not
results of any power radiating from the electrodes.

1 7. It is not essential that the electric current should pass both
into and oat of the metallic globule by the electrolyte ; with a glo-
bule of mercury in rather strong sulphuric acid and either of the
polar wires immersed in the acid, the other wire being in contact
with mercury, the movements occurred : also with the negative
wire touching a globule of mercury in a solution either of cyanide of
potassium or strong caustic potash and the positive wire in the
liquid, movements were readily obtained.

18. To ascertain whether the electrodes were essential to the
movements, I placed a large globule of mercury in the middle
part of a slightly bent horizontal glass tube, 20 inches long and
\ an inch diameter, then filled the tube with a strong solution of
cyanide of potassium, and immersed the polar wires a short di-
stance in the liquid at each end; a strong positive flow of the
solution over the surface of the mercury occurred, but no movements
took place at the surfaces of the electrodes, except such as were
produced by the evolution of gas. The electrodes evidently operate
merely as conductors of the electricity, and are not, in an abstract
sense, at all connected with the movements.

19. Herschel has shown that the approach of strong magnets has
no effect on the motions {vide Gmelin's Handbook, vol. i. p. 490),
and I have also found that the movements are not electro-magnetic.
A watch-glass — containing in one instance a solution of cyanide of
potassium, in a second instance a solution of hydrochlorate of am-
monia, and in a third instance oil of vitriol, — was placed upon one of
the poles of a vertical horse-shoe electro-magnet capable of sustaining
about 100 pounds, and the end of a large soft-iron armature

Phil. Mag. S. 4. Vol. 20. No. 131. Aug. 1860. M

154 Royal Society : —

which rested upon the other pole brought near the glass. The polar
wires from the Smee's battery of twenty-two pairs were now immersed
in the electrolyte on each side of the globule, and the magnet con-
nected with a separate battery of large surface. The direction of How
of the electrolyte was instantly changed to a circular one all round
the glass, and was reversed by reversing the polarity of the magnet.
In each case the direction of motion of the electrolyte corresponded
with that of the electric current beneath it ; i. e. with a south pole
beneath, the liquid moved in the same direction as the hands of a
watch ; — this circular motion was evidently a case of ordinary electro*
magnetic action, as it occurred equally well without the presence of
a liquid metal in the electrolyte. No real connexion of the mag-
netism with the movements under investigation was detected.

20. To ascertain whether the movements varied with the quantity
of the electric current, I prepared a single series of sixty-six pairs of
Smee's batteries, forty of which were charged with spring- water, and
the remainder with a mixture of one measure of sulphuric acid and
fifteen measures of water. The movements obtained on applying
the current from the whole series to very dilute sulphuric acid con-
taining a globule of mercury, were much more feeble and the amount
of electrolysis much less than when the current from the twenty-six
strongly-charged pairs alone was applied. On substituting distilled
water for the dilute acid, the movements were stronger and the
electrolysis greater with the whole series than with the twenty-six
pairs. In all cases the movements appear to be dependent upon
the quantity of electricity circulating.

21. It is highly probable, from the experiments just described, that
the movements are intimately dependent upon electro-chemical action
occurring at the surface of the liquid metal, especially as the amount
of motion varies with the quantity of electricity which passes from
the electrolyte into the metal, or vice versd ; and it would be very
desirable to obtain a negative proof of this by an experiment with a
globule of one liquid metal in a bath of some other liquid metal, as
already attempted (12).

22. With every liquid yet examined the movement of the liquid
has invariably been attended by a simultaneous movement of the
fluid metal ; and the greater the movement of the liquid the greater
was the movement of the metal, from which I infer that the move-
ments of the two substances are mutually dependent.

23. The results in general indicate that the sudden movements
are of the same general character as the continuous ones, the effect
in the former case being heightened by the concentration of the
electric force within a small compass, together with the additional
electric energy always displayed at the moment of making contact
with a battery.

24. The movements require for their production two substances
(6) ; both these substances must be in a liquid state (7), and be
conductors of electricity (8) ; one of them must be a metal or a
metallic alloy (9) ; any metal or alloy will do (1 0), and only a mere
film of it is essential (11) ; the other must be an electrolyte, and

On the Movements of Liquid Metals in the Voltaic Circuit. 155

need not contain water (13) : any electrolyte will do (14), and only
a thin layer of it is requisite (15) : the electric current must pass
from the electrolyte into the metal, or vice versd (16), but need not
pass both into and out of it by the electrolyte (17) ; the electrodes
are not essential (18) ; the movements are not electro-magnetic (19),
they are dependent upon the quantity of the electric current (20),
and are intimately connected with electro-chemical action (21) ; the
movements of the metal and electrolyte are mutually dependent (22),
and the momentary movements are of the same nature as the con-
tinuous ones (23).

25. The pure or abstract conditions of the production of the phe-
nomena are, — a liquid metal (or alloy) in contact with a liquid elec-
trolyte, and a quantity current of electricity passing between them.

B. Conditions of the continuance of the Movements.

26. With regard to the continuance of the movements: — 1st.
In some cases the metal becomes covered with an insoluble film,
produced by ordinary chemical action of the liquid, which prevents
the continuance of the action ; this occurs particularly with mercury
in strong solutions of sulphides, iodides, bromides, and chlorides.
2nd. If the positive wire is connected with the mercury and the
negative wire with the liquid previous to placing both the wires in
the electrolyte, films are in nearly all cases instantly produced (but
not with strong sulphuric acid) and interfere with further action ;
films are also frequently produced by a similar cause upon the end
of the mercury nearest to the negative wire when both the wires are
in the solution, and in many such cases the mercury creeps in a pecu-
liar serpent-like form beneath the film towards the negative wire.
3rd. In many instances the metallic globule becomes of a pasty
consistence by absorbing substances deposited upon its surface by
electrolysis, and the motion declines ; this takes place particularly
with mercury in solutions of salts of ammonia, baryta, strontia,
magnesia, and lime, but most with those of magnesia and lime ; and
it occurs very rapidly if, instead of placing both the polar wires in
the electrolyte, the negative wire is immersed in the globule of
mercury. It is evident from these facts, that it is essential to the
continuance of the movements, that the particles composing the sur-
face of the metallic globule should retain a sufficient degree of mo-
bility to admit of free motion.

27. The best method of obtaining a continuous movement is to
place a globule of pure mercury in a watch-glass, barely cover it
with dilute sulphuric (or nitric) acid, connect it with the negative
platinum wire and the liquid with the positive platinum wire of a
battery of sufficient power to produce a moderate flow without over-
heating the liquid : ten small Smee's batteries are sufficient. By this
means I have obtained undiminished motion for upwards of six hours.

C. Conditions of the direction of the Movements.

28. In speaking of the direction of the movements, I always
mean those of the supernatant liquid, unless otherwise stated, because
the true movements of the mercury are generally less easily detected

M2

156 Royal Society : —

than those of the electrolyte : the movements of the liquid are hest
observed by means of charcoal or asphaltum (5), and those of the
mercury by the aid of a few parallel scratches upon the under sur-
face of the watch-glass.

29. The directions of flow of the metal and liquid are intimately de-
pendent upon each other, for in every instance the metal moves in an
opposite direction to the electrolyte (see also 22) ; and in those cases
where two opposite flows of the liquid towards the centre of the vessel
occur (as with a solution of sulphate of potash), the globule of
mercury is elongated at both ends into a pointed shape, and its two
ends point toward the two electrodes, its largest diameter being
directly under the point of meeting of the flows of the solution, and
its acutest apex under the strongest flow. The relation between the
metal and liquid is apparently of a dual or polar character, the move-
ments of the two bodies being always opposite and equal. This
mutual dependence of the motions explains the necessity of both the
substances being in a liquid state (7).

30. With regard to the direction of the flows, there are three
cases to be distinguished: — 1st. The movements obtained by im-
mersing the negative wire in the metal and the positive one in the
electrolyte. 2nd. Those obtained whilst the positive wire is in the
globule and the negative one in the electrolyte. 3rd. Those pro-
duced by immersing both the wires in the supernatant liquid with
the globule between them.

31. Upwards of 150 different liquids, including organic and in-
organic acids, alkalies, salts of alkalies, earths and heavy metals, also
organic salts, were examined by the first of these methods, and in
almost every instance the flow of the supernatant liquid was positive,
the clearest exception being with a solution of persulphate of iron.
With concentrated sulphuric acid the motion (if any) was very feeble,
but with diluted acid of various degrees of dilution it was strongly
positive. The flow of the liquid declined quickly with solutions
which contained an alkali-metal, apparently in consequence of the
mercury becoming less mobile (?) by absorption of that metal ;
but with dilute acids it continued a long time ; with very dilute nitric
acid, in one experiment the movement was sustained with scarcely
any diminution during 2\ hours ; and with dilute sulphuric acid,
in a second experiment it continued 6J hours, and did not then
appear to slacken : the battery employed in this experiment con-
sisted of ten small Smee's elements. A globule of strong sul-
phuric acid was placed upon a surface of mercury, the latter
connected with the negative pole, and the end of the positive
wire dipped into the acid ; much gas was evolved from the anode, and
the liquid was not repelled on making contact, but collected in a
heap around the wire ; — a globule of solution of caustic potash
similarly treated exhibited repulsion on making contact. It is
evident from these uniform results that the direction of flow obtained
by immersing the positive wire in the electrolyte and the negative
one in the mercury is almost uniformly positive.

32. The movements obtained by this method are not produced by

On the Movements of Liquid Metals in the Voltaic Circuit. ]57

the act of deposited substances dissolving in the mercury, for they
occur equally well whether hydrogen gas is set free and escapes or
alkali-metal is deposited and dissolves in the mercury, until in the
latter case the diminished mobility of the globule interferes with the
result.

33. Considerable difficulty was experienced in examining liquids
by the second method, in consequence of the rapid and in many cases
instantaneous oxidation or filming of the metallic globule ; but by
using very dilute liquids and immersing the negative wire from
seventy-two small Smee's elements during only a moment at a time,
this difficulty was in most cases sufficiently overcome to allow di-
stinct starts of the mercury to occur in the particular direction
beneath its film, and thus to indicate an opposite motion of the
supernatant liquid, although in nearly all cases the movement of the
electrolyte itself could not be detected. Upwards of 100 liquids,
consisting of organic and inorganic compounds — acid, alkaline, and
neutral — were examined, and in more than three-fourths of them di-
stinct movements of the metal were obtained, which were in every
instance in a positive direction, thus indicating a negative flow of
the electrolyte. In some liquids, viz. oil of vitriol, moderately di-
lute nitric acid, strong solutions of sulphate of ammonia, iodide of
ammonium, and sulphite of potash, very dilute solutions of bisul-
phate of potash, iodide of potassium, nitrate of cobalt, hydro-
cyanic acid, cyanide of potassium, and acetic acid, — visible move-
ments of the liquid itself in a negative direction were also ob-
tained. The movements of the liquid and of the metal very quickly
ceased. These experiments show that the direction of flow ob-
tained by placing the positive wire in the metal and the negative
wire in the electrolyte is always negative.

34. The movements obtained both by methods 1 and 2 appear to
be produced by a mutual attraction of the liquid and metal ; in the
former case the mercury attracts an electro-positive element of the
liquid (hydrogen or an alkali-metal), and produces a positive flow ;
and in the latter case it attracts an electro-negative element (generally
oxygen), and produces a negative flow.

35. Herschel found by the third method of operating, that with
pure mercury in acids and saline liquids the flow was negative, and
was weaker as the base was stronger, and more rapid as the acid was
stronger and more concentrated ; and that in solutions of nitrates
two opposite flows occurred, one from each wire {vide Gmelin's
Handbook, i. 490). I have found by an examination of pure
mercury in various liquids the results exhibited in the following Table.
The arrows indicate the direction of flow of the liquid, -{- being po-
sitive and -¥ negative ; and the numbers affixed to them afford a
rough approximation of the velocity or magnitude of the movements.
The battery employed consisted of twenty-two small Smee's elements.
The substances were^dissolved in water, and the solutions were of mode-
rate strength unless -otherwise stated. Manifestly impure substances
were rejected, and fresh mercury was taken for each experiment.
The results obtained were in many cases verified several times : —

158

Distilled Water

Boracic Acid

Phosphoric Acid ....

Strong Sulphuric Acid..

Strong Sulphuric
Acid 1 measure

Water 5 „

Strong Sulphuric
Acid 1 measure

Water 15 „

Strong Hydriodic
Acid 1 measure

Water 15 „

Hydrobromic Acid,
very dilute j

Strong Hydrochloric
Acid 1 measure

Water 5 „

Strong Hydrochloric
Acid 1 measure

Water 15 ,,

Perchloric Acid, very
dilute

Strong Hydrofluoric Acid

Strong Hydrofluoric 1
Acid 1 measure I

Water 5 „

Strong Nitric Acid,
1 measure

Water 1 „

Strong Nitric Acid,
1 measure

Water 5 „

Strong Nitric Acid, 1
1 measure I

Water 15 „ J

Aqueous Ammonia,
strong

Sesquicarbonate of Am-
monia

Phosphate of Ammonia .

Sulphide of Ammo- 1
nium, 1 measure I

Water 15 „ J

Sulphate of Ammonia . . .

Hydrochlorate of Am-
monia

Nitrate of Ammonia

Caustic Potash

Carbonate of Potash . . .

Bicarbonate of Potash . . .

Sulphide of Potassium,
dilute

Sulphite of Potash

Sulphate of Potash

Bisulphate of Potash . . .

Iodide of Potassium . . .

Bromide of Potassium. . .

Chloride of Potassium . . .

Chlorate of Potash

Nitrate of Potash

► faint

h10

H-6

H-S

H-4
H-8

+-3

H-3

H-2

4-«

4- *

+-2

4-3
4-6

4-2

4-1
4-2
4-1
4-3
4-3

4-2
4-2

Royal Society : —

Caustic Soda

Carbonate of Soda -+ l

Bicarbonate of Soda -4- 2

Biborate of Soda

Diphosphate of Soda . . . -f24
Sulphide of Sodium,

dilute

Hyposulphite of Soda ... -+ i

Sulplrite of Soda

Sulphate of Soda -+4 and then -4-4

Chloride of Sodium -+ 4

Nitrate of Soda -4-3

Phosphate of Soda and

Ammonia -+t

Baryta Water

Carbonate of Baryta ... -+ 2

Chloride of Barium -+ 2

Nitrate of Baryta -+ 3

Strontia Water

Chloride of Strontium ... -+ 2

Nitrate of Strontia -#■

Sulphate of Magnesia ... -+ 3
Chloride of Magnesium,

strong -+

Chloride of Magnesium,

weak

Nitrate of Magnesia,

strong

Nitrate of Magnesia,

weak h-2

Lime Water

Sulphate of Lime -+ 2

Chloride of Calcium ... -+ 2
Chloride of Calcium in

Alcohol -4-1

Nitrate of Lime -+• 4

Sulphate of Alumina ... -4- 3

Potash Alum -J-4

Hydrofluosilicic Acid^ ... -4- 4

Silicate of Potash

Molybdate of Ammonia . -+
Chloride of Chromium,

very weak -+1

Monochromate of Potash -i- a

Nitrate of Uranium -+ 2

Sulphate of Manganese . -j-

Arsenic Acid -4- 2

Arseniate of Ammonia. . . -h3

Fluoride of Antimony ... -+ 2

Antimoniate of Potash ... -+ 4

Nitrate of Bismuth -+ -

Sulphate of Zinc -+ 4

Iodide of Zinc, strong ... -+

Nitrate of Zinc -+ 3

Iodide of Cadmium -+ 2

Iodide of Tin, strong ... -+ 6

Nitrate of Lead -+3

Protosulphate of Iron ... -+ 4

Persulphate of Iron -+

Chloride of Cobalt, weak -+

Nitrate of Cobalt -+»

4-4
4-*

4-2

4-
4-3

4-2
4-8
4-«
4-3

+-2

4-3
+-2
4-1*

4- 2

4-2

On the Movements of Liquid Metals in the Voltaic Circuit. 159

Sulphate of Nickel

. -+4

Oxalate of Ammonia . . .

<►!

mi

Nitrate of Nickel

. h-5

Acid Oxalate of Potash. . .

^3

Sulphate of Copper, weak ■+

Neutral Oxalate of Potash

■+«

4-3

Chloride of Copper, ver

Formic Acid

H-3

. -+

Acetic Acid

-+3

Nitrate of Copper

. H-3

Acetate of Potash

-J-3

4-1

Nitrate of Mercury

Strong Aqueous Hydrc

. H-1

Acetate of Soda

-J-3

4-3

-

Acetate of Baryta

H-2

4-2

cyanic Acid

+- 2

Acetate of Uranium

-+ fain!

Strong Aqueous Hy-^
drocyanic Acid,
4 measures )

Acetate of Zinc

-}-4

Acetate of Lead

H-1

+-10

Acetate of Copper

-f1

Aqueous Ammonia,
1 measure J

-+5

4-1

Monotartrate of Potash .

H-3

4-2

Cyanide of Potassium . .

+.10

Bitartrate of Potash

H-5

Strong Aqueous Hy-"1

Bitartrate of Soda

-*3

*t

drocyanic Acid,

Tartrate of Potash and

5 measures

•

4-8

Soda

+ 3

4-3

Caustic Soda Solution,

Tartrate of Potash and

Antimony

-+.3

Cyanide of Mercury. . . .
Ferrocyanide of Pc

_fr.4

)-

Succinic Acid

-8-4

tassium

4-*

Gallic Acid

-i-2

Sulphocyanide of Pc

-

Pyrogallic Acid

-+£

4- 3

Carbazotic Acid

-+.4
H-2

Oxalic Acid

Benzoic Acid

Numerous interesting phenomena of motion and of colour, especially
with solutions of salts of the earth-metals and with metallic iodides,
were observed during the examination.

36. On examining these numerous results we find : — 1st. That all
alkalies and some alkaline salts produce a positive flow only. 2nd.
That some alkaline and many neutral salts produce both positive and
negative flows. 3rd. That some neutral and many acid salts,
and nearly all acids, both organic and inorganic, produce a negative
flow only. The stronger influence of acids, compared to that of
alkalies (14, Note) in the production of these movements, is pro-
bably the reason why various salts of alkaline reaction give a negative
as well as a positive flow, ancfc why many neutral salts containing a
strong acid (chlorides, for example) give a negative flow only. No
substance of alkaline reaction has been observed to give a negative
flow only, nor any strongly acid substance to give only a positive
flow. An alkaline or electro-positive substance as the electrolyte,
produces therefore by the 3rd method a positive flow, and an acid
or electro-negative substance produces a negative flow. Numerous
analogies may be detected in the behaviour of similar salts on ex-
amining the Table.

37. The movements obtained by the 3rd method appear to be
results of a similar mutual attraction of the mercury and the ele-
ments of the liquid to those obtained by methods I and 2. The
mercury moves towards the cathode in acids because its positive end
has acquired, by the aid of the electric current, a stronger affinity for
the negative element of the liquid than its negative end has for the
positive element, and moves towards the anode in alkalies because
its negative end has acquired a stronger attraction for the positive

160 Royal Society : —

element of the liquid than its positive end has for the negative ele-
ment. J do not, however y give either this or the previous explana-
tion (34) as an ascertained fact, but merely as a temporary hypo-
thesis to aid further investigation.

38. The amount of positive flow produced by the 3rd method in
strong aqueous hydrocyanic acid, or strongest solution of ammonia, is
comparatively small, apparently on account of their inferior electric
conductivity ; but if the smallest amount of ammonia is added to the
hydrocyanic acid, the positive flow obtained is very strong ; also, if
instead of ammonia a small quantity of caustic potash, soda, baryta,
strontia, magnesia, lime, or even alumina is added to the acid, similar
effects are produced : a little strontia or lime causes the nearest part
of the mercury to dart up the watch-glass more than half an inch
towards the positive electrode, if the battery is sufficiently strong.
Silica had no effect. The addition of oxide of zinc, dioxide or
protoxide of copper to the acid, reversed the direction of the flow,
and dioxide of mercury neutralized the positive movement and
diminished the conduction. The strongest positive flows obtained
by the 3rd method were with strong solutions of alkaline cyanides,
and the strongest negative flows with sulphuric acid.

39. The behaviour of liquids upon mercury in V-tubes by the
three methods is not essentially different from their behaviour in a
watch-glass ; the former, indeed, may be safely predicted from the
latter. Sufficient pure mercury was placed in a V-tube of half an
inch bore just to fill it at the bend, then a strong solution of sulphate
of alumina poured upon it half an inch deep in each leg ; on con-
necting the platinum wires from twenty- two pairs of small Smee's
batteries with the solutions in the two legs, the liquid at once flowed
from the negative to the positive leg ; but by lowering the negative
wire into the mercury, it flowed from the positive to the negative leg :
no flow of the liquid was produced by placing the positive wire in
the mercury and the negative one in the solution of the negative leg.
If the mercury was too deep to allow the liquid to pass, the solution
insinuated itself down the sides of the mercury in the positive leg
(the positive wire being in the solution, and the negative one in the
mercury) ; but by using a suitable depth of mercury, the whole of
the liquid flowed from the positive into the negative leg. This is
the usual behaviour of an acid liquid (or of one in which the nega-
tive flow of method 3 predominated) with a suitable quantity of
mercury in a V-tube. With a strongly alkaline liquid the only
difference of behaviour is, that when the two wires are in the solu-
tions of the two legs, the liquid flows from the positive to the nega-
tive limb (see 16), i. e. opposite to the direction of flow with an
acid.

40. There is a fixed relation between the direction of the electric
current and the direction of each of the classes or movements ; for in
every case where the former is reversed, the latter also becomes
reversed ; but this effect is, of course, not observable in those cases of
method 3 where two opposite and equal motions to the centre of the
metallic globule exist.

41.1 have examined the influence of the chemical nature of the

On the Movements of Liquid Metals in the Voltaic Circuit. 161

metallic globule upon the movements obtained by the 1st method, in
the following manner. The globule of mercury was first connected
with the positive pole and the liquid with the negative pole for about
ten seconds, and then the wires placed as in method 1 ; a temporary
negative flow was produced for a few moments with certain liquids,
apparently in consequence of the mercury absorbing a minute portion
of an electro-negative constituent of the solution (?), and that sub-
stance causing a negative flow in the succeeding operation until the
whole of it was redissolved. The following liquids exhibited this
phenomenon of reversion : — very dilute solutions of nitric acid, nitrates
of ammonia, potash, soda, baryta, strontia (not of magnesia, appa-
rently on account of viscosity of the mercury being produced), lime,
zinc, lead, cobalt, nickel, copper, and dioxide of mercury; also
sulphates of ammonia and potash ; hypophosphite and diphosphate
of soda ; and, strongest, the alkaline nitrates ; — but not dilute solu-
tions of caustic potash, soda, baryta, or lime ; carbonates or bi-
carbonates of potash or soda ; carbonate of baryta ; chlorides of
ammonium, potassium, sodium, barium, strontium, magnesium, or
calcium ; iodide or bromide of potassium ; sulphites of potash or
soda ; biborate, hyposulphite, or sulphate of soda ; sulphate of
lime ; arsenic acid ; cyanide of potassium ; oxalate of ammonia. The
battery used was a series of 72 small Smee's elements. It appears
from these experiments, that the direction , of flow obtained by im-
mersing the positive wire in the electrolyte and the negative one in
the globule is strongly influenced by the chemical composition of
the metallic globule.

42. The chemical nature of the globule exercises an equally
powerful influence upon the direction of the movements obtained by
the second method. If the mercury was first connected with the ne-
gative wire and the solution with the positive wire for a few seconds,
and then the connexions reversed or made as in method 2, a temporary
and strong positive flow of the electrolyte for a few moments was
obtained, apparently in consequence of the mercury absorbing a
little alkali-metal or other electro-positive constituent of the liquid,
and that substance causing a positive flow of the solution until the
whole of it was redissolved. This positive flow did not occur while
there was above a certain quantity of the alkali-metal in the mercury.
The reversions were obtained in the following liquids : — dilute and
strong solutions of caustic potash ; weak solutions of caustic soda,
baryta, and lime ; carbonate of baryta ; chlorides of potassium,
sodium, barium, strontium (not of magnesium, owing to viscosity
of the globule), and calcium ; iodide and bromide of potassium ;
sulphites of potash and soda ; biborate, hyposulphite, and sulphate
of soda ; sulphate of lime ; arsenic acid ; cyanide of potassium ; and
oxalate of ammonia ; also in solutions of hypophosphite and diphos-
phate of soda ; — but not in very dilute nitric acid, nitrates of am-
monia, potash, soda, baryta, strontia, magnesia, lime, uranium, zinc,
cobalt, nickel, copper, or dioxide of mercury ; sulphates of ammonia,
potash, or alumina. It is worthy of notice that these two series are
almost precisely the reverse of those named with method 1 (41) ;
i. e. those liquids which have the property of reversing the flow of

163 Royal Society :—

one method have not that property with the other method, except
hypophosphite and diphosphate of soda. The explanation suggested
(34), of the cause of the true movements of methods 1 and 2 does
not appear applicable to these phenomena of reversion.

43. Herschel has shown that with pure mercury in solutions of
alkalies or of sulphate of soda (vide Gmelin's 'Handbook,' i. 490,492),
if a little alkali-metal be introduced into the globule by connecting
the latter for a few moments with the negative wire (the other wire
being in the solution), a positive flow occurs on placing both the
wires in the electrolyte with the mercury between them, and con-
tinues until all the alkali-metal is redissolved ; and that similar effects
are produced by adding small quantities of an easily oxidizable metal
to the mercury — for example, potassium, sodium, barium, zinc, iron,
tin, lead, or antimony, in the order given; but not by bismuth,
copper, silver, or gold. I have found that zinc added to mercury
under a solution of sulphate of potash changed the direction of flow
from positive and negative (obtained by method 3) to positive only ;
cadmium did the same, but more feebly, and tin still more feebly ;
bismuth had no apparent effect, but by using treble the electric
power its effect was also similar, antimony also the same ; gold had no
apparent effect even with a current from 72 pairs of Smee's elements.
No positive flow was obtained by connecting the mercury with the
negative wire and the solution with the positive wire for a short time
in a liquid consisting of acid and water, and then placing both the
wires in the electrolyte. Although there are many liquids (most of
those which contain an alkali-metal) in which a temporary positive
flow (or increase of positive flow) may be obtained by the 3rd me-
thod by first placing the negative wire in the mercury for a short
time and then returning it to the electrolyte, there are but few
(among which are diphosphate of soda and arseniate of ammonia)
in which a temporary negative flow is produced by placing the
positive wire in the mercury and then returning it to the solution.
It has been constantly observed with the 3rd method, that purity of
the mercury is essential to the production of uniform results. From
these various facts it appears that the chemical nature of the metallic
globule strongly influences the direction of the movements obtained
by method 3 ; also that an electro-positive globule produces a
positive flow, and an electro -negative substance dissolved in the
mercury produces a negative flow.

44. In some instances of the 3rd method — for example, with solu-
tions of chloride of magnesium and nitrate of magnesia (35, Table),
even the degree of dilution appears to determine the direction of the
motion. No variation in the direction of the movement obtained by
either method was observed on varying the strength of the electric
current, or on varying either the actual or relative distances of the
electrodes from the metallic globule.

45. The presence of an electro-positive metal in one portion of
the surface of the mercury will (by generating a small electric
current) sometimes cause rotation of the electrolyte after the battery-
wires are removed, especially if the mercury is touched with a pla-
tinum wire heneath the surface of the liquid ; this is seen most

On the Movements of Liquid Metals in tke Voltaic Circuit. 163

frequently with mercury into which some alkali-metal has been
deposited.

46. The general phenomena of the movements may be briefly
redescribed thus : — A. When both the wires are in the electrolyte,
and the mercury between them, several cases occur : 1 . With a
strongly alkaline liquid, a positive flow of the solution from the
positive wire over the mercury to the negative wire occurs ; 2. With
a strongly acid liquid, a negative flow of the solution takes place ;
and 3. With a solution of a neutral or slightly alkaline salt, espe-
cially of a salt composed of a strong acid and a strong base, two
flows occur, a negative one from the negative wire towards the centre
of the mercury, and a positive one from the positive wire towards
the centre of the mercury, — the negative one being generally the
strongest. If in this 3rd case the mercury contains any impurity,
or if a substance be caused by any means to dissolve in the mercury,
the movements are notably affected : an electro-positive substance
(zinc, alkali-metal, &c.) increases the positive flow so as partly or
completely to overpower the negative movement ; and an electro-
negative substance increases the negative flow, in a few instances, so
as to overpower the positive movement. These influences are also
frequently detectable when liquids are used of alkaline or acid reac-
tion, as in cases 1 and 2.

B. When the negative wire is in the mercury and the positive
one in the liquid, two cases occur : 1 . With pure mercury, the
motion is positive in nearly all liquids, whether acid, alkaline, or
neutral ; and 2. With mercury containing a small amount of an
electro-negative substance, imparted to it by reversing the connexions
of the wires for a short time, a temporary negative flow is produced
in certain liquids, chiefly nitrates, but not in certain other liquids.

C. When the positive wire is in the mercury and the negative
one in the liquid, also two cases occur : 1 . With pure mercury,
the motion is negative in all liquids — acid, alkaline, or neutral;
and, 2. With mercury containing a small quantity of an electro-
positive substance imparted to it by reversing the connexions of the
wires for a few moments, a temporary and strong positive flow is
produced in certain liquids and not in certain others — and these
liquids are almost precisely the reverse of those named under B, 2.

The general influence of electro-positive substances dissolved in
the globule is in all classes of cases to produce a positive flow, and
of electro-negative substances to produce a negative motion; and
the influence of electro-positive substances dissolved in the liquid
is, in cases of A only, to produce a positive flow, and of electro-
negative substances to produce a negative flow.

47. The primary motions of the liquid and metal are, in all cases,
wholly at their surfaces of mutual contact ; whilst the movements
observed are only secondary effects, useful in enabling us to infer
the direction of the original motions : the masses of liquid and
metal serve merely as conductors of the electricity, and as stores of
material for supplying the acting surfaces. The movements obtained
are singularly symmetrical, probably in consequence of their essen-
tially dual or polar character.

164 Geological Society : —

48. The essential nature or principle of the movements appears
to be electro-chemical motion, i. e. definite motion directly produced
by electro-chemical action.

49. To illustrate the action, I have constructed an apparatus
consisting of two pairs of electrodes of platinum foil and mercury,
suspended at opposite ends of two copper wires upon a central pivot,
and rotating in an annular channel tilled with dilute sulphuric acid ;
but the power was too feeble to produce revolution of the necessary
moveable parts : it was not more than sufficient to produce a manifest
tendency to motion.

In conclusion, I beg leave to suggest a trial of the sudden starts of
the mercury by momentary currents as signals in electro-telegraphic
apparatus.

GEOLOGICAL SOCIETY.

[Continued from p. 86.]

May 16, I860.— L. Horner, Esq., President, in the Chair.

The following communication was read : —

" Outline of the Geology of part of Venezuela and of Trinidad."
By G. P. Wall, Esq.

The district examined by Mr. Wall extends from the 8th degree
north latitude to the sea, and eastward of the 69th meridian. It
includes the Serrania (as the mountainous region is termed) and the
Llanos or plains to the south. The Serrania is a portion of the
Littoral Cordillera, and is continuous with the main ridge of the
Andes ; to the east it extends into the northern part of Trinidad.

The most ancient rocks in Venezuela consist of mica-schists and
gneiss, and compose the author's " Caribbian Group, h so called on
account of these rocks forming for a great distance the southern
boundary of the Caribbean Sea. This term was previously adopted
for the same series of mountain-rocks in Trinidad, where their
eastward extension had been already studied. These strata consist
of — 1st, a series of micaceous and siliceous schists, various in aspect
and constitution ; 2ndly, sandstones, coarse and micaceous, fine-
grained and without mica; 3rdly, shales, ferruginous, micaceous,
and carbonaceous.

These schistose rocks are highly distorted. In the western por-
tion of the district they have a breadth of about 30 miles, and rise
to the height of 8000 feet ; to the east they form lower ridges and
a narrower belt. They are interlaminated with numerous irregular
bands of quartz. Evidence is not wanting of the segregation of the
quartz having been subsequent to the formation of the strata, but
previous to the disturbances that the schists have undergone.

White and blue limestones, generally crystalline, but sometimes
compact, occur in the schists in Venezuela, but still more abundantly
in Northern Trinidad. Some of the schists are granatiferous ; and,
from the presence of smaragdite, they sometimes form an eklogite.

Gneiss also is present, and is markedly interstratified with the
mica-schists. The transition is occasionally gradual; but more
usually it is sudden and abrupt. The gneiss sometimes assumes
the irregular structure of granite, but is still distinctly bedded. It

On the Geology of part of Venezuela and of Trinidad. 165

is occasionally auriferous. Very small proportions of copper-ores
and argentiferous galena exist in some localities

The Serrania also comprises another great group of strata, flanking
the " Caribbian " rocks on the south, and in the eastern district
rising to a height of more than 7000 feet, with a breadth of from
30 to 40 miles. These consist of sandstones, fossiliferous limestones,
and shales ; and form the group provisionally termed " Older
Parian " by the author, from the circumstance of its occurring on
the shores of the Gulf of Paria. In Trinidad it is traced as a narrow
belt across the island.

Alternating with the sandstones and limestones are thick beds of
a rock containing 85 per cent, of clay and only about 3 per cent, of
carbonate of lime. This is provisionally termed " ArgiHine." An-
other peculiar bedded rock of this series is composed of nearly pure
and very fine siliceous matter : it is noticed by the author under the
name of " Chertine."

These Older Parian strata must be nearly 8000 feet thick. They
have been intensely disturbed. Though the fossils can rarely be
separated from the matrix, yet some were fortunately obtained from
near Cumana, — namely, Trigonice and small Gasteropoda. Mr.
Etheridge, F.G.S., suggests that most probably they indicate a
Lower Cretaceous age. These Lower Parian rocks extend west-
ward into New Granada ; and are probably related to the Neocomian
rocks of Bogota.

Near their junction with the "Caribbian Group," the Older
Parian strata are often interstratified and alternate with rocks of
igneous origin. The base of these pyrogenic rocks varies from
augitic to diabasic in their type.

The Llanos or grassy plains of Venezuela are entirely formed of
conglomerates and sandstones referable to the next great group of
strata, namely the M Newer Parian." In Trinidad a lower and
calcareous portion of this group exists. Altogether this group pro-
bably has a thickness of nearly 4000 feet. In the plains of the
mainland the strata are horizontal ; but in Trinidad they have suf-
fered great disturbance.

Fossils are abundant in the calcareous divisicn, and seem to repre-
sent the Lower Pliocene or Upper Miocene series of Europe.

The materials of the conglomerates and sandstones have been
mainly derived from the disintegration of the Lower Parian rocks.

The upper portion of the Newer Parian series, which is often
shaly, contains beds of lignite, frequently admitting of exploitation.
The lignite occurs at several localities on the mainland, and also in
Southern Trinidad. The lignitiferous beds have locally undergone
combustion to a great extent, from natural causes, such as the de-
composition of pyrites. The result is that the strata have been in-
durated and baked for a vertical extent sometimes of 70 or 80 feet ;
the clays assuming various conditions, and presenting the " porcel-
lanites " and " thermantides " of continental authors.

The asphalt of Trinidad and the mainland is almost invariably
disseminated in the upper part of the Newer Parian group. When
in situ, it is confined to particular strata, which were originally shales

166 Intelligence and Miscellaneous Articles,

containing a certain proportion of vegetable debris. The organic
matter has undergone a special mineralization, producing a bitumi-
nous, in place of the ordinary anthraciferous substances. This ope-
ration is not attributable to heat, nor of the nature of distillation ;
but is due to chemical reaction at the ordinary temperature and
under the normal conditions of the climate. After the solution
and removal of the bitumen from wood passing into asphalt, the
remaining organic structure presents peculiar appearances under the
microscope.

The occurrence of asphalt in New Granada and the Valley of the
Magdalena in all probability indicates the presence of the Newer
Parian strata in those districts.

The phenomena of salses or mud-volcanos (common in Trinidad
and on the mainland) are referred by the author to the chemical
decomposition and changes (such as the formation of asphalt) which
are in operation in the lignitic strata of this formation, since the
evolved gases are inflammable, and the discharges of muddy matter
are usually accompanied with asphalt and petroleum,

•Thermal waters are not rare. Those of Trincherras, issuing from
mica-schist, possess a variable temperature, according to the follow-
ing determinations : —Humboldt in 1800, 194°; Boussingault in
1823, 206°; and the author in 1859, 198°. The hot springs at
Chaguaranal near Pilar are much more interesting, as the water is
discharged, from a limestone of the Older Parian series, at a tempe-
rature even above the boiling-point. It deposits carbonate of lime,
sulphur, &c.

A souffriere near by, issuing from an Older Parian sandstone,
yields a variety of purely siliceous deposits, chalcedonic and agati-
form. The siliceous cement of the sandstone, being a hydrate, and
soluble in acidulated water, has probably afforded the material for
these deposits. The colour of these siliceous sinters are traceable,
some to the sulphur (yellow), others to the decomposing leaves
(brown, &c).

Earthquakes are of ordinary occurrence. The earthquake of
1853 destroyed the town of Cumana.

The probable relations of the Cretaceous rocks of Venezuela with
those of New Granada, Peru, Chili, Brazils, and the Straits of Ma-
gellan were alluded to by the author.

XIX. Intelligence and Miscellaneous Articles,

ON THE FORMATION OP ICE AT THE BOTTOM OF WATER.
BY M. ENGELHARDT.

''PHE author in 1829, undertook some experiments with a view to
explain the formation of ground-ice and has since repeated
them.

He took three iron boilers about 660 millims. in diameter, and a
wooden trough about the same dimensions. These were severally
filled with river- water of the temperature +2°: the temperature of
the air was —2° during the day, and sank to —5° during the night.
They were supported at a distance of 20 centims. from the ground, so

Intelligence and Miscellaneous Articles. 167

as to have the same temperature on all sides. The next morning
all the vessels were covered with a layer of ice of about 12 to 14
millims. thick ; and at the bottom and sides of the three iron vessels
there was a smooth layer of ice about 20 millims. thick, that on the
bottom being thinner. In the wooden vessel there was a layer about
2 millims. thick, and a few tufts of needles on the sides ; and on the
bottom there were a few isolated plates of ice 100 millims. long, 5
to 7 millims. wide, and 1 to 2 millims. thick, with other small plates
on the edges like the teeth of a saw. These experiments were re-
peated several times, and always gave the same result; that is,
the vessels were covered on the sides and bottom with a layer of ice,
the thickness of which varied with the conductibility and radiating
power of the vessel.

To observe the formation of ice at the bottom of water, iron dishes
of about 5 centims. depth were filled with water and placed on a
freezing mixture of ice and salt. The temperature of the room was
+ 15° ; and consequently there was no formation of ice on the sur-
face, but on the bottom. The congelation did not always take place
in the same manner. Sometimes needles formed at the bottom,
and gradually increased until the ascending force caused by their
lower specific gravity forced them to break loose and rise to the sur-
face. At other times the bottom was rapidly covered with a thin
layer of ice, sometimes marked with fine lines.

To come to the formation of ice at the bottom of rivers. The
water at a temperature of 0° only loses heat on the surface by ra-
diation, or by contact with colder bodies. The earth at the bottom
and sides of rivers is a bad conductor, but water and ice are still
worse conductors. Ice being specifically lighter than water, always
swims to the surface when its ascending force is able to overcome its
adhesion to the bottom. It can also carry with it heavy bodies from
the bottom of the water.

As the maximum density of water is at 4°, all large and tranquil
masses of water, and even those which have such a motion that the
layers are not prevented arranging themselves according to their
specific gravity, are at a temperature above 0° at the bottom of the
water, even when they are frozen on the surface. A pond at Nie-
derbronn, which is only a metre deep, was covered with ice at the
surface, while the water in the inside was + 3°, the temperature of
the air being — 1 1°.

Large masses of water never freeze at the bottom ; and even when
ice does form, it becomes detached and rises to the surface. But
when water at 0° is in a vessel also at 0°, ice forms at the bottom as
well as at the surface. In order that ice may form at the bottom of
water, it is necessary that the lower layers be cooled to 0°, and even
a little more, that this cold water sink to the bottom of the river,
cool the sides, and finally find in the midst of the motion some-
thing at rest where it can exert its force of adhesion and crystalli-
zation.

An obstacle placed in the current of water produces two different
effects. It either changes the direction of the liquid molecules
which strike against it, and gives them rotatory movements strong

168 Intelligence and Miscellaneous Articles.

enough to form eddies, or the liquid behind the obstacle comes to
rest, and these are stationary and almost immoveable points.

These are good conditions for the formation of ice at the bottom
of rivers. The eddying motion produced by obstacles brings cold
water to the bottom and cools the sides ; and the molecules of water
behind the obstacle exert their adhesive force and crystallize. But
to produce these effects an intense and continuous cold is necessary.

In conclusion, the author attributes the formation of ground ice to
obstacles in the current, which on the one hand, by the eddying
motion, cause the water below 0° to sink to the bottom and cool the
sides, and on the other hand produce stationary parts in which the
crystallizing power can exert its force. He observed the influence of
these foreign bodies in a conduit at Zinsweiler. In 1829, ice formed
at the bottom of the water in which there were large stones, trees,
&c. The formation of ice was entirely prevented by removing these
foreign bodies.— Comp tes Rendus, July 2, 1860.

ON A REMARKABLE ICE SHOWER. BY CAPTAIN BLAKISTON, R.A.
[Extract of a Letter to General Sabine, R.A.]

"On the 14th January, 1860, when two days out from the Cape
of Good Hope, about three hundred miles S.S.E. of it, in lat. 38°
53' S., long. 20° 45' E., we encountered a heavy squall with rain
at 10 a.m., lasting one hour, the wind shifting suddenly from east
to north (true). During the squall there were three vivid flashes of
lightning, one of which was very close to the ship ; and at the same
time a shower of ice fell, which lasted about three minutes. It was
not hail, but irregular-shaped pieces of solid ice, of different dimen-
sions, up to the size of half a brick. The squall was so heavy that
the topsails were let go.

" There appears to have been no previous indication of this squall ;
for the barometer at 6 p.m. on the two previous days had been at
30-00, therm. 70°; at 8 a.m. on the 14th, 29*82, therm. 70°; at
10 a.m. (time of squall), 29*86, therm. 70° ; and at 1 p.m., when the
weather had cleared, wind north (true), 29*76, therm. 69° ; after
which it fell slowly and steadily during the remainder of the day and
following night*.

" As to the size of the pieces of ice which fell, two, which were
weighed after having melted considerably, were 3£ and 5 ounces
respectively ; while I had one piece given me, a good quarter of an
hour after the squall, which would only just go into an ordinary
tumbler. And one or two persons depose to having seen pieces the
size of a brick.

" On examination of the ship's sails afterwards, they were found to
be perforated in numerous places with small holes. A very thick
glass cover to one of the compasses was broken.
• " Although several persons were struck, and some knocked down
on the deck, fortunately no one was seriously injured." — From the
Proceedings of the Royal Society for May 3, 1860.

* The weather on the morning preceding the squall was clouded, with close and
thick atmosphere, wind E. (true), 3. By night of the 14th the wind had hauled
to N.W. (true), 4; and the day following was W.S.W. (true), 5—6, cloudy.

THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

— , ♦

[FOURTH SERIES.]
SEPTEMBER 1860.

XX. On the Radiative Powers of Bodies with regard to the
Dark or Heat-producing Rays of the Spectrum, By Balfour
Stewart, M.A*

1. TN their communication which appeared in the August
-*- Number of this Magazine, Professors Kirchhoff and
Bunsen have furnished us with some very interesting and
important facts regarding the spectra of different kinds of flame :
the following is one of these : —

" It appears," they say (while describing the effect produced
upon flame-spectra by the presence of small quantities of metals
or bodies containing metals), " that the alteration of the bodies
with which the metals employed were combined, the variety in
the nature of the chemical processes occurring in the several
flames, and the wide differences of temperature which these
flames exhibit, produce no effect upon the position of the bright
lines in the spectrum which are characteristic of each metal"

2. Now when the particles of the body which mingle with
and characterize the flame are exceedingly divided, we may with
much probability (as far as the quality of the radiated light is
concerned) regard them as ultimate particles or molecules : the
spectra exhibited will then afford us the means of approximately
ascertaining what kind of light the molecules of certain sub-
stances give out when heated. It thus appears that we have
grounds for supposing that the ultimate particles of different
substances which possess in common some characterizing metallic
element, give out the same quality of light when introduced into
flame.

3. It becomes interesting to know if we have any means of
detecting a similar property of bodies (should such exist) having

* Communicated by the Author.
Phil Mag. S. 4. Vol. 20. No. 132. Sept. 1860. N

170 Mr. B. Stewart on the Radiative Powers of Bodies with

reference to radiant heat rather than to radiant light-— if we can
by any method ascertain whether there are bodies the particles
of which give out the same quality of heat at the same tempera-
ture. A law which flows from Prevost's theory of exchanges, as
proved by the author in a paper published in the last volume of
the Transactions of the Royal Society of Edinburgh, affords, it
is believed, a method of ascertaining this fact.

4. This law asserts that when a number of bodies exist in an
enclosure at a uniform and constant temperature, the heat ab-
sorbed by any particle is equal to that emitted by it ; and that
this equality subsists with regard to every individual description
of heat which goes to form the heterogeneous radiation of that
temperature.

5. Let us now suppose two plates M and N, composed of two
different substances more or less diathermanous, to be hung up
side by side in such an enclosure of which the temperature is = t ;
and for the sake of simplicity we may conceive the walls of the
enclosure to be covered with lampblack, a substance which
radiates, but which does not reflect heat. Let us also suppose
that the refractive indices of the two plates are the same, or nearly
so ; and finally, let us limit our consideration to those rays which
enter each plate at right angles to its surface. It may be shown
that the same quantity of heat will flow through the substance
of each plate.

6. Before the investigation be proceeded with, one hypothesis
requires to be made ; but one which, besides its apparent pro-
bability, has been proved by the author to hold good for mica
and glass, viz. that the mere heating of a substance through a
considerable range of temperature, if unaccompanied by any
chemical change, does not alter the absorptive power of its par-
ticles for a given description of heat.

7. Let ttj, a2) a3, &c. denote the absorptive power of the plate
M for the different kinds of heat which compose the lampblack
radiation of the temperature t, and let blf #2, b3, &c. denote the
same constants for the plate N.

(By the absorptive power of a substance is meant the quantity
of heat which would be absorbed by a plate of the substance of
thickness = unity when traversed by a ray of heat, the intensity
of which is kept equal to unity throughout the whole of this
thickness.)

Let Aj, A2, A3, &c. be the quantities of the different descrip-
tions of heat which together compose the whole radiation which
flows perpendicularly through M and N at the temperature t.

Also let MjoY, M26Y, M3oY, &c. denote the radiations for these
different kinds of heat of a particle or plate of exceedingly small
thickness oY of the body M at the above temperature ; and let

regard to the Dark or Heat-producing Rays of the Spectrum. 171

NjoV, N2oV, NsoV, &c. denote the same constants for the body
N for the thickness St1. It is here supposed that, for exceed-
ingly small thicknesses of the substances M and N, the radia-
tion (and consequently the absorption) is proportional to the
thickness. This will only hold good when such thicknesses
absorb only a very small proportion of the incident heat. It is,
however, possible that there are some kinds of heat which are
greatly absorbed even by a single set of particles. If there be
such rays, they may be supposed to be excluded from this inves-
tigation, as the test to which it refers, and which is furnished
by plates of sensible thickness supposed capable of passing heat,
is evidently in their case quite inapplicable.

8. Conceive now the plate M to be composed of a great num-
ber of slices laid side by side, the thickness of each slice being
St ; also let N be composed of the same number of slices, the
thickness of each being St1. Let us denote the total thickness
of M by t, and that of N by t1.

The quantity of the heat A, which will be absorbed by the
first elementary slice of M will be = A^St, while, again, the
quantity of the same heat which will be radiated by the same
slice will be =MjOt. Hence (art. 4) M1£t=A1«1oY, and

.*. MjSrA^.

In like manner,

M2=A20,

rt>J (i)

&c.
Also with regard to N, we have, similarly,

N2=AA/f (2)

&c. J

9. Now if the quality of the heat radiated by a particle of M
is the same as that radiated by a particle of N, we have

Mj : M2 : M3, &c. ; : If, : N2 : N3, &c. ;

hence, (1) and (2),

A1«l : A2«23 &c. : : A1i1 : A2#2, &c. ;
hence also

al:bl : '.a^'.b^'.'.a^: bs, &c.

Take alT=blTl, hence

t : t! : : bY : ax : : b2 : «2, &c.
Hence

N2

172 Mr. B. Stewart on the Radiative Powers of Bodies.

fee.

oYtfm=6V£m.

Now the quantity of heat Am absorbed by the first elementary
slice of M =AmamOT, and for N this is =Am£moY. Hence from
(3) it follows that the quantity of the heat Am absorbed by an
elementary slice of M is equal to that absorbed by a similar
slice of N. Hence the quantity of heat Am which is absorbed in
passing through a thickness of M=t is equal to that which is
absorbed in passing through a thickness of N = t7 ; and the same
equality subsists with respect to any other description of heat
which forms part of the heterogeneous radiation of the tempe-
rature t. •

Hence it follows that, with the above relations between the
thicknesses of the plates, the portion of lampblack heat of the
temperature t which passes the one plate is equal in quality as
well as quantity to that which passes the other.

10. It thus appears that if there are bodies of which the ulti-
mate particles or very thin plates radiate the same quality of heat
at the temperature t, and if such thicknesses of these bodies be
taken that they all pass the same proportion of the incident heat
for any one of the rays which compose the heterogeneous radia-
tion of that temperature, then they will also pass the same pro-
portion for any other of these rays.

11. Our hypothesis has hitherto been, that the bodies M and
N have ultimate particles which radiate the same kind of heat at
the temperature t. Let us further suppose that the particles of
these bodies possess the same property at the temperature t\ and
in fine through a considerable range of temperatures.

At the temperature f let us form equations similar to (1), (2),
(3). Now if we suppose, as we are undoubtedly entitled to do,
that the heat of t has some one ray in common with that of t,
we see at a glance that the plates M and N with their old thick-
nesses will perform the same office for the heat of temperature t1
which they did for that of temperature t} the proportion of the
former heat which passes being the same for M as for N in
quantity and in quality.

12. To conclude : if there be a group of bodies of nearly the
same refractive index the particles of which always radiate the
same quality of heat at the same temperature, and if we take slices
of these bodies of thicknesses such that they all permit to pass the
same proportion of any one kind of heat, then they will also pass
the same proportion of any other kind of heat.

Note on Chemical Analysis by Spectrum-observations, 173

13. We are thus furnished with a test by means of which we
may in all probability ascertain whether such groups of bodies
exist. In applying this test, it will be necessary to assume the
truth of the hypothesis of art. 6. Our method will be to con-
struct screens of the bodies under analysis such that they all
stop the same proportion of some one kind of incident heat ; and
if these bodies possess the property we are in search of, that is,
if their ultimate particles always radiate the same quality of
heat at the same temperature, the screens will all stop the same
proportion of any other description of heat. It is almost unne-
cessary to remark that the common proportion stopped by the
screens for one kind of heat will generally be different from that
stopped by them for heat of another description.

14. This test has possibly a still wider application. For let
it be supposed that we are comparing together two bodies
which possess in common the same characterizing or influential
element, but one of which possesses in addition another element
also influential, but relating to an entirely different set of rays.
It seems likely that for those kinds of heat which are character-
istic of the common element the bodies will conform to the test ;
but, on the other hand, for those kinds of heat which refer to
the element which the one body possesses and not the other, the
test will fail.

Some tables furnished by Melloni appear to confirm this idea;
but the subject will doubtless require a special experimental in-
vestigation.

Kew Observatory,
August 7, I860.

XXI. Note on Professors Kirchhoff and Bunsen's Paper " On
Chemical Analysis by Spectrum-observations" By Professor

Swan.

To the Editors of the Philosophical Magazine and Journal.

Gentlemen,

ON perusing Professors Kirchhoff and Bunsen's paper " On
Chemical Analysis by Spectrum-observations," I find it
stated that I have " already remarked upon the small quantity
of sodium necessary to produce the yellow line in a flame-spec-
trum." As I have not only remarked that a small quantity of
sodium suffices to produce the yellow line in a flame-spectrum,
but have distinctly announced the opinion that in all flames the
yellow line is due to the presence of sodium, you will perhaps
allow me to state the observations I adduced in support of that
view, as published in the Edinburgh Transactions for 1856.

174 Note on Chemical Analysis by Spectrum-observations,

n One-tenth of a grain of common salt, carefully weighed in a
balance indicating TApth °f a gram> was dissolved in 5000 grains
of distilled water. Two perfectly similar slips of platinum-foil
were then carefully ignited by the Bunsen lamp until they ceased
to tinge the flame with yellow light; for to obtain the total
absence of yellow light is apparently impossible. One of the
slips was dipped into the solution of salt, and the other into di-
stilled water, the quantity of the solution adhering to the slip
being considerably less than ^th of a grain, and both slips were
held over the lamp until the water had evaporated. They were
then simultaneously introduced into opposite sides of the flame,
when the slip which had been dipped into the solution of salt
invariably communicated, to a considerable portion of the flame,
a bright yellow light, easily distinguishable from that caused by
the slip which had been dipped into pure water. It is thus
proved that a portion of chloride of sodium weighing less than
t poo 000 th of a grain, is able to tinge a flame with bright yellow
light ; and as the equivalent weights of sodium and chlorine are
23 and 35*5, it follows that a quantity of sodium not exceeding
a boo ooo *n °f a^roy gram renders its presence in aflame sensible.
If it were possible to obtain a flame free from yellow light, in-
dependently of that caused by the salt introduced in the experi-
ment, it is obvious that a greatly more minute portion of sodium
could be shown to alter appreciably the colour of the flame. It
therefore follows that much caution is necessary in referring the
phenomena of the spectrum of a flame to the chemical constitu-
tion of the body undergoing combustion. For the brightest line
in the spectrum of the flame of a candle — the yellow line K of
Fraunhofer — can be produced in great brilliancy by placing an
excessively small portion of salt in a flame, in whose spectrum
that line is faint or altogether absent. The question then arises
whether this line in the candle flame is due to the combustion
of the carbon and hydrogen of which tallow is chiefly composed,
or is caused by the minute traces of chloride of sodium contained
in most animal matter. When indeed we consider the almost
universal diffusion of the salts of sodium, and the remarkable
energy with which they produce yellow light, it seems highly
probable that the yellow line R which appears in the spectra of
almost all flames is in every case due to the presence of minute
quantities of sodium. The view which would attribute a great
portion of the light of the envelopes of flames to the adventitious
presence of minute traces of foreign matter, may possibly serve
to explain certain anomalous diversities of colour which arc ob-
served in the envelopes of flames arising from the combustion of
the 8ame elements. Thus tallow, coal-gas, anhydrous alcohol,

M. C. Deville on the origin of Granite. 175

and weak spirit of wine all contain the same combustible sub-
stances,— carbon and hydrogen ; yet the envelope of the flame
of a candle is bright yellow, that of a coal-gas flame is purple,
and those of strong and weak spirit differ greatly in luminosity* "
I have also observed that " if the air be dusty from any cause,"
yellow light appears abundantly in the flame of the Bunsen
lampf; and "I have found that the column of heated air
arising from the flame of a spirit lamp with a salted wick is most
energetic in communicating yellow light " to the flame of the
Bunsen lamp %. I have likewise ascertained by repeated experi-
ments, that platinum, by mere exposure to the air, speedily
acquires the property of tinging flame with yellow light.

The use of a collimator, represented at the letter B in the
woodcut accompanying Professors Kirchhoff and Bunsen's paper,
is attended with much convenience and advantage in spectrum
experiments where angles are to be accurately measured. This
method of observation was devised by me some years ago ; and a
detailed account of it will be found in the Transactions of the
Royal Society of Edinburgh, vol. xvi. and vol. xxi. p. 421.
I am, Gentlemen,

Your obedient Servant,
Ardchapel, August 3, 1860. William Swan.

XXII. Considerations in reference to M. Rose's Memoir on the
different conditions of Silicic Acid. By M. C, Sainte-Claire
Deville §.

IN his valuable memoir " On the different conditions of Silicic
Acid ||," Prof. Rose discusses a subject which interests
both the chemist and the geologist, and upon which I wish
to offer certain considerations. Before, however, going into the
question, I wish to prevent the confusion which might arise from
a passage in M. Rose's memoir, in which, citing my researches,
he appears to attribute to me merit to which I am not entitled.

He says, " Gaudin and St.-Claire Deville have succeeded in
melting in large drops, and drawing into wire, considerable
quantities of crystallized quartz, in other words, silicic acid
having a density of 2*6. Subsequently Deville succeeded in
melting as much as 30 grms. of silicic acid."

1. I wish to observe that I have no claim whatever to the pro-
cesses by which M. Gaudin has been able to obtain a very ele-
vated temperature in a few minutes, in order to melt and draw

* Trans. Roy. Soc. Edinb. vol. xxi. part 3. pp. 413, 414.

t Ibid. p. 413. t Ibid. p. 424.

§ Translated from the Annates de Chimie, vol. lix. p. 14, by Dr. Atkinson.

|| Phil. Mag. vol. xix. p. 32.

176 M. C. Deville on the origin of Granite.

quartz, corundum, &c. I have simply borrowed the apparatus,
and the obliging assistance of that ingenious experimenter.

2. That where the name of Deville is mentioned a second time,
it refers to my brother M. Henri St.-Claire Deville, who has been
able to obtain enormous temperatures by other methods than
those of M. Gaudin.

I may be further permitted to mention, in reference to the
historical part of the question, that I was the first to show that
quartz-glass has a density of 2*22, which is therefore 0*17 lower
than that of the crystalline quartz from which it is derived.

I insist upon this fact ; for it is by no means isolated. For
me, its establishment is connected with a series of previous
researches on the properties which rocks and silicated minerals
acquire when they are melted and then rapidly cooled, but more
especially on the properties which sulphur assumes under these
conditions.

Lastly, I believe that these singular properties of quartz,
felspar, &c. may have exercised considerable influence on the
conditions under which granite is formed, and that, hence, it is
necessary to take them into account when the origin of this rock
is discussed.

For some time I have called the attention of scientific men to
these peculiar phsenomena of temper, and to the abnormal distri-
bution of heat which seems to prevail in the interior of one and
the same body.

The superfused substance holding for a greater or less time a
quantity of heat larger than it should normally possess, retains,
although in the solid form, the properties of a liquid : in cer-
tain cases it retains softness and plasticity, and in all an amor-
phous and vitreous structure, a greater solubility, and a less
considerable resistance to chemical agents. Another portion
(the external pellicle, the tempered exterior) retains, on the con-
trary, a lower latent heat, and presents different properties.

This view, whether it be adopted or not (and there are many
facts which might be cited in its support, — the well-known ex-
periments of M. Mitscherlich and of M. Regnault, my own
researches*, the researches of M. Favref, &c), led me to the
discovery of insoluble sulphur. I first prepared this body by
the direct tempering of sulphur; and by the application of this
principle I was led to think that flour of sulphur being obtained
by rapid cooling, and in a minute state of division, must have a
larger tempered surface, and consequently the largest quantity
of insoluble sulphur, — which was actually found to be the case.

* Comptes Rendus, vol. xxv. p. 857 ; vol. xxvi. p. 1 16; vol. xxxiv. pp. 534
and 561 ; and Annates de Chimie et de Physique, vol. xlvii. p. 94.
f Ann. der Pharm. vol. xxiv. p. 344.

M. C. Deville on the origin of Granite. 177

Slow cooling, or to speak more generally, a slow and gradual
mode of formation, allows the molecules to become associated
under circumstances in which each takes with it the normal
quantity of heat ; from this a stable equilibrium results, at any
rate under the actual conditions of temperature. In the case of
sulphur, for example, octahedral or normal sulphur is formed of
2*07 spec, grav., which is quite stable at ordinary temperatures ;
while the two others, soft or vitreous sulphur and insoluble
sulphur, become more or less transformed into octahedral sulphur,
either spontaneously or by simple actions of contact.

It must also be added that the fourth condition, prismatic
sulphur, whether prepared by fusion, or crystallized from a
hot solution of ether, alcohol, chloroform, or benzole, &c, cor-
responds to a condition in which the molecules, although
possessing more heat than the normal quantity, maintain their
equilibrium a certain time, and are then rapidly changed below
a certain temperature. But the curious part of this is, that this
temperature is not constant, but varies with the nature of the
solvent, and probably also with other circumstances; so that
this phenomenon of transformation does not appear to be con-
nected with a fixed temperature which the substance obtains on
cooling, but rather with the quantity of heat which the liquid had
assimilated and had abandoned at a certain moment. Lastly,
it may be concluded from my experiments*, that when sulphur
is heated in an open vessel, it appears to pass successively through
different conditions of equilibrium ; sometimes it strongly retains
heat, at others it rapidly parts with it : this seems to constitute
a sort of rotation, of which the prismatic condition, which com-
mences at about 109 degrees, is only the first term.

Among the very interesting researches which many chemists
have lately undertaken on the properties of insoluble sulphur,
that of M. Cloez has greatly struck me. Some years after I had
described the sulphur made insoluble by tempering, MM. Fordos
and Gelis announced that they had obtained an analogous and
probably identical sulphur by the action of water on sulphide of
nitrogen or chloride of sulphur, &c. M. Cloez, by varying the
conditions of the experiment, has produced indifferently soluble
or insoluble sulphur ; and he adds f, " It is thus shown that
chloride and bromide of sulphur produce insoluble sulphur by a
rapid decomposition, and soluble sulphur by slow decomposition,"
— an evident confirmation of what I had previously announced.

I have also been struck with M. Debray's curious experiment J,
in which he reproduces at will prismatic sulphur in bisulphide

* Ann. de Chim. et de Phys. 3 ser. vol. xlvii. p. 110.
t Comptes Rendus, vol. xlvi. p. 496.
X Ibid. vol. xlvi. p. 576.

178 M. C. Deville on the origin of Granite.

of carbon (which neither I nor M. Pasteur had been able to do),
provided that the liquid, heated at least to 80 degrees, undergoes
a sudden cooling.

Without further insisting on these ideas, which more and
more confirm my researches made during the last fifteen years,
may they not be applied to the consideration of the subject which
H. Rose has treated in his memoir? As he justly remarks,
the capital fact is that which results from a research of M. Schaff-
gotsch* in 1846; that is to say, that quartz in its natural
mode of occurrence is in two very different molecular conditions.
The one — the crystalline state — has a normal density of 2*65 ;
the density of the other does not differ much from 2*2. This
notion has been very happily developed by M. Hose, who has
shown that these two natural varieties of silica have not the same
chemical affinities. The one variety, comprising vitreous quartz,
compact quartz, and silex, resists hydrate and carbonate of pot-
ash very energetically; while the other variety (opal, whether
calcined or not, infusorial silica, &c.) is strongly acted on by these
agents. I had also observed in regard to the vitreous quartz ob-
tained by temper, that not only had it a density of 2*2, like the
natural amorphous varieties, but also that, like them, and per-
haps even better than them, it dissolved most readily and almost
completely in alkaline lyes.

This latter fact is closely connected with the preceding expla-
nation ; doubtless the very small residue left unattacked by the
solution of amorphous quartz in alkaline lyes is comparable to
that which the solution of the external coating of pieces of soft
sulphur, or even of prisms obtained by fusion, leaves in bisul-
phide of carbon.

As to natural opal, it is evidently formed, as Beudant and
Klaproth have long ago shown, from the gelatinous silica which
is found still soft in the altered Hungarian trachytes, and the
gradual hardening of which may be observed in the suites of
specimens in collections. Ebelmen's ingenious researches have
shown facts entirely analogous in the silica rapidly precipitated
from artificial solutions. " On the other hand," says M. Rose,
" the silicic acid of a higher density which constitutes flint, chal-
cedony, and crystallized quartz, might be formed from a perfect
solution of silicic acid. By the slow concentration of this solu-
tion, crystallized quartz might be produced."

Thu8,in almost all cases,silicic acidof 2*2 spec. grav. maybe con-
sidered as resulting from a sudden cooling or rapid precipitation f,

* PoggendorfFs Annalen, vol. lxvii. p. 147.

t Silica of organic origin, as that of the infusoria, is doubtless formed
under special conditions, which cannot be absolutely assimilated to purely
inorganic actions, and in every respect deserves a separate study.

M. C. Deville on the origin of Granite. 179

while silicic acid of spec. grav. 2*65 would in all cases be the
product of slow and gradual actions.

The concurrence of the two facts may be readily understood ;
gelatinous silica, cemented by solidified silica, would have a den-
sity intermediate between the two.

M. Rose rightly remarks that none of the natural varieties of
quartz of the density 22 appear to owe their molecular state to
fusion. And as the quartz fused in the laboratory in small
pieces is always vitreous, and of this low specific gravity, it must
be concluded that the quartz of granite has never been in a
state of igneous fusion. With regard to the felspar of granite,
a similar conclusion must be drawn frpm the fact that the expe-
rimenters who have succeeded in melting this body have never
been able to obtain it crystallized, but always in a state of glass.

All geologists will understand the hesitation I feel at follow-
ing this able chemist in his discussion on the origin of granite.
Not that the question appears to me as it does to him, as a barren
one. On the contrary, I am convinced that it is as fruitful and
as well deserving attention as any of those which are connected
with the habitable globe.

I cannot, however, but remark that the foregoing conclusions
cannot be legitimately deduced from the negative facts observed
in the laboratory. For my own part, I confess that if any one
had thus argued when I passed over the lava of Arso, which
burst out in 1308 in the Island of Ischia, and which is full of
the well-known beautiful felspars, it would have been difficult to
convince me that nature has not been able to form felspar* by
igneous action.

I will say as much for the micas of Vesuvius, and of those of
the lava and scoria of the Laacher See ; and, supposing even that
they did not contain a trace of fluorine, an element so variable in
the micas of granite, nor the small quantity of water the exist-
ence of which is very problematical in most cases, I should boldly
conclude that if the mica has in the above cases an eruptive
origin (and for a geologist there cannot be the slightest doubt),
the micas of granite have also been formed in the same manner.

This kind of negative argument cannot therefore be used to
combat the eruptive origin of two of the elements of granite.
There remains quartz : M. Rose (after many able chemists, and
particularly MM. Fuchs and BischofF) offers several objections to
its eruptive origin.

The first depends upon the negative results of the laboratory
— that a glass, and not a crystalline quartz, is always obtained by

* By felspar I understand orthose, which is the prevalent felspar in gra-
nite. What I say is much more true for oligoclase, and more especially for
Labradorite, which is so abundantly found in modern lavas.

180 M. C. Deville on tlie origin of Granite.

fusion. But it is scarcely necessary to dwell upon the absolute
difference of physical conditions between a few grammes of this
quartz fused and immediately cooled, and masses of the substance
imbedded in a granite block. If it be objected that in no case
in nature, not even in granitic veins of small dimensions, which
therefore are in conditions most resembling those of the labora-
tory, has quartz been found in a vitreous condition, it might be
answered that we are entirely ignorant of the limits to the sta-
bility of quartz in this condition. If, as I think, the vitreous
state is an abnormal condition for all bodies capable of acquiring
it* — a state in which the molecules are retained at too great
distances from each other by an excess of latent heat, — each of
them ought to tend to still further removal, in order to obtain
position of stable equilibrium, which is in fact the crystalline
state. This is well seen in sulphur, arsenious acid, &c. I have
shown that soft sulphur left to itself, although gradually ap-
proaching octahedral sulphur nearer and nearer, had not become
changed into that state even after several years : this was per-
ceptible from the differences of density. But inasmuch as there
are necessary limits to the operation, we see that by prolonging
the experiment as long as we like, we could never affirm that the
change was complete. Can it not be conceived that the quartz
of granite (originally vitreous like sulphur, like vitreous arse-
nious acid, like ordinary glass) has undergone, after a long time
and under favourable conditions, a molecular change which has
altered it into the crystalline state without imparting to it any
external geometrical form ?

The beautiful experiments in which M. de Senarmont and
M. Daubree have produced quartz in small but perfect crystals
or in concretionary masses, are well fitted to explain the origin
of quartz in veins, in geodes, and even in stanniferous masses ;
in short, to use an idea of the first importance introduced into
science by M. Elie de Beaumont f, they explain the presence of
quartz in all cases in which it is connected with the phenomena

* I have shown (Comptes Rendus, vol. xl. p. 769) that the properties of
superfusibility by temper are far from belonging to all bodies. The metals
which I have examined (lead, zinc, and bismuth) have not exhibited it ;
nor has chloride of sodium. It is remarkable that alumina, a body re-
sembling silica in many respects, is entirely free from it. While quartz
presented the greatest difference in density between the crystallized and
the vitreous state, fused and tempered corundum had exactly the same
density as natural corundum.

t Note on Volcanic and Metalliferous Emanations " (Bulletin de la
Socie'te' Giologique de France, 2 seV. vol. iv. p. 1250). M. Bernhard Cotta,
in giving a complete translation of this memoir (Gangstudien, 4th part,
1850), has performed a real service for those persons on the other side of
the Rhine who are interested in these questions.

M. C. Deville on the origin of Granite. 181

of eruptivity in the manner of sulphur, at the limit of which we
find the mineral waters and their sources. But these experi-
ments do not directly apply, in my opinion, to the case in which
quartz, like that of the granites, is a substance eruptive in the
manner of the lavas. For the silica obtained by these philoso-
phers has always been crystallized ; and it is superfluous to show
that it would be false to assume that crystallized silica could not
be obtained in any other way.

Supported by the possible and even probable superfusion of
quartz, M. Fournet has endeavoured to explain how that this
body in a great many cases, more especially in granite, solidified
after other substances which were more fusible than itself. From
well-known facts, M. Elie de Beaumont has shown* that there
was nothing improbable in such a hypothesis. If Mr. Faraday,
working with small quantities and under unfavourable conditions,
could retard the solidification of sulphur by nearly 100 degrees
(its fusing-point being 109°), what is there astonishing in the
assumption that quartz, which perhaps melts at 2000 to 2500
degrees, could be maintained in the soft state as low as 1000 to
1200 degrees, and that under conditions which must be assumed
to be favourable ? I will add that M. Fournet' s opinion, which,
when he published it, was only an ingenious hypothesis, seems
to me to have become much more probable since it has been
found that pure quartz is eminently well adapted to form a glass,
that is to say a superfused substance, and that up to the present
time it is the substance which presents the greatest difference
between its density in the crystalline, and its density in the
amorphous state. I therefore cannot see in that an absolute
objection to the eruptive origin of granite.

" But," the able author whom I contend with would remark,
' ' how can it be conceived that minerals which, like felspar, only
contain 60 to 65 per cent, of silica, or like mica, which is still
more, basic, could be separated from a fused mass in which the
granite is in excess ? Evidently this body, which at this tempe-
rature acts powerfully on the bases which constitute these mine-
rals, would not have allowed those substances to crystallize out
without combining with them."

To refute this objection, it is simply necessary to assume with
M. Delafosse, that, in reference to minerals of igneous formation,
silica plays a part analogous to that which water plays in refer-
ence to substances formed in it. In the latter case definite hy-
drates are formed, frequently poor in water. There is thus a
class of phenomena in which affinities find their limits. Further,
M. Senarmont's ingenious experiments prove that elevation of
temperature always produces a tendency to dehydration, even in
* Loc, cit. p. 1305,

182 M. C. Deville on the origin of Granite,

a liquid medium. For instance, gelatinous silica entirely loses
its water, and becomes deposited as crystalline quartz ; and a
solution of sesquichloride of iron decomposes into hydrochloric
acid and anhydrous sesquioxide.

My brother*, in his researches on the phenomena of disso-
ciation, has cited still more curious facts : oxygen and potassium
not only do not combine, but at a high temperature cannot
remain combined. In the presence of facts like these, it is not
astonishing that silica in a fused state should act as mother-
liquor to the felspar, only combining with the other elements
within limits appropriate to the physical and chemical pro-
perties of the granitic bath.

One of the objections which M. Rose raises against the
eruptive origin of granite, depends on the remarkable properties
of the so-called pyrognomic minerals. M. Scheerer, who has
profoundly studied this class of phenomena, has perfectly well
seen that to found on them an absolute argument against the
eruptive origin of granite is to exaggerate their importance. He
has even been led to conclude that the solidification of the rock
has taken place under special physical conditions. Indeed M.
Rose himself, who first presented this objection, does not seem
to attribute to it any considerable value; for he addsf, u It may
be assumed that these minerals, more especially gadolinite, are
produced by fusion while associated with granite, but that by
the prolonged action of the atmosphere, of wi.ter, of an ele-
vated temperature, and other influences they have changed this
condition."

If, as M. Rose observes, such a hypothesis is not opposed
to the ideas which he endeavours to enforce in his memoir, still
less is it opposed to those which I advocate.

But if we in turn examine the defence of the partisans of the
Neptunian origin of granite J, how are we to explain the division
of the different acid and basic elements, between the micas
and the felspars ? Why should there be formed at one 'time
two micas ? and more especially two felspathic minerals having
two formulae essentially different, orthose and oligoclase?
Evidently nothing that takes place in our laboratory solutions
can give the key to these natural phenomena. Let us admit,
then, that between the different elements of the rocks there

* Comptes Rendus, vol. xlv. p. 489 ; Phil. Mag. vol. xvi. p. 516.

t Phil. Mag. vol. xix. p. 39.

X I use the expression Neptunian origin employed by M. Rose, and not
that of aqueous origin. The latter, m fact, cannot be the antithesis of
plutonic or eruptive origin. I shall show further, that not only is water
present in eruptive phenomena, but there is actually no eruption in which
it does not play an important chemical part.

M. C. Deville on the origin of Granite. 183

is a very singular and complicated equilibrium, an idea of
which may in some measure be obtained if we represent it
by a certain number of indeterminate equations, for the solu-
tion of which one condition is wanting. But .this condition
must be sought for in the study of the phenomena of igneous
fusion.

M. Rose justly recommends geologists not to advance, without
weighty and powerful motives, hypotheses which are in contra-
diction with the known laws of chemistry. But may not
geologists well recommend chemists, who bring to these difficult
questions the aid of their special knowledge, to submit their
solutions to the control of natural facts ? However ingenious
these solutions may be, whatever support they may find in
laboratory experiments, the first and indispensable condition of
their adoption by a naturalist would be their agreement with
observed facts.

But there are fundamental analogies, which no geologist since
Hutton has refused to recognize, between the oldest granite and
the most recent eruptive rocks, the volcanic lavas. This will be
readily admitted by any one who has seen, or has even merely
read a description of a flow of Vesuvius or Etna, of the amphi-
genic or doleritic veins of the Somma or of the Val del Bove;
the trap-dykes and melaphyr of Scotland or of the Palatinate ;
the Elvan of Cornwall ; the quartziferous porphyry of Saxony or
of Morvan ; lastly, some of the granitic veins so frequently met
with in the latter places, and in innumerable others.

It is true that these general analogies of formation, the
establishment of which was one of the triumphs of the end of
the last century, do not amount to an absolute similitude : the
mineral elements, for example, vary from one group of rocks to
another. The presence of quartz, especially, has not been observed
in any true flow of lava, but it exists in the trachytes of the
Siebengebirge and of Mont-Dore : I have found it in the dole-
ritic rocks of Guadaloupe ; some considerable tracts of this latter
island, and of Martinique, are covered with a reddish earthy crust
which is full of innumerable fragments of transparent quartz,
arising, like it, from the decomposition of the volcanic rocks. It
likewise occurs with Labradorite in the doleritic trachyte which
constitutes the cone of the Soufriere. And since the density of
this quartz is 265, we cannot attribute to it an origin analogous
to that of the opals of Hungary. Thus step by step we succeed
in finding quartz in formations which, by their age,by their nature
and mode of occurrence, are nearest to the lavas which have
flowed under our own eyes. It is impossible to avoid establishing
a comparison between the conditions under which are formed the
crystals an agglomeration of which constitutes the rock, more

184 M. C. Dcville on the origin of Granite.

especially when we find that the predominant mineral in the
Vesuvian lavas is amphigene, a substance resembling quartz in
its infusibility. Can it be doubted that in such a case we
witness the more or less rapid transformation of a melted or
viscous magma (certainly, as M. Durocher remarks, more fusible
than the most refractory of the minerals which could be sepa-
rated from it) into a solid rock almost entirely composed of
crystalline elements ? Truly it is pre-eminently an eruptive act ;
for it is one by definition. But at the same that these streams
of liquefied earth, as M. Humboldt calls them, escape from the
volcano, bodies of quite a different nature are also disengaged, —
alkaline and metallic chlorides, a small quantity of sulphates and
phosphates, then at various intervals of time and place hydro-
chloric, sulphurous, hydrosulphurous, and carbonic acids, but
more especially aqueous vapour. The latter rises from the
lava many years after its eruption ; and any one who has fol-
lowed day by day, step by step, the chemical phenomena of
lava in motion, can have no doubt as to the origin of the water.
Like other substances, it forms an integral part of the magma ;
and like them it separates at a given moment, in proportion as
the internal reactions of the incandescent mass are affected*.

As far as I know, M. Elie de Beaumont, in the memoir pre-
viously quoted, was the first to establish this kind of preliminary
solution of water and of salts in incandescent lavas. He rightly
refers it to certain phenomena which are readily reproduced in
the laboratory, such as the spitting of silver, the experiments
on the spheroidal state, of bodies, &c. It may be added, that
the properties of obsidian and its artificial transformation into
pumice furnish also an indisputable proof of this fact.

But these gaseous exhalations which accompany lava do not
disappear without leaving some traces. The more or less com-
plicated reactions which are set up between their elements and
those of the rock or of the atmosphere produce the chlorides of
iron, of copper, of cobalt, of lead, specular iron, and protoxide of
iron, oxide of copper, alkaline sulphates, sal-ammoniac, apatite,
which, in varying quantities, doubtless impregnate all modern
lavas.

If, starting from the eruptive phenomena which we may daily
witness, we pursue the analogy to the older rocks, to the
granites, is it possible not to admit, with M. Elie de Beaumont,
the existence of granitic fumaroles, which separating from the

* I am strongly inclined to think that the powerful columns of aqueous
vapour which cause the explosions, which form, as it were, the first act of
all great eruptions, are only emanations from lavas below : they accumulate
until their expansive force bursts through the solid crust of the crat jr, and
projects it into the air.

M. C. Deville on the origin of Granite. 185

original bath, have deposited these oxides of iron, of tin, of
titanium, these sulphides of molybdenum, topazes, tourmalines,
even phosphate of lime — in a word, this pleiad of bodies which
Humboldt has called the penumbra of granite, and on the forma-
tion of which DaubreVs experiments have thrown so much light ?

Here, in fact, we meet with quartz. It is the most usual and
most abundant element of these deposits. It constitutes, so to
speak, the substance on which these varied minerals form a sort
of embroidery. But there can then be no doubt as to its origin.
It is a result of secretion. It is the product of molecular actions ;
and if, as everything tends to show, water has played a part in
these actions, this water must have formed an integral part of
the granitic magma, and separated in the state of fumarole,
carrying with it the other volatile elements of these reactions.
Here we have physical and chemical circumstances altogether
peculiar; we have a key to the explanation, furnished both by
observation and analogy, and which it is impossible not to take
into account.

If to the physical properties of superfusible bodies, on which I
have dwelt at the commencement of this article, we add this
intimate association, this kind of combination, which it is im-
possible to deny, and which takes place under the influence of
particular and unstable causes between the mineral substance
and water or other volatile substances, why give up the expla-
nation of the formation of quartz and felspar by purely eruptive
phenomena ? Is there not an intimate association between the
two classes of facts ? Is not the faculty which a viscous body
possesses of assimilating liquids or gases, related to the abnormal
assimilation of heat which constitutes superfusion in viscous
bodies ? If I am not deceived, so long as these delicate points
of molecular statics are unexplained, it will be impossible to
affirm anything as to the present question.

Before seeking to explain the formation of granite, let us try
to account for what takes place before our own eyes in a solidi-
fying lava. When we know something as to what influences the
division of the elements between the small number of minerals
formed, when we have some idea of the part played in these
curious phsenomena by the substances which gradually escape
in the gaseous form, it will be time to attempt the question on
its more complicated and difficult side. Only then shall we be
able to reason, without too great chances of error, on the cause
which, at the most ancient epochs of the globe, and under
physical conditions different perhaps from those of the present,
has produced, from the innumerable solid, liquid, and gaseous
elements of which we find the trace, the definite and stable
equilibrium from which granite has resulted.

Phil Mag, S. 4. Vol. 20. No. 132. Sept. 1860. 0

[ 186 ]

XXIII. On a new Theoretical Determination of the Velocity of
Sound. By the Rev. S. Earnshaw, M.A., Sheffield.

[Continued from p. 41. J
The Triplicity of Sound.

THAT the actual velocity of violent sounds should be greater
than that of ordinary sounds, and that the velocity of
ordinary sounds should be greater than was found by Newton,
are results which theoretically depend only on the hypothesis of
finite intervals as distinguished from that of continuity; but
that the numerical value of the velocity of ordinary sounds should
be exactly what it is, is a circumstance which depends also on
the particular law of force according to which the molecules of
the atmosphere act on each other. As far as I know, this law
has not hitherto been experimentally determined; it was open
to me, therefore, to assume any law to which there should be
no a priori objection. It is of course essential that the assumed
law must give a result agreeing with experiment ; and it might
have happened that no simple law of force could have been found
which would give a result agreeing with the experimental velo-
city of sound. But not only did a simple law present itself
capable of doing this, but the law which it was found necessary
to assume is seen to be the lowest power of the inverse distance
which the mathematical expressions themselves would permit us
to try. I take this to be a strong presumptive evidence in sup-
port of the theory advanced; and I shall not hesitate to employ
the modified forms of the preceding equations which this assumed
law of molecular action will enable us to introduce, — merely ob-
serving, in doing so, that the physical results obtained do not
really depend, as to their character, on the assumption of this
particular law, but follow from the more general equations also ;
only, the mathematical expressions are by this means rendered
shorter and more manageable, and consequently the results more
obvious to the general reader.

Q

14. Assuming, therefore, f'(z) — -4, the last equation of art. 6

gives

,- 7T* /Cn\

and by treating equation (7) in the same way we find

The Rev. S. Earnshaw on the Triplicity of Sound. 187

In the case of all ordinary sounds, h is indefinitely small com-
pared with Xj and the last term (as stated in art. 5) may be neg-
lected. But turning our attention to all possible sound-waves,
itthe last term may not be neglected, but will become more sen-
sible in proportion as X is less and less. This term leads to
results of great theoretical importance. For if we eliminate X
between equation (10) and the reduced equation for k (3), we
obtain

l-.hk=Vv-v*, (11)

which expresses the exact relation between k and v in the case
of every sound of the non-violent class as defined in art. 10.

15. The symbol k is proportional to the number of vibrations
per second executed by any given particle, and, being so, may be
taken as a measure of the pitch of the note sounded. This being
agreed upon, the equation just found, being a quadratic in v,
shows us that there are two different velocities with which a given
musical note may be transmitted. The equation shows, moreover,
that the sum of these velocities is always equal to V ; and hence,
in the case of such musical notes as are not too high for audibility
by human ears, one of these velocities must be indefinitely small,
since the other differs (see art. 5) insensibly from V. And,
further, the length of the wave by which sound is rendered
audible to human ears is always large compared with h, the
distance between two neighbouring particles of air; but the
length of the second wave, by which the same note is transmitted,
is always extremely minute, never exceeding 2h; and conse-
quently this wave is too minute and feeble as to quantity of
momentum to affect such ears as ours ; and if audible at all, can
be so to none but the most minute creatures whose existence
has been revealed to us by the microscope. And if any doubt
should be entertained as to the existence of this minute order of
waves on account of their having never been perceived by the
experimentalist, let it be remembered that equation (11) is exact,
and that there is consequently no more ground in theory for
believing in the existence of those finite waves whose existence
is admitted, than of these extremely minute waves whose theo-
retical existence is now for the first time pointed out. Equa-
tion (11) indicates that one kind of wave has in theory as real
an existence as the other. I take it therefore as proved, that a
musical note of any pitch is transmissible with two different velo-
cities ; and that there are two waves for every note.

16. Yet there is one essential difference between the two waves
corresponding to the same note, which is indicated by the fol-
lowing properties, viz. that the length of the ordinary wave in-

02

188 The Rev. S. Earnshaw on the Triplicity of Sound.

creases as k diminishes, while that of the other wave diminishes
under the same circumstances. An ordinary wave is therefore
essentially different from the other ; and the difference between
them may be made to rest on the properties here pointed out.
The second kind of wave is not and cannot be a wave of the
first kind. They may also be distinguished by this property —
that the length of a wave of the ordinary kind is always greater,
and that of a wave of the minute kind always less, than 2h, the
distance between two particles of the air.

17. Equation (11) shows that for any value of v there is a
corresponding value of £; but as in the preceding investigations
k was taken to be essentially positive, the only admissible values
of v are those which lie between zero and V. And of these,
those which lie between V and ^V belong to the class of ordi-
nary gentle sounds, and those which lie between f V and 0 to
the class of minute gentle sounds.

18. Equation (8) teaches us that when the sound is of the
type which we have termed violent, any value of v is possible
between V and Qo. And hence the conclusion with respect to
possible velocity is, that the atmosphere is capable of transmitting
sound-waves with any degree of velocity from zero to infinity. But
it must be noticed that this rauge of velocity divides itself into
three essentially distinct portions ; viz. from 0 to |V, from |Vto V,
and from V to x, corresponding to the three distinct kinds of
waves — minute , ordinary, and violent : and the two former belong
to the circular, and the last to the exponential type. And with
the same value of k there may coexist three distinct waves — one of
each of these kinds — all propagated with different velocities. This
is what is meant by the title at the head of this communication,
the triplicity of sound.

19. The form of equation (11) shows that k admits of a maxi-
mum by the variation of v, viz. ^. (It is easily seen that it is

the velocity corresponding to this value of k which separates the
two classes of gentle sounds.) Hence we perceive that the par-

V

tides of the atmosphere cannot execute more than -rj free vibra-

tions per second.

20. Much additional light will be thrown on the results
arrived at in the preceding articles with respect to the wave-pro-
perties of an elastic medium like the atmosphere, if we present
the relation between k and v to the eye by means of curves.
There are two types of waves — the circular and the exponential.
In the case of the former the analytical relation between k and v
is expressed by the equation (11). We may show this by a
curve, if we take the different values of kh for the abscissae, and

7T

The Rev. S. Earnshaw on the Trip licit y of Sound. 189

those of v for the ordinates. The curve
is evidently a parabola whose latus rectum

is — ; it is represented by A B C in the

A C is = V ; and A M, the maxi-

The

2tt
figure.

mum value of kh, is equal to g . AC.

magnitude of the parabola will vary for
different elastic media, but ABC will
always be a similar portion for all media.
In the case of the exponential type of
wave, the relation between k and v is ex-
pressed in terms of a by the equations (7f);

and if a curve be constructed as in the former case, we shall find
it to be of the form C D, touching at C the line A C produced.
If A K be any abscissa, and K R be drawn parallel to A C, then
there will be three ordinates, K P, K Q, K R, representing the
three different velocities of the three corresponding waves. The
figure therefore represents to the eye the triplicity of sound.

21. AM corresponds to the maximum value of k, which is
exceedingly enormous ; but in the case of all audible sounds k
does not much exceed 20,000, which is probably small in com-
parison with its maximum value. Hence the part of the curve
C B which corresponds to audible sounds lies close to C, where
it is obvious the ordinates are all nearly equal, which is the reason
why the velocity of transmission of all ordinary sounds is sen-
sibly the same. But since the curve C D has A C produced for
its tangent at C, the ordinates which lie near to C will differ
sensibly from A C in magnitude ; and hence a slight variation
of the value of k will be attended with a sensible variation in the
value of the velocity of transmission in this case ; and we may
therefore expect that the velocity of a thunder-clap will be greatly
different for small differences of intensity of the electrical dis-
charges.

22. In considering the question of the intensity of sound, we
cannot but think it depends chiefly, perhaps entirely, upon the
whole momentum which reaches the ear in a given time ; and
this will chiefly depend in a given case upon the velocity of pro-
pagation. Hence the sounds which belong to the whole of the
curve A B, and to a large portion of C B lying near to B, would
probably be inaudible for want of sufficient momentum, even
were there no other reason. Oil the contrary, sounds belonging
to C D, with a usual amount of force in their genesis, will never
be inaudible from this cause. And hence if any method should
be found of simultaneously generating the three different sound-
waves corresponding to any value of k within the limits of audi-

190 The Rev. S. Earushaw on the

bility, and if the genesis should be so managed as to begin from
k=0, and to be capable of changing to fresh values of k, then,
from the beginning, sounds corresponding to parts of the curves
CB and CD about C would be heard together; but as the
genesis went on, the sounds corresponding to the curve C B
would get less and less intense, and those corresponding to C D
more and more intense ; and the former would gradually become
inaudible, and the latter too loud to be borne. Those corre-
sponding to A B, if perceived at all, would be most sensible for
parts near to B.

23. Hence the portions both of C B and C D which are appli-
cable to the hearing powers of human beings are very limited,
and begin from C in both cases. But it has been supposed by
Wollaston that the Grylli take up the faculty of hearing where
we lay it down ; and there may be animals which take it up
where the Grylli lay it down ; and it is thus conceivable that thte
whole curve C B is portioned out among different orders of ani-
mals from man to the minutest insect. But the curve A B, for
the reason pointed out in art. 16, may not belong to waves which
affect the organ of hearing at all, but may appeal to some other
sense, of which we are probably not possessed, but which is
suited to the wants of the minute creatures which the micro-
scope has difficulty in revealing.

The Analogy of Sound and Light.

24. It is admitted on experimental grounds that a certain
degree of analogy exists between sound and light ; and it has
been considered allowable to consider the latter as being due to
the undulations of an elastic medium consisting of particles
separated by finite interval. Hence the preceding investigations
and results, after the necessary alteration of numerical constants,
will apply to the sethereal medium. There is therefore a maxi-
mum limit to the number of free vibrations which the particles
of the aethereal medium can execute per second ; and every num-
ber from zero to this limit is possible. For this medium also, as
lor air, there are two types of wave- disturbance — the circular
and the exponential ; and three distinct classes of waves, corre-
sponding to three different velocities of transmission for every
value of k. There is, in fact, a triplicity of light ; and every
degree of velocity from zero to infinity is possible for light as for
sound. The figure given in art. 20 preserves the same propor-
tions for all media, and will therefore serve for light : the only
question that occurs is, what part of it represents sensible light ?
Sensible sound, as we have seen, is represented both in the
curve C B and in C I) by a small portion of each near to C ; but
which parts of the three curves represent sensible effects in the

Analogy of Bound and Light. 191

case of light ? Do the three curves all represent light ? May we
not assume that one of them, as C D, represents heat ; another,
as C B, light ; and the other, A B, actinism ? And if this ap-
propriation of the three curves be allowed, what part of C D
represents sensible heat, what part of C B sensible light, and what
part of A B sensible actinism ? It seems reasonable to suppose
that heat will, by means of delicate instruments, be sensible from
C ; but the moderate variation in the lengths of the waves of
sensible light renders it probable that the portion of C B which
represents sensible light will commence at some distance from
C ; for the length of a wave is represented by the tangent of the
angle subtended at A by the ordinate which represents the velo-
city of its propagation. As to actinism, but little is known at
present to guide us in determining where the portion of A B
lies which represents its sensible effects. It seems almost cer-
tain, however, on account of the extreme smallness of the ordi-
nates of A B, which represent the velocity of its transmission,
that only the part of A B which lies towards B will represent
effects of actinism which come from the sun. Those represented
by the part of A B which lies towards A travel too slowly to
reach us, and must be, besides, extremely feeble. Judging then
on these principles, we conclude that, roughly speaking, the
part of C D beginning from C represents sensible heat ; the
middle of C B sensible light ; and the part of A B near to B sen-
sible actinism. And this being so, it would seem that heat, if
moderate, ought to be found at the red end of the spectrum, and
actinism at the blue end.

25. If the process by which the temperature of a body is
raised be such as to give rise to each of the three sets of waves
which correspond to a set of values of k, and if, further, the
process be such us to produce, as it goes on, larger and larger
values of "jfc it is easy to see, after what was said in the last
article, that the heat is sensible from the beginning ; but not so
the light, nor the actinism. But as the temperature rises, and
k takes larger values, we approach the middle of C B, so that
by-and-by the light will become sensible; and this will first
happen to the red light. As the process goes on, the other
colours will be added ; and the body, from appearing of a red
heat, will approach to white heat ; and ultimately the actinism
will have become sensible also. There is nothing forced in this
explaaation. It follows naturally from the principles previously
laid down, and the general results obtained : and thus the con-
nexion between light, heat, and actinism is shown to be essentially
due to the nature of the elastic medium in which they take place,
and to follow necessarily from the hypothesis of finite intervals
laid down at the commencement of these investigations.

192 Mr. J. Spiller : Photographic Observations of

There yet remain several results of great interest, which follow
from what has been done in the preceding articles ; but they
must be deferred for a while, as at the present time other en-
gagements press upon me.

Sheffield, July 25, 1860.

XXIV. Photographic Observations of the Solar Eclipse, July 18,
1860. By John Spiller, F.C.S.*

ON the occasion of the late solar eclipse, July 18th, the equa-
torial telescope belonging to the Royal Artillery Institution,
Woolwich, was through the kindness of Captain E. J. Bruce,
R.A., placed at my disposal, and an opportunity thus afforded
me of attempting the photographic representation of the solar
disc as it appeared from this station under the several phases of
partial eclipse. The successful termination of the day's labour,
resulting in the production of twenty-three photographic im-
pressions of the phenomenon in its consecutive phases, appeared
to justify a descriptive account of the general arrangement of
the apparatus and the mode of operating, which it is hoped will
possess some degree of scientific interest.

From previous experience in connexion with the similar event
of March 15th, 1858f, when the same telescope was employed, it
was found necessary to modify on the present occasion the dis-
position of apparatus then adopted ; and particularly to restrict
the admission of the solar rays by the substitution of a very
much smaller diaphragm for the large aperture then rendered
necessary by the unfavourable state of the weather.

The telescope, with its portable stand provided with means of
adjustment in altitude and azimuth, was, on the 18th of July,
erected in the open air within the enclosures of the Royal Mili-
tary Repository on Woolwich Common, and immediately con-
tiguous to all the appliances of a well-furnished photographic
laboratory. The object-glass, 4 inches in diameter, has a
sidereal focus of 77 inches, and gives a representation of the
sun's disc measuring, at this season of the year, *7 inch in
diameter. For photographic purposes the eyepiece was removed
from the telescope, and a small sliding-bodied camera adapted to
the end of the tube ; it was then easy to project upon the ground
glass a perfectly denned image of the solar disc, using the means
of adjustment which the camera afforded for the purpose of
obtaining the best optical focus ; and in this plane the prepared

* Communicated by the Author.

t Vide Journal of the Photographic Society, April 21, 1858.

the Solar Eclipse, July 18, 1860. 193

photographic surfaces were usually employed, for the chemical
and visual foci had previously been ascertained to be very nearly
coincident. The aperture of the object-glass was now stopped
down until, with a diaphragm of *25 inch, the exposure to the
powerful action of direct sunlight was rendered manageable ; and
in order to secure an easy and sufficiently rapid means of opening
and closing this small aperture, a card of about 6 inches square
was provided, having cut out from its centre a narrow slit of
about an eighth of an inch in diameter and nearly 2 inches in
length. This quickly moved by the hand in front of the dia-
phragm of the telescope lens, limited the period of exposure to
a small fraction of a second, and besides made it possible to
regulate the interval of time at the taking of each picture accord-
ing to circumstances at the moment, which were occasionally
varying as light fleecy clouds passed over the face of the sun.
Mr. Crookes, to whom I am indebted for taking charge of
this part of the apparatus, was provided with dark glasses, to
enable him, by watching the sun, to select the proper moment
and judge the length of time which each plate would require in
its exposure ; and he agrees with me in preferring this system
of operating to the use of a fixed mechanical contrivance for
opening and closing the aperture of the lens.

By proceeding in the manner indicated, we endeavoured to re-
strict the photographic action to the representation of the sun's
disc alone, and only in the first and second plates of the series
was sufficient time allowed for the highly illuminated clouds
around the sun to become imprinted in the camera; although
faintly visible sometimes in the field of view of the telescope, their
intensity was now so much lowered as not to be copied. It will
be evident also from the foregoing description, that no clockwork
mechanism was required for the purpose of making the apparatus
follow the diurnal motion of the sun.

The glass plates on which the pictures were taken measured
2| in. by 3| in., and were numbered at one corner by a scratch-
ing diamond ; they were cleaned previously and arranged in their
order of succession. The precise moment at which each plate re-
ceived its exposure in the camera was registered immediately ;
Greenwich mean time being taken the same morning from the
Woolwich Observatory, and kept by an ordinary good watch.

The collodion process seemed on all accounts the most avail-
able, and was that employed to furnish the negative pictures from
which copies on paper have afterwards been printed ; and in order
to guard against accidents, the silver baths, collodion, and the
more important solutions were provided in duplicate, so that no
difficulty was experienced in preparing the sensitive plates in
rapid succession. The services of two of my pupils in photo-

194 Archdeacon Pratt on the Thickness of

graphy (non-commissioned officers, Royal Artillery) were found
extremely valuable in conducting the fixing and subsequent
operations, taking from my hands the plate immediately after the
development of the picture.

In viewing the photographs thus produced, it may be stated
that several of them exhibit very clearly the position of the solar
spots, and that in many cases the lunar mountains are to be seen
sharply defined against the bright face of the sun. A passing
cloud rendered the " first contact " so imperfectly visible that no
opportunity for opening the camera was presented ; but the plate
representingthe moment of maximum obscuration, and the phases
both immediately preceding and following, are fortunately amongst
the most successful of our photographic results ; and further, on
comparing the present series with the disc of the sun taken at
the period of the former eclipse, March 15th, 1858, in precisely
the same apparatus, the diminished size of the image consequent
on the eccentricity of the earth's orbit is very strikingly exhibited.

As a concluding remark, I beg to call attention to the unusual
magnitude of a group of spots visible upon the sun's disc on the
9th instant. They were readily seen without the assistance of
the telescope, as a dark patch situated rather low in the southern
hemisphere. I have succeeded in securing three concordant
photographic proofs representing their appearance at noon and a
little later, which, besides exhibiting the principal group as an
aggregate of dark spots disposed generally in a horizontal line,
indicate likewise the position of several smaller ones irregularly
distributed over the face of the sun, and only visible with optical
aid. It cannot be said that any distinct indications of faculse
are afforded by these or the other photographs taken on the
occasion of the eclipse.

Royal Arsenal, Woolwich,
August 21st, 1860.

XXV. On the Thickness of the Crust of the Earth.
By the Venerable John Henry Pratt, Archdeacon of Calcutta.

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

I ADMIT that I did use the principle pointed out by Professor
Jellett in the note to his communication in your May
Number, and in so doing was wrong ; and therefore the part of
my argument against Professor Haughton's investigation in the
Irish Transactions, which depends upon that step, falls to the
ground.

But this does not affect the objection which I brought forward
in two of my communications (May 1859, p. 329, and October

the Crust of the Earth. 195

1859, p. 259), viz. that his investigation does not concern the
question of fluidity and solidity, but only of densities.

Even if Professor Haughton knew the law of density of the
fluid nucleus, and also knew every circumstance regarding the
solid portions of which the crust is composed, excepting only the
total thickness, his equations would not give any information
regarding that thickness. The constants involved in the ex-
pression for the law of the fluid density (which must be two at
least, except in the impossible case of homogeneity) would still
be arbitrary ; and his three equations (the two appertaining to
the outer and inner surfaces of the crust, and the third given by
the value of the mean density) would involve at least four un-
known quantities. The expression for the thickness would
thus come out a function of one or more arbitrary constants, on
which the density of the fluid nucleus depends. The greater this
density the greater must be the thickness, and vice versa. The
problem, in fact, which Professor Haughton' s equations would
solve is this : if the materials of the earth follow one or more
known laws of density (for the density of the crust may be dis-
continuous) down to a certain depth, and another known law
below that to the centre, what must that depth be that the total
mass may be what we know the earth's mass and dimensions to
be ? He introduces no physical principle into the problem
characteristic of the different properties of a solid and fluid
mass, such a principle as that which Mr. Hopkins introduces,
viz. that the fluid parts pressing against the solid shell give it a
precessional motion, which is a matter for external observation
and measurement; or such a principle as this (which would
suffice if experiment had determined the law), viz. the relation
between pressure and temperature which serve just to produce
solidity. Professor Haughton treats the question more mathe-
matically than physically. He shows that without an exact
knowledge of the laws we cannot have an exact solution. But
this we knew before as a matter of course, and it did not require
Laplace's analysis to prove it.

Our ignorance of the exact laws does not preclude our approxi-
mating to a solution. We may use laws which a priori con-
siderations may show to be highly probable, and the probability
of which may be still further increased by the results they lead to.

For example, the law of density, — , is a highly probable

law for the fluid portion. On the hypothesis that the earth
took its form from being in a fluid state, the same law, both of
density and ellipticity, is highly probable for the solid parts as
well as for the fluid. I think that the Table of Deflections of
the plumb-line caused by variations of density from the fluid

196 Chemical Notices : — M. Berthelot on a New Hydrocarbon.

law (which I have given in the Philosophical Transactions, 1859,
p. 768) tends to show that there cannot be any very important
departure from this law ; otherwise they would be detected by
comparing geodetic and astronomical measures of the amplitudes
of arcs, especially wherever those measures have been made in
countries free from large visible causes of disturbance, such as,
in this country, the Himmalayas and ocean.

Mr. Hopkins's solution he professes only to be an approxima-
tion— an answer, in fact, to the question, Is the thickness of the
earth's crust a large or a small fraction of the radius ? The
consideration of the geographical features of this part of the
world (the largest mountain mass anywhere known lying on the
north, and an unbroken ocean lying to the south of Hindostan)
which I have brought forward, is for the same purpose, — not
to attempt an exact solution, but to reply to the question I have

quoted- J. H. Pratt.

Calcutta, July 9, 1860.

XXVI. Chemical Notices fi-om Foreign Journals.
By E. Atkinson, Ph.D., F.C.S.

[Continued from p. 143.]

BERTHELOT* has described a new hydrocarbon. He calls it
acetylene, or quadricarburetted hydrogen. It has the for-
mula C4 H2, and is the prototype of the hydrocarbons C2n H2TC~2.

Acetylene is produced whenever olefiant gas, alcohol vapour,
ether, aldehyde, or even wood-spirit are passed through a red-
hot tube. It is also formed when chloroform acts upon copper
at a red heat : it is contained in illuminating gas. Ether yields
it in largest quantity.

In order to obtain it pure, it is formed into a compound with
subchloride of copper. This compound is identical with a red
detonating body obtained by passing the gases arising from the
decomposition of alcohol by the electric spark or by heat, into an
ammoniacal solution of subchloride of copper. It was discovered
by M. Quet, and examined by M.Bottger; but neither of these
chemists analysed the gas which is liberated when this body is
treated with hydrochloric acid. This gas is acetylene.

It is a colourless gas, somewhat soluble in alcohol, with a cha-
racteristic disagreeable odour. It burns with a very luminous
fuliginous flame. Mixed with chlorine, it detonates almost in-
stantaneously, with deposition of carbon, even in diffused light.
It cannot be liquified. Its density is 0*92. Its formula, C4 H2,
corresponds to four volumes.

* Comptes Rendus, April 1860. Repertoire de Chimie, June 1860.

M. Cahours on Organo-metallic Compounds. 197

It combines with bromine, with sulphuric acid, with the ele-
ments of water, and with hydrogen, to form derivatives parallel
to those of olefiant gas.

Acetylsulphuric acid is formed like ethylsulphuric acid, when the
gas is agitated for a long time with concentrated sulphuric acid.
The mixture, saturated with carbonate of baryta, filtered and
evaporated, yields crystallized acetyls ulphate of baryta. If the
mixture is distilled instead of being saturated, a peculiar liquid
is obtained somewhat more volatile than water, very alterable
and endowed with a peculiar odour, and soluble in 10 to 15
parts of water. It is acetylic alcohol, C4 H4 O2.

Acetylene may be changed into olefiant gas by causing the
nascent hydrogen produced by the action of zinc on ammonia to
act upon the compound of acetylene and copper. The olefiant
gas thus formed is mixed with hydrogen and a little acetylene,

C4H2 + H2=C4H4.

Berthelot* has effected the direct synthesis of iodide of ethyle.
A thin sealed tube containing about 20 cubic centims. of a satu-
rated solution of hydriodic acid, is introduced into a long-necked
globe of about a litre capacity ; the globe is filled with dry ole-
fiant gas and hermetically sealed. The tube in the inside is then
broken, and the flask heated for fifty hours to a temperature
of 100°.

The flask is then opened, the contents treated with a solution
of potash; the product, washed, dried, and rectified, yields
about 4 grms. of pure iodide of ethyle.

M. Cahours has publishedf an extended memoir on organo-
metallic radicals. We can only find space for a few of the more
interesting results.

When iodide of ethyle acts on alloys of tin and sodium con-
taining 2 to 12 per cent, of the latter, iodide of stan ethyle is
formed, mixed with a large quantity of an irritating oil smelling
like mustard. It boils between 234° and 236° C, and has the
formula (C4H5)3Sn2I. It is the iodide of sesquistanethyle.

With an alloy of 4 parts of tin and 1 part of sodium two pro-
ducts are obtained. One an oily, limpid, yellowish liquid, which
unites directly with oxygen or iodine to form oxide or iodide of
sesquistanethyle ; it is the sesquiethylide of tin, Sn2 (C4 H5)3.
The other is a viscous liquid, stanethyle, Sn C4 H5.

When this radical is treated with water a thick oil separates,
which, when heated, decomposes into metallic tin and a colour -

* Comptes Rendus, March 1860.

f Annates de Chimie et de Physique, vol. lviii. p. 5. Repertoire de
Chimie, vol. ii. p. 167.

198 M. Cahours on Organo-metallic Compounds.

less, mobile, etherial liquid: it is distanethyle, discovered by
Frankland and Buckton. It is not a radical, for it does not
unite directly either with oxygen, chlorine, or iodine. Cahours
describes a number of the salts of the oxide of stanethyle, which
is obtained by decomposing iodide of stanethyle by ammonia.
They are mostly obtained by directly combining the base and
acid. The salts are decomposed by the action of heat.

The iodide of sesquistanethyle y Sn2 (C4 H5)8 1, is a heavy oil
which boils between 235° and 238°. When treated by iodine, it
gives iodide of ethyle and iodide of stanethyle.

Oxide of sesquistanethyle is obtained in the state of hydrate,
(C4 H6)3 Sn2 O, HO, by treating the iodide with an aqueous solu-
tion of potash and distilling : it crystallizes in colourless prisms,
which melt between 44° and 45°.

Its aqueous solution acts upon colouring matters like a strong
base. Its salts are soluble, crystallizable, and possess a strong
odour ; they are obtained by treating the oxide with strong acids.

The iodide of methyle, when treated either with pure tin, or an
alloy of sodium and tin, yields similar results to those of iodide
of ethyle. Cahours has, however, not been able to isolate stan-
methyle and distanmethyle in a state of purity.

The salts of stanmethyle and of sesquistanmethyle are ob-
tained by directly combining the oxides with acids. They cry-
stallize extremely well. The salts of sesquistanmethyle are
isomorphous with those of sesquistanethyle.

Cahours concludes from these researches that tin forms three
definite compounds with methyle, which may be written in the
following manner : —

SnMe, Sn2Me3, SnMe2,
SnAe, Sn2Ae3, SnAe2,

which correspond to the oxides of tin,

SnO, Sn203, SnO2.

If the vapour-densities are taken into account, the formula of
some of them must be doubled, and they may then be compared
to the formula of bichloride of tin. Thus :

Sn2Ae4 = 4 vols. vap. Distanethyle.

Sn2 Ae8 CI = 4 vols. vap. Chloride of sesquistanethyle.

Sn2 Ae2 CI2 = 4 vols. vap. Chloride of stanethyle.

Sn2 CI4 = 4 vols. vap. Bichloride of tin.

The relations between all these compounds are seen in the
action of iodine on distanethyle. Iodide of ethyle is separated,
and according to the proportions of iodine taken, equivalents of
ethyle are successively removed and replaced by iodine, until
biniodide of tin is ultimately obtained.

M. Bauer on an Isomer of Aldehyde. 199

Magnesethyle. — Magnesium filings are placed in a long glass
tube with iodide of ethyle. The reaction set up is moderated by
cold water, the tube then sealed before the blowpipe, and heated
for some time to 120° or 130°.

The crude product in the tube is distilled in an inert gas ; and
after suitable rectification, a colourless liquid with an alliaceous
odour is obtained, which takes fire in the air, and decomposes
water with violence : at the same time the hydrocarbon C8 H10
is obtained. It decomposes into C4 H4 and C4 H6.

The action of magnesium on iodide of ethyle is therefore quite
similar to that of zinc.

Aluminethyle. — Aluminium, which in the cold is without action
on iodide of ethyle, attacks it at 100°, but the reaction is not
complete until 130°. A viscous liquid is obtained, which, di-
stilled in hydrogen, is colourless, and possesses an odour like
turpentine; it fumes in the air, and decomposes water with
violence, producing alumina, hydriodic acid, and a gas which
burns with a pale blue flame. It boils between 340° and 350° C.

The formula of this body is C12 H15A14P = API3, A12(C4H6)3.
It takes fire spontaneously in oxygen and in chlorine. It is
energetically attacked by zincethyle, yielding an inflammable
liquid which is probably aluminethyle.

Iodide of methyle attacks aluminium in a similar manner.
Glucinum appears to have the same comportment.

Bauer has obtained* a new isomer of aldehyde. He found
that chloride of zinc acted with considerable energy on gly-
col, producing aldehyde and several other oleaginous etherial
bodies. When the crude product of the action was treated with
chloride of calcium, an insoluble etherial layer rose to the sur-
face, which, when dried and rectified, was found to boil at 110°.
It is polymeric with aldehyde and oxide of ethylene : its vapour-
density, 2*877, corresponds to the formula G4 H8 O2.

It appears to be a derivative of aldehyde ; for, when heated
with acetic acid, it does not form acetate of glycol ; and it is also
produced by the action of chloride of zinc on aldehyde. Bauer
names it acre-aldehyde. It mixes with alcohol in all propor-
tions; it reduces ammoniacal nitrate of silver; it has a very
acrid taste, and a penetrating smell.

Kiindig has examined t the action of chlorine on valerianic
aldehyde. When a current of chlorine is passed into valeral, the
temperature rises ; to terminate the reaction, however, external
heat must be applied. The liquid product, on being distilled,

* Comptes Rendus, July 9, 1860.
t Liebig's Annalen, April 1860.

200 MM. Hiibner and Geuthcr on Acroleins

boils at 100°, disengaging hydrochloric acid gas, and the tem-
perature gradually rises to 190°, when nothing but a black
residue is left. The distillate between 140° and 148° consists
mainly of a chlorinated derivative of valerianic aldehyde,
CP^Cl'O. It forms a crystallized compound with bisulphite
of soda. No chloride of valeryle, Qb H9 CI 9, is produced in the
reaction.

When chlorine acts upon valeral in the sunlight, the result is
the same ; but if the chlorine is in excess, the crystallized com-
pound with bisulphite of soda is not obtained.

Cahours obtained a body, chloramylal, by the action of chlo-
rine upon amylic alcohol, for which Gerhardt has proposed the
formula €5 H8 CI2 0. Kundig repeated Cahours' experiments,
and obtained a compound similar to that from valeral.

Hiibner and Geuther have published* some investigations on
acroleine. For the preparation of acroleine, 200 grms. of glycerine
were treated in a retort of 20 cubic centimetres capacity with 400
grms. of bisulphate of potash. The product amounted to from
25 to 28 grms. of pure acroleine.

When pentachloride of phosphorus is mixed with acroleine, a
brisk action is set up unattended by the disengagement of gas.
The parts boiling below 100° are mixed with water, which precipi-
tates a colourless etherial oil resembling chloroform. When pure
it boils at 84°, and its density is 1-170. Its formula is C6H4C12,
and the authors name it chloride of acroleinef. It gives, with
ammonia, sal-ammoniac and acroleine-ammonia. It is trans-
formed by chlorine into a crystalline body, probably sesquichlo-
ride of carbon, C4 CI6. Heated with strong alcoholic potash in
a closed vessel, it yields a few drops of a volatile liquid which
appeared to be C6H3 CI.

Acroleine and ammonia combine to form a white amorphous
body, which resembles coagulated albumen. It is obtained
by. dissolving acroleine in a small quantity of alcohol, and gra-
dually adding an alcoholic solution of ammonia. When dried
over sulphuric acid it becomes reddish-brown coloured, transpa-
rent, and very hard. It dissolves easily in acids, and is precipi-
tated by caustic or carbonated alkalies. It forms double salts
with bichloride of platinum and with bichloride of mercury.

Analysis gave for it the formulaC12H10NO8,orC12H9NO2,HO.

Acroleine unites with anhydrous acetic acid to form a compound
analogous to that which Geuther obtained by heating aldehyde

* Liebig's Annalen, April 1860.

t Wurtz (Repertoire de Chimie, June 1860) objects to this name as lead-
ing to a false idea of its constitution : it is not a combination of chlorine
and acroleine, as this name would imply. He suggests the names chloride
of chlorallyle, or chloride of allydene, meaning by allydene the group C* H4.

M. Freund on the Synthesis of Acetone, 201

with anhydrous acetic acid. It boils at 180°, and has the for-
mula C14 H10 O8 = C6 H4 O2, 2 C4 H3 O3. It is decomposed by
potash into acroleine and acetate of potash.

When acroleine is treated with bisulphite of soda, a solution
is obtained which does not possess the odour of acroleine. It
does not disengage acroleine when treated with carbonate of soda,
nor sulphurous acid when treated with sulphuric acid.

Freund has made a series of experiments* on the synthesis of
acetone. By the action of chloride of acetyle on zincethyle, he
obtained a liquid difficultly soluble in water, and with an odour
resembling that of acetone. The boiling-point was found to be
between 77°*5 and 80°*5. When agitated with a concentrated
solution of bisulphite of soda, it became warm and gave a cry-
stalline compound.

The formula of the body is €4 H80, and its formation maybe
thus expressed : —

Zn€2H5+€2H3OCl=ZnCl + €4H80.
Zincethyle. Chloride of New body,

acetyle.

Chloride of propionyle and zincethyle gave a body of the com-
position G5 H10 O, difficultly soluble -in water, with the odour of
acetone. Its boiling-point was between 100° and 101° C.

The action of chloride of acetyle on zincmethyle gave rise to a
copious disengagement of gaseous products ; a liquid was obtained
which was entirely soluble in water, and also a liquid insoluble
in water, which is now under investigation. From the part
which dissolved in water a liquid was separated, which boiled
between 56° and 60° C. It had an odour exactly resembling
that of acetone, and gave with bisulphite of soda a compound
crystallizing in nacreous laminae. It was found to have the
formula G3 H6 O, and is consequently identical with acetone. Its
formation would be thus expressed : —

Zn€H3 + €2H3OCl=ZnCl + G3H60.
Zincmethyle. Chloride of Acetone,

acetyle.

Fittig has continuedf the investigation of pinakone%, the body
obtained by the action of sodium on acetone. It dissolves in
sulphuric acid to a clear colourless liquid, which when heated
became turbid, and separated as a yellowish oil, which distils
over colourless with aqueous vapour. This oil has the composi-
tion C12H1202. It is also produced by the action of hydro-
chloric acid and of chlorine on pinakone ; in the latter case it is
accompanied by small quantities of substitution products. Fittig

* Liebig's Annalen, July 1860. f Ibid. April 1860.

X Phil. Mag. vol. xix. p. 117.
Phil, Mag. S. 4. Vol. 20. No. 132. Sept. 18G0. P

202 MM. Loir and Drion on the Liquefaction of Gases.

names the oil pinakoline. It is a colourless transparent liquid,
with a pleasant peppermint odour. Its specific gravity is 0-8,
and it boils at 105°. From pinakoline the crystals of pinakone
could not be reproduced ; and Fittig thinks that it is not identical
with anhydrous pinakone, but is isomeric or polymeric with it.

By the action of chlorine on pinakoline, bichloropinakoline,
C12H10Cl2Oa, is formed. It crystallizes in fine needles, has a
very intense odour, and attacks the eyes violently. It boils at
178°. It dissolves in alcohol, from which it is precipitated by
water. It is not attacked by concentrated caustic potash. It
does not combine with alkaline bisulphites.

MM. Loir and Drion have described* a method by which
many of the gases may be liquefied in considerable quantities.
It depends on the cold produced by the evaporation of volatile
liquids, which was first used by M. Bussy in the liquefaction of
ammoniacal gas.

In describing the liquefaction of a gas, authors have generally
contented themselves with saying that it could be effected by a
certain freezing mixture, which in many cases has a lower
temperature than is absolutely necessary. Hence the liquefac-
tion of gases is generally thought to be a more difficult opera-
tion than really is the case.

By blowing a dried current of air, by means of a blowpipe
bellows, through several tubes into about 7 ounces of ether, a
temperature of —34° C. can be obtained: this temperature, which
is reached in about four to five minutes, and can be kept pretty
constant for fifteen to twenty minutes, is more than sufficient to
liquefy a considerable quantity of cyanogen gas. By regulating
the rapidity of the air-current, it was found that the tempera-
ture of liquefaction is —22°. By blowing slightly through an
ordinary pair of bellows over the surface of the liquid gas it
solidifies immediately.

By a similar arrangement a large quantity of sulphur oils acid
may be liquefied.

Chlorine cannot be liquefied by means of ether cooled to — 34°
C. ; but when liquid sulphurous acid is substituted for ether in
the foregoing experiment, considerable quantities of liquid
chlorine may be obtained.

Ammonia may also be obtained in the liquid state by means
of cooled sulphurous acid ; the minimum temperature of which is
— 50°, while liquid ammonia boils at — 35°*7.

When liquid ammonia is used as a cooling agent, by rapidly

evaporating it under the air-pump in the presence of sulphuric

acid, a temperature of —87° C. is attained; the limit of the

lowering of the thermometer is determined by the total solidi-

* Bulletin de la Socie'te' Chimique, p. 184.

On Poncelet's approximate linear Valuation of Surd Forms, 203

fication of the ammonia. By this temperature Loir and Drion
are able to liquefy carbonic acid under the atmospheric pressure.
They have also prepared liquid carbonic acid by heating bicar-
bonate of soda placed in one of the branches of a sealed tube.
On cooling, the carbonate of soda reabsorbs the carbonic acid gas.

The authors intend to investigate the physical and also
chemical properties of the liquid gases prepared at these low
temperatures ; under these conditions the ordinary affinities are
greatly modified. For instance, 20 cubic centimetres of liquid
ammonia placed on a quantity of concentrated sulphuric acid,
showed no action at first. Gradually an action was set up and the
liquids combined, but with much less violence than might be
expected.

The temperatures were measured in these observations by
means of an absolute alcohol thermometer, the fixed points of
which were determined by means of the temperature of melting
ice, and of that of about 2 pounds of frozen mercury. The
temperature of the latter was assumed to be —40° C.

XXVII. On Poncelet's approximate linear Valuation of Surd
Forms. By J. J. Sylvester, A.M., F.R.S., Professor of
Mathematics at the Royal Military Academy, Woolwich*.

M PONCELET' S method of approximately representing
• surd forms, and more particularly the square roots of
homogeneous quadratic functions by linear functions of the
variables, is given in Crelle's Journal, vol. xiii. 1834, pp. 277-291,
under the title " Sur la Valeur approchee des radicaux." By
this method, as applied to two variables, the resultant of two
forces in a plane may be approximately expressed as a linear
function of its two components, a case fully considered by M.
Poncelet ; and tables have been worked out applicable to this
case, which appear to have been found of great utility in some
important problems of mechanical and practical engineering.
But the illustrious author of this beautiful method has left his
theory imperfect in respect of its application to three variables.

To supply this slight but not unimportant omission, and to
indicate how this more general case admits of being treated, more
especially with reference to the approximate representation of the
resultant of three forces in space as a linear function of its three
components, is the object of this communication. At the close
of the memoir referred to, M. Poncelet uses these words : — " 11
serait inutile de pousser plus loin cet examen (referring to a dis-

, * Communicated by the Author, having been read at the Mathematical
Section of the British Association, June 1860.

P2

204 Mr. J. J. Sylvester on Poncelet's approximate

cussion of the form v^a2— £2), attendu que dans les applications
de la mecanique aux machines les radicaux de la forme \Zfl2— 62
sont rarement a. considerer. Nous en dirons autant de ceux de la
forme VW^W+c^, qui represented la resultante de trois forces
rectangulaires entre elles et situees dans Pespace. D'ailleurs,
si l'on connait les limites entre lesquelles demeurent compris les
rapports des composantes a, bt c, ou de leurs resultantes par-
tielles >/fi2 + &2, &c, on pourra toujours ramener ce cas au pre-
mier de ceux que nous avons examines," meaning to the case of
Vdt + b*. Now, in the first place, it is not clear how this
reduction can be effected in general, or indeed in the vast ma-
jority of cases that might be proposed. For instance, if we have
given a < Vb* + c2, a > b> a > c, I do not see how after, accord-
ing to M. Poncelet' s process, V a? + bq -\- c2 is put under the
form aa-f/3 Vb2-\- c2 by aid of the limit a < \^b2 + c2, any use
can be made of the other limits a > b, a > c in further reducing
this to the ultimate form aa + a! fib + fi'fic. Or if we take the
still simpler case, where a, b, c are left unlimited, in whatever
way we attempt to proceed we shall obtain different approxima-
tions, according to the order in which we effect the successive
reductions.

Furthermore, in those few exceptional cases where the process
indicated by M. Poncelet leads to the use of all the limits given,
the form arrived at is not and never can be the true best form, de-
fined as such, according to M. Poncelet's own principles, as that
which within the given limits has its maximum proportional error
the least possible. Thus M. Poncelet indicates as the linear form
for Va2 + b* -f c2, when the given limits are a2 > b2 -f c2, 62 > c2,
•96046a + '3820U + -15827c, with a maximum error textually
quoted from his memoir, *0507. It will be seen hereafter that the
true best linear form gives a maximum error about one-tenth less
than this. But it would be quite easy to give examples in which
the maximum error by Poncelet's process should exceed in an
indefinite proportion the necessary maximum error. This, for
instance, would be the case if we imposed the limitations

x^ + y^Xz*, y* + z*>\a:*, *2 + tf2>\y9,

on taking X inferior but indefinitely near to 2.

The geometrical method of demonstration given by M. Pon-
celet for the case of two variables, labours under the incon-
venience of beginning with a figure of three dimensions, and
consequently does not admit of being carried beyond that case,
although the result for three variables geometrically stated, when
the conditions of the question are set under an appropriate form,
are precisely analogous to that obtained by M. Poncelet for two

linear Valuation of Surd Forms. 205

variables ; for whilst his construction is begun in space, his result
subsides to a representation in piano. But between these two
cases there is a very marked distinction ; which is, that whilst
for a surd radical with two variables every change in the limits
proposed gives rise to a change in the corresponding linear form,
such is never the case with a surd form with three or more
variables, unless the limits be expressed by a single linear in-
equality between the variables which enter into the surd form,
and the surd form itself. Thus, for instance, if \/ a:2 -\- y* + z*
is to be represented linearly within the limits z > x, z>y (for
greater conciseness I throughout suppose the variables to be
positive), the linear representation will be precisely the same as
for the_single limit z > Va? + «/2, or, which is the same thing,
z — */\ Vx* + y2, + z2 > 0 ; and accordingly for the problem with
three variables there is usually a preliminary question to be
solved, viz. to find the single inequality of the kind proposed
which involves the satisfaction of the given limits, and is
capable of being substituted for them without increasing the
maximum proportional error. This preliminary question may
be reduced, as will be seen, to an elementary geometrical
form, and is strictly tantamount to the problem following : —
Imagine a pincushion with a number of pins stuck into it,
to find the least ring which can be made to take them all in, —
a problem proposed by myself some four or five years ago with
reference to points in a plane, in the Quarterly Mathematical
Journal, and of which Professor Peirce of Cambridge University,
U.S., has favoured me with a complete solution, which is equally
applicable to the sphere, the case with which we shall be prin-
cipally concerned in what follows.

I shall begin, then, with supposing R to be an integer homo-
geneous quadratic function of x, y, z, where Xj_ y, z, U are sub-
ject to the linear inequality Ax -f By + Cz— v'R > 0. The geo-
metrical solution, as such, will be seen to be equally applicable
to the case of two, and the analytical representation to which it
leads to any number of variables.

The problem to be solved is to find a linear form Lx + My + Nz

such that the greatest value of ^ -^ - — 1 shall have

the least possible arithmetical magnitude, without regard to sign
as positive or negative, for all values of x, y, z satisfying the
proposed inequality.

It is clear that, as the entire question is one of ratios, we
may subject x, y, z to the condition expressed by E = l without
affecting the result ; in other words, we may consider x, y, z as
the coordinates of a point limited to lie on the segment of the

206 Mr. J. J. Sylvester on Poncelet's approximate

surface R = 1 cut off by the plane Ax + By + Cz = 1 . Suppose,
then, that Lx -f My 4- Nr is the linear form sought. The pro-
portional error is Lx + My + Ns — 1 j so that if we draw the
plane Lx + My -fN*— 1=0, the error is expressible geometri-
cally (paying no attention to sign) as the quotient of the per-
pendicular upon this plane from any point x, y, z in the seg-
ment, viz. — - y — -_ , divided by the perpendicular from
the origin in the same plane, viz. Hence, then,

the geometrical question to be resolved is simply to draw a plane
for which the greatest value of this quotient, restricted to points
within the segment, shall be the least possible. From this it is
immediately seen to follow, that the portion of the surface cut
off by the plane Lx + My -f Ns— 1 =0 must be a portion of the
segment cut off by the given plane Ax -f By + Cz — 1 = 0. And
its actual position may be determined by means of a principle
generally known, but which, as it will occupy but a few words,
it may be well to deduce from first principles.

Suppose there are (r-f 1) quantities, each containing the same
system of r parameters ; for greater brevity, say three quantities,
p, q, r, each functions of the same two parameters X, /j, : let
us call the greatest of the quantities p} q, r, corresponding to
assigned values of X, /jl, the dominant ; so that, according as we
change X, //,, the name of the dominant is liable to change ; and
that we wish to find M the minimum value of the dominant
upon the supposition that the variations of p, q, r in respect to
X or /n are never simultaneously zero, and may be made positive
or negative at will ; then M will be found from the equations
M =p = q=:r. For if we had M =jt? and p> q, p>ry by vary-
ing at will X or /j, we could make Bp negative; and consequently
since by hypothesis p differs sensibly from q and r, the domi-
nant of^-f Sj», q -f 8p, r -f Br would necessarily be less than that
of/?, q, r, and thus M would not be the maximum dominant.

In like manner, if M=p = q, p>r,vre could by means of the
equations

so determine B\, Bp, as to diminish simultaneously p and q ; and
thus the dominant of p — e, g— rj, r + B?' would, as before, be less
than that of p, q, r. The same reasoning applies to any number
(r+1) functions of r variables. And if the number of func-
tions should exceed r-f 1, it would still serve to show that when

linear Valuation of Surd Forms. 207

the dominant is a maximum, (r + 1) out of the whole number of
the functions must all alike represent that dominant. Thus
leaving for a moment in our original problem the case of three
variables, and going down to that of only two variables, in which
case we have to deal with a curve of the second order in lieu of
a surface, and are to suppose that a segment of such curve is cut
off by a right line A, and are required to draw another right
line B such that the maximum square of the quotient of a per-
pendicular upon B from any point in the segment by the per-
pendicular from the centre upon B is to be a minimum, we evi-
dently have to solve the same problem as if we had to find
the least value of the dominant of three quantities involving two
parameters, two being the number of constants required to fix
the line B ; those three quantities being the squares of the frac-
tions whose numerators are the three perpendiculars from the
extremities of A, and from the vertex of the arc cut off by B
upon B, and. their denominators the perpendicular upon B from
the origin ; accordingly the line B must be so chosen as to make
the three perpendiculars in the numerators, without reference
to sign, all equal, so that B is parallel to A, and bisects the
sagitta of the segment cut off by A, i. e. the longest perpendi-
cular from any point in the segment upon A.

In the case of R being, as originally supposed, a function of
x, y, z, we may take an indefinite number of points in the sec-
tion of the surface R = 1 made by the plane Ax + By + Cz— 1 = 0,
and the summit of the segment made by the plane to be deter-
mined ~Lx + My + N,sr=l, and may show by the same reason-
ing as above (there being now three parameters) that four of
these perpendiculars must be equal inter se3 which proves, to
begin with, that at all events the two planes must be parallel ;
and then the reasoning applied to two functions of one parameter
will further show that this plane must bisect the sagitta of the
segment cut off by the given plane Ax + By + Cz — 1 = 0 *. And

* The absolute liberty of the plane sought for (Lx+My-\-T!sz=.l) to
take up all positions in space, and the absence of singular points in the
segment cut off by the plane Ax-\-By+Cz=l, suffice to show that the con-
ditions of variation necessary for the legitimate application of the theorem
employed above are satisfied. If the minimum dominant is not at one of
the points of equality given by the theorem, it must lie either at some mi-
nimum, or at all events at some singular point of one of the functions of
the system to which the dominant belongs, or else at some point corre-
sponding to the contour, so to say, if there be one, of the space within
which the parameters are contained. In the case before us, the parame-
ters, however chosen, to fix the position of the plane are perfectly inde-
pendent, so that there is no limiting contour ; and it is obvious that the
functions representing the distances concerned from this variable plane have
no maxima or minima values. I do not (nor ought I to) pretend to have
presented the theoretical principles involved in the limitation of the general

208 Mr. J. J. Sylvester on Poncelet's approximate

we have now a geometrical solution of the question, which it is
important to observe is in general, but, as will be presently seen,
not universally applicable to the case when the limiting relations
of x, y, z are defined by means of the position of a variable point
limited to lie within a triangular area upon the surface 11 = 1,
whose sides are determined by the traces upon that surface ot
three planes drawn through the origin ; the plane drawn through
the angular points of this triangle will then take the place of
the plane Atf + By-f 0^—1=0 in the preceding investigation.

The next thing to be done is to obtain the quantities L, M, N
in terms of A, B, C, and the coefficients of R, which is an easy
matter to accomplish. Let

R = ax2 + by2 + cz2 + 2fyz + 2gzx + 2hxy = (f> (x, y, z),

and call f , rj, f the coordinates at the summit of the segment ;
the equation to the tangent plane at that point, which is of the
form Ax + By + Cz=0, will be identical with

(«f+fc»+j'J)X+(«f+&»+/?)Y + (srf+/i, + eOZ=l.
Hence a% + hrj +g% = — ,

and

and therefore

<r <7 a

1 Pfl(A,B,C) ,
cr2 A</>(A, B, C) '

where A<£ is the discriminant, and P(</>) the polar reciprocal of
<j> (A, B, C). Hence

~v?.

law of equality with all the logical rigour and precision of which the subject
might admit, as this would be beside my present object, which is not to call
in question the grounds of admitted truth applicable to the question in hand,
but to advance it one step further in the direction of practical application.
* We see from the above, that if A#+lfy=l, or Aa?-f By+C^r=l be
the equation to the chordal line or plane of a segment of a line or surface
of the second degree, the ratio of the perpendiculars to such line or plane
from the centre of the line or surface and the vertex of the segment re-
spectively, or, which is the same thing, of a ray to any point in the segment
to the portion of this ray produced, intercepted between the line or sur-
face and the tangent at the vertex, is expressed by Va ; VP. It may at

linear Valuation of Surd Forms, 209

and the perpendicular upon the tangent plane is

4.

V

i/A*+B2 + C2 V A
Consequently the mean between this and the perpendicular upon
the given plane is

1 y/P + y/A.

VA2 + B2+C2 2«/A
and therefore the equation to the plane required is

so that

v/P + v/A * v'P + x/A \ s/Y+<s/± '

La? + My + N> being the approximate representation of V4Hp$y>z)i
and the maximum error being evidently

\ZP + \/a"
These results are perfectly general, and apply to a quadratic
radical of an integer homogeneous quadratic function of any
number of variables ; thus for \/$(#, y, z, t) the linear repre-
sentative form is

2^/A.A , 2\/A.B 2\/A.C , 2\/A.I> .

v/P + x/A x/P + x/A* v/P + v/A x/P-fVA
and the greatest proportional error is still

v/p-Va.

x/P+x/a'

D signifying the discriminant, and P the polar reciprocal of
*(A, B, C, D).

For the sphere, the perpendicular upon any tangent plane
being 1, the linear form ought to be that obtained from the
equation Ax + By + Cz = K, where

K _1 / 1 \

>v/A2 + B24-C2""2 \ + VW+W^C^'

first sight appear strange that P should be of the form of a contravariant
(in lieu of a covariant) ; but it must be remembered that the axes to which
the line or surface and its chord are referred are supposed to be orthogonal,
and for orthogonal substitutions, contravariants and covariants are indi-
stinguishable.

210 Mr. J. J. Sylvester on Poncelet's approximate

or

K=j(v/Aa+B* + C*+1),

that is to say, the approximation is
2A

14Va*Tb«+~c2*+&c-'

the maximum error being

y^A»+B«+Oa-l

which is easily seen to agree with the general formulae above
given.

When, as is usually the case in applying these results, the
plane A#-fB?/-f- Cz— 1 = 0 is not directly given, but is to be
found as the plane passing through three given points whose
coordinates are a, b, c; a', b'3 c' ; a", bn} c" respectively, we may
use the equations

where

A-F
,Q'

B4 c=

H

F= (Vd'-V'd) + (b"c-bc") + (W-Vc),

G,=(i>d'—c"ct) + (c"a-ca") + (eel— da),

H = (db"-a"b') + (a"b-ab") + (aV-a'b),

Q=

a b c
a1 V J
a" b» c"

But it may also sometimes be needful in practice, as will pre-
sently appear, to determine the plane with immediate reference
to only two points upon the surface.

Application to the surd form which represents the resultant of
three forces at right angles to each other.

Here R = \Zx* + y2 + -z2, and R = 1 represents a sphere. Two
cases will be shown to arise. The first, the more frequent one,
is that already alluded to, where a limiting plane has to be drawn
through three given points. For this case, using F, G, H in
the sense in which they have immediately above been employed,
the linear representation of y/x^+y^+z* becomes

2F 2G 2H

Q+N^ + Q + N^+Q+N*'

linear Valuation of Surd Forms. 211

with a maximum proportional error

N-Q

N representing

The second case is where the limiting plane has to be drawn
through two points upon the sphere so as to cut it in a circle,
of which the line joining the two points is a diameter.

In this case, calling the coordinates of the two points respect-
ively a, /3, 7; a', 0 7', and writing «a' + fi/3' + 77' = m, it is
easily seen that the perpendicular upon the limiting plane is

— ^r— , and consequently the perpendicular upon the plane
20

L* + My + N*=l is iii+v/l + w\.

Also this plane being parallel to the limiting plane, is perpendi-
cular to the line joining the origin to the point

<"!"*;" 2 " 2 ' 2 J

and therefore

j^kM, M=£±£, M*Ma5,

P P P

and

I --'-Ti gi-/5gV<

v/(«+a')4+(/3+/3')2 + (7 + 7')2_J I +V 2 J' .
that is to say,

= H^(l+m)4-(H-m)}i
so that the linear form required is

{y2(l+m) + l + m}{_^ * + fi^fr^S^iJpj
with a maximum proportional error
\/2—\/l+m

\/2 + x/l+m

(m is of course identical with the cosine of the angle between
the radii joining the two given points.)

The conditions of inequality which obtain between x, y, z may
be, and usually will be, such as correspond to the limitation of
the point (#, y} z) to an area contained within a triangle or

212 Mr. J. J. Sylvester on Poncelet's approximate

polygon upon the surface of the sphere.
Thus take X, Y, Z, each a quadrant apart
from the other, the points where the sur-
face of the sphere #2-f y2 + #2=l is
pierced by the axis. If no limitation is
placed upon the values of x, y, z further
than the one throughout supposed of their
remaining always positive, the limiting
area will be XYZ. If we suppose

we may take tan XK = k> and drawing the small circle KK', ZLM
will be the limiting area; if, again, Z<fc\/,r2-fy2, KK'YX will be
the limiting area ; if, again, Z < ks/x^-^y1, Z> lx, Z>my be the
limiting conditions, taking tan LX = /, tan MY = m, and drawing
LY, XM to intersect in 0, KK' MOL will be the corresponding
area, and so in general. Even so simple a set of conditions as
Z > Xy Z >■ y it is seen will give rise to a quadrilateral area,
limited in the figure by Z L 0 M, when ZL = ZM = 45°. Thus,
then, we approach the preliminary question to which allusion
has been already made, which is to determine the least circle
that will cut off from a given sphere a segment containing all a
given system of points lying upon it. The solution is precisely
the same, substituting arcs of great circles for right lines, as the
problem of drawing upon a plane the least circle containing a
set of points given in the plane.

We may, in the first place, obviously reject all those points
that are contained within the contour formed by arcs joining
the remaining points, so that the case of points lying at the
angles of a convex polygon alone remains to be studied.
Now if we confine our attention even to the simplest case of a
system of three points, we shall see at once that two cases arise.
If a circle be drawn through them, and these three points do not
lie in the same semicircle, no smaller circle than this can be
drawn to contain the three ; but if they do lie in the same semi-
circle, it is obvious that a circle described upon the line joining
the outer two as a diameter will be smaller than the circle pass-
ing through all three, and will contain them all. It was this
simple but striking fact in the geometry of situation which led
me to propose the question for any number of points in the
Quarterly Mathematical Journal ; and as Prof. Peirce's exhaust-
ive method of solution has not appeared in print, I may take
this occasion of presenting it.

Let A, Z, B, C, D, E be the given points. Let A Z B be a
circle whose centre is drawn through A, Z, B, chosen so as to
include all the others ; then if A Z 13 are not contained in the

linear Valuation of Surd Forms. 213

same semicircle, AZB is the circle re-
quired. But if A Z B be less than a semi-
circle, as in the figure, we may first reject
the consideration of all the points con-
tained between the arc A B and its chord.
We must then find 0', 0", &c, the centres
of the circles passing through A, B, C ;
A, B, D, &c. : these will all lie in the same
straight line Of 0" 0. Selecting the one the nearest to O, say
0", we describe the corresponding circle, in which A C will now
take the place of A B in the former circle. If the points A, B, C
are not contained in less than a semicircle, i. e. if A B C is an
acute-angled or right-angled triangle, A B C is the circle re-
quired ; but if they do lie within the same semicircle so that
ABC forms an obtuse angle, B will now have to be rejected, and
we must find a new centre as before, and so on continually. By
this process we must inevitably at last exhaust all the given
points ; and the final circle so obtained will be the circle sought,
unless the three points through which it has been drawn are
distributed over the same semicircle, in which case the circle
required is that described upon the chord joining the two ex-
treme points as its diameter. The- solution will evidently be
unique, and (as already hinted at) merely require the construction
upon the sphere either of a circle passing through a certain
set of three out of all the given points, or else passing through
only two of them, so as to be perpendicular to the radius bi-
secting their joining line.

If we imagine an india-rubber band (similar, we may suppose,
in form to a i ' parlour quoit " but more elastic) having the faculty
of maintaining its figure always circular, or which is more simple
in the case before us, capable of maintaining itself in the same
plane, and imagine this sufficiently stretched over the surface of
the sphere to contain all the given points (represented by very
minute pins5 heads given upon it), this band will by its contrac-
tion upon the surface of the sphere, however originally placed,
imitate the steps of Prof. Peirce's method of solution ; and after
(it may be) passing through and quitting successive sets of three
points, come to a position of geometrical equilibrium, either when
its circumference contains a triad of the given points lying at
the angles of an acute-angled triangle, or a duad at the extremi-
ties of one of its diameters *.

* The annexed is a more complete and, I think, a correct account of what
would happen to the band under the supposed conditions. It will begin
to move parallel to its own plane, and continue so to do until it comes in
contact with one of the physical points (call it A) upon the surface of the
sphere. Supposing that the position of equilibrium is not then attained

214 Mr. J. J, Sylvester on Poncelet's approximate

The following observation, which constitutes a veritable theo-
rem, and is presupposed in Prof. Peirce's solution, is very im-
portant:— "Any circle being found which, cither passing through
three of the given points such that no two of their joining lines
form an obtuse angle, or which described upon the line joining
two of the given points as a diameter, includes all the rest, is the
minimum circle which contains all the points of the given cluster;
so that one, and only one, circle exists satisfying the above alter-
native condition."

It may be instructive to proceed to the application of the
method now fully explained to some of the more salient cases of
inequality, it being understood that these cases are given to
afford some general notion of the precision of the method, and
by no means as specimens of such as it would be applied to in
practice, for which the limits I shall suppose would be far too
wide to furnish any useful result.

Ex. 1. x, y, z unlimited. Here the values of F, G, H, Q are
the minor determinants of the matrix,

1 0 0 I

0 10 1

0 0 11

F=G=H = 1,Q= 1, and the linear approximation to\/#2 -f- y2 + z1

2
becomes __^+&c^ or ^/3 _i)# 4.(^/3 _ 1)^(^3 _j)^

by the band passing at the same moment through one other point at the
opposite extremity of a diameter to A, or through two other of the given
points forming a non-obtuse-angled triangle with A, it will begin to re-
volve (always contracting the while) about a tangent at A to its intersec-
tion with the sphere as an axis, until it meets a second of the given points,
say B. If the line A B is a diameter of the band, cadit qucestio, the pro-
blem is solved. If not, the band will go on further contracting, revolving
meanwhile round A B as an axis until either A B becomes a diameter in
virtue of the contraction of the band's dimensions (and so the problem is
solved), or else before this can take place the band is arrested at a third
point C, either forming a non-obtuse-angled triangle with A B and so
solving the problem, or else an obtuse-angled triangle with A B and
lying exterior to the arc A B on one side of it or the other; on the latter
supposition the line joining C with the extremity of A B nearest to it, will
(it appears to me) form a new axis of rotation for the band, which will
quit the further extremity of the old axis, and thus the motion will continue
with an intermitting change of axes, until at last the band either finds out
for itself an axis which in the course of the contraction becomes a diameter,
or else brings the band into contact with a third point forming a non-obtuse-
angled triangle with such axis, in either of which cases the minimum peri-
phery is attained, the contraction comes to an end, and the problem is
solved.

0

0 1

i

0

\/i \/{

I

vl

o VI

I

linear Valuation of Surd Forms. 215

or say

•73025a? + '73025?/ + '73025*,

with a maximum proportional error

^t-\ or 2-^/3 = '26895.
v 3 + 1

The corresponding error for \/x2 + y2 under the form -8284#
+ •8284?/ is -17160, or about two-thirds of the one in question*.

Ex. 2. z >- \/ 1/*- + x1 . Here the determining matrix is

F = G=v/|-i = -207107
H=4

Q=i

N2=F2 + G2 + H2=l-v/I=-292893

N = -541196

N + Q=1041196 N-Q=041]96.

Thus the linear approximation becomes

•397825a* + -397825?/+ -960430*,
with a maximum error -039493.

Ex. 3. z> \A/2 + #2, y>x. This is M. Poncelet's example
(Crelle, vol. xiii. p. 291) . His a, b, c correspond respectively with
my z, y, x ; there are some misprints in line 6 of this page (in
M. Poncelet's Memoir) which may perplex the reader; it is in-
tended to stand thus :

8Va* + b* + c* + /3ZV¥Tc*=Va* + b* + c*. fo+^x/^ + y + gJ"'

Here the determining matrix corresponds to the areaZ KN (the
coordinates of N being found from the equations *2=a?2-f y2,
y=x, ,2'2 + tr2 + 2/2=l), and the matrix will be as subjoined.

* It would have been more exact to have treate/1 this as a case of a circle
to be drawn through four points, viz. Z the middle points of ZX, ZY and
the middle or lowest point (in reference to Z) of the small circle drawn
through these two, and having Z for its pole. But it is easily seen that
the small circle drawn through the three former will contain the one last

— 45

named, for the tangent of its circular radius will be V 2 X tan-^ , and con-
sequently its summit will be further from Z than from the point in question.
A similar remark applies to the subsequent and some other examples.

216 Mr. J. J. Sylvester on Poncelet's approximate

0 0 1 T

0 vf v/J T

1 i VI I

F=^J + iVl-i-i = 3v/];-l = -060660
G= ^-l^^-^T^^^

H=iv/i = *353553
Q=4v4= -353553
N*=F2+G2 + H2=iJL+S + i-7v'i

= ^-iv/24:5
= 2-625-2-474874
= •150126
N = -387461, N + Q=-741014, N-Q=-033908.

33908

The

maximum

error therefore is

741014 ~

•0457,

or about

one-

tenth less than that given by M

. Poncelet's

form

2F

N + Q"

6066
"37051'

= •1637,

2G

N+Q

14645
"37051"

= •3953,

2H

35355

=•9542.

N + Q"" 37051"

The last of these quantities is less, the first two greater than
the corresponding coefficients in M. Poncelet's form.

Ex. 4 and 5. The inequality system, \/x2 + y2 > z > y > x, is
represented by the triangle K N Q, and the corresponding deter-
mining matrix will be

0 V\ V\ I

1 * Vi I

Vi Si s\ I

•

So, too, the inequality system, \/#2 + y2 < z < y > x, has for
its locus the triangle Z K N, its determining matrix

0 •* V\ I

\ \ ^\ I
0 0 11
It would be superfluous to go on multiplying numerical ex-

linear Valuation of Surd Forms. 217

amples, that may be left to those who feel the want of the
Tables which this method affords. If the limiting conditions
were supposed to be -z > y, z> x} this would correspond to the
quadrilateral Z K' Q K in the last figure : it may easily be ascer-
tained that a circle passing through K'ZK would contain Q,
and would have its centre between N and Z. Hence by the
application of Peirce's law, we know that the minimum circle in
this case is that which can be drawn through K' Z K, and con-
sequently the linear form and maximum error will be precisely
the same as for the simpler case already considered, z >\/ 'x^ + y*.
On the other hand, if the conditions imposed were simply z < x,
z <y (conditions, be it remembered, far wider than ever would be
admitted in practice), the limiting figure becomes XQY; and
since MQ < MX or MY, the centre of the circle through XQY
would fall under X Y, so that the limiting circle in this case
would be that having M for its pole; the linear substitutive
form would not contain z, but would be the same as if z did not
appear, viz. -96046# ■+ *960467y, with -03954 as the maximum
proportional error. The same remark would apply to the system
of conditions z < \x, z<\y for any value of X not inferior to ^/\.
The conditions z> x, z>y, z < \J ' x1 + y2 would correspond
to the limiting area K K7 Q, which would give rise to the deter-
mining matrix,

0 v7!

VI

T

#1 o

V\

T

V\ V\

v\

I

The condition z < s/#2 + y1 would correspond to a limiting area,
KK'XY. If KY be bisected in G, and K'X in G*, and G'YGX
intersect in H, it is obvious that a small circle may be de-
scribed with H as its pole passing through all four points
X, Y, K, K;, which will be the minimum circle of limitation.
To assign the determining matrix, we may take any three of
these four points, as, for example, Y, X, K, which will give

0 1

0

1

1 0

0

T

^h o

^

T

J=-70711,

This gives

Q=V5

F=v/J, G=V% H = l-Vf= -29289,
N2=4-v/2=l-085786,
N = 104200,

N + Q=l-74911, N-Q=-33489.
Phil Mag. S. 4. Vol. 20. No. 132. Sept. 1860. Q

218 Mr. J. J. Sylvester on Poncelet's approximate

The linear approximation is accordingly

•8090* + -8090^ + '335 Is,

with a maximum proportional error '1914.

Finally, for z > y, y>x the limiting triangle will be Z K Q,
the determining matrix

0 0 1 T

0 S\ Si 1

•i ^y ^i 1

F=v/|-v/i = '1297, 0=^(1- •*} ='1692,

H=v/J=*4082,

N2 = f-VI-\/f=: '21207,

N=4605, N + Q=-8687,

Q=v/| = -4082, N-Q=0523.

The linear approximation is •2986#+,3895y + " 9397y, with a
maximum error *06 (more precisely -0602). This is a trifle
beyond half as much again as the maximum error of the best
linear approximation to isjx^ + y9-, subject to the limitation x>y,
which (see Poncelet's Memoir, p. 280) is a little under '04.

Poncelet has shown that for Sx2 + y2} when x, y are the co-
ordinates of a point limited within a sector whose bounding
radii make angles <f> and yjr with the axis of X, the approximate
linear form is

cos2 . cos2 ,

with a maximum error tan2 - , .

4

In like manner it follows immediately from the method given

in the text, that if the summit of the limiting segment make

angles X, p, v with the axes of X, Y, Z, and its spherical radius be

p, the approximate expression for Vx^ + y^ + z2 is

cos X cos Lb cos v
x+ —y+ z,

«P aP 9P

COS* ^ COS2 § COS2 §

A Z A

with a maximum error tan2£, which expressions are the precise
analogues of the former, as will immediately appear from the

linear Valuation of Surd Forms.

219

consideration that the summit of the spherical segment corre-
sponds with the centre of the circular arc.

As an example of the use of these formulae, suppose the given
limits to be

x < v^ + s2, y < \Z*2-f-#2, x < \/#2 + y2.

If we bisect the quadrants X Y, YZ,
Z X in L, M, N respectively, the vari-
able point will be limited to lie in
LMN, and the base of the correspond-
ing segment will be the circle passing
through LMN whose summit will be
at E, the point where the perpendicular
to XT at L and the arc bisecting
the angle X meet.

Here then we have

p = LE, \=/*=j/=XE,
tan p = cos 45 = s/\,

cotX= V\,

cosp

= ^h

2

'•- = £{1+ */f}, cos\= s/$,

Hence the linear approximation is

= -6356744(# + y+z),

with a maximum proportional error 5— \^24 = '10102.
More generally, if we assume the system of conditions

\/#2 + 2/2 > cz} vy2 + z2>- ex, vs2 + a?2 > cy,

c being any number intermediate between 1 and \/2, if in the
figure annexed, we take tan ZK=tanZK' = c, and join KK'by
a small circle intersecting YM which
bisects Z X in R, 0 remaining still the
summit of X Z Y, it is easy to perceive
that the limiting area will be included
within the triangular space cut out be-
tween K K' and the two other analogous
small circles ; X, p, ¥ will remain the
same as before, and 0 R will represent
p. Accordingly we have from the qua-

Q2

220 Mr. J. J. Sylvester on Poncelet's approximate

drantal triangle ZYR,

cosZR=sinRYcosRYZ,

sinRY
■. RY=tati

tan p = tan RO = tan RY - tan 0 Y =

When c=\/2, this vanishes ; and when c > y/2, the conditions
become incompatible.

/ 2 g Q

The equations tan <£== a/ -^ — - , or cos 2</>= § — ^, and

p = £- tan-1 ^2 = 0-54° 44'

are well adapted for logarithmic computation. Suppose

c=$, cos2<£=-±}=-, 44 2<£ = 180°— 63° 54'= 116° 6',
<£ = 58°3', /d = 3°19',

giving a maximum error tan (1° 39' 30")2 = -0008375. The
linear form corresponding to this is

i + rc* ^r + y + ^} = '5778^ + ,57'7% + ,5778^

If c< 1, the formula changes; the limiting area from a tri-
angle becoming a hexagon through all the angles of which a
circle will admit of being drawn, which circle will give the limit-
ing segment, p becomes the third side of a spherical triangle
of which the other two sides are tan-1 \/2 and tan-1 c respect-
ively, and the included angle 45° ; so that

""'- \/3irW\/3(TT?r(1+ ^mm>

and the maximum error, i. e. I tan2^ V becomes
•3(T+?j + l + V'c

linear Valuation of Sw*d Forms. 221

The only real difficulty in extending M. Poncelet's method in
the manner pursued in the above unpretending study, con-
sisted in forming a clear preconception of the mode in which
any given system of limits require for the purpose in view to
be regarded, viz. as enveloped, so to say, in a single condition
(no wider than absolutely necessary) expressed by a linear equa-
tion between the given surd function and the variables which
enter into it.

I may in conclusion just observe that if the relative values of
the variables be limited, not by a system of conditions giving
rise to a polygonal area of limitation, but by a condition ex-
pressed by the positivity of a single homogeneous function of
the variables of any degree, the variable point will then be limited
by the intersection of the sphere with a cone, and we should
have to solve a preliminary geometrical problem of circumscribing
a spherical curve by the least possible circle, — a question which I
have neither leisure nor inclination to discuss, but to which I
believe Mr. Cayley has paid some attention.

Before taking final leave of my readers and the subject, I
devote a word to the inverse case of Three Rectangular Forces.
This is the case where the resultant and two of the rectangular
components are given, and it is the third component which is to be
expressed linearly in terms of them. In this case an approximate
expression is to be found for </z2—y2—x2, and the geo-
metrical locus which replaces the sphere becomes an equi-
lateral hyperboloid of revolution of two sheets.

If the variable point be supposed to be limited to a segment of
one sheet of the hyperboloid cut off by the plane Ax + By + Cz = 1,
the discriminant of z^—y^—x2 being 1, and its polar reciprocal
of the same form as itself, the approximate linear form of the
surd becomes

2C* 2B?/ 2A#

v/C8-B2-As + l "WCF-Bs-A8*! ^/C2-B2-A2 + Y

Li • M 1 l~y/C2-B^A2

with a maximum proportional error — ^^^==r.

To envelope, however, any given arbitrary system of inequali-
ties between the coordinates x, y, z on. the hyperboloid within a
single condition, Ax + By + Cz — 1 > 0 becomes a geometrical
problem of somewhat greater difficulty than the corresponding
one for the sphere, and I do not propose to enter upon the dis-
cussion of it here.

I shall content myself, as M. Poncelet has done in the corre-

222 On Poncelet's approximate Valuation of Surd Forms.

spoiiding case in piano, with exhibiting a single numerical ap-
plication of the method.

Suppose the given limits to be defined by the equations

•* > | {y* +3?) y~>- #•

Here it is obvious that the enveloping condition will be expressible
by means of the equation to a plane drawn through three points
on the hyperboloid, the coordinates of one of which are found

1 8 y=0, x=0;

of a second by writing

*2-fy = 0, #=0;

and of the third by writing

«•-! |(3/*+*s)=0,
and for all three

y— x=0;

Hence we obtain the matrix

1 0 0

1

s/% \/2 0

1

\/3 1 1

I

And if we call the minors obtained by leaving out the first,
second, third, fourth columns respectively H, G, F, Q, the linear
form becomes

2Hz 2Gy 2F#

V/H2-G2-F2 + Q+v/H2-G2-F2 + Q+v/H2-G2-F2 + Q

s£ . Q_v/H2-G2-F2 A .

with a maximum error ~ . =. And since

Q + v/H2-G2-F2

Q=-v/2, H=v/2, -Grrx/3-1, -F= (\/2 -])(v/3-l

we have

V/H2-G2—F2= 11714 and Q= 1*4142,

so that the representative form becomes l#093ar — *566y— -089z,
with a maximum relative error of about -094.

[ 223 ]

XXVIII. Proceedings of Learned Societies.

ROYAL SOCIETY.

January 19, 1860.

[Continued from p. 164.]
■Sir Benjamin C. Brodie, Bart., President, in
the Chair.

and

HPHE following communication was read : —
-*■ ■ On Vacua as indicated by the Mercurial Siphon-gauge
the Electrical Discharge." By J. P. Gassiot, Esq., F.R.S.

That the varied condition of the stratified electrical discharge is due
to the relative but always imperfect condition of the vacuum through
which it is passed, is exemplified by the changes which take place
in the form of the striae while the potash is heated in a carbonic
acid vacuum-tube. In order, if possible, to measure the pressure
of the vapour, I had a carefully prepared siphon mercurial gauge
sealed into a tube fifteen inches long, at an equal distance between
the two wires A, B.

yt

u

V

This tube was charged with carbonic acid in the manner described
by me in a former communication. When exhausted by the air-pump
and sealed, it showed a pressure indicated by about 0*5 inch difference
in the level of the mercury; the potash was then heated ; the mercury
gradually fell, until it became perfectly level.

Dr. Andrews (Phil. Mag. February 1852) has shown, that with
a concentrated solution of caustic potassa, he obtained with carbonic
acid a vacuum with the air-pump so perfect as to exercise no ap-
preciable tension, as no difference in the level of the mercury in the
siphon-gauge could be detected.

On trying the discharge in the vacuum-tube after the potash had
cooled, I found it gave the cloud-like stratifications, with a slight
reddish tinge ; consequently not only was the vacuum not perfect,
as denoted by the form of stratification, but in this tube the colour
denotes that even a trace of air remains, — probably that portion in the
narrow part of the siphon-gauge, which, from its position, was not
displaced by the carbonic acid.

The potash was subsequently heated until the discharge was
reduced to a wave-line, with very narrow striae ; in this state moisture
is seen adhering to the sides of the tube ; but even in this state the
difference in the level of the mercury in the gauge did not ever vary
more than "05 inch. As the potash cooled, the discharge altered

224 Kuyal Society : —

through all the well-known phases of the strise, the mercury again
becoming quite level.

At first almost the slightest heat applied to the potash alters the
form of the stratifications ; as the heating is repeated, longer appli-
cation is necessary ; but it shows how sensibly the electrical discharge
denotes the perfection of a vacuum, which cannot be detected by the
ordinary method of mercurial siphon-gauge.

Jan. 26. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communications were read : —
" On the alteration of the Pitch of Sound by conduction through
different Media." By Sydney Ringer, Esq.

" On the frequent occurrence of Phosphate of Lime, in the crystal-
line form, in Human Urine, and on its pathological importance." By
Arthur Hill Hassall, M.D. Lond.

The author concludes from his observations and investigations : —

First. That deposits of crystallized phosphate of lime are of fre-
quent occurrence in human urine, much more so, indeed, than those
of the amorphous or granular form of that phosphate.

Second. That the crystals present well-marked and highly charac-
teristic forms, whereby the identification of this phosphate by means
of the microscope is rendered easy and certain.

Third. That there is good reason to believe that deposits of phos-
phate of lime are of greater pathological importance than those of
the phosphate of ammonia and magnesia.

Feb. 2. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communications were read : —

" On the Saccharine Function of the Liver." By George Harley,
M.D., F.C.S., Professor of Medical Jurisprudence in University Col-
lege, London.

From his experiments the author draws the following conclusions: —

1st. Sugar is a normal constituent of the blood of the general
circulation.

2ndly. Portal blood of an animal on mixed diet contains sugar.

3rdly. Portal blood of a fasting animal, as well as of an animal
fed solely on flesh, is devoid of sugar.

4thly. The livers of dogs contain sugar, whether the diet is animal
or vegetable.

5thly. Under favourable circumstances, saccharine matter may
be found in the liver of an animal after three entire days of rigid
fasting.

6thly. The sugar found in the bodies of animals fed on mixed
food is partly derived directly from the food, partly formed in the
liver.

7thly. The livers of animals restricted to flesh diet possess the
power of forming glucogen, which glucogen is at least in part trans-
formed into sugar in the liver ; — an inference which does not exclude
the probability of glucogen (like starch in the vegetable organism)
being transformed into other materials besides sugar.

De la Rue and Muller on the Resin of the Ficus rubiginosa. 225

8thly. As sugar is found in the liver at the moment of death, its
presence cannot properly be ascribed to a post mortem change, but
is to be regarded as the result of a natural condition.

" Hereditary Transmission of an Epileptiform Affection accident-
ally produced." By E. Brown-Sequard, M.D.

Feb. 9. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communications were read : —
" On the Resin of the Ficus rubiginosa, and a new Homologue of
Benzylic Alcohol." By Warren De la Rue, Ph.D., F.R.S., and
Hugo Miiller, Ph.D., F.C.S.

In this communication the authors give an account of a new alcohol
homologous with benzylic alcohol (C14 H8 02) which they have found
occurring in the state of a natural acetic ether in the exudation from
an Australian plant known as the Ficus rubiginosa.

This acetic ether, for which they propose the name of Acetate of
Sycoceryle, constitutes about 14 per cent, of the crude resin ; the re-
mainder consisting principally of an amorphous resin which they
name Sycoretine.

The different degree of solubility of the various constituents in
alcohol, afforded the means of the separation of the one from the
other ; none of them present any remarkable properties except the
new ether ; so that the authors have devoted their attention mainly
to the working out of the chemical relations of this substance.

Acetate of sycoceryle, having very characteristic properties, could
be readily obtained in beautiful crystals ; but some difficulty oc-
curred in obtaining it absolutely pure, on account of the presence
of a parasitical body which accompanied it constantly in solution, and
always cystallized upon it. At last means were found of removing
the latter substance by dissolving out the acetate of sycoceryle with
ether. The per-centage composition of this parasitical body was
found to be —

Carbon 76*56

Hydrogen 12*30

Oxygen 11-24

but it existed in too small a quantity to admit of its true chemical
relations being made out.

Acetate of sycoceryle gave on analysis the following per-centages as
the mean result of two accordant analyses : —

Carbon 79*09

Hydrogen 10*28

Oxygen 10*63

These numbers agree well with those required by the formula
C40 H32 04 based upon experimental evidence.

Acetate of sycoceryle, when acted upon by sodium-alcohol, yielded
acetic acid and a beautiful crystalline body resembling caffeine or
asbestos ; this proved to be a new member of the benzylic alcohol
series having the composition C36 H30 02, which requires the following
per-centage quantities : —

226 Royal Society :—

Mean of two analyses.

Carbon 82-44 82-39

Hydrogen 11-45 11*38

Oxygen 6-11 623

The authors, by acting with chloride of benzoyle on sycocerylic
alcohol, obtained the corresponding benzoate of sycoceryle ; and by
employing chloride of othyle (acetyle), have prepared the acetate of
sycoceryle which was identical with the original crystalline constituent
of the resin.

By treating sycocerylic alcohol with nitric acid, an acid was pro-
cured which appears to be sycocerylic acid.

The products of the action of chromic acid on sycocerylic alcohol,
were a white crystalline neutral substance and a body crystallizing
in large flat prisms. The latter appears to be the sycocerylic
aldehyde.

"Analytical and Synthetical Attempts to ascertain the cause of the
differences of Electric Conductivity discovered in Wires of nearly pure
Copper." By Professor William Thomson, F.R.S.

"On a new Method of Substitution; and on the formation of
Iodobenzoic, Iodotoluylic, and Iodoanisic Acids." By P. Griess, Esq.

In a previous notice* I have pointed out the existence of a new class
of nitrogenous acids which are generated by the action of nitrous
acid on the amidic acids of the benzoic group, the change consisting
in the substitution of one equivalent of nitrogen for three equivalents
of hvdrogen in two molecules of the amidic acid.

C29HuN208 + N03=3HO + C28HnN308

Two eqs. beuzamic New acid,

acid.

Under the influence of various agents these new acids undergo
remarkable changes, amongst which the transformation produced by
the mineral acids deserves to be particularly noticed. If the acid
CM Hn N3 08 be gently heated with strong hydrochloric acid, nitrogen
gas is evolved, the yellow colour of the original acid disappears, and a
red body separates, which may be separated by filtration and purified
by treatment with animal charcoal. Both the physical properties
and the analysis of the substance thus obtained, prove it to be pure
chlorobenzoic acid. The hydrochloric mother-liquor on evaporation
deposits crystals of the hydrochlorate of benzamic acid.
CMHnN3 08-f2HCl=Cu(H5Cl)04 + C14(H6HaN)04,HCH-N2.

To render intelligible this transformation, the acid C28 Hu N3 08
may be viewed as a double acid corresponding to two molecules of
water,

Cu(H3N'a)02 "1

Cl4 (H4 H2 N) 02 ^04=C14 (H4 N'a) 04

+ Cl4(H5H2N)04,

and splitting under the influence of hydrochloric acid into the two
* Phil. Mag. vol. xvii. p. 370.

Formation of Iodobenzoic, Iodotoluylic, and Iodoanisic Acids. 227

groups C14 (H4 N'2) 04 and Cu( H5 H2 N) 04, in the first of which
the two equivalents of monatomic nitrogen are replaced by hydro-
chloric acid, producing C14(H5C1)04, while the second simply com-
bines with hydrochloric acid, producing hydrochlorate of benzamic
acid. It deserves to be mentioned that the acid C28 Hu N3 08 may
be derived also from two equivalents of hydrated oxide of ammo-
nium, when its formula assumes the following shape : —
[(CuH403)a»Ni"HNJ»-l0

Further experiments are necessary to decide which of these two
formulae deserves the preference.

Iodobenzoic Acid, C14](H5"I)04.
This substance is produced by a process similar to that which
furnishes the chlorobenzoic acid, viz. by the action of hydriodic
acid on the acid C28 Hu N3 08, — beautiful white plates resembling
benzoic acid, easily soluble in alcohol and in ether and difficultly
soluble in water. Iodobenzoic acid is remarkable for its great
stability ; even fuming nitric acid fails to expel the iodine, and
transforms the substance simply into nitro-iodobenzoic acid. The
silver salt of iodobenzoic acid is a white amorphous precipitate con-
taining C14 (H4 1 Ag)04.

Iodotoluic Acid, C16 (H7 1)04.

This acid is formed from the analogous nitrogenous acid in the
toluic series, according to the equation

C32HlsN308 + 2HI=C16(H,I)01+C16(H,HaN)01,HI + N2.
It crystallizes in white plates of a pearly lustre, which in their che-
mical and physical properties are very similar to iodobenzoic acid.

Iodanisic Acid, Ci6 (H7 1) Oe
is obtained by the action of hydriodic acid upon the nitrogenous
acidC32H15N3012,

C32 H,5 N3 012 + H2 I2=C16 (H7 1) 06 + C16 (H7 H2 N) 06, HI + N2.
Exceedingly small, nearly white needles, almost insoluble in boiling
water, very soluble in alcohol and in ether.

The new method of substitution, by which the described products
were obtained, although less direct than the ordinary processes,
promises nevertheless to adapt itself to several cases of special interest.
I am at present engaged in pursuing these experiments, with the view
of producing fluo- and cyano-benzoic acids and their homologues,
which have never been obtained.

The experiments which I have described were performed in Pro-
fessor Hofmann's laboratory.

Feb. 16. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communications were read : —

" Description of an Instrument combining in one a Maximum and
Minimum Mercurial Thermometer, invented by Mr. James Hicks."
By Balfour Stewart, Esq.

About a fortnight since, Mr. James Hicks, the intelligent foreman

228 Royal Society .—

of Mr. L. P. Casella, Optician, called at Kew Observatory with an
instrument of the above description, for the purpose of having it
compared with the ordinary maximum and minimum thermometers.
This comparison proving very satisfactory, and the principle of the
instrument commending itseif to Dr. Robinson, Mr. Gassiot, Pro-
fessor Walker, and several other scientific men who examined it,
Mr. Gassiot requested me to write a short description of it, whioh
he thought might be of interest to the Royal Society. For many
particulars of this description I am indebted to Mr. Casella and
Mr. Hicks, who furnished me with details regarding the construction
of the instrument.

Its chief advantage consists in its furnishing us with a mercurial
minimum thermometer, no serviceable instrument of this description
having hitherto been made. At the same time it is also capable of
being used as a mercurial maximum thermometer.

The principle of the instrument is briefly as follows : —

It has a cylindrical bulb nearly 3^ inches long and half an inch in
diameter, filled with mercury. This gives a bore nearly ^th of an inch
wide, and a scale on which 1° Fahr. corresponds to about ^th of
an inch. When the graduation has reached 150° Fahr. or so, both
the tube and the scale are made to assume a position at right angles
to that which they occupied previously, so that the first portion of
the thermometer being vertical, the second will be horizontal. The
numbers on the horizontal scale are not, however, hi continuation of
those on the vertical ; for in the instrument from which this account
is taken, while 150° is the highest division on the vertical scale, the
first on the horizontal is —10°, the next 0°, the 3rd 10°, and so on.
The reason of this method of graduation will immediately appear.

Above the mercury there is a small quantity of spirits of wine
which extends some distance into the horizontal tube. The quantity
of this, and the graduation, correspond in such a manner, that the
extreme end of the spirit column denotes the same degree of tem-
perature as the mercury. The remainder of the horizontal tube is
filled with air. There are two moveable indices in the spirit column,
one in the vertical tube, the other in the horizontal, each about half
an inch long. The former, B, consists of a fine steel magnet enclosed
in glass. This forms the body of the index. At either extremity there
is a head of black glass, similar to that which occurs in the index
of an ordinary minimum thermometer. A fine hair is tied round
the neck of this index, between the body and the upper head ; and
it is made to hang down by the side, so that by its elastic pressure
against the tube, the index may be kept in its place, notwithstand-
ing its verticality. The index in the horizontal tube A, is in all
respects similar to that of an ordinary minimum thermometer.

Let us now suppose the instrument fixed in its position, the first
part of the stem being vertical. In order to adjust it, we must first
bring the vertical index into contact with the upper extremity of the
mercurial column. To do this, let us take two small but strong
horseshoe magnets, and lay the one above the other, so that the poles
of the one shall overlap to a small extent the corresponding poles of

On a Maximum and Minimum Mercurial Thermometer. 229

Bl

t>

the other. Bring the mag-
nets up to the index in such a
manner, that, while the poles
of the one bear against the
side of the glass tube, the
overlapping poles shall lie over
the tube so as to be in front
of the index : the index will
now follow the motion of the
magnets, and it may thus be
brought down to the surface
of the mercury. In order to
bring the horizontal index to
the extremity of the spirit
column, all that is necessary
is to incline the horizontal
tube a little downwards by
pressing on the end.

The indices being now set
and the instrument in adjust-
ment, let us suppose the tem-
perature to rise ; the mercurial

column will push the vertical index up, but this index will remain in its
place when the mercury again falls, and will therefore denote the
maximum temperature reached. On the other hand, let us suppose
the temperature to fall. "The mercury in falling is followed by the.
spirit column propelled by the air behind it. The spirit column, again,
will, on its edge coming in contact with the end of the horizontal index
draw the index with it into a position, where it will remain when
the mercury again rises. This index will therefore register the
extreme minimum point which the spirit column has reached ; but,
by the principle of graduation, this will correspond with the mini-
mum point reached by the mercurial column.

Let us now suppose that a small portion of the spirit column has
become separated, and lodged itself in the extremity of the tube.
The principle of graduation will immediately enable us to discover
this, by a want of correspondence being produced in the readings
of the mercurial and of the spirit column. If, for instance, before
the separation, the mercury read 50°, and the horizontal extremity
of the spirit column also 50°, it is clear that, after the abstraction
of spirits has taken place, the horizontal column will read lower.

We have thus a check upon this possible source of error, which
we have not in the ordinary minimum thermometer. Indeed, it is to
all intents a mercurial minimum thermometer that we are now de-
scribing, the spirits serving merely as a vehicle for the indices. It
will be remarked, that were both columns capable of acting in a hori-
zontal position, there would be no necessity for the bend, and the
instrument would be more portable ; but in this position it is found
that there is danger of the spirits becoming mixed with the mercury,
and thus interfering with the action of the instrument. Should this
ever be brought about by travelling, or any other cause, a smart jerk

230 Royal Society .— -

or two of the instrument will join the separated columns and put all
right.

The instrument is thus constructed : — The vertical tube, including
the bulb, is first made and filled with mercury to the proper height,
and the magnetic index is introduced ; then the horizontal tube is
joined, and the spirits of wine and the horizontal index are introduced.
The bulb is then placed in a freezing mixture, in order that the
mercury may retreat as far as possible, followed by the spirits
of wine. The tube is then sealed, care being taken that the bore
shall end in a small rounded chamber; for if pointed, some of the
spirits would be apt to lodge there, whence it would be difficult to
remove it. The object of cooling the bulb before sealing off, is that
we may have as much air in the tube as possible ; for its pressure, as
already mentioned, enables the spirits to follow the mercury when
the latter falls.

To graduate the instrument, set it with the mercurial stem hori-
zontal in melting ice, then point off the extremity of the mercurial,
and also of the spirit column as corresponding to 32° Fahr. Perform
a similar operation in water at 42°, 52°, 62°, &c.,and also in freezing
mixtures down to zero, or lower if necessary.

In conclusion, if used as a wet-bulb thermometer, this instrument
will give us the maximum and minimum temperatures of evaporation
obtained under precisely the same circumstances.

" On the Expansion of Metals and Alloys." By F. Crace-Calvert,
Esq., F.R.S., and G. Cliff Lowe, Esq. #

One of us having been engaged for some time in investigating
several of the properties of pure metals, it was thought desirable to
take advantage of having pure metals at our disposal, together with
a series of definite alloys of those metals, to determine their rate of
expansion. And we were encouraged in pursuing this course of
investigation, by finding that several of the authors who had pre-
viously published tables of the expansion of metals differed widely
in their results. These discrepancies, having reference to some of
the metals most extensively used, might, we thought, be due either
to the method employed, or to the fact that metals of different de-
grees of purity had been experimented upon. Therefore, being sure
of the purity of the metals that we intended to employ, we had
recourse to a method the accuracy of which we trust will appear
satisfactory.

Owing to the difficulty of obtaining the metals in a pure state in
large quantities, we found it necessary to employ square bars, having
a length of 60 millimetres by 10 millimetres of diameter. We
therefore devised a process to determine with accuracy the expansion
of such short bars. This, we believe, we have effected, as our appa-
ratus will easily indicate an expansion amounting to the 50,000th of
an inch, or about the 2000th part of a millimetre.

Omitting the description of our apparatus and of the details of
our operations, which would be long for this abstract of our results,
we give here a Table of the general results obtained with the fol-
lowing metals : —

Messrs. Crace-Calvert and Lowe on, the Expansion of Metals. 231

Mean for 100° C.

Divisions of the scale read r»- • • e ^
off in 25,000ths of an Dm"on» of SJ\me 8fca,e
inch in arising tempe- l^f'Z C°°ling ^
rature from 10° to 90°. 9° t0 10 ■

calculated from
these means and
corrected for ex-
pansion of ves-
sel, &c, by
deducting 20.

1st.

2nd.

3rd.

Mean.

1st.

2nd.

3rd.

Mean.

Cadmium 174

171

172

172-3176

173

172

173-7

196-2

155
142
120

156
142
120

157
145
120

156 1
143 1
120 1

61
47
22-5

160
148
121

159
147
122

1600
147-3
121-8

177-5
161-5
131-1

Tin

Aluminium

Forged zinc J119

121

120

120 1

20

119

120

119-7

129-8

Silver

110
106

109
105-5

109-5
106

109-5 1
105-8 1

11-5
03

110
1035

110
107

110-5
104-5

117-5
111-4

Copper (pure) cast

Copper (pure) 1
hammered... J

99

99

99

99 1

01

99

100

100

104-4

Gold

81
78
69

80-5

77

72

"it*

73

80-7
775
71-3

81-5
81-5
73-5

81
80
72

"80 '
72-5

81-3
80-5
72-7

81-3
78-8
70-0

Wrought iron

67
66-5

68-5
62-0

68-5
63

68-0
63-8

68
66-5

70-5
65

70-5
66-5

69-7
66

66-1
61-1

Steel (soft)

63
57-5

62

62-5
57-5

63

58

62

62-5

58-0

58-1
52-2

coefficients of linear expansion from 0° to 100°: —

Cadmium (pure)

0-00332

Lead (pure)

0-00301

Tin (pure)

0-00273

Aluminium (commercial)

0-00222

0-00220

Silver (pure)

0-00199

Gold (pure)

0-00138

Bismuth (pure)

0-00133

Wrought iron

0-00119

Cast iron

0-00112

Steel (soft)

0-00103

Antimony (pure)

0-00098

Platinum

(cor

nmer

cial)

0-00068

On comparing these coefficients with those found by previous ex-
perimenters, we find that they agree very closely in those cases where
commercial metals have been employed. But when we come to those
metals which we employed in a pure state, such as lead, tin, zinc,
silver, copper, bismuth, antimony, cadmium, and gold, we find a
marked difference, which we attribute to our experiments having
been made with pure metals ; and we are confirmed in this view by
several series of experiments made with impure or commercial
metals.

We give in our paper several series of experiments which prove

232

Royal Society :-

that, as for conductibility of heat by bodies, their molecular condi-
tion exercises the greatest influence on their expansion. For ex-
ample, we have found that the same bar of steel gives, according to
its degree of tempering, the following ratios of expansion : —

Raising temperature from
10° to 90°.

Cooling temperature from
90° to 10°.

Mean calculated

and corrected

for a bar 60 mm.

for 100°.

1st.

2nd.

3rd.

Mean.

1st.

2nd.

3rd.

Mean.

Steel bar as pur- "1
chased /

Ill

112

111-5

111-5

113

113

115

113-7

64-6

Steel bar at |

maximum of I
softness J

107

108

1075

107-5

107

112

111

110

62-5

Same bar at "|

maximum of >
hardness J

141

145

140

142

138

139

139

138-7

84-0

The influence of the molecular state of bodies is also clearly illus-
trated in the class of compounds or carbonates of lime : —

Chalk

Lithographic stone
Stalactite
Marble .

Rates of expansion
from 0° to 100°.

19*6
45-0
67*0
71-0

Influence of Crystallization.

Crystallization influences the expansion of bodies as it does their
power to conduct heat ; thus, the same zinc cast horizontally or ver-
tically has not only a different crystallized structure, but also expands
in a different ratio.

Raising temperature
10° to 90°.

Cooling temperature
90° to 10°.

Mean for
100° less
correc-
tion.

1st. I 2nd.

3rd.

4th.

Mean.

1st.

2nd.

3rd. Mean.

Zinc cast vertically

Zinc cast hori- Y

zontally /

224
187

226
186-5

227

187

226

226

186-8

232
190-5

233
193

I
234 j 233

192-5, 192

266-9
216-7

We have also examined the ratio of expansion in several series of
alloys made in multiple and definite proportions, but shall give here
only one series as illustrating our results.

Prof. Thomson on the Measurement of Electrostatic Force. 233
Copper and Tin.

10° to 90°.

Mean
for 100° j
less cor-j
rection.

Mean for

100° less

correction.

1st.

2nd.

3rd.

Mean.

| 1st.

2nd.

3rd.

Mean.

5Sn 90-271
ICu 9-73/

127

124

124

125

136-2

129

124

126-5

138-1

4Sn 88-141
Cu 11-86/

3Sn 84-791
Cu 15-21/

2Sn 78-791
Cu 21-21/

122

122

122-0

132-5

127

126

126-5

138-1

119

119-5

119-2

129-5

123

122

123-5

122-8

133-5

118

118

118

127-5

117

117

117

126-2

Sn 65-021
Cu 34-98/

109-5

111-5

110-5

1181 110-5

110-5

110-5

1181

Sn 48-171
2Cu 51-83/

111-0

111

111

118-7

113-5

112

112-7

120-8

Sn 34-21 1
3Cu 61-79/

112

111

111-5

119-3

113

112

112-5

120-6

Sn 31-731
4Cu 68-27/

Sn 27-101
5Cu 72-90/

Sn 15-681
lOCu 84-32/

102

105

103-5

109-3

106

105

105-5

111-8

104
101

104
101

104
101

110
106-2

106
101

106
101

106
101

112-5
106-2

Sn 11-03 1
15Cu 88-97/

95

94-5

94-7

98-3

94-5

95

94-7

98-3

Sn 8-51 1
20Cu 91-49/

97

99-5

98-2

102-7

99

99

99

103-7

Sn 6-83 1
25Cu 93-17/

99

99

99

103-7

100

100

100

105

Feb. 23. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communication was read : —

" Measurement of the Electrostatic Force produced by a Daniell's
Battery." By Professor William Thomson, F.R.S.

In a paper U On Transient Electric Currents," published in the
Philosophical Magazine for June 1853, I described a method for
measuring differences of electric potential in absolute electrostatic
units, which seemed to me the best adapted for obtaining accurate
results. The "absolute electrometer" which I exhibited to the British
Association on the occasion of its meeting at Glasgow in 1855, was
constructed for the purpose of putting this method into practice,
and, as I then explained, was adapted to reduce the indications of
an electroscopic * or of a torsion electrometer to absolute measure.

The want of sufficiently constant and accurate instruments of the
latter class has long delayed my carrying out of the plans then set

* I have used the expression " electroscopic electrometer," to designate an
electrometer of which the indications are merely read off in each instance by a
single observation, without the necessity of applying any experimental process of
weighing, or of balancing by torsion, or of otherwise modifying the conditions
exhibited.

Phil Mag, S. 4. Vol. 20. No. 132. Sept. 1860. R

234 Royal Society : —

forth. Efforts which I have made to produce electrometers to
fulfil certain conditions of sensibility, convenience, and constancy,
for various objects, especially the electrostatic measurement of gal-
vanic forces, and of the differences of potential required to produce
sparks in air, under definite conditions, and the observation of natural
atmospheric electricity, have enabled me now to make a beginning of
absolute determinations, which I hope to be able to carry out soon in
a much more accurate manner. In the meantime I shall give a slight
description of the chief instruments and processes followed, and state
the approximate results already obtained, as these may be made the
foundation of various important estimates in several departments
of electrical science.

The absolute electrometer alluded to above, consists of a plaid
metallic disc, insulated in a horizontal position, with a somewhat
smaller plane metallic disc hung centrally over it, from one end of the
beam of a balance. A metal case protects the suspended disc from
currents of air, and from irregular electric influences, allowing a light
vertical rod, rigidly connected with the disc at its lower end, and sus-
pended from the balance above, to move up and down freely, through
an aperture just wide enough not to touch it. In the side of the
case there is another aperture, through which projects an electrode
rigidly connected with the lower insulated disc. The upper disc is
kept in metallic communication with the case.

In using this instrument to reduce the indications of an electro-
scopic or torsion electrometer to absolute electrostatic measure, the
insulated part of the electrometer is kept in metallic communication
with the insulated disc, while the cases enclosing the two instruments
are also kept in metallic communication with one another. A charge,
either positive or negative, is communicated to the insulated part of
the double apparatus. The indication of the tested electrometer is
read off, and at the same time the force required to keep the move-
able disc at a stated distance from the fixed disc below it, is weighed
by the balance. This part of the operation is, as I anticipated,
somewhat troublesome, in consequence of the instability of the equi-
librium, but with a little care it may be managed with considerable
accuracy. The plan which I have hitherto followed, has been to
limit the play of the arm of the balance to a very small arc, by
means of firm stops suitably placed, thus allowing a range of motion
to the upper disc through but a small part of its whole distance from
the lower. A certain weight is put into the opposite scale of the
balance, and the indications of the second electrometer are observed
when the electric force is just sufficient to draw down the upper disc
from resting in its upper position, and again when insufficient, to keep
it down with the beam pressed on its lower stop. This operation is
repeated at different distances, and thus no considerable error de-
pending on a want of parallelism between the discs could remain
undetected. It may be remarked that the upper disc is carefully ba-
lanced by means of small weights attached to it, so as to make it hang
as nearly as possible parallel to the lower disc. The stem carrying it
is graduated to hundredths of an inch ; and by watching it through a

Prof. Thomson on the Measurement of Electrostatic Force, 235

telescope at a short distance, it is easy to observe ^fofytik of an inch
of its vertical motion.

I have recently applied this method to reduce to absolute electro-
static measure the indications of an electrometer forming part of a
portable apparatus for the observation of atmospheric electricity.
In this instrument a very light bar of aluminium attached at right
angles to the middle of a fine platinum wire, which is firmly stretched
between the inside coatings of two Leyden phials, one occupying an
inverted position above the other, experiences and indicates the
electrical force which is the subject of measurement, and which
consists of repulsions in contrary directions on its two ends, pro-
duced by two short bars of metal fixed on the two sides of the
top of a metal tube, supported by the inside coating of the lower
phial.

The amount of the electrical force (or rather as it should be called
in correct mechanical language, couple) is measured by the angle
through which the upper Leyden phial must be turned round an
axis coincident with the line of the wire, so as to bring the index to
a marked position. An independently insulated metal case, bearing
an electrode projecting outwards, to which the body to be tested is
applied, surrounds the index and repelling bars, but leaves free
apertures above and below, for the wire to pass through it without
touching it ; and by other apertures in its sides and top, it allows the
motions of the index to be observed, and the Leyden phials to be
charged or discharged at pleasure, by means of an electrode applied
to one of the fixed bars described above. When by means of such
an electrode the inside coatings of the Leyden phials are kept con-
nected with the earth, this electrometer becomes a plain repulsion
electrometer, on the same principle as Peltier's, with the exception
that the index, supported by a platinum wire instead of on a pivot,
is directed by elasticity of torsion instead of by magnetism ; and the
electrical effect to be measured is produced by applying the electrified
body to a conductor connected with a fixed metal case round the
index and repelling bars, instead of with these conductors them-
selves.

This electrometer, being of suitable sensibility for direct comparison
with the absolute electrometer according to the process described
above, is not sufficiently sensitive to measure directly the electro-
static effect of any galvanic battery of fewer than two hundred cells
with much accuracy. Not having at the time arrangements for
working with a multiple battery of reliable character, I used a second
torsion electrometer of a higher degree of sensibility as a medium
for comparison, and determined the value of its indications by direct
reference to a Daniell's battery of from six to twelve elements in
good working order. This electrometer, in which a light aluminium
index, suspended by means of a fine glass fibre, kept constantly elec-
trified by means of a light platinum wire hanging down from it and
dipping into some sulphuric acid in the bottom of a charged Leyden
jar, exhibits the effects of electric force due to a difference of poten-
tials between two halves of a metallic ring separately insulated in its

R2

£36 Royal Society .•—

neighbourhood, will be sufficiently described in another communi*
cation to the Royal Society. Slight descriptions of trial instruments
of this kind have already been published in the Transactions of the
Pontifical Academy of Rome*, and in the second edition of Nichol's
Cyclopaedia (article Electricity, Atmospheric), 1860.

I hope soon to have another electrometer on the same general prin-
ciple, but modified from those hitherto made, so as to be more
convenient for accurate measurement in terms of constant units.
In the meantime I find, that, by exercising sufficient care, I can
obtain good measurements by means of the divided ring electro-
meter of the form described in Nichol's Cyclopaedia.

In the ordinary use of the portable electrometer, a considerable
charge is communicated to the connected inside coatings of the
Leyden phials, and the aluminium index is brought to an accurately
marked position by torsion, while the insulated metal case surround-
ing it is kept connected with the earth. The square root of the
reading of the torsion-head thus obtained measures the potential, to
which the inside coatings of the phials have been electrified. If,
now, the metal case referred to is disconnected from the earth and
put in connexion with a conductor whose potential is to be tested,
the square root of the altered reading of the torsion-head required
to bring the index to its marked position in the new circumstances
measures similarly the difference between this last potential and that
of the inside coatings of the phials. Hence the excess of the latter
square root above the former expresses in degree and in quality
(positive or negative) the required potential. This plan has not
only the merit of indicating the quality of the electricity to be tested,
which is of great importance in atmospheric observation, but it also
affords a much higher degree of sensibility than the instrument has
when used as a plain repulsion electrometer; and, on account
of this last-mentioned advantage, it was adopted in the comparisons
with the divided ring electrometer. On the other hand, the portable
electrometer was used in its least sensitive state, that is to say, with
its Leyden phials connected with the earth, when the comparisons
with the absolute electrometer were made.

The general result of the weighings hitherto made, is that when
the discs of the absolute electrometer were at a distance of twenty
hundredths of an inch, the number of degrees of torsion in the port-
able electrometer was 3*229 times the number of grains' weight
required to balance the attractive force ; and the number of degrees
of torsion was 7" 69 times the number of grains' weight found in
other series of experiments in which the distance between the discs
was thirty hundredths. According to the law of inverse squares of
the distances to which the attraction between two parallel discs is
subject when a constant difference of potentials is maintained between
themf, the force at a distance of fa of an inch would have been
•¥uT» according to the first of the preceding results, or, according to

* Accadcmia Pontificia dei Nuovi Lyncei, February 1857.
f See § 11 of elements of mathematical theory of electricity appended to the
communication following this in the ' Proceedings.'

Prof. Thomson on the Measurement of Electrostatic Force. 237

the second, *$fa of the number of degrees of torsion. The mean of
these is .^L, or 1*2 ; and we may consider this number as represent-
ing approximately the value in grains' weight at -fa of an inch
distance between the discs of the absolute electrometer, correspond-
ing to one degree of torsion of the portable electrometer. By com-
paring the indications of the portable electrometer with those of
the divided ring electrometer, and by evaluating those of the latter
in terms of the electromotive force of a Daniell's battery charged
in the usual manner, I find that 284 times the square root of the
number of degrees of torsion in the portable electrometer is approxi-
mately the number of cells of a Daniell's battery which would pro-
duce an electromotive force (or, which is the same thing, a difference
of potentials) equal to that indicated. Hence the attraction between
the discs of the portable electrometer, if at -fa of an inch distance, and
maintained at a difference of potentials amounting to that produced by
284 cells, is 1*2 grain. The effect of 1000 cells would therefore be
to give a force of 14*9 grains, since the force of attraction is propor-
tional to the square of the difference of potentials between the discs.
The diameter of the opposed circular areas between which the attrac-
tion observed took place, was 5*86 inches. Its area was therefore * 187
of a square foot, and therefore the amount of attraction per square
foot, according to the preceding estimate for -fa of an inch distance
and 1000 cells' difference of potential, is 79' 5 grains. To reduce
the statement to consistent units founded on a foot as the unit of
length, we may suppose, instead of j1^ of an inch, the distance
between the discs to be j4» of a foot. We conclude that, with
an electromotive force or difference of potentials produced by 1 000
cells of Daniell's battery, we find for the force of attraction 55*3
grains per square foot between discs separated to a distance of y-J-g-
of a foot,

This result differs very much from an estimate I have made ac-
cording to my theoretical estimate of 2,500,000 British electro-
magnetic units for the electromotive force of a single element of
Daniell's and "Weber's comparison of electrostatic with electro-mag-
netic units. On the other hand, it agrees to a remarkable degree of
accuracy with direct observations made for me, during my absence
in Germany, by Mr. Macfarlane, in the months of June and July
1856, on the force of attraction produced by the direct application
of a miniature Daniell's battery, of different numbers from 93 to 451
of elements, applied to the same absolute electrometer with its discs
at '079 of an inch asunder. These observations gave forces varying,
on the whole, very closely according to the square of the number of
cells used ; and the mean result reduced according to this law to
1000 cells was 23#4 grains. Reduciug this to the distance y^y
of a foot, and dividing by "187, the area in decimal of a square foot,
we find 54*3 grains per square foot at a distance of y-J-g- of a foot.

Although the experiments leading to this result were executed with
great care by. Mr. Macfarlane, I delayed publishing it because of the
great discrepance it presented from the estimate I deduced from
Weber's measurement, which was published while my preparations

I

238 Royal Society.

were in progress. I cannot doubt its general correctness now, when
it is so decidedly confirmed by the electrometric experiments I have
just described, which have been executed chiefly by Mr. John Smith
and Mr. John Ferguson, working in my laboratory with much ability
since the month of November. I am still unable to explain the
discrepance, but it may possibly be owing to some miscalculation I
have made in my deductions from Weber's result.
Glasgow College, Jan. 18, 1860.

Postscript, April 12, 1860.
I have since found that I had inadvertently misinterpreted
Weber's statement in the ratio of 2 to 1. I had always, as it
appears most natural to me to do, regarded the transference of nega-
tive electricity in one direction and of positive electricity in the other
direction, as identical agencies, to which in our ignorance as to the
real nature of electricity we may apply indiscriminately the one
expression or the other, or a combination of the two. Hence I have
always regarded a current of unit strength as a current in which the
positive or vitreous electricity flows in one direction at the rate of a
unit of electricity per unit of time; or the negative or resinous
electricity in the other direction at the same rate ; or (according to
the infinitely improbable hypothesis of two electric fluids) the
vitreous electricity flows in one direction at any rate less than a unit
er second, and the resinous in the opposite direction at a rate equal
o the remainder of the unit per second. I have only recently
remarked that Weber's expressions are not only adapted to the
hypothesis of two electric fluids, but that they also reckon as a cur-
rent of unit strength, what I should have called a current of strength 2,
namely a flow of vitreous electricity in one direction at the rate of a
unit of vitreous electricity per unit of time, and of the resinous
electricity in the other direction simultaneously, at the rate of a unit
of resinous electricity per unit of time.

Weber's result as to the relation between electrostatic and electro-
magnetic units, when correctly interpreted, I now find would be in
perfect accordance with my own results given above, if the electro-
motive force of a single element of the Daniell's battery used were
2,140,000 British electro-magnetic units instead of 2,500,000, as
according to my thermo-dynamic estimate. This is as good an agree-
ment as could be expected when the difficulties of the investigations,
and the uncertainty which still exists as to the true measure of the
electromotive force of the Daniell's element are considered. It must
indeed be remarked that the electromotive force of Daniell's battery
varies by two or three or more per cent, with variations of the solu-
tions used ; that it varies also very sensibly with temperature ; and
that it seems also to be dependent, to some extent, on circumstances
not hitherto elucidated. A thorough examination of the electro-
motive force of Daniell's and other forms of galvanic battery, is an
object of high importance, which it is to be hoped will soon be at-
tained. Until this has been done, at least for Danielle battery, the
results of the preceding paper may be regarded as having about as
much accuracy as is desirable.

Geological Society. 239

I may state therefore, in conclusion, that the average electromotive
force per cell of the Daniell's batteries which I have used, produces a
difference of potentials amounting to '0021 in British electrostatic
measure. This statement is perfectly equivalent to the following in
more familiar terms : —

One thousand cells of Daniell's battery, with its two poles connected
by wires with two parallel plates of metal y^jth of a foot apart and
each a square foot in area, produces an electrical attraction equal to
the weight of 55 grains.

GEOLOGICAL SOCIETY.

[Continued from p. 166.]

May 16, 1860. — L. Horner, Esq., President, in the Chair.

The following communication was read : —

" On the co-existence of Man with certain Extinct Quadru-
peds, proved by Fossil Bones, from various Pleistocene Deposits,
bearing Incisions made by sharp instruments." By M. E. Lartet,
For.M.G.S. In a Letter to the President.

The author, having for some time past made observations upon fossil
bones exhibiting evident impressions of human agency, was requested
by the President, who had examined the specimens indicated, to
communicate the results of his researches to this Society.

The specimens referred to are : — 1st, fragments of bones oi Aurochs
exhibiting very deep incisions, made apparently by an instrument
having a waved edge ; 2ndly, a portion of a skull of Megaceros hiber-
nicus, bearing significant marks of the mutilation and flaying of a re-
cently slain animal. These wrere obtained from the lowest layer in
the cutting of the Canal de l'Ourcq, near Paris, and have been figured
by Cuvier in his ' Ossem. Foss.' Molars of Elephas yrimigenius
found in the same deposit are figured by Cuvier, who states that
they had not been rolled, but had been deposited in an original and
not a remanie deposit. 3rdly. Among bones, with incisions, from the
sands of Abbeville, are a large antler of an extinct stag (Cervus So-
menensis) and several horns of the common Red-Deer. 4thly. Bones
of Rhinoceros tichorhinus from Menchecourt, near Abbeville, where
flints worked by human hands have been found. 4thly. Portions of
horns of Megaceros from the British Isles. In reference to the re-
mains of the Gigantic Deer, M. Lartet alludes to the Rev. J. G.
Cumming's statement that »tone implements have been found in
the Isle of Man imbedded with remains of the Megaceros, and that
hatchet- marks have been seen on an oak-tree in a submerged forest
of possibly still older date. 5thly. Fragments of bone collected by M.
Delesse from a deposit near Paris, and exhibiting evidence of having
been sawn, not with a smooth metallic saw, but with such an in-
strument as the flint knives or splinters, with a sharp chisel- edge,
found at Abbeville would supply.

If, says the author, the presence of worked flints in the gravel
and sands of the valley of the Somme have established with certainty
the existence of man at the time when those very ancient deposits

240 Geological Society : —

were formed, the traces of an intentional operation on the bones of
Rhinoceros, Aurochs^ Megaceros, Cervus Somenensis, &c. supply
equally the inductive demonstration of the contemporaneity of those
species with the human race. M. Lartet points out that the Aurochs,
though still existing, was contemporaneous with the Elephas jnimi-
genius, and that its remains occur in preglacial deposits, and, in-
deed, that a great proportion of our living Mammifers have been
contemporaneous with E. primiyenius and R. tichorhinus, the first
appearance of which in Western Europe must have been preceded
by that of several of our still existing quadrupeds.

The author accepts M. d'Archiac's determination of the period of
the separation of England from the Continent as having been ante-
rior to the formation of the ancient alluvium or "loess," but subse-
quent to the great rolled gravel-deposits in which the flint hatchets
of a primitive people are found. If M. E. de Beaumont's hypothesis
of these gravels being due to the last dislocation of the Alps be
accepted, the worked flints carried along with the erratic pebbles
afford a proof of the existence of man at an epoch when Central
Europe had not yet fully received its present geographical features.

The author also remarks that though there is good evidence of
changes of level having occurred since man began to occupy Europe
and the British Isles, yet they have not amounted to catastrophes so
general as to affect the regular succession of organized beings.

Lastly, M*. Lartet announced that a flint hatchet and some flint
knives had lately been discovered, in company with remains of
Elephant, Aurochs, Horse, and a feline animal, in the sands of the
Parisian suburb of Grenelle, by M. Gosse, of Geneva.

May 30, I860.— L. Horner, Esq., President, in the Chair.

The following communication was read : —

" On certain Rocks of Miocene and Eocene age in Tuscany,
including Serpentine, accompanied by Copper-ore, Lignite, and
Alabaster." By W. P. Jervis, Esq., F.G.S.

Three distinct eruptions of serpentinous igneous rocks have been
recognized by the Italian geologists ; two are considered to have
occurred in Tertiary times, and one previously in the mesozoic period ;
dykes of diorite (also of Tertiary age) are more rare in the same
geographical area. From the abundant occurrence of these eruptive
rocks, and the extensive development of Miocene strata, unknown
in England, arise many specialities of Tuscan geology and mineralogy.
1st. The diallagic serpentine has pierced the Upper Cretaceous beds,
but does not enclose any fragments of Tertiary rocks. It is non-
metalliferous, and is employed in architecture. 2ndly. The eupho-
tide or " granitone " is unfit for building-purposes. The con-
tact of this with the diallagic serpentine has metamorphosed the
latter into the curiously marked " llanocchiaja." At Matarana
(Liguria) the crystals of diallage in the euphotide gradually decrease
in size towards the junction with the serpentine. 3rdly. Diorite,
penetrating the euphotide, and, like it, belonging to the Eocene
age. This and the serpentine acting on the" Macigno" has pro-
duced the "Gabbro rosso." 4thly. " Gabbro verde," or serpentine,

On certain Rocks in Tuscany of Miocene and Eocene Age. 241

without diallage, of Miocene age. This i3 much softer than the
diallagic serpentine. It forms dykes ; but more generally it is the
axial nucleus of hills and mountains, the strata of which are much
disturbed. In most cases the serpentine rocks, piercing the sedi-
mentary strata, have upheaved them from all sides : for this remark-
able species of axis the author proposes the term vericliml, indicating
that the strata fall off in every direction. It is frequently rich in
copper-ores at its junction with the metamorphosed schists or Gabbro
rosso ; here also several zeolites, all containing magnesia (from 1*11
to 1350 per cent.), abound; and limpid calcite in extremely obtuse
rhombohedral crystals occurs. The limestones are often altered by
the serpentine into dolomite (Miemmite), and are otherwise vari-
ously affected. Near Matarana a mouse- coloured limestone is
changed (by the alteration of the carbonate of iron to a peroxide) into
a brick-red marble, often brecciated and veined with serpentine and
calc-spar (" Ofiocalce"). The copper-ores (chalcopyrites, bornite,
oxide of copper, grey copper, native copper) at Monte Catini occur
in nodules or boulders enveloped in the serpentine, as though they
had been brought up simultaneously. Chalcedony abounds in the
serpentine north of Monte Verdi, where it occurs in large veins, and
is occasionally brecciated. Black flint, jasper, agate, waxy opal,
&c, are not uncommon.

Pure alabaster appears to be peculiar to Western Tuscany. It
occurs in ovoidal masses, often 3 feet in diameter, in selenitic
marls of Miocene age in the Val di Marmolajo. Coloured alabaster
is also found in some of the Pliocene beds of Tuscany. Gypsum is
widely distributed where serpentine has pierced limestones, as at
Matarana and Jano.

At Jano the palaeozoic coal is represented by isolated plants con-
verted into anthracite ; it is the only locality on the Italian continent
where Carboniferous fossils have been found ; but Miocene lignites
are abundant in Italy. At Sarzanello in Piedmont, 6& feet of
miocene coal occurs. This is used in the Sardinian steam-navy.
At Castiani, in the Maremme, good lignite, 3 feet 4 inches thick,
is worked ; and at Monte Bamboli, also in Tuscany, one bed,
4 feet 2 inches, and another, 2 feet thick, have long been in use.

June 13, 1860. — L. Horner, Esq., President, in the Chair.

The following communication was read.

" On the Ossiferous Caves of the Peninsula of Gower, in Gla-
morganshire, South Wales." By H. Falconer, M.D., F.R.S., F.G.S.
With an Appendix, on a Raised Beach in Mewslade Bay, and the
occurrence of the Boulder-clay on Cefn-y-bryn; by J. Prestwich,
Esq., F.R.S., Treas.G.S.

The object of this communication was to give a summary of re-
searches made during the last three years by the author and Lieut.-
Col. E. It. Wood, F.G.S., the latter of whom has carefully explored
at his own charge, since 1848, some of the caves previously known,
as well as several discovered by himself. The known bone-caves of
Gower (of which Paviland, Spritsail Tor, and Bacon Hole have
already supplied Dr. Buckland and others to some extent with ma-

242 Geological Society : —

terials for the history of the Cave-period) are in the Carboniferous
Limestone ; and, with the exception of that of Spritsail Tor, which
is on the west coast of the peninsula, they all occur between the
Mumbles and the Worm's Head. The most important are " Bacon
Hole," "Minchin Hole," " Bosco's Den," "Bowen's Parlour,"
"Crow Hole," '* Haven's Cliff Cavern," and lastly the well-known
"Paviland Caves." Bone-caves at the Mumbles, in Caswell Bay,
and in Oxwich Bay formerly existed; but the sea has destroyed
them. One cavern named "Ram Tor" between Caswell Bay and
the Mumbles, presumed to be ossiferous, remains unexplored.

Before proceeding to describe the bone-caves and their contents,
the author briefly noticed a raised beach and talus of breccia, which
Mr. Prestwich had lately traced for a mile along Mewslade Bay,
westward of Paviland ; and he pointed out their important relation-
ship to the marine sands and overlying limestone-breccia found in
several of the Gower Caves. Dr. Falconer also referred to Mr.
Prestwich's recent discovery of some patches of Boulder-clay on the
highland of Gower, and in Rhos Sili Bay.

" Bacon Hole " was first treated of. Jt has been worked out by
Colonel Wood, and described by Mr. Starling Benson. On the
limestone-floor of the cave are : — (1) a few inches of marine sand,
abounding with Litorina rudis, L. litoralis, and Clausilia nigricans,
with bones of an Arvicola and Birds ; (2) a thin layer of stalagmite;
(3) two feet or less of blackish sand, containing a mass of bones of
Elephas antiquus, with remains of Meles tawus and Putorius (vul-
garis}); (4) one to two feet of ochreous cave-earth, limestone-breccia,
and sandy layers, with remains of Elephas antiquus, Rhinoceros hemi-
toechus, Hycena, Canis lupus, Ursus spelceus, Bos, and Cervus; (5)
irregular stalagmite, partly enveloping a huge tusk of an Elephant
imbedded below it ; (6) limestone-breccia and stalagmite, from 1
to 2 feet thick, with bones of Ursus and Bos; (7) irregular bed of
stalagmite, 1 foot or more, with Ursus ; (8) dark-coloured super-
ficial earth, kept soppy by abundant drip, with bones of Bos, Cervus,
Canis vulpes, horns of Reindeer and Roebuck, together with shells
of Patella, Mytilus, Purpura, Litorina (probably brought into the
cavern as food by birds), and also pieces of ancient British pottery.
The marine sand at the bottom of tl Bacon Hole " was analogous to
that on the rocky floor of the San Ciro Cave, near Palermo ; but
contained fewer species of Mollusca. The uppermost layer of sta-
lagmite is about 30 feet above high water. The Elephant-remains
belonged to at least three individuals, one of which was adult, and
one young with milk-dentition.

"Minchin Hole" is the grandest and most spacious of all the
Gower Caves, being 1 70 feet long, by 70 feet where widest, and
35 feet high at the entrance; here the section gave — (1) Loose
limestone- breccia, 3 feet; (2) Yellow cave-earth, 9 inches; (3)
Sand, 1 foott (4) Blackish sandy loam containing abundant remains
of Rhinoceros, Elephas, and Bos, 2\ feet; (5) Greyish-yellow ma-
rine sand, varying in thickness from 1 to 4 feet, and resting on the
rocky floor. Some of the lower jaws of Rhinoceros from this deposit
exhibit Litorina and comminuted shells imbedded in the encrusting

On the Ossiferous Caves of the Peninsula of Gower. 243

matrix : and the black sand yielded Helix hispida similarly attached.
In the interior, the cave-earth was thicker, and the black sandy
loam more unctuous. The mammalian remains were closely analo-
gous with those from Bacon Hole ; but the Elephant remains (E.
antiquus) were fewer, and those of Rhinoceros hemitccchus were more
numerous and better preserved, including two skulls. No remains
of Elephas primigenius or of Rhinoceros tichorhinus were met with
in Bacon Hole or Minehin Hole.

" Bosco's Den " is a cavernous fissure, of great interest, between
" Bacon Hole " and " Minehin Hole." It is about 70 feet high,
and has been worked out by Col. Wood, who, having succeeded in
reaching a hole called (by the quarrymen) " Bacon's Eye," found it to
be an angular opening (2^ feet in diameter) at the top of one of the
great vertical fissures in the limestone, and leading into a fine cavern.
Beneath it the fissure was filled up with a mass of angular fragments
of limestone (with bones, teeth, and land shells) impacted in ochreous
loam, about 20 feet in height, resting on a solid platform of breccia,
beneath which the fissure had to a great extent been washed out by
the sea. On enlarging the aperture, by undermining the projecting
mass of loam and breccia, a cavity was found extending 76 feet
backwards, with a width of from 7 to 16 feet, and a general height
of about 15 feet. A line of fissure runs along the angle of the roof,
and towards the outer part of the cavern the crack widens into an
irregular flue, which had evidently communicated with the surface :
here the cavern rises to a height of 40 feet. When first opened,
the eastern wall only of the cavern was found to be coated with
stalagmite. The floor was tolerably smooth, and shelved down gra-
dually from the mouth to the extremity, the deposits being thicker
outwards. The floor having been excavated down to the hard brec-
cia, there were observed: — (1) at the top, a bed of sandy peat or
turf, formed chiefly of bits of sticks and comminuted vegetable mat-
ter, about 1 foot thick, except under the flue, where it formed a low
conical heap. In or on this peaty covering were bones of Ox and
Wolf, and bones and broken shed antlers of Deer, of species or
varieties allied to the Reindeer {Cervus Guettardi and Cerv. priscus).
(2) Stalagmite, regular, but usually less than a foot thick. At
one spot it rose into a boss 2 ft. 3 in. high, which was found in a
shattered condition, the fragments being loose, but still in place.
This must indicate — 1st, the operation of some shock since the for-
mation of the stalagmite, and even since the peat began to be
formed ; and 2ndly, the absence of drip in the cave since the shock
took place. (3) Sandy loam, 1 ft. 4 in, with fragments of rock
and without bones ; (4) sand, 2 ft. 6 in. ; (5) a bed of loose stony
breccia, 4 feet, without bones ; (6) ochreous loam, or the usual
cave-earth, 6. to 7 feet thick, resting on the solid cemented breccia
which forms a floor or diaphragm between the upper and lower
chambers of the fissure. Ursus spelceus, Canis lupus, C. vulpes,
Bos, Cervus, and Arvicola occur in the loam, the latter in abundance.
The most remarkable circumstance about these remains was the
great excess of Deers' antlers above the others. Upwards of one
thousand antlers, mostly shed and of young animals belonging chiefly

244 Geological Society : — #

to Cervus Guettardi, were collected. The lower chamber was pene-
trated by Col. Wood, Dr. Falconer, and a friend last September, and
found to have been washed out by the sea to a depth inwards of 3 1
feet; and at its extremity they met with a compact mass of marine sand
and gravel, about 9 feet thick. The solid breccia forming the roof
of the lower, and the base of the upper cave, increases in thickness
from 6 feet at the outside to a greater depth inwards. Its materials
correspond with the bed of angular debris observed by Mr. Prestwich
on the raised beach of Mewslade Bay.

" Bowen's Parlour," or " Devil's Hole," is also a cavernous fissure
in the limestone cliff, situated between Bosco's Den and Crow Hole.
It has been washed out by the sea ; portions only of its cave-deposits
remaining, especially a diaphragm of cemented breccia, which divides
the fissure into an upper and lower story ; the former about 20 feet
high at the mouth, the latter 14. Thin tabular aggregations of
sand adhere to the lower surface of the partition, showing that it
was deposited on a bed of sand. The same phenomena are repeated
in " Crow Hole " with modifications, the cave-deposits being still
in situ : here remains of Ursus, Meles, Rhinoceros, and some other
forms have been found by Col. Wood.

" Raven's Cliff" presents a cavernous fissure broad and high ex-
ternally, contracted within. Here a thin crust of stalagmite
formed a floor upon sand 9 feet thick, which filled the fissure close
up to the roof, leaving only an empty angular chamber about a
foot high above the stalagmite. Upon the latter, remains of
Mustela foina, Canis vulpes, and some Fish-bones and Bird-bones
were found. In the sand large coprolites of Carnivores, some fine
remains of Felis spelaa, bones of Rhinoceros, and the vertebrae
of a Fish were discovered. Below the sand, as usual in the Gower
Caves, there was a sandy breccia cemented by stalagmite, about
a foot thick. Upon it a large block of limestone, smoothed and
polished, probably by the rubbing of passing cave-animals, was
discovered ; and patches of polished surface were seen on the walls of
the cave. Remains of Elephas, Rhinoceros, Bos, and Cervus were
met with above the breccia. Below the breccia was a bed of dark-grey
gritty sand, indurated by calcareous infiltration, and attaining a maxi-
mum thickness of about 8 feet. In this sand, and close upon the
rock-floor, teeth of Hippopotamus major, young and old, and remains
of Ursus, Cervus, and Arvicola, were met with. There was evidence,
on the cliff beyond the aperture, of the cave and its contents having
formerly been continued further seawards.

The author pointed out that in all these caves the bottom appears
to have been first filled with sea-sand or shingle, with which were
occasionally intermingled the bones of pachyderms, ruminants, &c,
then living on the emerged land of Gower ; that when this deposit
was elevated above high-watermark, stalagmite and angular debris
of limestone rock formed a floor, on which subsequently cave-earth
or other common alluvial materials, with bones and antlers, often
in profusion, were accumulated through the fissure above, during a
long lapse of time after the rise had been accomplished. At last,
by a converse action, of comparatively modern date, the level of the

On the Ossiferous Caves of the Peninsula of Gower. 245

caves was depressed. The raised beach at Mewslade Bay, which
appears, according to the evidence of Mr. Prestwich, to be of later
date than the Boulder-clay, has without doubt partaken of changes
of level similar to what the caves and their contents have under-
gone, although, the marine deposits in the caves not being at a uni-
form level, either in relation to each other or to the raised beach, it
is probable that there have been locally unequal depressions of level
in comparatively modern times. The author thinks that the sea
has effected but a comparatively slight inroad on the cave- deposits
and raised beach ; and hence he infers that they belong to a rela-
tively modern epoch, — seeing also that they are probably of later
date than the Boulder-clay period, and rest on marine sands con-
taining existing species of shells.

Paviland Cave was next referred to ; but the author restricted his
remarks to the remains of Elephas primigenius and human bones that
were found in it, and argues that the latter (i. e. the skeleton of the
" Red Lady ") are of more recent date than the former.

In the cave at Spritsail Tor (cursorily examined by Sir H. De la
Beche, and thoroughly explored by Colonel Wood), under a stalag-
mitic bone-breccia, the irregular fissure of the rocky floor was im-
pacted with ochreous cave-earth full of bones and teeth of Elephas
antiquus, E. primigenius, Rhinoceros tichorhinus, E quits, Sus, Bos,
Cervus,Lepus, Arvicola, Mus, Ursus spelceus, U.priscusl)), Felis spelcea,
Hycena spelcea, Canis lupus, C. vulpes, Meles taxus, and Mustela.
Coprolites of Hycena, gnawed bones of Bos, Equus, and Cervus, and
a great abundance of the detached molars of horse, gave the cave the
undoubted character of having been a Hyaena's den. In the super-
ficial sand on the stalagmite, the antlers of a Reindeer and some
human bones were found.

General remarks on the distribution of the Mammalian remains in
the different caverns were offered, and the special anomalies pointed
out ; and, after a comparative review of the fauna of the Gower
bone-caves in relation with that of other cave- districts of England
in particular, and of Europe in general, the author arrived at the
following conclusions as being consistent with the existing state
of our knowledge : —

1 . That the Gower Caves have probably been filled up with their
mammalian remains since the deposition of the Boulder-clay.

2. That there are no mammalian remains found elsewhere in the
ossiferous caves in England and Wales referable to a fauna of a
more ancient geological date.

3. That Elephas (Loxodon) meridionalis and Rhinoceros Etruscus,
which occur in, and are characteristic of, the " Submarine forest
Bed " that immediately underlies the Boulder-clay on the Norfolk
coast, have nowhere been met with in the British caverns.

4. That Elephas antiquus with Rhinoceros hemitcechus, and E. pri-
migenius with Rh. tichorhinus, though respectively characterizing
the earlier and later portions of one period, were probably contem-
porary animals ; and that they certainly were companions of the
Cave-Bears, Cave-Lions, Cave-Hyamas, &c, and of some at least of
the existing mammalia.

[ 246 ]
XXIX. Intelligence and Miscellaneous Articles,

ON THE PERIODICITY OP THE SOLAR SPOTS, AND INDUCED
METEOROLOGICAL DISTURBANCES.

To the Editors of the Philosophical Magazine and Journal.

Gentlemen,

ASSUMING the mechanical energy exerted by the sun, as ex-
hibited in its heat, light, and magnetism, to be directly created
and sustained by the simplest yet grandest of the solar forces and
motions, viz. by the force exerted by the planetary bodies (through
gravity) acting upon the matter of the sun in rapid revolution around
its axis (producing, if that matter be in a solid or coherent state, a
violent and variable degree of tension, and if fluid, a violent agitation
in eddies or tides), — would it not be reasonable to suppose that the
orbital positions of the planets, especially at particular times, would
not be without an effect as a disturbing element in the physical
energy exerted by the sun itself ?

It might even be natural to suppose that when the principal or
larger mass of the planets are in (or nearly in) conjunction on
one side of the sun in their orbits, such a disturbance would take
place, owing to the centre of gravity of the solar system moving or
shifting its position within the body of the sun itself, from an in-
creased pull, or amount of attraction, exerted in one particular
direction. May not some such disturbance be even at this moment
taking place, and from this very cause ? We have Venus, Jupiter,
Saturn, and Uranus, all on one side of the sun, nearly in conjunc-
tion ; and we have likewise seen during the whole of the present year,
more or less, a great solar disturbance taking place, as proved by the
unusual number of spots that have been visible.

Schwabe has proved that there is a spot-period, of about 11*1
years from maximum to maximum ; and Col. Sabine, that this period
coincides again with a particular class of magnetic cycles. It would
indeed be a notable point gained to science, if the magnetic con-
dition or force of the sun itself could be shown to depend upon, or
possibly resolve itself into (as a correlated force), the force of gravi-
tation itself ! The most important thing then to ascertain is, whether
or not a certain position of the planets in their orbits does not tend
at certain times, through the force of gravitation, to create mag-
netical disturbance and increased mechanical energy in the sun?
Jupiter, as far the largest planetary mass, would naturally have a pre-
dominating effect, and would tend to regulate the period of pertur-
bation. Wolf, Carrington, and others have, I understand, already
considered as more than a coincidence, the Jovian period of nearly
12 years, as connected with the spot-period of 11*1 years, without,
however, arriving at any precise or definite results.

It would be desirable to ascertain how far the variations in the
belts and markings on Jupiter himself agree with the spot-periods of
the sun ; it is more than possible that a mutual connexion might be
traced.

Should the extremely cold, wet, and windy weather experienced

Intelligence and Miscellaneous Articles* 24*7

the last ten or eleven months in any way have arisen from solar
magnetic disturbance, which there is some reason perhaps for sup-
posing, and this, again, from the position of the planets above-named
in conjunction, there is reason to fear there may not be much
amelioration in our weather for some months to come, seeing that
Venus, Jupiter, and Saturn will remain some time longer in much
the same relative position.

M. Rudolph Wolf of Berne has shown that those years remark-
able for abundance of solar spots have also been more than com-
monly rich in aurora? boreales. The great auroral display at the
commencement of September 1859, occurring about the time for
the return of sun-spot maximum, and which seems to have been
visible over the greater portion of both hemispheres, appears to have
been the precursor of a great meteorological disturbance : in Eng-
land and Northern Europe more than an average amount of cold,
wind, and rain have prevailed ever since ; in North America and India
more than an average amount of drought and heat. The opinions
of philosophers differ respecting the influence of a paucity or an
abundance of solar spots upon the temperature and seasons of the
earth; the probability is, there is simply a general disturbance,
arising from increase of (solar) magnetic influence, which may pro-
duce greater heat and dryness in one part of the globe, and more
cold and rain in other parts.

I have merely hazarded these few remarks in the hope of drawing
further attention to such interesting and important topics.

Yours respectfully,
Manchester, 23rd August, 1860. Robert P. Greg.

ON THE PHENOMENA OF HEAT WHICH IN CERTAIN CASES ACCOM-
PANIES THE VIBRATORY MOTION OF BODIES. BY M. LE ROTJX.

The author observed that, in attempting to create a nodal line in a
body at a place at which it would not naturally be produced, there
is a disengagement of heat at this place, this being the form under
which the forces evoked by the vibratory motion manifest themselves.

The experiment may be made by clamping an elastic plate of any
material at some distance from one end, and presenting the other to
a toothed wheel. The heat produced is great enough to be per-
ceptible to the hand.

The same fact may also be observed by soldering a small piece of
brass to a steel spring, and then binding one end of the galvanometer
to the steel and the other to the brass. When the spring is made
to vibrate, the motion, which is obstructed at the place where the
brass is, creates an elevation of temperature which produces an
electric current.

It is important to compare this experiment with those of MM.
Sullivan and Ermann*. In Le Roux's experiment the place of the
soldering is not directly excited, and consequently all effects of
friction are eliminated. If his results appear to confirm those

"* De la Rive, Traite d'Electricite, vol. ii. p. 574.

248 Intelligence and Miscellaneous Articles.

obtained by these physicists, the author thinks that they do not
confirm their explanation, according to which the vibration com-
municated to the soldering of two heterogeneous bodies directly
produces an electric current. He thinks that the production of the
heat precedes that of the electric current. It is seen, on examina-
tion, how the existence of the current is connected with the vibration
— that the current ceases with the vibration, but not directly as if it
had been interrupted by cutting the wire.

It appears natural to consider the electric effect observed in these
experiments as a resultant of the heat disengaged at the surface of
contact of two heterogeneous bodies which tend to enter into a
common vibratory motion. — Comptes Rendus, vol.1, pp. 656, 729;
BibliotKeque Universelle, vol. viii. p. 151.

ON THE DENSITY OF ICE. BY M. L. DUFOUR.

The question of the density of ice is certainly not settled. The data
of different authors vary considerably, and even the latest researches
have not led to very concordant results. In 1807, Placidus Hen-
rich found this density to be 0*905 ; subsequently it was found by
Thomson to be 0*94; Berzelius, 0*916; Dumas, 0950; Osann,
0*927 ; Pliicker and Geissler, 0*920 ; C. Brunner, 0*918 ; and lastly,
H. Kopp, in 1855, found that it was 0*909. These divergencies,
expressed in the increase of volume at the moment of congelation,
correspond to values between ± and -fa.

In a series of researches on the congelation of water and of saline
solutions, the author has had occasion to investigate the density of
ice. The method which he has chosen, in order to avoid the serious
difficulties incident to the use of the ordinary methods in the case of
ice, consists in forming a liquid in which ice floats in equilibrium,
and then determining the density of this liquid. The liquid was a
mixture of water and alcohol, and all necessary precautions were
taken to avoid, as much as possible, sources of error. Preliminary
trials on bodies of known density showed that the method gave an
approximate value which was not more than 0*002 from the true.
The ice was quite free from air, and was obtained from distilled
water boiled for some time. The method gave a ready means of
determining the highest and lowest level of the density of each
specimen.

The details of the research are published in the Bibliotheque Uni-
versellede Geneve for June 1860. For the majority of the specimens
examined, 0*922 or 0*923 was certainly the highest, and 0*914 the
lowest limit of the density. Twenty-two experiments gave a mean
density of 0*9175 with a mean deviation of ± 0*0007. The greatest
deviations were + 0*002 and —0*0013.

The number 0*9175, which may be safely taken as giving the
density of ice at 0° C, is almost exactly that of C. Brunner
(0*9 180), which was obtained by a different method. This corre-
sponds to an increase of volume at the moment of congelation of
yj^, or very nearly Tir. — Comptes Rendus, June 4, 1860.

THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

♦

[FOURTH SERIES.]

OCTOBER 1860.

XXX. On the Electric Light of Mercury.
By J. H. Gladstone, Esq., Ph.D., F.R.8*

[With a Plate.]

PROFESSOR WAY has recently devised a plan by which a
brilliant electric light is produced in an interrupted current
of mercury. The metal is made to fall from a jet in a thin
stream into a cup, the jet being half an inch or thereabouts above
the surface of the metal in the cup. The upper reservoir and
the lower vessel are in connexion with the two wires of a Bun-
sen's battery. As the galvanic force traverses the thin stream
of mercury, it scatters and diffuses it in vapour with the produc-
tion of a most intense light. For obvious reasons the gaseous
mercury is confined in a well-closed glass cylinder ; and this is
made of sufficiently small diameter to become hot in the neigh-
bourhood of the electric flame, and thus prevent the condensa-
tion of the mercury on it.

"While inspecting this light about a year ago, I was struck by
the strange manner in which it modified the apparent colours of
surrounding objects, and especially with the ghastly purple and
green hues which it imparted to the faces and hands of the spec-
tators. This led me to a more careful examination and a pris-
matic analysis of the light itself. As these electrical flames are
attracting much attention at the present moment, the observa-
tions then made may prove of some interest as a contribution to
the general stock of facts.

Chevreul's "cercles chromatiques," when examined by this
mercury light, showed very little, if any, red, but the violet was
very luminous and distinct. Flowers, dyed wools, ribbons, &c.

* Communicated by the Author.
Phil. May. S. 4. Vol. 20. No. 133. Oct. 1860. S

250 Dr. Gladstone on the Electric Light of Mercury.

were generally altered in colour ; but the following substances of
known composition are more instructive in the contrast between
the colours they then exhibited and those they display by day-
light.

Crystals of protosulphate of iron appeared absolutely colour-
less instead of pale bluish green.

The blue sulphate of copper, and the yellow chromate of pot-
ash, were only enhanced in the brilliancy of their colours.

Bichromate of potash became of a yellow instead of a red-
orange, and dull instead of bright.

Red prussiate of potash showed a yellow powder, and dingy-
orange crystals.

Chloride of cobalt gave a dirty-brown instead of a pale-red
solution.

Nitrate of chromium, though in such strong solution as to
appear red by sunlight, was only dark dull green.

Amorphous phosphorus showed scarcely any red, or other
colour, but presented a dark metallic appearance.

Iodide of mercury was not scarlet, but of a brown colour, very
glistening, suggesting the idea of scales of tarnished silver.

Gold looked like brass.

Cochineal in aqueous solution appeared violet in a thin stra-
tum, red brown in a deep one.

A decoction of coffee with milk, as usually drunk, assumed a
dirty green hue.

A solution of bisulphate of quinine, uranium glass, and cer-
tain diamonds, exhibited the phenomena of fluorescence more
beautifully even than by sunlight.

Among substances that had much the same colour by daylight
and by the mercury flame, may be mentioned blue cobalt salts,
yellow nitrate of uranium green chlorophyll, and purple aniline-
dye, permanganate of potash and murexide.

On analysing this light by means of Prof. PowelPs refraction
goniometer, I found it to consist of a number of separate and
variously coloured rays. This appearance is represented in
Plate III. fig. 1, the angle of the prism being 45°. None of the
lines are of any appreciable breadth ; that is, they are only as
broad as the slit itself; but the more intense ones appeared
broader on account of irradiation, and of greater extent because
the slightly luminous environment of the spark gives a percept-
ible amount of these rays. These peculiarities of the pheno-
menon as actually observed are retained in the figure, because
they serve as a rough representation of the relative intensity of
the different rays ; but this is more correctly indicated by the
numbers affixed to the different lines : 1 denoting the brightest
lines, or those of the first magnitude ; 2 the next brightest, and

Dr. Gladstone on the Electric Light of Mercury, 251

so on. Fig. 2 represents the principal dark lines of the solar
spectrum, as seen by means of the same prism, and is introduced
to identify the positions of the luminous rays in fig. 1. The
following Table gives the angular measurements of the more im-
portant rays, those of Fraunhofer's lines being appended in a
separate Table : —

Colour.

Angular
measurement.

Magnitude.

Red

31° 8
31 24
31 26-5
31 27
31 32
31 35
31 35-5
31 46

31 49

32 1
32 6
32 9

32 47

33 11
33 15
33 22
33 31

33 38

34 10

8
5
6
7
4
1
1
1
4
6
3
3
1
3
2

Orange

Yellow

11
11
11
11

Green

n

ii
Blue

Violet

ii
11
ii
ii
ii

Angular

measurement.

A

3! 6

B

31 10

C

31 16

C6

31 23

D

31 32

E

31 54

b

31 59

F

32 13

G

32 51

G33

33 11

H

33 23

K

33 27

I

33 36

N

34 7

Whether the thin stream of mercury was longer or shorter,
whether the light was steady or intermittent, and whether it was
more or less brilliant, the relative intensity of these luminous
rays appeared the same, except as regards the most refrangible
ray, which varied considerably in visibility. This ray is situated
far beyond what is ordinarily considered the limit of the lumi-
nous spectrum, indeed at the utmost verge of the most refran-
gible light which I have been able to see with bright midsummer
sunshine and special arrangements for detecting it. It is evi-
dent, therefore, that this ray exists in the electric light of mer-
cury with an intensity vastly greater than it exhibits in the solar
beam ; and doubtless many objects (as cochineal) reflect or trans-
mit a colour when examined by this light, with which, under
other circumstances, we are unacquainted. It should be borne
in mind, moreover, that this ray, as observed through the refrac-
tion goniometer, had passed through several pieces of glass — a
medium which does not transmit freely the extra-violet rays. As
to its colour, it seems to differ considerably according to the in-
tensity ; and the eye is perhaps not a good judge of a colour
which, strictly speaking, it has never witnessed before. "When
bright, however, it may be best described perhaps as red- violet ;

S2

252 Dr. Gladstone on the Electric Light of Mercury.

but when seen through cobalt glass it appeared reddish grey, or
nearly colourless.

The prismatic analysis of this light explains at once the various
chromatic phenomena mentioned above. The brilliancy of the
yellow, blue, and violet rays accounts for the beautiful colour of
those objects which can reflect these rays ; while the feebleness
of the red shows the reason of the great changes which red sub-
stances invariably undergo — sometimes merely to brown, at other
times to purple, green, or whatever other colour in addition to red
is principally reflected by them. Thus the blood, wherever it
shows through the skin, as in the lips, appears of a bluish-purple
instead of a reddish hue. And this explains also why sulphate
of iron becomes perfectly colourless ; for the ordinary green tint
of this salt is due solely to its not transmitting with any freedom
the red rays : it transmits all others, and therefore all those
which prevail in the mercury-light. Hence it appears of the
same colour as the source of illumination itself, which the eye
ordinarily recognizes as white, though, as compared with the
sun, it is decidedly coloured.

On searching afterwards for previous observations on the light
of mercury, I found that Prof. Wheatstone, in his brief notice
" On the Prismatic Decomposition of Electrical Light/' in the
Report of the British Association for 1835, mentions the spec-
trum of mercury as containing seven definite rays ; but he does
not further describe it. Masson*, in his elaborate paper, does not
mention the light from mercury; neither does Eobiquetf, nor
Secchi %. Angstrom §, however, gives a drawing of the lines that
make their appearance in such a light. They agree closely with
the more intense lines of my drawing, but with this important
difference — that he has not figured any violet ray except the least-
refrangible one. Thus he never saw the beautiful rays about
and beyond H. In his investigation, the Swedish philosopher
made the notable discovery that the spectrum of an electric spark
is ordinarily composed of two distinct spectra — the one belong-
ing to the gas across which the spark leaps, the other to the
conducting metal or other body. By observing different metals
in different gases, he was able to distinguish these two spectra ;
and he gives drawings of the lines due to oxygen, nitrogen, &c.,
by a comparison of which with my map I find that the mercury
spectrum delineated by me is due solely to the gaseous metal,
and that no air was traversed by the electric spark in Professor

* Ann. de Chim. et de Phys. 3rd series, vol. xxxi. p. 295.
t Comptes Rendus, October 31, 1859.
X Nuovo Cimento, vol. i. p. 405.
§ Phil, Mag. S. 4. vol. ix. p. 327.

Researches regarding the Laws of Chromatic Dispersion. 253

Way's apparatus. Thus through his kindness I probably had
the advantage of examining a purer as well as a far more bril-
liant mercurial light than any previous observer.

Attention is being particularly directed at the present time to
the fact that the luminous bands of some artificial flames coin-
cide exactly with dark lines in the solar spectrum, and that cer-
tain flames absorb light of the same refrangibility as they emit.
With reference to the latter phenomenon, I have looked at
the double spectrum of the sun shining through the mercury
flame; but the rays from the metal were too intense to permit
of any evidence of absorption of the solar beams in the same
place. A glance at the preceding Table will show that a bright
line occurs in the spark of mercury as in many other artificial
lights just where D occurs in the solar spectrum ; another ray-
appears to have the same refrangibility as the most prominent
line between G and FT, namely G 33 : otherwise there seems to
be no coincidence.

XXXI. Further Researches regarding the Laws of Chromatic Dis-
persion. By Mungo Ponton, F.R.S.E*

THROUGH the kindness of Dr. J. H. Gladstone, the author
has been recently furnished with additional experimental
data by which to test the laws developed in his former commu-
nication.

He has also revised his method of determining the relative
values of the wave-lengths corresponding to the seven principal
fixed lines of the spectrum, referred to that of B as unity.

Calling E^H=/>, B-f-E = <r, C-kE = t, Eh-G=u, D-^-E = %,
and E-r-F =i|r, the relations subsisting among these six fractions,
as fairly deducible from Fraunhofer's two sets of observations,
may be expressed by the following six equations : —

(1) r-u=0-022'.

(2) /3 = 60(r-v) = l-33/.

(3) 3(%-^) = 5(r-t,) = 0-ll'.

(4) (o- + x) — (t + v) = 2(t-i;) =0-044'.

(5) 2(o--%) = 17(t-u) =0-377'.

(6) 2(o- + t + i; + x)=441(t-u) = 9'799'.
Hence the values of the fractions are—

* Communicated by the Author.

254 Mr. M. Ponton's further Researches regarding

Nos. Logs.

p = 1-333333' 01249387

a m 1-308333' 0*1167184

t = 1-247222' 0-0959439

v = 1-225000' 0-0881361

X = 1-119444' 00490025

$=1-082407' 00343906

The values of the normal wave-lengths thence arising are —

Nos. Logs.

B = 1-000000 0-0000000

C = 0'953291 1-9792255

D = 0-855626 1-932284]

E = 0-764331 1-8832816

F = 0-706140 1-8488910

G = 0-623944 1-7951455

H = 0-573248 1-7583429

Fraunhofer's two sets of observed values referred to B as
unity are —

C D E F G II

I. 0-954349 0-855962 0764660 0704053 0-623770 0-571035

II. 0-953168 0-855962 0765447 0706021 0624557 0-576151

-1181 +787 + 1968 +787 +5116

The differences between the calculated and the observed values
are —

C 2nd ob. D E 1st ol). F 2nd ob. G 1st ob. H mean.

+0-000123 +0000030 -0000329 +0-000119 +0000174 -0000345

These latter differences are greatly less than those between
the two sets of observations, and are so trifling as to be of no
account.

Among the observations furnished by Dr. Gladstone are the
following, on oil of cassia at temp. 13° C. Angle of prism
30° 35' 20":—

Deviations,

A 18° 58' 50", B 19° 11' 10", C 19° 18' 30", D19°37', E 20° 6' 10",
F 20° 34' 30", G 21° 36' 40".

Dr. Gladstone affirms that, owing to an absorptive action ex-
erted by this medium on the violet end of the spectrum, the line
II is imperceptible. The following arc the corresponding indices
of refraction : —

B 1-595416, C 1-599083, D 1-608243, E 1-623057, F 1-636980, G 1-667829.

the Laws of Chromatic Dispersion. 255

The observer gives the foregoing as the means of several ob-
servations, stating that, while the individual observations some-
times varied as much as ]/, he does not think that the mean
values can differ much above 30" from the truth. A difference
of 30" corresponds to one of 0*00035 on the index of B, and of
0-0003 on that of G.

In testing by these observations the general formula

it is needful, owing to the absence of H, to vary the method of
procedure, and to supply the index of H by calculation. The
exponent n must in this instance be found by trial. Then in
determining en and an we must make

(5BW + 3(T + Dn) - (5GW + 3F" + Era)

r V "B + *C + "D ' \ ^G + ^ + »W

and

1/BW + CW + DW+EW + F, + Gtt_/rB,,_1_CwJ _DW , Ew , Fra Qn\\ _

With the exponent w=3*l we obtain from these formulae
log en=0-1972574 and a* = 0-008186.

The index of H calculated from the formula fi=zXn-i an

e

is 1 '697760, and the differences between the other indices cal-
culated from that formula and their observed values are —

B+

c-

D+

E-

F-

G-

0-000068

0-000261

0000302

0-000002

0000005

0-000130.

These differences all lie within the assigned limits of experimental
error.

The extrusions or displacements of the fixed lines from their
normal relative positions, are with the calculated indices as
follow : —

bx~ cx~ <**+ ex+ fx+ gx- hx-

0001675 0-000615 9001103 0001832 0001624 0-000031 0002238.

This series corresponds to the regular type, thus removing
the anomaly presented by this medium, according to the obser-
vations of Professor Powell. Gladstone's observations were
made on the same specimen of the oil of cassia redistilled ; and
his statement that the line H is imperceptible raises a strong
probability that Professor Powell, in determining the index of
that line, had been deceived. This probability is enhanced by.

256 Mr. M. Ponton's further Researches regarding

the circumstance that if Powell's index of H be rejected, and if
his other indices be treated like Gladstone's, they exhibit the
same close agreement with the exponential law, and in like
manner conform to the regular type, as respects the laws of
extrusion.

Thus treated, PowelFs observations at temp. 22°*5.C. give, with
the exponent w = 3*l, the following values: log en=(H955608,
and an= 0008324, whence arise these indices : —

B C D E F G II

1-589507 1-592902 1-602713 1617366 1-631422 1662470 1-692841

Excluding H, the differences between these and the observed

indices are

B-f- C- D+ E- F+ G-

0-000007 0000098 0000113 0-000034 0-000042 0000030,

a result still more favourable than with Gladstone's observations.
Powell's observations at temp. 14° C, yield with exponent
n=3-4, log en=0'1979154, and «n=0'006895; but a better
equalization of errors is obtained by making #„= 0*006886.
Hence arise the following indices : —

B C D E F G H

1-594624 1-597724 1-606959 1621213 1*635279 1-667343 1699744.

Excluding H, the differences between these and the observed

indices arc

B+ C- D- E+ F- G+

0-000124 0000176 0000341 0-000513 0000521 0000243.

Those at temp. 10° C, yield with exponent n=3, log en=
0*1971516, and « = 0*008815 ; but a better equalization of errors
is obtained by making a =0*008840. Hence arise the follow-
ing indices : —

BCD E F G h

1-596758 1-600245 1-610314 1625189 1-639332 1670242 1700156.

Excluding H, the differences between these and the observed

indices are

B+ C- D- E-f' F+ G+

0-000458 0-000455 0-000086 0000289 0-000432 0000442.

The differences in these two latter cases exceed those in the
two former. Still, they are within the probable limits of error
for single observations, and are but slightly in excess of those
incident to mean observations.

In judging of these results, allowance must be made for pro-
bable variations of temperature or mechanical agitations occur-
ring in the course of the experiments. A change of 1° C. will
alter an index in this medium by about 0*001 on an average ;
so that a variation of a fraction of a degree, occurring while the

the Laws of Chromatic Dispersion. 257

observations are in progress, may produce a considerable effect
in augmenting or diminishing the apparent extrusions of the
fixed lines, and in altering the relations of the indices to each
other. In this manner we may account for the differences in
the proportion of extrusion, and the consequent variations in
the exponent, in the three observations by Powell, and for the
better agreement of one set than another with the exponential
law.

The extrusions for these three with the corrected indices, in
the order temp. 220,5, temp. 14°, temp. 10°, are

ftr— cx— dx+ ex-\- fx-\- gx— hx—

0-001703 0000625 0001123 0-001861 0001652 0000034 0002274

1920 722 1248 2115 1901 7 2615

1622 591 1074 1768 1563 40 2152

These all conform to the regular type, so that the anomaly
formerly presented by this medium may be now fairly regarded
as quite removed.

From the four sets of observations on oil of cassia, may be
determined the constant most suitable for ascertaining the ex-
ponent n with the improved normals. The most probable value
of this constant appears to be 10-953160, which is exactly twice
the sum of the normal wave-lengths. Hence the formula for
finding the exponent assumes the very simple form of
oy 4SX

n=l +2S x — , or ft=l H . Thus all the elements of cal-

a a

culation are linked together by determinate relations.

In a joint paper by Messrs. Dale and Gladstone in the Philo-
sophical Transactions, 1858, there are given the following indices
at temp. 15° C. for the bisulphide of carbon, the medium next
in importance to the oil of cassia : —

B

C

D

E

F

G

H

1-6177

1-6209

1-6303

1-6434

1-6554

1-6799

1-7035.

These numbers give n= 2* 6,loge„= 0*202221 6, ffn=0"009561.
The differences between the indices calculated from these
elements and the observed indices are

B- C+ D- E- F- G+ H-

0000010 0-000081 0000036 0000037 0000080 0000360 0000240

These differences all lie within the recognized limits of experi-
mental error.

The extrusions arising from the rectified indices are

lx-

Cx —

4*+

e*+

/*+

gx-

hx—

0-001091

0000385

0-000736

0-001178

0001021

0-000049

0001410.

Before the rectification of the indices the extrusions are
slightly irregular ; but the above conform to the regular type.
It is a delicate operation so to adjust the normals as to pro-

258 Mr. M. Ponton's further Researches regarding

duce the least amount of error in these two media — the oil of
cassia and the bisulphide of carbon — and to render both regular
lb their extrusions while at the same time preserving definite
relations among the normals themselves. Those adopted in the
foregoing calculations fulfil all these conditions, of which one or
other would be violated by even a comparatively small departure
from the values above assigned. Thus the exponential law,
combined with the laws of extrusion, while first detected by
means of an assumed set of normals, have in their turn become
the means of discovering the best values of the normals them-
selves. With media of lower refractive and dispersive powers,
any inaccuracy in the normals is of less moment, and might
easily escape detection.

For hydrate of phenyle, temp. 13° C, Messrs. Dale and Glad-
stone's indices are

B

C

D

E

F

G

H

1-5416

1-5433

1-5488

1-5564

1-5639

1-5763

1-5886,

whence n=2'34, log en= 0-1831359, and tfn=0«007193; but

an= 0*00721 5 gives a better equalization of errors.

The differences between the calculated and observed indices

are

B- C-f D-f E+ F- G+ H-f

0000115 0-000219 0 000270 0000244 0-000552 0000537 0000182.

The observed indices being the results of a single observation,
these differences all lie within the limits of probable error.
Before correction of the indices, the extrusions are slightly irre-
gular ; but with the corrected indices they become regular, and
are as follow: —

K- cx~ d*+ e*+ /*+ 9*- K-

0-000579 0000190 0000395 0000621 0-000531 0000036 0000733.

For anhydrous ether at temp. 15° C, Messrs. Dale and
Gladstone give these indices,

B C D E F G H

1-3545 1-3554 1-3566 1-3590 1-3606 1-3646 1-3683,

whence rc=2-73, log £n=0'1306117, and «n=0-002072. The
differences between the calculated and observed indices are

B+ C- D-f E- F-f G+ H+

0-000156 0000214 0-000076 0000214 0000111 0000113 0000058.

With the corrected indices the extrusions are

bx— Cx— dx-\- ex+ fx+ gx— Ax—

0-000278 0-000099 0000187 0000230 0000263 0-000012 0000361.

For absolute alcohol, temp. 15° C, their indices are

B C D E F G H

1-3612 1-3621 1-3638 1-3661 1-3683 1-3720 1-3751,

the Laws of Chromatic Dispersion, 259

whence »=l-9, log €„=0 1316156, and tfn= 0*003955. The
differences between the calculated and observed indices are

B+ C- D-f E+ F- G- H+

0-000080 0000122 0-000012 0000081 0000118 0000006 0000086

and with the corrected indices the extrusions are

bx— ex— dx-\- ex-\- fx-\- gx— hx—

0000154 0000051 0000107 0000163 0-000137 0000013 0-000189.

For distilled water, temp. 15° C, their indices are

B

C

D

E

F

G

H

•3300

1-3307

1-3324

1-3347

1-3366

1-3402

1-3431,

giving n=l-87, log en= 0*1215388, and ^=0*004023, or to
equalize errors, an= 0*004018. The differences between the
calculated and observed indices are

B+ C- D-f- E- F- G- H+

[0-000005 0-000030 0000016 0000036 0-000046 0000054 0000048;

and with the corrected indices the extrusions are

bx— Cx— dx-\- ex-{- fx-\- gx— hx—

0-000148 0000049 0-000102 0000158 0000131 0000012 0000182.

In these three last cases, the differences between the calculated
and observed indices all he within the limits of probable error,
and with the corrected indices the extrusions are all regular.

The results deduced from Messrs. Dale and Gladstone's ob-
servations on water are of the first class, and agree closely with
those deduced from Fraunhofer's two sets of observations. The
large discrepancies presented by Powell's observations on this
medium are thus shown to be entirely caused by experimental
errors.

These results all tend to establish the perfect universality of
the laws developed in the author's former paper.

For the six media above discussed, Messrs. Dale and Gladstone
have given the index of the fixed line A. Fraunhofer left no
record of the normal wave-length corresponding to this line. By
comparing together Messrs. Dale and Gladstone's indices, while
keeping in view the likelihood that this normal bears some
definite relation to the others, the conclusion has been reached
that its most probable value in reference to B as unity is
1-121019, log 0049613. This makes the value of the fraction
A-rE = 1-466', which is =66 (t — v), thus establishing a definite
relation between this and the other normals.

This value of A being assumed, we have the following discre-
pancies between the calculated and observed indices of this line
for the six media : —

260 Mr. M. Ponton's further Researches regarding

Observed. Differences.

Oil of cassia . . . 1589241 +0-000054
Bisulphide of carbon. 1-6114 -0-000145

Hydrate of plicnyle . 15377 -0-000195

Water 1*328 L +0000241

Alcohol 1-36 -0-000148

Anhydrous ether . .13529 +0-000748

These discrepancies, excepting the last, are quite moderate,
lying within the limits of probable error for mean observations ;
while even the large discrepance in the case of ether is within
the probable limits of error for single observations. The indices
for oil of cassia and bisulphide of carbon are those from which
the best judgment maybe formed; because any alteration of the
normal tells more on these indices than on any of the others.
The close agreement with observation in these two cases shows
that the above value of the normal wave-length corresponding
to the line A must be very nearly exact.

It may be interesting to show the effect of introducing A into
the account in the process for correcting the indices. Take, for
example, the bisulphide of carbon. Assuming the same ex-
ponent as before, ti=2*6, we obtain log €„= 0*2022496, and
«n = 0-009543. The indices thence arising differ very slightly
from those obtained without taking A into account. The distri-
bution of errors is somewhat different. The following are the
differences between the calculated and observed values : —

0-000074 0000017 0-000132 0000000 0-000026 0-00008G

/-i I IT

0000302 0000351.

Seeing that the greater the number of observations on which the
calculation is based the more likely are the individual indices to
be rendered accurate, the above are probably more correct than
those previously obtained without taking A into account.

It may accordingly be well, in all future observations, to take
the deviation of A, as well as those of the other seven principal
lines, and base the calculation on the whole eight. This, how-
ever, is rather practically expedient than theoretically needful.
Had we given only two extreme indices and one central, such
as ^A, KD, **H, and could we rely implicitly on their perfect
accuracy, it would be easy from these to determine all the other
five. It is only because of the imperfection of the present modes
of observation, and the consequent impossibility of obtaining
absolutely accurate indices for these three lines, that it becomes
expedient to take observations on all the eight indices into
account, the better to secure a mutual compensation of experi-

the Laws of Chromatic Dispersion, 261

mental errors ; for an inaccuracy in the determination of the
three assumed as the basis of calculation may be of such a cha-
racter as greatly to increase the discrepancies between the ob-
served and calculated indices of the other lines, and even to
make them appear to exceed the legitimate bounds of probable
error. Cases, however, may occur in which it may be necessary
to rest contented with determining the other five indices from
three being given.

To illustrate this point, and to exhibit the method of pro-
cedure in such a case, suppose that for the bisulphide of carbon
we have given only ^A, MD, and ^11, and let the corrected in-
dices be assumed as those given. The first step is to find the
exponent n. Call An"^A=a„, &+*& =4, and H^H = hn.
Make (An-DM) -r(D"— Hw) = 0 and (an-<4)-K4~^) = $
these two quantities, ©and 6, being either integral or fractional.
When the proper exponent is correctly found, then is © = 0. If
the exponent be too low, <B) is the greater; but if the exponent
be too high, 6 is the greater. Now, although the difference
between ® and 6 does not vary rateably with the difference be-
tween two exponents when the latter are widely apart, yet, if
the difference between the two exponents do not exceed 0*5, the
corresponding variations in the value of ® — 6, or 6— ®, are so
nearly rateable as to suffice for the purpose of calculation.
Hence if two exponents be taken, one too high, the other too
low, and differing by not more than 0*5, the true exponent may
be easily found.

If the medium be highly dispersive, like the oil of cassia, the
two exponents may be 3 and 3*5. If the dispersive power be
somewhat less, as in bisulphide of carbon, take 2*5 and 3, and
for lower dispersive powers 2 and 2*5, 1*5 and 2, 1 and 1*5,
according to a scale which will be easily found by practice.
Then by dividing by 5 the variation in the value of the dif-
ference between ® and 6, we obtain nearly the rate for each 0*1
of exponent, and can thence arrive at the true exponent to
within 0*1, or even nearer if required.

Thus, in the case of bisulphide of carbon, with exponent 2*5 we
have® = 1-525176, and 0 = 1-523900, whence@-0=O-OO1276.
With exponent 3 we have © = 1-786120 and 6 = 1*791053,
whence 6- (8) = 0004933. Adding these two, we obtain 0*006209
as the total variation, corresponding to a difference in the expo-
nent of 0*5 ; and one-fifth of this amount, or 0*001242, is the
variation for each 0*1 of exponent. It is thus seen that a rise
of 0*1 from 2*5 will make (B) so nearly equal to 0, that 2'6 may
be regarded as the true exponent.

This quantity found, it is easy to determine log en and an%

263 Researches regarding the Laws of Chromatic Dispersion.

For we have (AM-H'0^(»«^J = 6«> and

fA* + Dw-Hn , -Viifji
*{- 6n -(a« + < + ^n)j=«n,

whence all the other indices may be found from/x=Xn-j- — — an.

These will be the same as those deduced from all the eight
observed indices.

Take now the observed, instead of the coirected indices
MA, *D, *H. With exponent n = 3, we have 0 - 0 = 0004642 ,•
with 7i=2-5 we have 0-0=0-001587, sum = 0-006229, one-
fifth whereof, or 0*001246, is the rate for each O'l of exponent,
being nearly the same as before. This makes the true exponent
more nearly 2-62 ; but 2*6 is sufficiently near for calculation.
Hence we have log en= 0-022553, instead of, as formerly,
0-2022496, and «n=0-009553 instead of 0009543. The
differences between the calculated and observed indices thence
arising are

A- B+ C+ D+ E+ F-

0000033 0000099 0-000185 0000063 0000050 0-000002
G+ H-

0000427 0-000326.

These results, though probably less accurate than those ob-
tained by using the whole eight observed indices for mutual
correction, yet differ so little from them as to show that, except
where great accuracy is required, the foregoing abbreviated pro-
cess may be found practically useful. Indeed it may generally
be trusted, at least to the extent of ascertaining the exponent.

When all the eight indices are taken into account, the aspect
presented by the extrusions is wholly changed. The upper node
is shifted from between C and D to between B and C, so that
the transfer of motive energy appears to be from A, B, G, H to
C, D, E, F. The following are the extrusions arising with the
corrected indices, in the case of bisulphide of carbon : —

0-001837

0-000061

ffx-
0-000344

Cx+
0000481
hx-

0001880.

0001255

0001374

0001012

The mutual relations of these are exhibited in this formula,

(7ax + 5bx)-(Scx+dx) = (7hr + fyx)-(Sfx+cx);
also calling hx-ax=8l} gx-bx=B2)fx-cx=83) and ex-dx=84,
then 84— 8j, £2— 84, and83— $2 form an arithmetical progression.
In the above example the conformity to these two laws is not
quite exact ; but this arises merely from decimal imperfections.
The above extrusions probably represent the actual displace-
ments of the fhed lines, arising from that property of the

Mr. T. Tate on a new Self-registering Mercury Barometer, 263

medium which produces the irrationality, more correctly than
do the extrusions arising when only seven lines are taken into
the account. But this point cannot be satisfactorily ascertained
until recourse be had to such a method of experiment as shall
exhibit the irrationality apart from the dispersion.

Indeed it is manifest that, for the further elucidation of the
laws of refraction and dispersion, it is needful to resort to a
totally different method of experiment from what has been
hitherto pursued, and to adopt such arrangements as shall pre-
sent the effects of the refractive, the dispersive, and the extrusive
powers of the medium, each separately and distinctly. The
variations of each power, produced by change of temperature,
may then be studied with some reasonable prospect of arriving
at precise and satisfactory results.

XXXII. On a new Self-registering Mercury Barometefi\
By Thomas Tate, Esq.*

[With a Plate.]

THE advantage of this instrument consists in the extent of
its range as compared with that of the common barometer,
and in its adaptation for the purpose of self-registration. It
differs from the common barometer in having a floating cup,
which rises or falls according as the column of mercury, balan-
cing the pressure of the atmosphere, falls or rises, thereby pro-
ducing an increased variation in the level of the mercury in the
tube for any given change in the atmospheric column. The
construction of the instrument is shown in Plate III. fig. 3,
L K D is the barometer-tube fixed to the frame A B, having its
lower or open extremity, D, inserted in the mercury, I F, con-
tained in the glass float EGF; Q N a glass jar containing water
slightly acidulated with sulphuric acid to arrest the evaporation
from its surface. The glass float consists of two tubular por-
tions, E M, open at the top, and I F closed at the bottom, and a
globe G to give a force of floatation sufficient to balance the gra-
vity of the mercury contained in the tubular portion I F ; a light
cap, with projecting arms a and b, is attached to the top of the
tubular portion M E, to keep the float in position and to give
motion to the indices of registration ; b is a small weight touch-
ing the upper face of one of the projecting arms, and balancing
the index weight d by means of a fine thread or hair passing
over a wheel e ; in like manner a is a small weight whose upper
surface touches the under face of the other projecting arm ; the
index d registers the maximum pressure of the atmosphere, and c

* Communicated by the Author.

264 Mr. T, Tate on a new Self-registering Mei'cury Barometer.

that of the minimum pressure. A slit is made in the board A E,
covering the upper portion of the frame, to allow the tube E M
freely to ascend or descend, as the case may be. C, c, and d
are scales for reading off the height of the mercury column ba-
lancing the pressure of the atmosphere at any time. The upper
portion, K L, of the tube D L has a greater section than the lower
portion, and the section of the tube I F at the part I is greater
than that of the lower portion. The action of the instrument
is as follows.

If I C be the column of mercury in the tube corresponding to
mean atmospheric pressure, then the instrument is so adjusted
that the lower extremity, D, of the tube shall be at, or near to, the
middle of the mercury cup I F, and that the liquid in the jar shall
stand at, or near to, H, the middle of the tube EM. In this
position (as well as in all other positions) of the instrument, the
weight of the displaced liquid will be equal to the weight of the
glass float added to the weight of mercury equal in volume to
the space occupied by the mercury in the cup.

Wow supposing an augmentation to take place in the atmo-
spheric pressure, then the mercury will rise in the tube I C ; and
a portion of mercury being taken from the cup I F, the float will
rise ; and this will produce a further rise of the mercury in the
tube ; and this will go on until the loss of the force of floatation
is equal to the weight lost by the mercury in the cup. On the
other hand, when a reduction takes place in the atmospheric
pressure, the column I C will fall, and the mercury in the cup
being augmented, the float will sink, which will cause a further
fall in the column in the tube ; and this will go on until the in-
crease of the force of floatation is balanced by the gravity of the
mercury added to the cup. Hence it follows that the rise or
fall, as the case may be, of the mercury in the tube D L will be
greater than that which would be simply due to the change in
the height of the ordinary barometric column.

The scales C, c, d are uniform in their graduations when the
external sections of the tubes E M and D G are uniform, together
with the internal section of the tube K L. These scales are gra-
duated in the following manner : —

The actual height of the column I C is observed, and corre-
sponding marks are placed upon the different lines on which
the scales are to be formed ; after a change has taken place in
the atmospheric pressure, the height of the mercury column in
the tube I L is again observed ; and corresponding marks being
made on the different lines of scales as before, the intervals be-
tween these marks will have the same reading as the difference
between the two columns of observation : the scales may then
be extended according to the readings of these intervals.

Mr. T. Tate on a new Self-registering Mercury Barometer. 265

It must be observed that this increase of range is effected by
the action of two independent forces, viz. the force of floatation
of the cup, and the gravity of the mercury in the tube ; whereas
in the common wheel barometer, the change of barometric column
is simply multiplied by mechanical transmission.

Let P = the height of the mercury column I C measuring the

atmospheric pressure.
v = the corresponding volume of the liquid displaced by

the float, v1 being put for the volume corresponding

to p pressure.
M = the corresponding volume occupied by the mercury

in the float.
A = the internal section of the jar H N.
a = the external section of the tube E M.
D « the diameter of the globe G.
b = the internal section of the wide portion of the tube I.
c = the external section of the tube D K.
k = the internal section of the tube K L.
e = the descent of the float corresponding to p pressure

of the atmosphere.
x = the corresponding rise of the mercury in the cup I.
E = the corresponding fall of the mercury in the tube KL.
S = the specific gravity of the mercury, s being that of

the liquid.

Then, when the float descends e inches, we find —

Increase of volume of liquid displaced, v'—v=ea. ■. __- ;
Incr. vol. mercury occupied by the mercury in the cup = bx ;

A

.\ Sbx—sea

' A-a'

ea A,

Xi

S b A-a
Vol. mercury added to the cup = ec+(b-~ c)x;
Vol. mercury displaced from the tube KL=E£;
.\ ~Ek=ec + (b— c)x;

■r. e f sa A ., VT

But P—j» = E — e + x;

. _i_ = rs= * (1)

Phil. Mag. S. 4. Vol. 20. No. 133. Oct. 1860. T

266 Mr. T. Tate on a new Self-registering Mercury Barometer.
and

If 6= a, then equation (1) becomes

r= 7~4 - <3)

Now as e, in equations (1) and (3), is proportional to P— p, it
follows, the tubes being uniform in section, that the graduation
of the scale d or c must be uniform ; and equation (2) shows
that the same observation applies to the scale C. Equations
(1) and (3) express the range r of the instrument, estimated on
the scale d or c, compared with that of the ordinary barometer ;
and similarly, equation (2) expresses the ratio of the range esti-
mated on the scale C.

If k = c, that is, if the tube DG is selected so that it shall
exactly pass within the tube KL, then equation (1) becomes

r= r— (4)

sa A

Assuming b to be large as compared with k, then we get ap-
proximately,

E=6?+P-^, and.*. R=r + 1; ... (5)

that is to say, the ratio of range of the scale C exceeds that of

the scale d or c by unity

In the instrument which I have constructed, £='08, c=*04,

s 1
a = l, k = tz~e> A = 16; then from equation (3) we get

r= j jg = 2 nearly.

-04+i^xr5(1+'04)

In this case the range is double that of the ordinary barometer.

And from equation (2) we get 11 = 2*9, or 3 nearly. In this
case the range is three times that of the ordinary barometer.

Neglecting the weight of the float and the force of floatation
due to the displacement of the tubular portions of the float, we
find

*-vf3& ••■•■• n

This value of D is sufficiently exact for construction, inasmuch
as a little more or less mercury in the tube I F would correct
any slight error arising from the elements neglected. Thus if

Mr. T. Tate on a new Self-registering Mercury Barometer. 267

M = l*57, then D=3'4 nearly, and vol. globe =21 cubic inches.
Assuming a=l, MH = 3, vol. tube IF=1, then

i>= 21 + 3x1 + 1 = 25 cubic inches.

As regards the disturbances arising from change of tempera-
ture, it is to be observed that the instrument, under all eligible
forms of construction, is to a great extent self-corrective as
regards the scale d ov c; for whilst the gravity of the float, by
an augmentation of heat, is increased by the expansion of the
liquid, at the same time this gravity is decreased by the expan-
sion of the mercury which causes a portion of it to pass from
the cup into the tube, it being borne in mind that the tube is
wider at KL than it is at KD. But a certain value may be
assigned to a and D K which shall render this correction strictly
true for mean atmospheric pressure, and approximately true for
all other pressures.

In order that the float may remain stationary under a change
of temperature, the increment or decrement, as the case may be,
of the force of floatation must be equal to the increment or de-
crement of the weight of mercury in the cup. Keeping this
condition in view, let

Sj, sl = the weight of a cubic inch of mercury and liquid re-
spectively at tl temperature, S and s being their
respective values at t temperature.
v = the volume of displaced liquid at mean temperature t,

and mean atmospheric pressure P.
<?! =a internal section of the small tube DK.

-, 3, - = the expansion per unit of volume for mercury, water,

and glass respectively, corresponding to *x— t degrees

of temperature.
m = KC, the column of mercury in the wide portion of

the tube.
m' = ID, the length of immersion of the tube in the mercury.
h = DK, the column in the small portion of the tube.
h!= the length of the tube DK, measured from its fixed

point of attachment K to the frame.
H as the height of the liquid in the glass jar.

Then we find—

Vol. mercury in the tubes DK and KC before expansion

—c-Ji + km.
Vol. of this mercury after its expansion

= (c1h + km)(l+^\....{v').

T2

268 Mr. T. Tate on a new Self-registering Mercury Barometer.

"Rise of atmospheric column due to change of density of the

mercury = P-.

Vol. mercury in the tubes taking the expansion of glass and
mercury into account

=c-(1 + J>+i(1+|)("1+pD

Increase of vol. of the mercury in the cup due to the elonga-
tion of the tube DK=(c-c1)|-. . . (i/").

P

Now assuming that b is large as compared with k, and there-
fore that the level of mercury in the cup is not affected by the
expansion of the mercury which is in it, we have

Vol. mercury taken from the cup ==t/' — t/ — 1//;

= {(P-m)A-c,A} \ + {2(c,4 + Am)-(c-c,)A'} ^.

Neglecting (c— c^h' as being small compared with 2{clh-\-km),
and taking , ■ ■ = 1, which it is in all cases very nearly, we get

o ~— c

Weight lost by the mercury in the cup,

g
But Sj = z, h— m' + ro=P;

a
.\ Y—m=h—m', and m=P + m' — h;

••• * - tt .{<*-«>> (1-|>+(p+'»')*|H*}- (7)

Again, to find the changes produced by the expansion of the
liquid, &c, let z be put for the increment of height of the liquid
due to the change of temperature ; then we get

Vol. liquid before expansion = AH— v,
.-. Vol. liquid after expansion = (AH— v) (l+ 3).
But taking the expansion of the glass into account, we have also
Vol. liquid after expansion =Afl + 5-j(H-f-z)— v ( 1 + - )

-(>*&

Mr. T. Tate on a new Self-registering Mercury Barometer. 269

By equating these two expressions, we get

1 . 1 tTT^
Zp

(AH-^+v-i-AI

(A-*)(l+!)
Buoyancy float after expansion = sA 1 +-)+sla( 1 -f — h;
.'. loss of buoyancy of float, w'—sv— tMl-J — J—Sjflf 1 +a-)z*

m

Substituting the value of z9 and observing that sx = ~,

1+-0

we get

^.•ra«'-?)-M'-24)}- • *

Now in order that the float may remain stationary under
this change of temperature, w' must be equal to w" ; hence we
find by equating,

if I •1rH(-K)--("!f)} f W+">|}'

<MH£)

which gives the length of the small tube DK, so as to render
the instrument self-corrective at mean atmospheric pressure, as
regards the disturbances arising from change of temperature.

Now the relative values of a and v may be determined so as
to render this principle of compensation applicable to all other
atmospheric pressures.

Let the pressure of the atmosphere become Pj, and let the rise
of the float under this change of pressure be e} ; moreover, let
vx = the volume of liquid displaced by the float, Hj = the
column of liquid in the jar, m\ — the length of immersion of the
tube DK in the mercury; then

£=

P1 = P+£l. jjLm^M.^iuj HlS=H-/SL;
1 f A— a ] A— «'

and when b = a>

Substituting these values in equations (7) and (8), we get

270 Mr. T. Tate on a new Self-registering Mercury Barometer.

■*-'-iM(«-*)(-i-£K-i-}*<»>

*-r £-. ■ rh- i{$0 -a-^('-|)}«- m

Now in order that the float may remain stationary under

this change of temperature, we must have «■/' = wx' ; but vf^u/;

hence we obtain by equating (10) and (11), and putting

Aw.

-j = r, or A=n«,

A—a Ti—1

Eliminating r by means of equation (3), observing that

1 -J- Ot OL

T-~Ta ~ ~o very nearly, and solving the resulting equality for the
value of a, we get

«-")C-^-f-)<-i &

a= ; , . (12)

3(»-Dg-»

which gives the value of a in terms of k, c, n, &c., in order to
render the instrument self- corrective for changes of temperature
under all atmospheric pressures. No correction, therefore, being
required for the indications of the scale d or c, that of C will
require the same correction as in the ordinary barometer.

The rates of expansion of the substances being uniform, this
expression is independent of tx —■ t, that is, it holds true for all
temperatures. The same observation applies to equation (9).

Taking tl—t = 18°, then - = p^, - = . , fi„ ; and calculating

the mean rate of the expansion of water from the experi-
ments of Hallstrom between the temperatures of 46° and 86°, we

find i = ^ = - nearly. Also let *='08, c=-04, - = 13*5.

p ooU a * s *

w=16.

Then from equation (12) we find a = '94.

From equation (9), taking c, = «026, H = 17, P=29'5,m'=4,
and v = 25, we find h = 10*96, or 11 inches nearly.

The values of a and h here found, form the conditions of com-
pensation for the disturbances arising from change of tempe-
rature.

Mr. R. P. Greg on the Periodicity of the Solar Spots. 271
From equation (3), we find

r= °8 =2-16.

-°4+I^5Xl5('94 + -°4)
From equation (2), taking b = a,we find 11=2*94, or 3 nearly.
Hastings, September 4, 1860.

XXXIII. On the Periodicity of the Solar Spots.
By R. P. Greg, F.G.S.

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

IN the last Number of this Journal, while briefly suggesting
that the recent meteorological disturbances we have expe-
rienced might be connected with increased magnetic action in
the sun, as apparent in the phenomenon of periodicity in spot-
maximum, I at the same time alluded to the possibility of these
periodical changes on the sun's surface being likewise a result,
more remotely, of planetary influence. I stated that Mr. Car-
rington and M. Wolf had likewise entertained the same idea,
though without, I believed, arriving at any precise or satisfactory
results. In the Comptes Rendus for January 1859, M. Wolf
gives a formula which, according to the Rev. Robert Walker*,
" expresses the number of years from the mean frequency of the
spots in terms of the sines of angles dependent on the revolution
of Venus, the Earth, Jupiter, and Saturn, round the Sun. The
coefficients of the sines in the terms of this formula are in each
case the mass of the planet divided by the square of its mean
distance. According to this formula, the spots are determined
as to number and frequency by the position of these four planets :
Jupiter preponderates and determines the length and height of
the undulation of the curve ; the action of Saturn shows itself
by small variations ; Venus and the Earth transform the line of
simple undulation into a zigzag vibration." The Rev. R.
Walker adds that the " form appears to be entirely empirical^
which I believe to be the case.

The excess of 7 or 8 months in the sidereal period of Jupiter
over the supposed solar-spot period of 11*1 years, becomes also
a considerable discrepancy in the course of a moderate term of
years ; and his most favourable conjunctions with other planets
do not seem very constantly to agree with the periods given for
solar-spot maximum during the present century. The periods,
too, for Jupiter in perihelion, supposing that position naturally
to favour an increase of magnetic action or attraction in the sun,

* See his discourse " On the Physical Constitution of the Sun," read
before the late Meeting of the British Association at Oxford.

272 Mr. R. P. Greg on the Periodicity of the Solar Spots,

do not agree — in fact rather the reverse — with the nearest periods
of spot-maximum ; e. g. Jupiter was in perihelion in
July 1809-| fl816^

Feb. 1845 1 ] 1848 f maxima'

Dec. 1856 J LI860J

There are then certainly considerable difficulties in the way of
accounting for the spot-period of 11*1 years, if we suppose that
Jupiter's sidereal period of 11*8 years necessarily regulates it.

Being, however, strongly convinced in my own mind that pla-
netary influences would necessarily have some effect, one way if
not in another, upon the sun's physical constitution, and pro-
bably influence the phenomenon of periodicity in spot-maximum
and minimum, I requested a person of my acquaintance, natu-
rally endowed with a mathematical and astronomical turn of
mind, to see if he could not find some synodical period answer-
ing to the secular term of 11*1 years. I advised him, in the
first place, to investigate the period of Jupiter, and his conjunc-
tions with Saturn, the Earth, and Venus ; in the second place,
to take likewise into especial consideration their positions in their
own orbits as regards least distance from the sun, and the times
when they were in line with the sun's equator. He says in
reply, in one of his letters to me, "I have failed in finding
out some configuration of the planets to account for the spot-
cycle of 11*1 years; I can find nothing that comes at all near
it, but the return of Jupiter to the same point in his orbit once
in about 12 years; and this epoch is without any certainty of
either conjunction or opposition with any of the other planets.
Jupiter passes Saturn at periods of about 20 years, and Uranus
at periods of about 14| years; and he is passed by the smaller
planets at much shorter periods than 11 years. And it does not
appear that this particular point in the orbit of Jupiter, where
he is situated at the time of spot-maximum, is either the peri-
helion, aphelion, or either of his nodes. The perihelion of Jupiter
is in Aries, and he was last in that point (the nearest point to the
sun) about December 1856; and as the line of apsides moves
very slowly, he will return to the same point again in 1869, and
so on every 12 years for many returns."

On the 9th of September last I received from him the following
letter, which I give verbatim, as being, at least, curious and
interesting : —

"Dear Sir, — In searching for the solar-spots cycle, in some
arrangement of the planets, I hit upon a rather remarkable con-
junction, which is as follows : —

u Supposing the sun to make one revolution on his axis in 25

Mr. R. P. Greg on the Periodicity of the Solar Spots, 273

days 8 hours, say 25*3 days ; then in the time that the sun makes
160 revolutions on his axis, Mercury will make almost exactly
46 revolutions in his orbit, and Venus 18 ; and this singular
conjunction will recur at periods of about 11 years and 31 days,
or about 11*08 years, which does not differ materially from the
solar-spot cycle of 11*1 years. The statement is as follows : —
Revolutions. Time of Revolution. Days.

Sun ... . 160 (on axis) x 25-30 =4048
Mercury . . 46 (in orbit) x 87*97 =4047
Venus ... 18 „ x 224*70 =4045

Earth . . . 11*08,, x 365*25 =4047

" It appears, then, that in periods of about 11*08 years a con-
junction of Mercury and Venus takes place with the same side
of the sun presented to them. This phenomenon may occur at
several places in the ecliptic, one of which happens to be at
the perihelion of the orbit of Mercury, and also within a few
days of his passing the ascending node. Now the orbit of Mer-
cury is considerably more eccentric than that of any of the other
planets — as much as one-fifth of his semi-major axis; there
must therefore be a considerable increase in his attractive
energy at that particular point of his orbit ; this, added to the
fact that he is very nearly in a line with the sun's equator
(being nearly in the node), combined also with the conjunction
of Venus, would tend to increase the amount of attraction
acting on the sun's surface at that time. This singular con-
j unction will sometimes be strengthened by that of some of the
other planets ; but this will only be a casual occurrence. For
instance, at the last conjunction, which happened in March
last, Jupiter was less than 30° from that point of the ecliptic ;
he should therefore have some influence. At the next return
of the period Jupiter will be almost, if not quite, in exact con-
junction with Mercury and Venus; this will take place in April
1871. The following statement shows the times when this
phenomenon has last occurred : —

November 1815.

December 1826.

January 1838.

February 1849.

March 1860.

" These years, I believe, do not exactly agree with the years of
maximum spots, but yet so nearly as to challenge further atten-
tion to the coincidence, and induce one to think that the pheno-
menon will have something to do with them ; if so, I should be
inclined to think the occurrence of spots, in a lesser degree,
should be more frequent, viz. at intervals of 88 days, which is
the time in which Mercury goes from his perihelion to his peri-

274 Mr. R. P. Greg on the Periodicity of the Solar Spots.

helion again ; now, he passed his perihelion in June last, and
there was an extraordinary number of spots at that time ; since
then the sun has been comparatively free from spots. Mercury
is in perihelion now ; and I was observing the sun] on Friday,
and the spots had increased very much both in number and
size. " I remain, dear Sir,

" Quarry Bank, near Wihuslow, " Yours truty>

Sept. 8th, I860." "J. Henshall."

Should future investigation prove that this peculiar conjunc-
tion of Mercury and Venus is something more than a mere co-
incidence, taken in connexion with the interval of 11*1 years
between the solar-spot maxima, it will not fail, I think, to create
surprise that two such small planets should produce apparently
so strong an influence upon the sun, as that required to regulate
the periodicity of his spot- energy; it would have been more
natural to suppose that the intensity of the planetary disturbance
or effect would at least have been to some extent proportional
to the masses, and inversely as the squares of the distance. One
can only suppose that Mercury (and probably Venus similarly,
though to a minor extent), owing to his extreme density, possesses
a metallic constitution highly favourable to electro-magnetic
action ; he may indeed intrinsically be a more powerful magnet
than all the rest of the planets put together. His proximity to
the sun, great eccentricity of orbit, as well as considerable incli-
nation of orbit to the ecliptic, may help to favour his magnetic
energy upon the sun, direct or reflex ; while generally it may
perhaps be found that whatever magnetic action may exist between
a planet and the sun, it will be most powerful when the planet is
in one of its nodes, in a line with the sun's equator. This, at
least, we should be inclined to imagine would be the case, should
the solar magnetic poles coincide with his poles of axial rotation,
and consequently in a direction perpendicular to the supposed lines
of planetary magnetic force. It is worthy of remark that Jupiter
passed his ascending node about the 1st of September last year,
about the time of the great magnetic auroral disturbance, at a
time likewise when the spots and markings on his own surface
were remarkably numerous and distinct, and also near the time
of solar-spot maximum.

Manchester, Yours respectfully,
Sept. 18, 1860. R. P. Greg.

Note. — Since writing the above, I have received a short note
from Mr. Carrington, to whom I wrote respecting the peculiar
conjunction of Mercury and Venus, mentioned by Mr. Henshall ;
and I am inclined to agree with him, that it would be natural to
expect nearly as decided solar effects from the ordinary and more
frequent conjunctions of Venus and Mercury, There is likewise

M. Regnault on the Elastic Force of Vapours, 275

a difficulty in knowing the precise time for a revolution of the
sun on his axis, the period varying (I presume as measured by
the spots on his surface) as much as two days in certain regions
or latitudes, in excess of the equatorial. Still the influence and
position of the planet Mercury may have considerable magnetic
effects.

It must also be borne in mind, while attempting to connect
planetary influences through mass-attraction, with the secular
returns of &pot-maximum and minimum, that those periods are
not, as far as they have hitherto been examined, precisely regular
or fixed; the average, taken from before 1800 to 1860, gives,
according to Wolf, a period of 11*1 years; but from the years
1826 to 1850, the best observations made by Schwabe show that
the period was then a decennial one, with maximam 1828, 1837,
and 1848, and minima in 1833 and 1843; and Sabine states
" that during the same period the solar magnetic variations show
likewise a decennial period strictly coincident with the solar spots."

XXXIV. On the Elastic Force of Vapours. By M. Regnault.

[The important researches of M. Regnault on the Elastic
Force of Vapours under various conditions, abstracts of which
have been given in the Numbers of this Magazine for October
1854 and January 1855, have just appeared in full in the
twenty-sixth volume of the Memoires de I' Academic. In calling
attention to their publication, in the Comptes Rendus for June 11,
1860, the author at the same time communicates an account of
some further developments which he has given to a part of this
research — that which treats of the tension of saturated vapours
in vacuo, a translation of which we proceed to lay before our
readers. — Eds.]

The various apparatus which I have used in these researches
are described in the original memoir. I will merely remark
that they refer to two different methods.

The first, which I call the statical method, consists in deter-
mining the pressure which is equal to the elastic force of a vapour
at rest disengaged from a liquid in excess. In the second method,
which is called the dynamic method, the vapour is always in motion,
and a determination is made of the temperature of the vapour
continually emitted by the liquid boiling under different pressures.

Both methods give the same results,

1. When the liquid is quite homogeneous. This is not the
case when it is impure ; the presence of the smallest quantity of
a volatile foreign body is immediately seen in the non-superpo-
sition of the two graphic curves which belong to one or the other
of these methods.

276 M. Regnault on the Elastic Force of Vapours.

2. Where the liquid does not possess a great molecular cohe-
sion; for otherwise the liquid boils in an intermittent manner
with violent j urn pings, and the determinations by the dynamic
method become very uncertain.

Both methods have been successfully applied to mo3t of the
volatile liquids taken for experiment, and I have been able to
determine their tensions from the lowest temperatures to those
which correspond to pressures of 12 to 15 atmospheres. Most
liquefiable gases give liquids having a great molecular cohesion,
and which boil with great difficulty in spite of their extreme mo-
bility. Their tensions can only be determined with certainty by
the statical method. In order to apply the dynamic method —
that of ebullition — the thermometer can only be placed in the
vapour of a boiling liquid when its boiling-point is above that of
the surrounding atmosphere, for otherwise the vapour might
become superheated, and the indications of the thermometer
would be faulty. If the thermometer dips in the boiling liquid,
it exhibits variations of temperature during ebullition, although
the pressure remains the same. The indications of the thermo-
meter often change according to the manner in which the heat
is applied. The ebullition is not continuous; violent jumpings
take place accompanied by a sharp sound like that emitted by
inverting the water-hammer. These effects greatly vary with
the pressure. In certain liquids they take place at pressures
below that of the atmosphere. In others they only take place
under high pressure.

In this limited space I must omit any mention of the obser-
vations I have made on each substance, of the graphic method of
constructing the results, and of the interpolation formula by
which I have endeavoured to represent my researches. I will
only say that, of all the methods of interpolation tried, the ex-
ponential formula proposed by Prony, and applied by Biot to
aqueous vapour under the form

log F=« +&*'+<*',
applies best to all the substances I have tried. This formula
has the advantage of containing five constants, for the de-
termination of which, five points of the curve may be chosen
having equidistant abscissae, so that the curve represented by
the formula can deviate in the intermediate parts very little
from the graphic curve. For a great number of the substances
which I have studied, by a convenient arrangement of the fixed
points which serve to calculate the constants, and without de-
viating too much from the observed data, a formula with two
exponentials may be calculated,

logF=a + fot' + c£',
in which the term c& only introduces values which are less than

M. Regnault on the Elastic Force of Vapours, 277

the probable errors of observation, so that it can be reduced to

the much simpler formula

log £ = a 4- ha.

This consideration, and the great resemblance which the graphic

curves belonging to different substances bear to each other when

F
logr^r- is taken for ordinates, lead me to think that the law of

variation of the tensions of vapours with the temperatures would
appear under a very simple form by taking as an independent
variable, not the temperature such as we define it in a completely
arbitrary manner, but another element which would be in a direct
relation with the constitution of each body, and whose origin
would be fixed for each of them.

The Tables of the elastic forces of the vapours of alcohol,
ether, chloroform, bisulphide of carbon, and essence of turpen-
tine have already appeared in this Journal. In the new Table
these tensions are determined for every 5 degrees; and there
are further determinations of the tensions of benzole, quadri-
chloride of carbon, C2 CI8, of chloride, bromide, and iodide of
ethyle, of methylic alcohol, essence of lemon, acetone, and oxalic
ether. In the following Tables we shall give the tensions of
mercury vapour, and also of some liquefied gases.

Mercury.

Mercury.

T.

F.

T.

F.

mm

mm

00

00200

270

12301

10

0-0268

280

15517

20

0-0372

290

194-46

30

00530

300

24215

40

0-0767

310

299-69

50

01120

320

368-73

60

0-1643 '

330

450-91

70

0-2410

340

548-35

80

0-3528

350

663-18

90

0-5142

360

797-74

100

0-7455

370

954-65

110

10735

380

1136-65

120

1-5341

390

1346-71

130

21752

400

1587-69

140

30592

410

1863-73

150

4-2664

420

217753

160

5-9002

430

253301

170

80912

440

2933-99

180

1100

450

3384-35

190

14-84

460

3888-14

200

19-90

470

4449-45

210

26-35

480

5072-43

220

34-70

490

5761-32

230

45-35

500

6520-25

240

58-82

510

7353-44

250

75-75

520

8264-69

260

96-73

278

M. Kegnault on the Elastic Force of Vapours.

The temperatures refer to the air-thermometer. The ebulli-
tion of mercury is regular enough at pressures below that of the
atmosphere. Under the atmospheric pressure, jumpings com-
mence, and they increase in proportion as the pressure increases :
under a pressure of ten atmospheres the shocks are so violent
that they produce a noise like that of a hammer striking an anvil.
Every moment the apparatus may be expected to burst into
pieces.

Very volatile Liquids.

Liquefied Gases.

Sulphurous acid.

Ammonia.

Sulphuretted hydrogen.

T.

F.

T.

F.

T.

F.

o

mm

mm

o

mm

-30

-78-2

15795

-78-2

441-52

-25

37379

-40

52861

-30

2808-57

-20

479-46

-35

684-19

-25

3508-02

-15

607-90

-30

876-58

-20

427301

-10

762-49

-25

111212

-15

509018

- 5

946-90

-20

1397-74

-10 594500

0

116506

-15

1740-91

- 5

6822-74

+ 5

142114

-10

2149-52

0

7709-27

+10

1719-55

- 5

2632-25

+15

2064-90

0

3162-87

20

246205

+ 5

3854-47

25

2915-97

10

461219

30

3431-80

15

5479-86

35

4014-78

20

646700

40

4670-23

25

758116

45

5403-52

30

8832-20

50

6220-01

35

1014400

55

712502

40

11776-42

60

8123-80

65

9221-40

The condensation of the gases was effected in the same appa-
ratus which served to determine the tensions, and which was so
arranged as to be quite freed from the last traces of air or any
other gas which it might contain. The liquefaction of sulphurous
acid is readily effected at the ordinary atmospheric pressure, when
the apparatus is placed in a cooling mixture. For ammonia and
sulphuretted hydrogen the apparatus is placed in a mixture of
ice and crystallized chloride of calcium, and then the gas com-
pressed with a hand force-pump. Care must be taken that
the ordinary grease of the pumps is replaced by fixed oils which
are not saponifiable. By a pressure of 2 to 3 atmospheres the
desired quantity of liquid ammonia is obtained ; but for sulphur-
etted hydrogen the pressure must be raised to 7 or 8 atmo-
spheres.

I have had occasion to liquefy these gases on a large scale for
researches (of which I shall presently lay the results before the

M. Regnault on the Elastic Force of Vapours, 279

Academy) on the determination of the latent heats of evaporation,
nnder different pressures, of very volatile liquids, and on the quan-
tities of heat which these gases absorb under pressure. I shall
briefly describe the method adopted.

I prepare carbonic acid by a regulated and continuous addition
of dilute hydrochloric acid to broken marble placed in a large
flask. The solution, freed from acid and charged with chloride
of calcium, flows out as fast as it is produced, and the gas passes
into a gas-holder of a cubic metre capacity. A force-pump, with
several barrels, and worked oy my steam-engine, draws the gas
in the gas-holder, having made it previously traverse several
drying materials. It forces the gas into a first receiver of 3
or 4 litres capacity, which simply serves as regulator. The gas
then passes freely into the apparatus in which it is to be con-
densed, and which is placed in a mixture of ice and crystallized
chloride of calcium. The non-condensed gas passes into a second
closed receiver of 5 litres, placed at the end of the apparatus.
This serves to receive the air and the non-liquefiable foreign
gases, which can be allowed to escape from time to time by
opening the stopcock.

Protoxide of nitrogen and bisulphuretted hydrogen can be
liquefied in large quantities by the same arrangement. But for
gases which readily alter in contact with fatty matters, I employ
a special force-pump, in which the gas is only in contact with
mercury. This pump consists of two equal barrels of cast iron,
joined so as to be U-shaped. The first barrel contains a solid
piston, which in its motion simply acts on a quantity of mercury
which exactly fills one of the barrels. The system of two
valves, exhausting and forcing, is arranged in the second barrel.
It is evident that by this means the gas never comes in contact
either with the piston or the greased sides.

I have been especially interested in liquid ammonia, in con-
sequence of its great calorific capacity, of its great latent heat
of evaporization, and of the ease with which it is obtained and
afterwards collected in the gaseous state. I propose to use it
principally in obtaining very constant low temperatures by
causing it to boil under different pressures. I prepare ammo-
niacal gas by causing a stream of strong liquid ammonia to fall into
a copper vessel contained in a small boiler in which water
is kept boiling by means of a gas-lamp. The vessel is con-
sequently always surrounded by the vapour of boiling water ;
the ammonia flows in a spiral along the sides ; and the liquid,
which is almost freed from ammonia, runs out by a tube at the
bottom, which plunges to a depth of several decimetres in cold
water. The ammoniacal gas exhausted by the pump passes
through several copper receivers full of fragments of soda-lime ;

280 Prof. Challis on a Theory of the Force of Electricity.

the pump regulates the production of gas, and drives it into a
receiver placed in a mixture of crystallized chloride of calcium
and ice. In this way many litres of liquid ammonia may be
prepared in a few hours.

In order to expose an apparatus to a stationary low tempe-
rature, it is hermetically adjusted in the receiver; this receiver is
placed in the freezing mixture, and ammoniacal gas liquefied in
it. When it is sufficiently full of the liquid gas, the freezing
mixture is removed, and the receiver connected with one of my
large reservoirs of air, by which the'pressure can be kept perfectly
constant, either greater or less than that of the atmosphere.
The ammonia distils in this manner at as low pressures as can be
desired ; and it is easy to keep them perfectly constant provided
the ammoniacal gas is prevented from reaching the air-reservoir.
For this purpose a cylindrical vessel containing pieces of ice is
placed before the reservoir ; the ice in liquefying almost entirely
redissolves the ammonia, and the little which escapes is caught
in a second vessel full of pumice soaked in acid.

By this arrangement I hoped to obtain low temperatures per-
fectly stationary, but have been disappointed, for the reasons
stated above (page 2Y6). A certain regularity can only be
obtained when a continual stream of small air-bubbles is passed
into the liquid ammonia through a rose, which continually
agitates the liquid, and destroys its viscosity. An air-thermo-
meter ought to be connected with the apparatus. By means of
a regulating screw, the supply of air-bubbles can be regulated
so as to keep the thermometer stationary.

XXXV. A Theory of the Force of Electricity.
By Professor Challis*.

A FTER an interruption occasioned by close occupation with
-*** astronomical work, I propose now to resume the expla-
nation of my theory of the physical forces. The principal
hypothesis of the theory is, that the physical forces are all
consequences of the motions and pressures of a uniform and
highly elastic medium pervading space. The variations of
the pressure of the medium are supposed to be proportional
to variations of its density; and this supposition forms the
basis of a mathematical investigation of the relations between the
motions and the pressures. Further, it is assumed that the
medium acts immediately by pressure on the ultimate atoms of
bodies, which are all supposed to be spheres of invariable mag-
nitudes, and of the same intrinsic inertia. According to these
hypotheses, the different phenomena and properties of bodies
* Communicated by the Author.

Prof. Challis on a Theory of the Force of Electricity, 281

depend only on the magnitudes of their atoms, the proportions in
which they are composed of atoms of different magnitudes, and
on the arrangements of the atoms. But the explanation of the
sensible properties of matter must be preceded by a mathematical
investigation of the laws of the dynamic action of the assumed
setherial medium. Already I have entered to some extent on
such investigations relatively to light, heat, the force of gravity,
and the forces of molecular aggregation. I proceed now to treat
of the force of electricity on the same principles. First, how-
ever, it should be stated, with respect as well to this investiga-
tion as to those which preceded it, that I do not profess to give
complete and final explanations of the laws of the forces under
consideration. As the proposed general theory either embraces
all the physical forces, or fails altogether, my object at present
is to adduce prima facie evidence that it is as comprehensive as
it is required to be.

1. According to the "Theory of Molecular Forces" contained in
the Number of the Philosophical Magazine for last February,
the atoms of any substance are kept in positions of equilibrium
by attractions and repulsions resulting from the dynamical action
of vibrations of the sether, which have their origin at the atoms.
Each atom is the centre of vibrations propagated from it equally
in all directions, and that part of the velocity of the vibrations
which, as shown by the mathematical formula?, is unaccompanied by
change of density, gives rise to a repulsive action on the surround-
ing atoms, varying inversely as the fourth power of the distance.
This action is the calorific repulsion which keeps the individual
atoms asunder. The remaining part of the velocity, which is
accompanied by a proportional condensation, acts repulsively also,
according to the law of the inverse square, but with a force which
at the surface of the atom is incomparably less than the other
repulsion. When, however, the effect of all the repulsions of
the second kind from an aggregation of atoms, constituting a
spherical molecule, is considered, the resultant may be of sensible
magnitude at sensible distances from the centre of the molecule.
To this molecular action the repulsion of aeriform bodies is attri-
buted in the theory referred to. It appeared also from the the-
oretical investigation, that the separate waves from the atoms of
a spherical molecule of a higher order of magnitude, consisting
of a number of atoms very much larger than those constituting
the molecule of the first order, might merge at a certain distance
from its centre into continuous waves of another order of breadth
and condensation, the dynamic action of which might be such
as to account for the molecular attraction of aggregation in fluids
and solids.

For the sake of distinction, the first of the above-mentioned
Phil Mag, S. 4. Vol. 20. No. 133. Oct. 1860. U

282 Prof. Challis on a Theory of the Force of Electricity.

forces, that which is described as emanating from individual
atoms, will be called atomic repulsion) the second, or that ema-
nating from the smaller aggregation of atoms, will be called
molecular repulsion ; and that emanating from the larger aggre-
gation, molecular attraction. The last two are the forces which
will chiefly come under consideration in the following theory of
electricity.

2. In the ordinary or neutral state of any substance, the
sphere of activity of each of these forces appears to be extremely
small. Hence if a plane be conceived to pass through the posi-
tion of an atom situated in the interior of a uniform medium,
not very close to its boundary, the forces of each kind, ema-
nating from the atoms on opposite sides of the plane, just
counteract each other, and the atom is thus maintained in a
position of stable equilibrium. But an atom situated at the
boundary of the substance is held in equilibrium by the equal
and opposite actions of the attractive and repulsive forces. As
the sphere of activity of the attraction was shown in the theory
to be much greater than that of repulsion, and to vary much
more slowly with the distance, the equality of the attraction and
repulsion on a superficial atom may be supposed to be the con-
sequence of a rapid degradation of the density of the substance
towards the bounding surface. The effect of this would be, to
diminish the resulting repulsion on a superficial atom from
within to without, so as to reduce it to an equality with the
resulting attraction from without to within, which is less affected
by the gradation of density at the surface, on account of its
larger sphere of activity. It is possible that the diminution of
density may be such that at the boundary the atomic repulsion
becomes of very small magnitude, as is the case, according to
the theory, in the interior of aeriform bodies, by reason of the
comparatively large intervals between their atoms. Supposing,
however, the body to be surrounded by air, the atomic repulsion
must be such as would suffice to counteract the pressure of the
air. The molecular repulsion would then be counteracted by the
molecular attraction, excepting so far as a slight excess must be
attributed to the latter very close to the surface, in order to
account for the phamoincna of capillary attraction. As these
forces both vary with the distance from their origins, according
to the law of the inverse square, their resultants would neutralize
each other at all sensible distances from the surface of the sub-
stance from whose, atoms they emanate. In this manner the
theory accounts for the fact that the molecular forces of bodies
have in general no perceptible effect at sensible distances from
the boundaries.

3. Now this equality between the superficial molecular repul-

Prof. Challis on a Theory of the Force of Electricity. 283

sion and the superficial molecular attraction would be destroyed
by any extraneous action, such as the friction of one substance
against another, by which the relative positions of the atoms
would be changed, and the normal state of the superficial degrada-
tion of density be disturbed. Such disturbance would produce
the electric state. If the result of the disturbance is to cause
the molecular attraction to be in excess of the molecular repul-
sion, the electricity is of a certain kind, different from that in
which the molecular repulsion is in excess. The theory thus
accounts for the existence of two kinds of electricity, and for the
fact that electricity is confined to the surfaces of bodies.

4. It seems evident that, according as the superficial mole-
cular attraction is greater or less than the superficial molecular
repulsion, the superficial density is greater or less than that in
the neutral state. It does not, however, readily appear to which
of the two kinds of electricity the denser, and to which the rarer,
condition of the superficial strata applies. But since experiment
indicates that when two substances are electrified by friction,
that which is the more yielding, or more susceptible of mole-
cular displacement, is negatively electrified, it may perhaps be
inferred that in the case of negative electricity the superficial
density is greater than in the neutral state, and the molecular
attraction in excess ; and in that of positive electricity, the super-
ficial density is less than in the neutral state, and the molecular
repulsion in excess.

5. Upon the cessation of the friction it might be expected
that the superficial atoms would quickly return to the neutral
positions, and the normal gradation of density be resumed.
What, then, is the reason that the electric state of a substance
is found by experiment to continue with little abatement long
after the exciting cause has ceased to act ? The answer to this
question involves the consideration of the part which the air
performs in electrical phenomena, which, as experience shows,
is so essential that no theory of electricity can be complete which
does not give an account of it. The explanation which the pre-
sent theory offers is as follows. When the law of density of the
superficial strata has been altered by the disturbing action of
friction, and the equality of the molecular attraction and repul-
sion is destroyed, so that, for instance, the former exceeds the
latter, immediately the surrounding air is attracted towards the
electrified body, and condensed on its surface, and at the same
instant an equilibrium is established at the surface between the
repulsion of the condensed air and the atomic repulsion of the
body. Considering the rapid change of the atomic repulsion
with distance, and the small sphere of its activity, this equaliza-
tion of the two repulsions may be the result of a change of the

US

284 Prof. Challis on a Theory of the Force of Electricity.

superficial density extending to a distance from the surface in-
comparably smaller than the distance to which the original
disturbance affected the atoms. Consequently the excess of the
molecular attraction above the molecular repulsion, to which that
disturbance gave rise, will continue so long as the condensation
of the air is undisturbed, and thus the body will remain in a
state of negative electricity.

6. Similarly, if the friction disturbs the atoms in such a
manner that the superficial molecular repulsion is in excess, the
surrounding air is repelled from the electrified body, and the
parts contiguous to the surface are rarefied. At the same time,
the atomic repulsion of the body being equalized, by an extremely
small change of the superficial density, to the repulsion of this
rarefied air, the excess of the molecular repulsion above the
molecular attraction remains, and the body continues in a state
of positive electricity.

7. It is evident that the air can operate in this manner only
to a limited extent, depending on its density, and that the
amount of the permanent electricity, of which any substance is
capable, is limited by this circumstance. The electricity will be
permanent in proportion as the air adheres to the body without
being replaced by other air. For this reason dry air is more
favourable to the permanence of electricity than air containing
vapour of water, which being only connected with the air me-
chanically, and not a constituent part of it, is liable to relative
displacement by extraneous causes.

8. As the excess of molecular attraction, or of molecular re-
pulsion, acts through considerable spaces, the resulting con-
densation or rarefaction of the air at any point of the surface of
the electrified body, depends on the curvature of the surface at
that point, being less as the curvature is greater. This explains
the escape of electricity at sharp points, where on account of the
great curvature of the surface, the sum of the molecular attrac-
tions or repulsions is too feeble to produce a degree of condensa-
tion or rarefaction sufficient to maintain the electric state.

9. When two substances are rubbed against each other, the
external force applied to cause the friction, by putting the con-
tiguous superficial atoms of both into states of disturbance, gives
rise to mutual molecular actions, which in fact determine the new
positions that the atoms assume. Now, whatever be the resultant
of these actions on a given atom, it is evident that those atoms
of one of the bodies which are most nearly contiguous to atoms
of the other, must be acted upon by resulting forces very nearly
of the same magnitude and in the same direction as the forces
which act upon the latter. Hence, if for one of the substances the
resulting force be from within its boundary to without, for the

Prof. Challis on a Theory of the Force of Electricity. 285

other it must be from without to within ; and if in one case the
superficial density is made less than it is in the neutral state, in
the other it is made greater. Thus the fact that two bodies
take by friction opposite electricities, is in accordance with this
theory. The circumstances which determine one to take the
positive electricity and the other the negative, depend most pro-
bably on differences of atomic constitution and arrangement.
But this is a question distinct from the present inquiry, which
is concerned only with the kind of agency by which electric
phenomena are produced.

10. A good conductor of electricity may, in the language of
the theory, be defined to be a substance which has the property
of transmitting along its surface the effect of a disturbance made
at any point of the same, so that the law of superficial gradation
of density which the disturbance induces obtains equally over
the whole of the surface. In bad conductors and non-conductors
the change of the state of superficial density is transmitted
slowly, or not at all, and the gradation of density may at the
same instant be different at different points of the surface.
What the constitutional difference may be between a conductor
and a non-conductor, it does not belong to the present theory
to inquire.

11. The tenacity with which the electric state is maintained,
depends not only on the condition of the air, but also on the
form of the surface of the electrified body. We have already
seen that the condensation or rarefaction of the air contiguous
to the body, which in fact keeps it in the electric state, is greatest
where the curvature is least, and that it is very small at sharp
points. This explains what has been called the accumulation of
electricity at points of great curvature, which, according to this
theory, is only a less degree of retention of the electricity at
such points, and a greater tendency to be affected by the ap-
proach of a disturbing cause.

12. The uniform distribution of electricity over the surface of
a good conductor may be modified by circumstances, the consi-
deration of which leads to the theory of electricity by induction.
Conceive a good conductor, whose form, for the sake of simpli-
city, we will suppose to be spherical, to be brought within the
influence of another sphere in a state of negative electricity. As,
according to what has been said, the dynamic action of the latter
attaches to itself the surrounding air, and the extent of its influ-
ence, as is known by experiment, may be very considerable, it
may be supposed to act attractively also on the other sphere, or
at least on the superficial atoms that are turned towards it. I
do not gather from experiments, that electric action can pass
freely through the substances of bodies as the force of gravity

286 Prof. Challis on a Theory of the Force of Electricity.

does, so that the opposite side of the sphere in the present
instance could be immediately acted upon by the first sphere.
The fact rather seems to be that a partial disturbance of the
normal atomic condition of a body, at whatever part it takes
place, is transmitted through the intervention of its proper
molecular forces to all other parts, so that the relative positions
of the atoms both in the interior and contiguous to the bound-
aries are in some degree changed. This remark may be illus-
trated as follows. Suppose a cylindrical rod to be held by the
hand near its middle point, and to be moved in the direction of
its length. The force which causes the motion is applied at
certain parts only ; but if we admit that the rod is composed of
discrete atoms, the disturbance immediately impressed gives rise
to molecular action which extends throughout the substance of
the rod, causing each atom to move in the same direction and
through the same space as the rod itself. If we consider an
atom at the preceding extremity of the rod, it is evident that its
motion must be due to an excess of molecular repulsion from
within to without above molecular attraction in the contrary
direction, so that, according to the theory, this end would be in
a state corresponding to positive electricity. At the other ex-
tremity the motion of an atom must be caused by an excess of
molecular attraction from without to within above molecular
repulsion in the contrary direction, and the superficial condition
would correspond to that of negative electricity. At the same
time there must be a gradual increase of density from the pre-
ceding to the following end, to account for the movements of the
interior atoms by molecular action, there being no such action
in the interior if the density be uniform.

13. Now it may be presumed that the electrified sphere, in
the case before us, by acting partially on the other sphere, that
is, by attracting only the superficial parts which are turned
towards it, produces effects on the whole sphere analogous to
those above described. By attracting towards itself the atoms
on which it immediately acts, it conspires with the repulsion
from within to without of the other sphere, and thus produces
an apparent excess of repulsion, and consequently a positive
state of electricity. Thus the electricity directly induced is con-
trary to that of the electrified sphere. At the same time, since
all the atoms of the sphere submitted to the electric influence
must tend to move in the direction of the partial impulse, and
since those of its atoms which are not immediately acted upon
can only move by its proper molecular action, it follows, just as
in the case given above for illustration, that there must be a
gradual increase of density from the nearer to the further side
of the sphere to produce internal molecular action in the direc-

Prof. Challis on a Theory of the Force of Electricity . 287

tion of the immediate impulse ; and at the boundary furthest
from the electrified sphere, there must, for the same reason, be
an excess of molecular attraction from without to within above
the opposite molecular repulsion. Thus the further side of the
sphere is electrified negatively. The opposite electricities would
plainly have been induced if the first sphere had been electrified
positively. These inferences are in accordance with well-known
results of experiment.

14. The induced electricity is maintained by the presence of
the electrified sphere, which supplies the pulling or pushing
force by which the electric condition of the other sphere is gene-
rated. On the removal of the former, the electric state of the
latter would immediately vanish, for the same reason that, in the
case of the rod, as soon as the hand ceases moving it, the mole-
cular action also ceases.

15. It has been supposed in the above reasoning that the
body on which the electricity is induced, is insulated by a non-
conductor, and is of limited extent. If it were connected by a
conductor with the earth, it must be considered, as far as regards
its electric state, to be a body of unlimited extent, and in that
case the argument which accounted for induced electricity on the
more remote parts of the same kind as that of the electrified body
would no longer apply. This electricity would be removed, as
it were, to an infinite distance, and the only induced electricity
would be that of the opposite kind.

16. It is found by experiment that if a spherical shell of
metal, perforated at one part, be electrified, little or no electri-
city is found on the interior surface. This fact is accounted for
by the neutralization of the electricities on opposite parts of that
surface by induction. The same explanation applies in the case
of an ingenious experiment made by Faraday, in which an elec-
trified hollow cone, having an acute vertical angle, was turned
inside out by pulling a thread. The electricity was always on
the surface which was exterior, that on the interior surface being
neutralized by induction.

17. An electric discharge takes place when on the approach of
two bodies oppositely electrified towards each other, the condensa-
tion of the air due to the negative electricity of one is neutralized
in the space between them by the rarefaction of the air due to the
positive electricity of the other. The spark is probably a conse-
quence of the disturbance of the aether caused by the sudden
return of the superficial atoms of both bodies, at the instant of
the discharge, to their normal positions.

18. It might at first sight appear that the theory which
accounted for induced electricity would also explain the attrac-
tions and repulsions by which bodies in a state of induced elec-

288 Prof. Challis on a Theory of the Force of Electricity*

tricity are found to act upon each other so as to produce motions
of translation. But these motions cannot be due to the attrac-
tions and repulsions which have hitherto been under considera-
tion ; for if so, an electrified body, according as its electricity is
negative or positive, would attract or repel another on which it
induces electricity. Whereas the fact is, attraction takes place
in both cases, and it is only after the bodies have been in con-
tact, and their electricities have become of the same kind, that
they mutually repel. Also the attractions and repulsions hitherto
considered act directly upon only an extremely small portion of
the whole mass, and for this reason must have a feeble translating
power. If they are at all operative in producing motions of
translation, such motions must be veiled by the action of more
powerful forces of a different kind. It is clear that forces by
which two bodies at one instant attract, and at the next repel
each other, cannot be intrinsic or resident in the bodies them-
selves, but must be attributed to the dynamic action under dif-
ferent conditions of the agent to which the force of electricity is
ascribed. Now we have just seen that the dynamic action which
the setherial medium — the agent assumed in this theory — exerts
by means of waves, fails to give the requisite explanation, and we
are thus restricted to the supposition that it acts by currents.
This, I think, will be found to be the true explanation. That
there exist steady setherial currents, is indicated by magnetic
phsenomena, as I hope at some time to show. Assuming the
existence of such currents, in whatever direction they traverse
oodies, whose atoms are so arranged that the density increases
with the distance from a fixed plane, secondary currents must
be generated which flow from the rarer to the denser parts with
a velocity depending on the magnitudes of the atoms, and the
number in a given space. The reason for this assertion is derived
from the hydrodynamical equation generally applicable to cases
of steady motion, which is of this form,

Pressure =/ (/) — ^-j

showing that where the velocity is greater the pressure is less.
But the velocity of a steady current is greater through the
denser parts of a medium than through the rarer, because in the
former the space the aether fills is less than in the latter, on
account of the greater occupation of space by the atoms of the
medium. Hence there is a constant accelerative force from
the rarer towards the denser parts, generating a current in that
direction. These secondary currents may be regarded as instances
of steady motion to which the equation above is applicable.
19. Now it has been shown (in arts, 13 and 14) that in a

Prof. Challis on a Theory of the Force of Electricity. 289

body electrified by induction there exists that gradation of den-
sity here supposed, and the condition required for generating a
secondary current is consequently fulfilled. A body inductively
electrified acts reciprocally on that by which its electricity was
induced, and thus both are in a condition proper for generating
secondary currents. If the electricities on the adjacent sides are
of opposite kinds, the two currents are in the same direction,
either towards the right hand or towards the left. And as the
velocity of the streams diminishes rapidly with distance from
the surfaces of the bodies by divergence and lateral Spreading,
there will be a position on the shortest distance between them at
which the conspiring streams will produce a maximum of velo-
city, and consequently a minimum of pressure. Towards this
point, therefore, there will be a tendency of both bodies to move
by the action of the pressure of the medium on the individual
atoms, and thus a reason is given by the theory for the attraction
towards each other of bodies oppositely electrified.

20. If the electricities on the adjacent sides of the bodies be
of the same kind, the currents will be in opposite directions, either
from or towards the space between. In both cases there will be
a minimum of velocity, and consequently a maximum of pres-
sure somewhere in the shortest line joining the bodies, because
there must be a point at which the difference of the opposite
velocities is least. The maximum of condensation at this point
is produced by the meeting of the currents when they flow
towards it, and by the confluence of the adjacent fluid wThen they
flow from it. Thus in both cases the pressure of the fluid will
tend from the intermediate position, and will separate the bodies
by pressure on their individual atoms. In this manner the
theory accounts for the observed mutual repulsion of two sub-
stances having the same electricities,

21. As the efficacy of these currents must be in proportion to
the molecular attractions and repulsions before treated of, to
which they owe their origin, and as these forces vary inversely as
the square of the distance, it follows that the effective force of
the currents varies with the distance according to the same law.
This result accords with experiment.

22. The above explanations give an account of motions of

electrified bodies the same in kind as those observed. Whether

the agency be sufficient in degree, cannot be readily determined.

On this point it may be remarked, first, that the pressures do

not act partially on the bodies, but, as in the case of gravity, on

every atom, and for this reason they are the more likely to be of

sufficient motive power; and again, the moving force of the

dV
pressure on a given atom, being proportional to V-p depends

290 Chemical Notices : — M. Wurtz on Oxide of Ethylene.

on the magnitude of the increment dV of velocity corresponding

dV

to the increment ds of space, and the factor —r- may be large,

although V is small.

Cambridge Observatory,
September 20, 1860.

XXXVI. Chemical Notices from Foreign Journals.
By E. Atkinson, Ph.D., F.C.S.

[Continued from p. 203.]

WURTZ* has continued his researches on oxide of ethylene,
which have led to further interesting results.
It combines directly with acids and neutralizes them. Oxide
of ethylene also unites with acids, forming basic salts. When
it is treated with anhydrous acetic acid, acetate of glycol is
formed. When this body has been separated by fractional di-
stillation, a considerable quantity of a liquid boiling above
200° C. remains. By working on large quantities, three pro-
ducts may be obtained from this liquid, which can be regarded
as basic acetates of oxide of ethylene, and which really are ace-
tates of polyethylenic alcohols f.

The first product boils at about 250°, and is the acetate of
diethylenic alcohol, formed in accordance with the reaction :

€2H4 1
2(G2 H4 G) + G4 H6 G3= G2 H4 [ O3.

Oxide of Anhydrous (G2 H3 G)2 J
ethylene. acetic acid. Diethylenic acetate.

When this compound is saponified by baryta, it is resolved

(G2 H4)2"|
into acetate of baryta and diethylenic alcohol, v ip f G3, or

Lourenco's compound J.

The second product boils towards 290° C, and is the acetate
of triethylenic alcohol : —

G2H4 "|

3(G2 H4 G) + G4 H6 G3 = ^ h* f °4-

Oxide of Anhydrous ,~a H3 ~. 2
ethylene. acetic acid. V^7 "■ &) J

Triethylenic acetate.

The third product, the acetate of tetrethylenic alcohol, boils at
above 300°, and must be distilled in vacuo. It is a thick liquid,
but perfectly colourless.

* Comptes Rendus, June 26, 1860.

t Phil. Mag. vol. xix. p. 124. X Ibid. p. 122.

M. Wurtz on Oxide of Ethylene, 291

£2H4 -.
G2H4

4(G2H40) + €4H603= G2H4 ^O5.

Oxide of Anhydrous €2 H4
ethylene. acetic acid. (C2H80)2^

Tetrethylenic acetate.
The last two bodies, when saponified by baryta, give respectively
triethylenic alcohol, > tt2 fO4, and

tetrethylenic alcohol, vT JH V05.

Thus one, two, three, or four atoms of oxide of ethylene can
unite with one atom of anhydrous acetic acid (which is equiva-
lent to two atoms of hydrated acetic acid) to form in the first
case a neutral acetate (diacetate of glycol) ; in the other cases
acetates, more and more basic, which give rise to more and more
complicated polyethylenic alcohols. The same acetates are
formed by the action of ordinary acetic acid on oxide of ethylene,
but in this case water is eliminated.

Oxide of ethylene unites directly with diacetate of glycol
(ethylenic acetate) to form polyethylenic acetates — a reaction per-
fectly comparable to the transformation of acetate of lead into
basic acetate when the neutral salt is digested with oxide of
lead. Thus :

€2H40 + £5* lo2= €2H4 lo».
Oxide of \\j* ^ J (€2 H3 Q)2 J

ethylene. ^~ Diethylenic acetate.

The basic properties of oxide of ethylene are well seen in its
action on salts.

Oxide of ethylene mixes with a concentrated solution of chlo-
ride of magnesium j but after some time the mixture solidifies,
magnesia is precipitated, and hydrochlorate of oxide of ethylene
is formed. This latter body is decomposed by potash, with the
formation of chloride of potassium and disengagement of oxide
of ethylene. Consequently oxide of ethylene displaces magnesia
from its compounds, but is in turn displaced by potash.

Oxide of ethylene precipitates hydrated sesquioxide of iron
from a solution of perchloride. It precipitates alumina from a
solution of alum, and subsulphate of copper from a solution of
the sulphate.

Its basic properties are thus seen to be very distinct. Capable
of neutralizing acids, of forming combinations with excess of
base, and of displacing certain oxides, oxide of ethylene consti-
tutes a true organic base, an alkaloid without nitrogen.

292 M. Wiirtz on the Synthetical Formation of some New Acids,

In continuing his researches*, Wurtz has examined the action
of oxidizing agents on these polyethylcnic alcohols, and has ob-
tained results of great interest, wnich will throw considerable light
on the constitution of the complicated vegetable acids.

By oxidizing glycol, Wurtz obtained glycolic, lactic, and oxalic
acids by reactions quite analogous to those by which alcohol is
transformed into acetic acid. By oxidizing diethylenic alcohol,
an acid isomeric with malic acid is obtained ; and by oxidizing
triethylenic alcohol, a still more complicated acid is produced.

The oxidation of diethylenic alcohol was effected either by
means of platinum-black, or by the action of nitric acid. In the
latter case the reaction was very violent, and a tumultuous dis-
engagement of nitrous fumes was observed. The acid liquid,
evaporated to dryness, formed a mass of crystals. These crystals
were dissolved in water, saturated with milk of lime, boiled, and
separated by filtration from a deposit of oxalate of lime which
had been formed. The liquor deposited, on cooling, a lime-salt,
which crystallized in long brilliant needles. Dried at 170°, these
crystals had the composition of a neutral and dry malate of lime.
The formula of the crystals is G4 H4 Ca2 O5 + 6 Aq j and they do
not completely lose this water below 160°. They are almost
insoluble in cold, and are difficultly soluble in boiling water.
The boiling saturated solution gives with nitrate of silver a gra-
nular precipitate, whose composition is €4 H4 Ag2 O5, which is
the formula of malate of silver.

AVhen this silver salt is diffused in water and decomposed by
sulphuretted hydrogen, an acid liquor is obtained, which, when
concentrated, deposits large rhomboidal prisms, very soluble
in water and in alcohol. Its composition is expressed by the
formula €* H6 O5 + H2 0. The new acid effloresces slowly in the
air, and loses an atom of water of crystallization, which it parts
with much more rapidly in vacuo, or at 100°. The dry acid
melts at 148°, and solidifies to a crystalline mass. At about 250°
to 270° it decomposes, with disengagement of a combustible gas ;
the residue is a strongly acid liquor, which after some time soli-
difies to a crystalline mass, and which is a true pyrogenic acid.

The new acid has the composition of malic acid, but differs
from it in form, in the amount of its water of crystallization, in
its efflorescing, and in comportment when heated. In one
respect it strongly resembles malic acid; fused with hydrate of
potash it gives off hydrogen, and forms acetic and oxalic acids : —
G4 H4 K2 O6 + KHO = €2 K2 O4 + €2 H3 KG2 + H2.

Potash salt. Oxalate of Acetate of

potash. potash.

When a solution of the acid is half-neutralized with potash,
* Comptts Rendus, July 30, 1860.

M. Louren9o on some new Polyethylenic Alcohols. 293

an acid potash salt is obtained which closely resembles cream of
tartar. The salt is anhydrous, and contains €4 H5 KG5.

The oxidation of triethylenic alcohol is accompanied by the
same phenomena as that of diethylenic alcohol. By suitable
treatment two lime-salts are obtained : one, slightly soluble in
cold water, is identical with that just described ; the other is
more soluble in water, and forms silky tufts like asbestos. The
composition of this salt is €6 H8 Ga2 O6. Its aqueous solution
gives a white precipitate with nitrate of silver ; this precipitate,
decomposed by sulphuretted hydrogen, yields a liquid which
contains a new acid, and which does not crystallize, but after
evaporation forms a syrupy mass.

Comparing these acids with the polyethylenic alcohols from
which they are formed, relations of a very simple character are
found to exist between them, analogous to those which exist
between alcohol and acetic acid ; a certain quantity of hydrogen
disappears and is replaced by an equivalent quantity of oxygen.
When glycol is transformed into glycolic acid, we may assume
that the radical ethylene, €2H4,is changed into glycolyle, C2H20;
in the case of diethylenic alcohol, we may suppose that both the
ethylene radicals are converted into glycolyle. Diethylenic
alcohol thus becomes diyly colic acid. The acid formed from tri-
ethylenic alcohol is similarly derived ; two ethylene radicals are
converted into glycolyle, while the third remains intact. In this
manner diglycolethylenic acid is obtained. The following formula?
exhibit these relations : —

?«*

Glycol.

Glycolic acid.

G2Hn

€2H20]

C2H4 ^O3

€2H20 lo3.

H2J

H2 J

Diethylenic alcohol.

Digly colic acid.

g*h4i

€2H4 -]

€2H4

>04

€2H20 L4
€2H20 f w '

€2H4

H2J

H2 J

Triethylenic

alcohol.

Diglycolethylenic acid.

Other acids may be formed from these polyethylenic alcohols.
Those here described possess the molecular complication and the
characters of the true vegetable acids, and they have been gra-
dually built up by synthesis from olefiant gas.

Some additional members have been added to the series of
polyethylenic alcohols by Lourenco*. In his original method
* Comptes Rendus, September 3, 1860.

294 M. Cannizaro on Anisic Alcohol.

for preparing these bodies by heating glycol with bromide of
ethylene, a liquid is formed containing, besides water and hydro-
bromic acid, a series of polyethylenic alcohols. By repeating
this operation on a large scale, and by fractional distillation, he
obtained diethylenic and triethylenic alcohols. The residue
could not be distilled under the atmospheric pressure without
decomposition. But by distilling it under a pressure of 0-025
millim., three compounds have been isolated. The first, tetrethy-

lenic alcohol, €8H1805=4(G2 j^ |o5, boils at 230° under this

pressure ; it is identical in properties with the body obtained by
Wurtz.

Pentethylenic alcohol, €10 fl*QP=B(& H*!9"' b°ils &t 281°
under the pressure 0*025 millim. It is a viscous liquid resem-
bling glycerine.

The third compound, hexethylenic alcohol,

Gi2H2607=6(C2I^)\o7j

boils at about 325°, and is distinguished from the former by its
greater viscosity.

If the operation were conducted on a sufficiently large scale,
the higher homologous compounds could be obtained. They

have the general formula n\ IU iow+1. They are more vis-
cous in proportion as their equivalent is higher, and there is a
difference of about 45° between their boiling-points. Lourenco
has examined the direct action of hydrobromic glycol on glycol,
the lowest member of the series, and he represents the general
equation for their formation in the following manner : —

^*?W+J +€T}°= (,,+ 1)(0ig?}^+f + HBr.

Br

The hydrobromic acid formed reacts on the excess of glycol
and regenerates the hydrobromic glycol, which in turn acts on
the higher polyethylenic alcohols. Hence it is that no other
bromine compound than hydrobromic glycol is formed, whatever
be the stage at which the reaction is interrupted.

Anisic alcohol, €8H1092, contains twice as much oxygen as
the ordinary alcohols ; and it may be regarded either as an
alcohol containing an oxygen radical, or as being analogous to
the class of glycols. In the former case its formula would be

written ^^lo, and in the latter €8^8/}o2. On the

M. Schischkoff on Fulminic Acid. 295

supposition that it is a glycol, cinnamene (styrol), C8 H8, would
be its radical. Cannizaro is occupied with the question of the
constitution of this body*. His researches are not yet finished ;
but in the meantime he publishes an account of two oxygenated
alkalies which appear analogous to those obtained by Wurtz from
oxide of ethylene.

When hydrochloric acid is passed into anisic alcohol, an ether
is obtained which has the formula Q8 H9 0 CI. It i3 analogous
with chlorhydrine of glycol. When this body is treated for some
time with strong alcoholic ammonia, a white deposit is obtained
consisting of a mixture of sal-ammoniac and two organic bases.
They are separated from sal-ammoniac by treatment with alcohol,
and are separated from each other by solution in water and cry-
stallization. The more soluble in water is a primary anisammine,

C8H90 "I
€8 H11 9N= TT2 f N* and the other is a secondary anisam-

mine, €16 H19 O2 N = £f R9 ^*\ N. The first one crystallizes

in small needles, and the second in white plates. Both of them
are strong bases. Both of them form compounds with bichloride
of platinum. The compound of primary anisammine and bi-
chloride crystallizes in small lustrous yellow plates of the for-
mula €8 H11 NO, HC1 Pt CI2. The other compound crystallizes
in small yellow needles, and has the formula

C16 H19 NO2 HC1 Pt CI2 + H2 0.

In some recent researches on fulminic acid, Schischkofff has
been led to a formula for this acid different from that which he
formerly proposed}. He considers it to be C2 (NO2)2 H4 (CN)2,
which represents alcohol in which the cyanogen replaces
oxygen, and two equivalents of the group NO2 two equiva-
lents of hydrogen, — a formula which explains the formation^ of
fulminic acid from alcohol.

The action of nitric acid on alcohol always gives rise to the
formation of hydrocyanic acid ; Schischkoff assumes that there
is produced at the same time a binitro- ethylene, C2 (NO2)2 H2,
which, combining with hydrocyanic acid, forms fulminic acid,

C2 (NO2) H2 + 2CN H=€2 (NO2) H4 (CN)2.
Binitro- Hydrocyanic Fulminic acid,
ethylene. acid.

The reasons for this mode of viewing fulminic acid are, —
1. That the fulminates have the characteristic properties of
the cyanides ; treated with chlorine they yield chloride of cya-
nogen, and with hydrochloric acid they give hydrocyanic acid.

* Comptes Rendus, June 11, 1860.

t Ibid. July 16, 1860. % Phil. Mag. vol, xiv. p. 100r

296 Margueritte and Sourdeval on the Formation of Cyanogen.

2. When the fulminates of silver or of mercury are treated
with alkalies, a cyanate is formed, — a formation due to reduction
of the nitro-compound under the influence of the affinity of the
alkaline cyanides for oxygen.

3. The explosive properties of the fulminates would be readily
explained by the excessive instability of binitro-ethylene.

4. Although the group binitro-ethylene is hypothetical, the
discovery of the analogous bodies, nitroform, €(NG2)8 H, and
triacetonitrile, €2(N92)3N, renders its existence by no means
impossible ; and its combination with hydrocyanic acid would be
perfectly analogous to the combination of the hydracids with the
hydrocarbons.

MM. Margueritte and Sourdeval* have made a series of
researches on the formation of cyanogen, and the production of
ammonia by means of atmospheric nitrogen. Their experiments
have been made on a large scale, and they state —

1. That baryta, calcined in the presence of carbon and of
atmospheric air, readily assimilates nitrogen and carbon, and
that this cyanuration of barium is a very simple operation.

2. At a temperature of 300° C. cyanide of barium is decom-
posed by a current of aqueous vapour, and disengages the whole
of the nitrogen which it contains under the form of ammonia.
The industrial consequences of these two reactions are the ma-
nufacture of the cyanides of barium and potassium, of prussian
blue, of ammonia, and of nitric acid and nitrates by known
methods.

The authors add that the methods which they adopt for pre-
paring baryta yield this base in such quantity that it may be
practically used in the manufacture of sugar.

Von Hauerf has described some seleniates, and has also mo-
dified the methods of preparing selenic acid. Selenium is dis-
solved in nitric acid, and the selenious acid is converted into
selenic acid by fusing with nitrate of soda. The mixture of
seleniate and acetate of soda thus obtained is mixed with a solu-
tion of nitrate of lime. The seleniate of lime which forms is
almost as insoluble as the sulphate. It is treated with oxalate
of cadmium, which completely decomposes it : after filtration
from the insoluble oxalate of lime, a current of sulphuretted hy-
drogen is passed through the solution of seleniate of cadmium.
After filtering the precipitate of sulphuret of cadmium, the solu-
tion of selenic acid is freed by heating from excess of sulphur-
etted hydrogen.

* Comptes Rendus, June 11, 1860.

t Sitzungsberichte der K. Academie der Wissenschaflen zu Wien, January
I860.

M. Weber on Selenium Compounds. 297

The following seleniates were prepared by dissolving the car-
bonates or hydrates in selenic acid : —

Seleniate of Soda, NaO, Se03 + 10 Aq — Large crystals resem-
bling Glauber's salt.

Seleniate of Lime, CaO, SeO3 + 2 Aq.— Needles like sulphate of
lime.

Seleniate of Nickel, NiO, SeO3 + 6 Aq. — Thesecrystals resemble
the corresponding sulphate, as has been shown by Mitscherlich.
They lose four equivs. of water at 100°.

Seleniate of Nickel and Potassium, KO, NiO, 2Se03 + 6Aq. —
Obtained by the spontaneous evaporation of a solution of the
two salts. They lose four equivs. of water at 100°. The analo-
gous sulphate is not perceptibly altered at 100°.

Seleniate of Cadmium, CdO, SeO3 + 2 Aq.— These crystals differ
both in form and composition from those of the corresponding
sulphate. They lose 1 equiv. of water at 100°.

Weber has described the formation of oxy chloride of selenium
and of the alum of selenic acid*. The former body is obtained
by distilling chloride of selenium, SeCl2, so that it comes in con-
tact with an equal volume of selenious acid. The two bodies
combine to form white vapours of oxy chloride of selenium,
which is redistilled over selenious acid.

It is a yellowish liquid which fumes in moist air ; it has the
density 2*44, and boils at about 240°. It dissolves readily in
water, forming hydrochloric acid and selenious acid. Its compo-
sition may be expressed by the formula SeCl2 4- SeO2, according
to which it is a compound of selenious acid and of chloride of
selenium. It may also be considered as being selenious acid
in which an atom of oxygen is replaced by an atom of chlorine.
Oxychloride of selenium is also formed by the action of a small
quantity of water on chloride of selenium.

It was found impossible to prepare a compound corresponding
to Regnault/s chlorosulphuric acid. Chlorine is without action
on dry selenious acid.

To prepare selenic acid, selenite of soda was fused with nitrate
of potass, the mixture treated with nitrate of lead, and the pre-
cipitate of seleniate of lead decomposed by sulphuretted hydro-
gen. The solution of selenic acid was concentrated, and a
quarter of it neutralized with carbonate of potass ; the remaining
three quarters were digested with pure hydrate of alumina. The
mixed liquids were left to spontaneous evaporation, and after the
expiration of twenty days, beautiful crystals were obtained. Their
composition was Al2 O3, 3Se03, KO, SeO3 + 24 HO. The crystals

* Poggendorff's Annalen, vol. cviii. p. 613.
Phil Mag. S. 4. Vol. 20. No. 133. Oct. 1860. X

298

Mr. T. Tate on the Construction of

have just the form of those of ordinary alum ; they are combina-
tions of the octahedron and cube. They have all the lustre of
alum crystals, than which they are somewhat more soluble.
When heated, they give off water and finally selenious acid and
oxygen.

XXXVII. On the Construction of a new Air-thermometer.
By Thomas Tate, Esq.*

AIR, from the uniformity and extreme range of its expansion
under an increase of temperature, seems to be the sub-
stance best fitted for measuring changes of temperature. But
the indications of the ordinary air- thermometer at present in use
are subject to derangement from the varying pressure of the
atmosphere. In the differential thermometer, it is true, the
atmospheric pressure is altogether excluded ; but then this in-
strument cannot be employed, as in the case of the common
thermometer, for indicating the temperature of the surrounding
air. Now in the instrument here proposed (represented in the
annexed diagram), the variations of pressure of the atmosphere
are corrected by an easy adjustment ; and the air in the instru-
ment being thus maintained at a constant pressure, the volume
of this air becomes a true measure of the change of temperature.
G and N are small glass globes, about an inch and a tenth in
diameter, connected with the bent
tubes, as shown in the diagram;
A K C a barometer-tube about
20 inches in length; E L a wide
thermometer-tube about TJTtn °f
an inch diameter ; LNM a tube,
somewhat larger in diameter, con-
nected with the globe N, which ter-
minates with an open tube; B an
india-rubber ball, about 1 £ inch dia-
meter, having an open tube proceed-
ing from it, forming an air-tight
connexion with the globe N ; S the
head of an adjustment-screw, which,
working in a hollow screw formed in
the cross bar H I, compresses the
ball B as may be required ; A B C and
M Ij D are mercury columns ; the
globe G and tube A E D contain dry
air, and the space above the mercury
C is a Torricellian vacuum, so that the

* Communicated by the Author.

a new Air-therrmometer. 299

column of mercury B C is a constant measure of the pressure of
the air in the globe G ; E F a scale of degrees, the graduation of
which will be hereafter described. A mark is placed at A, so
that the air in the globe may be always brought to a constant
pressure by means of the adjustment screw S. Suppose the
temperature of the air to change, then a slight change will
be observed in the level of the mercury at A; by relaxing or
tightening the screw S, as the case may require, the mercury is
brought on a level with the mark A (which may be done with
mathematical precision), and then the number on the scale E F
coincident with the surface of the mercury in the thermometer-
tube will give the temperature of the surrounding air. The
scale E F is graduated in the following manner : —

The tube A K C is filled with mercury in the same manner as
that of an ordinary barometer. The globes and tubes being
filled with dry air (by a process not necessary to describe here),
and a sufficient quantity of mercury being introduced at M, the
air is exhausted (by means of an air-pump attached to the tube
of the globe N) until the mercury falls for a short space in the
tube B C ; then after allowing the external air to euter the globe
N, the mercury will rise in the tube ME, say to J, so that the
sum of the columns B C and N J will be equal to the column of
mercury balancing the pressure of the atmosphere at the time ;
that is to say, if this column be 30 inches, and B C be 18 inches,
then N J will be 12 inches. The india-rubber ball, in a some-
what flaccid state, being attached to the globe N, and the screw'
bar I H fixed, the screw-head S is turned so as to compress the
air in the ball until the mercury in the tube M E stands at D
about the middle of the tube E J when the air is at or near to
mean temperature ; a mark is then made at A coincident with
the level of the mercury. The ball of a delicate standard ther-
mometer being placed beside the ball G, two extreme tempera-
tures, / and tv are noted, and marks placed coincident with the
corresponding levels of mercury in the tube L E ; then the space
between these marks will give a reading of degrees equal to the
difference between the two temperatures; hence the scale is
readily formed.

Let V = the volume of the air at / temperature.

P = its corresponding pressure measured by the column

of mercury B C.
p = the length of the column of A K B.
a = section of the tube D.
b — section of the tube ABC.

V, = the volume of the air at tl temperature, PA being-
its corresponding pressure.

X2

300 Mr. T. Tate on the Construction of

L/(_f= change of the column of mercury D corresponding
to tx—t difference of temperature.

-, — = the expansion of mercury and glass respectively
a p

per unit of volume, for tl—t degrees change of

temperature.

Then we have

When the expansion of the mercury and glass are neglected,
P,=P, and in this case equation (1) becomes

V-V-gJ^fc-Ol
but

•••L'.-'=^+7)^-')« • • • • • »

which shows in this case that litx-t is proportional to tl— 1} and
consequently that the graduations on the scale EF must be
uniform.

From equation (2), we have

V 1

Length of 1 degree on the scale = - • ^ ,

and

V T
Range for T degrees . . . = - • jgg^

If V=l, a = -006, *=50,andT=54; then we find the length
of one degree on the scale to be about one-third of an inch, and
the range or length of the whole scale E F to be about 18 inches.

It will be observed that the glass ball G need not greatly ex-
ceed the size of the bulbs of some of our ordinary thermometers ;
and the whole length of the instrument may be 5 or 6 inches
less than that of a barometer.

These formulae are sufficiently exact for determining the pro-
portion of the different parts of the instrument ; but it is neces-
sary that we should determine the amount of the disturbances
arising from the expansion of the mercury and glass.

Throughout the following investigation, all terms are neglected

which contain as a factor the product of - and -, or the square
of either of them.

a new Air-thermometer. 301

Let z = the increment of the column B C due to the change
of temperature ; then

Volume of mercury in A B C before expansion

Volume of this mercury after its expansion

= (P+p)b(l+l). ...... (8)

Section of the tube after its expansion

Volume of mercury in A B C after its expansion

^(P+p+z)b(l+~). ... (4)
Therefore, by equating (3) and (4), we get

p+*=

but

H

Pl(i+i)=p+*;

p v+vJ, . 3 p : . i

1+fP 1+«

-('>'fX'-f-|('-i)'

On the supposition that the marks corresponding to the tem-
peratures t and tl are made upon the glass, V being the volume
of the air at t temperature ; then we have

V1=v(l + I)+L(l_(x«(l + !).

Let —f and —, be put for the expansions for one degree, then

P

Substituting the values of ^~ and Vt in equation (1), and solv-

302 Mr. T. Tate on the Construction of

ing the resulting equality for Lf,_<, we get

x{l-(^)f(i-^)}. • (5)

Neglecting (ti — t)'p (-, — oi) as being very smali compared
with 1, we have

where htl_t is proportional to tx — t. This expression is an ex-
ceedingly near approximation to the true formula.

Let the space L^_j, expressed by equation (5), be divided into
/1 — t equal parts, then each part will be the length of one
degree on the scale, that is,

Length of 1 degree on the scale rsL^x A

.\ Length of t9 degrees on the scale =L^_f x a .

But the true length of a degree will be derived from equa-
tion (5) by making ff— tss 1, that is,

True length of 1 degree =L2, and

True length of /2 degrees =s L,3 ;

."'. Error in t2 degrees = L,2— L^* x j^—.-

t\ — i

Putting arNfe the error in t^ degrees taken as a proportional
part. of the length of one degree on the scale; then

a' =

T 1

^■^vf6^) (7)

This expression gives the correction for any temperature t + tq
or t — t2, that is, for any temperature t2 degrees above or below /.

The only dimensions of the instrument involved in this ex-
pression are the lengths of the columns A K B and B C.

a new Air -thermometer. 303

When t2 is less than tl — ti the value of x1 is positive; in this
case, therefore, the value of od must be added to the temperature
indicated by the scale.

When t2 is minus, or when t% is greater than tx — t, then in
both cases the value of x' is negative ; in these cases, therefore,
the value of x' must be subtracted from the temperature indi-
cated by the scale. In both these cases the value of x' increases
with /2.

If t and tx be taken as the extreme temperatures of the instru-
ment, then we have as the condition of maximum error,

whence we find

Max. value of a;'=(^)2|(I-33p,). . (8)

T i. f QOO ± OfiO P_ £ *_ ■*- * f

Leu-o^^-oo, p_6, a,-18x550> ^-18x4160'

then we find max. value of x =*01; that is, in this case the
maximum error would be the hundredth part of a degree.

But as it would be more convenient for construction to take /
and tx at certain mean limits, thus, let 3(^ — t) be the extreme
range of temperature, that is, tx — t degrees above tv and tx — t
degrees below t ; then we find, by substituting -f 2{tx — t) or
— (tl— t) for t2 in equation (7),

Max. value of x' = -2(-,-02f (j- 3-,)- • (9)

Let £=50°, ^ = 68°, giving an extreme range of temperature
between 32° and 86° ; then taking the values of the other quan-
tities the same as before, we find the

Max. value of x1— -0096 ;

that is, in this case the maximum error would be less than the
hundredth part of a degree, — an almost inappreciable quantity.
Within this range of temperature, therefore, the indications
of the instrument may be taken as perfectly true.

Hastings, September 14, 1860.

[ 304 ]

XXXVIII. On the presence of Arsenic and Antimony in the
sources and beds of Streams and Rivers. By Dugald Camp-
bell, Analytical Chemist to the Hospital for Consumption,
Brompton*.

SOME months ago I had a specimen of iron pyrites from coal,
or coal pyrites as it is familiarly called, sent to me, to exa-
mine for arsenic, and I was somewhat surprised to find in it the
quantity of arsenic which I did, arsenic not being generally set
forth in the analysis which I have seen of such pyrites, although
my own impression was that, if looked for in a proper manner,
it would be found.

Having been informed that the coal associated with this
pyrites crops out in the beds of the streams and rivers of the
district from which my specimen of coal pyrites was sent, it
occurred to me that if the sand from the beds of such streams or
rivers were carefully examined, arsenic would be found in it.

Having obtained a specimen of the sand, after a great many
experiments (for I was at first beset with difficulties about the
purity of the various materials I used in my examinations, and
other causes) I at last succeeded in obtaining arsenic from it in
every experiment, and really in notable quantity.

Besides arsenic, I also got antimony, which I had not ob-
served in my coal pyrites, although it may very likely have been
there in small quantity.

The quantity, however, of both the arsenic and the antimony
appearing so considerable in this specimen of sand, induced me
to think that their occurrence was due to other sources besides
the coal pyrites, and led me to the opinion that I should find
these metals in the sand from the sources or beds of most streams
or rivers in greater or less quantity, depending upon the geolo-
gical formation from which such sand had its origin ; and after
making several experiments, I found my views confirmed in this
respect ; and in every specimen of sand from these sources which
I have hitherto examined, I have obtained arsenic, and generally
also antimony, and, as I had supposed, in some instances the
arsenic was in considerable quantity, in others in small quantity ;
but in no instance is its presence in a doubtful quantity.

I say " generally also antimony/' although it is more than
likely that antimony exists in every specimen of sand which I
have examined; but the process I followed was especially for
arsenic, not for antimony, although, as I have stated, I very often
got some antimony at the same time with the arsenic.

Although I speak of the arsenic being in greater quantity in
the one sand than in the other, this is observed as yet only by
* Communicated by the Author.

Presence of Arsenic and Antimony in Streams and Rivers. 305

qualitative tests. I have not directly estimated quantitatively
the arsenic in any one instance ; nor do I think that by the pro-
cess which I follow to detect the arsenic, and which I shall give,
should I get, in most instances, if not in all, anything like the
quantity which the sand contains.

The process which I adopt is as follows : — The sand is first
dried by means of a bath at not too high a temperature, and
sifted, if necessary, through a coarse sieve, to remove anything
larger than sand ; the portion for the experiment I then weigh
out. I seldom require more than two ounces of the dry sifted
sand. I then ascertain that my hydrochloric acid is free from
arsenic (or rather how far it is contaminated with it, for it is
rarely indeed that this acid is found entirely free from arsenic),
which I do by introducing into a drachm of the acid diluted with
about three 'drachms of distilled water, when brought to boil in a
small flat-bottomed flask, about the eighth of a square inch of
bright copper-foil, specially prepared as free from arsenic as it is
possible to be obtained*, and gently boiling the same from about
half an hour to three-quarters or so, avoiding much evaporation
by having a small funnel in the mouth of the flask. Should this
piece of copper get coated with arsenic, I take it out and replace
it by a similar piece, and boil it in a similar manner ; should this
piece likewise get coated, I should scarcely like to use such im-
pure acid ; but if no coating has taken place, or only one piece
was coated, I measure out into a small flat-bottomed flask (a flask
capable of holding about three liquid ounces is the size I prefer),
half an ounce of the acid, and gradually add to it the two ounces
of the dry sifted sand. I now close the bottle with a cork, and
allow it to stand for some hours until the acid has thoroughly
penetrated the sand, when I remove the cork, and at once attach,
by means of a perforated cork, a bent tube about 3 feet long,
leading into a receiver through a cork, a little loose at first, but
capable of being made tight afterwards, the receiver being placed
in water. Heat is now applied by means of a sand-bath, gently
at first, gradually increasing when the cork at the receiver is
made to fit tight. I also apply wet rags or bibulous paper
down the tube. In about an hour the greater part of the distil-
late will have passed into the receiver, when it may be detached.
The distillate, which varies in quantity according to the nature of
the sand, I measure. I have found it to average 190 grains;
but, as stated before, it varies in quantity according to the nature
of the sand.

The test which I generally first apply is the copper one,

* I have lately examined a great many specimens of copper said to be
free from arsenic; of these, eight specimens were electrotype, but in all I
found arsenic.

306 Presence of Arsenic and Antimony in Streams and Rivers.

exactly as I have described in testing the acid, only, instead of a
drachm, I use a less quantity, proportionate to the acid used and
the distillate obtained. After one piece of copper is coated, it is
withdrawn and another substituted, and so on until no more
coating takes place ; much evaporation of the liquid is made up
from time to time by a little boiling water.

When antimony is in the distillate, it deposits more readily
than the arsenic upon the copper, and the first pieces coated
have more of a purple or blue tint than the steel-grey colour of
the arsenic.

The remainder of the distillate may be tested by a Marsh's
apparatus, heating the gas as it passes through a quill-tube
drawn to a fine point, in order to get the metallic arsenic de-
posited upon the tube.

The metallic arsenic, deposited in this way from the residue of
the distillate from two ounces of the sand, is in many instances
of sufficient quantity to dissolve or sublime and examine by other
tests.

The sands which I have examined have been selected with
much care ; and in most cases, when taken from the beds of streams
or rivers, they have been taken above where they could receive
contamination from coal-pits or works, or contamination of any
description whatever : I append a list of them, in order that any
one may repeat the experiments.

I am indebted to Mr. Woodcroft, of the Great Seal Patent
Office, for the first eight specimens, and to Mr. George Phillips,
of the Inland Revenue Laboratories, for the next four specimens,
both these gentlemen having taken much interest and trouble in
the matter. For most of the other specimens I am indebted to
kind friends, and one or two I have procured myself.

List of Sands examined.

From Cragg Hall, Cheshire.

From Black Brook, which falls into the Dane, Staffordshire.

From the source of the Wye, the Buxton Water supply.

From the source of the Goyte, Derbyshire.

From Oaks Clough Redmires, supply of Sheffield.

From the source of the River Porter, Fulwood, Sheffield.

From Hog Shaw Brook, Buxton.

From the source of the River Dove, Derbyshire, where it issues

from a compact limestone, rock at Mr. Marsden's Dowal.
From Middle Lake, Dinish Island, Killarney, Ireland, County

Kerry.
From Flesk River.

From Flesk River, Killarney, Ireland, County Kerry.
From Ogiven River, near Penrhyn Slate Quarries, about four or

Meditation on the Idea of Poncelet's Theorem. 307

five miles from the outlet of Ogiven Lake, Carnarvonshire,
North Wales.

From Snowdon, 100 yards above the Ceunant Maur Fall, Car-
narvonshire, North Wales.

From the junction of the River Kinder and Sett, Derbyshire.

From the Brent, two miles below Apperton Bridge,

From the Thames, a quarter of a mile above Teddington lock.

From the Mardyke, near Stifford, Essex; falls into the River
Thames at Grays.

From the River Lea, Essex, 300 yards above the East London
Water Works.

From brook emptying itself into the Wrike, Melton Mowbray,
Leicestershire.

From Ladies Well Spring, Pitlour, Fifeshire, Scotland.

From Garden Brook, Pitlour, Fifeshire, Scotland.

Although in my experiments I have not yet met with a sand
from the source or bed of a stream or river that does not contain
arsenic, and perhaps antimony also, yet, judging from the ex-
ceeding variability in the quantity in each, I am far from think-
ing that sands will not be found, though I should say they will
be few in number, that will not contain these metals.

XXXIX. Meditation on the Idea of Poncelet's Theorem. By
J. J. Sylvester, M.A., F.R.S., Professor of Mathematics in
the Royal Military Academy, Woolwich*.

HITHERTO Poncelefs theorem has been regarded as a
method sui generis and complete in itself; but in truth it
is' but the first germ or rudiment of a vast and prolific alge-
braical theory ; and not only so, but the principle which it con-
tains admits of applications of the utmost valine in various
dynamical and analytical questions, which it is surprising should
have been allowed to lay so long dormant. For the present,
however, I mean to confine myself to a very brief indication of
one direction in which the theorem admits of being generalized.
And first I will make a remark upon so simple a matter as the
extraction of the square root, which seems to have escaped obser-
vation, and at all events is so far from being generally known,
that two of the highest authorities for mathematical erudition in
this country whom I have consulted on the subject provisionally
accept it as new.

Let r be an approximate value of */N ; then by that mode
of application of Newton's method of approximation to the equa-
tion a?2 = N which is equivalent to the use of confinued fractions,

* Communicated by the Author.

308 Mr. J. J. Sylvester : Meditation on the

we may easily establish the following theorem, viz. that
r8 + N r* + 3rN r^ + fo^N + N2 r5+10r8N + 5rN9 '*
2r ' 3r2+N' 4^ + 4r^i ' 5r4+10r2N~+N2 ■ ' "

will be successive approximations to VN, whose limits of error
can be assigned when a limit to the error of the first approxi-
mation r is given. The coefficients of the qth approximation, it
will be observed, are for the numerator the alternate binomial
coefficients

1 c£zi Q (£=1>. fe=?). «=? &

i, q 2 > g- 2 3 4 ,«c,

and for the denominator the intermediate ones,

q-1 q-2 9

Mr. Cayley has reminded me that the third approximation,

— -g — ~-, is a special case of a formula for any root of N given

in the books ; and to Mr. De Morgan I am indebted for a hint
which has led me to notice that all these forms may be deduced
from the Newtonian method of approximation f.

If we call the ith approximation <f>(i, r), we shall find that the
functional equation <f>(j, <f>(i, r]) = <f>(ij,r) will be satisfied;
which is not so mere a truism as might at first sight be supposed,
as any one may satisfy himself by studying the analogous theory
for cubic or higher roots, a part of the subject to which 1 may
hereafter return.

Now as to the limits of accuracy afforded by the successive
approximations. Let e be a known limit to the relative error of

the first approximation r, by which I mean that ( =J- J <e2.

•

* In other words, if r be the first approximation to VN, the »th approxi-
mation will be

(r+VN)*+(r-VN)fV5r

(r+VN)'-(r-VN)« '

so that the relative error becomes

2(r— VN)'

(H- V1T)«— (r-VNy'

in which form the theorem is self-subsistent, and needs no proof. But the
fact remains interesting, that the application of Newton's method of ap-
proximation to the equation #3=N will be found to lead to the form above
written at the »th step of the process conducted after the continued-fraction
fashion.

t The expansion (after Newton) of VN introduces the binomial coef-
ficients— a curious fact ! What are the analogous integers which the con-
tinued-fraction process applied to \/N will produce?

Idea o/Toncelet's Theorem, 309

For greater simplicity, I take separately the cases where r is too
great and r is too small.

1. Let \/N<.r< (1 + €) ^N ; then the errors will be through-
out in excess ; and we may assign as a limit of error to the ith
approximation a quantity, say ei} which is a known function of

2 . . 6*

e, viz. /n~~i — fv — v wn^cn *t mav ^e noticed is less than ^r~^,

2. Let \/N>r>(l— rj) -i/N; then the errors will be alter-
nately in defect and excess, and to the zth approximation we may

assign a limit of error rjif where 9?f= g -i _iv_/ -i\i*-
We may now apply these results to Poncelet's linear approxi-

* If we write

€{— ${€,{) and ?;£=%,«),

then if « be any odd number,

6(d(€,i)J)=0(e,ij),
S($(ri,i),j)=S(ri,ij);
and if i be any even number,

*(*(«, *).i)=*(*V)>

Or more simply, if the error in excess be treated as positive, and in defect
as negative, and 8 be the first and 8{ the ith limit of error, we shall have

and calling 8; —6{i, 8),

N+a?2
Thus, then, if we call — g — =\jrcc, yjrqx will correspond to the (2q)th

order of approximation, and the absolute value of the error w,ill be less than

2»*

(2+bf-lF

By way of example, suppose we take 6 as our first approximation to v31,
then

and if we make ylrx=z J~x , we shall have
2a?

* Vr46: V31::l+«:1,

where

2

G><

23i6— r

which serves to exemplify the prodigious rapidity of the approximation in
this method of extracting the square roots of numbers.

310 Mr. J.J. Sylvester : Meditation on the

mate representation of K/a + bx + cx*. Suppose f-r-gx is the

first approximation, as found by Poncelet's method, with a maxi-

i . ^ (/+<7*)2+ {a + bx + cx*) ... ,
mum relative error e. then -¥ — * ', » ; — will be a

much closer approximation, with a relative error never exceeding

e* . e2

pt — in excess, nor « in defect. So a still nearer approxi-

2 + e 2—e rr

.n, (f-\-gx)3 + S{/+gx){a-hbx-hcx2) ., .-.£
mation will be w * ' i , x~ , * ': — - — « \ with a relative

3(f+gx)* + a + bx + cx2

e8 e*
error never exceeding ~-r — ~ — jc-Q in excess, nor - — ^ jr-s in

° 4 + 6e + 3e2 4— 6e-f-3e*

defect, and so on. The marvellous facility which these formulae
afford for the calculation of elliptic and ultra-elliptic functions,
and not merely for their computation as by a method of quadra-
tures, but (which is of far greater importance) their quasi-repre-
sentation under circular and logarithmic forms, with assignable
limits of proportional error, will be illustrated in a future com-
munication. As regards the idea of substituting rational for
irrational functions, I have only to-day learned from Mr. Cayley
that I am anticipated in this by Mr. Merrifield*, in a paper very
recently read before the Royal Society, but not yet printed in the
Transactions f-

* I quite concur with Mr. Merrifield, and in fact before being made ac-
quainted with the existence of his paper, had emitted the same opinion
(among others to Dr. Borchardt of Berlin), that the substitutive method,
consisting in the employment of rational functions in place of the radical,
affords by far the most expeditious means for the calculation of elliptic
functions of all orders, especially the third, and supersedes the necessity
for the construction of special auxiliary tables. I believe, however, that
my substitutions, founded on Poncelet's views, are in general the best that
can be employed for the purpose. In addition to other advantages they
possess this, which deserves notice — that as we know a priori a superior
limit to the proportional error, the arithmetical values of the integrals to
which they are applied may be brought out correct to any required place
of decimals, without its being necessary to calculate and compare a superior
and inferior limit to the integral, either one of these being sufficient
in my method to indicate its own reliable degree of precision.

t In general it is obvious, if <f>x between the limits a and b retain always
the same sign, and tyx within these limits be sometimes greater and some-
times less than (f>x, but the difference between them be always less than

f <f>x, then I dxtyx will differ from 1 dx<f>x by considerably less than

/•a Jb Jb

( I dx(f>x. Paradoxical, however, as it may at first sight appear, there are

extreme cases where this difference tends to a ratio of equality with
< 1 dx<\>x. The complete elliptic function of the first order may be made

Idea 0/ Poncelet's Theorem. 311

The method, however, of Mr. Merrifield in working out this
conception is, I believe, entirely different from that here indi-
cated: how the many mathematicians of a practical stamp,
English and foreign, who have worked with Poncelet's method
during the last quarter of a century, should have managed to

to furnish an example of this. Let

frr- l = V(l-a*)+W

V(l-«*)(l-c**») Vl-#2(l-cV)
(sothat62=l-c2), and let

Vl-a?2 (1-cV) '
if we make

f— z

s/2-\

1 + V2 1 + vV V2 + 1

it follows from Poncelet's theorem, that for all values of x intermediate
between 0 and 1, yjsx will differ from (£>x by less than e(px.
Now it will easily be found by ordinary integration that

b

tan-1
c

Hence I dx <f>x must be always less than
Jo

/ . 1+c g b

2(13^ lo^T^ + (T3^tan-i -,

I , 1 + e 1 6

*•«• ^^^l^+c^11"1?

when c becomes indefinitely near to unity ; that is, when b becomes inde-

2 7T

finitely small, this approaches indefinitely near to logr+o- But we

know, by a theorem of Legendre, that the approximate value for the inte-

• 4 f i

gral in such case is log t ; so that the superior limiting value of I dx (fix,

Jo
found by the application of Poncelet's method, approaches in this instance
indefinitely near to the value itself. The explanation of this is easy. As
c approximates to unity, the only important values of x in the integral

dx

I

Va-^Xl-eV)

are those which lie in the immediate vicinity of 1 ; and for all such values
the relative error is at a negative maximum.

It is not a little remarkable that so rude an application of Poncelet's
method should serve to indicate almost with the force of rigorous demon-
stration the approximate formula F(c) = log r-f constant, when c ap-

312 Mr. J. J. Sylvester: Meditation on the

overlook so obvious and important an extension of the principle
and its applications, I find hard to realize; and my wonder
is even greater that I should not have been anticipated twenty
years ago, than that I should have been anticipated so recently.
But the algebraical theory to which this extension points the
way is replete with interest of a far higher order than its appli-
cations to practice ; for plainly the derived approximate frac-
tions, however sufficient for the purposes of computation, are

proaches indefinitely near to unity, the constant left undetermined being

known to be less than log 2+ q*

Nay, the demonstration may be made absolutely rigid if we set about to
find an inferior limit. To this end make

we shall find without difficulty

i i l-f-y-6 y+b

I

*dx=jr logy_1+6 • ;pj, where y = Vl +b\
and consequently we shall obtain as an inferior limit to F(c) the expression

yiog^n+6 '-yip

2

which approaches indefinitely near to logr- as c approaches indefinitely

near to unity. It is thus seen that Legendre's F(c), when c is indefinitely

2 2 77

near to 1, lies between log r and log ^ -f qJ the arithmetical mean between

'2. TV 1

these limits is log^ + j, i. e. log ^ +1*4785, differing by only *0923 from

the true value log^ + log 4. Of course, when the form of F(c) in the case

supposed is known, viz. log ^ -f C, there is no difficulty in determining C

(as may be seen in Verhuist's Traits de Fonctions Elliptiques) ; but the
process above given of throwing the general value of F(c) between limits,
is, I believe, by far the easiest and most natural method of obtaining this
form. The limits themselves, it should be noticed, have virtually been
found by the method, simple to naivete, of writing Vl — cV= V^+g2,

where »= V I — x2 and q= bx, and then substituting for -7-7- * —7— as an

p+q .... V^+23 p+q

inferior, and a , a as a superior limit in the quantity to be integrated.

Closer and calculable limits ad libitum to the integral may be arrived at by

substituting for / 8 a one or the other of the two following rational

functions of p, q, according as we wish to obtain an inferior or superior

Idea of Vonceie^s Theorem* 313

not, nor ever Can be the best and closest of their respective kinds*.
To fix the ideas, let us confine ourself to the second Ponceletic
approximation to Va + bx + cat1*, viz. that which has the form

~-r 1 where \, fju3 v are to be determined. The problem

to be solved is the following.
Let \-f-^# + v#2=V,

(l+qx) \/a + ba: + cx2 = U ;
it is required to assign the four constants X, ft, v, q, so that the

limit to the integral, viz.

(p+q+ ^pt+q'f+ip+q- ^p+q9f Vp2+?2
or

(p+q+Vp*+q*)i-i-(p+q-A/p2+q2)i l

in which formulae the greater i is taken the closer will be the approxima-
tion. I am not aware that any of these limits to F(c) (even the simplest of
which, viz. those given above, may have some value for computational pur-
poses, and have fallen thus very incidentally in my way) have ever before
been noticed.

It is not unworthy of notice that the second superior limit to / -= .

viz. 7-— — £*?ii;i is an arithmetic mean between the first superior and

(p + q)(pa+qiy ...

first inferior limits, and consequently our second superior limit to the

integral when b is indefinitely small becomes log t-Hj which brings the

constant much nearer to its true value than did the use of the first limit ;
and as this approximation will evidently not stop at the second step of the
process, we may safely infer that the integral derived from either formula
when i=Mco (for all values of b, whether finite or indefinitely small), not
merely bears to F(c) a ratio differing infinitely little from that of equality,
but is absolutely equal to, and may for all analytical purposes be employed
to represent F(c).

I have been at the trouble of calculating the inferior limit afforded by
the second approximation, and find that for b indefinitely small it is

9 7T 1

log- -f =rjl3> i. e. log ^ + 1*2977 ; the superior limit has beenshown to be

1 i

log£ + 1*4785, the mean is therefore log^ + 1'3881, differing by only '0018

from the true value ! As the constant continues for all values of i to be a
multiple of 7T, the ith. approximations a supra and ab infra, which are
always effectible, will give (on making i=so ) two new expansions for 7r,one
infinitesimally in excess, the other infinitesimally in defect of its true
value expressed as a multiple of log 2, which it might well repay the trouble
of some young analyst to develope.

"**' That the fractional forms derived from the linear substitutive form are
not the best of their respective kinds, appears immediately, so far as the
Phil. Mag. S. 4. Vol. 20. No. 133. Oct. 1860. Y

314 Mr. J. Sylvester : Meditation on the

maximum value of ( rr — 1 ) for values of a? intermediate between

a and b shall be the least possible. Some little way, but only a
little way, into the solution of this problem we can look in ad-
vance. In the first place, if we seek for the maximum values of

( jj — 1 \ , we obtain the rational equation

derivatives of the odd order (subsequent to the first) are concerned, from
the consideration that the limits of error in excess and in defect will be
actually attained for values of x lying within the prescribed limits ; but
these errors, c* and rji (when f=»7, which is true by hypothesis), are
never equal, the former (the extreme error in defect) being always the
greater of the two ; but if any such derivative were the best of its kind,
the absolute values of the extreme errors of excess and defect ought to be
equal to each other. But more generally, if possible, let the ith deriva-
tive to L(x) (where L(x) represents the radical linear approximant fx+b

to */a + bx+cx\ say Q(x)), viz. V ' }J- — , f- Q(x), be sup-

7 (Lx+Qx)1— (LxQx)%

• . , . 2(L# — Qx)1
posed the best of its kind : then the relative error is * — . '- ,-,

v (La?+Qa?),-(La?-Qa?)

and the maximum value of this must be equal (to the sign prhs) to the
value which it has when we give to x either of its extreme connecting values*

Now obviously the above is a maximum only when - _q is a minimum,

and therefore when ^- is a maximum ; but by hypothesis, the value of x,

La?

say m, which makes this a maximum, gives to ^ — 1 the same value with

the opposite sign to that which it would have in writing for x either of its
limiting values, say k or k'.

Thus we have two equations for determining -=-7;, t^-{, viz.

q,k y(wi)

Lm_._1 Lk
Qro ~QP

and

(&'M£-')'-<~H(^0'-(S-')T

Thus, suppose i = 2, we should obtain from the second equation
— = — ^rp which is inconsistent with the first ; so if z=3, we should

obtain ( — — ) =( — - ) , and therefore, on account of the first equation,
VQm/ \QkJ

7^7^=1 j and so in like manner for any value of i, we should derive one
Q(ro) *

Lwi . ...

or more numerical values for q—, which is absurd, since this quantity is a

function of k, k't the two connecting values of x.

Idea of Poncelet's Theorem, 315

which will easily be seen to be a cubic (not a biquadratic) equa-
tion in x. Call (^y — 1 ) =<£(#) ; then the three roots of this

equation being named xXi x2f x3, the law of equality explained in
my preceding paper would seem to show* that we must be able
to satisfy the following equations,

(<K)2= (<K)2= (<K)2= (*«)*= (**)'.

which amount to four independent equations, the precise num-
ber of constants X, p,, v} q to be determined. So in like manner
the ith rational approximant will contain 2i disposable constants ;

the differentiation of the quantity analogous to ^r will give rise to

an equation of the (2i — l)th degree ; and there will be 2i — 1 -f-2,
that is, 2i + 1 functions of these 2* quantities to be equated,
which furnish precisely the required number of equations to
make the problem definite. It is, however, apparent that in
solving these equations we shall find a multiplicity of systems, by
which I mean a definite number of systems of values of the dis-
posable constants which will equally well satisfy the equations.
For instance, in the theory of the second approximation, the
equalities (^1)2=(^2)2==(^3)2 w^ De satisfied by supposing
xl-=XcL-=x3\ . But it is by no means evident a priori that this
system of equalities will correspond to the absolute minimum of
which we are in quest : nay, though even we had (px1 = </>#2= <f>%3)
those equations do not necessarily imply xl = x2=x3. Of the
multiplicity of solutions referred to, one only gives the true
minimum ; but to assign a priori the distinguishing marks of

* Is it not, however, somewhat uncertain whether the equalities

must all, in all cases (that is to say, for all given values of the limits) sub-
sist ? since the law of equality will not apply to such values of x as lie
without the prescribed limits, and non constat a priori that the roots of the
cubic do all lie within these limits. The subject at the very threshold is
beset with doubts and difficulties of a peculiar kind, which we can hardly
hope to overcome without calling in geometrical imagination to our aid.

T If this is so, we shall have for determining the four constants the fol-
lowing equations :

x1=x2-=x3, (pa=(pb= — (/)#!•

But more probable than this seems the conjecture, that, supposing X\, %»> x*
to be arranged in the order of their relative magnitudes, the determining
equations might be

xi=x3, (£a=<£&=(/>#2= — (f)Xv

Or is it possible that the character of the solution may be discontinuous,
and may depend upon the magnitudes, relative or absolute, of the given
limits a and b ? Probably Dr. TchebitcheiF would be able better than
any other living analyst to answer these queries. But what an endless
vista of future research does the prosecution of the Ponceletic method
open out to us!

Y2

316 Royal Society .*—

this truest and best, hie labor, hoc opus est. It will be delightful

P

to find, if it turn out to be true, that for the best form, -^ repre-

*4

sen ting \'X (P being a rational function of the «th degree,
and Q of the (i — l)th in x), the rational quantity

XQf-^XP^(Q^X)

must.be a perfect (2i — l)th power of a linear function of a?; but
in the present state of my ignorance I dare not do more than
affirm that there is a bare probability in favour of this being
true : whoever shall first succeed in discovering the true form of
the expression will have established a remarkable theorem. Here
for the moment I break off, contented with having pointed to a
theory as yet, if the expression may be allowed, sleeping in its
cradle, but destined, I am persuaded, at no distant day to set in
motion as large a mass of algebraical thought as has been set in
motion by the never-to-be-forgotten Hessian discussion of the
flexures of the cubic curve, — the turning-point between the old
algebra and the new.

Henceforward Poncelet's theorem figures no longer as a de-
tached method, a mere stroke of art in aid of the computer, but
becomes integrally attached to the grand and progressive body
of doctrine of the modern algebra.

XL. Proceedings of Learned Societies,

ROYAL SOCIETY.
[Continued from p. 239.]
February 23, I860.— Sir Benjamin C. Brodie, Bart., President,
in the Chair.
H^HE following communication was read : —
-*- " Measurement of the Electromotive Force required to produce
a Spark in Air between parallel metal plates at different distances."
By Professor W. Thomson, F.R.S.

The electrometers used in this investigation were the absolute
electrometer and the portable electrometer described in my last
communication to the Royal Society, and the operations were ex-
ecuted by the same gentlemen, Mr. Smith and Mr. Ferguson. The
conductors between which the sparks passed were two unvarnished
plates of a condenser, of which one was moved by a micrometer
screw, giving a motion of -^ of an inch per turn, and having its
head divided into 40 equal parts of circumference. The readings
on the screw-head could be readily taken to tenth parts of a division,
that is to say, to ^— of an inch on the distance to be measured.
The point from which the spark would pass in successive trials being
somewhat variable and often near the edges of the discs, a thin flat
piece of metal, made very slightly convex on its upper surface like an
extremely flat watch- glass, was laid on the lower plate. It was then

Prof. Thomson on the Measurement of Electromotive Force. 317*

found that the spark always passed between the crown of this con-
vex piece of metal and the flat upper plate. The curvature of the
former was so small, that the physical circumstances of its own elec-
trification near its crown, the opposite electrification of the opposed
flat surface in the parts near the crown of the convex, and the electric
pressure on or tension in the air between them could not, it was
supposed, differ sensibly from those between two plane conducting
surfaces at the same distance and maintained at the same difference
of potentials.

The reading of the screw-head corresponding to the position of
the moveable disc when touching the metal below, was always deter-
mined electrically by making a succession of sparks pass, and ap-
proaching the moveable disc gradually by the screw until all appear-
ance of sparks ceased. Contact was thus produced without any force
of pressure between the two bodies capable of sensibly distorting their
supports.

With these arrangements several series of experiments were made,
in which the differences of potentials producing sparks across differ-
ent thicknesses of air were measured first by the absolute electro-
meter, and afterwards by the portable torsion electrometer. The
following Tables exhibit the results hitherto obtained.

Table I. — December 13, 1859. Measurements by absolute electro-
meter of maximum electrostatic forces * across a stratum of air
of different thicknesses.
Area of each plate of absolute electrometer=*187 of a square foot.
Distance between plates of absolute electrometer =^0 of a foot.

Electrostatic force,

Weight in grains

or electromotive

Length of

required to ba-

Electromotive

force per inch of

spark in

lance in absolute

force in units of

air, in tem-

inches.

electrometer.

the electrometer.

porary units.

«.

w.

slw.

•007

6

2-4495

349-9

•0105

9

3-0000

285-7

•0115

10

31622

2750

•014

13

3-6055

257-5

•017

16

4-0000

235-3

•018

19

4-3589

242-2

•024

30

5-4772

228-2

•0295

40

63245

214-4

•034

50

7-0710

208-0

•0385

60

7-7459

201-2

•041

70

8-3666

204-1

•0445

80

8-9442

2010

•048

90

9-4868

197-6

•052

100

100000

192-3

•055

110

10-4880

190-7

•058

120

10-9544

188-9

•060

130

11-4017

1900

* See § 3 below.

318

Royal Society : —

These numbers demonstrate an unexpected and a very remarkable
result, — that greater electromotive force per unit length of air is
required to produce a spark at short distances than at long. When
it is considered that the absolute electrification of each of the op-
posed surfaces* depends simply on the electromotive force per unit
length of the space between them, or, which is the same thing, the
resultant electrostatic force in the air occupying that space, it is
difficult even to conjecture an explanation. Without attempting to
explain it, we are forced to recognize the fact that a thin stratum of
air is stronger than a thick one against the same disruptive tension
in the air, according to Faraday's view of its condition as trans-
mitting electric force, or against the same lifting electric pressure
from its bounding surfaces, according to the views of the 18th cen-
tury school, as represented by Poisson. The same conclusion is
established by a series of experiments with the previously-described
portable torsion electrometer substituted for the absolute electro-
meter, leading to results shown in the following Table.

Table II. — January 17, 1860. Measurements by portable torsion
electrometer of electromotive forces producing sparks across a
stratum of air of different thicknesses.

Electrostatic force,

Length of spark
in inches.

Torsion in degrees

Electromotive

or electromotive

required to balance

force in units of

force per inch of

in electrometer.

the electrometer.

air, in tem-

s.

9.

ve.

porary units.

•001

3

1-732

1732

002

7

2-646

1323

•003

11

3-31G

1105

•004

14

3-742

935

•005

18

4-243

849

•006

22

4-G90

782

•007

27

5-196

742

•008

30

5-477

685

•009

33

5-744

638

010

38

6164

616

•on

43

6-557

596

•012

48-5

6-964

580

013

54

7-348

565

•014

68

7-681

549

015

66

8-124

542

016

73

8-544

534

017

79

8-888

523

•018

85

9-219

512

The series of experiments here tabulated stops at the distance
18 thousandths of an inch, because it was found that the force in the

* See § 4 below.

Prof. Thomson on the Measurement of Electromotive Force. 319

electrometer corresponding to longer sparks than that, was too strong
to be measured with certainty by the portable electrometer, whether
from the elasticity of the platinum wire, or from the rigidity of its
connexion with the aluminium index being liable to fail when more
than 85° or 90° of torsion were applied. So far as it goes, it agrees
remarkably well with the other experiments exhibited in Table I.,
as is shown by the following comparative Table, in which, along
with results of actual observation extracted from Table II., are
placed results deduced from Table I. by interpolation for the same
lengths of spark.

Table III. Experiments of December 13, 1859, and January 17,
1860, compared.

Col. 1.

Col. 2.

Col. 3.

Col. 4.

Electromotive force

Electromotive

per inch of air,

force per inch of

Length of spark

Dec. 13, in tempo-

air, Jan. 17, in tem-

Ratios of numbers

in inches.

rary units of that

porary units of

in Col. 3. to

s.

day.

that day.

numbers in Col. 2.

sjw

M*

s

s

•007

349-3

742

213

•0105

285-7

606

2-12

•0115

275-0

588

2-14

•014

257-5

549

2-14

•017

235-3

523

2-22

•018

242-2

512

2-11
Mean 2- 14

• The close agreement with one another of the numbers in Col. 4,
derived from series differing so much as those in Cols. 2 and 3,
and obtained by means of electrometers differing so much in con-
struction, constitutes a very thorough confirmation of the remarkable
result inferred above from the experiments of the first series, and
shows that the law of variation of the electrostatic force in the air
required to produce sparks of the different lengths, must be repre-
sented with some degree of accuracy by the numbers shown in the
last column of either Table I. or Table III.

The following additional series of experiments were made on pre-
cisely the same plan as those of Table II.

320

Royal Society :—

Table IV. — January 21, I860. Measurements by portable torsion
electrometer of electromotive forces producing sparks across a
stratum of air of different thicknesses.

Electrostatic force,

Torsion in degrees

Electromotive

or electromotivo

Length of spark

required to haltnca

force in units of

force per inch of

in inches.

in elect romotcr.

the electrometer.

air, in tem-

s.

e.

V0.

porary units.

•001

3-2

1-79

1790

•002

6-4

232

1160

•003

105

324

1080

•004

132

363

907

•005

14-2

3-77

754

•006

18-2

4-27

712

•007

21-7

4-66 ,

666

•012

41-2

6-42

535

•013

46-7

6-83

525

•014

53-2

7-29

521

•015

572

7-56

504

•016

63-2

7-95

497

•017

68-2

8-26

486

•018

78-2

8-84

491

Table V.— January 23, 1860.

Similar experiments repeated.

,

0.

V0.

^fr*

•001

3-5

1-87

1870

•002

6-5

2-55

1275

•003

9-5

308

1027

•004

12-7

3-56

890

•005

15-5

3-94

788

•006

18-5

4-30

716

•007

230

4-80

686

•008

25-62

5-06

632

•009

30-5

5-52

613

•010

350

5-92

592

•011

39-5

6-28

571

•012

440

6-63

553

013

500

7-07

544

•014

540

735

525

015

590

7-68

512

•016

63-5

797

498

•017

69-5

8-34

490

•018

74-5

8-63

479

The difference between the numbers shown in these two Tables
and in Table II. above, are probably due in part to true differences
in the resistance of the air to electrical disruption ; but variations
in the electrometer, which was by no means of perfect construction,
may have sensibly influenced the results, especially as regards the

Prof. Thomson on the Measurement of Electromotive Force. 321

differences between those shown in Table II. and those shown in
Tables IV. and V., which agreeing on the whole closely with one
another fall considerably short of the former.

Table VI. Summary

of results reduced to absolute measure.

Col .1.

Col. 2.

Col. 3.

Col. 4.

Col. 5.

Length

of spark

in inches.

s.

Electrostatic forces ac-
cording to simple deter-
minations of Dec. 13,
1859.

Electrostatic
forces according
to estimated
average of va-
rious determi-
nations.
X.

Differ-

Pressures of electricity
from either metallic surface
balanced by air immediately
before disruption, in grains

s X5X V -187

ences.

weight per square foot t.

X*

=X.

87TX32-2*

•001

11480

162800

•002

• • .

8000

...

79080

•003

6840

57810

•004

5820

41820

•005

5090

■ . .

32010

•006

4700

27300

•007

4600

4530

+ •0070

26200

•008

4200

21830

•009

3990

19690

•010

3860

18390

•0105

3760

3770

-•0010

17450

•011

3720

17130

•0115

3620

3630

-•0010

16200

•012

3550

15580

•013

3480

14970

•014

3390

3390

•0000

. 14200

•015

3320

13580

•016

3260

13110

•017

3000

3140

-•0040

11800

•018

3190

3170

+•0020

12500

•024

3100

3000

11100

•0295

2820

2820

9830

•034

2740

2740

9250

•0385

2650

2650

8650

•041

2690

2690

8900

•0445

2650

2650

8640

•048

2600

2600

8350

•052

2530

2530

7910

•055

2510

2510

7770

,•058

2490

2490

7630

•060

2500

2500

••

7720

* Distance between discs of absolute electrometer =■£■$ foot=£ inch.

Area of each =•187 square foot.

Force of gravity at Glasgow on unit mass =32*2 dynamical units of force;
that is to say, generates in one second a velocity of 32*2 feet per second.

f This is most directly obtained by finding the force between the discs of the
absolute electrometer per square foot, and reducing, according to the inverse
proportion of squares of distances, to what it would have been if the distance
between them had been equal to the length of the spark.

322 Royal Society ;- -

Appendix.

In order that the different expressions, " potential," " electromotive
force," "electrostatic force," "pressure of electricity from a me-
tallic surface balanced by air," used in the preceding statement, may
be perfectly understood, I add the following explanations and defini-
tions belonging to the ordinary elements of the mathematical theory
of electricity.

1 . Measurement of quantities of electricity. — The unit quantity
of electricity is such a quantity, that, if collected in a point, it will
repel an equal quantity collected in a point at a unit distance with a
force equal to unity.

[In British absolute measurements the unit distance is one foot ;
and the unit force is that force which, acting on a grain of matter
during a second of time, generates a velocity of one foot per second.
The weight of a grain at Glasgow is 32*2 of these British units of
force. The weight of a grain in any part of the earth's surface may
be estimated with about as much accuracy as it can be without a
special experiment to determine it for the particular locality, by the
following expression : —

In latitude A. average weight of a grain

= 32-088 X (1 + -005133 X sin2 X) British absolute units.]

2. Electric density. — This term was introduced by Coulomb to
designate the quantity of electricity per unit of area in any part of
the surface of a conductor. He showed how to measure it, though not
in absolute measure, by his proof plane.

3. Resultant electric force at any point in an insulating fluid. —
The resultant force at any point in air or other insulating fluid in
the neighbourhood of an electrified body, is the force which a unit of
electricity concentrated at that point would experience if it exercised
no influence on the electric distributions in its neighbourhood.

4. Relation between electric density on the surface of a conductor,
and electric fores at points in the air close to it. — According to a
proposition of Coulomb's, requiring, however, correction, and first
correctly given by Laplace, the resultant force at any point in the
air close to the surface of a conductor is perpendicular to the surface
and equal to Aitp, if p denotes the electric density of the surface in
the neighbourhood.

5. Electric pressure from the surface of a conductor balanced by
air. — A thin metallic shell or liquid film, as for instance a soap-bubble,
if electrified, experiences a real mechanical force in a direction per-
pendicular to the surface outwards, equal in amount per unit of area
to 2vp2y p denoting, as before, the electric density at the part of the
surface considered. This force may be called either a repulsion (as
according to the views of the eighteenth century school) or an attrac-
tion effected by tension of air between the surface of the conductor
and the conducting boundary of the air in which it is insulated, as it
would probably be considered to be by Faraday ; but whatever may
be the explanation of the modus operandi by which it is produced, it

Prof. Thomson on the Measurement of Electromotive Force. 323

is a real mechanical force, and may be reckoned as in Col. 5 of the
preceding Table, in grains weight per square inch or per square foot.
In the case of the soap-bubble, for instance, its effect will be to cause
a slight enlargement of the bubble on electrification with either
vitreous or resinous electricity, and a corresponding collapse on being
perfectly discharged. In every case we may regard it as constituting a
deduction from the amount of air-pressure which the body experiences
when unelectrified. The amount of this deduction being different
in different parts according to the square of the electric density, its
resultant action on the whole body disturbs its equilibrium, and
constitutes in fact the resultant electric force experienced by the
body.

6. Collected formula of relation between electric density on the
surface of a conductor, electric diminution of air-pressure upon it,
and resultant force in the air close to the surface. — Let, as before,
p denote the first of these three elements, let p denote the second
reckoned in units of force per unit of area, and let R denote the
third. Then we have

R=4tf^,

7. Electric potential. — The amount of work required to move a
unit of electricity against electric repulsion from any one position to
any other position, is equal to the excess of the electric potential of
the first position above the electric potential of the second position.

Cor. 1 . The electric potential at all points close to the surface of
an electrified metallic body has one value, since an electrified point,
possessing so small a quantity of electricity as not sensibly to in-
fluence the electrification of the metallic surface, would, if held near
the surface in any locality, experience a force perpendicular to the
surface in its neighbourhood.

Cor. 2. The electric potential throughout the interior of a hollow
metallic body, electrified in any way by external influence, or, if in-
sulated, electrified either by influence or by communication of elec-
tricity to it, is constant, since there is no electric force in the interior
in such circumstances.

[It is easily shown by mathematical investigation, that the electric
force experienced by an electric point containing an infinitely small
quantity of electricity, when placed anywhere in the neighbourhood
of a hollow electrified metallic shell, gradually diminishes to nothing
if the electric point be moved gradually from the exterior through
a small aperture in the shell into the interior. Hence the one value
of the potential close to the surface outside, mentioned in Cor. 1, is
equal to the constant value throughout the interior mentioned in
Cor. 2.]

8. Interpretation of measurement by electrometer. — Every kind
of electrometer consists of a cage or case containing a moveable and a
fixed conductor, of which one at least is insulated and put in metallic
communication, by what I shall call the principal electrode passing

324 Royal Society :—

through an aperture in the case or cage, with the conductor whose
electricity is to be tested. In every properly constructed electrometer,
the electric force experienced by the moveable part in a given position
cannot be electrically influenced except by changing the difference
of potentials between the principal electrode and the uninsulated
conductor or conducting system in the electrometer. Even the best
of ordinary electrometers hitherto constructed do not fulfil this con-
dition, as the inner surface of the glass of which the whole or part
of the enclosing case is generally made, is liable to become electrified,
and inevitably does become so when any very high electrification is
designedly or accidentally introduced, even for a very short time ;
the consequence of which is that the moving body will generally not
return to its zero position when the principal electrode is perfectly
disinsulated. Faraday long ago showed how to obviate this radical
defect by coating the interior of the glass case with a fine network
of tinfoil ; and it seems strange that even at the present day electro-
meters for scientific research, as for instance for the investigation
of atmospheric electricity, should be constructed with so bad and
obvious a defect uncured by so simple and perfect a remedy. When
it is desired to leave the interior of the electrometer as much light
as possible, and to allow it to be clearly seen from any external
position with as little embarrassment as possible, a cage made like a
bird's cage, with an extremely fine wire on a metal frame, inside the
glass shade used to protect the instrument from currents of air, &c,
may be substituted with advantage for the tinfoil network lining of
the glass. It appears therefore that a properly constructed electro-
meter is an instrument for measuring, by means of the motions of a
moveable conductor, the difference of potentials of two conducting
systems insulated from one another, of one of which the case or cage
of the apparatus forms part. It may be remarked in passing, that it
is sometimes convenient in special researches to insulate the case or
cage of the apparatus, and allow it to acquire a potential differing
from that of the earth, and that then, as always, the subject of
measurement is the difference of potentials between the principal
electrode and the case or cage, while in the ordinary use of the
instrument the potential of the latter is the same as that of the
earth. Hence we may regard the electrometer merely as an instru-
ment for measuring differences of potential between two conducting
systems mutually insulated ; and the object to be aimed at in per-
fecting any kind of electrometer (more or less sensitive as it may be,
according to the subjects of investigation for which it is to be used),
is, that accurate evaluations in absolute measure, of differences of
potential, may be immediately derivable from its indications.

9. Relation between electrostatic force and variation of electric
potential. — § 7, otherwise stated, is equivalent to this : — The ave-
rage component electrostatic force in the straight line of air between
two points in the neighbourhood of an electrified body is equal to
their difference of potentials divided by their distance. In other
words, the rate of variation of electric potential per unit of length in
any direction, is equal to the component of the electrostatic force in

Prof. Thomson on the Measurement of Electromotive Force. 325

that direction. Since the average electrostatic force in the line joining
two points at which the values of the potential are equal, is nothing,
the direction of the resultant electrostatic force at any point must be
perpendicular to the equipotential surface passing through that
point ; or the lines of force (which are generally curves) cut the
series of equipotential surfaces at right angles. The rate of varia-
tion of potential per unit of length along a line of force is therefore
equal to the electrostatic force at any point.

10. Stratum of air between two parallel or nearly parallel plane
or curved metallic surfaces maintained at different potentials. — Let a
denote the distance between the metallic surfaces on each side of the
stratum of air at any part, and V the difference of potentials. It is
easily shown that the resultant electrostatic force is sensibly constant
through the whole distance, from the one surface to the other ; and
being in a direction sensibly perpendicular to each, it must (§9)

V

be equal to - . Hence (§ 4) the electric density on each of the

y

opposed surfaces is equal to - — . This is Green's theory of the

4ira

Ley den phial.

11. Absolute Electrometer. — As a particular case of No. 10, let
the discs be plane and parallel ; and let the distance between them
be small in comparison with their diameters, or with the distance of
any part of either from any conductor differing from it in potential.
The electric density will be uniform over the whole of each of the

opposed surfaces and equal to - — , being positive on one and nega-

tive on the other ; and in all other parts of the surface of each the

electrification will be comparatively insensible. Hence the force of

V2
attraction between them per unit of area (§§5 and G) will be - — ^

if A denote the area of either of the opposed surfaces ; the whole

y-2
force of attraction between them is therefore A- — ■ . Hence, if the

oira*

observed force be equal to the weight of w grains at Glasgow, we
have

32-2 xw=A-

and therefore

=v

87ra*'
32-2 X 8tt x iv

Addition, dated April 12, 1860.

Experiments on precisely the same plan as those of Table I.
December 13, have been repeated by the same two experimenters,
with different distances from *3 to *6 of an inch between the plates

326

Royal Society,

of the absolute electrometer, and results have been obtained con-
firming the general character of those shown in the preceding Tables.
The absolute evaluations derived from these later series, must be
more accurate than those deduced above from the single series of
December 13, when the distance between the plates in the absolute
electrometer was only *2 of an inch. I therefore by permission add
the following Table of absolute determinations : —

Electrostatic forces according to

Length of spark

estimated average of determina-

in inches.

tions of February 15, 23, 28, and

*.

29, and March 2.

X.

•0034

5793

•005

5574

•006

5688

•0075

4862

•0111

4351

•0161

3287

•0222

3125

•023

3029

•0271

3055

•0356

2925

•0416

2865

•0522

2841

These results, as well as those shown in the preceding Tables,
demonstrate a much less rapid variation with distance, of the electro-
static force preceding a spark, at the greater than at the smaller
distances. It seems most probable that at still greater distances the
electrostatic force will be found to be sensibly constant, as it was
certainly expected to be at all distances. The limiting value to
which the results shown in the last Table seem to point must be
something not much less than 2800. This corresponds to a pressure
of 9600 grains weight per square foot. We may therefore conclude
that the ordinary atmospheric pressure of 14,798,000 grains per
square foot, is electrically relieved by the subtraction of 9600 on two
very slightly convex metallic surfaces, at a distance of ^_th of an
inch or more, before the air between them is cracked and a spark
passes. By taking into account the result of my preceding com-
munication to the Royal Society, we may also conclude that a
Daniell's battery of 5510 elements can produce a spark between two
slightly convex metallic surfaces at ^th of an inch asunder in
ordinary atmospheric air.

[ 327 ]

XLI. Intelligence and Miscellaneous Articles.

ON THE DIFFERENCE IN SIZE OF MEDALS OF DIFFERENT METALS
OBTAINED BY STAMPING, AND BY CASTING IN THE SAME
MOULD. BY H. W. DOVE.

T> AUDRIMONT has found {Ann. de Chim. et de Phys.voh Ix. p. 78)
-"-* that wires of different metals drawn through the same press are
not all of the same thickness ; for they are of different degrees of
elasticity, and after being drawn through the press they expand to
different amounts, This expansion is proved by the fact that, with
the exception of gold wire, no wire can be drawn through the same
aperture through which it has been pressed. Silver requires the
least force, but the expansion caused by elasticity continues for
several weeks.

It appeared probable that in stamping medals something similar
would prevail, and that medals of different metals stamped in the
same die would be different in size. This is most readily seen in those
medals in which the impression is symmetrically arranged in reference
to the edge, as is the case with the medals of the French Exhibition,
in which the coats of arms encircle the French eagle in the middle.
One of those in silver, and one in bronze were placed in the stereo-
scope, the eagle being fixed in the middle. After some time the
stereoscopic combined medal was seen in the form of a hollow escut-
cheon, and of the colour of an alloy of the two metals. Evidently
the reason of this lies in the nonius-like shifting of the individual lines
of the impression. This result, which I have described (Optische Stu-
dien, p. 29), I have also obtained with large gold and silver medals
which were kindly entrusted to me from the Royal Mint in Berlin.
It was probable that medals obtained by casting would show the
same thing, and this was found to be the case with tin, bismuth,
and lead. The casts were very beautifully executed for me for this
purpose by Professor Kiss. Hiero's crown led to the application of
specific gravity to detect an adulteration ; the stereoscope is a new
means. — Poggendorff's Annalen, vol. ex. p. 498.

ON ATMOSPHERIC ELECTRICITY. BY M. VOLPICELLI.

Of the two characters which distinguish electricity, its tension
and its nature, the first depends on the hygrometric state of the
atmosphere, and the second is independent of it. The author de-
scribes a series of experiments on the latter point made on days which
were not stormy.

1st. The upper extremity of a copper rod, well insulated and
fixed on the roof of the Physical Museum of the University of Rome,
was 45m,39 high above the sea-level. If the upper end terminated

328 Intelligence and Miscellaneous Articles.

in a point or a ball, and the lower end in a gold-leaf electroscope, it
seldom showed the existence of atmospheric electricity. But when
the lower end was connected with a dry pile condensing electroscope,
signs of electricity were always obtained, sometimes positive and
sometimes negative ; and this is the only means by which, with a
fixed rod, the nature of the atmospheric electricity may always be
obtained. Before commencing the experiment, it must be ascertained
if the instrument is in the natural state ; this is the case when, after
touching both plates and then separating them, the gold leaf remains
at rest. In the second place, the electricity must be collected first
by the upper, and then by the lower plate, in order to ascertain that
the two results agree. After each experiment both plates of the
condenser must be connected with the ground, and separated from
one another by an uninsulated metallic foil. These precautions are
essential in detecting the small traces of electricity usually met with
in the atmosphere.

2nd. The nature of the atmospheric electricity sometimes varies
four or five times in the space of three or four minutes.

3rd. The electricity is the same, whether the rod terminates in a
point or in a ball ; the quantity varies little, but seems less with a
ball than a point.

4th. When a flame, or an incandescent ball, or even ignited
charcoal is placed on the point, the electricity which was negative is
changed into positive. If the atmospheric electricity is positive,
flame and incandescent metals simply increase the intensity. The
hotter the flame, the greater the quantity of electricity. The effects
of a spirit-lamp exceed those of an oil-lamp. Hence flame is liable
to introduce a source of error, when used in making observations on
atmospheric electricity.

5th. If, in some very rare cases, flame does not change the nega-
tive electricity exhibited by the point into positive electricity, it not
only does not increase the tension, but seems to diminish it, and
thus another source of serious perturbations is introduced into the
observations.

6th. In a room and by the methods described, the author has
always obtained traces of positive electricity by means of flame. —
Comptes Rendus, July 16, 1860.

MAGNETIC PHENOMENON.

M. RuhmkorfF has the following notice in the Comptes Rendus,
vol. 1. p. 1 66 : — " If a stay (bride) of soft iron be pressed against
one of the poles of an artificial magnet, the soft iron is observed
to become hard, it is more difficult to file. If the stay be removed,
it loses its hardness and resumes all the properties of soft iron."

THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

♦

[FOURTH SERIES.]

NOVEMBER I860.

XLII. On a new Species of Stereoscopic Fhcenomeno n.
By F. August*.

[With a Plate.]

THE object of this paper is to communicate an experiment
which seems to have an important bearing on the theory
of binocular vision.

Wheatstone, it will be rememberedf, has called in question
the doctrine of identical retina-points, on certain grounds con-
nected with stereoscopic vision. A body of suitable dimensions,
especially at the distance of distinct vision, will, he says, appear
simply solid, though it is obviously impossible that the corre-
sponding points of the images received by the two eyes can fall
on the corresponding points of the retinse. This objection, how-
ever, has not prevailed on physiologists to abandon the doctrine
of corresponding retina-points, since that doctrine is confirmed
by many other considerations. Briicke, indeed, has advanced J
an explanation of stereoscopic vision which has hitherto been
generally regarded as sufficient, and which at first sight appears
to afford a solution of the difficulty. According to Briicke, the
eyes during vision are never at rest, but are constantly making
small movements, by means of which the images of continually
different points of the body regarded fall successively in the two
eyes on corresponding points of the retina?; and thus single
vision arises, since the images of points which fall on parts of the
eyes that do not correspond escape consciousness, because in
general the recognition of double impressions is resisted. The
impressions, however, perceived by corresponding retina-points

* Translated from Poggendorff's Annalen for 1860, by F. Guthrie, Esq.
t Phil. Trans. 1838, vol. ii. p. 371. Pogg. Ann. Suppl. vol. i. p. 1.
X Muller's Archiv, 1841.
Phil. Mag. S. 4. Vol. 20. No. 134. Nov. 1860. Z

330 M. F. August on a new Species

survive the period of the eyes' vibration (if the expression may
be allowed) ; and thus we have the durable representation of the
entire body, whose dimensions we estimate by the difference of
the convergence of corresponding rays. To this theory Dove
has objected that the two images of a stereoscope may be seen
united so as to give the impression of solidity by the almost in-
stantaneous illumination of the electrio spark : this, however,
may be explained on the grounds of an incredibly rapid move-
ment of the eye, however improbable that may be. Briicke's
theory has therefore continued tq be generally received without
any essential modification, even on account of Meissner's* pro-
found research concerning the horopter and the position of the
corresponding retina«-points, or of the controversy connected
therewith.

2. The experiment above-mentioned is as follows : — A thin
cylinder of metal, as straight and smoothly polished as possible,
is so united with a fixed axis that its own geometrical axis cuts the
other at right angles. The experiment may be performed with
sufficient accuracy with two needles fixed in a cork at right angles
to each other. The one needle forms the rotating cylinder, the
other the axis of rotation. If the cylinder be placed at rest in
the sunlight and regarded on either side with one eye, then, pro-
vided its length be sufficient, the reflexion of the sun, or rather
a bright spot (which we shall call the point of reflexion), will be
observed somewhere in its length. If now the first eye be shut
and the cylinder be regarded with the other, the point of reflexion
will be perceived in another position. On opening both eyes,
two points will be seen at the same time in different places ; and
if lines be imagined drawn from each of these points to the corre-
sponding eye (which lines may be called the reflected rays " corre-
sponding to each eye"), it is obvious that these lines do not lie
in the same plane except when the cylinder itself lies in the same
plane with the line joining the optic centres of both eyes, which
we shall call as usual the " ground-line." If the cylinder be
rotated, each of the points of reflexion will obviously change its
place on the cylinder, and will therefore describe a curve in the
plane of rotation; and this curve, if the rotation be sufficiently
rapid, will appear continuously illuminated. A somewhat dif-
ferent curve will of course appear when the apparatus is regarded
with the other eye. If, however, the apparatus be regarded with
both eyes, instead of two curves in the plane of rotation as might
be expected, a single curve of double curvature is generally per-
ceived, not confined to the plane of rotation, but formed by the
intersection of the conical surfaces described by the two reflected
rays during rotation.

* Beitr'dge zur Physiologie des Sehorgans. Leipzig, 1854.

of Stereoscopic Phenomenon. 331

3. Before the further consideration of this experiment and its
consequences, the following short analytical introduction may be
permitted.

Let the axis of rotation be the axis of z, the plane in which
the cylinder rotates be the plane xy. Let the eye A be at the
distance r from the origin 0 ; the line OA making the angles
u, (S, y with the axes of x, y, and z respectively. And let the
angles made by the parallel incident rays with the same axes be
called uvj3v and yx. The axes of x and y may, however, be so taken
that the axis of y is in the plane passing through the axis of z and
the ray of light incident on 0, so that 0^ = 90°, 0l = 9O°— yv
Let the angle formed at any moment by the cylinder (which
must be regarded as infinitely thin) with the axis of x be called
<f>. We have now to inquire what is the distance of the point
of reflexion 11 from the origin O. Let the distance in question
be called p. In the first place, the angle ROA is easily deter-
mined as follows :

cos ROA = cos <f> cos a + sin <f> cos j3.

The angle ARO made by the reflected ray with the cylinder
must, from the property of the cylindrical surface, be equal to
that made by the incident ray, whence

cos ARO = sin yl sin cj>0

In the triangle AOR we know, therefore, the angles ROA and
ARO, and the side AO = r. Whence we get

_r sin (ARO 4- AOR)
AK~P- ^sinlARO) ;

which, on substituting the values of ARO and AOR, becomes
cos <fy cos a. + sin <p cos /3 + sin yY sin <f>

/] — (cos <f cos a + sin $> cos /3)2 ~|
V 1 — sin2 7j sin2 <f> J

a curve of the sixth order, closed, unless 7^90°, and passing
through the origin.

When the incident rays are parallel to the axis of rotation,
yx = 0, and the part of the above expression containing the square
root disappears. The equation being then referred to rectan-
gular coordinates, becomes

/ r \2 / r \2 r2

[x-^cosuj +(^/-~cos£j =-sin27,

that is to say, the equation of a circle having the projection of
OA for a diameter, and being the intersection of the plane xy

Z2

=r\ (

332 M. F. August on a new Species

and the sphere of which OA is the diameter. (This result
should be observed, since it can easily be deduced that the re-
flected ray forms a right angle with the cylinder, according to
the well-known property of the sphere.)

The equation to the conical surface having this circle as a
base, and the point A as an apex, may be easily shown to be as
follows :

(a?2 -f if) cos2 7 — zx cos a cos ft— zy cos ft cos y + zr sin2 7 cos y
— rx cos2 7 cos a — ry cos2 7 cos2 ft = 0.

If, now, the eyes be placed symmetrically with respect to the
plane yz, so that both the lines drawn from the origin to the
eyes make the angle ft with the axis of y, and 7 with the axis
of zy and a and 180°— a respectively with the axis of x, then the
equation of the corresponding conical surface for the other eye
will be

(a?2 -f y2) cos2 y + zx cos a cos ft — zy cos ft cos 7 -f zr sin2 7 cos 7
-f rx cos2 7 cos a — ry cos2 y cos ft = 0.
The subtraction of the two equations gives

2zx cos a cos 7 + %rx cos2 7 cos a = 0,
or

2 cos a cos yx (z — r cos 7) = 0.

The conical surfaces corresponding to the two eyes cut each
other, therefore, in two planes, (1) #=0, and (2) z=—r cos 7.

The curve in the first plane is an ellipse, hyperbola, or para-
bola. (The case in which it becomes a circle cannot arise.)

The curve in the second plane, z= —r cos 7,1s a circle, of which
the equation referred to rectangular coordinates is

a72-f-7/2=r2sm27.

The particular case above considered may be very easily exhi-
bited experimentally ; the axis of rotation of the apparatus is
placed parallel to the incident rays, the eyes are put in such a
position that they are both equally distant from 0 the origin and
Oz the axis of rotation. (Since yl = 0, the axis of y may be taken
anywhere in the axis of rotation without affecting the formula?.)
In this position of the eyes a stereoscopic image of a circle will
be observed as far behind the plane of rotation as the eyes are
before it, or conversely, as far before it as the eyes are behind,
having its middle point in the axis of rotation, and a radius equal
to the distance of either eye from the axis. It appears, therefore,
that it is the second only of the two curves mentioned above that
presents itself. Why this is the case shall be explained hereafter ;
our immediate purpose was only to verify our calculations by
comparison with a simple experiment.

of Stereoscopic Phenomenon. 333

4. With reference to the experiment itself, it should be men-
tioned that the stereoscopic curve displays itself with particular
distinctness in comparison with the single images when the
plane of rotation is parallel to the incident rays and consequently
the axis of rotation is perpendicular, and when the apparatus is
regarded from behind and on one side. The single curve is,
however, still more clearly discernible when there are two differ-
ent sources of light ; these give rise to distinct curves, from the
comparison of which the stereoscopic effect is increased.

It hardly needs to be observed that, instead of the parallel
rays of the sun, any other source of light with diverging rays
may be employed, and that the above calculations, when the
source of light is not too near, are still sufficiently accurate.
Moreover the equation of the curve described by the point of
reflexion when the light proceeds from a point L at the distance
rx from 0, and OL makes with the axes of x, y, and % the
angles alt /3P ylf may easily be shown to be as follows :

r-LsinLOB, _ r sin APR

v^ + p^+Ir^cosLOR" VrH^+2r^osWEJ

where for LOR and AOR the values found above must be sub-
stituted.

5. Though it is stated above that the two images generally
unite into one, it should be observed that this property depends
on the extent to which it is possible to bring them into super-
position. Images which in size or form are too different cannot
be stereoscopically united. As, according to the formula, p is
directly proportional to r (the distance of the eye from the origin),
stereoscopic images will be more easily perceived in proportion
as the distances of the two eyes from the origin are equal; but
even wrhen these distances are the same, the angles may be so
different that the images cannot, or can only with great diffi-
culty, be superimposed.

6. The conclusion that may be drawn with certainty from the
experiment is as follows. Since two points of the separate curves
which unite to form one point of the steroscopic image are not
seen at the same moment with both eyes, it is impossible for the
eyes to be so accommodated that corresponding points throw
their images on corresponding points of the retinse of the two
eyes. That the eyes arrange themselves by anticipation is not
credible ; and even if they did, for every revolution of the cylinder
only one point would appear single, the rest double.

It is moreover impossible that the two curves that exist in the
two eyes can be compared as wholes, and received point by point
on corresponding retina-points ; for since the images are only
virtual, that is, only produced by the endurance of the impres-

334 M» F. August on a new Species

aion in the eye, the image in an eye in motion must appear
different from that in an eye at rest, while on the other hand
the image of a real object must be the same in an eye in rapid
motion as in one at rest. As now the virtual image of the
point of reflexion moving along the curve is precisely identical
as to form with the curve itself, it is impossible that the eye
can make any sensible movements. Or to express the same
thing in other words, no movement of the eyes would bring two
virtual images on to corresponding retina-points, which do not
already lie on such parts, since their images are necessarily con-
fined to those points of the retina on which they are excited.
The experiment therefore compels us to regard Brucke's theory
of binocular vision as untenable, especially since it has already
been rendered doubtful by Dove's objection.

7. It may be asked how the experiment can be reconciled
with the well-supported doctrine of identical retina-points.
With reference to this point the observations made in paragraph
5 may be of some assistance. If the curves are too dissimilar
they afford no stereoscopic image ; that is to say, if the images
fall on parts of the retinae too remote, our imagination is unable
to unite them. This is precisely the same case as when we
regard an object whose dimensions are too great in proportion
to its distance from the eyes ; in that case only a small part of it
is seen stereoscopically, all the rest appears double. The identical
retina-points would thus, practically, in regard to solid vision,
only have the negative signification that two particular impres-
sions can be united into one when that in the one eye is not too
far removed from the place that corresponds to the position of
the impression in the other eye. If this condition be fulfilled,
the solid image appears at the intersection of the two rays, which
may be considered as drawn through the middle point of each eye
and the points of the retinas affected ; if these do not cut (if they
are not in the same plane), it is impossible, as is well known, to
perceive a single image. There are therefore two conditions
necessary for the formation of a single solid image.

The limits within which the point of the retina impressed may
vary from the true corresponding point is probably partly
dependent on the will, but may be extended or reduced by
practice. This at least seems to be the explanation of the fact
that those accustomed to the clear observation of a point see
more easily all surrounding objects double, while those who
accustom themselves to stereoscopic vision can unite very remote
images into one. The principal difficulty in the way of the
experimental determination of these relations would arise from
subjective differences.

How far this view is admissible others must decide. It is

of Stereoscopic Phcenomenon. 335

substantially consistent with an observation made by Wheatstone
on the horopter, towards the conclusion of his memoir above-
mentioned, and also with the views expressed by Johannes
Muller and Meissner on stereoscopic vision.

8. We can now explain why, in the experiment mentioned
towards the conclusion of the third paragraph, we saw only the
circle and not the conic section in the plane perpendicular to the
ground line, and passing through the axis of f (#=0). Imagine
(PL IV. fig. 6) that with the eye A we only saw the rays a
and a ; with the eye B the rays b and /3 (so that the points in
order are a b, a /3) ; then, on looking with both eyes, should
we perceive stereoscopically the points ab and a/3, or the
points a fi and b a ? It is clear that if the point b a were
seen, the rays a and /3 would impinge on very different points
of the retina (according to either Meissner's or Recklinghausen's
theory), so that they would not be stereoscopically united, — so
much so, indeed, that if there actually were points at a /3 and
b a, they could not be seen stereoscopically at the same time.
If, however, the point a b be observed, the rays a and /3 fall
on parts of the retina nearly corresponding, and their impressions
can therefore be easily united. This is the reason why the two
latter points are seen and not the former. It will also be easily
understood that it is precisely for the same reason that, in the
above experiment, the circle was perceived and not the curve in
the plane y z, because, when one point of the circle is seen
stereoscopically, the images of the other corresponding points
are much nearer the identical retina-points in the two eyes than
is the case when one point in the curve in y z is so observed ; so
that if the curve in y z actually existed, it could not for this very
reason be seen stereoscopically, but would always present a
double image.

The foregoing observations will perhaps be rendered clearer
by the particular case represented in fig. 7. Here the incident
rays are supposed parallel to the axis of rotation z} which bisects
the ground-line AB at right angles, the plane of rotation
being the plane xy. The eye A sees the circle EGO (drawn in
perspective in the figure), the eye B the circle L H 0. These
circles meet in 0, and have a common tangent. The two cones
generated by the reflected rays intersect, and are, from their
position, symmetrical, the lines A E and B E' being perpendicular
to the plane yz. The intersections of the two cones are (1) the
parabola 0 K N in the plane perpendicular to A B, and (2) the
circle CD C in the plane parallel to the plane of rotation (ocy).
If, now, the point O, for instance, in the parabola be seen stereo-
scopically, in order to observe the point K, the rays A G and
B L must be united, which obviously fall on very different points

336 On a new Species of Stereoscopic Phenomenon.

of the retinae (since the image on the retina almost corresponds
with the object, though of less dimensions, and in an inverted
position*). If, on the other hand, a point in the circle be seen
stereoscopically, the rays A G and B H, which cut each other in D,
fall on parts of the retinae almost corresponding, since in this
particular case, indeed, the arcs E G and 0 H are absolutely
equal ; and therefore the images on the retinae will almost entirely
coincide. In complicated cases the geometrical coincidence is
not so approximately exact, but in' any case it is very evident
that the rays that unite in a point in the circle fall on points of
the retina? of the two eyes far more nearly correspondent than
those belonging to a point in the curve at right angles to the
circles. And if, in any position of the apparatus and the eyes,
the sections are no longer a circle and conic section, a similar
observation will always enable us to determine which of the
intersections of the two cones we shall see stereoscopically j\

* The above observations appear to contradict the views advanced by
Mr. W. B. Rogers (American Journal, vols. xx. and xxi. 1855 and 1856),
in a memoir which only came to my knowledge after I had written the
above paper. In this memoir there is a very complete investigation of the
appearance presented by very dissimilar drawings when united by means
of a simple stereoscope of suitable construction. In mentioning different
stereoscopic drawings, it is stated (vol. xxi. p. 1 /6) that two equal circular
arcs which are convex ) ( or concave ( ) to each other, unite themselves
stereoscopically into a hyperbolic arc. This, therefore, is analogous to our
seeing a parabola (ellipse or hyperbola) in the experiment described in this
paper. This is in general correct, if only the arcs are not too great in
proportion to the visual angle, since, when the arcs are considerably curved,
the experiment requires eyes much practised in the use of the stereoscope,
and even then it is effected with difficulty. Two complete circles, more-
over, appear, as far as these experiments extend, never to be seen united
in this way ; and it is certain that if the mind has the choice to conceive
the impressions united in different ways, it prefers that arrangement which
unites stereoscopically the impressions on the points of the retinae which
most nearly correspond. If, therefore, on account of this fact, the remarks
made in this essay are deprived of complete generality, the same circum-
stance seems, on the other hand, to confirm the general principle, that it
is difficult to unite stereoscopically two images that belong to very different
points of the retinae ; especially since the above-mentioned experiment of
Mr. Rogers's seems to require a greater exertion than most other stereo-
scopic experiments.

That, moreover, only one stereoscopic image ought in general to be anti-
cipated from more complex drawings (if the left-hand drawing were not
sometimes observed with the right eye, and conversely) hardly needs to be
mentioned, since it obviously must be so.

f Fig. 7 shows that the rays seen at the same time are necessarily in
different planes. While, for instance, the eye B sees the point II, that is
to say, while the cylinder passes through the position OH, the eye A sees
the point H', which also lies in the line Oil, and it is clear that AH' and
BH are not in the same plane.

[ 337 ]

XLIII. On a Problem of Double Partitions.
By A. Cayley, Esq.*

It «+&+c+ . . = m, a + /3 + 7+ . .=fju (the quantities being
all positive integer numbers, not excluding zero), then
(a, a) -f- (b, ft) + (c, 7) + . . is considered as a partition of (m, fj,) .
And the partible quantity (m, /ju) and parts (a, a), (b, ft), fee.
being each of them composed of two elements, such partition is
said to belong to the theory of Double Partitions. The subject
(so far as I am aware) has hardly been considered except by
Professor Sylvester, and it is greatly to be regretted that only an
outline of his valuable researches has been published : the pre-
sent paper contains the demonstration of a theorem, due to him,
by which (subject to certain restrictions) the question of Double
Partitions is made to depend upon the ordinary theory of Single
Partitions.

Let the question be proposed, " In how many ways can (m, p)
be made up of the given parts (a, a), (b, ft), (c, 7), &c" under
the following conditions (which are, it will be seen, necessary in
the demonstration of the theorem constituting the solution), viz.

-, 75, -, &c. are unequal fractions, each in its least terms,
a ft y

and

a, ft, 7, &c. each less than //,-}- 2.

The number of partitions is

= coeff. xmyfX in n „ . .- , fl ■ — — ,

* (1 — xa7f)(l— xbi/){\ — xcyy)..'

the fraction being developed in ascending powers of x, y.

Considering the fraction as a function of y, it may be expressed
as a sum of partial fractions in the form

Afoy) 1 Bfey) - cfoy)'.,

l—xayx l—x^yP l—xcyv '

where

A(x, y) is rational in x, rational and integral of degree ct — l'my,

B(^2/) M » „ ft-1 „

c(*>y) ,> „ >, 7-1 >,

&c.

«

To find A (a?, y) we have, when y=x~«,

1

A(x, y) =

(l-xbf){I-xcyy)...'
* Communicated by the Author.

338 Mr. A. Cayley on a Problem of Double Partitions.
or what is the same thing, we have

A(*> *"■«)= ~aj a~y '

This in fact determines A(x, y) ; for the right-hand side of the
equation may be rdduced to the form

_o (a-l)a

A0 4- A,a? « i . . + Aa_iic «
(1— #«*-«£) (1 — a?«c-«y) . . . '

where A0, Ax . . . Aa_! are rational functions of x : to do this, it
is only necessary (taking o> an imaginary a-th root of unity) to
multiply the numerator and denominator by

n{l-coxb-f)II(l--coxc-ai)

where II denotes the product of the factors corresponding to the
a — 1 values of m \ the denominator is thus converted into

(i-Ab-a£)(i-Ac-a«)) . . . ,

which is of the form in question ; and the numerator becomes

a a

a rational function of x and af~«, integral as regards #~«, and
therefore at once expressible in the form in question. And the
equation, viz.

_a (a— l)a

Ate S-K A°+A'a' ;--+A,-.» -s"

_a a

remains true if instead of x « we write <w#_« ; in fact, instead

_a

of writing in the first instance y=x «, it would have been allow-

m

able to write y = oox «, to being any a-th root, real or imaginary,
of unity. Hence recollecting that A(x, y) is a rational and inte-
gral function of the degree a — 1 in y, the equation

A(x ,_ A0+A,y...+A«.lir-1

which is true for the a values <»# « of y, must be true identi-
cally; or this equation gives the value of A(x, y). And the
values of B(x, y), C(x, y)} &c. are of course of the like form.
Now consider the term

A(x, y)

1 —xay«'

where A(x, y) is a rational and integral function of the degree

Mr* A. Cayley on a Problem of Double Partitions, 339

a — 1 in y, and - is by hypothesis a fraction in its least terms.

The coefficient therein of xm y* (the fraction being developed in
ascending powers of x, y) is

= coeff. ^^ in ^^
1— -x*y

(the fraction being developed in ascending powers of x, y). In
fact the two fractions only differ by a wholly irrational function

of x, as is at once obvious by developing — in ascending

1— x*y
powers of y. We have, separating the integral part,

A(x,

l—x<xy 1—x^y

where U is a rational and integral function of the degree a — 2
in y. But a being by hypothesis ■< fi -f 2, or what is the same
thing, a — 2 < p, U does not contain any term of the form xm y*,
and therefore

coeff.a^^inA^f)
1 — x*y

., . A(x, x « )

= do, in —

a

■X*

And this last is

\ut

= coeff. xm in x* A(x, x «),

= coeff. #w * in A(x, x «),
= coeff. ic^-^in A(x«, x~a).

And from the foregoing equation

_^ 1

A(#, x «) = -

(1— a? «)(!—# «
this is

i
= coeff. x*m~av- in

(1— a?*6-^)(l— #**'-**)
The last-mentioned expression is thus the value ef

coeff. **# in *&A}
u 1 — xa ya'

340 Mr. A. Cayley on a Problem of Double Partitions.
and hence, Theorem,

coeff. xm if in

(l-*«y«)(l-arV)(l-tf^)..
1

= coeff. xam-a>x in — r- a

(1— xab-a^) (I— xac-av) .

1

+ coeff. a^m_*'i in
+ coeff. a?v»-<v in

(l-^°-*a) (l—^c-*y).

1

(1—^ya -) (1 -#**-<*)..
+ &c,
the fraction of the left-hand side being expanded in ascending
powers of x, y, and those on the right-hand side being expanded
in ascending powers of x, and the data satisfying the above-
mentioned conditions. The number of partitions of (m, (j,) is
thus found to be equal to the expression on the right-hand side.
It is to be noticed that on the right-hand side, when any of the
indices um—afi, fim—bfi, . . is negative, the corresponding co-
efficient vanishes ; and that when the index of the power of x in
any factor of a denominator is negative, e. g. if ub—a/3=—p,
then (in order to develope in ascending powers of a?) we must in the

1 1 . xp x

place of - -t— s = -= write — , = — , and de-

1 1 — xab~afi 1—x-p xp — V l—xp

velope in the form — (xp + x2p 4- %3p + . . . ). The right-hand side

is thus seen to be the sum of a series of positive or negative

numbers, each of which taken positively denotes the number of

the single partitions of a given partible number into given parts.

If, using a term of Professor Sylvester's, we say that

coeff. m in (1_aa)(11_^).,.

(where m, a, b, c . . are positive or negative integers, and the
fraction is developed in ascending powers of x) is

= Denumerant of m in respect to the elements (a, b, c, . ..), say
= Denum* (m ; a, b, c . . ).
Then when m, a, b, c. are positive, but not otherwise, Denu-
merant (m ; a,b,c . . ) denotes the number of ways in which m
can be made up of the parts a,b,c... And the foregoing result
showa that the number of ways in which (m, fi) can be made up
of the parts (a, a), (b, /3), {c, 7), &c. is equal to the sum
Denum* (am—afi; ab—aj3, etc— ay, . . )
+ Denum* {ftm—b^; fta—boc, /3c— by, . . )
4- Denunr* (ym—cft; ya—cu, yb—cfi,..)
+ &c.

Mr. A. Cayley on a System of Algebraic Equations. 341

But, as appears from what precedes, a denumerant may be equal
to zero, or may denote a number of partitions taken negatively;
and it is not allowable, in the place, e.g., of the first denumerant,
to write simpliciter, number of partitions of ctm—a/jb in respect of
ab—a(3, ac—ay, &c. The notion of a Denumerant is, in fact, an
important generalization of the notion of a number of partitions.

2 Stone Buildings, W.C.,
October 4, 1860.

XLIV. On a System of Algebraic Equations.
By A. Cayley, Esq.*

npHE determination of a, b, c from the system of equations

b^ + ca=zfjbj

tf + ab — v,

in the case where \, fi, v have the values 16, 17, and 18 respect-
ively, is the problem known as Colonel Titus's Arithmetical
Problem. See Maseres' ' Tracts on the Resolution of affected
Algebraic Equations,' Lond. 1800. If for shortness we put

(J — V — C1,

then the third equation gives b—- ; and substituting this value

of b in the two other equations, we have

2 , ac ^
a2+ — =\,

a

<r2

■^ + ca=fi-,

or what is the same thing,

a3—\a +crc=0.
c«3-^2 + o-2=0,
And from these equations, eliminating «, we have

<74-3cV+(3c4-2X^)o-2-c2(c4-X)a)c7 + cV-^(^ + ^3)
+ \V=0,

where a — v— c2. The equation in c2 is thus of the fourth order ;
and in like manner, if instead of c2 we take <t as the unknown
quantity, and substitute therefore for c2 its value v— -a, the equa-
tion in <r will be also of the fourth order. And effecting the

* Communicated by the Author.

342 M. 11, Schneider on the Volumetric

reduction, this equation is

8o*-}2vo* + (6v2-2V)(72+ (V+^-^-X/uvJo-

+ (vX-A62)(v/i-\2)=0.

It may he remarked that if <r=0, then a or b vanishes; and
therefore, from the original equations, vX— /a2=0, or v/j,— X2=Q,
which agrees with the result afforded by the foregoing equation
in a. Again, if <r=v, then c=0; and therefore, from the ori-
ginal equations, v2 — X/x = 0. The left-hand side of the equation
in a; writing therein a=v, should therefore contain the factor
v2-Xyrx; its value in fact is v4-2X//,v24-Xy, or (v2-X/a)2.

If in the original equations we write a= -, b = ^, the equa-

Z ST

tious become

x2 + cyz — \z"2 = 0,

l/+CZX—fJLz'2 = 0,

(c2—v)z* + xy=:0,

which are three homogeneous equations of the second order;
from which, if the variables x, y, z are eliminated, we have the
required equation in c. And it would not, I think, be difficult,
from the known formula for the general case, to deduce the fore-
going result corresponding to the very particular case which is
here in question.

2 Stone Buildings, W.C.,
September 25, I860.

XLV. On the Volumetric Determination of Antimony.
By R. Schneider*.

IN most analytical processes antimony is separated as sul-
phuret of antimony. As this body varies in composition,
and cannot therefore be directly determined, it is necessary to
convert it into some form in which it is easily estimated. As
far as ordinary quantitative analysis is concerned, this question
may be considered as settled; Bunsen's methodf of changing
sulphuret of antimony into antimoniate of oxide of antimony
leaves nothing to be desired for accuracy and certainty. Hitherto,

* Translated from PoggendorfPs Annalen, vol. ex. p. 634.

f Bunsen's method consists in precipitating the antimony in the usual
way by sulphuretted hydrogen, and oxidizing the sulphide of antimony by
means of strong nitric acid of spec. grav. 1*524, instead of ordinary nitric
acid. By another modification which he adopted, the sidphide was oxidized
by being heated with a large excess of oxide of mercury. For the details
of the process the reader is referred to the Chemical Gazette for 1858,
page 311, which contains a full translation of Bunsen's original memoir.
—Eds.

Determination of Antimony. 843

however, there has been no method for directly determining sul-
phuret of antimony by the method of volumetric analysis. This
is attempted to be solved by the following process. The sul-
phide of antimony, whether precipitated by sulphuretted hy-
drogen from solutions containing antimonic acid or oxide of
antimony, is decomposed by boiling hydrochloric acid in such
a manner that for every equivalent of antimony three equivalents
of sulphuretted hydrogen are liberated. Consequently the de-
termination of this gas is a measure for the antimony, and its
accurate estimation affords an indirect method of determining
that body. Hence the real point is an accurate volumetric
estimation of sulphuretted hydrogen. This can be effected in
several ways.

The determination of sulphuretted hydrogen liberated from
sulphide of antimony by treatment with boiling hydrochloric
acid, by passing it into solution of sesquichloride of iron, and
then estimating the protoxide of iron formed by means of per-
manganate of potash, gives very inaccurate results. The error
is caused by the fact that part of the sulphur which separates
from the sulphuretted hydrogen is oxidized by the excess of ses-
quichloride of iron to sulphuric acid, in consequence of which
some protoxide of iron is formed, which is added to that reduced
by the sulphuretted hydrogen. H. Rose observed a long time
ago, that when sulphuretted hydrogen was passed into a warm
solution of sesquichloride of iron, a small quantity of sulphuric
acid was formed. The present case offers these conditions ; for
the solution of sesquichloride becomes heated by the hydro-
chloric acid vapours which pass into it. The quantity of sul-
phuric acid formed is never considerable ; it varies with the tem-
perature, and small quantities of lower oxides of sulphur appear
also to be produced. In no case can the resulting protoxide of
iron serve as an accurate measure for the sulphuretted hydrogen.

More accurate results are obtained when the sulphuretted
hydrogen is determined by means of iodine.

The accuracy of this method has been doubted on many hands.
Bunsen himself* does not appear to consider it particularly
accurate, and Mohrf obtained results differing with the concen-
tration of the solutions employed.

It must be admitted that the direct measurement of sulphur-
etted hydrogen by means of solution of iodine is by no means so
accurate as that of sulphurous acid by the same process ; yet,
when certain precautions are used, the method gives accurate
results. These precautions are, that the solution of sulphuretted
hydrogen must be greatly diluted, that water free from air must

* Bunsen, Iodometrische Bestimmungen, p. 26.
t Lehrbuch der Titrirmethode, vol. i. p. 302.

344 M. R. Schneider on the Volumetric

be used in the dilution, and that the determinations must be
made as rapidly as possible. The transient red colour produced
on the addition of iodine to a sulphuretted hydrogen solution
containing starch, is only feeble when the solution is greatly
diluted; it rapidly disappears, and does not prevent the true
iodine reaction.

The details of the process are as follows : —

The sulphide of antimony which lias been precipitated by
sulphuretted hydrogen from a solution containing tartaric acid*,
is collected on a filter of Swedish paper and completely washed
out, the last washings being with hot water.

The filter with the partially dried precipitate is carefully
removed from the funnel, and pressed into such a form that it
can be conveniently introduced into the neck of a small flask.
With a little practice this is effected without breaking the filter,
and without any loss ; it is of course easier when the precipitate
is quite dry, for then it occupies less room.

In decomposing the sulphide of antimony and collecting the
sulphuretted hydrogen, an apparatus may be used similar to
that which Bun sen has described in his paper on iodometric de-
terminations. The size of the flask varies with the quantity of
sulphide of antimony : for quantities of 0*3 to 0*4 grm. SbS3, a
flask of 100 cubic centims. capacity is sufficient ; for 0*4 to 1
grm. SbS3, the capacity maybe 200 cubic centims. The bottom
of the flask must be circular, the neck sharply tapering off, long,
narrow, and cylindrical. The retort which serves as receiver
must have two large bulbous enlargements blown in the neck :
the bulb part of the retort must be filled with water freed from
air; and from 30 to 50 cubic centims. of caustic ammonia must
be added, according to the quantity of the sulphide of antimony.

The sulphide of antimony is then introduced into the flask,
hydrochloric acid mixed with one-fifth its volume of water added
in excess, the gas delivery-tube affixed, and then the distillation
commenced.

The liquid in the receiver must still be alkaline when the
distillation js complete. It is left in the retort until cold, and
is then placed in a measuring vessel and its volume made up to
a litre or to half a litre with boiled water, according to the
quantity of sulphuret of antimony taken.

An aliquot part of this, one-fifth or one-tenth, is used for the
determination. It is poured into a beaker and diluted with its
own volume (or twice its volume) of water free from air ; a strip

* The addition of tartaric acid is quite essential ; for the sulphide of an-
timony precipitated from a hydrochloric acid solution persistently retains
some chloride of antimony, which is not the case in the presence of tartaric
acid.

Determination of Antimony. 345

of litmus paper is placed in the liquid, and dilute sulphuric acid
added until the mixture is feebly acid. Solution of starch is
added, and the determination, by means of iodine, proceeded with
in the usual manner.

If a is the quantity of sulphuretted hydrogen corresponding
to 1 cubic centim. of solution of iodine, t the number of cubic
centimetres of the solution of iodine used, the value for the an-
timony is obtained from the equation

_ Sb 4

To test the method, 0*326 grm. of pure antimony-glance was
decomposed by hydrochloric acid, and the determination made
in the above manner.

a=0'000803, *= 123-5.
Calculated. Found.

71*48 per cent, antimony 71*74 per cent.

28*52 „ sulphur
10000

A higher degree of accuracy than this is obtained by collect-
ing the sulphuretted hydrogen gas in a solution of arsenite of
soda, and determining the rest of the arsenious acid by solution
of iodine.

Mohr was the first to propose the combination of an alkaline
solution of arsenious acid with iodine, and he prefers this in
many respects to Bunsen's method. I cannot unconditionally
agree with him. If any alteration is to be made in Bunsen's
original method, the only reasons for which would be the great
dilution required, and the changeability of the sulphurous acid,
hyposulphite of soda ought to be preferred to arsenite of soda.
The reasons urged by Mohr against its use are not perfectly
tenable. That its decomposition by chlorine is different to its
decomposition by iodine is unimportant, as it never comes in
contact with free chlorine, but always with free iodine ; the con-
sumption of iodide of potassium which it occasions is the less to
be regarded, as comparatively small quantities of substance are
used in iodometric determinations ; that its acid solution changes
is equally unimportant, as it is only in contact with acid during
the short time of the determination. On the other hand, the
poisonous properties of arsenious acid are a formidable objection
to its use for volumetric purposes, so long as suitable substitutes
can be obtained.

For the determination of sulphuretted hydrogen, arsenious
acid is well adapted. It affords a precision which is scarcely
attainable with any other means.

Phil Mag. S. 4. Vol. 20. No. 134. Nov. 1860. 2 A

346 M. R. Schneider on the Volumetric

In using it the above method may be modified as follows.

The same apparatus is used for decomposing the sulphide of
antimony and collecting the sulphuretted hydrogen. A solution
of arsenious acid, prepared by dissolving arsenious acid (purified
by resublimation) in water, pure soda being added until a neu-
tral or feebly alkaline reaction is set up, is placed in the receiver.
The solution is so strong that 1 cubic centim. contains about
0*005 — 0*006 grm. of arsenious acid, and it is compared with a
solution of iodine which contains a known quantity of iodine*.
According to the quantity of sulphide of antimony, 50, 100, or
200 cubic, centims. are used. The latter quantity would be
quite sufficient for the sulphuretted hydrogen disengaged from
1*5 grm. sulphuret of antimony.

From the hydrochloric acid gas which passes along with the
liberated sulphuretted hydrogen into the receiver the liquid soon
becomes acid, and then sulphuret of arsenic is deposited. The
decomposition of the sulphuretted hydrogen is rapid and com-
plete. Chloride of antimony does not distil over if the distilla-
tion be not continued too long. Nor are any organic substances
formed by the action of the boiling hydrochloric acid on the paper,
which might subsequently exert a reducing action on the solution
of iodine f.

As soon as the liquid in the retort is cold, it is transferred to
a measuring-flask, some solution of tartaric acid is added J, and
the flask filled up to the mark. After this liquid has been filtered
an aliquot part is measured off, and after saturation with bicar-
bonate of soda the quantity of arsenious acid is determined by
solution of iodine.

The calculation of the result is very simple. If the volume
of solution of iodine corresponding to the arsenical solution
taken be called V, the volume of iodine solution corresponding
to the arsenical solution after the distillation be called o, and the

* This is best effected by adding to a known quantity of the arsenical
solution a few drops of hydrochloric acid till it is feebly acid, and then
excess of bicarbonate of soda, some solution of starch, and finally solution
of iodine.

t A paper filter, 2 inches in diameter, was boiled in hydrochloric acid,
and the vapour disengaged collected in water to which 8 cubic centims.
solution of arsenic (10 cubic centims. = 23*3 cubic centims. solution of
iodine) had been added. After the distillation, the arsenical solution (after
the addition of bicarbonate of soda and of starch) required 18*7 cubic cen-
tims. solution of iodine. Now 10 : 8 = 23*3 : 18*64.

X The error in the volume caused by the suspended sulphide of arsenic
is so small, that in the majority of cases, and where unusually large quan«»
tities of substance are not operated upon, it may be neglected.

The sulphide of arsenic precipitated from a hydrochloric acid solution
persistently retains some chlorine, doubtless as chloride of arsenic, even
after washing. This is not the case when the solution contains tartaric acid.

Determination of Antimony. 347

quantity of iodine contained in 1 cubic centim. of solution of

iodine be called a, the quantity of antimony #= -^r (V—v)a.

The following determinations show the applicability of the
method.

(1) 0*200 grm. pure antimony-glance (from Arnsberg) were
directly measured.

10 cubic centims. arsenical solution = 23*5 solution of
iodine. V = 235 cubic centims. v = 184*8 cubic centims.
a = 0-006 grm.

From which #= 0*14625 grm. antimony.

Calculated. Found.

71*48 per cent, antimony 71*33 per cent. [ference.
28*52 „ sulphur 28*67 „ from the dif-

100*00 100*00

(2) 0*325 grm. pure antimony- glance was decomposed by hy-
drochloric acid, the strongly diluted solution was mixed with tar-
taric acid, the antimony precipitated by sulphuretted hydrogen,
and the sulphide of antimony measured.

10 cubic centims. arsenical solution = 23*3 cubic centims.
solution of iodine.

100 cubic, centims. arsenical solution were employed.

V= 233 cubic centims. v = 151 cubic centims. a =0*006 grm.

From which # = 0*239 grm. antimony.

Calculated. Found.

71*48 per cent, antimony 71*66 per cent.

28*52 „ sulphur 28*34 v

100-00 100*00

(3) 0*407 grm. chemically pure antimony was dissolved in hy-
drochloric acid with the addition of some nitric acid • tartaric acid
was added, and the sulphide of antimony precipitated from the
diluted solution was measured.

10 cubic centims. arsenical solution = 18*25 solution of
iodine.

150 cubic centims. arsenical solution were taken.

V=273*75 cubic centims. v = 160*5 cubic centims. « =
0*00758 grm. . .

Taken. Found.

0*407 0*4065 (=99*87 per cent.).

It scarcely needs mention that this method may advantage-
ously be used in determining the sulphur in those compounds
which are decomposable by hydrochloric acid.

Berlin, July 1860.

H2

[ 348 J

XLVI. Illustrations of Symmetrical Integration. By the Rev.
Robert Carmichael, Fellow and Tutor of Trinity College,
Dublin*.

] . 1 ET the partial differential equation

"*T px* -f qy* = kz2

be proposed for integration.

Writing this equation in full, we get

X dx+y dy-kZ>
which is obviously equivalent to

dz dz

and this again to

kz*,

but the solution of this equation is at once

where u0 is an arbitrary homogeneous function of the order zero ;
or

where <j> is any arbitrary function.

Similarly, the integral of the partial differential equation in
three independent variables,

dw dw 2dw_ k q

X dx+V dy+Z dz-kW>

is

i i

w 3 \x y zj

More generally, the integral of the partial differential equation
in n independent variables,

mdu mdu , mdu , m du 0 , m
xm-r+ym-T-+z>m-r +wm -r- + kc.=:kum,
dx dy dz dw

* Communicated by the Author.

Illustrations of Symmetrical Integration. 349

is

l l J_

a™-1 n\^w~1 ym~l zm~l J ov ' J

2. The method employed in solving the primary type, in ex-
amples of this species, suggests the possibility of the instanta-
neous integration of such partial differential equations as

p cos2 x + q cos2 y = k cos2 3 ;

or, more generally, taking three independent variables,

„ dw t » dw t c> dw % t\

cos^ a? . t- + cos^5 v . -j- + cos^ 2 . -j- — k cosz w; : . . (a)
<to «y «*

or, again, such equations as

{a*-x*f . ~ + (b*-ff . ~ + (c*-z*f . ~ = k(m?-w*f; (0)
or

(l + ^).-J + (l + ^).J+(l + ^).J=*(l+^). . (7)

These equations, in fact, are respectively reducible to the forms
d . tan w d . tan w d . tan w

d . tan x d . tan y d . tan z

= *, . . . («')

a. sin 2— a. sin x — a. sin-1 —

« + S+ !?«*, . m

a. sin"1- «.sin_17 a.sm-1-
a b c

d.tan_1w d.t&n~1w cLtan_1w_, . ,.

dA2xs-xx rf'.tan-1^ "^.tan-1* ~~ 5 ' V'J

the solutions of which equations are respectively

k
tan w = ^ (tan a? + tan y + tan z) + w0(etan*, e*"1*, etan*), .... (a")
o

^11-^=1(^11-^ + sin-1! + siii-^)^^^"^, ^sin-1^ ^ -1"), m

tm~1w=^{tm-1x+tm-ly+t3in-1z)+u0{et&n~lx} et&n~^f etan_1*). (7")

3. Let it be proposed to integrate the partial differential
equation

"T" — a •

x y y2
The solution of this equation is, by the ordinary operational

350 The Rev. R. Carmichael's Illustrations of

method, in its full expanded form,

which may be instantly condensed into the shape

;sr=y. <£(#*— if).

In the same manner it may be shown that the integral of the
equation

1 dw 1 dw 1 dw _w

x dx y dy z dz~ z*
is

w=.z .<£(#*— ?/2, yt—z*, zi—xi).

4. The following partial differential equation, which was ori-
ginally suggested by Laplace, has been discussed by Sir John
Herschel (Transl. of Lacroix, p. 690),

dz y dz m ■
dx z dy

Now if we multiply this equation by x} and convert the depend-
ent variable, the equation becomes obviously

Vdx +ydJ ' (n-l)z»-> -X°l+1>
+ uQ{x,y).

dy/ (n—l)zn
and the solution is at once

1 _ xm+1

(n— l)sn-! ~~m + l

More generally, the integral of the equation

dw y dw z dw ■ J m n

t- + - -7- + - -j- —x y zV wq

dx x dy x dz *

is

1 xm+lynzP

■ " \q^\)vfl- x ~ S+S+P + 1 + U°[X' Vi Z)'

5. If it be required to integrate the symmetrical partial differ-
ential equation

dz dz .

lb' dy=Pq=kz\ .

we find by the method of Lagrange, as perfected by Charpit,

where a is an arbitrary constant, and <f> any arbitrary function.
Upon inspection of the solution now found, and consideration
of the mode in which the partial differential coefficients derived

Symmetrical Integration. 351

from it satisfy the given equation, and the characters of these
derivees, we see at once that, similarly, the solution of the partial
differential equation in three independent variables,

d2u d% d*u _,
dx dy dz dx dy dz~~ '
is

u = k*(x + a) (y + <fm) (z + %a)i

% being a new arbitrary function.

Similarly, we see that the solution of the partial differential
equation in four independent variables,

dsu dsu d3u dsu ,

dxdydz dwdxdy dzdwdx dydwdz '
is

«= k*(x + «)(?/ + <f>ot) (z + %a) (w + i/ra),

where i|r is a third new arbitrary function.

6. Let it be required to determine the values of u and v, being
given the system of simultaneous partial differential equations,

aj)xu + bfiyU + cj)zu + a^)xv + b^DyV + c^)zv = kxu + &2v,l
fljl)f« + bfiyV + CjD^v -f ^D^w + b^DyU + c2D,~w = &, v + >fc2w, J

where the coefficients aly bv cv &c. are supposed to be constants.
These equations may be thrown into the form

(aj), + byDy 4 CiD*— kY)u + (<?21)^+ 62Dy + c^— &2) 0=0/1

%(a1T>s + bJ)& + c1I)z—k1)v+(aJ)x + bfiy + CiPas--k^u = OiJ

whence we derive

fpfi9 + bfiy + pj^| - kxf . u - («2D, + bj)y f c2Vz - &2)2. u = 0.

This equation may evidently, in general, be reduced to the form

(«1D# + /31Dy + 7lD,-l)(«2D, + ftDy + 79D1B-l).tt=0,

where ax, &, y^ &c. are known constants. And the solution
required is

* JL £. ?L JL ?L

^=^(6% e\ <?^)-f-\P\(eave&, e72)>

where $>v ^ are arbitrary homogeneous functions of the first
degree.

The value of v is then to be had by substitution of the ex-
pression for u just found, in either of the given equations.

Trinity College, Dublin,
October 1860.

[ 352 ]

XLVII. The Dichrooscope. By H. W. Dove*.

[With a Plate.J

THE apparatus to which I have given the above name is in-
tended for the following purposes : —

1. To represent interferences, and spectra in different-coloured
lights, both separately and combined.

2. To imitate the phenomena of dichroism both in the case
in which the dichroitic crystals are viewed through a double-
refracting arrangement, as, for example, Haidinger's dichroitic
lens, and also in the case of the phenomena produced when the
dichroitic crystals themselves are used as analysers in a polarizing
arrangement.

3. To combine elliptically, circularly, and rectilinearly polar-
ized and unpolarized light, not in such a manner that the one
is produced by the polarizing, and the other by the analysing
arrangement, but so that they traverse the doubly refracting
media simultaneously, and are then submitted to any analysing
arrangement.

a b, fig. 1, Plate IV. is the three-sided brass prism of my
polarizing apparatus {Farbenlehre, page 202), moveable in a
brass case on an ordinary telescope-stand, in horizontal and
vertical directions. At one end there is the lens with the polar-
izing mirror c d, and at the other end at a the analysing Nicol
with the ocular, hegfis the dichrooscope, which can be placed
in one of the ordinary slides which carry the other arrange-
ments, in which case these other arrangements (the polarizing
Nicol and the circular-polarizing mica plate) may be placed on
one side.

The dichrooscope is a four-sided brass box 81 millims. long,
75 millirns. high, and 70 millims. broad. The posterior side of the
box represented in the figure is closed, and in the middle of this
side there is a cylindrical piece in which a rod is inserted. This
rod is attached either to a piece of glass ef, or to a moveable glass
disc, which can thus be exchanged for one another. The piece
of glass or the disc are turned by means of a knob which pro-
jects from the outside of the box, after the end of the rod
which reaches out of the cylindrical piece has been tight-
ened by a screw, but not so as to prevent rotation. In the open
sides of the box hf and fg coloured glasses can be inserted,
while h e, when other slides are not used, is destined to receive
cooled glasses or crystals, or a large rotating circular-polarizing
plate of mica. The sides hf and gf can be closed by slides ; and
slides can be placed in he which have a longitudinal slit for prism-

* Translated from Poggendorff's Annalcn, vol. ex. p. 265.

Prof. Dove on the Dichrooscope. 353

experiments, or a circular aperture for grating-experiments. Two
mirrors belong to the apparatus, 108 millims. long and 60 millims.
broad, one of which is silvered, and the other blackened. Either
of these mirrors can be placed at g in the polarizing angle, by-
means of a cleft in the direction g e ; in this case the polarizing
mirror c d is removed. For the future the mirror at g will be
designated by c d.

The apparatus is intended either for ordinary daylight, or for
sunlight directly incident on c d at the polarizing angle.

In order to simplify the phenomena of the different com-
binations, I assume that the linear-analysing arrangement is so
placed, that in a calc-spar cut at right angles to the axis the
rings with the black cross are visible. It is assumed that the
ocular is at right angles. If the plate of a body with feeble
double refraction, or if a plate of crystal with a large axial angle
is to be viewed, the polarizing microscope [Farbenlehre, p. 209)
is used as an analysing arrangement. It is so arranged that the
mica plate which serves for circular or elliptical analysis can be
used in the same manner as the ordinary ocular. If, on the
contrary, cooled or pressed glasses, or crystals, are viewed beyond
the distance of perceptible vision, the ocular is removed on one
side, and the ordinary analysing Nicol is used. *

The following combinations are obtained : —

l.cd silvered mirror, ef the glass disc. Natural light reaches
the analysing arrangement from c d} and linear-jpolarized from ef.

(a) fg closed by the slide ; white light linear-polarized.

(b) fg closed by the. slide, in hf coloured glass ; according to
the nature of the glass, monochromatic or polychromatic linear-
polarized light.

(c) Without slide and without coloured glass ; white natural
light and white linear-polarized light, consequently partially
polarized, the rings scarcely visible. If, after looking for some
time at the rings with the black cross, the slide at fg is rapidly
removed, the complementary rings with the clear cross are seen
at first.

(d) Without slide, the coloured glass at fg ; combination of
unpolarized coloured light with white linear-polarized light.
The cross brightly coloured in the colour of the glass ; the rings
in white light are somewhat changed by the uniform coloured
light.

(e) The coloured glass at hf without slide ; coloured polarized
light with white unpolarized. The rings almost invisible, on
account of the preponderating white light.

(/) Different-coloured glasses at hf and gf The system of
rings appears as if the analysing arrangement had been turned
90° 3 the cross is coloured, and the rings appear as changes from

854 Prof. Dove on the Dichrooscope.

the colour of the two glasses ; for the parts which arc dark in
homogeneous light are illuminated by the coloured light from fg.

(g) If a large rotating mica plate be placed at e h, the cor-
responding combinations of circular and elliptical light with
unpolarized light are obtained.

2. The silvered mirror is replaced by the polarizing mirror.
There reach the analysing arrangement two masses of light
linearly polarized in the same plane, or if the mica plate is placed
at h e, circularly or elliptically polarized. They are, •

(a) Both white or both coloured, if at hf and gf there are
either no glasses at all or both of the same colour (as in 1 a, b.)

(b) White and coloured, if at hf or fg there is a coloured
glass, by which the white preponderates so greatly that the
action of the coloured almost disappears.

(c) Different-coloured, if at hf and hg there are glasses of
different colours, in which case, strictly speaking, the plane
glass must not be parallel to the mirror, but each must be in-
clined at the maximum polarizing angle which corresponds to
that of the colour.

If with a polarizing apparatus without a dichrooscope the light
of a white flame be concentrated on the polarizing Nicol, and if a
piece of cobalt glass 6 millims. thick be placed before the eye,
the blue and red rings in carbonate of lead are obtained quite
distinct*, but intersecting one another; in calc-spar splendid
alternations of deep-red, blue, and violet concentric circles are
obtained. By adding a green glass the blue rings may be
isolated, by adding a red glass the red rings. But cobalt glasses
which completely extinguish the middle of the spectrum are ex-
tremely rare ; and the darkening of the light is so great, that in

* Both in this case, and also where, instead of a thick cobalt glass, blue
and red are combined in the dichrooscope, it may appear surprising that the
dark rings in blue light appear much more elongated in the direction of the
line joining the middle points of both systems than those in red light,
although the axial angle in red light is greater than in blue light. The
reason of this phenomenon is at once seen from the prism analysis ; the
spectrum of the flame seen through the cobalt glass appears to consist of
two masses of light separated by a dark space, — of which the red is homo-
geneous, for the form of the slit is very distinct ; while on the contrary the
blue mass of light extends over a larger space, and passes from light blue
to dark blue. The rings produced by this light are not simple, but appear
like the circular waves which are formed by drops falling in water after one
another in a straight line. Just as in this case two straight waves some-
what inclined to each other result from the simultaneously produced ele-
mentary waves, so in the case of the light, dark lines are formed which
accordingly appear rectilinear on the side, while at one end they are limited
by a flatter curve than at the other. This formation becomes distinct if a
green glass is combined with the cobalt glass. With prism analysis the
blue mass of light appears narrower, and in the polarizing arrangement the
rings were rounded.

Prof. Dove on the Dichrooscope. 355

apparatus with feeble light the phenomenon is greatly attenuated,
and in ordinary daylight is not apparent, for the red rings then
quite disappear. Dichromatic combinations by superposing
different-coloured glasses are impossible with many colours, for
a pure red and a pure green glass become then quite opake.
These evils are obviated by the arrangement (c) . By combining
monochromatic and dichromatic glasses, which are placed at hf
and fg, any desired union of colours for polychromatic illumina-
tion may be obtained, which by covering either hf or fg are
immediately decomposed into their components. Indeed, by
combining a red and a green glass, Newton's rings with white
light at once appear.

To make this more apparent, I have given in figs. 2, 3, 4,
5 the appearance of two crossed, plane, polished gypsum
crystals in red, yellow, green, and blue light, in which the
white lights in the figure must be considered as appearing in
the corresponding colour of the dark interference lines. If two
of these figures are imagined to be superposed, we obtain the
phenomenon of the combined illumination. As the square
which is common to both the gypsums shows five interference
lines in red and seven in blue, the alternation of red and blue
lines is then directly apparent, for the diagonals of both colours
appear black. A very instructive phenomenon is obtained, if,
while fg is covered by the slide, only one gypsum is examined
and at hf a glass is inserted, half of which allows one colour to
pass, and the other half the other colour. This sharp removal
of the interference lines is especially manifest. If it be desired
to show the part which each colour plays in the phenomenon
with white light, a glass is chosen for hf of which one half is
colourless and the other half coloured.

I know no transparent bodies which transmit homogeneous
yellow light. Another arrangement was accordingly made for
this colour. The mirror c d was removed, the polarizing glass
substituted for the glass plate at ef and a condensing lens
placed at b. Near its focus was a spirit-lamp coloured yellow
by common salt, and immediately behind this a white flame ;
between these two there was a glass plate intended to colour
this flame. Since light of a different colour penetrates a homo-
geneous flame, the desired combination is attained in this
manner.

In the place of well-polished gypsums, cooled glasses or com-
pensators of rock -crystal may be used.

In order to extend the results obtained for interferences where
the same spaces are traversed with unequal velocities to inter-
ferences where different spaces are traversed with the same velo-
cities, the dioptric grating may be used.

356 Prof. Dove on the Dichrooscope,

I have shown (Poggendorff's Annalen, vol. xxvi. p. 310) that,
on looking at a brightly illuminated aperture on a flame through
two crossed glass gratings held close before the eye, there is seen
the splendid phenomenon of the spectra distorted in the form of
quadrants, which Fraunhofer has depicted in the sixth plate of
his grating-experiments.

These obliquely distorted spectra may be shown to be connected
with the apparent deflection of light depending on the length of
the wave, by interposing a monochromatic, dichromatic, or tri-
coloured glass, — in which cases the unchanged figures of the
aperture at regular distances are seen to form systems of qua-
drants with mutual edges ; in the first case there is one, in the
second two, and so on. In using the dichrooscope, the circular
aperture is in a slide at h e. It is viewed from the distance of
distinct vision, through gratings rotating on each other. The
alternate closing of hf and gf gives the components.

In all these interference experiments, it is of course desirable
to know the homogeneous colours which prevail in the combined
action of the glasses. This is effected if the circular aperture is
changed for a narrow slit, and if a strongly refracting flint-glass
prism is used instead of the crossed or simple grating. In this
manner the component spectra and the result of their combina-
tion are obtained.

3. Between the silvered mirror c d and the plane glass ef the
rotating mica plate is inserted.

In this manner are obtained combinations of circularly or ellip-
tically polarized light with light linearly polarized by ef, which
reach the eye from gf.

(a) If, without coloured glasses, the light incident through gf
is right-circularly polarized, and that through hf linearly polar-
ized, the distorted cross in the plate of calc-spar shows that the
light passing out is right-elliptically polarized light.

(b) If, without coloured glasses, the light through gf is left-
circular, it gives with the linearly-polarized light incident through
hf left-elliptically polarized light.

(c) If by turning the mica plate the light through gf is right- or
left- elliptical, it remains elliptical even if combined with the right-
or left-linearly polarized, but it approximates more towards linear,
and becomes so when the azimuth of the principal section is 0°.

(d) If a coloured glass is inserted so as to colour either the
linear or the circular or elliptical light, the white light prepon-
derates so as to make it appear that the figure of the circular or
elliptical or that of the linear is seen in white light.

(e) If, on the contrary, two coloured glasses are inserted, the
succession of colours on the rings of the straight quadrant
appears different and removed from those in the crooked one,

Prof. Dove on the Dichrooscope. 357

while the cross becomes distorted and appears of the colour of
the circular (elliptical) light.

4. The parallel glass is replaced by the polarizing glass, and
the silvered mirror c d inserted at g.

(a) The glass is so placed that the light entering at fg and
then polarized by refraction is equal in intensity to that which
enters at hf, and is then polarized at right angles to it by re-
fraction. No figure is formed on the plate of calc-spar ; the
light is unpolarized.

(b) The slide is gradually pushed forward at fg ; and by the
gradually increasing difference between the masses of light
polarized at right angles to each other, the unpolarized light
passes through the middle stage of partially polarized into com-
pletely polarized. The phenomenon is the same as if two flat
prisms of tourmaline, whose edges are parallel to the axis of the
crystal, were gradually pushed one over the other so as to form
a plate becoming continually thicker.

(c) The slide at hf is gradually pushed forward after the one
at gf has been removed. The phenomenon obtained appears as
if two prisms of topaz (smoky quartz) parallel to the axis were
superposed on one another.

(d) Coloured glasses are placed in hf and fg ; the phenomena
of dichroitic crystals are obtained as follows : —

(a) The plate of calc-spar is removed, and the Nicol exchanged
for a doubly refracting achromatic prism. When a round aper-
ture is inserted at h e, two figures of it are obtained in different
colours, which by rotating the analysing prism, pass into one
another. This is the dichroitic lens. By using a Nicol, a
picture is seen to change its colour. If glasses of the same
colour are placed at hf and gf, and if the glass piece is arranged
so that the refraction and reflexion of the polarized masses of
light are of unequal intensity, two figures of the same colour,
but of unequal intensity, are obtained, and the emergent light is
partially polarized. This represents the crystals which are
improperly termed dichroitic, but which are so far connected
with them that, when used as an analysing arrangement, they
produce the phenomena of tourmaline to a feebler extent. If
the intensity and the colour are equal, the arrangement repre-
sents the plate of a doubly refracting crystal which has no
dichroitic properties.

(/3) The calc-spar plate is inserted; and the phenomena are
obtained which dichroitic crystals exhibit when they are used in
the polarizing apparatus as an analysing arrangement. Strictly
speaking, that is the polarizing arrangement in this case which
is the analysing in the other, and vice versa ; but since, from
the law of reciprocity, one arrangement results directly from the

358 Prof. Dove on the Dichrooscope.

other, I have preferred to retain the same arrangement of the
apparatus as in the preceding case.

\\ e shall most readily appreciate the phscnomena which now
appear, if that which is obtained in the calc-spar plate with a
certain-coloured light and with coincident planes of reflexion of
the polarizing and analysing mirror be considered as applied to
the phenomena which this plate exhibits when it is looked at in
light of another colour, the mirrors being crossed. The rings
are a combination of two coloured systems of rings with a light
and a dark cross, and which therefore appears brightly coloured
in the colour corresponding to the bright cross. The succession
of colours of the rings is consequently highly peculiar, and is
very distinct when well-annealed glasses are examined. If it be
desired to imitate the phenomena seen when a dichroite, dichro-
itic mica, a rubellite, repidolite, or smoky quartz is employed as
analysing arrangement, we have merely to use the proper
coloured glasses. In the first case the cross appears blue; in
the second it appears red with preponderating green rings ; in
rubellite the cross is the red of the alpine rose ; in repidolite
deep grey and almost black, as in dark smoky quartz, while the
rings appear brownish yellow. What we shall obtain by turning
the Nicol 90 degrees is manifest if we imagine that the pheno-
menon of the dark cross for one colour is changed into the light
cross, and, on the contrary, the phenomenon of the light cross
for the other colour is changed into that of the dark cross.
It is especially beautiful when an achromatic prism of calc-spar
is used as analysing arrangement with a red and blue glass.
The systems of rings, one with the blue and the other with the
red cross, then partially intersect one another.

An idea is obtained of the colours which result from the com-
bination of the system of rings, if a longitudinal slit is inserted on
the side towards the eye, and this is viewed through a prism
of rock-crystal. By the intermixture of both spectra, colours
are obtained which would not be expected from the components,
corresponding to the investigations of Wiinsch and Helmholtz.
The active components are, however, obtained in the most differ-
ent intensities if a rotating Nicol is interposed between the prism
of rock-crystal and the eye.

(7) The arrangement remains the same, but a rotating mica
plate of one- quarter difference of path is inserted at eh.
Right or left circular or elliptical light of one colour is seen to
combine with right or left circular or elliptical light of another
colour. The appearances here presented give a key to the com-
plicated phenomena seen in the polarizing apparatus when the
circular-polarizing mica or gypsum plate is changed for one
which has a much greater difference of path.

Prof. Dove on the Dichrooscope. 359

The conditions for circular polarization, that is, equal inten-
sity of two masses of light polarized at right angles to each
other, whose difference of phase is an odd multiple of a quarter
undulation, can, as is well known, be satisfied in two ways, —
either by two total internal reflexions in a single-refracting body,
or by refraction in a double refractor. The condition of equal
intensity is satisfied in the first case if the azimuth of thejplane
©f reflexion with the primitive plane of polarization is plus or
minus 45°, and in the second case if that of the principal
sections is + 45°. "FresnePs rhombohedron serves for total
reflexion, or if the light is to remain in the axis of the instru-
ment, my reversion prism {Farbenlehre, p. 240) . In total reflexion

the difference of phase after n reflexions is * ; using double-

o

refracting bodies, it is proportional to the thickness of the plate,
and to its double-refracting power. Airy accordingly splits a
plate of mica* until it has the required difference of phase,
while in Babinet's compensator the change is gradually pro-
duced by wedges of rock-crystal moved gradually over each
other. In both cases with an equal double-refracting power the
thickness changes. The thickness, on the contrary, remains
the same with a change in the double-refracting power if, as I
have shown, circular polarization is produced by pressing or
warming a glass plate between the polarizing and analysing
arrangement ; but since the length of waves is different for dif-
ferent colours, the condition of a determinate difference of phase
can only be simultaneously satisfied for a determinate colour ;
and it follows directly from the formulse for both the rays sepa-
rated by double refraction, that with increasing thickness of the
plate the difference in this respect between the various colours
increases in a corresponding degree; so that the same arrange-
ment in one part of the linear-polarized spectrum changes the
light into circularly polarized light, in another into linearly
polarized light, in others into light polarized at right angles, with
all transitions through right and left elliptical. I have shown this
in the experiments on circular polarization by allowing, by means
of a rotating prism, the individual parts of the spectrum to pass
over the aperture of a polarizing Nicol. In this case the system
of rings in calc-spar, and then all changes of form correspond-
ing to the various stages of polarization, are seen to pass in single
colours, from which the very complicated phenomenon in white
light finds a direct explanation. The dichrooscope gives another
derivation of the same phsenomenon. For if a plate of mica is
inserted at he, a blue glass at hf} and a red glass at #/, on covering

* Darker uses a plate of gypsum, aud a combination of several in the
beautiful apparatus which he calls the retarding slide.

360 Prof. W. Thomson's Notes on Atmospheric Electricity.

fg the system of rings in the quadrant is seen in right-circularly
(elliptically) polarized light ; if hf is covered, the rings in the
quadrant in red light are seen in left-circular (elliptical) light ;
by removing the slide, the cross whose arms are on one side of a
different colour than the other.

The polarizing apparatus which I have described gives an
objective representation of the phenomena. It is simply neces-
sary to concentrate an intense light on the aperture of the
polarizing Nicol through an objective, and to remove the ocular
from the analysing nearer to the polarizing Nicol. The light
emerging from the analysing Nicol is caught on a white surface,
on which the rings are represented in corresponding size. I
have not applied this to the dichrooscope, for in fact the darkening
of the objective pictures is considerable when a deeply-coloured
glass is held before the eye which is examining it.

The dichrooscope can be combined with Nuremberg's appa-
ratus in the following manner. For the composition of the
interference colours, a plate must be added parallel to the po-
larizing plate; the coloured glasses stand then one over the
other in the same vertical plane. For imitating the dichroitic
phenomena, the glass plates are placed so that these planes of
reflexion are at right angles to each other. On account of the
difficulty of the illumination, the apparatus can only be used
immediately in the neighbourhood of the window, which, on
account of the side light, greatly limits the intensity of the
colours of polarization. In this respect an apparatus is to be
preferred which, as it can be directed towards the source of light
like a telescope, can be used as well by day as by night in any
part of a room. When it is placed parallel to the earth's axis,
it can be used as a sun-clock even in twilight, according to a
process described in PoggendorfPs Annalen, vol. xxxv. p. 596, —
an application which I made {Maas und Messen, p. 62) in 1845,
ten years before these apparatus appeared under the special
name of Polar-clocks.

Several of the dichrooscopes which I have described have been
very neatly made by Langhoff, the philosophical-instrument
maker.

XLVIII. Notes on Atmospheric Electricity.
By Professor W. Thomson, F.R.S.*

TWO water-dropping collectors for atmospheric electricity
were prepared, and placed, one at a window of the Natural
Philosophy Lecture-room, and the other at a window of the

* Communicated by the Author, having been read before the British
Association, June 1860. •

Prof. W. Thomson's Notes on Atmospheric Electricity. 3G1

College Tower of the University of Glasgow. A divided ring-
electrometer was used at the last-mentioned station; an elec-
trometer adapted for absolute measurement, nearly in the form
now constructed as an ordinary house electrometer, was used in
the lecture-room. Four students of the Natural Philosophy
Class, Messrs. Lorimer, Lyon, M'Kerrow, and Wilson, after
having persevered in preliminary experiments and arrangements
from the month of November, devoted themselves with much
ardour and constancy during February, March, and April to the
work of observation. During periods of observation, at various
times of day, early and late, measurements were completed and
recorded every quarter minute or every half minute, — the con-
tinual variations of the phenomenon rendering solitary observa-
tions almost nugatory. During several hours each day, simulta-
neous observation was carried on on this plan at the two stations.
A comparison of the results manifested often great discordance,
and never complete agreement. It was thus ascertained that
electrification of the air, if not of solid particles in the air (which
have no claim to exclusive consideration in this respect), between
the two stations and round them, at distances from them not
very great in comparison with their mutual distance, was largely
operative in the observed phenomena. It was generally found
that after the indications had been negative for some time
at both stations, the transition to positive took place earlier by
several minutes at the tower station (upper) than at the lecture-
room (lower) . Sometimes during several minutes, preceded and
followed by positive indications, there were negative indications
at the lower, while there were only positive at the upper. In
these cases the circumambient air must have contained negative
(or resinous) electricity, if a horizontal stratum of air several
hundred feet thick overhead, containing as much positive elec-
tricity per cubic foot as there must have been of negative per
cubic foot of the air about the College buildings on those occa-
sions, would produce electrical manifestations at the earth's
surface similar in character and amount to those ordinarily ob-
served during fair weather.

Beccaria has remarked on the rare occurrence of negative
atmospheric indications during fair weather, of which he can only
record six during a period of fifteen years of very persevering
observation by himself and the Prior Ceca. On some, if not all,
of those occasions there was a squally and variable wind, changing
about rapidly between N.E. and N.W. On several days of un-
broken fair weather in April and May of the present year the
atmospheric indication was negative during short periods, and
on each occasion there was a sudden change of wind, generally
from N.E. to N.W., W., or S.W. For instance, on the 3rd of
May, after a warm, sunny, and very dry day, with a gentle N.E.

Phil Mag. S. 4. Vol. 20. No. 134. Nov. 1860. 2 B

362 Prof. W. Thomson's Notes on Atmospheric Electricity.

breeze and slight easterly haze in the air, I found about 8*30 p.m.
the expected positive atmospheric indication. After dark (nearly
an hour later) it was so calm that I was able to carry an unpro-
tected candle into the open air and make an observation with my
portable electrometer. To my surprise I found a somewhat
strong negative indication, which I observed for several minutes.
Although there was no sensible wind in the locality where I
stood*, I perceived by the line of smoke from a high chimney at
some distance that there was a decided breeze from W. or S.W.
A little later a gentle S."\V. wind set in all round, and with the
aid of a lantern I found strong positive indications, which con-
tinued as long as I observed. During all this time the sky was
cloudy, or nearly so. That reversed electric indications should
often be observed about the time of a change of wind may be
explained, with a considerable degree of probability, thus . —

The lower air up to some height above the earth must in
general be more or less electrified with the same kind of elec-
tricity as that of the earth's surface ; and, since this reaches a high
degree of intensity on every tree-top and pointed vegetable
fibre, it must therefore cause always more or less of the phe-
nomenon which becomes conspicuous as the " light of Castor and
Pollux," known to the ancients, or the " fire of St. Elmo " de-
scribed by modern sailors in the Mediterranean, and which
consists of a flow of electricity of the kind possessed by the
earth into the air. Hence in fair weather the lower air must be
negative, although the atmospheric potential, even close to the
earth's surface, is still generally positive. But if a considerable
area of this lower stratum is carried upwards into a column over
any locality by wind blowing inwrards from different directions,
its effect may for a time predominate, and give rise to a negative
potential in the air, and a positive electrification of the earth's
surface.

If this explanation is correct, a whirlwind (such as is often
experienced on a small scale in hot weather) must diminish, and
may reverse, the ordinary positive indication.

Since the beginning of the present month I have had two or
three opportunities of observing electrical indications with my port-
able electrometer during day thunder-storms. I commenced the
observation on each occasion after having heard thunder, and I per-
ceived frequent impulses on the needle which caused it to vibrate,
indicating sudden changes of electric potential at the place where
I stood. I could connect the larger of these impulses with thunder
heard some time later, with about the same degree of certainty
as the brighter flashes of lightning during a thunder-storm by
night are usually recognized as distinctly connected with distinct
peals of thunder. By counting time I estimated the distance of
* About six miles south of Glasgow.

Prof. W. Thomson's Notes on Atmospheric Electricity. 363

the discharge not nearer on any occasion than about four or five
miles. There were besides many smaller impulses ; and most
frequently I observed several of these between one of the larger
and the thunder with which I connected it. The frequency of
these smaller disturbances, which sometimes kept the needle in
a constant state of flickering, often prevented me from identify-
ing the thunder in connexion with any particular one of the im-
pulses I had observed. They demonstrated countless discharges,
smaller or more distant than those that gave rise to audible
thunder. On none of these occasions have I seen any lightning.
The absolute potential at the position of the burning match was
sometimes positive and sometimes negative; and the sudden
change demonstrated by the impulses on the needle were, so far
as I could judge, as often augmentations of positive or diminu-
tions of negative, as diminutions of positive or augmentations of
negative. This afternoon, for instance (Thursday, June 28), I
heard several peals of thunder, and I found the usual abrupt
changes indicated by the electrometer. For several minutes the
absolute potential was small positive with two or three abrupt
changes to somewhat strong positive, falling back to weak posi-
tive, and gathering again to a discharge. This was precisely
what the same instrument would have shown anywhere within a
few yards of an electrical machine turned slowly so as to cause a
slow succession of sparks from its prime conductor to a conductor
connected with the earth.

I have repeatedly observed the electric potential in the neigh-
bourhood of a locomotive engine at work on a railway, some-
times by holding the portable electrometer out a window of
one of the carriages of a train, sometimes by using it while
standing on the engine itself, and sometimes while standing on
the ground beside the line. I have thus obtained consistent
results, to the effect that the steam from the funnel was always
negative, and the steam from the safety-valve always positive. I
have observed extremely strong effects of each class from carriages
even far removed from the engine. I have found strong nega-
tive indications in the air after an engine had disappeared round
a curve, and its cloud of steam had dissolved out of sight.

In almost every part of a large manufactory, with steam-pipes
passing through them for various heating purposes, I have found
decided indications of positive electricity. In most of these
localities there was some slight escape of high-pressure steam,
which appeared to be the origin of the positive indications.

These phsenomena seem in accordance with Faraday's obser-
vations on the electricity of steam, which showed high-pressure
steam escaping into the air to be in general positive, but negative
when it carried globules of oil along with it.

2B2

[ 364 ]

XLIX. Experimental Researches on the Laws of Absorption of

Liquids by Porous Substances. By Thomas Tate, Esq.*

[With a Plate]

THE ascent of liquids in porous substances has hitherto been
regarded by physicists as similar to, if not identical with,
the ascent of liquids m capillary tubes ; but the following re-
searches show that the former phenomena are regulated by pe-
culiar and distinctive laws. I was first led to this inquiry by
observing the large portion of water which had been evaporated,
in the course of a day, from a vase of flowers. Vegetable and
animal life are, no doubt, intimately connected with the laws
regulating the absorption of liquids by porous substances.

The following general laws have been derived from the results
of these experiments.

In an atmosphere saturated with the vapour of the liquid,

(1) The rate of diffusion varies inversely as the space through
which the liquid of absorption has moved.

(2) The rate of diffusion, at equal distances from the surface
of the liquid with which the absorbent is in contact, is equal in
all directions, that is to say, the rate of diffusion is independent
of the force of gravity.

(3) The rate of diffusion, other things being the same, in-
creases with the temperature.

(4) The liquid diffuses itself equally over the surface of the
absorbent ; that is, the weight of the liquid absorbed by a unit
of surface is everywhere the same.

(5) In equal times the force of absorption performs the same
amount of work or dynamic effect.

(6) If an absorbent, saturated with moisture, be exposed to a
dry atmosphere, the evaporation goes on for the most part uni-
formly. And so on to other laws, which will be hereafter
illustrated.

1. Rate of diffusion of liquids through absorbents in an atmo-
sphere saturated with the vapour of the liquid.

The absorbents employed in these experiments were strips of
unsized paper, calico, linen, &c, of various thicknesses and
texture, and also thin columns of plaster of Paris. The liquids
used were distilled water, turpentine, linseed oil, alcohol, solu-
tions of starch, together with solutions of different salts, &c.
The line formed by the liquid in its ascent on the strips of un-
sized paper is so distinct and sharply defined as to enable us to
determine, with the greatest precision, the distance of this line
from the level surface of the liquid. The strips of paper, calico,
* Communicated by the Author.

On the Laws of Absorption of Liquids by Porous Substances. 365

linen, &c, were prepared for experiment in the following man-
ner : after being cut to their desired widths, and in some cases
graduated, stout platinum wires were attached to their lower
extremities, to give them a uniform tension and to sink these ex-
tremities in the liquid ; they were then steeped in boiling distilled
water, and afterwards thoroughly dried by evaporation ; and im-
mediately before being used they were suspended for about an
hour in the atmosphere, saturated with the vapour of the liquid.
The ascent of the liquid was, for the most part, observed by
means of a cathetometer ; but in some cases the strip itself was
graduated. The space S, moved over by the liquid through the
pores of the absorbent, is the elevation of the liquid line on the
absorbent measured from the level of the surface of the liquid
in which the absorbent is immersed. This liquid line was some-
times best observed by transmitted light, at other times by re-
flected light. Plate IV. fig. 8 represents the apparatus which
was, for the most part, employed in these experiments : —

A B a glass jar having a welt at the top ground smooth to
receive the ground brass plate CD; S a stuffing-box attached
to the plate, through which passes the stout wire F G, support-
ing the absorbent G K immersed in the liquid B K ; E a stopcock
communicating, when required, with the stopcock of an air-pump ;
LM a water-bath maintained (when required) at a constant tempe-
rature by means of a jet of steam. The sliding wire, F G, enables
us to raise or depress the absorbent as may be required ; and
the stopcock E and ground plate enable us to keep the absorbent
suspended in an atmosphere saturated with the vapour of the
liquid, or it may be in a vessel exhausted of air. The apparatus
was modified to suit peculiar circumstances. In experimenting
with such substances as turpentine, or with linseed oil, the vessel
A B was exhausted of air by means of the air-pump, and then
the external air was allowed to enter the vessel through a tube
filled with dry chloride of calcium. The absorbent having been
for some time suspended in this dry air, its lower extremity, K,
was immersed in the oil by depressing the sliding wire F G.

Experiment I.
The liquid used in this experiment was water. The absorbent
was unsized paper, 2 inches in width, close in texture, and weigh-
ing '72 gr. per square inch. The temperature was 56° through-
out the experiment.

The experimental value of the velocity of ascent, v, in the
third column, is found by dividing the increment of space *25
by the mean interval of time ; thus we find corresponding
•25

toS=3^=iTl5^^3) = ,°83-

366

Mr. T. Tate's

Experimental Researches on the

Ascent of

Corresp.

Velocity

Value of v

Value of v

Value of T

liquid in

time in

of ascent

by formula

by formula

bv formula

inches,

minutes,

per minute,

T = 3S-'.

S.

T.

v.

r 6S*

9 2T

0

0

0

•75

175

1-68

100

310

•166

•166

016

3-00

1-25

475

4-68

1-50

6-82

675

175

9-20

918

2-00

1200

083

•083

•083

1200

225

15-20

..V...

15-18

2-50

18-66

• . •••

1875

300

2700

•055

•055

•055

27-00

3-25

31-50

31-68

3-50

36-50

3675

4-00

47-50

•045

•042

•042

48-00

4-25

5300

5418

4-50

5900

6075

475

67-00

67-00

500

7500

031

•033

•033

7500

5 50

90-50

9075

6-00

10800

026

•027

•027

10800

650

128-50

12675

It will be observed how very nearly the velocity, as determined
by the formula u= ^, coincides with the velocity found by ex-
periment. Hence we conclude that the velocity of ascent of the
liquid through the absorbent varies inversely as the space.

The relation between T and S may be generally expressed by
the formula

T=«(S+/8)«-ft (1)

where a, /8, and p are constants.

By differentiation, we get

dS_ 1_

but

dS

dT-

1

'• ™**(S + /3); (2)

and when /8=0, or is very small, as in the foregoing experiment,
we have

1

v=

2aS'

From equations (1) and (2) we get
S-f/3

(3)

(4)

Laws of Absorption of Liquids by Porous Substances. 367

In this expression we may consider that the space is estimated
from a point situated at /3 inches from the level of the liquid,
and that the time is estimated from a period of time p minutes
anterior to the actual commencement of the motion.

When /3=0, oris very small, as it is in most of the results ob-
tained for the diffusion of water, then equation (4) becomes

v=WfF) (5)

Now when T is large as compared with p3 or when p is
neglected, we have

«*m <6>

Experiment II.

The absorbent in this experiment was very thick unsized paper,
2 inches wide, and weight 1*18 gr. per square inch. The tem-
perature was 60° throughout the experiment. The formulas in
this case are

T=3-3S2-l-3, (7)

and

•~sfe <8>

Ascent

Corresp.

Velocity of

Value of v

Value of

Value of T

of liquid

time in

ascent per

by formula

s

by formula

(7).

in inches,

S.

minutes,
T.

minute,
v.

1

"=2T

0

0

•9

1-40

10

2-00

•150

•151

20

11

2-75

1-9

1000

20

11-33

•075

•075

11-9

21

12-66

2-9

25-25

3-0

2725

•052

•050

•055

28-4

31

29-50

3-9

45 50

4-0

48-16

•038

•038

•040

51-5

4-9

7400

50

77-00

•033

•030

•032

81-2

5-9

11000

60

11400

•025

025

•026

117-5

6-9

152-00

7-0

157-00

•020

•021

•022

160-4

8-0

207-00

•018

•018

•019

209-9

8-1

212-50

8-9

261-00

9-0

267-00

•016

•016

•016

266-0

9-9

327-50

100

334-00

•015

•015

•015

328-7

368 On the Laws of Absorption of Liquids by Porous Substances.

Obs. In accordance with observations before made, the value

B

of the velocity derived from the formula r=^= only holds true

when T is large compared with p.

Nearly the same results were obtained with an absorbent of
one-half the width. Hence it appears that the rate of diffusion
is not dependent upon the width of the absorbent.

This experiment was repeated with the vessel AB exhausted
of air. The results were nearly the same as those above recorded.
Hence it would appear that the rate of diffusion is not affected by
the presence of air.

Rate of evaporation. — In order to determine the rate of evapo-
ration from the surface of an absorbent saturated with moisture,
the absorbent of this experiment was taken out of the water and
suspended in the air from the scale of a delicate balance, the dry
bulb of the thermometer being 62°, and the wet bulb 58°. The
weight of the whole water absorbed was found to be 24'3 grs.,
that is, 1*215 gr. per square inch of surface. The weight lost
during each successive interval of 30 minutes was found to be
very nearly 4-74 grs. At the end of 2 J hours the rate of evapo-
ration sensibly declined, and the last few grains of moisture were
retained with considerable tenacity. Hence it appears that the
rate of evaporation, from the surface of an absorbent saturated
with moisture, is for the most part uniform.

An absorbent thus placed in contact with water (as will be
hereafter more fully shown) becomes saturated with moisture ;
and when it is exposed to the action of the atmosphere, it becomes
equally dry at all parts in the same time. But if the whole
surface of the absorbent be plunged into the water and then
suspended in the air, the lower portion of the absorbent retains
a sensible film of water by adhesion to the surface ; this portion
of the absorbent maybe said to be supersaturated with moisture,
and it will be found that the higher portion of the absorbent will
become dry much sooner than the lower, and also that the rate
of evaporation will not go on uniformly.

The absorbent of this experiment, after being dried, was
suspended in contact with water as usual, and exposed to the
air. For the first 4 inches of the ascent of the liquid through
the absorbent, the law of ascent closely corresponded with that
of the foregoing experiment ; but after this the rate of ascent
rapidly decreased, until the liquid had risen to the height of
about 8 inches, where it appeared to become stationary. At
this time the dry bulb of the thermometer indicated 65°- 5, and
the wet bulb 62°, giving a difference of 30,5. When the differ-
ence between the indications of the two bulbs had become 5°,
the liquid stood at the height of 9 inches ; and when this differ-

Mr. J. Cockle on Transcendental Roots.

369

ence was only 2°*5, the liquid stood at the height of 7'6 inches ;
in this manner the liquid fell and rose according as the air con-
tained more or less moisture.

The results of the two foregoing observations will be more
fully considered when I describe the construction of a new
hygrometric instrument.

The following experiment was made to determine the rate of
diffusion under an increase of temperature.

Experiment III.

The absorbent was the same as that used in Experiment II.
The temperature of the water-bath, LM, was maintained at 110°.

Ascent of

Corresp.

Velocity

Value of v

Value of

Value

liquid

time in

of ascent

by formula

of T by

in inches,

minutes,

per minute,

2T J

formula

s.

T.

v.

" 3-64 S

experim.

T = 1-82S2.

0

0

0

•75

100

102

1-00

175

'277

•275

•285

1-82

1-25,

2-80

2-84

1-50

4-08

409

175

5-60

5-57

2-00

7*30

•138

•137

•137

7-28

2-25

9-20

9-21

2-50

11-50

11-37

3-00

1700

•096

•092

•089

16-38

3-25

19-60

19-22

3-50

22-80

22-29

4-00

29-50

•067

•068

•067

29-12

4-25

33-26

32-87

The results of this experiment, on being compared with those
of Experiment II., show that the rate of diffusion is considerably
increased by an increase of temperature.

Hastings, October 18, 1860.

[To be continued.]

L. Note on Transcendental Roots.
By James Cockle, M.A., F.R.A.S., F.C.P.S. #c*

FILLING up that part of my "Sketch," &c. in the last August
Number which relates to a cubic, and making

from

b= Vl-a?,

. doc 6b

* Communicated by the Author.

370 Mr. J. Cockle on Transcendental Roots.

we deduce by differentiation

d2x __ a<pb 1 d<\>b db
da* "■""" W~"3b"W' da

a<l>b I ( <l>a\/ a\
" 3b3 36 V 3a) \ b)'

This becomes, on reduction,

d2x a dx

+ O.M ^=0f

*fo2 1-a* da ' 32(l-a2)

a linear differential equation, the integral of which is

A . /sin-1 a j\
#=Asml — ■= — + i> ).

Substitute this value of x in the given cubic. The result must
vanish identically and independently of a ; and from the relations

A3-4A=0, A3-8 = 0, sin3B=0,
we infer

rt . /sin-1« + 2w7r\

a?=2slnV 3~ -J'

The unsymmetric trinomial form

xn—nx + n{n— 1)« = 0

is in some respects more convenient than that employed in the
" Sketch," and, through

„ dx x dfx *
J da n da
it leads to

Each unsymmetric form indeed leads to a derived equation,
which, by properly combining it with the given equation, may
be made linear in x.

I might have supported an early objection (S. 3. vol. xxxv.
p. 436) which I took to a portion of Mr. Jerrard's investigations,
by citing a paper* by the late Thomas White, of Dumfries Ma-
thematical Academy, which (received April 1816) was printed in

* " On the Algebraical Expansion of Quantity, by Division and Evolution;
and on the Symbol V — 1, which is usually considered to denote impossible
or imaginary Quantity." White (p. 61), in reference to the series " usually
but whimsically .... denominated neutral" says that " all ambiguity va-
nishes when it is considered that this series is finite, and that attention
must always be paid to the remainder."

Mr. J. Cockle on Transcendental Roots. 371

the Appendix to ' The Ladies' Diary ' for 1839. CommentiDg
on such an expansion as

1 x

l—x + x2— ±xn~1 +

White observes (pp. 60, 61) that " in summing such finite
serieses, the remainders must never be neglected The in-
troduction of the remainders removes all paradox. Hence, how-
ever great n may be supposed, the remainders must never be
neglected in serieses generated by algebraic division," &c. And
I presume that White would have maintained that the equation
i

1 — # + #2— ±xn~1 + &c. in infin.

1+x

was always algebraically false, though it might be arithmetically
true.

Other doubts (Ibid. p. 437), to which I sought to direct Mr.
Jerrard's* attention, he seems to have cleared up (S. 4. vol. hi.
p. 457). Butf, in leaving unassailed the theory of Abelians with
composite indices, he virtually leaves his own processes without
defence from the objections to which that theory gives rise. As
observed by M. Kronecker, all the distinct values of a cyclical
function of x0, xv . . x4 being given, the five roots x may be de-
duced from them rationally %. Now Mr. Jerrard's functions S,

* Mr. Jerrard (Ibid. p. 459) has adverted to some researches of Legendre
on cubics,in connexion with which I would call attention to "a few remarks"
of James Lockhart " on the roots of the cubic a?3— 3a?— 1=0, which apply-
to all cubic equations," and which I communicated to the Mechanics' Ma-
gazine (vol. lv. p. 1J3). Lockhart's theorem respecting quintics (Ibid,
vol. liii. p. 449; et vide lv. pp. 172, 173) may be easily demonstrated by-
multiplying the quadratic into x, eliminating ar3 and repeating this process
as far as may be necessary.

t M. Kronecker states that every (algebraically) soluble equation of a
prime degree fx is an Abelian, if we regard as known a quantity which
itself is a root of an Abelian of the (fx. — l)th degree (see Serret, Cours, 1854,
p. 564). There is not, as I once suspected, a corresponding proposition
when fi is not prime. The solution of the problem for a composite number
n is obtained the moment that we have resolved it for the case in which
the degree of the Abelian is one of the powers (of a prime number) con-
tained in n (M. Kronecker, ibid. p. 566 ; M. Hermite, ib. pp. 569 et seq.).

X See M. Hermite's Essay, Sur la Theorie des Equations Modulaires et
la Resolution de V equation du cinquieme degre (Paris, 1859), p. 27; consult
also M. Hermite's " Considerations sur la Resolution Algebrique de l'equa-
tion du 5° degre," at pp. 326-336 of vol. i. of the Nouvelles Annates de
Mathematiques, par. MM. Terquem et Gerono, 1842. I am not aware that
these important researches of M. Hermite have been completed. Mr. T.
T. Wilkinson informs me that the " suite " is not found in any subsequent
volume up to the present date.

I may add that, if we had an irreducible non-cyclical reduite of the 5fith

372 Mr. J. Cockle on Transcendental Roots.

P, and W are cyclical. Consequently he would obtain the general
solution of a quintic in a form which involved no quintic radicals.
Such a result is of course inadmissible*.

Without reiterating objections which I urged in the last May
Number, let me observe that of the two systems (<r,) and (<r2)
suggested by Mr. Jerrard (S. 4. vol. iii. p. 114), the last is in-
admissible. To admit it, would be to ignore the principle (a
neglect of which led me into an objection to Wantzel's argument)
that interchanges of the constituent symbols do not affect the
form of the function. There is no other conclusion than that

Ir«(a?«)(«i8) = 1r«(a?/j), .. 1»'«W(«f):=VflW,

so that (o-j) must hold universally. If (<r2) also holds, (o";) (lb.
p. 115) takes the form

(V» + r,(0)V* + r#)V + ra(0)>1=0,

which is inconsistent with the supposition (Ibid. p. 112) that
V15-|-C1V,4+ . . =0 cannot be depressed. Hence (compare lb.
p. 116)

V* + B^2 + r2{w) V + rd(*) = 0

is the form of one of Mr. Jerrard's cubics ; and in order to con-
struct it, we have to encounter the difficulty of solving the
general equation of the fifth degree, for in no other way can r{oc)
be determined. Apart, then, from Cauchy's theorem and M.
Hermite's argument, Mr. Jerrard's process presents intrinsic
objections fatal to its success. Let me add that although, by a
theorem of Abel, every value of ^H at p. 79 of Mr. Jerrard's
' Essay ' be a root of (ac), so that we may deduce

S-V{P/(^)}=0,

degree in t, the function

(in which h, t3, . . fo are the \i values of t formed by permuting all the
roots excepting x0) cannot be symmetric in x for all values of m, otherwise
the reduite would not be irreducible. Hence m may be so assigned as to
render

(/)(n*)=a-f&#0+ . . +ex0A ;

and xQ, which may be found as a rational function of 0, can contain no other
radicals than those which enter into tly t2, . . t^.

* The moment we proceed to the practical application of our formula;,
we are led to conclude that in those cases in which the root is expressible
by quintic (with or without quadratic) surds, the sextic in 6 has a rational
linear factor ; and that when cubic radicals appear, the given quintic and
its resolvent sextic are, each, reducible. i

A. and F. Dupre : Spectrum-analysis of London Waters. 373

still, if we would reconcile this with the other conclusions of
theory, we must give the equation the form

a result which gives us no aid whatever in our search after a
finite root.

4 Pump Court, Temple, London,
September 17, 1860.

LI. Spectrum-analysis of London Waters.
By A. and F. Duphe*.

HAVING been lately engaged in the analysis of several
London waters, we took occasion to examine them by the
recently published method of Bunsen and Kirchhoff; and since
this spectrum -analysis adds two new constituents (i. e. lithium
and strontium) to those already known, the results obtained may
not be uninteresting to some of the readers of the Philosophical
Magazine. If a small portion of the dry residue of any of the
waters examined is brought into the flame of an apparatus such
as described in Bunsen and KirchhofPs paper f, the lines Li a and
K a are seen with more or less distinctness as soon as the first
glare of the sodium and calcium spectrum is somewhat dimi-
nished. After the Li, K, and Na have volatilized, the calcium
lines come out with increased brilliancy ; and if the wire is now
dipped into HC1 and again brought into the flame, the lines Sr a
and Sr 7 are seen, as well as a very brilliant calcium spectrum.
The strontium lines come out generally with greater brilliancy if
the wire, before being moistened with HC1, is held for some time
in a reducing flame, easily obtained by closing the air-holes of
the Bunsen's burner. In some of the waters, especially the deep-
well waters, the line Li « is somewhat masked by the bright so-
dium and calcium spectra : it is, however, in all cases seen with
great distinctness if the residue of the water is treated with sul-
phuric acid and alcohol in the manner described by Bunsen and
Kirchhoff under the head of lithium. The strontium lines may
also be seen with great brilliancy on dissolving in hydrochloric
acid some of the crust deposited in boilers and kettles, and bring-
ing a drop of the solution into the flame of the apparatus. The
shallow waters appear to be rather richer in Li and Sr than the
deep-well waters ; the presence of Li in the latter can, however,
easily be demonstrated in an ounce or even in half an ounce of
the water.

The following are the waters examined : — Thames water, taken

* Communicated by the Authors,
t Phil. Mag. vol. xx. p. 89.

374 Chemical Notices : — M. Scheibler on the Tungstates.

at low and high tide, Westminster Bridge ; also two samples as
supplied by the Chelsea and Lambeth Water Companies. Water
supplied by the New River Company; and water from the
undermentioned wells : —

Duck Island Well, St. James's Park. . \ Above the London

Pump H, Lincoln's Inn J clay.

Burnett's Distillery, Vauxhall "1 From the sand above

Whitbread's Brewery, Chiswell Street, j the chalk.

Guy's Hospital well icha]k

1 ratalgar Square well J

The above waters may be taken to represent the whole of
the London supply, since, beside the specimens from the Thames
and New River, others from the three principal water-bearing
strata of London are included.

To guard against all possible sources of fallacy, the waters
were evaporated in platinum vessels, and all filtration avoided.
It need scarcely be mentioned that the alcohol, HO, SO3, and
HC1 used were free from lithium and strontium.

LIL Chemical Notices from Foreign Journals,
By E. Atkinson, Ph.D., F.C.S.

[Continued from p. 298.]

SCHEIBLER has published* an account of researches on
the tungstates, with which he has been engaged during
the last six years.

Tungstic acid exists in two distinct modifications — one inso-
luble in water (ordinary tungstic acid), and a modification soluble
in water (metatungstic acid). And there are two corresponding
groups of salts.

The tungstates, the salts of the insoluble modification, have
been repeatedly investigated. The alkaline salts are somewhat
soluble in water ; those of the alkaline earths and metals, which
are obtained by double decomposition, are insoluble, amorphous
or crystalline precipitates. These tungstates are characterized by
the fact that, when treated with a stronger mineral or organic
acid, a yellow pulverulent or white caseous precipitate of hydrate
of tungstic acid is formed, according as the decomposition is
effected in the warm or in the cold. To these salts, which have
usually been considered acid salts, Scheibler assigns the formula
3RO, 7W03-f # Aq, or perhaps more correctly
2RO,3W03 + RO, 4W03 + *Aq.

* Ber. der Akad. der Wissensch. zu Berlin, April 1860.

M. Scheibler on the Tungstates. 375

Tungstate of Soda, 3NaO, 7W03 + 16 Aq, crystallized in the
cold, and 3NaO, 7W03 + 14Aq, crystallized in the water-bath,
forms beautiful large monoclinic prisms.

Tungstate of Potass, 3KO, 7W03 + 6Aq, crystallizes in small,
difficultly soluble, scaly crystals.

Tungstate ofLithia, 3LiO, 7W03 + 16Aq, crystallizes in easily
soluble, very beautiful large monoclinic prisms.

Metatungstates. — The only salt of this class hitherto described
is the ammonia salt discovered by Margueritte.

The solutions of these salts are not decomposed by acids with
separation of a yellow or white hydrate of tungstic acid. The
metatungstates are formed from the tungstates by adding a
strong acid to their solutions as long as the precipitate redissolves,
— or better still, by continuously boiling the tungstates with an
excess of hydrate of tungstic acid. This hydrate is obtained by
the double decomposition of tungstate of soda with chloride of
calcium, and digesting the precipitate which is formed with
hydrochloric acid.

The metatungstates are very soluble, and crystallize only when
the solution is very concentrated. The alkaline salts crystallize
in octahedra. The ammonia salt melts in water like phos-
phorus ; its solution is strongly refracting. Its formula is NH40,
4W03 + 9Aq. The potash and soda salts are similar. On
mixing a warm concentrated solution of metatungstate of
ammonia with solution of chloride of barium, no precipitate is
formed, but on cooling there is deposited

Metatungstate of Baryta, BaO, 4W03 -f 9 Aq. — It crystallizes in
large fatty crystals, which are a combination of the octahedron
with the prism. The crystals have a considerable specific
gravity, and are readily soluble in hot water.

When a warm concentrated solution of metatungstate of
baryta is treated with an equivalent quantity of sulphuric acid,
the liquor, after filtration from the sulphate of baryta, deposits,
on evaporation in vacuo, small quadratic octahedra of meta-
tungstic acid, which apparently have the composition 2HO,
4W03 + 7Aq. It is a strong acid, and expels nitric and hydro-
chloric acid from their combinations. Its solution can be boiled
for some time without change, and can be evaporated to the con-
sistence of syrup in the water-bath ; but if it be further concen-
trated, it passes into the insoluble modification.

Metatungstic acid is an admirable reagent for nitrogenous
bases, which are all precipitated by it in white flakes ; it exceeds
phosphomolybdic acid in delicacy. Acid solutions which only
contain 2001000 of quinine or strychnine are made distinctly turbid,
and after twenty-four hours small flakes are deposited on the
bottom of the vessel. The free metatungstic acid itself is not

376 M. Caron on Calcium,

necessary ; any of its salts, mixed with a mineral acid, will do
equally well.

By double decomposition of the baryta salt with the corre-
sponding sulphates, Scheibler has obtained the magnesia,
copper, manganese, nickel, cobalt, zinc, and cadmium salts.
The stroutia and lime salts were obtained by treating their chlo-
rides with free metatungstic acid.

Metatungstic ether was obtained by treating crystallized tung-
state'of silver with iodide of ethyle. Besides these tungstates
and metatungstates, the author has described some new com-
pounds of oxide of tungsten, obtained partly by new and partly
by known methods.

TVohler* has described some new salts of suboxide of silver.
Molybdate of Suboxide of Silver, Ag20, 2Mo03, is a heavy, black,
lustrous powder consisting of well-defined regular octahedra.
It is obtained by dissolving molybdate of oxide of silver in strong
ammonia, and passing hydrogen gas through the solution. The
operation succeeds best when the temperature is about 90°. At
a higher temperature metallic silver is formed.

Tungstate of Suboxide of Silver, Ag2 0, 2 WO3, is prepared in
the same manner, and forms a black, crystalline, glittering
powder, the particles of which under the microscope appear to
possess rhombic faces.

Chromate of Suboxide of Silver. — The reduction of ehromate
of silver is effected at the ordinary temperature ; but it is impos-
sible to obtain the suboxide salt pure, as it always contains an
admixture of metallic silver.

The preparation of metallic calcium is effected by M. Caron
as follows f. 300 parts of fused and powdered chloride of cal-
cium are mixed with 400 parts of granulated zinc, and 100 parts
of sodium in pieces ; the whole is placed in a crucible heated to
redness ; when the action commences, the fire' is moderated so
as to prevent the volatilization of the zinc, but it is ultimately
raised as high as possible.

In this manner a crystalline regulus is obtained containing 10
to 15 per cent, of calcium, the remainder being zinc and a
small quantity of iron. To obtain the calcium, this alloy is
heated in a carbon crucible in tolerably large pieces. The cal-
cium thus prepared contains traces of iron ; it is of a pale
yellowish colour; its density was found to be 1*6 to 1*8, but
this is somewhat too high.. It is not perceptibly volatile ; but
the zinc in volatilizing carries away traces of it. It keeps toler-

* Liebig's Annalm, April 1860.
t Comptes Rendus, March 1860.

MM. Wohler and Michel on Alloys of Aluminum. 377

ably well in dry air, but first becomes covered with a layer of
oxide.

It burns with difficulty in the blowpipe flame, because it
becomes covered with a layer of lime ; but the combustion of its
wire gives rise to red scintillations of great beauty.

In the anticipation of obtaining crystallized titanium, AVb'hler*
fused a mixture of titanic acid with cryolite and a piece of alu-
minum, together with a flux of chloride of sodium and potassium.

The aluminum was found afterwards in the form of a lamellar
porous slag, which, when treated with soda lye, left a quantity
of lustrous brownish crystals ; by treatment with hydrochloric
acid these became quite colourless. The body is a combination
of aluminum with titanium and silicon, but not apparently in
any definite proportions. It is decomposed by chlorine, forming
chloride of titanium, silicon, and aluminum. It is slowly
attacked by hydrochloric acid, forming hydrogen gas and oxide
of silicon.

Michelf, at Wohler' s suggestion, has prepared a series of
compounds of aluminum and the metals.

Tungsten- Aluminum was obtained by melting together 15 parts
of tungstic acid with 30 of cryolite, 30 of chloride of potassium
and sodium, and 15 of aluminum. On treating the slag with
hydrochloric acid, the excess of aluminum was dissolved out, and
the compound was left as a grey crystalline powder, containing
individual crystals several millimetres in length, which under
the microscope were found to consist of rhombic prisms with
terminal faces. Their spec. grav. was 5*58, and they were very
hard and brittle. Their formula was found to be Al4 W. Treated
with caustic soda, all the aluminum was dissolved out, and pure
tungsten left.

Molybdenum-Aluminum. — Molyhdic acid was dissolved in
hydrofluoric acid, and the solution evaporated to dryness, and
fused with cryolite, flux, and aluminum in the manner de-
scribed above. The regulus, by successive treatment with soda
and nitric acid, yielded a crystalline powder which was found to
consist of iron-grey rhombic prisms. Analysis led to the formula
Mo Al4.

Manganese- Aluminum. — Obtained by fusing 10 parts of
chloride of manganese, 30 of chloride of potassium and sodium,
and 15 of aluminum. The regulus, by treatment with dilute
hydrochloric acid, left a quantity of interwoven stellate-group
needles, some of them 5 or 6 lines long. The needles were
quadratic prisms of the specific gravity 3*402. The compound
is easily dissolved by concentrated hydrochloric acid. The analysis

* Liebig's Annalen, February 1860. f Ibid. July 1860.

Phil. Mag. S. 4. Vol, 20. No. 134. Nov. 1860. 2 C

378 MM. Heintz and Richter on Artificial Boracite.

indicated the formula Mn Al8» Part of the manganese was
replaced by iron.

Iron-Aluminum. — Obtained by fusing aluminum with proto-
chloride of iron, and the alkaline flux. The regulus was very
crystalline, and on careful treatment left the compound in fine
hexagonal prisms. The analysis pointed to the formula Fc Al2.

Nickel- Aluminum. — Obtained in a similar manner to the above
compounds, in large crystalline scales of a tin-white colour. Its
specific gravity is 3*647. It is readily soluble in concentrated
hydrochloric acid. Its composition is NiAl6.

M. Michel has obtained titanium-aluminum in microscopic
quadratic plates ; his analysis led to the formula Ti Al3.

Heintz has communicated* some experiments of Richter on
the preparation of artificial boracite. 200 grms. of a mixture of
chloride of sodium and chloride of magnesium were mixed with
5 grms. of a compound of boracic acid and magnesia, obtained
by precipitating a boiling solution of sulphate of magnesia and
borax by carbonate of soda. To the mixture thus prepared 10
grms. of finely powdered boracic acid were added, and the whole,
well mixed together, heated in a platinum crucible. The fused
mass was heated with dilute hydrochloric acid, which left undis-
solved a crystalline powder. This powder was seen under the
microscope to consist of two kinds of crystals, some of a pris-
matic form, while others were tetrahedra and octahedra. On
digesting this mass for several days with hydrochloric acid, the
former were dissolved, while the latter were scarcely if at all
attacked. These latter were found on analysis to have the com-
position 6MgO, 8Bo3, MgCl, which is the formula of boracite.
When heated, they exhibited the pyro-electrical phenomena cha-
racteristic of the powder of tourmaline.

The prismatic crystals appear to be a mixture of two com-
pounds, one of which Heintz supposes has the formula MgO Bo3,
and the other the formula 2 MgO Bo3.

Nordenskjold and Chydeniusf describe some experiments on
the crystallization of thoria.

Thoria, prepared by the ordinary method from orangite, was
mixed with four times its weight of borax glass, and placed in a
flat platinum dish, which, coated with magnesia, was fitted in an
unglazed porcelain vessel, and this again in an ordinary clay
crucible, and the whole exposed to the heat of a porcelain fur-
nace. The highest heat of the furnace continued forty-eight
hours, and the cooling was very slow.

After the operation the borax glass presented two layers — the

* Poggendorff's Annaltn, August 1860. f Ibid.

M. Bauer on Hydride of Amyle. 379

upper a colourless glass, and the lower an opake white mass. In
the clear glass and on the sides of the crucible there were inter-
spersed individual brown crystals, which were left undissolved
when the whole mass was treated with hydrochloric acid : the
white mass also left after this treatment a heavy hard powder,
seen under the microscope to consist of crystals like the larger
ones.

A crystallographical examination of the larger crystals was
made. Though small, they were frequently found as well deve-
loped as the most perfect crystal models. Their form was that
of a dimetric prism with a pyramid. Hence, if this is correct, the
oxide of thorium is isomorphous with oxide of tin and titanic
acid. It is a binoxide, ThO2, and not ThO and Th203, as has
hitherto been supposed.

A similar experiment was made with tantalic acid, by fusing it
with microcosmic salt under the same circumstances. The slag
contained a crystalline powder consisting of tantalic acid, besides
some individual larger needles of the same substance, the form of
which on examination was found to be that of a rhombic prism*

In his researches on oxide of amylene*, Bauer obtained hy-
dride of amylene as an accessory product in the preparation of
amylene. It is not possible to separate these sul?stances by frac-
tional distillation, as their boiling-points are too near; but by
acting on the mixture with bromine, bromide of amylene,
€5H10Br2, is formed, while hydride of amyle remains intact.
Bromide of amylene boils at 170°, and hence the latter body is
readily separated by fractional distillation.

When chlorine is passed into hydride of amyle, a brisk action
is set up, the gas is absorbed, hydrochloric acid gas is liberated,
and considerable heat is disengaged. The first product of the
action is chloride of amyle, €5HnCl; when this body, which
boils at 102°, is separated by fractional distillation, and chlorine
gas passed into the residue for several hours, the liquor becomes
very thick : when it is distilled it begins to boil at 180°, and
the thermometer rises quickly to 230°, and remains for some
time between this point and 240°. It afterwards rises to 300°,
and then decomposes, leaving a black residue. The body which
distils between 230° and 240° has the formula G5 H8 CI4, and is
the chloride of trichlorinated amyle formed in accordance with
the equation

€5H12 + 8C1=G5H8C14 + 4HC1.
It is a colourless liquid insoluble in water : it is heavier than

* Phil. Mag. vol. xx. p. 44.
2C2

380 MM. Griess and Leibius on Amido-acids.

water, and burns when heated, with the flame characteristic of
chlorine compounds.

Acted on by potash, chloride of potassium and trichlorinated
amylene are formed, thus : —

€5H8C14 + KHG=KC1+€&H7C13 + H*0.

Trichlorinated amylene boils at about 200° ; in other respects it
resembles the chloride of trichlorinated amyle.

Bromine acts on hydride of amyle at 100°, forming similar
products.

By the action of sodium-alcohol on chloroform, Kay obtained
a body of the composition Q7 H1603, which may be regarded as

the ethylic ether of the triatomic alcohol tt3 >93, that is,

/£2tt5x3 f O3. Regarding the body in this light, M. Sawitsch*

has examined the action of acetic acid'upon it, expecting that the
reaction would take place in the following manner, and yield the
triatomic alcohol :

(% n"\s\Q3 + ZG* H4 0*=3(C4 H8 0«) + Q£ZX&.

V^ " ; J Acetic acid. Acetic ether. XTJ J . .

JNevv alcohol.

The result, however, did not correspond to this anticipation : the
only products of the reaction were formiate and acetate of ethyle,
acetic acid, and water; and it appears that the body GH403
does not exist in the free state. The action of acetic anhydride
on the body gave equally unfavourable results.

The researches of Hofmann and Cahours have led to the con-
clusion that amidobenzoic acid (benzamic acid) comports itself
as a base. Griess and Leibius f have examined it from this
point of view, and have found that it combines with cyanogen,
as does aniline, but the product of the action has acid instead of
basic properties. It has the formula C18 H7 N3 O4, and is a com-
bination of one equivalent of benzamic acid with two equivalents
of cyanogen. It does not crystallize, it is insoluble in water, and
difficultly soluble in alcohol and ether. It forms salts with bases.

The authors have found that a great many amido-acids com-
bine in a similar manner with cyanogen, as do also their ethers.

Mucic acid has a composition analogous to that of citric acid,
and both acids are decomposed by fusion with potash in a similar
manner. How formerly found that the fermentation of citric

* Societe Chimique de Paris, April 27.
t Liebig's Annalen, March 1860.

M. Boutlerow on the occurrence of Acrylic Acid. 381

acid yielded acetic and butyric acids. Rigault* has recently sub-
mitted mucate of lime to fermentation, and has found that the
products were exactly the same as with citric acid.

By the action of sodium-alcohol upon iodoform, iodide of me-
thylene is formed. Boutlerow, who examinedf this question,
has repeated J his experiments on a larger scale, and has found
that two organic acids are also formed. When the crude product
of the action was mixed with water, iodide of methylene was pre-
cipitated ; and when the supernatant liquor was distilled with
excess of tartaric acid, an acid distillate was obtained, which was
neutralized with soda and evaporated to dryness. On treating
this mass with hydrochloric acid, an oily liquid separated which
was submitted to fractional distillation. The first portion boiled
at a little over 100°. It was found to consist of acrylic acid. Its
silver salt had the characteristic serrated form of acrylate of silver,
and was reduced on boiling. The analytical results confirmed
this conclusion.

The other portion of the distillate boiled between 195° and
198°; but was decomposed by further rectification. It is a
colourless, thickish fluid, with a taste suggestive of both acetic
acid and Pelargonium zonale. It decomposes carbonates, and
forms with the alkalies and alkaline earths soluble crystalline
salts. It has the formula G6 H10O3. Boutlerow considers it to
be analogous to Heintz's new acid§, and calls it valerolactic
acid. The small quantity formed has, however, prevented the
determination of this point.

Gerhardt expressed the opinion that furfurol was the aldehyde
of pyromucic acid. Schwanert and Schulz have recently found ||
that this hypothesis is correct. According to Schulz, furfurol
by treatment with oxide of silver is converted into pyromucate
of silver, with the separation of metallic silver. Schwanert has
found, on the other hand, that freshly prepared furfurol forms a
crystalline compound with alkaline bisulphites when it is mixed
with a concentrated solution and left to spontaneous evaporation
over sulphuric acid.

By the destructive distillation of mucate of ammonium, Mala-
guti obtained a body of the formula Qb H6 N2 O, which he called
pyromucamide. Schwanert has investigated this body, and con-
siders it to be the amide of a new acid, carbopyrrolic acid.

* Comptes Rendus, April 1860.
t Phil. Mag. vol. xviii. p. 28/.
% Liebig's Annalen, May 1860.
§ Phil. Mag. vol. xix. p. 385.
|| Liebig's Jnnalen, April 1860.

382 Kolbc and Lautcmann on Salicylic Acid and its Homologues.

When the above body is heated in a sealed tube with baryta
water, it is converted into ammonia and the acid:

^H^N^O+H^Grr^^NO^ + NH3.

Carbopyrrolamide. Carbopyrrolic

acid.

The product of the action is carbopyrrolate of barium, which
crystallizes in nacreous laminae. It can be boiled with potash
without decomposition, but when treated with hydrochloric acid,
a white crystalline precipitate of carbopyrrolic acid is formed.

When the free acid is heated at 60° an atom of carbonic acid
is liberated, and the brown flocculent substance is separated
which Anderson calls pyrrol-red. The decomposition is as
follows :

€5H5N02=C02+€4H5N.

This action is quite analogous to the decomposition of anthra-
nilic acid by destructive distillation,

Kolbc and Lautemann have published a memoir on the con-
stitution of salicylic acid*. They consider that this acid is ana-
logous to lactic acid, and monobasic. For the development of
their reasons, which by no means settle the question, the original
memoir must be consulted ; we shall here merely describe cer-
tain new bodies which they have discovered in the course of their
investigation,

The starting-point for their research was salicylic acid. This

acid has the formula C14 H6 O6, and is isomeric with oxybenzoic

acid. The authors consider both these acids as having the same

TC12fl4 "1
rational formula, which they write HO,^ n^2 >C202, 0,

but as containing two different radicals. Benzoic alcohol and
cresylic alcohol have the same composition, C14 H8 O2, and doubt-
less the same constitution, but they differ in containing different
radicals. In like manner, in salicylic acid the radical is phenyle,
C12 H5, while in oxybenzoic acid there is a radical of an alcohol
next lower in the series than benzoic alcohol.

When one part of salicylic acid is mixed with three parts of
pentachloride of phosphorus, a violent action is set up, torrents
of hydrochloric acid are evolved, and a colourless liquid distils
over, which consists principally of the chloride C14 H4 O2 CI2, and
of oxychloride of phosphorus. Besides these there is some
chloride of salicyle, C14H504C1, and an oil which is unacted
on by water.

The chloride, C14 H4 O2 CI2, is obtained in larger quantity by

* Liebig's Annalen, August 1860.

Kolbe and Lautemann on Salicylic Acid and its Homologues. 383

treating salicylate of soda with pentachloride of phosphorus.
The authors name it chloride of chlorsalyle. When it is treated
with water, an acid is obtained which has the composition of
chlorobenzoic acid, C'4H5C104, and was formerly thought to
be that acid until Limpricht and Uslar showed that this was not
the case. Kolbe and Lautemann name the acid chlorsalylic acid.
It differs from chlorobenzoic acid in having a different crystalline
form, and in being about three times as soluble in water as that
acid. The two acids also differ in their melting-point. Unlike
salicylic acid, chlorsalylic acid gives no purple colour with per-
chloride of iron, but, like chlorobenzoic acid, a yellow precipitate.
The acids likewise differ in their deportment towards sodium-
amalgam : chlorobenzoic acid is attacked with great difficulty,
but chlorsalylic acid is readily converted into a new acid.

To obtain this acid, a quantity of sodium-amalgam was added
to a concentrated aqueous solution of chlorsalylic acid, and the
mixture ultimately heated to boiling for some time ; the mercury
having been separated, the filtrate was treated with hydrochloric
acid, by which a crystalline magma was separated. This, on
appropriate purification, was obtained in beautiful crystalline
needles.

This new acid the authors name salylic acid: it has the for-
mula C14 H6 O4. It is isomeric with benzoic acid, and stands to
salicylic acid in the same relation as propionic acid does to lactic
acid*. It crystallizes in small, microscopic needles, the form of
which differs from that of benzoic acid. It is about three times
as soluble as benzoic acid ; it is more volatile, and, unlike that
acid, it melts in hot water to a clear oil before it dissolves. The
salts, of which many were examined, also differ considerably
from those of benzoic acid.

In these investigations there was frequent occasion to deter-
mine the solubility of the different acids. This was effected by
preparing a solution of the acid of such a strength that, on cool-
ing, very little crystallized out. This was cooled to 0° for several
hours and filtered. A measured quantity was then determined
by means of a standard alkaline solution.

Chloride of Salyletrichloride, C14H4C14. — This is the oil left
after the crude product of the action of pentachloride of phos-
phorus on salicylic acid has been treated with water. It forms
a yellowish oil, which, when dried over chloride of calcium, distils
over colourless, and solidifies to a brilliant mass of crystals. Its
specific gravity is 1*51 ; it melts at 30°, and boils at 265°. It
has a strong tendency to crystallize. Heated in a closed tube
with water, it is converted into hydrochloric and chlorsalylic
acids.

* Phil. Mag, vol. xix. p. 384.

384 Kolbe and Lautemann on Salicylic Acid and its Homologucs.

When salicylate of soda is treated with excess of pentachloride
of phosphorus, a syrupy fuming liquid distils over, which, on
cooling, deposits tabular crystals of a body free from chlorine.
The mother-liquor smells of phenylic alcohol. The body is
soluble in ether, and on evaporation of the etherial solution,
remains as a white woolly mass of crystals. This body has the
formula C26H804; it appears to be a compound of oxide of
phenyle with an acid which differs from salicylic acid by contain-
ing two atoms of water less. This acid, C14 H4 O4, the authors
name provisionally lasylic acid; it would stand to salicylic acid
in the same relation that acrylic acid does to lactic acid :

C14 H4 O4 Lasylic acid. C6 H4 04 Acrylic acid.
C14 H6 O6 Salicylic acid. C6 H6 O6 Lactic acid.

It has been already stated* that these authors obtained sali-
cylic acid by the action of carbonic acid on sodium-phenylic
alcohol. They then regarded this acid as being analogous to
carbovinic acid. This view they have given up. Such an acid
is formed ; but as carbovinic acid is decomposed by hydrochloric
acid into carbonic acid and alcohol, so the acid is decomposed
into phenylic alcohol and carbonic acid; while salicylic acid,
which is formed at the same time, is unaltered by it.

When a stream of dry carbonic acid is passed into gently
heated cresylic alcohol, C14H802, and sodium added from time
to time, a mass is obtained from which, when dissolved in water
and treated with hydrochloric acid, a new acid is precipitated
crystallizing in beautiful large prisms. It is homologous with
salicylic acid, and greatly resembles it. It gives with iron the
beautiful purple colour, and when heated it decomposes into
carbonic acid and cresylic alcohol. Although it has a higher
atomic weight, it melts at 153°, which is 6° below the melting-
point of salicylic acid. The formation is thus : —

C14 H8 02 + C2 04=C16 H8 O6.

Cresylic Cresotic

alcohol. acid.

In like manner, by treating the homologous hydrated oxide of
thymylc, C20H12O2, with carbonic acid and sodium under the
same circumstances, a new acid is obtained, thymotic acid, homo-
logous with salicylic and cresotic acids, and with similar proper-
ties. Although it contains 22 equivalents of carbon, its melting-
point, 120°, is lower than either of the foregoing acids. Its
formation is quite similar.

C20 H14 02 + C2 04=C22 H14 O6.

Thymotic Thymotic

alcohol. acid.

* Phil. Mag. vol. xix. p. 213.

Royal Society. 385

In the course of these investigations the authors were led to
examine* the acids contained in gum benzoin. They found that
benzoic acid is not contained in all varieties of the resin. In
some cases, especially in the benzoin from Sumatra, an acid was
found which crystallized differently from benzoic acid, and melted
under hot water to a clear oil, yet by oxidation yielded oil of
bitter almonds. This acid they believe to be identical with the
toluylic acid obtained by Strecker from vulpic acidf.

LIII. Proceedings of Learned Societies.

ROYAL SOCIETY.
[Continued from p. 326.]

February 23, 1860. — Sir Benjamin C. Brodie, Bart., President,
in the Chair.
rpiIE following communications were read : —
•*- " On the Lines of the Solar Spectrum." By Sir David Brew-
ster, K.H., D.C.L., F.R.S., and Dr. J. H. Gladstone, F.R.S.

In a paper in the Transactions of the Royal Society of Edinburgh
for 1833, Sir David Brewster stated that he had examined the lines
of the solar spectrum, and those produced by the intervention of
nitrous acid gas, and had delineated them on a scale four times greater,
and in some parts twelve times greater than that employed in the
beautiful map of Fraunhofer. None of these drawings, however, were
published at the time ; they were increased by frequent observations
continued through succeeding years ; and now having been collated,
arranged, and added to by Dr. Gladstone, they form the diagrams
accompanying this paper.

The figures consist of —

1st. A map of the whole spectrum 58 inches long, and exhibiting
about 1000 lines and bands. This map includes a great prolongation
of the spectrum at the least refrangible end, before A, with a series
of bands and lines not hitherto described.

2nd, 3rd, 4th, and 5th. Enlarged delineations of the portions of
the spectrum between A and B, and between E and F, exhibiting
additional lines, with still more magnified views of the groups a and b.

6th. A map of the two extremities of the solar spectrum as observed
by Dr. Gladstone about noon-day at midsummer, consequently when
the sun was at its greatest altitude. This shows several bands between
A and B, and a series of lines in the lavender rays extending as far
as M. Becquerel's N, and corresponding evidently with the maps
published by him and by Professor Stokes, with the addition of finer
lines. Yet this map represents the extreme spaces of the spectrum
where there is no effect on the organ of vision, while that of M.
Becquerel represents the want of chemical action, and that of Pro-
fessor Stokes the absence of fluorescent power.

* Liebig's Annalen, July 1860.
f Phil. Mag. vol. xix. p. 211. . .

386 Royal Society :~

7th. A map of the " atmospheric lines " compiled from the
independent observations of the two authors. These lines and hands
are visible only when the sun is rising or setting, that is to say, when
his beams traverse a long stratum of our atmosphere. In some cases
they are merely the deepening of bands seen at any time, in other
cases they are bands which appear for the first time when the sun
is close to the horizon. Professor Piazzi Smyth has represented some
of these lines in his delineations of the spectrum as observed from
the Peak of Teneriffe, whence he had the advantage of seeing the
sun at an altitude of — 10,1. The most remarkable of the atmo-
spheric lines are situated in the orange and yellow spaces, and one
band just beyond D is discernible in the diffused light of a dull day
at any hour, though it covers what is about the brightest part of the
prismatic image obtained from direct sunshine. The western sky
after sunset exhibits these phenomena in a striking manner, and with
some variations that do not appear to depend altogether on the
absence or presence of moisture, although when the sun looms red
through a fog these lines also make their appearance. They are in
no respect due to the mere reduction in the quantity of light.

The dispersion and absorption of the more refrangible rays by the
atmosphere, and by fogs, smoke, and such media as dilute milk'and
water, is a quite independent phenomenon.

8th and 9th. Enlarged views of A and B, when the light is acted
upon by a long passage through the atmosphere.

10th. A map of the spectrum, exhibiting on a large scale the dark
lines and bands which were seen by Sir David Brewster when nitrous
acid gas is interposed between the prism and the source of light.
Their position is identified by the insertion of the principal lines of
the solar spectrum. They differ considerably from a smaller drawing
of the same by Professor W. A. Miller, who employed a deeper
stratum of the red gas.

The light of the moon, which is only that of the sun reflected from
her surface, exhibits all the principal lines from about B to H, and
no fresh ones ; and when the luminary was near the horizon, the more
prominent atmospheric lines were detected. The green colour was
observed to extend a little beyond F in the spectrum of moonlight,
and the space between G and H appeared lavender or lavender-grey
instead of violet.

In respect to the origin of these lines, it is conceivable that the light
when emitted from the photosphere itself is deficient in these rays,
or that they are due to absorption by the atmosphere of the sun, or
by that of the earth. The first of these suppositions scarcely admits
of a positive proof. If the second be true, it might be expected that
the light from the edge of the solar disk would exhibit more of these
absorption bands than that from the centre, which must have traversed
a smaller amount of atmosphere ; but such was not found to be the
case. The third supposition is favoured by the fact that the atmo-
sphere has unquestionably much to do with the manifestation of many
of these lines, and by the analogy of the bands produced by nitrous
acid gas, bromine vapour, and other absorbent media. The experi-

On some New Volatile Alkaloids given off during Putrefaction. 387

mentum cruets of observing an artificial light through a long space of
air was attempted by means of the revolving light on Beachy Head,
as seen from Worthing at a distance of twenty-seven miles. It gave
a negative result ; but on account of the great difficulty of detecting
slight breaks in a faint thread of light, no great reliance is to be placed
on the experiment. A similar doubt rests on the authors' observa-
tions of fixed stars, and on the non-recognition by Fraunhofer of the
ordinary lines in the light of Sirius and Castor, while on the other
hand he did detect D and b in that of other stars. The origin of
these lines is still an open question.

The spectra of artificial flames sometimes exhibit bright lines
coincident with the dark spaces of the solar spectrum. Thus the
yellow band in the flames of soda, and several other substances, is
identical in refrangibility with D ; but the most remarkable case is
that of charcoal or sulphur burnt in nitre ; the spectrum shows three
very prominent lines, two of which coincide with A and D, while a
faint red line appears at B, and a group between it and A.

A map is also given of the bright lines, principally orange, that
make their appearance when nitrate of strontia is placed on the
ignited wick of a spirit-lamp.

"On some New Volatile Alkaloids given off during Putrefaction."
By F. Crace Calvert, Ph.D., F.R.S. &c.

Some eighteen months ago my friend Mr. J. A Ransome, surgeon
to the Royal Infirmary, Manchester, induced me to make some
researches with the view of ascertaining the nature of the products
given off from putrid wounds, and more especially in the hope of
throwing some light upon the contagion known as hospital gangrene.
I fitted up some apparatus to condense the noxious products from
such wounds ; but the quantity obtained was so small, that it was
necessary for me to acquire a more general knowledge of the various
substances produced during the putrefaction of animal matter, before
I could determine the nature of the products from sloughing wounds.
I therefore began a series of experiments, the general results of which
I now wish to lay before the Society.

Into each of a number of small barrels twenty lbs. of meat and
fish were introduced, and to prevent the clotting together of the mass,
it was mixed layer by layer with pumice-stone. The top of each
barrel was perforated in two places, one hole being for the purpose
of admitting air, whilst tln'ough the other a tube was passed which
reached to the bottom of the barrel. This tube was put in con-
nexion with two bottles containing chloride of platinum, and these
in their turn connected with an aspirator. By this arrangement air
was made to circulate through the casks, so as to become charged with
the products of putrefaction and to convey them to the platinum salt.
A yellow amorphous precipitate soon appeared, which was collected,
washed with water and alcohol, and dried. This precipitate was found
to contain C, H, and N, but what is highly remarkable, sulphur and
phosphorus enter into its composition. The presence of C, H, and
N was ascertained by elementary analysis ; for the sulphur and

388 Royal Society .—

phosphorus, a given weight of the platinum salt, 0'547 grm., was
oxidized with nitric acid, and gave 0*458 grm. of sulphate of baryta
= 11 per cent, of sulphur, and 0'266 of pyrophosphate of magnesia
= 6#01 per cent, of phosphorus. I also ascertained the presence of
these two substances by heating a certain quantity of the platinum
salt with strong caustic ley, when a liquid, volatile and inflammable
alkaloid was obtained, whilst the sulphur* and phosphorus remained
combined with the alkali and were easily detected. I satisfied myself
during these researches, which have lasted more than twelve months,
that no sulphuretted nor phosphuretted hydrogen was given off ; and
my researches, as far as they have proceeded, tend to prove that the
noxious vapours given off during putrefaction, contain the N, S, and
Ph of the animal substance, and that these elements are not liberated
in the simple form of ammonia, and sulphuretted and phosphuretted
hydrogen. I also remarked during this investigation, that, as putre-
faction proceeds, different volatile bodies are given off.

Before concluding, I may add, that when the platinum salts are
heated in small test-tubes, they give off vapours, some acid and
some alkaline, possessing a most obnoxious and sickening odour,
very like the odours of putrefaction ; and that at the same time a
white crystalline sublimate, which is not chloride of ammonium, is
formed.

March 1, 1860. — Sir Benjamin C. Brodie, Bart., President, in the

Chair.

The following communications were read : —

" On the Electrical Phenomena which accompany Muscular Con-
traction." By Professor C. Matteucci.

Dr. Radcliffe has recently communicated to the Royal Society
some observations on the nature of the electrical phenomena accom-
panying muscular contraction. It is known that M. du Bois-Rey-
mond admits that the muscular current diminishes during contrac-
tion, and that he attributes the phenomena indicated by the galva-
nometer to the momentary predominance of currents due to the
polarization of the electrodes of platinum over the muscular current.
In my last memoir on Electro-physiology, which was communicated
to the Royal Society and appeared in the Philosophical Transactions
for 1856, I proved that these phenomena take place independently
of the existence of secondary currents of the electrodes, and I hence
concluded, at least as regards the muscles pf frogs, that during con-
traction there is a current, or rather an instantaneous electrical
discharge, which takes a contrary direction to that of the relaxed
gastrocnemius y and in general to that of the current which is found
on applying the extremities of the galvanometer to the extremities
of the limbs of a frog.

In order to avoid the influence of secondary polarity, M. du Bois-
Reymond, and after him several other German physiologists, have

* Some of the platinum salt was treated with C S2, which did not remove any
free S, and the beautiful orange-yellow colour of the precipitate showed the
absence of sulphuret of platinum.

Electrical Phenomena accompanying Muscular Contraction. 389

thought it expedient to contract and tetanize the gastrocnemius
before closing the circuit of the galvanometer ; the deviation thus
obtained is feebler than that which is due to the current of a muscle
in repose, but never in a contrary direction to that due to this
current.

I have already remarked* that this result accords with that
which is obtained by the ordinary experiment, in which the muscular
current is in circulation previously to the contraction of the muscle.
In fact, we know that by continuing to keep the muscle in contrac-
tion, above all when the muscle remains tetanized, the electric phe-
nomenon accompanying contraction (the effect of which is to pro-
duce a deviation of the needle in a contrary direction to that of the
current of a relaxed muscle) becomes gradually less intense as the
contractions are more and more feeble.

The method employed by Dr. Radcliffe is the same as that which I
followed in my latest experiments ; .that is, he made use of amalgam-
ized plates of pure zinc as electrodes, immersed in a neutral solution
of sulphate of zinc, and after having ascertained that there was no-
thing to fear from the effects of secondary polarity, he says that he
finds that the needle deviated by the muscular current descends,
during contraction, towards zero, but only more slowly than it would
have done had the circuit been opened.

Dr. Radcliffe next examines another of my experiments, in which,
instead of placing a gastrocnemius in the circuit, I employ a thigh
cut transversely at the upper extremity, so that the needle remains
deviated in a contrary direction to that of the gastrocnemius. In
this arrangement of the experiment, when contraction is produced,
the deviation of the needle increases, which is perfectly in accordance
with the idea that during contraction a muscular current is developed
in a contrary direction to the current of the relaxed gastrocnemius.
Dr. Radcliffe attempts to explain this result by supposing (if I
rightly understand his idea) that during contraction the contacts
with the electrodes are deranged so as to facilitate the passage of the
current of the relaxed muscle.

Being unwilling to remain in doubt as to the nature of the elec-
trical phenomena of muscular contraction, I have of late repeated
and varied my experiments.

As to Dr. Radcliffe' s first remark, I shall only observe that in
the principal experiment the needle does not merely move slowly
towards zero during contraction, but is seen, during the first con-
tractions, especially when the frog operated on is vivacious, to move
rapidly down to zero, to oscillate, to pass to the opposite side, and
sometimes even to remain fixed, while thus deviated, for a very short
interval of time. This result, which is easily obtained and can be
verified without difficulty, is the same, whether the electrodes are
of platinum, like those employed by M. du Bois-Reymond, or of
zinc.

It is easy to understand that, in order to succeed in these experi-
ments, it is desirable that the needle should be as little deviated as
* Nuovo Cimento, September 1858, p. 238.

390 Royal Society :—

possible before the contractions : this object is best ensured in the
following way: — I prepare the frog by reducing it to two thighs,
leaving a single lumbar nerve in order to obtain contractions in one
of the thighs. Instead of saturated solution of sulphate of zinc, I
employed a weak solution of this salt, in order to avoid any alteration
of the surface of the muscles ; and finally, in order to maintain exactly
the same points of contact between the two electrodes and the two
near points of the middle portion of the thigh, I employ two fine
woollen cords or two thin strips of card-board fixed with sealing-wax
on a plate of glass and soaked in the same solution. The experi-
ment is made by applying the glass plate with a certain pressure
on the thigh, so that the two cords on one side touch the thigh, and
on the other are placed in contact with the cushions of flannel or
card-board which are immersed together with the electrodes, accord-
ing to the method followed by M. du Bois-Reymond.

I think it useful to describe in a few words a little apparatus
which affords a good deal of facility for making these experiments.
It consists in a small square block of wood, with a cavity deep
enough to receive the electrodes and the cushions. It is hardly
necessary to say that this cavity is coated with a varnish of sealing-
wax and divided in the middle by a glass plate. Another cavity in
the same block serves as a recipient for the two thighs ; the sciatic
nerve extends beyond the block, and rests on two platinum wires
which communicate with the pile or with the electro-magnetic ma-
chine. The communication between the thigh and the electrodes is
established by means of the glass plate in the manner above de-
scribed, that is, I press this strip of glass slightly on the middle of
the thigh on one side, and at the same time the extremities of the
two woollen cords come to rest on the cushions. The movements of
the needle are observed through a telescope (lunette). I have re-
peated this experiment thirty or forty times. Sometimes, and this
case is the most frequent, the first deviation produced by the muscle in
repose is directed in the same sense as that of the current of the
gastrocnemius ; sometimes the current is null, or almost null ; some-
times, and this case is the most rare, the deviation is in a contrary
direction, and this occurs most frequently in operating on the hinder
portion of the thigh.

In all these experiments, the moment that the thigh begins to
contract, the needle moves in a constant direction ; the deviation
which intervenes is greater or less according to the force of the
contraction, and indicates constantly a descending discharge or
current of extremely short duration, which traverses the thigh in the
direction of the ramification of the nerves, and in a contrary direction
to the current of the gastrocnemius.

"An Inquiry into the Muscular Movements resulting from the
action of a Galvanic Current upon Nerve." By Charles Bland Rad-
cliffe, M.D., F.R.C.P.

In a lecture delivered about two years ago*, in which he treats
* Lectns sur la Physiologic ct Pathologic du systome ncrvcux. Tome 1.
LeconlO. Paris,. 1858.

Dr. RadclifFe on the Action of a Galvanic Current upon Nerve. 391

among other things of the muscular movements resulting from the
action of a galvanic current upon a motor or mixed nerve, Pro-
fessor Claude Bernard says that some of the more important of
these movements have been overlooked, and he quotes an account
of some investigations by Dr. Rousseau of Vezy, which do away with
certain very perplexing variations in the order of these movements.

The movements resulting from the action of a galvanic current upon
nerve are usually divided into the three periods of double, alternate,
and single contraction which are set down in the following Table : —

Table I.—

The Nerve divided and lifted up at its end.

Direct Current.

Inverse Current.

Beginning.

End.

Beginning.

End.

Period of double
contraction . .

Strong
contraction.

Contraction.

Contraction.

Contraction.

Period of alternate
contraction . .

Contraction.

0

0

Contraction.

Period of single
contraction . .

Contraction.

0

0

0

Apparent irregularity — •" Voltaic alternatives."

Professor Bernard proposes to place another period before the
first of these — a period corresponding to the normal unexhausted
and undisturbed state of nerve, and characterized by contraction at
the beginning of the two currents, direct as well as inverse.

The investigations of Dr. Rousseau show how it is that the order
of these contractions is altered by certain Changes in the arrange-
ment of the nerve acted upon by the current. If the nerve acted
upon be divided and lifted up at its end, so as to break the circuit of
the derived current*, the order of contraction is that which is put
down in the preceding Table ; if the nerve acted upon be raised in a
loop (either without dividing it, or, after dividing it, by dropping down
the end); so as not to break the circuit of the derived current, the
order of contraction is that which is represented in the following
Table :—

* Figures 3 & 4 on page 396 may serve to illustrate all that need be said
respecting the derived current. In figure 3, the sciatic nerve of a frog's leg is
arranged in a loop across the poles P N of a galvanic apparatus ; the primitive
current, indicated by the black arrow, passes by the shortest route from the
positive pole P to the negative pole N ; the derived current, indicated by the dotted
arrows, passes by the longest route between these poles, and as it also proceeds
from the positive pole P to the negative pole N, it passes in the contrary direc-
tion to that of the primitive current. In fig. 4, the sciatic nerve is divided
between P and the thigh, as is meant where the nerve is spoken of as divided
and lifted up at its end ; and being divided, the only current passing is the primi-
tive current ; for the circuit of the derived current being broken, there can be no
derived current in this case.

Royal Society : —
Table II. — The Nerve in a loop.

Direct Current.

Inverse Current.

Beginning.

End.

Beginning.

End.

Period of double
contraction .

Strong
contraction.

Contraction.

Strong
contraction.

Contraction.

Contraction.

Contraction.

Strong
contraction.

Contraction.

Period of alternate
contraction . .

0

Contraction.

Contraction.

0

Period of single
contraction . •

0

0

Contraction.

0

!

Apparent irregularities — " Voltaic alternatives."

Now Dr. Rousseau shows that the order of contraction set down
in the second Table is due to the action of this derived current. He
shows, also, that by excluding the derived current (which he does
by means of an ingenious triple arrangement of poles called the
" rheophore bifurque "), the order of contraction becomes one and
the same in the case where the nerve is divided and lifted up at its
end, and in the case where the nerve is arranged in a loop, the order
being that which is set down in the first Table.

On inquiring into these matters experimentally, the author finds
reason to believe that Professor Bernard has wandered into some
degree of error, and that the path of inquiry opened out by Dr.
Rousseau is not only a right path, so far as its discoverer has traced
it out, but that it leads to the explanation of some very curious
alternating movements which have not hitherto been described. He
has been led, also, to form certain conjectures respecting the modus
operandi of electricity in muscular motion which he trusts may serve
to simplify this very difficult and complex subject.

1. When nerve is in its normal, unexhausted, undivided state,
there is, as Professor Bernard points out, contraction at the begin-
ning of both currents, inverse as well as direct, and at the beginning
only, if a feeble current be used. This, for example, will be the result
of the application of the feeble current produced by partially
moistening the small galvanic forceps of Bernard with saliva. But it
is also a fact, that a stronger current — the current for example of a
Pulvermacher's chain of ordinary length moistened with vinegar —
will produce contraction at the end as well as at the beginning of
both currents (as in the period of double contraction), if applied
to a nerve similarly circumstanced. Nay, it is a fact, that the feeble
current of the forceps will give contraction at the, beginning of both
currents, and at this time only, after the stronger current of the chain
has produced contractions at the end as well as at the beginning
of both currents, and that we may produce alternately again and
again the contraction confined to the beginning, and a contrac-

Dr. Radcliffe on the Action of a Galvanic Current upon Nerve. 393

tion occurring at the end as well as at the beginning, of the cur-
rents, by applying alternately the feeble current of the forceps
and the stronger current of the chain. The author finds, also, that
the feeble current of the forceps will produce contraction at its end
as well as at its beginning, if the nerve be raised and placed as a
loop across the points of the forceps ; and not only so, but that the
same current will produce contraction only at its beginning, if it be
applied after slipping away the points of the forceps, and so allowing
the nerve to fall back upon the muscles. Hence the single con-
traction at the beginning of a feeble inverse or direct current, and
not at the end, instead of indicating, as Professor Bernard supposes,
the normal state of undisturbed and unexhausted irritability in the
nerve, must only be looked upon as the result of the action of a
feeble current under particular circumstances. In a word, the fact
is one which reflects the strength of the current rather than the
condition of the nerve.

2. The curious alternating movements, which do not appear to
have been described hitherto, and which may be explained by means
of the key which Dr. Rousseau has put into our hands, are best
seen when the current is made to act upon the lumbar nerves of one
side, but they are also seen in the case where a loop of sciatic nerve
is acted upon.

Take the back, loins, and hind limbs of a frog with the lumbar
nerves properly exposed, raise the nerves on one side into a loop
without dividing them, place them over the platinum poles of a
galvanic apparatus (a Pulvermacher's chain of ordinary length), and
pass the current. On doing this, as might be expected, there is in
the first instance, contraction in the limb to which the nerves acted
upon belong, but this contraction is slight and transient when com-
pared with the contraction which is set up in the opposite limb, the
nerves of which are not acted upon. In this opposite limb, indeed,
the contraction is sure to be both strong and tetanic. A little later
(and it is to the phenomena of this stage that the author wishes to
direct attention), and the results are as follows : — With the inverse
primitive current there is contraction in the leg belonging to the same
side when the current begins to pass, and contraction in the leg be-
longing to the opposite side when it ceases to pass ; with the direct
primitive current this order of contraction in the two legs is
reversed.

In bringing about these curious alternations, the action of a
derived current is obviously concerned ; for on excluding this current
by means of Dr. Rousseau's rheophore bifurque, they come to an
end, and the movements resulting from the action of the current
are confined to the leg, the nerves of which are directly acted upon.
It is evident, also, that a derived current is what is wanting to pro-
duce the contraction in the limb belonging to the opposite side; for
after breaking the circuit of the derived current by dividing the
lumbar nerves where they emerge from the spine, and separating the
divided ends, and after then completing the circuit by dropping
down the end of the divided nerve, or by bridging over the gap by
Phil. Mag. S. 4. Vol. 20. No. 134. Nov. 1860. 2 D

394

Royal Society : —

a piece of wet string or paper, by a strip of the animal's skin, by a
piece of wire, or by any other conductor, it matters not what, the
contractions occur alternately in the two legs just as they did before
the nerve was divided. Nay, it may be argued from the following
experiment, that reflex nervous action has nothing to do in producing
these alternations. Divide the lumbar nerves on one side, not where
they emerge from the spine, but where they pass into the thigh ;
raise the divided end of the nerve, and place it across the poles of
the galvanic apparatus. In this case the circuit of the derived cur-
rent is broken, and the action of this current is therefore put out of
the question. In this case, the nerve acted upon by the current is
still in connexion with the spinal cord, and through the cord and the
nerves proceeding from this cord, with the limb on the opposite side ;
and hence it might be supposed that the current might irritate the
cord, and so provoke contraction in the limb on the opposite side.
But the simple fact is, that the current may be passed inversely or
directly without producing contraction anywhere, except now and
then a few flickers in the muscular fibres in the lumbar region of the
side corresponding to that of the nerve operated upon. The simple
fact, indeed, appears to show that reflex nervous action can have
nothing to do with the contractions in the limb belonging to the
opposite side, which contractions are produced by the action of the
galvanic current on one set of lumbar nerves ; and, certainly, with
the key furnished by Dr. Rousseau, reflex nervous action is not
required to explain the phenomenon.

The following diagram will give the case in which the lumbar
nerves on one side are acted upon by the inverse primitive current,
a a being the lumbar nerves, P N the poles of the galvanic appa-
ratus, the black arrow the primitive current, the dotted arrows the
derived current. The results, as seen in contraction in the limb
belonging to the same side, or in that belonging to the opposite side,
are seen in the Table below the figure. The case is plain.

Fig. 1.

The Inverse Current.

Beginning.

End.

On the same side . . .
On the opposite side . .

Contraction.
0

0
Contraction.

Dr. Radcliffe on the Action of a Galvanic Current upon Nerve. 395

On the side acted upon by the inverse primitive current, the por-
tion of nerve nearest to the muscles supplied by the nerve (the
muscles of the leg) is traversed, not by the inverse primitive cur-
rent, but by a direct derived current ; and hence we should expect
to find in the leg on this side (for at the time of these alternate
contractions the nerve is in the state in which the current produces
contraction alternately at the beginning of the direct current and at
the end of the inverse current) the effects of a direct current — con-
traction at the beginning of the current. We should expect to find
this ; for of two currents acting upon the same nerve, it is the one
nearest to the muscles supplied by the nerve which acts upon these
muscles. In the limb on the opposite side we should expect, on the
contrary, the effects of an inverse current — contraction at the end of
the current, for the lumbar nerves on this side are traversed by an
inverse derived current ; and this, as the Table shows, is actually
the case.

A similar diagram and table will show that the results of passing a
direct primitive current through a portion of the lumbar nerves on
one side are in accordance with the same law. In this case, as in
the other, the acting current on both sides is the derived current.
On the side acted upon by the direct primitive current, the acting
derived current (acting because nearest to the muscles supplied by
the nerve) is inverse ; and therefore the limb on this side ought to
contract at the end of the current. On the opposite side, the course
of the derived current is direct, and therefore the limb on that side
ought to contract when the current begins to pass : and so it is.

Fig. 2.

The Direct Current.

Beginning.

End.

On the same side . . .
On the opposite side . .

0
Contraction.

Contraction.
0

The results of the action of a galvanic current upon a loop of
sciatic nerve are, after a time, analogous to those which have just
been mentioned. At first, the contraction attending upon the
beginning and ending of both currents affects the whole limb ; after
a time, the leg and thigh contract alternately, in an order which
changes with the direction of the current.

21)2

;wg

Royal Society : —

Let the following diagram and table represent the case in which a
loop of sciatic nerve is acted upon by the direct 'primitive current,
a being the nerve, P N the poles of the galvanic apparatus, the black
arrow the primitive current, the dotted arrows the derived current ;
and it will be seen that the portion of nerve between the negative
pole and the leg is acted upon by an inverse derived current, and
that the thigh is traversed by a direct derived current. Thus —

Fig. 3.

The Direct Current.

Beginning.

End.

Thigh

Leg

Contraction.
0

0

Contraction.

Hence there ought to be, as there is in fact, and as the Table
shows, contraction in the thigh when the current begins to pass, and
in the leg when the current ceases to pass.

A similar diagram and table will give the case in which a loop of
sciatic nerve is acted upon by the inverse primitive current, and show
at a glance that the leg ought to contract at the beginning of the
current, because the current, acting upon the portion of nerve nearest

Fig. 4.

The Inverse Current.

Beginning.

End.

Thigh

Leg

0

Contraction.

0

0

Dr. Radcliffe on the Action of a Galvanic Current upon Nerve. 397

to the leg, is direct derived current. The diagram will also seem to
show that the thigh ought to contract at the end of the current, for
the thigh is traversed by inverse derived current. In fact, however,
the thigh does not contract either at the beginning or at the end of
the current ; and this perhaps is not to be wondered at ; for the
author finds that contraction attends upon the beginning of a direct
current of a given strength for some time after it has ceased to
attend upon the end of an inverse current of the same strength.

3. The modus operandi of galvanism upon a motor or mixed nerve
is a subject beset with difficulties ; but some of these difficulties do
not appear to be altogether insurmountable.

(a) In looking at the movements belonging to the first period —
that of double contraction (vide Table I.) — it is not difficult to find
a reason which will in some degree explain how it is that contraction
is confined to the beginning and end of the current. It is not diffi-
cult to see that the beginning and ending of the galvanic current in
the nerve may involve certain changes in the strength of the nerve-
current, and that these changes may in their turn give rise to
momentary induced currents in the nerve and in the neighbourhood ;
for such momentary currents are induced, not only when a current
begins to pass and when it ceases to pass, but also at the moments
when it undergoes any change of strength. It is not difficult to see,
also, that the muscular fibres to which the nerve is distributed may
be the seat of some of the secondary currents thus induced, and that
these fibres may be thrown into contraction by these currents. Nor
is it difficult to see — if the contraction be thus connected with the
induced currents — that there will be no contraction in the interval
between the beginning and ending of the inducing galvanic current ;
for if the inducing current exhibits no variation in strength, there is
no secondary current induced in this interval.

(b) It is, perhaps, too much to expect at present a full explana-
tion of the second period of contraction — of that period, that is, in
which the contraction alternates at the beginning of the direct and at
the end of the inverse current ; but the author is disposed to think
that a partial answer may be found in the collation of the three facts
which follow.

The first fact is this — -that the direction of the nerve-current in the
sciatic and lumbar nerves of a frog (except in those last moments of
all in which the action of the galvanic current upon the nerve gives
rise to the " voltaic alternatives") is inverse. In these last moments
the nerve-current in these nerves may be sometimes direct, some-
Fig. 5.

times inverse, and this change of direction may take place more
than once ; but except in these last moments, the author finds the
direction of the nerve-current to be invariably inverse.

398

Royal Society : —

The second fact is furnished by Professor du Bois-Reymond in an
experiment in which the two ends of a long portion of nerve are
placed upon the cushions of two galvanometers, and the middle of
the nerve is laid across the poles of a galvanic apparatus. Looking
at the needles of the galvanometers before passing the galvanic cur-
rent, they are seen to diverge under the action of the nerve-current ;
and from the direction of the divergence, it is evident that this cur-
rent passes from the end to the side of the nerve. Looking at the
needles while the galvanic current is passing, one needle is found to
move still further from zero, the other is found to return towards
zero. Let A B be the nerve ; let the arrows a d and b bf be the
nerve-currents included between the cushions a af and b b' of two
galvanometers ; and let the arrow P N be the current between the
poles P N of the galvanic apparatus ; and under this arrangement
the needle of the galvanometer will recede, and show increase of cur-

Fig. 6.

.7V

V

1B

rent ( + ) at the end B, where the nerve-current and galvanic current
coincide in their direction ; and at the end A, where the two currents,
natural and artificial, do not coincide in their direction, the needle
of the galvanometer will go back, and show decrease of nerve-
current (—).

The third fact, which has been recently furnished by Professor
Eckardt, is to be found in an experiment which may be illustrated
by means of the two following figures. In this experiment, the
nerve of a properly prepared frog's leg is placed, one portion (that
nearest to the leg) across the poles I I' of an induction coil, another
portion across the poles P N of a galvanic apparatus. Having done
this, the leg is first thrown into a state of tetanus by passing a series
of induced currents, and then (the tetanizing influence still con-
tinuing in operation) the continuous current of the galvanic apparatus
is transmitted from P to N. This is the experiment. The result
is that the tetanus ceases when, as in fig. 7, the inverse current

Fig. r.

passes, and continues when, as in fig. 8, the direct current passes.

Fig. 8.

I' 7T

Nor is this result altered by inverting the order in which the con-

Dr. Radcliffe on the Action of a Galvanic Current upon Nerve. 399

tinuous and induced currents are made to act upon the nerve. Thus
the induced currents produce contraction if applied after the direct
continuous current, but not if applied after the inverse continuous
current. Nay, it would even seem as if the direct current is actu-
ally favourable to contraction ; for a solution of salt, which of itself
is too weak to produce tetanus when applied to a nerve, will have
this effect when a direct current is made to pass through another
portion of the same nerve. In performing this experiment, Professor
Eckardt proceeds as follows : — First of all he tetanizes a frog's
hinder limb by placing a portion of the nerve nearest to it in a strong
solution of salt ; after this he adds water until the strength of the
saline solution is no longer sufficient to keep up a state of contraction
in the muscles ; then, all things being as they were, he passes the
direct current through a portion of nerve which is not immersed in
the solution. The result is that the tetanus immediately returns.

Now, on comparing this last fact with the two previous facts, we
may have, as it seems to the author, some insight into the mode in
which the galvanic current acts upon nerve in the period of alternate
contraction. On the one hand, it is seen that tetanus is prevented or
arrested by the inverse current ; that is to say, tetanus is prevented
or arrested when (as the first and second facts show) the galvanic
current coincides in direction with, and imparts power to, the nerve-
current. On the other hand, it is seen that tetanus is not prevented
or arrested by the direct current ; that is to say, tetanus is not pre-
vented or arrested when (as the first and second facts still show) the
galvanic current differs in direction from, and diminishes the power
of, the nerve-current. The one result is in harmony with the other ;
for if contraction is counteracted by imparting power to the nerve-
current, it is to be expected that contraction will be favoured by
detracting power from the nerve-current ; and certainly it is no
matter of wonder that contraction should be favoured by detract-
ing power from the nerve- current, for it is an established fact that
rigor mortis is coincident with absolute extinction of the nerve and
muscular currents, and that ordinary contraction is attended by un-
mistakeable weakening of these currents. It is also an established
fact, that muscular contraction is produced by the discharge of ordi-
nary statical electricity, and not by the charging and charge. Nay, it
is not improbable that the contractions at the beginning and ending
of the current, in the period of double contraction, which contractions
have been referred by the author to the action of induced currents,
may in reality be due to the withdrawal rather than to the commu-
nication of these currents ; for these induced currents are of moment-
ary duration, disappearing at the very instant of appearing, and
exhibiting peculiarities in disappearing which connect the disappear-
ance with the discharge of statical electricity, rather than with the
more quiet cessation of current electricity.

A.nd if this be so — if the inverse current antagonizes and the
direct current favours contraction — then we may in some degree un-
derstand how it is that contraction occurs alternately at the beginning
of the direct, and at the end of the inverse current.

400 ( Geological Society.

When the inverse current passes, there is no contraction at the
beginning of the current, for the influence of this current upon the
nerve-current is one which antagonizes contraction ; when the inverse
current ceases to pass there is contraction, for then the influence
which antagonized contraction is removed. When, on the other
hand, the direct current passes, there is contraction at the beginning
of the current, for the influence of the current upon the nerve-current
is one which favours contraction ; when the direct current ceases to
pass, there is no contraction, for then the influence is no longer one
which favours contraction.

(c) In the third period — that of single contraction — the muscular
movements resulting from the action of a galvanic current upon
nerve are at first sight somewhat perplexing; but with a little
thought, it may be seen that the same key will apply to their
interpretation.

If, as has just been mentioned, contraction attends upon the
beginning of the direct current because this current is found to
favour contraction, it is not difficult to find a reason which will ex-
plain in some degree, not only why in the period of double contrac-
tion the strongest contraction is at the beginning of the direct
current, but also why in the first part of the period now under con-
sideration— that of single contraction — contraction should continue
to attend upon the direct current after it has ceased to attend upon
the inverse current. Nor are the apparent irregularities in contrac-
tion, the "voltaic alternatives," entirely inexplicable; for it may be
that these seeming irregularities — this apparent shifting of contrac-
tion from the beginning of the direct to the beginning of the inverse
current, and so backwards and forwards once and again — may be
nothing more than the natural consequence of the changes which at
this time have taken place, and are taking place, in the direction of
the nerve-current.

" Letter from Lord Howard de Walden and Seaford, on a recent
severe Thunder-storm in Belgium."

GEOLOGICAL SOCIETY.

[Continued from p. 245.]

June 13, 1860. — L. Horner, Esq., President, in the Chair.

The following communications were read : —

" On some Arrow-heads and other Instruments found with Horns
of Cervus megaceros in a Cavern in Languedoc." By M. E. Lartet,
For. M.G.S. (In a letter to the President.)

In a cavern of the limestone at Massat, near Tarascon in Lan-
guedoc (Department of the Ariege), examined by M. A. Fontan,
the floor was found to consist of a blackish earth, with large rounded
pebbles, among which were mixed, in great disorder, bones and
horns of a Chamois, Cervus pseudovirginianus, C. megaceros, and Bos,
together with implements of stone and bone, to which MM. Isidore
GeofFroy Saint-Hilaire and E. Lartet have referred in the ' Comptes
Rendus ' of May 10, 1858.

M. E. Lartet, in his letter, has furnished drawings and descriptions

Intelligence and Miscellaneous Articles, 401

of some barbed arrow-heads of bone, some having indented grooves,
probably for the appliance of poison ; also needles, and a flute-bevelled
tool of bone, a splinter or knife of hard flint, and the horn of an
Antelope hacked at the base, probably when the animal was flayed.

" On the occurrence of Crag Shells beneath the Boulder-clay in
Aberdeenshire/' By T. F. Jamieson, Esq.

In a former paper (Q. J. G. S. vol. xiv. pp. 522-525) the author
referred to the existence of gravelly beds containing marine shells
underlying the boulder- clay between Cruden and Slains, on the
coast of Aberdeenshire, over an area of about 6 miles by 3£ ; these
shelly sands and gravels he has since more carefully examined, and
he refers them to the age of either the Red or the Mammaliferous
Crag of England. Cyprina rustica, C. Islandica, Astarte spp., Venus
spp., Artemis lincta, Cardium spp., Pecten opercularis, var. Audouini,
P. maximus ?, P. princeps ?, Pectunculus glycimeris, Tellina solidula,
Mya truncata ?, Fusus antiquus and its var. contrarius, Mangelia,
Purpura Lapillus, var. crispata, occur in worn fragments. Cyprina
Islandica is the most abundant.

Chalk-flints are common among the materials of the beds in ques-
tion ; also fragments of fossiliferous limestone and of red and grey
sandstones, of undetermined age.

M On some small fossil Vertebrae from near Frome, Somersetshire."
By Prof. Owen, F.R.S., F.G.S.

In this communication Prof. Owen described three minute Verte-
brae discovered by Charles Moore, Esq., F.G.S., in an agglomerate
occupying a fissure of the Carboniferous Limestone near Frome
in Somersetshire, in company with teeth of a small Mammal allied
to the Microlestes of Plieninger. The vertebrae are stated to cor-
respond in size with the teeth of Microlestes ; but to have Reptilian
characters, especially in their biconcave structure, — a character
common in Mesozoic Saurians, but rare in the existing genera.
There appears to be but very slight grounds for supposing that such
a character may have ever belonged to any Mammals, although some
of the existing Monotremata have peculiar vertebral modifications
somewhat resembling, in these respects, the structural features of
Reptiles. In their large and anchylosed neural arch, however, these
little vertebrae present a mammalian character.

Remains also of small Saurians and Fishes occur in considerable
numbers with the vertebrae in question, as well as the more rare
mammalian teeth.

LIV. Intelligence and Miscellaneous Articles.

ON THE LAW OF THE PROPAGATION OF ELECTRICITY IN IMPER-
FECT CONDUCTORS. BY J. M. GAUGAIN.

rf^HE phaenomena of tension, which always accompany the propa-
-*- gation of electricity, manifest themselves in imperfect conductors
with an intensity which greatly facilitates their study, — as, for ex-
ample, when the electricity developed by a machine and accumulated
on a conductor passes into the ground through a cotton thread, a

402 Intelligence and Miscellaneous Articles.

silk ribbon, or a column of oil. On the other hand, no electro-
dynamic effects are seen under these conditions, and it is not
evident a priori that the slow movement of electricity is subject to
the same laws as that which regulates electric currents. The object
of this memoir is to show that Ohm's law, which applies to a
constant current, applies also to the slow propagation of electricity
in cases in which the electric flow may be considered to be constant.
He has found that the mode of propagation is the same in both
cases, and that the results attained in studying the case of imperfect
conductors, throw great light on important questions in reference
to true currents.

The instrument which serves to measure the tension is a gold-
leaf electroscope ; the separation of the leaves is determined by
means of a telescope and a scale. The author employs two different
methods for measuring the intensity of the electric flow. The
method of the duration of the flow consists in giving such a charge
to the electroscope that the gold leaves take a position A ; it is put
in communication with the ground by means of the conductor
through which the electricity flows, and the time t is measured
which elapses while the gold leaves pass from the position A to
another position B. Q being the quantity of electricity lost by the

electroscope, — is the electric loss of the electroscope in the unit of

time. The conductor is removed and the experiment is repeated,

and rp is obtained, which is the electricity lost by the electroscope

alone in the unit of time. Consequently Q( — J represents the

intensity of the electric flow in the conductor employed. The
second method consists in employing a discharging electroscope
the gold-leaf of which comes in contact with a small copper ball
communicating with the ground. The conductor in which electricity
is propagated puts a reservoir of electricity in connexion with this
electroscope ; and the intensity of the flow may be obtained from the
number of its discharges in a given time.

Some of the principal results only can be enumerated here.

The intensity of the flow is inversely proportional to the length of
the conductors. — This law has been verified for cotton threads of
different lengths by both of the above methods. It only obtains
with exactitude where the electric loss in the thread is inconsiderable
in reference to the flow itself. Where this condition does not pre-
vail, the author has found that the loss is proportional to the square
of the length of the thread, as it ought to be from the law of tensions.
According to M. Gaugain, the following are the conditions to be
fulfilled in order to obtain results agreeing with Ohm's laws, — laws,
that is to say, which ought to apply to the case of a constant flow,
and a loss by the air which may be neglected : —

1. A reservoir of great capacity must be added to the electroscope.
The author used a condenser.

2. Feeble tensions must not be used, and the initial tension of
the electroscope must not differ by more than a few degrees.

Intelligence and Miscellaneous Articles. 403

3. The conductor must have such dimensions that the flow is
considerable.

4. Before commencing each experiment, the tension of the appa-
ratus must be kept constant for some time, in order that the con-
ducting wire may attain a permanent state.

Variation of the tension in different parts of the conductor. — The
tension of the string, which at one end is connected with the
electroscope, and at the other with the ground, has half the tension
of the source. It has been found, moreover, that, by employing
the method of discharges, the dynamic charge of a string, that is to
say, the quantity of electricity with which it is charged while the
discharge takes place, is half the static charge, or the charge which
it has while in connexion with the source of electricity not insulated
from the ground.

The laws of derived currents have been verified by the same
method, by connecting the electroscope with the ground by several
strings simultaneously, and by forked strings.

The intensity of the flow is proportional to the tension of the source,
if the extremity of the string is in contact with the ground. — The
gold-leaf electroscope was graduated so as to determine two tensions,
which were in the ratio of 1 to 2 ; and the method of discharges
showed that the intensity of the flow was perceptibly in the same
ratio.

The intensity of the flow is proportional to the section of the con-
ductor.— A first series of experiments showed that the flow did not
vary, when the section of the conductor was constant, even when
the surface varied. With cotton threads, whether insulated or
bound together, the intensity of the flow was not modified. The
same result was obtained with a silk ribbon, which was successively
folded so as to form a plain surface, rolled several times on itself,
and lastly rolled once so as to form a cylindrical sac.

A second series of experiments was made by using columns of oil
of different lengths and sections, and measuring each time the corre-
sponding flows.

On the dynamic charge. — The meaning of this term has been
explained, and it has been seen that it is double the statical charge.
This result agrees with Ohm's law on the distribution of tensions
on the course of a conductor, and shows at the same time that the
dynamic charge, like the statical, is distributed on the surface of
the conductor. The author has endeavoured to confirm this principle
by other experiments, showing that the dynamic discharge depends
on the surface of the conductor, and not, as with the flow, on the
section solely. Thus the dynamic discharge of ten insulated cotton
threads bears to these threads united in a bundle the ratio 2 to 1 .
Analogous results have been obtained by using silk ribbons in
different shapes. — Annates de Chimie et de Physique, vol. lix. p. 5 ;
Bibliotheque Universelle for June 1860, p. 146.

wood's fusible metal.
Dr. B. Wood, of Nashville, U.S., has secured a patent for an alloy
composed of cadmium, tin, lead and bismuth, which fuses at a tem-
perature between 150° and 1 60° F. The constituents of this fusible

10 A Intelligence and Miscellaneous Articles.

metal may be varied according to the other desired qualities of the
alloy, viz. cadmium, one to two parts ; bismuth, seven to eight
parts ; tin, two parts ; lead, four parts. It is recommended as being
especially adapted for all light castings requiring a more fusible
material than Rose's or Newton's " fusible metal," it having the
advantage of fusing at more than 40° F. lower temperature than
these alloys, and, owing to this property, may replace many castings
heretofore made only with amalgams. Its fusing-point may be
lowered to any extent by the addition of mercury, which may be
employed, within certain limits, without materially impairing the
tenacity of the metal. In a letter to the Editors, dated Nashville,
June 9th, 1860, Dr. Wood says,—

" One point in particular that strikes me as being worthy of note,
is the remarkable degree in which cadmium possesses the property
of promoting fusibility in these combinations. The alloy of one to
two parts cadmium, two parts lead, and four parts tin is considerably
more fusible than an alloy of one or two parts bismuth, two parts
lead and four parts tin ; and when the lead and tin are in larger
proportion the effect is still more marked. It takes less cadmium to
reduce the melting-point a certain number of degrees than it requires
of bismuth, besides that the former does not impair the tenacity and
malleability of the alloy, but increases its hardness and general
strength.

" Bismuth has always held a preeminent rank among metals as a
fluidifying agent in alloys. Its remarkable property of ' promoting
fusibility' is specially noted in all our works on chemistry. But I
do not find it intimated in any that cadmium ever manifests a similar
property. The fact indeed appears to have been wholly overlooked
— owing perhaps to the circumstance that as an alloy with certain
metals cadmium does not promote fusibility.

" Cadmium promotes the fusibility of some metals, as copper, tin,
lead, bismuth, while it does not promote the fusibility of others, as
silver, antimony, mercury, &c. (i. e. does not lower the melting-
point beyond the mean). Its alloy with lead and tin in any pro-
portion, and with silver and mercury within a certain limit, say,
equal parts, and especially if two parts silver and one of cadmium
or two parts cadmium and one of mercury are used, are tenacious
and malleable, while its alloys with some malleable metals (gold,
copper, platinum, &c), and probably with all brittle metals, are
* brittle.'

" I notice a great discrepancy among authors as to the melting-
point of this metal. It is usually put down the same as that of tin
(442° F.). Brande (Diet, of Science and Arts) says it ' fuses and vola-
tilizes at a temperature a little below that at which tin melts.'
Daniell (according to the New American Cyclopaedia) gives its melt-
ing-point at 360° F. ; while Overman places it at 550°, and gives
600° as the temperature at which it volatilizes.

" The latter is doubtless the nearest the truth. The metal requires
for its fusion a temperature too high for measurement by the mer-
curial thermometer ; but from relative tests with other metals I should
place its melting-point in round numbers at 600° F., as it melts and

Intelligence and Miscellaneous Articles.

405

congeals nearly synchronously with lead, the melting-point of which
is stated by different authorities as 594°, 600°, and 6I2°F. It vola-
tilizes at a somewhat higher heat.

" I draw attention to these facts, believing that the metal possesses
properties valuable to art and interesting to science, and that it
merits more thorough investigation than appears to have been be-
stowed upon it." — Silliman's American Journal for September 1860.

DESCRIPTION OF AN APPARATUS FOR GENERATING HYDROGEN,
CARBONIC ACID, AND SULPHURETTED HYDROGEN. BY G.
GORE, ESQ.

Having frequently during the last two years found the following
apparatus of great convenience in generating hydrogen, carbonic
acid, and sulphuretted hydrogen for lectures and other purposes, I
beg leave to submit a description of it to the readers of the Philo-
sophical Magazine.

A is a large glass jar with a capacious hol-
low glass stopper B (shown in section) fitted
perfectly gas-tight; C is a perforated and
greased cork fitted into the central hole of the
stopper ; a cylindrical rod of glass, D, of very
uniform diameter, and slightly enlarged at the
ends to a knob-like form,passes tightly through
the cork, and supports by means of a ring E
and hook F (see separate sketch), a copper or
leaden bucket G ; the bucket is perforated at
its sides, and has also radial slits in its conical
lower end to admit the acid water ; the hollow
stopper has two small openings — H to re-

ceive a cork, and I to receive a bent exit-tube
J, for the escape of the gas ; K and K' is a sec-
tion of an annular leaden weight placed for the

N^

purpose of preventing the pressure of the en-
closed gas lifting the stopper ; and L is a small
clamp-screw to prevent the rod D slipping
downwards by accident. The rod D should be
rather thick, to prevent risk of fracture ; and the
brass ring E, which supports the hook F, should
be sufficiently loose upon the rod to turn round
freely. The different parts of the sketch are
drawn of their relative sizes.

For hydrogen a copper bucket is used, and
for sulphuretted hydrogen a thin leaden one.
The bucket and its contents, i. e. granulated
zinc, chalk, or sulphide of iron, in small frag-
ments, can be readily lowered and sustained at
any depth of immersion in the acid water, and
a steady flow of gas obtained : for hydrogen I
have most frequently used a mixture of 2 mea-
sures of hydrochloric acid and 1^ of water, or a

M)G Intelligence and Miscellaneous Articles.

previously cooled mixture of 1 measure of oil of vitriol and 5 of water;
and for purifying it, 1st, a solution of potash ; 2nd, a solution of
protonitrate of mercury; and 3rd, sticks of caustic potash. The
second purifier was a three-necked Woulfe's bottle, to the central
neck of which was fitted, 1st, a Welter's tube containing 3 inches
of mercury, to indicate the pressure of gas ; and 2nd, a bent tube with
a thin vulcanized india-rubber bag at its extremity : the bag received
any excess of gas which could not readily escape at the burner, and
its elasticity effectually prevented the pulsations and irregularities
in the jet of burning gas caused by the bubbling through the liquids.

The most effectual gas-burner I have used has been formed of a
piece of iron gas-tubing, 8 inches long and half an inch in diameter,
closed at one end by a very thin plate of iron, in which were drilled
seven exceedingly fine holes. The holes require to be occasionally
cleaned by means of a very small steel broach*.

With a generator containing \\ gallon of acid water and 3 pounds
of zinc, and with a pressure of gas of 1 pound per square inch, I
have obtained a splendid pencil of flame 20 inches long and fths of
an inch in diameter, which quickly melted copper wire ^th of an
inch thick, and melted moderate-sized platinum wire. I have found
it of especial value in the analysis of infusible silicates, as a white
heat is obtained at a moment's notice, and conveniently maintained
for half an hour or more. A ball of spongy platinum held about 4
or 5 inches above the burner when the gas is issuing at a pressure
of 1 pound per square inch, produces a loud roaring noise and a sin-
gular glow of light without igniting the gas down to the burner, and
forms an interesting experiment.

The chief advantage which this apparatus appears to me to possess
over others, is the convenience with which it may be used when sud-
denly required.

Birmingham, Oct. 22, 1860.

ON NEW FORMS OF ACTINOMETERS.

To the Editors of the Philosophical Magazine and Journal.

21 Ainslie Place, Edinburgh,

Gentlemen, August 5, 1860.

I send a short Appendix to my paper on Actinometers in your

Journal of July, which, as more distinctly explaining some points

as to registry, and more particularly as to actinometry by phosgene

gas, you may perhaps consider worthy of insertion.

I remain, Gentlemen, your obedient Servant,

G' J* Burnett.

First. For the benefit of those who have not seen my paper of 1858,
I must state that although I have described a mode of applying photo-
graphic registry to a continuously acting gas-evolving actinometer,
it must be understood that there are great difficulties connected with
it, — particularly in determining what would be the direction on the
paper of the diagonally rising line which would be the representative
of a uniform actinic action, influenced as it must be by the continually

* A plate of platinum instead of iron would probably obviate this neces-
sity, and be an improvement.

Intelligence and Miscellaneous Articles. 407

decreasing strength of the sensitive liquid, and also by the phenomena
which may be roughly characterized as persistence in chemical rest,
and persistence in a state of chemical change in the sensitive liquid.
Till the errors arising from these sources can be determined and
allowed for, such photographic registry can be of little use. By
operating, however, not continuously with one portion of liquid, but
with separate portions successively uncovered for a fixed period, and
again covered up by a proper clockwork or similar arrangement, all
difficulty as to registry is removed. Supposing, for instance, that
such a compound actinometer has been at work for a day of twelve
hours, registering successive hours or half hours, the observer has
only to note at the expiry of the twelve hours, or before refilling
and setting the instrument to work again, at what point the oil in the
register-tube of each of the twelve (or of the twenty-four) separate ac-
tinometers stands. Photographic assistance is hardly required.- Still,
for very compound instruments, intended to work for a long period
without attendance, it may be usefully employed ; and even in other
cases it is quite possible that the phenomena connected with per-
sistent rest and action of the sensitive liquid may render its employ-
ment advantageous ; and this can be readily managed, e. g., by making
the same clockwork which shuts up each separate actinometer, im-
mediately before it shuts it, uncover a slip of photographic paper
behind it. Another plan would be to have the full number, corre-
sponding to the periods to be registered, of sensitive-liquid reservoirs;
but instead of giving each its own register-tube, to have them all
communicating with one registry-liquid reservoir and register-tube.
This would simplify much the photographic registry, which would
be effected by making the register-tube, as elsewhere, close a slit,
and having the paper moved past behind it by a jerk at every half
hour or other period, corresponding with that at which the sensitive
reservoirs are closed. The exact amount of rise due to each reser-
voir's exposure would be thus shown on the paper.

Second. Actinometry by means of a mixture of carbonic oxide and
chlorine having been in my paper only alluded to in passing, I may
now state that this mixture has some advantages over that of hy-
drogen and chlorine. In the first place we have no risk of explosion,
the gases uniting quietly even in sunshine. In the second place we
have a ready means of estimating the amount of action which has
taken place by the condensation effected, as the two gases, in com-
bining to form phosgene or chlorocarbonic acid gas, shrink to half
their previous volume. To render this condensation conveniently
visible, we have only to carry a tube from the reservoir containing
the mixed gases into a vessel containing eupion, or some similar
liquid, which will neither absorb nor in any way be acted on by
them, — the absorption being of course indicated by its rise, and the
exact amount of that being easily shown by the attachment of a
scale. It is, I think, unnecessary to describe the various modifica-
tions of this instrument which suggest themselves, or to say more
than that the same plans of combining a number of them into one
compound instrument for registry of successive intervals, which we
have indicated as applied to the sensitive -liquid actinometer, are

408 Intelligence and Miscellaneous Articles.

equally applicable here, as are also the same contrivances for pho-
tographic registry, with trifling alterations corresponding to the dif-
ference between expansion and condensation of gas.

Having alluded to the application of convex lenses to increase the
sensitiveness of actinometers, I may as well add that, to avoid the
concentration of heat as well as light, we must, at least when opera-
ting with the sun's rays, make them pass, either before entering or
after leaving the lens, through some medium which will intercept (or
metamorphose) the heat rays, e. g. blue glass or coloured solutions,
or some one of those salts (either solid or in solution) which are
known for their adiathermic properties, or else we may have the lens
itself constructed of one of these substances.

In conclusion, the amount of success which has already attended
the efforts to measure what we may for convenience call the cyanic
actinism, suggests the desirableness of attempts being made to obtain
some similar system of registry (either by properly prepared papers,
or liquids, or gases) of the strength of that opposite influence lower
down in the spectrum which has been made known to us by Dr.
Draper and Mr. R. Hunt ; and our success thus far may then suggest
further the possibility of our being able separately to identify and to
contrive some measurement for some of the many other powers pro-
bably contained in the light of the sun and other luminaries, both as
originally emitted, and as altered by reflexion or transmission.

ARSENIC IN COAL.

At a recent meeting (Oct. 16) of the Manchester Literary and
Philosophical Society, Dr. R. Angus Smith gave a short account of
his examination of coal pyrites for arsenic. He stated that although
the knowledge of the existence of arsenic in the iron pyrites found
in coal may not be considered perfectly novel, it certainly does not
seem to be known that arsenic is so widely disseminated as to form
an ordinary constituent of the coals burnt in our towns ; and chemists
of celebrity have held, and now hold, it to be absent there. He
had examined fifteen specimens of coal in Lancashire, and found
arsenic in thirteen. He had also found it in a few others ; but Mr.
Binney having promised a collection, properly arranged, the exa-
mination will then be made more complete. Mr. Dugald Campbell
had also lately found arsenic in coal pyrites ; this had a very direct
bearing on our sanitary knowledge, as we must now be obliged to
add arsenic to the number of impurities in the atmosphere of our
large towns. It is true that he had not actually obtained it from the
atmosphere ; but when the pyrites is burnt the arsenic burns and is
carried off along with the sulphur. One or two coal brasses (as they
are called) contained copper, a metal that is also to some extent
volatilized, as may be readily observed wherever copper- soldering
takes place. Although an extremely small amount of copper is car-
ried up from furnaces, it is not well entirely to ignore it. The
amount of arsenic, however, is probably not without considerable
influence ; and we may probably learn the reason why some towns
seem less affected than others by the burning of coals, by examining
the amount of arsenic burnt as well as sulphur.

THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

DECEMBER 1860.

LV. On the Form of Satellites revolving at small distances from
their Primaries, By Daniel Vaughan*.

SECONDARY planets which revolve at comparatively small
distances from great central orbs, experience very singular
effects from a kind of disturbing action, which is either wholly
imperceptible on the primaries themselves, or is only manifested
in producing an alternate rise and fall of their extensive oceans.
The powerful attraction of Jupiter must cause his nearest satel-
lite to feel a tidal force several thousand times greater than that
which every day swells our terrestrial waters ; and the variation
of gravity on the surface of the small world, from this disturb-
ance alone, may be estimated as nearly five times as great as our
own globe exhibits in consequence of its diurnal movement.
In the Saturnian system, where many attendants are much closer
to the primary, they must be more seriously affected by its un-
equal attraction on their parts. Were the size of the orbit below
a certain limit, the disturbing influence of the central body would
so far neutralize the attractive power of the satellite in two direc-
tions as to render it incapable of maintaining the usual planetary
form; and it appears that, in the zone occupied by Saturn's
rings, no large secondary planets could roll in security unless
they were considerably more dense than the kind of matter
which predominates in that part of the solar domain. During
the year 1853, in announcing the result of my researches on this
subject, I ascribed the existence of the rings to their proximity
to Saturn ; and, though the theory has been slow in receiving
attention, I hope that it may now claim a degree of interest
sufficient to justify me in submitting to scientilic men, in the

* Communicated by the Author.
Phil. Mag. S. 4. Vol. 20. No. 135. Dec. 1860. 2 E

410 Mr. D. Vaughan on the Form of Satellites

present article, some mathematical investigations of the chief
cases of planetary instability.

The peculiar arrangement which is supposed to prevail in all
secondary systems, for keeping the same sides of satellites always
turned to their primary, is well calculated to preserve these
second-rate worlds from the injurious effects of excessive tides,
since they must always have their oceans elevated and their forms
elongated at the same localities. The exact synchronism of the
rotary and the orbital motion mainly contributes to secure this
important end ; but, to remove entirely the dynamic effects of
the great disturbance, it is necessary that the satellite should
rotate around an axis perpendicular to the plane in which it re-
volves, and that its path should be a true circle. In describing
an ellipse sufficiently small for the production of a very great
disturbing force, the planetary structure would have its safety
much endangered by the oscillatory movements of its parts; and
the oscillations would be attended with more fatal results if, from
a want of the other conditions, it presented different sides alter-
nately to the primary. In calculating the dimensions of the
smallest orbit in which it is possible for a secondary planet to
hold its parts together by the tie of gravity, we are necessarily
restricted to the cases most favourable for stability ; and I shall
accordingly suppose that the body has its axis perpendicular to
the plane of its orbit, that the latter is exactly circular, and that
the rotation takes place in the same time and in the same direc-
tion as the periodical revolution. In such circumstances the
relative direction of the primary from every part of the satellite
must ever remain Unchanged, and its powerful attraction must
be productive of the least derangement on the surface of the
latter body.

In a very small orbit there appears to be a physical necessity
for a synchronism of the orbital and rotary movements of a satel-
lite similar in constitution to our globe; for the rotation would
be gradually changed by the action of enormous tides, until it
finally occupied the same time as the orbital revolution. Nor
can our conclusion be very different if we agree with Lagrange
in ascribing the arrangement to the deviation of these humble
worlds from true spheres, and to the consequent tendency of
their longest diameters to point towards the central body. In
two secondary planets of the same size, form, and density, this
tendency would be inversely proportional to the fourth power of
their distances from the primary ; but were the ellipticity of both
bodies such as the attraction of the latter might occasion on a
yielding solid mass, the tendency would be in inverse proportion
partly to the seventh, and partly to the higher powers of the
same quantities. There are accordingly sufficient grounds for

revolving at small distances from their Primaries. 411

the hypothesis I have adopted ; and it would seem that in this,
as in many other problems of physical science, the cases which
occur in nature are such as the powers of analysis can reach with
the greatest facility.

To begin with the case of a solid spherical satellite, which I
shall suppose to be capable of preserving its form unchanged by
the disturbance previous to the final rupture : let r denote its
radius, r3 the radius of the primary, and g the measure of the
attraction exerted at the distance k by a portion of matter taken
as unity, and of equal density with the satellite, but immeasurably
inferior to it in magnitude. Put it for 3* 141 6; R for the radius
of the spherical space which the matter of the primary might
fill if reduced to the same density as the satellite ; and x for the
distance between the centres of both bodies. In the absence of
every disturbing influence, the force of gravity on the surface of
the satellite will be

&|f. . a)

The diminution of this gravity at the point nearest to the pri-
mary, by the attraction of the latter, is equal to

4ffft27rR3 4ffft27rR3
3{x-r)* 3a2 '

or

4^VR3/n 3r2 4T3 5r40 \

At 90 degrees from this point, gravity is augmented by the
quantity

4^2ttR3/ 3r3 15?-50 \

Now if M and m denote the attractive force of both bodies at
the distance k, the period of the satellite's revolution (which I
shall call T) will be expressed by the formula

T- 27r*f . (4)

*VM + m ....... v ;

As its time of rotation is also equal to T, the equatorial velocity
of the satellite is = kr !t3±S. Calling this v, the centrifugal

X*

V*

force at the equator will be equal to — , or

*2(M + m)r ' _

^ • • \P)

2E2

412 Mr. D. Vaughan on the Form of Satellites

Substituting for M and m their values, -^ — and — „— , this

becomes

4y*V(R3 + r3)r

3x*

(G)

Subtracting the sum of the expressions (2) and (6) from (1),
there results the equation

in which F represents the force of gravity at that part of the
satellite in conjunction with the primary. If, instead of adhering
to the hypothesis I have adopted, we suppose the axis of rotation
to form an oblique angle with the plane of the orbit, F will be
variable, and formula (7) will express only the lowest limit which
it attains during every revolution. Were the satellite homoge-
neous and very inferior to the primary in magnitude, all the
matter between its centre and any point on its surface must lose
weight in nearly the same ratio by the disturbing force.
By making F in equation (7) equal to nothing, we obtain

This value of x represents the radius of the circular orbit in which
a spherical satellite would be incapable of retaining disconnected
bodies at the place next the primary, and could give only a very
insignificant weight to the matter on a direct line between this
and the opposite part of its surface. In the case of the earth
and moon, the value of x in equation (8) would be a little over
7500 miles ; and were the lunar orb made to revolve in a circle
of so small a radius, gravity would disappear at the part of its
surface nearest to us, so that there could be no adequate coun-
terpoise to the enormous pressure arising from the weight of
matter in other localities. It therefore becomes necessary to
correct our hypothesis respecting the figure of a satellite in such
circumstances. A far less degree of proximity to our globe would
be sufficient to give the moon a very considerable distortion from
a true sphere ; and as their cohesive force, when once overcome,
could oppose little resistance to their arrangement, the lunar
materials would ultimately exhibit a form differing little from
that which a fluid might assume under the operation of the same
forces.

In taking up the case in which the satellite is to be regarded
as fluid, I think it advisable to have recourse to an approximate
method of investigation, which may be conveniently extended
for the attainment of any desirable degree of accuracy, while it

revolving at small distances from their Primaries. 413

serves to remove a peculiar difficulty attending the solution of
problems of this character. In his investigations respecting the
stability of a fluid planet as dense as the earth, Laplace finds
that a rotation performed in less than '10090 of a day would be
incompatible with its existence in a spheroidal figure ; but as its
equatorial gravity is only partially neutralized by centrifugal
force, he concludes that such a rapidly rotating mass would
remain undivided under some form which analysis does not
reveal. A complete cessation of gravity in certain directions is
not, however, essential to an unstable equilibrium, either in the
case considered by Laplace, nor in the one now under considera-
tion, which seems to be better suited for the removal of the diffi-
culties of questions of this nature, as the time of rotation is pre-
vented from changing with the alterations in the figure of the
body. The stability of a fluid satellite, consigned to a small
orbit and elongated in the direction of its primary, is evidently
at an end — not when gravity is wholly suppressed at the parts
through which the greatest diameter passes, but when the force
with which a column of matter coincident with this line presses
to the centre ceases to acquire, from a further elongation of the
body, any preponderance over the pressure of a similar column
of matter extending from the centre to the nearest point of the
surface. Thus putting P and P' for the pressures which the cen-
tral region sustains from two similar columns of matter extend-
ing along the greatest and the least diameters, and e for the
excentricity of the section made by a plane passing through both
and supposed to be an ellipse, the distance from the primary
when dismemberment must occur, and the greatest deviation
from a sphere, may be determined from the equations

P-P'=0, (9)

£-? = 0 (10)

de de

Another method of arriving at the same result will appear when
we consider that a satellite, in this critical situation, must have
its ellipticity increased to an enormous extent by a slight increase
of the disturbance or by a small diminution of the distance ; and
instead of (10) we may have recourse to the equations

I = infinity, or J=0, . . . (11)

where x, as in the previous notation, represents the radius of the
orbit.

Were the satellite small compared with the central sphere, it
could not deviate much in form from an ellipsoid, the minor and
mean axes of which differ by a quantity much less than the

414 Mr. D. Vaughau on the Form of Satellites

excess of the major axis over either of them. They may there-
fore be considered equal, at least in the first approximation ; and
if greater accuracy be required, it may be obtained by introdu-
cing corrections depending on the square, the fourth, and the
sixth powers of the excentricity of the elliptical section in which
both arc situated. Accordingly, let the satellite be regarded as
a homogeneous prolate spheroid ; and let A and B represent the
major and minor semiaxes, the former of which always ranges
with the primary's centre. To find the attraction at the extre-
mity of the major axis, conceive the body to be divided into
innumerable sections by planes passing through this line, while
these sections are subdivided into a corresponding number of
infinitely small pyramids, having their vertices all terminating
at the proposed point, which shall be taken as the origin of the
coordinates. Put 0 for the angle which any section makes with
the plane of the orbit, / for the length of any of its pyramids
whose inclination to the major axis is denoted by <f>. The vertical
angles of this minute pyramid will be d<f> and dd sin <f>, and the
component of its attraction in the direction of the major axis is

gkH sin </> cos <f) d<f> dd (12)

Substituting for / its value .2 . g ? — g-r, this expression

becomes

2gh*AB* sin <f> cos2 <f> dcf> dO 2^2B2 sin cf> cos2 </> d6 dd

A2sin*(/> + B2cos2</> °r A(l-e2cos2<£) ; "6>

and the double integral of the last quantity, or

^HtSS? <»>

taken within the proper limits, will represent the attraction of
the satellite at the extremity of the major axis. Now

J cos2 (f> sin <j> dcf> __ cos </> 1 , l + ecos<£ ~ ._R.
l-e2cos2tf> -"l2~"""2?10gl-€2cos</,+L' ' (16j

IT

When this is taken within the limits of </> = 6 and <j> = — , and sub-
stituted in (14), the latter becomes

and making a second integration between the limits of 0— +w
and 0= — 7r, the expression for the attractive force is

4^2ttB2/ 1 . 1 + e 1 \ nm

-^W>gi^€-?> • • • (17)

revolving at small distances from their Primaries. 415

In estimating the effects of centrifugal force and the disturb-
ing action of the primary in diminishing this attraction, we may
use, with some modifications, the formulas already obtained for
the case of a spherical satellite. The entire diminution arising
from both disturbances may be found by adding formulas (2)
and (5), substituting A for r in the result, and retaining only
the term containing the first powers of A, the rest of the series
being small in comparison to it. There results the amount

JL~^ nearly; (18)

and this being subtracted from (17), we obtain

the approximate value of the force of gravity at the points near-
est to the primary and most distant from it. To find the weight
or the pressure of a uniform column of the fluid extending from
either locality to the central region of the satellite, denote by S
the distance of any part from the centre ; the force of gravity

operating on it will be ~-r-, and dV is equal to — -r — ; whence

P=|£. ...... (20)

Taking this integral within the limits of S = 0 and S = A, and
substituting for G its value from equation (19), there results

in which P represents the pressure when the transverse section
is unity.

To determine the pressure of a similar column of matter coin-
cident with the axis of rotation, let either extremity of this line
be taken as the origin of three coordinate planes, — one being
tangent to the spheroid at that point, the second vertical and
ranging with the primary, and the third perpendicular to the
line in which both planes intersect. Through this line of inter-
section let planes be conceived to pass, dividing the body into
an infinite number of sections which are subdivided into infinitely
small pyramids, whose vertices all terminate at the origin of the
coordinates. If 6 denote the inclination of any section to the
second plane, and </> the inclination of any of its pyramids to the
third, the length of the pyramid being /, the angles at its vertex
will be dcj> and dd cos </>, and the vertical component of its attrac-
tive force will be

gkH cos2 j> cos 6d<i>dd (22)

416 Mr. D. Vaughan on the Form of Satellites

This expression, on substituting for / its value

/ 2A2B cos <ft cos fl \
VA^os^E^2*/'

becomes

or

<£ + B2sin2</»

2^fc2A2B cos8 <f> cos*0d<t> d6
A2cos2</> + B2sin2<£ '

2^2Bcos8<£cos20 d$ dd

l-e2sin2</> ; {Zd>

and the attraction of the spheroid at the point in question will be

29k*B$coMSpi-™l»™*dt (24)

The last integral, or

J(l — sin2 <f>) cos <f> d<f>__ sin <f> __ 1 — e2 1 + e sin <f>
l-e2sin2<£ ~ " ~? 2?" S 1-esin^

7T IT

which becomes, on taking <f> within the limits of + ^ and — »
2 l-es. l + <= „ '

s-^ri0SYzre- • m

Substituting this value for the last integral in (24), and making
a second integration, there results

A 721I/sin20 , 6\(\ 1-e2 1 + A

and this, taken within the limits of 0= + g- and — ^-, becomes

2*VB(l-^-2logi±^). . . . (26)

This expresses approximately the attractive energy of the body
at the extremity of its axis of rotation. The augmentation of
gravity which the disturbance occasions at this locality may be
deduced from formula (3), which, on substituting B for r, and
retaining only the first term of the series, becomes

4^2ttBR8

3s3 ™'

Adding this to (26), we arrive at the following equation for the
value of G', which shall be used to represent the force of gravity
at the poles of the satellite,

A course similar to that pursued in deducing formulas (20) and

revolving at small distances from their Primaries, 417

(21) will enable us to derive from (28) an equation for the pres-
sure of a fluid column having its section equal to unity, and ex-
tending from the centre to either of the poles. Denoting by P'
its pressure at the centre.

Now, in accordance with the condition of equilibrium expressed
in formula (9), make the values of P and P' in equations (21)
and (29) equal; substituting for B2 its equal, A2(l— e2), and
dividing by y£27rA, we obtain

n Jl, 1 + e 2\ 2R3 2(1 -OR* *

(1-^log — -_J-_ = _L_-^+(l-e2)

/l 1-62 l + 6\

V^~-2^l0Sl^>
which after some reductions and transposition gives

R3 3(l-e2)/3-e2 1 + 6 3\ ^

It appears from equation (11), and from the principles on which

it has been deduced, that when the stability of the satellite ceases to

doo
be possible, -j- is equal to nothing ; and accordingly equation (30)

and its differential might enable us to determine the size of the
smallest orbit such a body could describe, and its deviation from
a sphere previous to the final dismemberment. To avoid, how-
ever, the difficulties of the resulting equation and the ambiguity
of its roots, it will be advisable to make the estimate from a com-

R3

parison of the following values of — g-, corresponding to different

degrees of excentricity, and calculated from formula (30).

Values of e.

Values of ^.

Values of e.

Values of — ,
x3

•80
•81

•82
•83
•84
•85

•060500
•061418
•062289
•063080
•063793
•064293

•86
•87
•88
•89
•90
•91

•064688
•064924
064951
•064740
•064239
•063391

An inspection of this Table shows that the elongation of a
satellite increases to a most enormous extent with the disturb-
ance, and that the dismemberment is inevitable when the value

418 Mr. A. Cay ley on the Cubic Centres of a Line

of e is between 87 and 88. From the corresponding value of

R3

-j-, it appears that x at this critical period is equal to 2*489 R.

This expresses approximately the least distance from the primary
at which a satellite could be preserved. To give greater gene-
rality to the formula, designate by D and d the densities of both
bodies, r' being, in accordance with the previous notation, equal
to the actual radius of primary, and R the radius of the sphere
which it might fill if it became as dense as the satellite. It will

3/5"

be easily seen that R=?ja/ -r, and accordingly x' is equal to

2-489 r^! (31).

It appears also to be independent of the actual size of the
satellite. If indeed we retained in our investigation the square
and the higher powers of r, the result would exhibit a slight
difference in favour of the stability of smaller attendants ; but
this is more than counterbalanced by the superior density of
larger bodies composed of the same materials, but capable of
compressing them by a greater attractive force.

It appears, therefore, that the laws of equilibrium prevent the
existence of satellites over a large space around each primary
planet ; and it might also be shown that, beyond this region, the
existence of planetary rings is equally impossible. The extent
of this region will be different for satellites unequally dense, and
it may be easily calculated in each case by our last formula.
Although our data is somewhat defective in the case which pre-
sents itself in the Saturnian system, yet when we calculate the
density which a satellite should possess to maintain its planetary
form in different parts of the zone occupied by his rings, it seems
impossible to resist the conclusion that the condition of this an-
nular appendage is the necessary consequence of its proximity
to Saturn.

Cincinnati, October 29, 1859.

LVI. On the Cubic Centres of a Line with respect to Three Lines
and a Line. By A. Caylby, Esq*

CONSIDER a line L in relation to the three lines X, Y, Z
and the line I : through the point of intersection of the
lines X, L, draw any line meeting the lines I, Y, Z, and let the
harmonic of the intersection with I, in relation to the intersec-

* Communicated by the Author.

with respect to Three Lines and a Line. 419

tions with Y, Z, be £ ; then the locus of the point f is a conic
passing through the points YI, ZI, YZ.

If, in like manner, through the point of intersection of the
lines Y, L, there is drawn any line meeting the lines I, Z, X,
and the harmonic of the intersection with I, in relation to the
intersections with Z, X, is called tj, the locus of the point ?) is a
conic passing through the points ZI, XI, ZX.

And so, if through the point of intersection of the lines Z, L
there is drawn any line meeting the lines I, X, Y, and the har-
monic of the intersection with I, in relation to the intersections
with X, Y, is called £, then the locus of £ is a conic passing
through the points XI, YI, XY.

The pairs of conies, viz. the second and third, third and first,
first and second conies, have obviously in common the points
XI, YI, ZI respectively. They besides intersect all three of
them in three points, which may be termed the cubic centres of
the line L in relation to the lines X, Y, Z and the line I.

The line L may be such that two of the three cubic centres
coincide ; the locus of the coincident centres is in this case a
conic which touches the lines X, Y, Z harmonically in regard to
the line I ; that is, it touches each of the three lines in the point
which is the harmonic of its intersection with I in relation to its
intersections with the other two lines.

Except that the line I is there taken to be infinity, the fore-
going theorems occur in Pliicker's System der analytischen Geo-
metrie (Berlin, 1835), p. 177 et seq.; and they play an import-
ant part in his classification of curves of the third order (see
p. 220 etseq.). It is, I think, an omission that he has not sought
for the curve which is the envelope of the line L in the above-
mentioned case of the two coincident centres : I find that the
envelope is a curve of the fourth order, having four-pointic con-
tact with the lines X, Y, Z harmonically in regard to the line I ;
viz., if the equations of the lines X, Y, Z are x—0, y=0, z—0
respectively, and the equation of the line I is x-\-y-\-z — 0, then
the equation of the envelope in question is

a result which is also interesting as exhibiting a geometrical con-
struction of the curve represented by this equation.

The investigation of the series of theorems is as follows ; taking
a7 = 0 for the equation of X,

y=o „ Y,

x+y + z=Q „ I,

\x + fiy + vz=0 „ h,

420 Mr. A. Cayley on the Cubic Centres of a Line

Then, first, in order to find the curve which is the locus of f,
the coordinates of the point XL are given by x : y : z=0 : v : —fi ;
or if, as it is convenient to do, we take X, Y, Z (instead of x, y, z)
for current coordinates, by X : Y : Z = 0 : v : — fi. Hence taking
xy y, z as the coordinates of f , the equation of the line through
XL, f is

X, Y, Z =0,

0, v, -ft

VIZ.

X{fiy + vz) -x(jiY + vL) = 0.

And at the point where this line meets the line I, the equation
whereof is

X + Y + Z=0,
we have

(Y + Z)(^ + v^)+^Y + vZ)=0;
that is,

Y(fix + fiy + vz) + Z(vx + fiy + vz) = 0.

Hence this line, and the line

Yz-Zy=0,
with the lines

Y=0, Z=0,

are the lines which pass through the point YZ and the four har-
monic points, and they form therefore a harmonic pencil ; or we
have

y(jjux+fiy + vz)— z{vx+fiy + vz)=0,

or what is the same thing,

(fiy— vz){x + y+z) + 2yz(v— fi) = 0,

as the locus of the point f : the locus is therefore a conic pass-
ing through the points YI, ZI, YZ.

The equations of the conies which are the loci of X, Y, Z
respectively, are therefore

V = (fiy— vz){x + y + z)+2yz(v— fi) =0,

Y=(vz— \x)(x + y + z)+2zx{\— v)=0,

W={\x-fjLy){x + y + z) + 2xy(p-\)=0;

and the identical equation,

UKx + Vpy + Wvz=0,

shows that these conies have three points of intersection in
common. The three equations, and a fourth one to which they
give rise, may be written

with respect to Three Lines and a Line. 421

g v 2(v-/i) =0

z y x + y + z ' *

*±.*£=A =0,

x z x + y + z

^__P + 2(/*--\) =0

y a? # + ?/ + .? '

x y z

and each of these is the equation of a conic passing through the
three cubic centres.

If two of the three centres coincide, then the conies all touch
at the coincident centres. Consider the first and second conies :
these intersect at the point z=0, x + y + z = 0; and the line
x + y + z=2kz, if k be properly determined, or what is the same

thing, the line x\-y+z= -^—^ — -z, if 0 is properly determined,

will be a line passing through the last-mentioned point and one
of the other points of intersection : k or 0 will of course be de-
termined by a cubic equation ; and if this has a pair of equal
roots, the conies will touch. But the equation of the line, com-
bined with those of the two conies, gives

_i i i

and substituting these values in the equation of the line, we
have

1 +JL+_L_3=0

0 + \ 6 + iJu 0 + v 0

which is (as it should be) a cubic equation in 0,
If the equation in 0 has equal roots, then

1 1 12

"*~ tQ i ..\2' I A i ,.\2 /32 — ">

(0 + \)*^(0 + p)* ' (0 + V?

and putting in these two equations,

_ m m m

we have

0 + V y-$ + p' 0 + v'

2m n
x + y + z- -g-=0,

x* + y* + z*-2-^=0-,

or eliminating m,

(* + y-M)2=2(*2-ry+32);

422 On the Cubic Centres of a Line.

that is

x* + y* + z*-2yz- 2zx-2vy=0;
or what is the same thing,

s/~x + \/y + i/J=0,

for the equation of the locus of the coincident centres : such
locus is therefore a conic touching the lines x = 0, y=0, z=(), in
the points of intersection with y— z=0, z—x = 0, x—y = 0
respectively ; it is a conic touching the lines X, Y, Z harmoni-
cally in regard to the line I.

To find the envelope of the line L, the most convenient course
is to take the equation in 6 in the reduced form

^~0(/*]/ + v\ + \//,)-2Vv = O;

this will have a pair of equal roots if

{fiv + vX + \/x)3-27AV"2=0 j
that is, if

or if

or finally, if

fiv + v\ -f \/ul — 3 (X/av)* = 0 ;

which is the relation between X, fj,, v in order that the line

\x-\-fjby-\-vz=Q

may have two coincident centres ; this gives at once for the equa-
tion of the envelope

\/x + y~y + V~2 = 0,
which is the equation of a curve of the fourth order having four-
pointic contact with the lines x=0, y=0, z=0, at the points of
intersection with the lines y—z = 0, z—x=0, %—y=0 respect-
ively, i. e. it has four-pointic contact with the lines X, Y, Z
harmonically in regard to the line I.

It may be noticed that the rationalized form of the equation
\/x + \/y + \/z=0i8

x4 + 2/4 + z4 — 4(ys8 + 'fz + zx3 + z3x + xy8 + a?y)

+ 6{y*z* + z*x* + xy)-124(x*yz + y'izx + z'2xy)=0.

If, to fix the ideas, the signs of the coordinates x, y, z are so
determined that a point within the triangle x=0, y=0, z=0
has its coordinates positive (in which case the line x + y + z = 0
will cut the three sides produced), the curve X/lc + \/y + %/ z = 0
will lie wholly within the triangle, and will be of the form shown

On Darwinite, a new Mineral Species from Chile. 423

by the annexed figure.
This is, in fact, the
form of the curve in
the case considered by
Plucker, where the line
Iisat infinity, thepoints
of contact being the
middle points of the
sides. And his five
groups of curves, a, (3,
7, B, e, and two subdi-
visions of the group /3
(see pp. 221-224), cor-
respond to the following positions of the line in regard to the
triangle and curve, viz. —

a. The line cuts the three sides produced.

/3. It passes through an angle, {a) cutting, or (b) not cutting
the curve.

7. It cuts two sides and a side produced, but does not cut or
touch the curve.

6\ It cuts two sides and a side produced, and touches the
curve.

€. It cuts two sides and a side produced, and cuts the curve.

It is hardly necessary to remark that, in the general case, the
tangential equation of the curve is

or what is the same thing,

and that the curve is therefore of the sixth class.

2 Stone Buildings, W.C.,
October 16, 1860.

LVII. On Darwinite, a new Mineral Species from Chile,
By David Forbes, F.R.S. $c*

1THIS mineral, a specimen of which was given me as being
native arsenic, is stated to occur near Potrero Grande, not
many miles to the south-east of the town of Copiapo in North-
ern Chile, where it is said to present itself as small veins or
strings cutting through the porphyritic claystones which form
the mountain range at that place, and which represent the upper
oolitic formation in geological age.

* Communicated by the Author.

424 Mr. D. Forbes on Darwinite,

These strings or veins are described as entirely composed of
this mineral in a state of great purity, but very narrow, seldom
attaining the breadth of more than 2 inches across. The spe-
cimen which was examined appeared to represent the entire
thickness of such a vein, and is a mass of about 1£ inch across,
.composed of the pure mineral free from gangue or extraneous
metallic compounds, but having its sides coated with red oxide
of copper, and in some parts spots of a green arsenite or arseniate
of copper.

From its colour, lustre, and great specific gravity, it had, on
discovery, been supposed to be native silver, and workings were
accordingly commenced on the veins, — which, however, were at
once abandoned when the assays made at Copiapo showed the
very small amount of silver entering into its composition; and
as when thrown into a forge it evolved arsenical fumes in abun-
dance, it was regarded as " Arseniko," or native arsenic, and,
strange enough, does not even appear to have been assayed for
copper.

The mineral is massive, without trace of cleavage, is rather
brittle ; but although easily broken, its surface may be distinctly
impressed by the hammer before yielding : fracture even ; hard-
ness 35.

Lustre metallic ; colour of freshly-fractured surface dark silver-
grey, tarnishing on exposure to a dirty bronze-yellow; streak
metallic, dark silver-grey ; opake.

The specific gravity of three separate fragments was found to
be respectively 8'69, 8*67, and 8-57 ; consequent mean 8*64.

Heated in a closed tube, the mineral does not alter, or at
most a faint trace of arsenious acid sublimes on to the side of
the tube, arising from the action of the air contained in the same ;
in an open tube, a distinct white sublimate of arsenious acid is
obtained.

Before the blowpipe on charcoal in reducing flame, it fuses
readily to a silver-white globule, which in the act of cooling
evolves arsenical fumes and becomes slightly red on surface ; in
the oxidizing flame on charcoal, it evolves abundant arsenical
fumes, rotates, and ultimately leaves a globule of metallic copper,
malleable, but still retaining some arsenic : on cupelling this but-
ton of copper with lead, a minute globule of silver is obtained ;
with fluxes, it gives the reactions of copper only.

A qualitative examination by the wet way confirmed these
results, and showed the presence of copper, arsenic, and silver
without other admixture. Sulphur and iron were especially
tested for, but not found present. In one specimen a trace of
lead was detected, which appeared evidently to be an accidental
impurity.

a new Mineral Species from Chile, 425

On quantitatively analysing the mineral, the following results
were obtained : —

A.

B.

C.

D.

Copper .

. . 88-35

88-07

88-11

88-02

Silver . ,

, . 038

0-24

008

0-42

Arsenic . ,

, . 11*27

11-69

11-81

11-56

100-00

10000

10000

100-00

In the Analysis A the arsenic was determined from the amount
of arseniate of magnesia and ammonia, previously dried at 2 12°F.,
obtained by dissolving 11 -01 grs. of the mineral in nitrohy-
drochloric acid, supersaturating with ammonia, and afterwards
adding chloride of magnesium along with chloride of ammonium.
The silver was determined by cupellation, and the copper reck-
oned as loss.

In the Analyses B, C, and D, the silver was, as before, esti-
mated by cupellation with lead; but the arsenic, on the con-
trary, was reckoned as loss after determining the copper present
by the blowpipe as follows : —

From 1 to 2 grains of the mineral were fused upon charcoal
in reducing flame along with a very small amount of borax-
glass and a previously tared globule of pure gold, the globule of
gold being from 3 to 4 grains in weight : when perfectly fused,
the united globule was separated from the adherent borax-glass
by dipping it into water after solidification, but whilst still hot,
This globule was then placed in a charcoal bore, and, after fusion,
very carefully treated with a gentle oxidating flame as long as
arsenical flames were evolved, and until the instant when the
greenish appearance peculiar to melted copper when pure was
observed, when it was found to have eliminated all the arsenic,
and there remained a perfectly malleable red metallic button of
an alloy of gold and copper, the weight of which, less that of the
globule of pure gold added, gave the amount of copper and silver
present in the ore; and deducting from this the proportionate
quantity of silver found by cupelling with lead a separate portion
of the mineral, the quantity of copper present was ascertained.

The results obtained by this method are very accurate ; and it
can frequently be used with advantage in determining copper in
compounds of this metal with arsenic when free from sulphur.
Iron and gangue do not affect its accuracy, as they are slagged
off easily in the fusion with borax-glass. In the assay of mala-
chites and oxides or silicates of copper, the copper present can
easily be brought to the state of an arsenide by a previous opera-
tion, and then determined as above.

The results above stated leave no doubt that the constitu-
tion of this mineral may be represented by the formula Cu18 As,

Phil. Mag. S. 4. Vol. 20. No. 135. Dec. 1860. 2 F

426 M. G. R. Dahlander on the Form assumed by a Fluid

which by calculation would afford the following per-centage
composition : —

Copper . . . 88-37

Arsenic . . . 11*63

100 00

closely approximating to the results obtained; the mean of
which, if the silver be added to the copper, would give —

Copper . . . 88-41
Arsenic . . . 11*59

100*00

It is interesting to note the occurrence of the three compounds
of copper with arsenic in Chile, although, as far as I am aware, no
two of these are found at the same locality ; but all three occur
in veins of the same geological age. Their chemical composition
is as follows : —

Domeyldte, Cu«As {^JjjJ * ' S-86

100 00

Aigodo„ite,c«^AS{£PP- ; ;Jjg

10000

Darwinite, Cu«As {A>j# \ \ g.'g

100*00

The name Darwinite has been adopted in honour of Darwin,
whose admirable geological examination of this part of South
America is so well known as to require no comment.

LVIII. On the Form assumed by a Fluid Shell revolving freely
within a Hollow Spheroid. By G. R. Dahlander*.

LET there be a shell of solid matter whose internal and ex-
ternal surfaces are both spheroids having the same axis and
centre. Within this suppose there to be a hollow fluid shell
having the same centre, but not being in contact with the in-
ternal surface of the other ; and suppose it to revolve about the
common axis with a uniform velocity : then, under the joint in-

* Communicated by the Author.

Shell revolving freely within a Hollow Spheroid. 427

fluence of the force of attraction and its own centrifugal force, it
will under certain circumstances assume a position of equilibrium
in which its bounding surfaces will be two spheres concentric
with the spheroidal surface of the external solid shell.

In order to show this, let the axis of rotation be the axis of z
of a system of rectangular coordinates, whose origin is in the
common centre of the spheres and spheroids. Let X, Y, Z be
the component parts parallel to the axes x, y, z of the attraction
which the hollow spheroid and the fluid shell exert on a particle
of the latter. The component parts of the attraction of the outer
spheroid may be denoted by

— M#, —My, — ptJt,
and those of the inner spheroid by

-Woe, -Mty, -Wz,
where M, N, M;, and N' are quantities independent of x% y, z.
Let p' be the density of the fluid. Then the attraction which the
fluid shell exerts on the point x, y, z, has for components

4 4 v v

r3y

-3*+f^7F*

a_l_,,2_j_*9\8

5# + 5 V/

3 fJ \/{a:* + yC2 + z*)s

where r is the radius of the inner sphere.

The component parts of the attraction of the hollow spheroid
and the fluid shell will consequently be

liSlf^lpS^^^ t: (1)

Z=(-^ + W^~7ro'f+~7rp!f , — }z.

V T 3 HJ^3 rJ t/(x2 + y<2 + zZfJ

The differential equation for the surfaces de niveau, when w
denotes the angular velocity, is therefore

(_M+M'-|v/+}v/Vp=qrpp+^)(^+^)

2F2

428 M. G. It. Dahlander on the Form assumed by a Fluid

for the innermost bounding surface is x2-\-y9 + z<i=ri, and
xdx -f ydy -f- zdz = 0. Hence we find that

w*-M + M'=-N + N' . . . (3)
is a conditional equation, and equation (2) will therefore be

(_N + N'-^7+ \*pf v^f+^d* + ydy + 2d:)=Q. (4)

The surfaces de niveau are therefore all spherical. If their
radius be denoted by r1) we get

xdx + ydy-\-zdz=rJd?J ; (5)

and if the pressure be denoted by p, we get

^=(-N+N'-|v/+|^)^- • (6)
By integrating this we find

J - (-N + NO j - 1 -*w*- \ v/$ + c

But ^ = r when p = 0, whence

J.(_N + NO £=3- 1 V/V2-'-2)- 1 Tf^(p-l)- (7)

Equation (7) gives the pressure which takes place in dif-
ferent parts of the fluid. If r1 be taken as the radius R of the
outer sphere, then p must be =0. Thus we get the conditional
equation,

(-n+no £!=£ U|«^it_^+ 1 v^(i-e)=o. (8)

Equations (3) and (8) determine the relation which must exist
between the quantities therein occurring,in order that equilibrium

may be possible under the given conditions. If |r be denoted by

k, then equation (8) becomes

^_N_fN'_3v/^(1 + A) + 4v/^=a > {9)

Hence we find that if, under the given conditions as to the
dimensions of the spheroid and the density of the fluid, equili-
brium is possible in one case, there are an infinite number of
other cases in which equilibrium can also take place, provided r
and R may vary but Xr^is supposed to be constant.

Equation (9) is of the second degree with regard to k ; but

Shell revolving freely within a Hollow Spheroid. 429

it is easy to see that it can only have one positive root, because
the first term must be negative.

Let us particularly consider the case in which the outer
bounding surface of the spheroid is spherical, and the inner sur-
face is oblate. Then

N=M=^/,

M'=2^/(i±^(arctanX- j^),

N'=47rp/i-±^( X- arc tan X),
where p denotes the density of the spheroid. Putting

(10)

t«r

Zvp'f

equations (3) and (9) become
E = m(3-^_3(1±^

g _m+l
l+k~~ 2

= E, and £

r

X3

3 (1 + X2)

arc tan X

)■

(11)

2

X3

(A,-arctan\)=^(l-E). (12)

Equations (11) and (12) determine the relations which must
exist between X, e, m} and k, in order that equilibrium may result.
If the right-hand member of (12) be denoted by n} we get

TTk=n'

This equation, if equilibrium be possible, must give a positive
fraction as the value of k. If resolved in regard to this quantity,
we get, observing that n must necessarily be positive,

*=tv?+»>

which gives as the condition for k < 1,

n < 1, or 1 - ^ * t^ (X- arc tan X) < 0. . . (13)

This condition is always fulfilled when X > 0. In order that
n may be positive,

m(l-?^iX5(X-arctanX))+1^0,ore<:l. (14)

This inequality determines the greatest value m can have when

430 Form assumed by a Fluid Shell revolving in a Hollow Spheroid.

\ has a given value. Hence it appears that when X is given, we
can always find such positive values for m, that the condition
given by the inequality may be fulfilled. Equation (11) in that
case always gives positive values for e when X and m are deter-
mined.

Suppose, for example, \=1, then the condition (14) will be

-0-2876m+ 1 > 0, or m < ^^.

Suppose, for instance, m = l, or that the densities of the solid
spheroid and of the fluid sphere were equal, then we should get

,— 7 =0-3562, whence k =0-801.

1 + a:

The inner radius of the hollow sphere ought therefore to be
about four-fifths of the outer one. Lastly, we find from (11)
that

€=0-2876.

There is another class of forms of equilibrium which may be
assumed by fluids revolving in a hollow spheroid, which we will
only mention here, as being of comparatively of less interest. A
heavy homogeneous fluid, revolving in the cavity of the hollow
spheroid, may assume a spheroidal figure of equilibrium. In
fact, when M, M', N, and N' have the same signification as
before, and — M"#, — M"y, and — Wz denote the component
parts of the attraction of the fluid spheroid, then the equation of
equilibrium will be

(--M + M'-M,'4-^2)^ + ^//) + (--N + N,--N,0-^=O,(15)

where M, M', M", N, N', N", w are independent of x, y} z. If
the equation of the fluid surface be supposed to be

*2 + ?/2 , _£!__-,
a2 i"a2(l+\2)~i'

then the condition of equilibrium will be

-M + M'-Mff + uf
1+X" -N + N'-N" ■• ' * <16)
By putting the values for M, M;, M", N, N', N" in equa-
tion (16), we find that equilibrium is possible under an infinite
number of different conditions with regard to the form and
density of the spheroids, and the velocity of rotation of the fluid
mass.

Gothenburgh, October 24, 1860.

[ 431 ]

LIX. A Theory of Galvanic Force. By Professor Challis,F..R.£.*

HAVING argued in previous communications that the laws
of Light, Heat, Gravity, and Electricity may be conse-
quences of the dynamic action of an elastic fluid medium, I
proceed now to apply the principles of the same theory to the
facts of galvanism. As it is hardly possible that so comprehen-
sive a theory could escape the contradiction of facts, unless it
were well founded, every extension of it to new classes of facts
without meeting with contradictions, and without the necessity
of new hypotheses, adds greatly to the evidence for its truth.
In art. 18 of the " Theory of Electric Force," given in the Oc-
tober Number, I have shown that electrical attractions and repul-
sions might be explained consistently with hydrodynamic action
by the hypothesis of setherial currents. Now it is this very
hypothesis which is required for explaining by the same kind of
action the laws of galvanism. It must be assumed, on the
hydrodynamical theory, that there exist in the neighbourhood of
the earth steady setherial currents, which within considerable
spaces may be considered to be of uniform velocity and density.
By the solution of Problem II., in the " Theory of Attractive
Forces" contained in the Philosophical Magazine for No-
vember 1859, it appears that these currents would produce no
motion of translation of small solid spheres, such as the ulti-
mate atoms of bodies are assumed to be. But the same cur-
rents might, under the circumstances stated in art. 18 above
referred to, give rise to steady secondary currents, which, not
being uniform as to velocity and density, might be capable of
acting dynamically to a sensible amount on ultimate atoms.
That the hypothesis of steady primary currents is also in accord-
ance with magnetic phenomena, I hope to show hereafter, and
at the same time to consider what may be their origin. •

1. One of the primary facts of galvanism is its intimate con-
nexion with electricity. The following illustration may help
to form a distinct idea of the explanation which the hydro-
dynamical theory gives of this fact. Conceive any solid sub-
stance to be suspended by attachment at one of its points to an
immoveable body, and to be acted upon by gravity. Then as-
suming it to consist of discrete atoms all equally urged by the
force of gravity, the lower superficial atoms must be kept in
equilibrium by an excess of molecular attraction above molecular
repulsion, and the higher by an excess of molecular repulsion
above molecular attraction. Also the force of gravity on any
atom in the interior of the body must be just counteracted by
the resultant of forces emanating from the atoms. But the

* Communicated by the Author.

432 Prof. Challis on a Theory of Galvanic Force.

internal atomic actions are equal and opposite at any point of
the interior if the density of the body be uniform. Hence,
besides the rapid gradations of density near the boundary, which
give rise to the superficial attractions and repulsions, there must
be a much slower gradation of density throughout the interior
of the substance ; and as the atomic and molecular repulsions
are much more affected by difference of density than the mole-
cular attractions, the force of gravity is counteracted by repul-
sions, and the density consequently decreases from the lower to
the upper part of the body. Now it is clear that in this example
the deviations of the superficial atoms, and those of the interior
atoms, from their undisturbed state, are mutually dependent, and
that all are connected with the molecular action at the point of
attachment; for if the attachment were suddenly cut off, the
atoms would immediately return to the undisturbed state, and
would all equally obey the force of gravity. While in this
instance the atoms are all in disturbed positions, because all are
acted upon by the force of gravity, the counteracting atomic
and molecular forces consequent upon this state of disturbance,
must evidently have a single resultant at the point of attach-
ment. It is therefore conceivable that conversely a superficial
disturbance at a single point, or at several points, may extend
its influence over all the atoms of a body. This, as a matter of
experience, appears to be the case when two dissimilar substances,
conductors of electricity, are in contact.

2. The definition of physical contact is, that the superficial
atoms of each body are acted upon at the points of contact by
the molecular forces of the other ; not that the atoms them-
selves come into contact, this being prevented by the atomic
repulsion, which is the most energetic of all the physical forces.
When two dissimilar substances are in contact, the superficial
atoms of each at and near the points of contact must, in general,
on account of the dissimilarity, be put by the molecular forces
into positions of disturbance ; that is, according to the theory of
electricity which I have proposed, the two substances are in an
electric state. If they are good conductors of electricity, the
local disturbance extends throughout their superficial atoms,
and the substances are in a state of induced electricity, which
would immediately disappear upon separating them. Under
these circumstances, from what is argued above, there would be
a gradation of density throughout the interior of each, and thus
the conditions for generating secondary currents, stated in art.
18 of the "Theory of Electricity," would be fulfilled. The in-
tensity of these currents will depend on the amount of disturb-
ance at the points of contact ; and this again must depend on
the constitutions and qualities of the two substances. It might

Prof. Challis on a Theory of Galvanic Force, 433

be anticipated that the action between a solid and a fluid would
be considerable, on account of the dissimilarity of their super-
ficial molecular conditions. If a chemical affinity exists between
the solid and the fluid, the disturbance may be expected to be
still greater, because such affinity exhibits itself by a tendency
in the superficial action so far to disturb the atoms as to put
them into new relations. The action' between two gases (as
oxygen and hydrogen) which tend to combine might produce
sensible secondary currents, while no such effect would follow
from the contact of two gases (as oxygen and nitrogen) which
have no chemical affinity. These are, in short, facts of experi-
ence which are at once seen to be in accordance with the theory,
if it may be assumed that the secondary tetherial currents of the
theory are the same as the galvanic currents of experiment.

On this assumption the theory explains the fact that sub-
stances which generate galvanic currents are good conductors of
electricity, and exhibits the connexion of the development of
electricity with the generation of the currents.

3. It appears from experiment that different substances have
different powers of transmitting galvanic currents. There are
conductors and non-conductors of galvanism, as of electricity;
and, generally, the substances which conduct electricity also
conduct galvanic currents. Air is a non-conductor as well of
galvanic currents as of electricity. The ratio of the two con-
ductive powers does not appear to be the same for different
substances. It does not belong to the present theory to inquire
into the reasons for these facts, which are mentioned here only
because they bear upon the subsequent explanation of the
hydrodynamical theory.

For instance, it may be asked, if the origin of galvanic cur-
rents be such as the theory indicates, why do not the same
attractions and repulsions of light bodies take place in the
neighbourhood of the voltaic battery as in the neighbourhood of
a body whose electricity is excited by friction ? To this I reply
that the induced electricity at any point of the voltaic battery is
very much feebler than the electricity induced when the original
disturbance of the superficial atoms is caused by friction, and
the currents due to a feeble induction are proportionally feeble.
Any perceptible motive power of partial currents, acting through
the air, may be prevented by the non-conductiveness of the air
itself, and the insulation of the battery. But when the separate
streams excited at a great number of points (as in a large
battery consisting of numerous cells) are, as it were, concen-
trated in an electrode of fine wire, considerable motive power
acts through the air, as is evident by the known action of such
electrodes on each other when, being arranged so as to be near

434 Prof, Challis on a Theory of Galvanic Force,

and parallel to each other, they are at the same time free to
move.

4. The question as to whether the galvanic currents owe
their origin to the contact of dissimilar substances, or to che-
mical action, has been much discussed on experimental grounds.
Looking at it from the point of view of the hydrodynamical
theory, the conclusions that will be come to are, that the cur-
rents are due to the mutual molecular actions of dissimilar
substances in contact; that chemical affinity between the sub-
stances augments the molecular actions, and consequently the
strength of the currents ; and that chemical combination, or
analysis, is not necessary for the generation of the currents, but
may be a consequence of them. I consider the theory to be in
complete accordance with the two following inferences, which
occur in an exposition of the experimental evidence bearing on
this point by Mr. Gassiot (Philosophical Transactions, 1844,
p. 39). " Elective affinity is greatly concerned in the antecedent
action, of which chemical combinations, when the circuit is
closed, are the consequence" (§ (26)). " The higher the che-
mical affinities used, the greater was the evidence of the deve-
lopment of tension " (Note at the end of the Paper).

5. The explanation which the hydrodynamical theory gives of
the chemical action consequent upon the generation of the cur-
rents, will be best stated after a more particular consideration
of the nature of the currents, considered as instances of steady
iiuid motion. The origin of the movement being at the battery,
and the current flowing from the right hand through the battery
to the left hand, the fluid will be impelled on the left hand, and
will be drawn on the right hand. It will enter the conductor
at one pole, and issue out at the other ; and by this circum-
stance the two poles will be permanently distinguished. The
direction of the stream depends on the order of the elements,
the stream resulting from a difference of action of the elements ;
and if the order be not the same throughout the battery, op-
posing streams will be generated. Now it does not appear
possible for steady currents to give rise to forces adequate to
produce chemical analysis, except by considerable changes of
velocity within small spaces. By hydrodynamics, the variation
of pressure dp in an elementary portion ds of a line s drawn
in the direction in which the stream flows, is proportional to
— WV, d\ being the corresponding variation of the velocity V
of the stream. Hence an increment of velocity in the direction
of the stream is accompanied by a decrement of pressure, and
consequently an accelerative force, in the same direction ; and,
on the contrary, a decrement of the velocity in the direction of
the stream produces an accelerative force in the opposite direc-

Prof. Challis on a Theory of Galvanic Force, 435

tion, — the forces, in each case, being proportional to the rate of
change of pressure.

6. In the " Mathematical Theory of Attractive "Forces/' given
in the Philosophical Magazine for November 1859, 1 have shown
by the solution of Problems II. and III., that when a small
spherical body in a fixed position is submitted to the action of a
uniform stream, the pressures on opposite hemispheres are equal,
and consequently that the stream would impress no velocity on
the sphere supposing it free to move, nor alter any velocity
which it may have otherwise acquired. The effect, however, is
different if the stream, though steady, be not uniform, that is,
if there be change of velocity, and consequently change of den-
sity, from point to point in its course. In that case, the mere
statical effect of change of density would produce an accelerative
force of the body in the direction of the decrement of density.
The total effect will, however, be due both to the motion of the
fluid and to the variation of its density. I shall not now
attempt to solve the problem of calculating this effect mathe-
matically, as the following general considerations may suffice for
the present purpose. It has already been stated, as a result of
mathematical reasoning, that when a small solid sphere moves
uniformly in an elastic medium, the pressures on the preceding
and following hemispherical surfaces are equal. Hence there is
no tendency to acceleration or retardation of the sphere; and
the motion of the fluid being the same in successive instants,
the total momentum of the fluid and sphere remains the same
in successive instants. This permanence of the momentum in
cases where no external force acts, may be regarded as a general
law of the mutual action between a solid and a fluid. Accord-
ingly, since in the case before us the spherical body is accelerated
by the fluid, it will impress at each instant on the fluid in the
contrary direction by the reaction on its surface, a momentum
equal to that which it receives. But the reactions of spheres
of different radii are, cateris paribus, proportional to their sur-
faces, that is, to the squares of the radii. Hence the instanta-
neous increments of momentum of the spheres are in the same
proportion, and the accelerations are therefore in the inverse
proportion of the radii. Prom this reasoning it follows that
when the atoms of any substance are submitted to the action of
a steady aetherial current of variable density and velocity, they
are accelerated in the direction of the decrement of density in
proportion to some function of the decrement, and the less are
more accelerated than the greater.

If the decrement of density be in a direction contrary to that
of the stream, the acceleration of the atoms still takes place in
the direction of the decrement.

436 Prof. Challis on a Theory of Galvanic Force.

7. Let us now consider the process of generation of setherial
currents, and their dynamical action, in the experiment of the
galvanic battery. It will suffice to take the simple case of a
plate of zinc and a plate of copper immersed in an acid solution.
The chemical action between the fluid and zinc may be such as
to produce analysis of the fluid anterior to any galvanic current,
while no such action takes place at the surface of the copper.
This difference between the relations of the metals to the fluid is
an essential condition of the generation of a current. The che-
mical affinity between the acid solution and the zinc, causes a
change of position of the superficial atoms of the latter, and
puts it into an electric state, the action of the fluid taking the
place of friction in the phenomena of ordinary electricity. If
the zinc plate were alone immersed in the fluid, all the points of
its surface would be in the same electric state ; but being in
the presence of the copper, the latter is electrified inductively,
and reacts upon the zinc. Thus both metals are put into a
state in which a gradation of interior density exists, and conse-
quently, according to our theory, each tends to generate second-
ary currents. Also the tendency is in the same direction for
both, because the adjacent parts are oppositely electrified. No
current, however, flows unless a continuous route is provided by-
means of a metallic connexion between the zinc and the copper.
Till this is done the current is driven back by the insulation of
the battery and the non-conductiveness of the air. But when
the circuit is complete, the internal atomic conditions of the
zinc and copper, which originate the secondary current, main-
tain its dynamic action. So far as relates to the action of the
current, the case is exactly analogous to that of electrical attrac-
tion, considered in the "Theory of Electricity." As the attraction
towards each other of the electrified bodies was due to a steady
current, having a position of maximum velocity, and therefore of
minimum density between them, so in this instance there will,
for like reasons, be a position of minimum density of the sether
between the zinc and the copper. Consequently there will be a
decrement of density more or less rapid from the zinc towards
this position ; and if it be assumed that the current flows in
that direction, from what is argued in the preceding paragraph,
its dynamic action, being more energetic on the atoms of hydro-
gen than on the larger atoms of oxygen, will urge the former
towards the copper. After accumulating on the surface of the
copper, the hydrogen will rise in the fluid in the form of bub-
bles. In the mean time the oxygen set free obeys the law of
its affinity for zinc, and combines with it more copiously than it
did before the flow of the current. In this way the theory
accounts for electrolysis by the dynamic action of an setherial

Prof. Challis on a Theory of Galvanic Force, 437

current. I have assumed the atoms of hydrogen to be smaller
than those of oxygen in accordance with a theoretical result
obtained in the Philosophical Magazine for February 1860. If
this be a true explanation, the theory decides that the flow of
the galvanic current is from the zinc to the copper, that is, from
the positive to the negative pole of the battery.

8. In the usual experiment for decomposing water, the ter-
minals being of platinum wire, there is no direct action between
the metal and the fluid ; but as one wire is connected with the
positive pole of the battery, and the other with the negative,
they must have opposite electricities, and will also act upon
each other inductively. Hence, by the same reasoning as be-
fore, an setherial current is generated, which may be capable of
separating the hydrogen from the oxygen by impelling the
atoms of hydrogen more energetically than those of oxygen. In
this case the oxygen, not having an affinity for platinum, rises
in bubbles at the positive terminal, while the hydrogen is driven
off to the negative terminal. As there must be a decrement of
density at the negative terminal towards the position of mini-
mum density between the two, it is possible there may be a
decomposition of the water at this terminal also, but in less
degree than at the positive, because the decrement of density is
in the direction contrary to that of the stream. If there be
such decomposition, all the oxygen liberated may unite with
hydrogen sent from the other terminal, and thus hydrogen alone
will rise from the negative terminal, as is known to be the fact from
experience. This last remark applies also to the case considered
in the preceding paragraph, if there should be any decomposi-
tion, by the agency of the current, at the surface of the copper.

9. It will be seen from the above explanations, that the gene-
ration of a galvanic current without actual analysis of the fluid,
the possibility of which appears to be proved by the water-bat'
tery, is consistent with the theory.

10. The investigation of the motion of the setherial current
along an electrode of fine wire is a very difficult hydrodynamical
problem, the solution of which I shall not attempt to give at
present ab initio. But admitting the existence of such currents,
and that they are steady, it is not difficult to state what must be
their chief characteristics. In the first place, if not confined
within limits by non-conducting substances, they must exert
an influence at considerable distances from the electrode. Hydro-
dynamically it would be impossible for an unconfined stream to
flow along the electrode without producing motion in the sur-
rounding fluid. The velocity of the sether is greater within the
wire than without, because the wire is the effective channel of
the stream, and the motion of the surrounding fluid is the result

438 Prof. Challis on a Theory of Galvanic Force.

of lateral action. The velocity within the wire is also increased
by the contraction of the channel by the occupation of space by
the atoms. Now as the axis of the electrode thus becomes a
line of maximum velocity, and therefore of minimum density,
there must be a tendency of the contiguous fluid to flow towards
this axis. But if this motion actually took place, the stream
would immediately be stopped. Hence this tendency must be
counteracted by a uniform circular movement kept up by the
accelerative force due to the decrement of density towards the
axis. Thus the resulting motion will be in spiral lines about the
electrode. This conclusion will be put to a severe test when we
come to consider the mutual action of galvanic currents and
magnets.

11. It is readily seen from this theory why the current flows
as soon as two wires connected with the poles of a battery are
put in contact ; for by the action of the battery the fluid is im-
pelled along one wTire, and draiun along the other, and the circu-
lation of the stream results from the junction. Simple contact
suffices to produce the effect, apparently because it provides an
axis for the spiral movement, which, as explained above> is ne-
cessary for maintaining the current. It is not so easily seen
why there is no current unless the poles are brought into con-
nexion. "When the ends of the wires are in air, it is sufficient
to say that the air, being a non-conductor, stops the flow of the
current, the explanation of the non-conductive property being
not at present under consideration. But the experiments of
Mr. Gassiot have proved (Phil. Trans, vol. cxlix. part 1. p. 150)
that a perfect vacuum is a non-conductor. The explanation of
this fact must be drawn from the laws of movement of the rcthc-
rial fluid. On this point I have the following considerations to
offer. Assuming that galvanic currents are identical with a? i he-
rial currents, experience shows that the conductive property of
a substance allows an setherial stream to permeate freely through
its whole interior, and, supposing it to be insulated, that its
bounding surface contains the stream wTithin limits, just as a
closed channel of any shape contains a stream of water. In this
manner a metallic wire is a channel for the setherial current ; but
in this case, if the insulation be not perfect, on account of the
narrowness of the channel, the surrounding sether is perceptibly
acted upon, so as to make a spiral movement necessary, as above
stated, for the maintenance of the current. The spiral motion
may be conceived to originate where the stream issues from a
wider space into the electrode, just as the same phenomenon
occurs when water issues from a vessel through an orifice ; also,
where the stream issues from the electrode into a wider space, a
like movement may be produced. In both cases, a rapid change

Prof. Challis on a Theory of Galvanic Force. 439

of the transverse dimensions of the channel is a necessary con-
dition, the stream being throughout confined within limits. But
when the extremities of the electrodes are in vacuum, the con-
tinuity of the channel is broken ; and as from hydrodynatnical
principles it may be shown that the sether is incapable, by the
mutual action of its parts, of maintaining a spiral movement,
this movement ceases, first at the extremities of the electrodes,
then through their whole lengths, and the current is consequently
stopped.

12. It appears from experiment that discharges of great
lengths may be passed from the extremity of one electrode to
that of the other, within glass tubes of small bore, wholly or
nearly exhausted. This may be explained on the principles of
the theory by saying that the form and non-conductive quality of
the tube are favourable to the maintenance of the spiral move-
ment.

13. The current is maintained when the electrodes are con-
nected with the earth instead of being connected with each other,
simply because the earth is a conductor which may be considered
to be of unlimited extent. On this account the drain which
takes place at the extremity of one of the electrodes cannot pro-
duce an exhaustion of sether sufficient to cause a revulsion of the
stream, nor can the flow at the extremity of the other electrode
cause a repletion which would send back the stream.

14. It is stated in Davy's ' Elements of Chemical Philosophy '
(vol. i. p. 152), that with the same battery an electric discharge
took place in air of ordinary density between charcoal points
distant from each other about one-thirtieth of an inch, and in
rarefied air which supported one-fourth of an inch of mercury,
the sparks passed through nearly half an inch : also that in the
former case the constant or galvanic discharge took place in the
heated air through a space equal at least to four inches, and in
the latter through a space of six or seven inches. These facts
prove experimentally, not only that air resists the passage both
of electricity and of the galvanic current in greater degree as its
density is greater, but seem to show also that the galvanic dis-
charge may go on while the battery is in a state of electric ten-
sion. This inference is consistent with the hydrodynamical
theory.

15. The theory distinctly separates the electric from the gal-
vanic discharges, the former being abrupt and violent streams
produced by the sudden return of superficial atoms in disturbed
positions to their natural relative state, and the latter being the
continuous effect of a disturbed state of the interior atoms.
These conditions of the superficial and the interior atoms are,
however, so intimately connected, that when the galvanic current

440 Prof. Challis on a Theory of Galvanic Force,

is flowing in a closed circuit, it must be supposed that very
minute and rapid electric discharges arc taking place at the
same time.

16. The light and heat accompanying electric and galvanic
discharges may, according to the Undulatory Theories of Light
and Heat which I have proposed, be ascribed to vibrations of the
atoms of aeriform or solid bodies, excited by the dynamic action
of aetherial currents. When the electrodes terminate in charcoal
points, the dynamic action is increased both by the condensation
of the streams due to the pointed form, and, on approaching the
points, by the impulse given to the streams in consequence of
the opposite states of electricity of the terminals.

It seems to be a sufficient explanation of the voltaic arc, to
say that the air between the poles, being heated by the galvanic
discharge, continually rises, and that consequently the path of
least resistance, which depends only on the density of the air, is
not the straight line joining the poles, but a course above this.

17. The coloured light in the tubes with which Mr. Gassiot
experimented seems to be caused by vibrations of some gaseous
substance enclosed within them, the atoms of which, it being of
extreme rarity, may be made to perform large excursions by the
dynamic action of the current, and reciprocally may produce
agitations of the aether rendered sensible in the form of light.
If the gas were of considerable density, its elastic force would
resist the action of the stream, and the excursions of its atoms
might consequently be too small to produce a sensible amount
of light. The stratification may be due to the nodes and loops,
that is, positions of minimum and maximum vibration, which
are always consequent upon exciting vibrations of elastic gases
in tubes. The colour is probably to be ascribed to the particular
quality of the gas. The glow at the terminals appears to have
a different origin from that of the stratification, and may possibly
be due to the agitations of the aether, caused by the sudden
changes of the stream on its passing out of, or entering into, a
terminal.

18. Different dynamic effects of the motions of the aether
may co-exist without mutual disturbance, if the motions be
vibratory ; but the dynamic effects of steady currents interfere
with each other. This known result from hydrodynamical prin-
ciples at once explains the disturbance of a galvanic current by a
magnet, supposing the magnetic influence to be due to steady
aetherial currents.

19. If two electrodes be placed near each other and parallel,
and galvanic currents pass along them in the same direction,
they are attracted towards each other. The explanation of this
fact by the theory is, that the contiguity of the electrodes de-

Dr. P. L. Rijke on the Inductive Spark. 441

stroys the symmetrical arrangement of the density of the sether
about them ; and since when they are distant from each other
the density decreases towards their axes, on their being brought
near, the space between them becomes a position of minimum
density, towards which they are consequently attracted. If the
currents pass in opposite directions, by their interference they
produce an excess of density between the electrodes, which are
consequently impelled, as is known experimentally. The inter-
ference of the transverse motions would produce the contrary
effects. It seems, therefore, that the observed attractions and
repulsions are due to the excess of the longitudinal above the
transverse action of the currents.

20. It is scarcely necessary to say that the velocity of a gal-
vanic current in an electrode is very different from the velocity
with which the commencement of the current, or any interruption
of it, as in the use of the electric telegraph, would be propagated
along the electrode through space. The latter velocity, on hy-
drodynamical principles, would be comparable with the velocity
of transmission of light through solid substances, and would
probably exceed the velocity with which light would traverse
a substance of the same density as the electrode.

The foregoing explanations seem to justify the conclusion that
the facts of galvanism may with much probability be referred
to the dynamical action of the setherial fluid, and consequently
be included within the proposed hydrodynamical theory of the
physical forces.

Cambridge Observatory,
November 16, 1860/

LX. Note on the Inductive Spark. By Dr. P. L. Rijke, Pro-
fessor of Natural Philosophy in the University of Ley den*.

1. \ BOUT five years ago Vicomte du Moncel first called
XjL attention to the fact f that the inductive spark obtained
from RuhmkorfTs apparatus differs materially from the spark
obtained on discharging, by ordinary means, a common electri-
fying machine or a Leyden jar. In the latter case the spark is
homogeneous, and consists of a simple point of light, while the
spark obtained from RuhmkorfTs apparatus is composed of two
parts altogether different from each other, — the one being a point
of light precisely similar to the ordinary spark, the other a lumi-
nous atmosphere that admits of being displaced by means of a

* Communicated by the Author.

t Comptes Rendus, vol. xl. p. 313 ; and Phil. Mag. S. 4. vol. ix. p. 546.

Phil. Mag. S. 4. Vol. 20. No. 135. Dec. 1860. 2 G

442 . Dr. P. L. Rijke on the Inductive Spark.

current of air or gas. Another French philosopher, M. Perrot,
afterwards discovered* that the heating power of this luminous
atmosphere is much greater than that of the true spark ; and at
the same time he found the means of completely separating the
atmosphere from the rest of the spark. For this purpose M.
Perrot opposed to one of the electrodes another of a V-shape,
and found that, by suitably regulating the distance of the extre-
mities of the latter from the former, he could establish an atmo-
spheric current which carried the luminous atmosphere towards
that branch of the V-shaped electrode which was more remote
from the opposite pole. Under these circumstances the lumi-
nous atmosphere appeared only at this latter branch, the other
• branch receiving the ordinary spark. About the same time
M. du Moncel submitted the inductive spark to the action of
powerful electro-magnets, and discovered that while the ordinary
spark is entirely unaffected by magnetic force, this luminous
atmosphere appears affected in precisely the same manner as the
voltaic arc under similar circumstances.

2. When an ordinary Ruhmkorff's apparatus is made use of,
most of the phenomena I am about to mention would require to
be observed by means of a microscope. This, however, is not
the case when more powerful apparatus is employed. I have
recently repeated all these experiments with a machine lately
constructed by M. Ruhmkorff, and which produces sparks 31
centims. long. With this apparatus the phenomena in question
are produced on a scale of such magnitude as to be perfectly
visible to the naked eye.

3. M. du Moncel has endeavoured, as is well known, to ex-
plain these phsenoniena by means of a theory which he has pro-
pounded in several communications to the Academy of Sciences f.
Unfortunately, however, this theory has not, I believe, obtained
the general assent of physicists ; and the same may be said of
other attempted explanations that have been advanced by various
other distinguished philosophers. There is, therefore, a want
here which I am about to satisfy by means of a new theory,
which will be seen, however, to bear some resemblance to that
of M. van derWilligen J.

4. If we inquire what is the electric state of the inductive wire
at the moment before its discharge, it seems to me that but one
answer can be given : — the middle, portion is in its natural state,
and the two extremities arc charged, the one with positive, and

* Comptes Rendus, vol. xlix. p. 175.

t This theory is also advocated in a work entitled " Researches on the
Non-homogeneity of the Electric Spark," by Vicomte du Moncel. Paris,
1860.
• % PoggendorfPs Annalen, vol. xcviii. p. 494.

Dr. P. L. Rijke on the Inductive Spark. 443

the other with negative electricity*. As to the intermediate
parts, they are also electrified ; and although we are unacquainted
with the precise law that connects the degree of electric tension
with the distance from the middle point, we know at least that
these magnitudes increase together. It is, then, evident that when
the inductive wire is discharged, the electric charges of the two
extremities first unite, and the charges from the parts nearer
and nearer the centre follow in succession. Now the fluids con-
tained in the two extremities obviously unite in the form of an
ordinary spark ; but the same cannot be the case with the charges
of the parts nearer the centre. In fact the experiments of Mr.
Wheatstonet show that when two electric fluids, before uniting,
have to traverse a metallic wire TJjth of an inch in diameter and
half a mile long, the duration of the spark is greatly increased,
even to a degree that cannot be accounted for by the mere time
that electricity would require to traverse half a mile of such wire,
which proves that this prolonged duration of the spark is to be
attributed to that particular property of matter that physicists
have agreed to call electric resistance. Now if a wire of y^th
of an inch diameter, and only half a mile long, sensibly increases
the duration of the spark, what must be the effect of the second-
ary wire of Ruhmkorff' s apparatus, the resistance of which is
much more considerable ? We can form some estimate of it by
the time taken, according to the experiments of M. W. Weber J,
by an electric battery to discharge itself when the current has to
traverse a wet hempen cord. It is therefore evident, according
to my view of the subject, that the electric spark ought to have
some duration j and we know from an experiment of M. Lissa-
jons§, that when the inductive spark is observed in a mirror
which is at the same time shaken by the hand, the luminous
atmosphere presents the appearance of an elongated band, of
which the true spark occupies the posterior extremity, — thus
showing that the atmosphere in question really does endure for
some fraction of a second.

5. We know that the appearance of the electric spark is gene-
rally changed when the two fluids, before uniting, have under-
gone any considerable resistance. Its colour is then altered, it
becomes tinged with violet and blue, while its illuminating power
is much diminished ; at the same time its form is changed, its
volume augmented, and it acquires the power of inflaming bodies

* In the first machine constructed by Ruhmkorff, free electricity was
only found at one extremity of the wire ; this, however, was only in con-
sequence of a defect in the insulation, that M. Ruhmkorff has since remedied.

t Phil. Trans. 1834.

X Electrodynamische Maasbestimmungen, p. 295,

§ Comptes Rendus, f vol. xlix. p. 1009. ' i

2G2

444 Dr. P. L. Rijke on the Inductive Spark.

which resist the effect of the ordinary spark : thus, for example,
gunpowder can be exploded by the spark of a Ley den jar, if the
electric fluid is first passed through a wet cord. Now these are
precisely the characteristics that have been recognized as existing
in the luminous atmosphere of the inductive spark.

6. According to the theory here advanced, we ought to be able
to augment the luminous atmosphere at the expense of the true
spark, and, conversely, the spark at the expense of the atmosphere,
as follows : —

7. In order to increase the spark at the expense of the lumi-
nous atmosphere, all that is necessary is to unite each extremity
of the inductive wire to the armatures of a Leyden jar by means
of metallic conductors, and to pass the charge through a Henley's
discharging rod, which has one extremity of one of its branches
communicating with the knob of the jar, and one extremity of
its other branch connected with the external coating, the spark
passing between the other two ends of its two branches. Thi3,
it will be seen, is precisely the experiment of Messrs. Masson
and Grove. It is evident that when the two extremities of the
secondary wire communicate with the armatures of a Leyden jar,
the distribution of the electric fluid in the wire undergoes a very
great alteration, since, before the actual passage of the charge,
the greater part of the two fluids will have accumulated in the
armatures of the jar, whence it must result that, the two fluids
having now to traverse conductors offering little resistance, the
discharge ought to take the form of an ordinary spark; and this
is found to be the case. M. du Moncel has himself acknowledged
that, under these circumstances, the luminous atmosphere no
longer makes its appearance. My theory, then, not only accounts
for this disappearance of the luminous atmosphere, but it also
explains why, in the experiment of MM. Masson and Du Moncel,
the brilliancy of the spark is so greatly increased.

8. When, on the other hand, we wish to get rid of the point
of light and to retain the atmosphere, all we have to do, accord-
ing to my theory, is to compel the electricity distributed through-
out the secondary wire to traverse a path in which it finds con-
siderable resistance. This I effected as follows : — For my elec-
trodes I took two brass wires about 1 millim. in diameter, and
3 or 4 centimetres long, and having fixed them to insulators, I
united them to the extremities of the inductive wire by means of
two wet hempen cords, about 5 millims. in diameter and 0*7
metre long. The inducing current was then produced by means
of two elements of a Bunsen;s battery. Under these circum-
stances the ordinary spark was no longer visible, the luminous
atmosphere alone remained, and the whole of it would be dis-
placed by means of a current of air.

Dr. P. L. Eijke on the Inductive Spark. 445

9. If the want of homogeneity of the inductive spark be really
due to the cause to which I attribute it, then it ought to be pos-
sible to discharge ordinary friction electricity so as to exhibit
both the point of light and the luminous atmosphere ; and the
discharge so modified, when submitted to the action of external
agents, ought to behave similarly to the spark produced by
Ruhmkorff's apparatus. It will easily be understood that I
attached great importance to the success of this experiment,
which may be considered as the touchstone of my theory. The
way I contrived it was as follows : — The conductor of a hydro-
electric machine, the grate of which possessed a surface of 9
square decimetres, was put in metallic connexion with the inte-
rior of a Leyden jar, the external coating of which presented a
surface of 738 square centimetres, and was in communication
with the boiler of the machine. The knob of the jar was also
connected by means of a wet hempen cord, 5 millims. in dia-
meter and 45 centims. long, with an insulated metallic sphere
of 29 centims. in diameter. The two branches of a Henley's
discharging rod constituted the two electrodes. The end of one
of them was in connexion with the external covering of the jar,
that of the other was at the distance of about 10 millims. from
the metallic sphere. The other two extremities of the two
branches, which were pointed, were about 7 or 8 millims. apart.
It is evident that, with this arrangement of the apparatus, the
Leyden jar ought to be discharged whenever the tension of the
electricity in the sphere attains a certain amount, and that this
discharge ought to appear as a luminous spark between the
pointed extremities of the discharging rod.

The electricity which thus passes between these two electrodes
proceeds from two different sources, viz. from the sphere, and
the interior of the jar. The electricity of the sphere having but
a short metallic path to traverse, ought to give rise to the appear-
ance of an ordinary spark; while, on the contrary, the fluid
accumulated in the jar having to overcome the very considerable
resistance of the hempen cord, ought to give rise to the appear-
ance of a luminous atmosphere. Now the discharge actually
observed presents precisely this double appearance.

10. On submitting the luminous discharge of this apparatus to
the action of an air-current, I obtained precisely the same results
as those observed by M. du Moncel in the case of the inductive
spark, — the luminous atmosphere being carried away from the
point of light, on which the air-current did not seem to exercise
the slightest effect. M. Perrot's experiment also succeeded per-
fectly. Finally, I examined the nature of the action of magnetic
force on the discharge, and I found that the luminous atmo-
sphere under the action of an electro-magnet behaved precisely
as in the experiments of M. du Moncel.

446 Mr. C. W. Merrifield on Approximation to the Integrals

11. I trust that physicists will admit that we are justified in
concluding, from the foregoing facts, that in the inductive s}mrk
the point of light is to be attributed to the recomposition of the
electric charges accumulated in the extremities of the secondary
wire, while the luminous atmosphere is produced by the electric
fluids contained in the parts of the wire nearer to its middle point.

Leyden, October 31, 1860.

LXI. On Approximation to the Integrals of Irrational Functions
by means of Rational Substitutions. By Charles W. Merri-
pield, Esq.*

IN his " Meditation on Poncelet's Theorem '* in the October
Number of this Journal, Mr. Sylvester has done me the
honour to mention a theorem of mine upon the subject expressed
at the head of this paper. I have now to communicate an ex-
tension of that theorem. It is but right to state that this exten-
sion has been suggested to me by Mr. Sylvester's remarks on
the connexion between his method and the Newtonian system of
approximation to the roots of equations.

We had both taken the pure quadratic as our base of opera-
tions ; but while he took the method of continued fractions to
obtain his converging terms, I took (under another shape) the
method of successive substitution. I am compelled to differ
from him as to the practical advantages of the two methods for
the purposes of the computer.

In my paper, which Canon Moseley communicated to the
Koyal Society this year, I started from the principle that the
geometric mean between two quantities is also a geometric mean
between their arithmetic and harmonic means, and again between
the arithmetic and harmonic means of those means, and so on, —
the series of arithmetic means on the one side, and the series of
harmonic means on the other, giving a continual approximation
to the geometric mean. Now this process is but a particular
case of the Newtonian approximation to the roots of an equation :
viz., let a be a first approximate solution, obtained by trial, of the
equation fx=0, and c&Wfx the differential coefficient offx; then

a second approximation is a—i—^b; a third approximation will

fb J a

evidently be b— jj-r = c, and so forth. If we apply this method

to the pure equation xn=p> the convergent terms which we obtain
are as follows : —

* Communicated by the Author.

of Irrational Functions by means of Rational Substitutions. 447
{n— l)an+p

na"
(n-

(n — l){(n— l)an+p}n + nn.p.a<n~V
n2an-1{(n—l)an+p}n~l ~~!

If we make ti=3, we have for the fractions converging to the
cube root,

2a3 +p 2{2a3+p)8 + 27pa6 „
a> 3a* ' 9a*{2a?+p)* '

Applying this to the cube root of 2 by making a = 1,^=2, we
obtain successively,

i> t^-333' S=i'36389>andiSSS-8=1-3599335'

the true value being 1*25992105.

The mode of finding the limit of the error is given in the
books on the theory of equations.

The above formula? obviously enable us to approximate to
2
functions of the form tyndx. In fact our first approximation

would be I ; * dx, a and y being both rational func-

J nan~l

tions of x, the former chosen pro arbitrio. But we are by no
means restricted to pure radical forms. The process applies with
equal generality to the functions which are given implicitly as
the roots of equations. Thus, if the given equation be ym + \y= v,
a first approximation to \ y dx is

J'

mam~l + X

Here a and y are supposed to be rational functions of x, and \
andj? to be constant.

If we make n — 2 in the formulae for the simple radical, we
obtain the series of arithmetic means which I gave in the memoir
above quoted, viz.

gt+p gt + GaZp+p2 as + 2Sa6p 4- 7(ky .+ 2Sa,y +p4 fr
a' ~2a~~' 2a{a*+p) s "" 8a{tfi+7rfp + 7ay +f) >
The harmonic series of means is obtained by multiplying the
reciprocals of these into ap.

"With reference to the question as to which method is the
most advantageous for the purposes of elliptic functions, it may
be observed that the labour attending the mth approximation in
my scale is about equivalent to that of the 2mth in Mr. Sylves-
ter's. It will therefore be a sufficient test to try his tenth and

448 M. H.Dcville on the Decomposition of Bodies by Heat,

my fifth term on the square root of 2. Making a or r=l, p or
N=2, his tenth term gives

..'* = 1-41 421 36249;

my fifth term gives

ggg = l-41421 35623 7469;

while the real value of */2 is 1-41421 35623 73096. My
method thus appears to give twelve figures correct, while the other
gives seven. I have tried several cases with a similar result.

A remarkable expression for Mr. Sylvester's successive approxi-
mations is afforded by Dr. Booth's Trigonometry of the Parabola.
Divested of any peculiarities of symbol it is as follows : — let 6m
be determined by the equation

C'm Mm '_ C* d6x

J0 cos0w-mJo COS 0,'

then if we make \/N . sin #!=r, the with approximation will be

expressed by ** ■ .
, sin0m

Kensington, Nov. 6, 1860.

LXII. On the Decomposition of Bodies by Heat, and on Disso-
ciation. By M. H. Sainte-Claiue Deville*.

FROM what has long been known on the subject, and from
facts which I myself have published, it appears well esta-
blished that the action of heat finally decomposes all bodies. As
this decomposition does not take place suddenly, I have assumed
that the elementary or constituent molecules of a compound
body, before reaching the point at which affinity ceases to act,
gradually remove from each other, or dilate under the influence
of heat, as do the compound or integrant molecules themselves.
1. Simple decomposition. — When the divergence of the elements
has become so great as to overstep the sphere of activity of the
force which keeps them united under the ordinary circumstances
of affinity, and when, further, the molecules have not the power
of combining again by the simple fact of their contact, the de-
composition is definite, and shows itself by its products. We
see such a case of simple decomposition when we subject to the
action of heat ammonia, nitric acid, all nitrogen compounds in

* Communicated to the Societe de Physique et d'Histoirc Naturelle de
Geneve, September 8, 1860; translated by Dr. E. Atkinson.

and on Dissociation, 449

general, the oxides of the precious metals, &c. ; sometimes, even,
these decompositions are accompanied by a sudden disengage-
ment of heat, as is the case with the chloride, iodide, and
sulphide of nitrogen.

Decompositions which are attended with disengagement of
heat are evidently an exceptional case, and embarrassing even to
some of the most plausible theories of chemical combinations.
They characterize in a general manner the compounds of nitro-
gen, which are never formed directly, or by the simple and
immediate contact of their elements. The accuracy of this
observation is evident for the majority of explosive nitrogenized
substances, which are resolved into simple bodies at the moment
of their destruction. But for non-explosive nitrogen compounds,
it may be deduced from this important fact, which is confirmed
by MM. Favre and Silbermann, that protoxide of nitrogen in
the phenomena of combustion which it produces, developes more
heat than the oxygen which it contains would furnish if burnt
alone. It is clear that protoxide of nitrogen, and therefore other
compounds of the same class, disengage heat at the moment of
their destruction.

If two combustion experiments are made with the same quan-
tities of potassium and sulphur, employing in succession crystal-
lized octahedral sulphur and soft sulphur, the latter will disengage
a larger quantity of heat than the octahedral sulphur, and the
difference will be precisely equal to the quantity of heat observed
by M. Itegnault when he heated soft sulphur to 92°, and observed
its temperature spontaneously rise to 110°. The quantity of heat
latent (this is the term used, but it ought to be altered) or dis-
simulated in the sulphur, maintains an unstable equilibrium. It
may be assumed that in this respect sulphur, protoxide of
nitrogen, and the fulminating compounds of nitrogen are con-
stituted in the same manner ; and it is at the moment at which
this unstable equilibrium is broken by the influence of the heat
itself that the calorific effect shows itself in the experiments of
MM. Eegnault, Favre and Silbermann, and in the destruction
of the fulminating compounds of nitrogen.

On the other hand, my brother has shown how considerable
is the influence of temper on the properties of sulphur. Besides
soft sulphur, which was well known, and which only differs
from ordinary sulphur by its physical properties, he discovered
insoluble sulphur, which is distinguished from all the rest by a
chemical property — insolubility in bisulphide of carbon. This
modification has been obtained without the intervention of any
other cause than the sudden change of temperature by which
the phenomenon of temper is produced in steel and in explosive
Dutch drops. It is therefore certain that, by tempering or sudden

450 M. H. Deville on the Decomposition of Bodies by Heat,

cooling, bodies can be obtained whose physical properties (soft
sulphur), or whose chemical properties of a certain kind (inso-
luble sulphur) are completely modified. These properties even
bear a certain relation to the quantity of dissimulated heat which
the bodies retain under the influence of tempering ; they also
retain them in a state of unstable equilibrium, which is physically
characterized by a diminution in the density, and is exhibited
by the greater or less facility with which they revert to the
ordinary and definite state.

I hope I make myself clear in assuming that nitrogenous
compounds, and in general all those which decompose with ex-
plosion and disengagement of heat, are comparable to tempered
bodies, retaining more heat than is adequate for the state of
stable equilibrium of their molecules ; and it is at the moment
at which this stable equilibrium is destroyed that the liberated
heat becomes sensible, when it is more than sufficient to pro-
duce a simple decomposition or separation of the elements.
By this mode of view, the phenomena of inverse combination,
or of decomposition with disengagement of heat, may be brought
under the same category.

As to the formation of tempered bodies, or the fixation of this
heat which renders unstable the condition of equilibrium of
combined bodies, it may take place in the conditions of the
nascent state, which is indispensable for the union of nitrogen
with many bodies; for, from the experiments of my brother,
of MM. Fordos and Gelis, of M. Berthelot, and of M. Cloez,
insoluble sulphur and soft sulphur, which are obtained by tem-
pering, are also obtained in the ordinary phajnomena of decom-
position during the exchange of the molecules, and under
conditions which constitute the nascent state in chemical re-
actions.

By continuing these comparisons, we shall remove an anomaly
which is truly to be regretted even in some of our most reliable
chemical analogies. It might be conceived that it is nitrogen
which carries with it the property which these bodies possess of
becoming tempered — that it is nitrogen in the nascent state that
can fix the heat borrowed from the bodies in the midst of which,
and with which, it combines ; so that free gaseous nitrogen and
combined nitrogen are really two distinct bodies, which differ
just as octahedral sulphur differs from insoluble or soft sulphur,
perhaps by chemical properties, or perhaps simply by a physical
property such as the density. This hypothesis would explain
how it is that nitrogen possesses a density 0*972 which corre-
sponds to two volumes of vapour, while phosphorus and arsenic
only represent one volume of vapour for one equivalent, as is
shown by the experiments of M. Dumas, of M. Mitscherlich, and

and on Dissociation, '. 451

some of M. Troost and myself made at high temperatures. But
all experiments made up to this time, and especially the latest
researches of MM. Hofmann and Cahours, establish in the most
incontestable manner the closest analogy between nitrogen,
phosphorus, and arsenic, — but simply between these bodies in a
state of combination. It might, it is true, be objected that if a
certain number of difficultly volatile bodies, such as arsenic,
selenium, and tellurium, only represent one volume of vapour for
one equivalent, it depends on the high temperature of the
boiling-point. But mercury, according to M. Dumas, cadmium,
and especially zinc, which boils at 1040°, and whose density has
just been determined by MM. Troost and myself at 1100°, re*
present two volumes of vapour for one equivalent. This objec-
tion will disappear before examples which we wish to be able to
multiply.

In short, the hypothesis according to which nitrogen enters
into combination in the state of a tempered body, like sulphur,
would explain the instability of these compounds, would remove
the majority of cases of inverse combination (that is, the decompo-
sitions accompanied by a disengagement of heat, which embarrass
the various theories of affinity), and it would, lastly, account for
the anomaly of removing nitrogen from phosphorus and arsenic,
its natural allies, which is at the present day a blot in our
systems of chemical analogies.

I further think that the curious phenomena observed in
tempered sulphur, which my brother has minutely described, are
susceptible of a wide generalization.

2. Dissociation. — The phsenomena of decomposition under the
influence of heat, of which nitrogen compounds furnish such an
excellent example, are not so evident when they take place at the
expense of bodies whose elements can unite during cooling, and
by simple contact. Mr. Grove's experiment, which I have had
occasion to repeat in conjunction with M. Debray*, by throwing
into water several kilogrammes of melted platinum and lighting
the explosive mixture which is abundantly disengaged, shows
clearly the products of the decomposition of water at this tem-
perature, but is far from telling what quantities of gas heat alone
could produce. In fact, the melted platinum is not in contact
with water, and can only decompose the small quantity of

* On one occasion this experiment gave rise to a fearful explosion ; a
cast-iron mortar, weighing 16 to 20 pounds and full of water, was raised to
a considerable height ; 500 grammes of platinum were projected to a great
distance in a state of fine powder. The platinum usually traverses 30 to 40
centimetres of water, sinks in a fused or soft state to the bottom, and forms
a regulus with a mammillary surface ; the transparency of the water is dis-
turbed by thousands of small gas bubbles, which can be exploded at the
surface. .

452 M. H. Deville on tlie Decomposition of Bodies by Heat,

vapour which forms an atmosphere round the metal ; besides, as
the greater part of the gas recombines by the slow cooling of its
molecules, only that portion of gas is liberated which by a sudden
cooling escapes the action of the decreasing temperature. The
phenomenon is in relation with the rapidity of its development,
as I have shown in the case of the dissociation of potash, soda,
of chloride of magnesium, and of water itself under other cir-
cumstances.

I have shown that water comports itself like a substance
whose molecules are separated, when it is submitted to a tem-
perature of about 1000° (fusion of silver) ; on the other hand,
hydrogen and oxygen separated produce, in combining, more
heat than is necessary for melting platinum and even iridium,
whose fusing-point may be taken at least at 2500° (I shall
assume in what follows, but simply for facility of expression, that
these 2500 degrees exactly represent the temperature of the
detonating mixture itself at the moment of combustion) . How
is it then that the combination of hydrogen and oxygen produces
sufficient heat to melt platinum, while this melted platinum can
itself decompose water, and restore it to its elements, hydrogen
and oxygen ? Much more, according to my experiments, does
this property which water possesses of dissociating, exist at a
temperature far below 2000°, a temperature which I consider to be
approximately the fusing-point of platinum ; it takes place even
at a temperature of the fusion of silver. How then can water be
decomposed at a temperature far below that developed by the
combination of hydrogen and oxygen ? This contradiction must
be explained ; it appears to me to escape all the theories which
have hitherto been propounded to interpret the different actions
of heat on chemical combinations.

It is difficult to regard the integrant molecule of a compound
body other than as composed of an assemblage of constituent
molecules, separated from each other by a space, finite, though
extremely small, and which further varies with the affinities of
the elements concerned. Thus each compound molecule is a
group of simple molecules separated from each other by finite
distances, as compound molecules themselves are. Affinity is the
force which keeps the constituent molecules united : it causes
the stability of a compound ; the force of cohesion opposes the
separation of the integrant molecules, and it is clear that affinity
and the cohesive force would cease to act when the molecules are
at a certain distance from each other.

The action of heat tends to diminish affinity as well as the
force of cohesion ; by dilating bodies, it increases the distance
between compound or integrant molecules until cohesion is
nil; it appears to me that it ought also to increase the di-

and on Dissociation, 453

stance of elementary or constituent molecules by producing a
dilatation, which is very small, and perhaps insensible in refer-
ence to the dilatation of the integrant molecules ; but as this
distance increases until it becomes equal, then superior to the
radius of the sphere of activity of affinity, the compound body
decomposes by heat. Between the temperature at which this
decomposition takes place, and the temperature at which the
body possesses all its stability, there is an interval during which
the constituent molecules are at a distance comparable to the
radius of the sphere of activity of the affinity. Just as the loss
of cohesion suddenly reduces the entire body to a liquid state
(if it is solid), so the loss of the stability of bodies under the in-
fluence of heat, during this interval of temperature, reduces the
molecules to the particular state of superheated bodies to which
I have given the name dissociation. The least cause can then
produce decomposition ; a mechanical cause, such as platinum
decomposing water at 2000°; a simple solvent action, as the
solubility of oxygen in silver or in lead, produces the decompo-
sition of water at 1000°; lastly, a chemical action, usually elective,
but devoid of this character at a high temperature, as iron assi-
milating oxygen in the presence of hydrogen and potassium in
the decomposition of potass by Gay-Lussac and Thenard's
method.

I may thus affirm that, in this interval of 1000° to 2500°, the
constituent molecules of aqueous vapour are free in spite of
affinity, just as from 0°to 100° (Cent.) the integrant molecules
of liquid water are free in spite of the cohesive force, which is
sensibly nil.

Molecular attraction produces in bodies cohesion, which for
each special substance assumes different intensities, the values
of which vary with the temperature. There are sudden changes,
one of which, corresponding to the liquefaction of solid bodies,
takes place at the same time that a considerable quantity of heat is
absorbed, without any change in the volume of bodies, while even
in some cases there is a contraction, as is the case with water,
bismuth, &c. In like manner affinity communicates stability to
compound bodies, which diminishes as the temperature increases.
This variation, which is insensible within extended limits, may
be considerable at a certain temperature, and fixed like the
fusing-point, and without the volume of the compound becoming
sensibly increased. The compound body (which I shall consider
for the moment as being in a gaseous state) is then in a state
of dissociation. It could then even absorb a considerable
quantity of latent heat of dissociation, without its volume, and
consequently the uniformity of its expansion, being notably
modified.

454 M. H. Dcvillc on the Decomposition of Bodies by Heat,

When a liquid is boiled, there remains in the vapour no trace
of the properties which characterize cohesion, and the quantity
of latent heat absorbed during the passage of a gas into a gaseous
state is often considerable. Similarly, when by the simple action
of a high temperature a gas has been decomposed into its ele-
ments (this temperature is evidently higher than that which
these elements develope during their combination), there remains
in the mixture no trace of this effect of the force of affinity which
constitutes the stability of a compound ; and as the gaseous volume
generally increases at the moment of the separation of the ele-
ments, there ought to be an absorption of a certain quantity of
latent heat of decomposition.

Thus water melts at 0°, and its volume varies little; it boils
at 100°, and its volume increases considerably ; it dissociates at
1000° without any material deviation in its volume from Gay-
Lussac's law of expansion ; it decomposes above 2500°, and its
volume suddenly increases in the ratio of 2 to 3.

In other words, at 0° the cohesion of water approaches its
maximum j above 0° it is nil, or almost nil ; at 100° it is ne-
gative. At 100° the stability of aqueous vapour is at its maxi-
mum up to 1000°, a temperature at which it almost disappears,
and suddenly, in dissociated vapour ; lastly, above 2500° it is
negative in decomposed vapour : the constituent molecules then
repel each other as if they were of the same kind.

If heat acts by expansion a3 well on the .constituent as on the
integrant molecules of compound bodies, we see that stability,
like cohesion in solid bodies, may exist in gases with a positive
value, which is the condition of combinations at temperatures
at which we usually work ; that it may exist with a volume almost
nil, like cohesion in liquids (this is the state of dissociation, con-
firmed in the case of water, potass, soda, chloride of magnesium
at temperatures of 1000° to 1500°); that, lastly, stability may
become negative, like cohesion in gases, in bodies entirely decom-
posed by heat, like anhydrous carbonate of ammonia at 60°,
ammonia at a red heat, water at 2500°.

This conception may be rendered palpable by assuming that in
gaseous compounds in, a stable state the constituent molecules
are solid; that in dissociated bodies the molecules are liquid*;
lastly, that in decomposed bodies the molecules are endowed with
an indefinite mobility — in other words, the molecules themselves
are gaseous.

* On this hypothesis, the constituent molecule might have a tension
varying with the temperature, and which is greatest at the temperature of de-
composition. The quantities of water decomposed in the experiments of
Mr. Grove and of myself, during the state of dissociation, would be the quan-
tities of uncondensed vapour corresponding to this state of tension.

and on Dissociation. 455

This mode of expression introduces great simplicity into the
scientific language relating to this question, but it does not
involve a new idea. It has often guided me in connecting phe-
nomena of total or partial decomposition, phenomena of ebulli-
tion, and of the formation of vapours with variable tensions in
solids or liquids. I shall use this formula in explaining the
meaning and the range of some experiments which I have made
during the last winter. It is, however, to be understood that
I simply rely on the analogies which I have established between
affinity and the forces of cohesion ; and I reserve to myself the
opportunity of showing how these two forces (which are exerted
on two kinds of distinct molecules — the constituent molecules,
and the integrant molecules, of compound bodies) produce in
analogous cases identical effects.

When two volumes of hydrogen and one volume of oxygen
are combined in a medium whose temperature is 100°, two
volumes of aqueous vapour are produced, whose temperature for
a few moments is at least 2500°. The two effects observed are
the contraction, and the elevation of temperature, of the water;
the apparent physical condition (gaseous) of the three bodies,
water, hydrogen, and oxygen, has not changed. Either, then,
the contraction must have produced all the heat, or the hy-
drogen and oxygen have- given out from themselves the heat
which is disengaged. But the heat due to contraction would
simply raise the temperature of aqueous vapour to 137° instead
of to 2500°; hence the second hypothesis can alone be ad-
mitted.

Further, chlorine and hydrogen combine without condensa-
tion ; a simple ray of light is sufficient to produce an enormous
elevation of temperature in the gaseous mixture. As hydro-
chloric acid could only borrow from its elements the heat which
it has manifested, and consequently lost at the moment of combi-
nation, it is clear that it does not possess the physical state, of
one at least, of the two gases which compose it; and as the
distance between the molecules has not changed, it is in the
constituent molecule itself that the modification must be sought
from which the disengaged heat results. There are then two
sources of heat in the combination of gases : 1st, the contraction
in volume, the effect of which can be calculated with precision ;
2ndly, an intimate modification in the constitution : with this
latter I am now concerned.

In order to elucidate at least one part of the question, I have
sought to ascertain what would be the influence of the heat due
to contraction when the state of bodies which combine evidently
Undergoes no change, when, for example, two liquids combine to
form a compound which is also a liquid. In order to solve this

456 M. H. Deville on the Decomposition of Bodies by Heat,

problem, I have verified directly the temperatures produced in
the liquids on which I have operated ; I thus obtained numbers
comparable with each other, and independent of the variation
in the specific heats of bodies. The latter is only introduced
into the calculation in the slight corrections which must be made
in the temperatures to allow for the heat absorbed by the vessels,
and for the heat expended in water evaporated in experiments
made at a high temperature.

I assume that in a large number of gases (the specific heat of
the product is necessary for the corrections) there is determined
the temperature of combination of two liquid bodies, the density
of the two bodies at the initial temperature, and, lastly, the co-
efficient of expansion of the body from the initial temperature to
a point somewhat higher than the temperature of combination ;
we have then all the elements necessary to calculate —

1st. The volume of the components before their combination.

2ndly. The volume of the compound after combination, and in
consequence of contraction.

3rdly. The heat of contraction, or the temperature at which the
compound would have the same volume as the components.

It is clear that if there is no difference between this tempera-
ture of contraction thus calculated, and the temperature of com-
bination observed directly, the heat disengaged by the contrac-
tion is sufficient to explain the disengagement of heat observed
during combination. When this difference is positive (and this
has always been the case in my numerous experiments, except
with sulphate of soda which has 10 equivs. of water), it represents
the loss of temperature (of vis viva), or the cooling effected during
the act of combination, which always accompanies solution.
Thus a cooling is sometimes observed with bodies which really
combine, such as water and acetic acid.

Hence the temperature corresponding to contraction is always
higher than the temperature observed directly during the act of
combination — and that with almost a single exception, the cause
of which is readily found : the heat disengaged in the combina-
tion of two liquids by contraction is then more than sufficient to
explain the effects produced, provided, of course, that there is no
change of condition.

This observation will suggest that there is, on the contrary,
change of condition whenever two gases combine with disengage-
ment of heat, producing a body also gaseous, especially when
there is no contraction. In order to make my meaning clear, I
shall use the mode of expression which I have previously ex-
plained.

Suppose the molecules of hydrogen and of chlorine are liquid,
and that the constituent molecules of hydrochloric acid are solid,

and on Dissociation. 457

the disengagement of heat produced during combination, and
arising from this solidification, might be considerable without
any change in the volume, or without any sensible variation in
the distance of the compound.

Pursuing the comparisons which I have made between affinity
and the force of cohesion, and supposing (which is in accordance
with prevalent ideas, especially in organic chemistry*) that each
molecule of hydrogen and chlorine is double, we see in fact that
everything I have said about compound bodies and their disso-
ciation applies to hydrogen and to chlorine. They are in the same
physical state as water dissociated at 1000° ; and at the moment
at which they combine, by rendering it sensible they lose a
quantity of heat corresponding to that which the dissociated
vapour of water ought to give up, in order to revert to its ordi-
nary condition of stability. From this point of view I can con-
sider hydrogen and chlorine themselves as bodies dissociated at
the ordinary temperature like water heated above 1000°.

Continuing this comparison, and anticipating a research with
which I am occupied relative to the temperature of decomposi-
tion of bodies which disengage a gaseous element, I think I am
authorized in assimilating these phenomena to those of the
ebullition of liquids, or the vaporization of non-liquifiable solids.
Water deprived of air boils with great difficulty in glass, and,
according to M. Donny, can even remain in the liquid state up
to 140° at the ordinary pressure. But if a fragment of pla-
tinum, or some metallic powder be thrown in, the vapour is
disengaged with extreme violence. It is a phenomenon of
the same kind which is produced when oxide of copper or
of manganese is placed in fusing chlorate of potass. The
boiling-point is lowered, if I may so express myself, or, in lessen-
ing by a mechanical means the stability of the compound, the
decomposition of the chlorate of potass may be likened to the
destruction of the cohesion of water heated above 212° by a
platinum point. This I believe to be the simplest explanation
of the singular experiment which we every day perform in our
laboratories in preparing oxygen from a mixture of oxide of man-
ganese and chlorate of potass.

In a subsequent communication I shall describe the experi-
ments which I have made with a view of defining the influence
of velocity in chemical actions, and shall oppose the hypothesis
which Berthollet has introduced into science under the name of
action of mass.

M. Thenard, by a most ingenious and conclusive experiment,

* To make the hypothesis 9=16, H=l, Cl=35'5, is exactly the same
as dividing the molecule of hydrogen and chlorine so that 0=8, H=i,
C1=17'7j and referring these equivalents to one volume instead of to two,
as is proposed at present.

Phil. Mag. S. 4. Vol. 20. No. 135. Dec. 1860. 2 H

4-") 8 Prof. W. Beetz on the Molecular Changes

has already shown the nullity of the action of mass when a very
weak acid is mixed with a very stable salt, — boric acid and sulphate
of potass. I have also shown that this action is nil even in the
decomposition of aqueous vapour by zinc, which is as easy as
that of oxide of zinc by hydrogen*. There only remain then
two capital experiments in which the influence of mass inter-
venes ; these are, on the one hand the decomposition of water by
iron and the reduction of oxide of iron by hydrogen, and on
the other, the inverse reactions of carbonic acid on sulphide of
potassium and of sulphuretted hydrogen on carbonate of potass.

Without explaining the first phenomenon, I shall show that it
is too complicated to be completely accounted for by Berthollet's
hypothesis. For the other, that hypothesis is quite unnecessary.
Berthollet's law of the decomposition of salts sufficiently explains
it. For when a continued current of carbonic acid is passed into
solution of sulphide of potassium, a layer of carbonic acid forms
at the surface of the liquid, in which sulphuretted hydrogen is
volatile, while the dissolved carbonic acid acquires fixity. Hence
volatile sulphuretted hydrogen, fixed carbonic acid, and potass
are in presence of each other. By Berthollet's law sulphuretted
hydrogen would escape, and carbonate of potass be formed ; but
this decomposition would not take place without a continual
renewal in the composition of the atmosphere being produced
by a rapid current of carbonic acid ; and this explains why a
considerable excess of carbonic acid is needed to complete the
operation, and why the bubbles of sulphuretted hydrogen are
not visible in the liquid which is changed into carbonate at the
ordinary temperature.

Changing the terms, the same reasoning applies to the inverse
decomposition of carbonate of potass by sulphuretted hydrogen.
But here, as the carbonic acid is less soluble in water than
sulphuretted hydrogen, it is disengaged more rapidly in an
atmosphere of sulphuretted hydrogen, and the decomposition of
carbonate of potass is more rapid than that of sulphide of
potassium.

LXIII. On the Molecular Changes produced by Magnetization.
By W. Beetz t«

THE molecular changes which take place when a bar of steel
or iron passes from the unmagnetic to the magnetic state,
may, as M. Weber J has shown, be regarded in four different

* Annales de Chimie et de Physique, 3rd series, vol. xliii. p. 473 and 477 .

t Translated from Poggendorff's Annalen, September 1860.

X " Electrodynamische Maasbestimmungen, insbesonderc liber Diamag-
netismus," Abh. d. K. Sachs. Ges. d. IVissensch. phys. math. CI. 1852, i.
p. 541.

produced by Magnetization. 459

ways, which, however, may be reduced to three essentially di-
stinct. It may be supposed —

1. That two magnetic fluids exist, which are capable of being
set in motion independently of the ponderable body in which they
reside.

2. That two magnetic fluids exist, which can only be set in
motion in conjunction with the molecules of the ponderable bodies
in which they reside, or that there are molecular streams of a
permanent character rotating with the molecules, and formed by
the two electric fluids.

3. That there are two electric fluids, which may be set in
unresisted motion in certain paths, about the stationary molecules
of the ponderable body.

Of these three hypotheses, Weber felt himself compelled
to regard the last as the correct one, in order to bring the
fundamental phenomenon of the origin of diamagnetism into
agreement with that of the origin of magnetism ; he remarked,
however, in the course of his work, that as far as magnetism
itself is concerned, experience is in favour of the hypothesis of
rotatory molecules*. According to this latter hypothesis, the
amount of magnetism which can be induced in a body has a
limit when the axes of all the molecular magnets of which it is
composed have become parallel ; whereas the existence of such
a limit is incompatible with the hypothesis of the presence of
an inexhaustible store of a separable neutral magnetic (or electric)
fluid. Even, indeed, when the quantity of this fluid is not re-
garded as inexhaustible, still, according to the latter hypothesis,
the ratio between the amount m of the magnetism induced,
and the magnetizing power ja, must remain constant until the
whole of the neutral magnetism contained in the molecules of
the body is separated ; while, according to the other hypothesis,
that ratio must be a variable quantity, continually diminishing
according to some fixed law.

m

Lenz and Jacobif in their researches found this ratio, — ,

V
constant. Joule \ has confirmed this view. J. Miiller§, on the
contrary, found the ratio in question variable according to a
fixed law. Buff and Zamminer || have thrown a doubt over this
conclusion; but W. Weber f, who found it in general corro-
borated, expressed an opinion that the difference between these

* Jbh. d. K. Sachs. Ges. d. Wissensch. 1852, i. p. 556.
f Pogg. Ann. vol. xlvii. p. 225. Bull, de VAc. d. St. Pet. vol. iv. p. 337.
t Phil. Mag. (4) vol. iii. p. 32.

§ Pogg. Ann. vol. lxxix. p. 337; lxxxii. p. 181. Miiller, Fortschritte
er Phys. p. 502.
** ||Lieb. u. Wohl., Ann. der Pharm. vol. lxxv. p. 83.
IT lb. p. 566.

2H2

460 Prof. W. Beetz on the Molecular Changes

contradictory results might be removed, if the experiments were
carried on under precisely similar circumstances. Add to this,
that Koosen* and von Feilitzschf came, on entirely different

grounds, to the same conclusion, viz. that the ratio — was not

constant, but approximated to a limit ; and the old view of the
separation of neutral magnetism present in inexhaustible quan-
tities, must be regarded as altogether inadmissible, as must also
be the case with the hypothesis of the separation of two electric
fluids capable of being set in motion in quantities without
limit about the molecules of the magnetized body.

There remains, therefore, the choice between two hypotheses —

1. That magnetization is due to the separation of two
magnetic or electric fluids, which are only present in limited
quantities.

2. That it is due to the change of position of the molecules
of the body magnetized, whether these are to be regarded as
molecular magnets on account of the simple separation of the
two fluids, or on account of the molecular currents continually
circulating about them.

As above remarked, the observations that have been made

concerning the law according to which the magnitude — ap-
proaches its limit, render it probable that the latter of these
two hypotheses is correct : the intimate relation, which Wiede-
mann J found to exist between the phenomenon of magnetism
and the torsion of a steel rod, are still more positively in favour
of the theory of the cooperation of the material particles of the
magnetized iron, since it would be hard to discover any other
explanation of these relations than that suggested by the above-
named physicist, the supposition, namely, of moveable particles.

The experiments I am about to communicate will furnish new
and, I trust, conclusive evidence in favour of this hypothesis.

I first endeavoured to produce a magnet which should possess
a maximum charge, that is to say, which should be so perfect a
permanent magnet, that its magnetism could not be increased
by any temporary magnetizing current.

Proceeding on the hypothesis of rotatory atoms, such a state
must necessarily be attained if we so manage as not to operate
on a ready-made iron bar by means of a polarizing force, but
cause the separate molecules, under the influence of such a force,
to arrange themselves, side by side, with their axes parallel, and
thus form themselves into a magnetic bar. In order to effect

* P°gg- ^nn' v°l- lxxxv. p. 159. f lb. vol. lxxx. p. 321.

X lb. vol. cvi. p. 161.

produced by Magnetization. 461

this, 1 made use of the method described by Bottger* to obtain
by the electrolytic process a coherent precipitate of iron, — but
with this difference, that the precipitation was conducted between
the poles of a powerful magnet. A cylindrical glass vessel was
divided by means of a porous partition into two cells, each of
which contained a solution of iron (sulphate or chloride with
sal-ammoniac). In one cell a steel plate was plunged perpen-
dicularly as the positive pole, in the other, parallel to the first, a
rectangular strip of plated metal of any kind as negative pole.
The longer side of the latter was horizontal, the shorter side
touched the side of the vessel. A strong magnet (sometimes a
magnet of seven plates and 50 lbs. attractive power, sometimes
a Logemann's magnet of 25 lbs. attractive power) was placed
horizontally on the table, so that the glass tube projected partly
between its limbs, and the inner polar edge of the magnet
touched the outside of the glass vessel exactly where the
negative plate lay against it on the inside. A simple DanielFs
battery served as electromotor.

The iron plates thus obtained were hard as glass, and always
magnetic. In fact, however, so strong a magnetic influence was
by no means necessary to render them permanently polar; on
the contrary, almost any magnetic force operating during the
formation of the precipitate, was sufficient to determine its
polarity. Every electrolytic iron plate, for example, is magnetic
if the cathode has been placed in the direction of the magnetic
inclination.

In order to test the power of the magnets thus obtained, they
were placed on edge near a mirror magnetometer, so that their
axis passed through the axis of rotation of the mirror, and lay
magnetically east and west. Then, to measure the temporary
magnetism and the changes produced in it by magnetizing
currents, this whole arrangement was placed within one of the
large magnetizing coils taken from a Kleiner's electromagnet.
As, however, the magnetism produced by such a coil, even when
weak currents were employed, turned the mirror through so
great an angle that the graduated scale passed entirely out of
the field of vision of the telescope, the other coil was placed near
the magnetometer on the other side, and the current was made
to pass through both in succession, under which circumstances
the deviation of the electrometer only amounted to a few divisions
of the scale. The natural position of the mirror of the magneto-
meter was then observed, and its positions noted when a current
was made to pass through the coil, first in one direction, then
in another; the bar magnet under examination was then inserted

* Polyt. Notizbl. vol. i. No. 4. p. 849. Pogg. Ann. vol. lxvii. p. 117.
Dingl. Pol, Joum. vol. xcix. p. 296.

462 Prof. W. Beetz on the Molecular Changes

in the coil, and the deviation caused by it alone was determined ;
and lastly, the magnetizing current was again passed through the
coils, first in one direction, then in the other, and the deviations
due to the temporary and permanent magnetism of the bar were
read off. The numbers given below are only comparable for the
same magnet, since the distance of each of the magnets was
always so chosen that the reading off of the scale might be as
practicable as possible.

Although in the above disposition of the experiment the pre-
cipitated particles had the opportunity of arranging themselves
in regular order, I nevertheless found, contrary to my first ex-
pectation, a considerable difference between the temporary and
permanent magnetism. In fact, however, assuming the hypo-
thesis of rotatory atoms equal in magnitude and magnetic power,
such atoms could only retain their parallel position, on the
cessation of the magnetizing current, on one condition, namely,
that all were at equal distances from each other. If this be not
the case, on the cessation of the current each molecular magnet
will place itself in the direction of the resultant of all the forces
acting on it, as is speedily the case when the precipitated plate
in the above experiment is removed from between the poles of
the magnet. Moreover, even between the poles of the strongest
magnets the precipitated molecules will not all arrange them-
selves in the same direction; for when once the cathode is
covered with a thin film of precipitated iron, the atoms that
follow are subjected to a double influence, viz. to that exerted at
a finite distance by the poles of the magnet, and secondly, to
that exerted at an insensible distance by the atoms already de-
posited. Now the latter force is directly opposed to the former,
as any one may easily convince himself experimentally, if, instead
of employing a horseshoe magnet as above described, the iron is
precipitated on a magnetic steel plate. The precipitate will then
be found to have a polarity contrary to that of the steel plate.
If, therefore, the precipitate between the poles of a magnet be
suffered to increase, each atomic layer partly cancels the polarity
of the other, and it is therefore impossible to obtain a thick
magnet as completely saturated as a thin one. A fully charged
magnet would be produced, if a row of polarized particles could
be obtained in a straight line. In order to accomplish this as
nearly as possible, I stretched a thin silver wire tightly over a
glass plate, and covered it with a thin layer of varnish, which,
when it had become dry, I scratched away from the side turned
away from the plate, so as to expose a strip of the surface of the
wire as narrow as possible. The plate was then placed in the
electrolytic apparatus between the poles of a magnet ; and in a
few minutes the wire was covered with a precipitate of iron. It

produced by Magnetization,

463

was then dried and placed within the spiral, very near the mag-
netometer, and its own magnetism, as well as that induced in it
by a magnetizing current (produced by a 6-celled Grove's battery),
was measured. In two such experiments I found —

1. 2.

Original magnetism . . . 3*60 3*59

Temporary 3*70 3*69

Permanent 3'60 3*58

Magnetic plates broader, but equally thin with the above, con-
sisting of precipitates of iron on the surface of silver, easily acquired
a temporary magnetism greater than their original magnetism ;
but neither by the most powerful current, nor by rubbing them
with the pole of a powerful plate-magnet, could a permanent
magnetism be induced in them greater than that possessed by them
originally.

3.

4.

Length in millimetres

Breadth in millimetres

Time being precipitated ...

72
15
10 minutes.
14-37
25-18
14-27
13-42

72
21

15 minutes.
18-93
28-70
19-08
18-12

Temporary magnetism

Permanent magnetism

After friction

Thicker magnetic plates not only exhibited a greater difference
between their original and temporary magnetic powers, but their
permanent was greater than their original magnetism.

Length

Breadth

Weight

Specific gravity

Thickness

Original magnetism

Temporary magnetism

Permanent magnetism

After friction with magnet

5.

72 millims.
15 „

8-825 grm,

6-81

1-2
19-36
64-5
24-28
22-37

G.

33 millims.

M >,

3-246grm,

6-63

1-06
16-34
35-38
18-26
16-90

In experiments 3 to 6, a six-celled Groye's battery was em-
ployed.

If we suppose that magnetizing currents effect a separation of
the two magnetic fluids in the metallic mass, which separation
partly continues after the cessation of the current only on
account of its coercive power, it is difficult to understand why
different magnets give results on measurement so totally at
variance. We must suppose that the coercive power of thin
magnets is greater than that of thick ones, which, to say the

464 Prof. W. Beetz on the Molecular Changes

least, is very improbable. On the hypothesis of moveable par-
ticles, however, this difficulty entirely disappears, since the very
natural supposition, that the particles of the magnet are at un-
equal distances from each other, completely explains the observed
differences between different magnets. From the same supposi-
tion it follows, moreover, that there never can be a magnet com-
pletely saturated with temporary magnetism. The most power-
ful magnetizing currents will never be able to bring the axes of
the particles into perfect parallelism with each other. The posi-
tion of the axis of each particle will depend on the resultant of
the force of the current and the forces exerted on it by the
neighbouring molecular magnets ; so that, as the strength of the
current increases, the temporary magnetism approaches asympto-
tically to a limit. It is sufficient to refer to W. Weber's* re-

searches on the magnitude of the ratio — and the accompanying

graphic delineation of his results, to be convinced of the truth
of this fact.

Additional vouchers for the truth of the hypothesis of rotatory
particles are furnished by the phsenomena which accompany the
reversal of the poles of a magnet. From a series of experiments
in which a hard steel bar is magnetized by rubbing it with a
magnet first in one direction and then in the other, Suchelett
came to the conclusion, that the primary magnetism is the
strongest; that by reversing the poles the magnetic power is
diminished, and, moreover, that it continues to diminish for
every subsequent change that may be made, but only to a fixed
limit. Moser J, in communicating these experiments, adds the
remark, " It is very natural that the reversal of the original
polarity of a magnet should weaken its intensity, as in fact it is
known to do, since, owing to the coercive power of the bar, a
residuum of its original polarity is always left behind ; but that
the same diminution of intensity should accompany subsequent
reversals of polarity does not admit of the same explanation, and
is therefore, at first sight, very remarkable."

To this observation, which relates only to the permanent
magnetism of a steel bar, may be added another, which is just
as little explicable on the hypothesis of magnetism consisting of
a separation of magnetic fluids. Wiedemann § found that a steel
bar, magnetized by means of a current of intensity I, and after-
wards unmagnetized by a weaker current of intensity — I, can-
not be further magnetized in the opposite direction by the latter
current. Now the hypothesis of the separation of magnetic fluids
* Op. cit. p. 569 et seq.

t Ann. de Chimie et de Physique, vol. liii. p. 248.
£ X Dove's Repertorium der Physik, vol. ii. p. 140. § Op. cit. p. 173.

produced by Magnetization. 465

would certainly suppose that when, from any cause, the two
magnetisms had neutralized each other, the further effect of the
current —I would be to induce a new and contrary separation
of the fluids.

A comparison between the effects of alternate magnetization
on ordinary steel bars, and on magnets formed by electrolytic
precipitation, led me to the following results. With respect to
the temporary magnetism induced by means of magnetizing
currents, electrolytic magnets behave in general precisely the
same as ordinary steel bars.

Number of plate

7.

8.

9.

10.

11.

12.

Length in millimetres ...

72

72

33

31

40

25

Breadth in millimetres...

15

15

15

15

Weight in grammes

2-764

3-38

Specific gravity

6-81

6-73

Calculated thickness in \

thin
plate
+3-95

thin

plate

+ 8-52

| 0-82
+ 3-06

1-08

1-08

0-82

Original magnetism

+10-57

+ 7-73

+ 4-95

Strength of current

51-35

50-28

-71-47

-15-32

50-04

62-31

Temporary magnetism ...

4-72

12-84

-30-13

-24-38

-33-72

26-22

-2-30

- 8-79

-25-05

-13-94

-25-20

-2028

+ 4-30

+ 12-25

+29-00

+22-44

+33-02

+25-63

-2-35

- 8-72

-25-01

-1406

-25-12

-19-88

-f-4-13

+ 12-15

+28-24

after 25
changes
+22-01

+32-82

+25-60

-2-23
+4 07

- 8-80

+ 11-95

8-81

-24-94

after 20
changes

— 19-87

+ 11-70
— 8*91

-14-43

+31-23

+21-87

-24-80

-14-51

+21-20

Plates 11 and 10, and plates 12 and 9, had been originally
united, but had been broken apart on removing them from the
deposit-plates.

For the sake of comparison, I subjoin a similar Table of the
results observed on the magnetization and demagnetization of
three bars of hard steel.

1.

2.

3.

Strength of current

16-38

51-34

15-48

Temporary magnetism

+23-40

+24-11

+21-44

-15-45

-20-49

-13-13

+ 19*95

+22-41

+ 18-08

-14-90

-19-40

-13-10

+ 15-83

+21-80

+17-74

-14-78

-19-10

-12-96

The succession of the numbers, in columns 9 and 11, is pre-
cisely the same as that exhibited by the steel bar. In the ma-
jority of my experiments, I found that the magnetism in the
original direction continually diminished, as was the case like..

466

Prof. W. Beetz on the Molecular Changes

wise, though in less degree, with the magnetism in the opposite
direction. Neither in the case of the electrolytic magnets, nor
in the case of the steel bars, was the magnetism induced by the
stream —I ever equal to that induced by the stream +1: the
difference between the two kinds of magnets is in this respect
only quantitative ; but in the case of electrolytic magnets, the
difference between the magnetisms induced by the — m and +m
currents is always greater than in the case of steel bars. The
former may be compared with steel bars which have been first
magnetized by a powerful current, and have been alternately de-
magnetized and remagnetized by a weaker one. In divisions
7, 8, and 10, there are small deviations from the general course,
to which we shall refer hereafter.

With regard to permanent magnetism, the electrolytic magnets
behave quite differently from ordinary steel-bar magnets. If a
steel bar is magnetized alternately in one direction and the
other, the positive as well as the negative magnetisms continually
decrease, so that the two extremes lie between continually
narrowing limits, which is exactly what Wiedemann found to be
the case with respect to the magnetic maxima and minima of a
steel bar which had been magnetized by a current I, and de-
magnetized by a lesser current —I.

If the magnetizing currents are weak, the positive values re-
main always much greater than the negative ; the stronger the
currents the more nearly the positive and negative values ap-
proximate to each other ; and in the case of currents which are
capable of almost completely saturating the bar, each positive
value lies between two negatives. This is shown in the following
Table :—

Strength of current

1286

29-11

47-11

57-81

Permanent magnetism

+ 5-80

+ 711

+ 9-10

+ 14-46

- 018

- 0-91

- 7-16

-11-60

+ 3-60

+ 5-91

+ 6 96

+ 11-43

- 0-12

- 0-66

- 6-64

-1119

+ 3-52

+ 5-90

+ 10-11

- 0-09

-1009

after 100 changes:

+ 9-03
- 8-54

after 100 changes:

+ 8-53

1

- 8-43

On the other hand, the negative magnetism of electrolytic
magnets is always less than the positive, even when they are
subjected to the influence of the most powerful currents, which
would have completely saturated steel bars of the same dimen-
sions. The plates from which the following measurements have
been derived were those already described, with the addition of
No. 13, of which the length was 42 millims. ; breadth, 15 mil-

produced by Magnetization*

467

lims. ; weight, 5*17 grms. ; specific gravity, 6*54 ; and thickness,
1*24 millim.

7.

8.

9.

10.

11.

12.

13.

Original magnetism ...

+3-95

+8-52

+3-06

+ 10-57

+ 7-73

+4-95

-12-12

Strength of current . . .

51-35

50-28

71-47

15-32

50-04

62-31

69'23

Permanent magnetism

+3*95

+8-89

+5-26

+10-87

+ 9-23

+ 7-21

+20-11

-1-60

-7-36

-4-10

- 2-41

- 5-97

-4-81

-14-86

+3-34

+8-54

+4-91

+ 8-70

+ 9-04

+ 7-19

+ 16-54

-1-62

-7-30

-3-76

- 2-32

- 5-93

-4-79

-14-29

+3-37

+8-40

+4-70

after 25
changes
+ 8-19

+ 7-73
- 2-25

+ 9-02

+7-07

+ 15-89

-1-70
+3-20

-7-48
+8-30
-7-52
+8-12
-7-60

-3-72

after 20
changes
+ 8-34
- 5-91

-4-63

-14-01
+ 13-79
-15-57

+ 7-65

In none of these sets of experiments is there any such equali-
zation of the positive and negative magnetisms as is effected by
powerful currents in the case of steel bars, although, in fact,
very powerful currents were applied to some of these electrolytic
magnets. The currents employed in 9, 12, and 13 were excited
by a six-celled Grove's battery. Divisions 7, 8, and 9 exhibit
the same irregularity as occurred with respect to temporary
magnetism ; the values of the negative magnetism rose slightly
instead of falling.

Plates 7 and 8 were very thin, and therefore very perfectly
magnetized. The current which acted on 10 was very weak. If
the entire magnet be again supposed to be made up of a num-
ber of molecular magnets, whose axes are at first, for the most
part, parallel to each other, and in the same direction as the poles
of the entire magnet, then every force which tends to reverse the
polarity of the entire magnet will have to turn these axes out of
their original positions. A weak current only effects this by
repeated efforts (as in experiment 1 0) ; and any force succeeds in
it with more difficulty in proportion as the angle at which it
acts on the axes is more acute — that is to say, the more nearly
the axes of the molecular magnets are parallel to the geometrical
axis of the entire magnet (as in experiments 7 and 8). If, how-
ever, the current is strong and the axes of the particles deviate
far from parallelism, as is the case in thick plates, then the cur-
rent at once succeeds in producing a maximum effect.

Repeated changes of polarity must, however, in general increase
the mobility of the particles, and therefore diminish their per-
manent magnetism, that is to say, their tendency to assume a
particular position on the cessation of the magnetizing current,
whence the general approximation of the positive and negative
magnetisms to equality. It is clear that all these changes must

468 On the Molecular Changes produced by Magnetization.

also exhibit themselves in values of the temporary magnetism.
Steel magnets can only behave in the same way as these elec-
trolytic plates when the force by which they were originally
magnetized was greater than that subsequently employed to
change their polarity. If, on the other hand, the latter force is
the greater, steel bars behave, as Wiedemann has shown, as if
freshly magnetized.

For the sake of comparison, I made some experiments in
which the polarity of an electrolytic magnet was repeatedly re-
versed by rubbing with another magnet. The results were not
in this case so uniform, but nevertheless they clearly proved
that an electrolytic magnet, even when rubbed with the pole of
a powerful permanent magnet, behaves precisely in the same
way as a steel bar when rubbed with the pole of a magnet less
powerful than that by which it had been originally magnetized.
Even thickish plates were generally weakened by the first stroke,
which magnetized them in the direction of their original mag-
netism ; and after repeated changes they exhibited an increase in
the amount of negative magnetism, precisely as in the experi-
ments with magnetizing currents.

Plate 14. Length, 48 millims. ; breadth, 30 millims. ; weight,
16*42 grms. ; specific gravity, 6*12; consequent thickness, 17
millim.

Plate 15. Length 65 millims. ; breadth, 10 millims.

14.

15.

+ 1350

25 lbs.

+ 11-86

- 7-75
+ 11-41

- 9-68
+ 10-85

- 9-64
+ 9-61

+ 19-10
50 lbs.
+ 18-84
-1815
+ 18-70
-18-48
+ 18-52

Attractive power of magnet

On reversing the polarity

This manner of conducting the experiment admits, however,
of very little precision, partly because it is impossible entirely
to avoid shaking the plate, partly because it is uncertain whether
the axis of the magnet which is being rubbed remains always
the same.

The hypothesis of a separation of magnetic fluids consequent
on magetization is altogether insufficient to explain the foregoing
results. According to that hypothesis, it is impossible to con-
ceive that when an iron bar has been deprived of its magnetism,
it should behave differently when exposed to those influences
which tend to magnetize it again in the same way as at first, from

Royal Society, 469

what it does when exposed to those which tend to magnetize it
in the opposite direction. An electrolytic magnet, however,
always retains a preference for magnetism similar to that origi-
nally impressed upon it, though this preference is not always
equally strong. On the hypothesis of rotatory particles, this is
precisely what might have been expected.
Erlangen, July 1860.

LXIV. Proceedings of Learned Societies.

ROYAL SOCIETY.

[Continued from p. 400.]

March 8, 1860. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.

THE following communication was read : —
"On the Solar-diurnal Variation of the Magnetic Declination
at Pekin." By Major-General Edward Sabine, R.A., Treas. and
V.P.R.S.

When the first year of hourly observations of the declination,
January 1 to December 31st, 1841, was received at Woolwich from
the Magnetic Observatory at Hobarton, and when means had been
taken of the readings of the collimator-scale at the several hours in
each month, and these monthly means had been collected into an-
nual means, it was found that the mean daily motion of the declina-
tion magnet at Hobarton presented, as one of its most conspicuous
and well-marked features, a double progression in the twenty-four
hours, moving twice from west to east, and twice from east to west ;
the phases of this diurnal variation were, that the north end of the
magnet moved progressively from west to east in the hours of the
forenoon, and from east to west in the hours of the afternoon ; and
again from west to east during the early hours of the night, return-
ing from east to west during the later hours of the night : the two
easterly extremes were attained at nearly homonymous hours of the
day and night, as were also the two westerly extremes ; the ampli-
tudes of the arcs traversed during the hours of the day were con-
siderably greater than those traversed during the hours of the night.

When, in like manner, the first year of hourly observations, July
1st, 1842, to June 30th, 1843, was received from the Toronto Ob-
servatory, and the mean diurnal march of the declination magnet
was examined, it was found to exhibit phenomena in striking corre-
spondence with those at Hobarton. At Toronto also a double pro-
gression presented itself, of which the easterly extremes were attained
at nearly homonymous hours, as were also the westerly ; whilst the
hours of extreme elongation were nearly the same (solar) hours at
the two stations, but with this distinction, that the hours at which
the north end of the magnet reached its extreme easterly elongation
at Hobarton were the same, or nearly the same, as those at which it
reached its extreme westerly elongation at Toronto, and vice versa.
Pursuing, therefore, the ordinary mode of designating the direction
of the declination by the north end of the magnet in the southern
as well as in the northern hemisphere, the diurnal motion of the
magnet may be said to be in opposite directions at Hobarton and

470 Royal Society : —

Toronto ; but if (in correspondence with our mode of speaking in
regard to another magnetic element, the Inclination) the south end
of the magnet is employed to designate the direction of the motion
in the southern hemisphere, and the north end in the northern
hemisphere, the apparent contrariety disappears, and the directions,
as well as the times of the turning hours, are approximately the
same at both stations.

The double progression in the diurnal variation, which was thus
so distinctly and concurrently marked at stations so distant from
each other, and at which the observations had been conducted with
an elaborate care which would admit of no doubt as to the depend-
ence to be placed on their general results, was at that time in great
measure an unexpected and even a startling phenomenon. In the
well-known description given by M. Arago (in the instructions drawn
up for the voyage of the 'Bonite' in 1836) of the general pheno-
mena of the diurnal variation in different parts of the globe, as then
known, they are represented as consisting of a single progression
only, with but one easterly and one westerly extreme, both occurring
during the hours of the day ; and no reference or allusion whatso-
ever is made to the existence of a double progression, or of a noc-
turnal interruption to the continuous motion in the one direction
between the two extremes*. That the diurnal motion must be a
consequence, in some way or other, of the sun's action, could not
be doubted, from the fact that the period in which the variation
takes place is a solar day ; and whilst the progression was regarded
as a single one in the twenty-four hours, it accorded sufficiently well
with the prevailing notion, that the magnetic variations were pro-
duced by variations of temperature, to meet the general view, not-
withstanding the grave doubts and dissents which from time to
time had been expressed by those who more closely examined the
phenomena of particular localities. As the existence of a well-
marked double progression at some stations on the globe could,
however, no longer be disputed, the difficulty which now presented
itself was to explain in what way this apparently double action of
the sun was produced.

On a careful examination of the diurnal motion of the declination
magnet on different days of the years referred to at the commence-
ment of this paper, it soon became obvious that, both at Hobarton
and Toronto, many days occurred in which the diurnal march was a
single progression, the nocturnal retrogression wholly disappearing ;
and that there were many more days in which this was more or less
approximately the case. It further appeared, on subsequently com-
paring the observations of the same years at both stations, that the
days most distinguished by a large and even sometimes an extrava-
gant interruption of the otherwise continuous single progression,
were generally the same days at both stations ; and by extending
the comparison to other though less complete series of observations

* From the omission on the part of M. Arago of any notice of a nocturnal
feature, it might perhaps be inferred that the diurnal variation at Paris is actually,
as described by him, a single progression: it seems very improbable, however,
that this should be the case, since the observations at Greenwich and Kew have
shown that the progression is double at those stations.

Solar-diurnal Variation of the Magnetic Declination atPekin. 471

in other parts of the glohe, these days were identified as those on
which magnetic storms had prevailed; viz. days which had been
distinguished by the occurrence of perturbations, often of very con-
siderable magnitude, affecting simultaneously the magnetic elements
in all parts of the globe as far as observation extended, presenting a
remarkable uniformity in the effects produced at contiguous stations,
but (as shown by the simultaneous observations at Toronto and
Hobarton) manifesting a great variety both in the character and the
amount of disturbance in parts of the globe distant from each
other. To separate the observations affected by these exceptional
and casual influences from the ordinary and what might be deemed
the normal position of the declination magnet, and to study the
laws of each taken separately, as well as in their combination, be-
came therefore a preliminary work to the right understanding of
either. That some such mode of examination would be required,
had indeed been anticipated in the instructions drawn up with so
much sagacity by the Committee of Physics of the Royal Society,
for the guidance of those who should engage in the direction of the
Colonial Magnetic Observatories then in contemplation. In the
preface to those instructions, it is expressly stated that " the pro-
gressive and periodical magnetic variations are so mixed up with the
transitory changes, that it will be impossible to separate them so as
to obtain a correct knowledge and analysis of the progressive and
periodical, without taking express account of and eliminating the
transitory or casual." The difficulties which impeded, and which
still impede an entire compliance with this instruction, viz. the per-
fect elimination of the transitory and casual changes, were found to
be very great. The direction which the magnet assumes when it is
under the influence of 'a perturbation of this nature, is not distin-
guishable from the direction assumed under the ordinary magnetic
influence, by any other criterion yet known than by the magnitude
of its deflection from the mean or normal position in the same
month and at the same hour ; the magnitude of the abnormal de-
flection may be thus taken, to a certain extent, as a means of recog-
nizing the existence of a perturbing force, and it is the only one we
possess. If we employ this criterion of magnitude as manifesting a
disturbed observation, and separate the observations so disturbed
from the others, we must still be aware that there may exist, and
that probably there do exist, amongst the body of observations from
which the large disturbances have been separated, some which may
be affected by the same disturbing cause or causes operating in a
minor degree ; and assuming the disturbances to have different
laws from the general body, the unseparated minor disturbances
may still impede the perfect deduction of the laws of the other class
with which they are so intermixed.

But though the criterion of magnitude may not enable us to effect
a complete separation of the two classes, it will suffice to accomplish
an approximation to that end ; it will separate a sufficient body of
disturbed observations, — disturbed beyond the limit of any other
known influential cause, — to permit the laws of the disturbing action
to be investigated ; and when these laws are known, we are furnished

472 Royal Society : —

with the means of making at least an approximate estimation of the
influence exercised hy the uneliminated minor disturbances on the
laws which we may proceed to deduce for the class of observa-
tions from which we have not been able to effect their perfect
separation.

Adopting this method of partially eliminating the influence of the
magnetic storms in the observations at Hobarton and Toronto, and
proceeding in the first instance with the caution suitable to a first
experiment, an unnecessarily high value (as it subsequently proved)
was taken as that which should distinguish a perturbed observation,
and consequently but a small body of disturbed observations was
separated. On a recalculation of the diurnal variation after the
elimination of these, and a comparison of the results with the diurnal
variation obtained previously from the whole of the observations, the
character of the influence of the magnetic storms was very manifest.
By the elimination of the larger disturbances, the interruption to a
continuous progression from the afternoon of the one day to the
morning of the following, was considerably diminished both in con-
tinuance and amount. A smaller separating value was then taken,
and consequently a larger body of disturbed observations was
eliminated ; the effect produced was a still further reduction of the
nocturnal feature. These first essays were sufficient to show that
the mean effects of the magnetic storms on the declination magnet,
both at Hobarton and at Toronto, attained a maximum in the early
hours of the night, and constituted at both stations a very con-
siderable part, if not the whole, of the nocturnal portion of the
double progression which has been described. By still further
diminishing the separating value, but still keeping it well within the
limits in which no complication of disturbing causes would be
hazarded, so little was found to remain of the nocturnal interruption,
that I ventured, in the 1st volume of the 'Toronto Observations,*
published in 1845, to express the opinion that "if the whole in-
fluence of the magnetic storms could be eliminated from the obser-
vations, the residual portion of the diurnal variation would be a
single progression with but one maximum and one minimum in the
twenty -four hours."

The peculiar character of the magnetic storms (or disturbances as
they are sometimes called), and the periodical laws exhibited in their
mean effects, have been the subject of frequent investigations since
1845. It is not necessary to notice on this occasion the results
of these further than as they are connected with the explanation of
the phenomena of the diurnal variation, which forms the subject
of this paper. It has been shown, by abundant evidence, that
though apparently casual in the times of their occurrence, the mag-
netic storms nevertheless produce mean effects, which, when the ob-
servations of more than a very few days are combined, are seen to be
of a highly systematic character in all parts of the globe where their
effects have been examined : — that the mean deflections which they
occasion have always their particular hours of extreme elongation,
with continuous intermediate progression : — that these hours are dif-
ferent in different parts of the globe, exhibiting apparently every

Solar- diurnal Variation of the Magnetic Declination at Pekin. 473

possible variety : — that the disturbance diurnal variation, as for di-
stinction's sake it may be called, constitutes everywhere a sensible
portion of the diurnal variation shown by the mean of the hourly
observations from which no elimination of disturbed observations has
been made : — that the diurnal variation so obtained is in fact a result-
ant of two diurnal variations superposed, both referable to the sun
as their primary cause, but manifesting by the difference in the cha-
racter of the effects produced, a distinction in the mode of operation
to which they are severally due. The disturbance variation is caused
by deflections which are only of occasional occurrence ; the more
regular solar-diurnal variation is distinguished, on the other hand,
by the regularity of its daily occurrence ; and its hours of extreme
elongation, or (as they may be more familiarly termed) its turning
hours are the same, or nearly the same hours of local solar time in all
parts of the globe, whilst those of the disturbance variation show
almost every possible variety. The relative magnitudes or proportions
of the two components differ also very greatly at different stations ;
and thus, by the operation of causes which as yet are but very im-
perfectly known, at localities where the magnetic storms are ex-
cessive, the disproportion of the components becomes excessive also,
and the phases of the regular variation are rendered altogether
subordinate to those of the disturbance variation. Until therefore
the extension of observations shall give rise to and establish some
general theory whereby the influence of the disturbances in different
parts of the globe may be predicated, their particular laws at every
station must be sought by a special investigation; and no con-
clusion in regard to either of the components of the diurnal variation
is entitled to be viewed as final which has not been preceded by
such an investigation.

It has appeared desirable to enter more at length into this pre-
liminary statement than may at first sight be thought to be required
by those who have followed the different stages of the inquiries re-
ferred to, because the interpretation, which was given so far back as
1845, of the diurnal variation at Toronto and Hobarton, has scarcely
received the consideration which might seem due to a laborious and
apparently successful analysis of the phenomena ; and there are some
eminent physicists who have framed or adopted theories for the ex-
planation of the diurnal variation, in which theories the existence of
a double progression as a universal and necessary phase is essentially
implied. Amongst these, the most prominent perhaps, and the one
which has obtained the widest circulation, is the theory of the
R. P. A. Secchi, Director of the Observatory of the Collegio Romano,
published originally in Italian in 1854 in the ' Correspondenza Sci-
entifica' in Rome, translated into English in the edition of 1857 of
the late Dr. NichoPs ' Cyclopaedia of the Physical Sciences/ and
more recently adopted in the third volume of M. de la Rive's ' Traite
d'ElectiiciteV In M. Secchi's memoir, the diurnal variation, with its
double movement in the day and night, is ascribed to the direct
action of the sun as a distant and powerful magnet, influencing the
magnetic needle at different stations on the globe in a manner con-

Phil Mag, S. 4. Vol. 20. No. 135. Dec. 1860. 2 I

474 Royal Society : —

tingent upon the direction of the magnetic meridian at each place,
and producing extreme deflections to the East and to the West twice
in the twenty-four hours, the turning hours being about six hours
apart, and stated to be appropriately represented by a formula of two
terms, one involving the sine of the hour-angle, and the other the
sine of twice that angle : the phenomena of the double progression
at Toronto and Hobarton are thus viewed by him as " Types of all
that happens beyond the limits of the torrid zone."

If I have represented M. Secchi's views correctly, and I think I
have done so, the question between the conformity to nature of his
views and mine would be tested by the facts (when they should be
known) of the diurnal variation at a station in the middle latitudes
where the principal influence of the magnetic storms should take
place, not in the hours of the night, but in those of the day.
According to my interpretation of the phenomena at Toronto and
Hobarton, such a station ought to exhibit a single progression ; ac-
cording to M. Secchi's, a double progression with turning hours
about six hours apart. Such a station would therefore furnish what
might be deemed a crucial experiment. In the extension of our ex-
perimental knowledge which might be expected to follow from the
adoption by Her Majesty's Government of the recommendations of
the Royal Society and of the British Association, which have been
communicated to Lord Palmerston with so much earnestness of pur-
pose, and with so just an appreciation of their importance, by His
Royal Highness the Prince Consort, as President of the British As-
sociation, it had been anticipated that it would not be long before
the evidence derivable from such a station would be secured to us.
I have found it, however, sooner than I had expected, or had hoped
for, in the three years and ten months of hourly observations of the
Declination at Pekin, from January 1, 1852, to October 31, 1855,
made under the superintendence of M. Scatchkoff, attached to the
Russian Embassy at Pekin, and published by our distinguished
foreign member, M. Kupffer, in the volumes of the 'Annales de
l'Observatoire Physique Central de Russie.' The results of these
observations, as far as they bear on the questions of the general phe-
nomena of the diurnal variation, and on the mode in which these
may be explained, form the subject of the present communication.

The examination of these observations was first undertaken by me
for the purpose of ascertaining, as far as possible by their means, the
precise epoch of minimum in the so-called decennial period of the
magnetic storms. "With this view a separation was made of the
larger disturbances in the usual manner, and their laws at Pekin in-
vestigated. In this process it was soon perceived that the hours of
principal disturbance were those of the day, both in the easterly and
in the westerly disturbance deflections ; and on subsequently receiving
from the computers the annual mean of the diurnal variation cor-
responding to the whole period of observation (in which the omission
of disturbed observations during the hours of the night had been com -
paratively very inconsiderable), I was not surprised to find that it exhi-
bited no trace of a double progression. The results were as follows : —

Solar -diurnal Variation of the Magnetic Declination at Pekin. 475

Local

Local

Local

Astron.

Variation.

Astron.

Variation.

Astron.

Variation.

Time.

Time.

Time.

h m

h m

h m

0 6

i-55 W.

8 6

6-19 W.

16 6

0-53 E.

1 6

2-26 W.

1 9 6

0-10 W.

17 6

0-57 E.

2 6

2-32 W.

j 10 6

000

18 6

0-94 E.

3 6

1-85 W.

! 11 6

0-15 E.

19 6

1-51 E.

4 6

1*21 W.

! 12 6

0-30 E.

20 6

2-06 E.

5 6

0-65 W.

13 6

0-45 E.

21 6

210 E.

6 6

0-29 W.

I 14 6

0-49 E.

22 6

1-24 E.

7 6

0-21 W.

15 6

0-52 E.

23 6

0-20 W.

If we examine these figures, we perceive that the motion from west
to east, commencing at the turning hour between 1 and 2 in the
afternoon, though comparatively slow during the hours of the night,
is continuous and uninterrupted until the extreme easterly elonga-
tion is reached between 8 or 9 in the following morning, and
that no other turning hours intervene between those of the extreme
easterly between 8 and 9 a.m. and the extreme westerly between
1 and 2 p.m.

The phases of the solar-diurnal variation, as they are shown by the
Pekin Observations, may be stated as follows : — The north end of the
magnet is at its extreme eastern elongation about half-past 8 in
the morning ; at this hour it begins to move to the west, and moves
rapidly in this part of its daily course, completing its whole move-
ment in that direction in five hours, and reaching its extreme western
elongation at about half-past 1 p.m. From this hour it returns,
somewhat less rapidly than in its forenoon excursion, until about
6* p.m., when the rate of progression is considerably lessened, but
continues in the same direction through the hours of the night, until
about 5 a.m., when it again accelerates until the eastern extreme
is attained, as already stated, about 8^ a.m. There is thus
a very unequal division of time in the direction of the motion,
which takes five hours in the progress from east to west, and
nineteen hours in returning from west to east through the same
arc. We find a more equal division of time if we regard the
greater or less rapidity of the motion : there are about twelve
hours in which the motion is comparatively quick, and twelve hours
in which it is comparatively slow ; the quick hours being those of
the day, the slow hours those of the night.

Thus far the notice we have taken of the Pekin results has been
limited to the diurnal variation which we find when we take an
average of the whole year, and which we may theoretically suppose
would take place in every month of the year if the sun were always
in the plane of the equator. But similar investigations had already
made known to us the existence of a semiannual inequality, having
opposite phases according as the sun has north or south declina-
tion; with turning epochs about the times of the solstices, and
the phases passing into each other about the times of the equinoxes.

212

476

Royal Society :■

I have already, on a former occasion (Proceedings of the Royal So-
ciety, May 18, 1854), submitted to the consideration of the Society
the concurrent evidence from three stations, Toronto, Hobarton, and
St. Helena, of the existence of this inequality, and of the almost
uniform character of its phases at those stations, from which I ven-
tured to infer the probability that an inequality having a similar cha-
racter would be found to be a general phenomenon. I am now
able to add to the evidence which was then adduced, a representation
of the semiannual inequality at three additional stations, viz. at the
Cape of Good Hope, of which the particulars in detail will be found
in the 2nd volume of the * St. Helena Observations,' — at the Kew Ob-
servatory, taken from the hourly tabulations from the photographic
curves obtained by the self-recording declinometer at that station, —
and at Pekin, as shown in the following tabular view : —

Semiannual Means of the Solar-diurnal Variation at Pekin.

Local

April

October

Local

April

October

Local

April

October

Astron-

to

to

Astron.

to

to

Astron.

to

to

Time.

Sept.

March.

Time.

Sept.

March.

Time.

Sept.

March.

h m

h m

002 E.

h m

0 6

234 W.

076 W.

8 6

6-40 W.

16 6

6-84 E.

6-21 E.

1 6

3 09 W.

1 44 W.

9 6

0-29 W.

009 E.

17 6

115 E.

000

2 6

3-06 W.

1-58 W.

10 6

0-26 W.

0-26 E.

18 6

207 E.

019 W.

3 6

2 53 W.

118W.

11 6

008 W.

0-39 E.

19 6

3 04 E.

002 W.

4 6

179 W.

0-64 W-

12 6

013 E.

0-46 E.

20 6

3-46 E.

0-66 E.

5 6

102 W.

0-27 W.

13 6

0-43 E.

0 47 E.

21 6

2-80 E.

1-40 E.

6 6

0-43 W.

0-16 W.

14 6

0-63 E.

0 36 E.

22 6

115 E.

1-33 E.

7 6

0 34 W.

008 W.

15 6

073 E.

0 31 E.

23 6

076 W.

0 36 E.

As the correspondence of such phenomena is often far better
judged of by the eye, when exhibited in the form of curves, than by
the comparison of tables, I have exhibited in a diagram the phases of
the semiannual inequality at the six stations, by which it will be seen
that they add their confirmation to the inference which I had previ-
ously drawn. With this additional evidence of its uniform character
in different parts of the globe, it may be hoped that the claim of the
semiannual inequality to be received as a successful generalization
from a careful and comprehensive induction may be admitted, and
that as an accession to our positive knowledge it may have a recognized
place amongst the facts of the diurnal variation, which have to be ac-
counted for in the theories which may be hereafter adduced for their
physical explanation.

We now, therefore, recognize three classes of phenomena derived
from three different sources, which are superposed in the diurnal va-
riation obtained from the unreduced observations, and which for a
proper understanding of the whole, require to be separated from each
other by a proper analysis, so that the part due to each may be di-
stinctly ascertained : these are — 1st, the mean effects of the magnetic
storms ; 2nd, the semiannual inequality of the regular solar-diurnal
variation ; and 3rd, the mean solar-diurnal variation of the year

Solar -diurnal Variation of the Magnetic Declination at Pekin. 477

into which the semiannual differences merge. The distinctive
characteristics of the first, viz. the disturbance diurnal variation,
have already been stated in the early part of this paper, together
with the evidence they supply of being due to some modification
of the solar action, — justifying their being treated as distinct and
separate from the affections which constitute the more regular
variation. There are also distinctive characters in the pheno-
mena of the semiannual inequality, and in those of the mean va-
riation, which appear to point out a difference in the mode in which
the primary cause operates in producing the two classes of pheno-
mena. For the purpose of explaining this difference, we may em-
ploy, as more likely to be generally understood, the usual custom of
referring all deflections, whether in the northern or the southern
hemisphere, to the north end of the magnet ; we say then that, in
the mean variation, the directions of the deflection are uniform
throughout the year in the middle latitudes of the one hemisphere,
and (although opposite) are also uniform throughout the year in the
middle latitudes of the other hemisphere ; whilst in the semiannual
inequality, the directions of the deflection are uniform in the two
hemispheres, but opposite in the two half years. In the one case
the effects are hemispherical, in the other semiannual. It is this pe-
culiarity which gives to the M April to September " branch of the
semiannual inequality its analogy with the diurnal variation which
prevails throughout the year in the middle latitudes of the northern
hemisphere, and to the "October to March " branch its analogy
with the diurnal variation which prevails throughout the year in the
middle latitudes of the southern hemisphere. The analogies extend
even to the small but apparently systematic difference which exists
between the turning hours of the mean variation in the two hemi-
spheres, and of the semiannual variation in the two half years. The
turning hours of the variation in the northern hemisphere, and of the
" April to September " semiannual branch, appear to occur system-
atically about an hour earlier than those of the southern hemisphere,
and of the "October to March" semiannual branch. This is a
connecting link which draws still nearer the analogies of which the
broader features have been frequently noticed and commented upon ;
and is the more remarkable on account of the diversity which in other
respects seems to distinguish the mode of operation by which the
solar influence produces in the one case hemispherical difference with
annual agreement, and in the other case semiannual difference with
hemispherical agreement.

Thus at Pekin, regarded as a station in the middle latitudes of the
northern hemisphere, if we view the semiannual mean of the six
months from April to September, we see repeated the general fea-
tures of the annual mean, reinforced by the semiannual inequality of
kindred character with itself; the deflections of both having the
same direction at the same hours, the range becomes enlarged, but
its characteristics are unchanged ; the progression is still a single one,
as is the case in the annual mean, with but one easterly and one
westerly extreme, the hours of which are slightly earlier than those

478 Royal Society : —

Solar-diurnal Variation of the Magnetic Declination. — Semiannual Inequality.

The Black line indicates the Mean Solar-diurnal Variation in the year.
The Broken line indicates Semiannual Means, October to March.
The fine dotted line indicates Semiannual Means, April to September.

Astronomical Hours.

12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12

_-_j 1 . l 1 1 1 I 1 1 1 1 1 1 « 1 1 1 « 1 1 « 1

Astronomical Hours.

Solar-diurnal Variation of the Magnetic Declination at Pekin. 479

of the annual mean, by reason of a particular feature of the semi-
annual inequality spoken of above. When, on the other hand, we
direct our attention to the semiannual mean from October to March,
we see the consequence of the superposition upon the annual mean
of the opposite semiannual inequality belonging to these months :
this is most particularly shown in the effect produced upon the semi-
annual mean by the great semiannual loop which culminates about
6 or 7 a.m. This deflection, which is opposite in direction to that
appropriate to the hemisphere, prevails over it so far as to interrupt
the progression, which on the mean of the year is continuous, and to
produce a secondary maximum at about 7 a.m. This opposite de-
flection to that which is normal in the hemisphere, taking place at
the hours when the semiannual inequality is greatest, is a common
feature whenever, in the middle latitudes of either hemisphere, the
mean diurnal variation of the one hemisphere is combined with the
semiannual inequality which has the opposite analogy. The hour
of principal discordance between them is always nearly the same,
being determined by that of the principal deflection on the semiannual
curve, which, as seen in the diagram, is nearly identical in solar time
in all parts of the globe. In the semiannual mean from October to
March the principal turning hours are a little later than in the an-
nual mean, just as we have seen above that, in the April to September
mean, the turning hours are a little earlier than in the annual, and
for the same reason. Finally, it is this combination of the hemi-
spherical and semiannual effects which creates the differences we ob-
serve in the amount and hours of the solar- diurnal variation in the
different months in the middle latitudes of both hemispheres.

There is one more feature of some importance to the general
theory of the diurnal variation, which is illustrated by the Pekin obser-
vations, and requires a brief notice. A distinction has been elsewhere
pointed out (Cosmos, English Translation, Longman's Edition, vol.
iv. p. 504, Editor's Note) between the diurnal variation of the equa-
torial zone and that of the middle latitudes, consisting in the circum-
stance that in the equatorial zone the amount of the semiannual de-
flection is greater than that of the hemispherical deflection at the
hours when they are opposed to each other, and by its preponderance
changes the character, instead of simply diminishing the amount,
of the hemispherical deflection. The change in the signs of the de-
flection at 6 and 7 a.m. in the semiannual mean from October to
March at Pekin is an illustration of this peculiarity, and ought
perhaps in strictness to cause Pekin to be included in the magne-
tically equatorial zone ; but being only just within the border, it has
been found more convenient to dwell on this occasion upon the fea-
tures which it has in common with stations in the middle latitudes.

The diurnal variation at Pekin reaches its extreme deflections at
the same hours of solar time, as is the case at the other stations in
the northern hemisphere where the phenomena have been examined
with equal care. This fact is not in accord with the opinions of those
physicists who regard the solar action as conditioned in its exercise
by the direction of the magnetic meridian at the particular station.

480 Royal Society :—

In the different stations in the northern hemisphere, where the ex-
treme deflections have been found to take place at the same hours of
solar time, the differences in the direction of the magnetic meridian
have not been less than 70°, equivalent to a difference of solar time
of between four and five hours.

I ought not to close this paper without adverting to the success
which has attended Mr. ScatchkofFs employment of native Chinese
as his assistants in the work of the Pekin Observatory, holding out
as it does an encouraging example to Directors of Observatories who
may be similarly circumstanced. A very close test of the care and
fidelity with which observations have been made and recorded is fur-
nished by the lunar-diurnal variation, deducible from them when they
have been re-arranged under the lunar hours to which they severally
belong. Thus tested, the Pekin observations show no inferiority to
those of other stations which have been similarly examined.

It is understood that the observations, which were discontinued at
Pekin at the end of 1855, are about to be recommenced, or have been
so already. It is greatly to be desired that hourly obervations of
the Horizontal and Vertical Forces should be combined with those
of the Declination at this important station. The self-recording ap-
paratus of the three elements which has been in action at Kew during
the last two years, has been found, by the reduction of its tabulated
values at hourly intervals, to be in no respect practically inferior to
the method of eye-observation, whilst it possesses many advantages
which are peculiarly its own. The tabulation from the Photographic
Curves, as well as the reductions, might be made, if more convenient,
at the central Physical Observatory at St. Petersburgh.

March 15. — Sir Benjamin C. Brodie, Bart., President, in the Chair.

The following communication was read : —

" Analysis of my Sight, with a view to ascertain the focal power
of my eyes for horizontal and for vertical rays, and to determine
whether they possess a power of adjustment for different distances."
By T. Wharton Jones, Esq., F.R.S. &c.

Besides the well-known differences of sight in respect to farness
and nearness, there are differences in respect to the power of the
eyes of different persons to bring the rays of light to one exact focus.

From observations and experiments in which I have for some time
been engaged, I have been led to suspect that astigmatism or inca-
pacity of the eye to collect all the rays of light which enter it to
one exact focus, is, if not the rule of sight, at least of very common
occurrence. I do not here refer to the cases in which astigmatism is
of so exaggerated a character as to be a positive defect of sight.

It would be of great importance, both in a scientific and practical
point of view, to possess some accurate data as to the frequency of
the occurrence of astigmatism ; but such can be obtained only by a
number of different persons — qualified observers — contributing each
an analysis of his own sight. I have thought, therefore, that by
bringing under the notice of the Royal Society an analysis of my own
sight, some of the Fellows and others accustomed to exact observations

On the Focal Power of Eyes for Horizontal and Vertical Rays. 481

might, perhaps, be induced to make similar contributions. The
adjustment of the eyes for different distances being intimately con-
nected with the question of stigmatism or astigmatism, I have included
it in my analysis.

If I view a vertical and
horizontal line, both equally
strong and black, I see them
with medium distinctness at
the distance of about 10
inches.

At the distance of about
3|- inches, I see the vertical
line with greater distinctness
and better definition — the
greatest distinctness and best
definition my eyes are ca-
pable of ; but the horizontal
line I see indistinctly — with
much less distinctness than
that with which I see any part of the figure at the distance
of 10 inches. At the distance of 12 inches, I see the horizontal
line with the greatest distinctness and best definition my eyes
are capable of; but the vertical line I see indistinctly — with much
less distinctness than that with which I see any part of the figure at
the distance of 10 inches. It thus appears that my eyes collect to a
focus on the retina the rays which diverge horizontally at the distance
of 8 J inches ; and the rays which diverge vertically at the distance of
12 inches. Whilst seeing the vertical line with perfect distinctness
and definition afr the distance of 8J inches, I cannot alter the adjust-
ment of the eye so as to see the horizontal line more distinctly and
the vertical one less distinctly ; and vice versa, whilst seeing the
horizontal line perfectly defined at the distance of 1 2 inches, I can-
not alter the adjustment of the eye so as to see the vertical line
more distinctly and the horizontal one less.

In short, I find that I have no power of altering the adjustment of
my eyes. I see vertical lines with perfect distinctness and definition
only at the distance of 8| inches, and horizontal lines with perfect
distinctness and definition only at the distance of 12 inches, and both
vertical and horizontal lines simultaneously with medium distinctness
only at the distance of 10 inches.

At the distance of about 7 inches I see the vertical line with medium
distinctness, but the horizontal line very indistinctly.

At the distance of about 14 inches I see the horizontal line with
medium distinctness, but the vertical line very indistinctly.

At a nearer distance than 7 inches I see both lines indistinctly, but
the vertical less so than the horizontal. At a further distance than 14
inches, on the other hand, I see both lines indistinctly, but the hori-
zontal less so than the vertical.

If now I view two oblique lines, both of which are equally strong
and black, I see both legs with medium distinctness at the distance of
10 inches.

482 Royal Society.

At the distance of about
S\ inches I see the two
oblique lines equally well,
but not so distinctly as at
the distance of 10 inches.

At the distance of 12
inches I see the two oblique
lines with much about the
same distinctness as that
with which I see them at
the distance of 8£ inches.

It thus appears that I
cannot see either of the
oblique lines with perfect
distinctness and definition
at any distance ; but that
I can see them both simultaneously distinctly enough at any di-
stance from 8^ inches to 12. At a nearer distance than 8| inches,
or a further distance than 1 2 inches, the distinctness diminishes, and
that equally for the two lines.

I cannot by any adjustment of my eyes vary the distinctness with
which I see the oblique lines at a given distance.

The preceding analysis of my sight shows that my eyes are not
monostiymatic, that is, are not capable of collecting all the rays of
light which enter them to one exact focus. It shows, on the contrary,
that my eyes are distiymatic, that is, they have each two distinct
foci to which they bring the rays, viz. one focus for horizontal rays,
and one for vertical rays.

The preceding analysis also shows that my eyes do not ppssess any
intrinsic power of adjustment whereby they can bring to foci rays
diverging from a nearer or further distance than the two distances
above specified for horizontal and for vertical rays.

It is true that I can see the different objects in a room distinctly
enough without the aid of glasses, and that in the street or open
country I can see objects distinctly enough for all practical purposes
with the aid of concave glasses Nos. 2 and 3, but, critically speaking,
the definition is far from being exact.

Directing my eye to an object 2 or 3 feet from me, I see it
distinctly enough whilst an object in the same field of view at the
distance of 1 0 or 1 2 feet is at the same moment seen very indistinctly.
If now, I direct my eye to the object at the distance of 10 or 12 feet,
I see it distinctly enough, but the object at the distance of 2 or
3 feet now appears very indistinct.

This is commonly considered an evidence of adjustment of the eye
to the two different distances. There is, however, no real intrinsic
adjustment in the case. I see distinctly enough, either the nearer
or the more distant object, merely because by directing my eye to
it, its image falls on the central and most sensitive part of the retina,
whilst the image of the other object falls on the circumferential and
least sensitive part of the retina.

It is to be observed that at neither the nearer nor the further

Geological Society, 483

distance, do I see the object exactly defined on directing my eye to
it. On directing my eye to the further object, I see it, of course,
less defined than I do the nearer object when I direct my eye to it ;
but the difference is not at a glance very striking.

This experiment must not be confounded with another adduced
by the late Professor Miiller as a proof of the existence of an adjusting
power in the eye. The experiment T refer to is as follows : —

If we regard with one eye only (the other being closed) the ends
of two pins placed one before the other at different distances in the
line of the axis of the eye, one will be seen distinctly when the other
appears indistinct, and vice versd. Both images lie in the axis of the
eye, one over the other ; and yet it depends on a voluntary effort,
the exertion of which can be felt in the eye, whether the first or the
second pin shall be seen distinctly. " The two images of the pins,"
says Miiller, " fall upon the same point of the retina; one lies over the
other, and yet I see the nearer through the cloud-like image formed
by the rays from the other more distant pin, and vice versd."

If any person is able to see the phenomena here described, he is
undoubtedly endowed with an adjusting power in his eye.

I have never succeeded in seeing the phenomena myself.

In viewing objects at different distances, the sight is no doubt
aided by the movements of the eyebrows, eyelids, eyeballs, and pupils ;
but in this we have no example of adjustment properly so called,
viz. intrinsic adjustment.

That the focal power of my eye may become slowly altered, for
instance by prolonged examination of near and minute objects, and
again slowly return to its former state, I am satisfied ; but this, again,
is no example of adjustment properly so called.

P.S. It would oblige me very much, if any one into whose hands
this paper may happen to fall, and who may take the trouble to
analyse his sight in the manner herein described, would communi-
cate to me the results of his observation on the following points : —

1. The distance at which the vertical line is seen with the greatest
distinctness and best definition.

2. The distance at which the horizontal line is seen with the greatest
distinctness and best definition. — Or,

3. If there be no difference in the distance at which the vertical
and horizontal lines are seen with the greatest distinctness and best
definition. — And, lastly,

4. Whether or not the observer can satisfy himself that he has
the power of adjusting the eye, so as to be able to see the lines with
perfect distinctness and definition at any other than one distance.

N.B. If spectacles are worn, mention the kind of glasses — whether
convex or concave — and their power.

Note also if there be any difference in the sight of the two eyes.

GEOLOGICAL SOCIETY.
[Continued from p. 401.]
November 7, 1860. — L. Horner, Esq., President, in the Chair.
The following communications were read : —
1. "On the Denudation of Soft Strata." By the Rev. O. Fisher,
M.A., F.G.S.

484 Geological Society : —

The author first described the general features of the north-
eastern portion of Essex, with its table-lands of gravel, clay valleys,
and tidal rivers. The present configuration of the district cannot be
due, in the author's opinion, to the action of such causes as we see
now in operation on the coast, combined with a slow elevation of the
land. As a rule, the sea-waves cannot excavate long narrow inlets
in horizontal and homogeneous beds, such as the gravel and clay of
the district under notice, but give rise to long, approximately straight
lines of cliff. The rounded sides of the Essex valleys seem to show
they were not formed by wave-action ; nor are there any evidences
of shingle-beds at the foot of the hills. Mr. Fisher believes that
the surface of this district, and that of many other districts composed
of yielding strata, must have been formed by a superincumbent
mass of water draining off from a flat or slightly dome-shaped area.
Slight depressions, cracks, or lines of readily yielding materials would
determine the drainage-streams as the water retreated ; and these
channels would be more or less scoured out according to the velo-
city of the water. Where the gravel covering of such a district was
cut through, the clay beneath would be channelled with a narrower
valley ; and where the gravel was wholly removed, the valleys would
be wider and the intermediate high ground rounded instead of being
flat-topped, just as is presented in those parts of the district where
the clay composes the surface. Similar appearances may be seen
on a small scale in the mud of a tidal river. Tidal action, however,
is not, according to the author, calculated to excavate narrow valleys
in horizontal beds.

Mr. Fisher suggests that the land must have been elevated by a
sudden movement sufficient to have caused a rush of water from the
raised portions to seek a lower level, — either the land being raised
high and dry at once, or the sea-bottom raised to a higher level,
though still remaining beneath water. Such an elevation might be
repeated again and again, with intervals of submergence ; and such
conditions appear to have obtained in Norfolk as well as in Essex.

The author states that, in his opinion, escarpments, such as are so
common among the secondary and tertiary beds, are rarely old cliffs,
and their often rounded forms must be due to agencies similar to
those which have produced the valleys of Essex. In some deep
gorges of the Chalk near Dorchester the author has seen flints and
great blocks of Tertiary puddingstone so arranged as to leave little
doubt of their having been left by violent currents of water. The
position of the Marlborough " Wethers " is also attributed by the
author to torrential action.

Brick-earth is in part referred by Mr. Fisher to the deposition of
sediment from turbid waters ; but also in great part to the unlading
of icebergs.

With regard to the manner in which the uprising of the land,
which brought about these aqueous cataclysms, has been effected —
whether by one slow and continued movement, or by one or more
sudden movements, or by a mixed succession of these, the author
argued that a slow and gradual elevation is not in accordance with
the contour of the existing surface of our softer strata ; that the ele-

On a Fossil Fern from the Lower Coal-measures of Nova Scotia. 485

vation of the land previous to the period of the great-mammalian
fauna, when its present contour was mainly given, was not gradual ;
and that, after subsequent depressions, there have been sudden eleva-
tions since that period.

Lastly, it was pointed out that sudden vertical movements of the
surface on a grand scale are of as probable occurrence as those
lesser movements with which we are historically acquainted, be-
cause, both in the case of strata previously unbroken and in that of
strata once faulted but at rest, the pressure requisite to rupture or
to fold them will accumulate enormously before they yield to it,
when, after some slight slow and gradual movements, they will be
thrown up or down with a sudden movement, with or without
flexures, as the case may be. Thus, by mechanical considerations,
the author is led to believe that the ordinary nature of movements
of the earth's crust must be sudden.

2. " On an undescribed Fossil Fern from the Lower Coal-measures
of Nova Scotia." By Dr. J. W. Dawson, F.G.S.

In a paper on the Lower Carboniferous rocks of British America,
published in the 15th volume of the Geological Society's Journal,
Dr. Dawson noticed some fragmentary plant -remains which he re-
ferred with some doubt, the one to Schizopteris (Brongn.), and the
other to Sphcereda (L. and EL). With these were also fragments
of a fern resembling Sphenopteris (Cyclopteris) adiantoides of Lindley
and Hutton. Since 1858 the author has received a large series of
better-preserved specimens from Mr. C. F. Hartt ; and from these he
finds that what he doubtfully termed the frond of Schizopteris is a
flattened stipe, and that the leaflets which he referred to Sphenopteris
adiantoides really belonged to the same plant. Mr. Hartt's speci-
mens also show that what Dr. Dawson thought to be Sph&reda were
attached to the subdivisions of these stipes, and are the remains of
fertile pinnae, borne on the lower part of the stipe, as in some modern
ferns. This structure is something like what obtains in the Cuban
Aneimia adiantifolia, as pointed out to the author by Prof. Eaton,
of Yale College. No sporangia are seen in the fossil specimens.

Dr. Dawson offers some remarks on the difficulties of arranging
this fern among the fossil Cyclopterides, Noeggerathice, and Adian-
tites ; and, placing it in the genus Cyclopteris, he suggests that it be
recognized as a subgenus (Aneimites) with the specific name Acadica.

The regularly striated and gracefully branching stipes, terminated
by groups of pinnules on slender petioles, must have given to this
fern a very elegant appearance. It attained a great size. One
stipe is 22 inches in diameter, where it expands to unite with the
stem ; and it attains a length of 21 inches before it branches. The
frond must have been at least 3 feet broad. The specimens are ex-
tremely numerous at Horton.

The author then notices that the long slender leaves so common in
the Coal-measures of Nova Scotia, and hitherto called Poacites, though
sometimes like the stipes of Aneimites, are probably leaves of Cordaites.

On some specimens of Aneimites Acadica, markings like those made
by insects have been observed ; also a specimen of the Spirorbis
carbonarius.

486 Intelligence and Miscellaneous Articles.

3. " On the Sections of Strata exposed in the Excavations for the
South High-level Sewer at Dulwich; with Notices of the Fossils
found there and at Peckham." By Charles Rickman, Esq.

In the autumn of 1859, open cuttings were made at Peckham, in
connexion with the " Effra branch of the Great South High-level
Sewer," for the "main drainage" of the metropolis south of the
Thames ; and in the following spring a tunnel (330 yards in length)
was being constructed under the Five-fields at Dulwich. The beds
exposed in both sections belonged to the " Woolwich and Heading
Series " of the Lower London Tertiaries (Prestwich) .

Four shafts were sunk to facilitate the driving of the tunnel ; and
the following beds were exposed ; but, as some of the beds are not
persistent, but die out even within the extent of the tunnel, the
several shafts differed as to the sections obtained from them.

1. Soil, 9 inches. 2. Loamy clay (probably London Clay) ; 12 ft.
Not in shaft No. 1 (the most easterly), nor in No. 4 (the most
westerly), owing to the convex surface of the ground. 3. Light-
coloured clay ; 6 to 9 ft. 4. Reddish sand ; 5 ft. Not in No. 4 shaft.
5. Dark clay; 1 ft. 10 in. 6. Blue clay ; 2 ft. Not in No 4. 7.
Dark clay ; I ft. In No. 1 only. 8. Paludina-bed ; 6 to 15 inches.
Fossils : Pitharella Rickmani (Edwards), Paludina lenta, P. aspera (?).
Bones and scales of Fish. Leaves. 9. Cyrena-bed ; 1 to 2 ft.
Cyrena cunei/ormis, &c. 10. Oyster-bed ; 1 to 3 ft. Ostrea tenera,
O. pulchra, 0. Bellovacina, 0. elephantopus, 0. edulina, Bysso-arca
Cailliaudi (?), Cyrena cunei/ormis, C. deperdita, C. cordata, C. ob-
ovata, Melania inquinata,Melanopsis brevis,Modiola elegans, Fusus (?),
Calyptrcea trochi/ormis, Corbula. 11. Loamy sand ; 8 in. In No. 4
only. 12. Red sand ; 2 ft. In No. 4 only. 13. Blue clay ; 2 ft. 6 in.
Leaves. 14. Dark sand ; 8 to 28 in. 15. Blue clay ; 18 in. to
9 ft. Laminated ; rich in Leaves, Lignite, Seed-vessels. Rissoa,
Cyrena Dulwichensis (Rickman). 16. Dark sand ; 2 to 4 ft. 17.
Light-coloured clay; 2 ft. 6 in. In No. 4 only. 18. Shell-rock;
4 ft. thick, sometimes intercalated with stiff blue clay. Cyrena
Dulwichensis (Rickman), C. cordata, C. deperdita, C. cunei/ormis,
Melania inquinata, Melanopsis, Neritina, Pitharella Rickmani (Ed-
wards), Unio, Teredines in Lignite, Scutes of Crocodile, Fish-scales, Che-
Ionian and Mammalian bones. 19. Clay ; 14 ft. and more. Reached
only by the main shaft, No. 3, which appears to have been sunk at
the apex of a low anticlinal ; the beds gently dipping away E.and W.

All the fossils appear in their respective beds both at Peckham
and Dulwich.

LXV. Intelligence and Miscellaneous Articles.

ON THE RELATION BETWEEN THE DIRECTION OF THE VIBRATION
OF LIGHT AND THE FLANE OF POLARIZATION. BY F. EISENLOHR.

To the Editors o/ the Philosophical Magazine and Journal.
Gentlemen, — I observe that Mr. Stokes has some remarks in your
Periodical for December 1859, upon a paper of mine, which was first
published in the 104th volume of PoggendorfTs Annalen, and trans-

Intelligence and Miscellaneous Articles. 487

lated in the September Number of your Magazine for 1 859. As some
passages of this translation do not agree with the original, in order to
express my own views correctly I beg your permission to insert the
following corrections and explanations : —

P. 187 of the translation, line 9, instead of 'it was read it would be.

— 188, line 18 from below, instead of to another occasion read to

the immediately following paper (in Poggendorff's Annalen).

— 188, line 4 from below, instead of if this be so read if we do

this (that is, if we consider the stratum infinitely close to the
surface).
If Mr. Stokes will compare these corrections, he will find that I
never assumed " that the diffracted ray may be regarded as pro-
duced by an incident ray agreeing in direction of propagation with
an incident ray which would produce the diffracted ray by regular
refraction, but in direction of vibration with the actual incident ray."
On the contrary, I said that such a ray would represent the incident
ray in its effects on the diffracted ray only in the surface of the glass,
not in the stratum infinitely close to that surface. The calculus by
which I have obtained the formula of p. 189, I have given in the
paper which in Poggendorff's Annalen succeeds the article trans-
lated in this Periodical ; it rests only on the hypothesis that, at the
bounding surface of the two mediums, the motion, and the differen-
tial of the motion with respect to the normal on the surface, must
be the same for the two mediums in the intervals of the grating, but
absolutely zero at the bars of the grating. Now we may regard the
motion in the second medium as composed of an infinite multitude
of motions propagated in all possible directions, and we may deter-
mine, according to the theory of Fourier's double integrals, the ampli-
tude of each of these undular motions by the above-named conditions
for the surface. In my paper I have given for the sake of simplicity
a somewhat abridged calculus, which, as it rests on the same princi-
ples, leads necessarily to the same results. Since then, by a quota-
tion in the paper of Mr. Stokes " On the Dynamical Theory of Dif-
fraction" (Cambridge Transactions, vol. ix.), which the author had
the kindness to present me with, I became acquainted with a paper
by M. Cauchy (Comptes Rendus de V Acade^mie des Sciences, vol. xv.
p. 670), in which the author had already explained the principles of
the above-given solution, but without giving any of the analyses*.
Nevertheless the result of M. Cauchy's theory (that is, the formula
of my paper) is at variance with that of Mr. Stokes's investigation ;
only I would not concede that for that reason alone the assumption
on which it rests cannot be admitted, though I value very highly
the merit of Mr. Stokes's disquisition.

The theory of Mr. Stokes, as does that of M. Cauchy, rests on the
assumption that the screen which contains the diffracting apertures is
infinitely thin ; so that the motion at the issue of the apertures, where
it occasions secondary waves in the second medium, is the same as
at the entrance, or as in the unbroken incident wave. It appears very

* It was also on this occasion I saw that, when I said that Mr. Stokes
had not communicated the details of his experiments, I was in error,
into which I was led by an extract of Mr. Stokes's paper, and for which I
beg to be excused.

!SS Intelligence and Miscellaneous Articles.

improbable that any sensible error will arise from this assumption,
especially if the thickness of the screen (soot or any other opake
medium) may be neglected in comparison with the breadth of the
apertures, though a further theoretical examination of the question
would be desirable. But both theories differ in what regards the
propagation of the secondary waves after their having left the aper-
tures. Mr. Stokes assumes that this propagation is the same as if
the screen were not there ; indeed he says (in the introduction of the
Dynamical Theory of Diffraction), " It is an hypothesis (exceedingly
probable d priori) that we may find the disturbance in front of the
aperture by merely taking the aggregate of the disturbances due to
all the secondary waves, each secondary wave proceeding as if the
screen were away, in other words, that the effect of the screen is
merely to stop a certain portion of the incident light ; " and further
(§ 31 at the end), " In determining the law of disturbance in a se-
condary wave we have nothing to do with the aperture." On the
contrary, according to the theory of M. Cauchy and that given in
my paper, the secondary waves produced by the motion at the issue
of the apertures must in proceeding satisfy the condition that the
motion resulting from all secondary waves is, on that side of the
screen or of the bars of the grating which regards the second me-
dium, absolutely zero. It is true that this condition is fulfilled only
when the screen is of a substance which absorbs the light in a very
high degree (as, for example, soot or silver) ; but for the majority
of the substances used as screens the error will not be sensible.

To this difference in the principles of both theories I should trace
the difference of the results ; but after examining that difference, I
must give it as my opinion that the assumption of M. Cauchy, while
it is confirmed by experiment, is also the true interpretation of the
conditions under which the experiment is made ; whereas that of
Mr. Stokes, that the secondary waves produced at the apertures may
be regarded as proceeding freely in all directions, seems to me to be
contrary to these conditions, and the consequences derived from it
to be therefore erroneous.

Yet with the opinion expressed by Mr. Stokes, " that the whole
question must be subjected to a thoroughly searching experimental
investigation before physical conclusions can safely be drawn from
the phenomena," I cannot but concur.

I am, Gentlemen,

Yours respectfully,

Heidelberg, August 14, 1860. F. Eisenlohr.

ON THE SPECIFIC AND LATENT HEAT OF NAPTHALINE.
BY M. ALLUARD.

Repeated investigations have led Alluard to the following results.
Napthaline melts at 79°*9, and solidifies at the same temperature.
Its specific heat in the solid form is 03249 between 20° and 66°,
and 0*3207 between 0° and 20°; for the liquid condition between
80° and 130° it is 04 176. Its latent heat of fusion is 35*68 ther-
mal units. Its specific gravity in the liquid state at 99°02 is 0*9628.
— Liebig's Annalen, February 1860.

THE

LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

SUPPLEMENT to VOL. XX. FOURTH SERIES.

LXVL On the Pressure of Earth on Revetment Walls* By
J. J. Sylvester, Professor of Mathematics at the Royal
Military Academy*.

Part I. Critique of the Hypothesis of Parallel " Planes of
Rupture."

THE ensuing investigation deals with the pressure of Mathe-
matical earth. By mathematical earth, I mean earth
treated according to the idea of Coulomb, viz. as a continuous t
mass separable by planes in all directions, but whose separating
surfaces exert upon one another forces consisting of two parts,
one of the nature of ordinary friction, the other of so-called
cohesion. Of the latter, for greater simplicity, I shall com-
mence with taking no account, so that the matter with which
we have to deal becomes, so to say, " a frictional fluid." If we
isolate in idea any element of this fluid — suppose, to fix the
ideas, a molecule bounded by plane faces, this molecule will be
kept at rest by its own weight, the pressures on the several
faces, and the forces of friction acting along these faces : these
last-named forces are limited not to exceed the product of the
corresponding pressures by a certain coefficient, termed the co-
efficient of friction.

In order to render the inquiry before us quite definite, let us
begin with supposing two vertical side walls and a back of solid
immoveable masonry, between which the earth is piled up in a
determinate form, fronted by a pier of given specific gravity,
whose minimum thickness is to be determined by the condition
that it may just suffice to prevent the pier from being either
forced forward or turned round over its further edge. The
earth is thus of course supposed to have only one free face, being
entirely supported at the sides and the back by the masonry
just spoken of. The problem then that we have to solve is

* Communicated by the Author.

t The only essential quality of our mathematical earth which differen-
tiates it from actual vulgar earth is this of continuity.

Phil. Mag. S. 4. No. 136. Suppl. Vol. 20. 2 K

490 Prof. Sylvester on the Pressure of Earth

evidently the following : — " Of all the possible states of equili-
brium of the earth consistent with the assigned conditions, to
determine that one which shall make the greater of two quan-
tities to be named the least possible," — one of these quantities
being the thickness of the wall determined by the condition
that its friction with the ground shall be just equal to the sum
of the horizontal pressures on the wall, the other by the condi-
tion that its moment about the edge most remote from the
earth shall be just equal to the sum of the moments of the
entire thrust upon the wall at each several element thereof in
respect to the same edge.

Whenever Coulomb's method leads to a right solution of the
problem of revetments, the thrusts on the several elements of the
wall will be all parallel ; and it may easily be seen that, in solving
the problem for this case, we are solving the problem of making
the statical sum of the thrusts a minimum ; and the result will
be the same, whether the pier can only be pushed bodily on its
base, or can only turn over an edge, or can do both one and the
other. But it must obviously be erroneous to assume as a uni-
versal principle, that in the state bordering upon motion, or what
is going still further, in a state antecedent to this, the statical
sum of the pressures will be a minimum ; and if Mr. Moseley's
" principle of least resistance," quoted by Professor Rankine,
means this, I have no scruple in proclaiming my entire dissent
from such an assumption. I do not here enter at all into the
question of determining pressure, except in the state of equili-
brium bordering upon motion ; and in that state common sense
points out that it is not the pressure or sum of pressures, but the
effect of such pressure or pressures in inducing motion in a certain
possible manner, or in any one out of a choice of possible
manners, that governs the determination of the minimum. This
principle of least resistance is one of the shoals upon which Mr.
Rankine's investigation appears to me to have split.

Be it observed that the only physical assumption which I pro-
pose is this, that if equilibrium can be preserved consistently with
the imposed conditions, equilibrium will be preserved. Without
such a supposition the question would be incapable of treatment
without further laws regulating the interior forces than we
suppose given. The legitimacy of such an assumption cannot, I
think, be seriously called into question, and once made, the
problem of determining the wall's thickness becomes a purely
mathematical question ; one undoubtedly of great difficulty,
but perfectly determinate, and falling under the dominion of
the Calculus of Variations, as will easily be recognized from the
circumstance that the integration of the general equations of
equilibrium, if it could be performed, would necessarily contain

on Revetment Walls. 491

arbitrary functions, whose form would have to be assigned so as
to make a certain quantity or the greatest of a set of quantities a
minimum ; but the peculiar manner in which the internal forces
are defined as subject to satisfy not an equation or system of
equations, but a law of inequality, must render it a task exceed-
ing the present powers, at all events,' of the writer of this paper, to
arrive at a result by the direct application of the Calculus referred
to. In order to pave the way to the discussion of the more
general inquiry, I shall commence with examining whether
under any and what circumstances the forced solution of Coulomb
and his followers, founded upon the notion of what have been (it
seems to me incautiously) termed planes of fracture or rupture
(but which really mean no more than planes for which friction at
each point thereof is acting with its utmost energy, i. e. if we
please so to say, planes of greatest frietional energy*), is the true

* It is obvious that the notion of the planes in question being the planes
in which the earth would begin with crumbling, if the equilibrium were
disturbed by the wall giving way (for such is the idea intended to be con-
veyed by their being called planes of rupture), is quite irrelevant to the
determination of their position, and to the solution of the question of the
thrust in the wall. But such a notion in itself is objectionable, as assuming
a physical fact for which there is no just ground. The idea, or rather I may
say the metaphysical process, which unconsciously has swayed Coulomb
and his followers to give them this name, appears to me to be the follow-
ing. " Since it is only along these planes that friction is acting at its full
energy, and since, when motion ensues, friction must be acting at its full
energy, therefore a change must have taken place in the friction of any
other plane before motion can take place along it, which change does
not take place along the planes in question. Now every change must
operate in time, therefore the motion must have begun along the planes
of greatest friction before it can have taken place along any other." But
it is a most dangerous proceeding, and fraught with errors familiar to
mathematicians, to attempt to reason from the conditions of equilibrium
to those of incipient motion ; and that dynamical considerations, and not
statical, must decide the incipient directions of the motion in the case before
us, will be obvious when we reflect that the friction might be supposed to
become nil, and then we should be treating of a perfect fluid, in which case
the planes of rupture disappear, but none the less would motion take place
in determinate directions on any wall of the reservoir containing the fluid
giving way. A notable example of the important distinction between rest
and equilibrium is afforded by the question (which, I am informed, ori-
ginated in Caius College, Cambridge) of finding the tension of a rope by
which a bucket full of water, with a cork tied to its bottom, is fastened to
a fixed point, at the moment when the fastening is cut or gives way. At
that moment the vertical pressure in the bottom of the bucket, supposing
the specific gravity of the cork to be one-fourth that of water, if it could
be estimated on statical principles, i. e. with reference to the elevation of
the surface of the fluid [and some non-mathematical physicists might
easily suppose it could be so estimated, since motion has not yet taken
place, but is only imminent], would be the weight of the bucket together
with that of the water, together with four times that of the cork, and so it
would appear as if the tension would be increased by the cutting of the

2 K2

492 Prof. Sylvester on the Pressure of Earth

solution ; that is to say, I shall investigate under what conditions
the surfaces of "rupture " or "of greatest energy of friction"
are or can be planes ; and I shall easily be able to ascertain
these conditions, and to prove that when they are satisfied (but
not otherwise) the results of the received theory are exact.

Professor Rankine, in the light in which he appears in a paper
published in the Transactions of the Royal Society, is not to be
ranked among those whom I have called the followers of Cou-
lomb. He is entitled to the merit of having perceived that the
received hypothesis rested on no solid foundation, and of having
been the first (publicly at least) to assert that the equations of
internal equilibrium must be resorted to for the satisfactory dis-
cussion of the question ; but, notwithstanding the sincere esteem
in which I hold the great abilities of this gentleman, I have been
compelled to come to the conclusion, and trust to be able to
satisfy himself, that the use he has made of these equations is
illusory, and that his results bear upon their very face a demon-
strable character of error.

Under the supposed data, it is, if not obvious, at all events
assumed by all writers on the subject, that the equilibrium of
every vertical section of the earth, parallel to the side walls, may
be determined per se, and that we may treat the question as one
regarding space of only two dimensions. I shall therefore, with
a view to clearness, treat of the equilibrium of any one such sec-
tion ; the molecules, whose equilibrium is to be considered, will
be spoken of as bounded by lines instead of planes, and so we
shall speak of lines instead of planes of " rupture," and we may
thus conform our language to the relations of the figure actually
represented upon the paper.

For the benefit of those to whom the conditions of molecular
equilibrium are new, it may be well to indicate briefly how they
may be obtained, still keeping within our prescribed framework
of two-dimensioned space (although the reader will not expe-
rience the slightest difficulty in extending them to space of
three dimensions) *. Through any point in the interior of the

string, whereas, in fact, precisely the contrary effect will take place ; for
since downward momentum must result from the impending motion of the
cork upwards and the water downwards, part of the weight of the water
and cork is spent as downward moving force, and consequently only a
portion remains to act as vertical pressure upon the bucket, just as an air-
cushion will press with less force than its weight on the seat which bears
it, when, in consequence of the air being let out, part of the weight is being
expended in lowering the top of the cushion.

* I have purposely begun with the beginning, because I wish to give per-
fect precision to the terms Thrust, Pressure, and Stress, as I shall use them.
Some recent authors on mechanics have wished to distinguish force measured

on Revetment Walls. 493

plane-mass at rest, imagine a small rectilinear element to be
drawn. The entire molecular force exerted on this actual
element might be termed the thrust ; but by the thrust I shall
understand the unit of thrust, corresponding to the well-known
conception of unit of pressure for the particular case of a fluid
mass. This thrust (or unit of thrust) may be imagined separated
into two parts, one perpendicular to the element, which may be
termed the pressure, the other parallel to it, which may be termed
face-force [for the case we shall have more especially to consider,
the face- force receives the name of friction, and is limited to be
less than the pressure multiplied by the so-called coefficient of
friction] . As the element acted upon turns round, the thrust
changes in magnitude and direction, and to the totality of the
thrusts going forth in all directions from a given point we may
give the name of stress*. We shall now be able to obtain two
sorts of conditions — one giving the necessary law connecting the
various thrusts of the same stress, the other expressing the law
of the variation of the pressure and facial force (together consti-
tuting the thrust) upon an element given in direction in passing
from one stress to another ; we may call these respectively the
equations of distribution and the equations of variation.

Let P Q R S be any infinitely small molecule
bounded by lines at right angles to one another.
Since this is kept at rest by its own weight, by
the lines of pressures perpendicular to Q R and
P S, and the other pair perpendicular to P Q
and R S, and by the facial forces acting along
P Q, Q R, R S, S P respectively, if we call /
the face-force [i.e. the unit of face-force] on P S,
it is obvious that the corresponding quantity for Q R will differ

statically from force measured by acceleration, by giving to the former the
name of pressure. But surely unnecessary confusion is introduced into
mechanical language when we are thereby reduced to speak of the pressure
of friction, and ought to enunciate the cardinal law of friction by stating
that the pressure of friction bears to the pressure of pressure & certain
limiting relation. I acknowledge an objection scarcely less valid (except
that it has antiquity to plead in excuse) to the use of the term accele-
rating force ; as we may be thereby reduced to speak of the accelerating
force of a retarding influence, as friction, or of an influence which does not
necessarily either accelerate or retard, as in the case of a centripetal pull
upon a body moving uniformly in a circle. I think this difficulty in lan-
guage may be met to some extent by giving to force, usually called accelera-
tive, the designation of alterative, and to force measured by weight or mo-
mentum that of quantitative force. There is no magic in names, however
well selected, but there may be a great deal of mischief arising out of a
confused and uncertain nomenclature.

* Thus, stress stands in somewhat the same relation to its component
thrusts, as a radiant point to the luminous rays which it emits.

494 Prof. Sylvester on the Pressure of Earth

from it by an infinitely small quantity ; in like manner /' may
be taken as the face-force on Q R, PS respectively. Hence the
couples whose moments are (f. Q R) x Q P and (/' . P Q) QR re-
spectively must be equal and opposite, or in other words, / being
understood to act to or from Q, according as f acts to or from Q,
we must have /=/'. To fix the ideas, conceive the face-forces to
tend towards Q. Let us now consider the equilibrium of the
triangular molecule P Q R. Call the pressure on P Q (R), the
pressure on RQ(P) the face-force on PQ or QR (Q). In
comparison with the thrusts on the faces of our triangular mole-
cule, gravity or other impressed forces may be neglected as giving
rise to quantities of an inferior order of smallness.

Let QP, QR be regarded as two fixed rectangular axes, and
let QPR=0. Let the pressure and face-force on PR (always
understanding thereby the units of such forces) be called N and
F respectively (F, to fix the ideas, being taken to act from P to
R), Then resolving the forces perpendicular to PR, we obtain

N . PR=R . PQ . cos QPR+ P . QR cos QRP

+ Q.PQ sinQPR + Q.QRsinQRP,
or

N = R (cos 6f + 2Q cos 6 sin 6 + P (sin Of ;

and resolving parallel to PR, we have

F x PR = R . PQsin QPR-P . QR sin QRP

+ Q . PQ cos QPR - Q . QR cos QRP,
or

F = (R-P)sin0cos0.

Imagine now QRR to be represented by a single point 0.
R, P are respectively the pressures, and N the face-force (" units
of pressures and of face-force ") on elements drawn in the ortho-
gonal directions OX, 0 Y ; N the pressure, and F the face-force
on an element drawn in the direction OP, making an angle 6
with OX. Obviously, therefore, if we draw in all directions
from 0 lines whose lengths are as the inverse square roots of
the pressure-part of the thrust acting on those lines, calling
the length of line corresponding to 0, r, we have

-\ = R (cos 0)2 + 2Q sin 6 cos 6 + P (sin 0)2,

R, Q, P being constant quantities.

Consequently the locus of the extremities of these lines is a
conic ; and taking new axes of coordinates in the directions of
the principal axes of this conic, and understanding by R and P
the pressures perpendicular to those axes respectively, the equa-
tions obtained assume the form

on Revetment Walls. 495

N=R(cos<9)2 + P(8in0)2, (1)

F=s(R-P)sin0.'cos0; (2)

showing that in elements in the directions of the principal axes
the face-forces vanish, and the thrusts become purely pressures,
I. e. forces perpendicular to the surfaces upon which they act.
R and P are of course essentially positive, as otherwise the mo-
lecules would be subject to a force of separation instead of
compression, and consequently the conic in question is an ellipse.
The total value of the thrust = \/N2+F2

=V/R2(cos(9)2 + P2(sm^)2- ....(*)
R and P will evidently be in the directions in which, for a
given point, the entire thrust, as well as the pressure-part of it,
are the least and greatest. These directions may be said to be
those of " principal thrust." If we start from any point and
proceed from that point always in the direction of a line of
principal thrust so as to form a continuous curve, two such curves
cutting each other at right angles will intersect every point of
the mass at rest, of which, in the case of mathematical earth, I
may state, by way of anticipation, that only one can cut the free
surface when that surface is supposed to form part of a horizontal
plane.

These lines may also be termed the principal lines of pressure,
or simply the lines of pressure ; and this name may be considered
indifferently to have reference either to the fact that the thrust
in the direction of the tangent at any point in any such curve is
the thrust acting upon the normal, or to the fact that the thrust
upon the tangent at any point is in the direction of the normal;
as either one of such conditions implies the other.

The cosine of the angle between the pressure and the thrust
will be

R(cosfl)2 + P(sinfl)2

\ZWJcwdf+¥* (sin Of '

which, calling the principal semiaxes of the ellipse referred to a
and b respectively, and the rectangular coordinates of any point
therein x and y, becomes

x* y1

a^+ b* 1

which is equal to the perpendicular from the centre on the tan-
gent divided by the radius vector, showing that the direction of
the thrust on any radius of the ellipse in question is in the
direction of the conjugate diameter, whereby it is seen that the

496 Prof. Sylvester on the Pressure of Earth

line of thrust and the line thrust upon stand in a reciprocal re-
lation to each other.

I may add the cursory remark as regards the value of the
total thrusts in the case more immediately before us, that [as
is apparent from the equation (a)] they will be represented in
relative magnitude by the radius vector drawn in the direction
of the line thrust upon, to meet, not the ellipse of pressures just
described, but another ellipse whose major and minor axes are
to one another in the duplicate ratio of the other two.

If we wish, however, to present the above results in a form
more immediately translateable into the actual case of nature,
I mean that of space with three dimensions, it becomes expe-
dient to use a different ellipse, or rather the same ellipse in
another position, to represent the stress at any point.

In the equations above found, connecting N and F with
P, Q, R, 0 is the angle made with a fixed axis, not by the line
of pressure It, but by the element on which this pressure is
exerted. Let <f> be the angle made by the pressure itself, so that

<£ = 6 + ^, then we have

N = P (cos (f>Y- 2Q sin <f> cos <j> + R (sin <£)2

F=(P-R)sin<£cos<£.

And the same process as has been already employed will serve
to show that we may construct an ellipse such that the inverse
square of the radius vector in every direction may represent the
magnitude of the pressure in that direction (i.e. the magnitude
of the normal part of the thrust upon the element perpendi-
cular to that direction), and in this ellipse the radius vector
and perpendicular to the tangent at each point will represent
the corresponding directions of pressure and thrust, which
obviously will coincide for the directions of greatest and least
pressure.

If, now, we go out into space of three dimensions, it will
readily be anticipated, and may easily be proved, that an ellip-
soid whose radii vectores represent the relative magnitudes of the
inverse square roots of the pressures takes the place of the
ellipse, the thrusts and pressures correspond respectively (in
direction) to the normal and radius vector at each point, and in
three directions, at right angles to each other, these latter come
together.

It is desirable that the reader should bear in mind that the
ellipse of which I have spoken is in fact only a principal section
of this ellipsoid. The assumption which (following in the track
of my predecessors) I shall make, that the greatest energy of

on Revetment Walls. 497

friction exerted at any point will be exerted in some direction in
a vertical plane parallel to the revetment wall, will be seen from
what follows a little further on, toimply that every such plane
contains the radius vector which makes the greatest angle with
the normal, and consequently the section of the ellipsoid of stress
with which we are dealing will be the plane of greatest and least
thrust, or greatest and least pressure. By way of aid to the
imagination in seizing this subtle conception of stress (a real
conquest in physical ideology due to the last quarter of the
present century, although its first germ may be recognized in
the much earlier molecular view of the circumambient pressures
round about each internal point of a perfect fluid), 1 have gone
thus briefly into the generation of the ellipse and ellipsoid above
described ; but I shall have very little occasion, except for
occasional facility of reference, to have resort to them, as the
equations (1) and (2) will suffice for my purpose in the present
inquiry.

These are the equations which govern the distribution of
stress; and it may be convenient to confer upon the ellipse
whose radii vectores are in length inversely as the square roots of
the pressures acting upon them, the name of the ellipse oi pres-
sures s in order to obviate any possibility of the position of this
ellipse being confounded with that of the one which would, I
believe, more ordinarily go by the name of the ellipse of stress.
Every point in the mass is the centre of such an ellipse ; and
those ellipses, if properly drawn, will represent completely, and
on the same scale, the magnitude and distribution of the pres-
sures round about any point. It is almost needless to add that
for a perfect fluid these ellipses would become circles.

Let us now proceed to establish the law of the variation of
the stresses, or, to speak more accurately, of the thrusts acting
on planes drawn in any given directions, on passing from one
point of the mass to another. Returning to our little rect-
angular element PQRS, and considering the lines PQ, PS to be
given in direction, so that we may consider PQ = cfo? and PS — dy,
and calling the units of pressure on PQ and RQ L and N,
the unit of face-force M, the impressed forces of acceleration X
in the direction of x, and Y in the direction of y, and the unit of
mass p, by simple estimation of the forces in the directions of x
and y respectively we obviously obtain, due attention being paid
to the mode of fixing the positive directions of X and Y,

dh dM_

dy dx ~~ * '

Jn dM_ x

dx dy ~~

498 Prof. Sylvester on the Pressure of Earth

If, as in the case with which we shall have to deal, the sole
impressed force is that of gravity, and if we treat the weight of a
unit of the mass as unity, and make the axis of x horizontal and
of y vertical, the equations become

dh ,£M

dy dx '

dx dy '

These, being the equations which control the law of the variation
of the thrusts estimated in given directions in passing from one
stress to another, I call the equations of variation of stress.

I now proceed to the application of the principles above set
forth to the treatment of the particular question in hand.

Let fi be the coefficient of friction of the. earth upon itself,
and /i=tan X, so that X is the angle of repose; by this is to be
understood that the thrust on any element can never make,
with the perpendicular to that element, an angle greater than
X. Now the general law of the distribution of stress proves
that the actual angle between the perpendicular to the element
and its thrust will in two directions be zero. Hence at any
given point it will pass through all gradations, from zero up to a
certain limit. Here presents itself the question, Is that limit X,
or can it be X for every point in the mass ? As we have no right
to assume a priori that this limiting angle in that state of equi-
librium which we wish to determine must be equal to X through-
out the mass, and obviously it will not be so for actual cases of
equilibrium which arise, we want a name to distinguish the
maximum ratio which friction bears to pressure in any specified
stress from the absolute maximum which this ratio is capable of
attaining. We may name the former the coefficient of frictional
energy ; and for every point where this is equal to the absolute
coefficient of friction, we may say the friction of the stress is at
its maximum energy. Let (fi) be the coefficient of frictional
energy for any given stress, and (X) =tan-1 (/*) the corresponding
angle of repose. [We may also, if we please, term (//,) and (X)
the relative coefficient and relative angle of repose respectively,
t. e. relative to any assigned stress.] Let the ratio between the
maximum and minimum thrust of any stress be called 7*: a
simple relation connects 7 and (X) *.

For calling, as before, L the pressure, and M the face-force
(now the friction), we have by equation (1),

* This relation and its importance are well known to Professor Rankine.

on Revetment Walls. 499

L=P(cos0)9 + R(sin0)2,
M=(P-R)sin0cos0,

M

tan (\) == (fi) = maximum value of -j-.

To find this maximum, we have

8{cot0 + 72tan0}=O.
Hence

7 tan 0=1,
and therefore

27

cot (X) =

1-72'
therefore

(l-72)-27tan\=0,
or

.7=8ec(X)-tan(X) = I^Uan(45-^).

This equation expresses the universal relation between the
form of the ellipse of pressures for any stress and the relative
angle of repose for such stress.

The problem we have just solved may be presented advan-
tageously, in order to make the impression of it more vivid (as
it is of cardinal importance), under a geometrical point of view.
Taking any radius vector of the ellipse of pressures, the angle
between it and its conjugate radius is 90° at any vertex ; at some
point therefore it will be at a minimum, and this minimum
will be the complement of the relative angle of repose.

From the preceding investigation, it will easily be seen that,
to find the ray-directions which give this minimum, we have
only to construct a rectangle circumscribing the ellipse, and
either of its two diagonals will be in the direction required, and
the angle between either such ray and the principal axes plus
or minus half the angle between it and the normal (which angle
is the relative angle of repose) will be half a right angle*.

* In fact the diameters which coincide with the directions of these
diagonals are conjugate diameters, equally inclined to the principal axes ;
and these, as I suppose must be well known, are the conjugate diameters
whose inclination to each other is a minimum.

[To be continued.]

[ 500 ]

LXVII. Experimental Researches on the Laws of Absorption of

Liquids by Porous Substances. By Thomas Tate, Esq.

[Continued from p. 369.]

THE following experiment was made to show that, at equal
distances from "the surface of the liquid, the rate of diffu-
sion is equal in all directions, that is to say, that the rate of dif-
fusion is independent of the force of gravity.

Experiment IV.
The absorbent used in this experiment was unsized paper, 2
inches in width, cut longitudinally through
the centre to within 1 inch of the lower
extremity; and whilst one portion was
suspended vertically, the other portion
was bent after the manner shown in the
annexed diagram. Each branch was gra-
duated from the water-line of immersion,
so that the space of ascent in the follow-
ing Table is the distance traversed on the
paper measured from the level surface of
the water.

On the vertical

On the bent

Ascent of liquid

portion.

portion.

Value of T

in inches,

Corresp. time

Corresp. time

by formula
T=-9S2.

S.

in minutes,

in minutes,

T.

T.

0

0

0

0

1

•84

•80

•9

2

3-50

333

3-6

3

8-00

800

8-1

4

14-90

1492

14-4

5

23 00

24-42

22-5

It will be observed how very nearly the results in the second
and third columns coincide with each other, thereby establishing
the law above enunciated.

The following experiment was made to test the truth of this
law of equal diffusion.

Experiment V.

The absorbent used in this experiment was unsized paper, cut
in the form represented in the annexed
diagram. The width of the portion at A
was as fine as possible. The paper was
graduated from A along the vertical line
A E, as well as from A along the hori-
zontal line B C. The ascent recorded in
the following Table is the vertical as well
as the horizontal space traversed by the
liquid on the paper estimated from the

On the Laws of Absorption of Liquids by Porous Substances. 501

point A, which stood about half an inch from the level of the
liquid.

The line formed upon the surface of the absorbent by the
liquid throughout the course of its diffusion, was a perfect semi-
circle, B D C, having the point A as its centre. The breadth
of the absorbent being 3 inches, the semicircle attained its
greatest diameter at S = 1'5 inch. After this the line of liquid
absorption became a curve of contrary flexure, EKF, having
points of contrary flexure at E and F, which may be mathemati-
cally explained on the assumption of the law of equal diffusion.
The point A appeared to form the central point of liquid diffu-
sion, from which the liquid was diffused equally in all directions.

Ascent of liquid

Corresp. time

Velocity of diffu-

in inches,

in minutes,

sion per minute,

i

S.

T.

v.

16 S

0

0

•4

1-23

•5

1-83

•125

•125

•6

2-83

•7

3-83

•8

500

•080

•078

•9

6-33

10

783

•060

•062

11

9-66

1-4

15-58

1-5

1800

•041

•041

20

3208

3-0

72-00

The same results were obtained with an ab-
sorbent cut in the form represented in the an-
nexed diagram.

The following experiment was made to de-
termine the manner in which the liquid^diffuses
itself over the surface of the absorbent.

Experiment VI.
This experiment was made with
the apparatus represented in the an-
nexed diagram. H G the absorbent
suspended in the jar AB, contain-
ing a small portion of water, by means
of a hooked wire, G S, attached to the
pan C of a delicate balance ; E F a stage
supporting the pan of the balance :
this stage admits of being raised or de-
pressed as may be required, and the
adjustment is such that the lower edge,
H, of the absorbent shall exactly come
in contact with the surface of the water,

-J >~i

^

t

H

G

^

■J

r~j^-i_'

.'. '_"

Mr. T. Tate's Experimental Researches on the

B, whilst the pan rests upon the stage; AD a ground plate
covering the top of the jar, having an orifice through its centre
to allow the wire G S to pass freely through it.

The absorbent being carefully graduated from its lower edge,
was suspended for some time in the humid air of the jar A B ;
the paper and hook, thus suspended, was balanced by weights
placed in the opposite pan of the balance ; the stage was then
lowered until the edge, H, of the absorbent came in contact with
the water. When the liquid had arrived at the different marks
upon the absorbent, the beam of the balance was elevated so as
to withdraw the absorbent from contact with the water ; in this
position the increased weight of the absorbent was determined,
and the weight thus found was entered in the second column of
the following Table. The numbers entered in the third column
are the weights in grains requisite to break the contact of the
absorbent with the water ; and the numbers in the fourth column
are the differences between the corresponding numbers in the
second and third columns. The absorbent used in this experi-
ment was unsized paper, 1*5 inch in width and 6 inches in
length.

Ascent of liquid
in inches,

s.

Corresp. weight

of liquid ab-
sorbed in grains,
w.

Corresp. weight

to break contact,

wx.

Weight of water
of cohesion
in grains,

Value of w
by formula

w=2-6S.

1
2
3
4
5
6

2-63

5-22

7-80

10-40

12-93

15-44

15-08
17-60
2014
22-64

7:28
7-20
7-21
7-20

26
5-2

7-8
10-4
130
15-6

It will be seen how nearly the value of w, obtained from the
formula w=2'6 S, coincides with the experimental results in the
second column of the Table. Hence we conclude that the liquid
is equally diffused over the surface of the absorbent.

As this result was not anticipated, its truth was tested in the
following manner : —

A similar strip of unsized paper, 10 inches long and 1*5 inch
wide, was suspended with its lower extremity in contact with the
liquid, as in the foregoing experiment. When the liquid had
reached the top of the absorbent, the augmentation of weight
due to the liquid absorbed was determined. After the absorbent
had been thoroughly dried it was cut transversely through the
middle, and the process was repeated with this half portion.
The following results were obtained :— -

Weight of liquid absorbed by the 10-inch strip = 22 03 grs.
Weight of liquid absorbed by the 5-inch strip = 1095 grs.

Laws of Absorption of Liquids by Porous Substances. 503

But the formeivresult is almost exactly double the latter : hence
it follows that the weight of water diffused through the upper
half of the 10-inch absorbent must have been very nearly equal
to the weight of water diffused through the lower half.
Let U = the work performed by absorption per minute.
k = the number of inches in one foot.
kx = the number of grains in one pound.
wf = the weight of water in grains diffused through each
inch of the absorbent.

Then

But w=VS

S

TxU-"2AX*l + \

(.

v \2 w

ok) x%qT;

T-^and^gg;

U:

2kk\ T 14400^a2S3J
But for all appreciable values of S the fraction
is indefinitely small as compared with 1 ;

I

144<%*a2S3

which expression, being independent of S and T, is the same for
all points of ascent. Hence we infer that in equal times the force
of absorption performs the same amount of work.

Experiment VII.

The absorbent used in this experiment was fine calico, 2 inches
in width, and uniform in its texture. The temperature was 56°
throughout the experiment. As in the preceding experiments,
the liquid was distilled water.

Ascent of liquid

Corresp. time

Value of T

in inches,

in minutes,

by formula
T=1-12S2.

8.

T.

0

0

0

1

112

112

2

4-50

4-48

3

9-50

1008

4

1733

1792

5

2700

28-00

6

4000

40-32

7

56-50

54-88

In this case the velocity of ascent is expressed by the formula

1

v=

2-24S*

504 Mr. T. Tate's Experimental Researches on the

In order to compare the absorbing powers of Afferent absorb-
ents, let / and f be put for the velocities corresponding to the
same time T of ascent of the liquid on two different absorbents,
then we get from equation (2),

/=— i_

* 2 */«(T-p)'

••/~V «(T+p)

and neglecting p and p', we get

/-AA'.

7-VJT'

(9)

(10)

that is, in this case the absorbing power varies inversely as the
square root of a, or inversely as the square root of the time which
the liquid takes to ascend one inch.

Now taking the absorbing power of the unsized paper of
Exp. I. as unity, we find from equation (10),

The absorbing power of the calico in the above experiment

= v/i-i=1,63'

that is to say, the absorbing power of the calico is 1*63 times
that of the unsized paper.

In this manner the powers of different absorbents may be defi-
nitely expressed.

These formulae also give us the relative diffusibility of differ-
ent liquids in any given absorbent.

Experiment VIII.

The liquid used in this experiment was turpentine, and the
absorbents were unsized paper and calico. The temperature was
55° throughout the experiment.

A. Unsized paper of Experiment I.

B. Calico of Experiment VII.

Ascent of
liquid in
inches,

s.

Unsized paper A.

Calico B.

Corresp. time

in minutes,

T.

Value of T

by formula

T=3S-\

Corresp. time

in minutes,

T.

Value of T
by formula
T=17 82.

0

1

2
3
4
5

0
2<)
120
270
503
800

0
3
12
27
48
75

0

1-6

6-5

146

26-5

430

0

17

6-8

15-3

272

425

Laws of Absorption of Liquids by Porous Substances. 505

The results of this experiment, on being compared with those
of Experiments I. and VII., show that the diffusibility of turpen-
tine on unsized paper is the same as that of water, and that its
diffusibility on calico is somewhat less than that of water.

Taking the diffusibility of water on calico as unity, we get
from equation (10),

Diffusibility of turpentine on calico = \/ =-8124.

In like manner, taking the absorbing power of the unsized
paper A in relation to turpentine as unity,

/2*9
The absorbing power of the calico = a / r—

1-3.

Experiment IX.

The absorbents used in this experiment were strips of linen
and unsized paper. The liquids were distilled water, and a solu-
tion of starch containing 1 part of starch to 100 parts of water.

L. Linen absorbent weighing *8 gr. per square inch.

E. Unsized paper absorbent.

Ascent of

Liquid. Solution of starch.

Liquid. Distilled water.

Absorbent L.

Absorbent E.

Absorbent L.

Absorbent E.

liquid in

J J

II

KSi

Efl*

5|

M*

s.

• 2 .

° B?

• g .

ti*

cLcEh

!|s

p.cH

U*

I*

s a

3,2 ||

1&*

5.S

5 Jul
If*

p

2& «

0

0

0

0

0

0 0

0

0

1

25

2-5

50

5

1-50

1-5

2-25

2-25

2

9-6

100

21-0

20

700

60

9-75

900

3

21-5

22-5

450

45

1400

13-5

23-75

20-25

4

400

400

78-5

80

23-75

240

3700

3600

5

630

62-5

36-50

375

56-00

56-25

The results of this experiment show that the diffusibility of
the solution of starch is very low as compared with that of water.

Taking unity as the diffusibility of water on each of the absorb-
ents respectively, the diffusibility of the solution of starch on

/2'25

the paper absorbent will be expressed by a /— — =*67;

whereas on the calico absorbent it will be expressed by

1*5

— ='77. Whence it appears that the diffusibility of liquids

<vO

varies with the nature of the absorbent. In comparing, however,
the absorbing powers of two substances with each other, as a
Phil. Mag. S. 4. No. 136. Suppl. Vol. 20. 2 L

V:

506 Mr. T. Tate's Experimental Researches on the

general rule the substance which has the higher absorbing power
for one liquid will also have the higher absorbing power for any
other liquid.

Experiment X.

The liquid used in this experiment was linseed oil, and the
absorbent was unsized paper, whose absorbing power for water
at 60° is expressed by the formula T = 3S2. The experiment
was made at two different temperatures.

Ascent of liquid

At the tempe

•ature of 60°.

At the temperature of 85°.

in inches,

Corresp. time

Value of T

Corresp. time

Value of T

S.

in minutes,

bv formula

in minutes,

by formula

T.

T = 64 8*.

T.

T=48 SP.

0

0

0

0 0

•25

...

3 3

•50

16

16

12 12

•75

26 27

100

65

64

46 48

1-25

73 75

1-50

147

144

200

261

256

Taking the diffusibility of water as unity, that of the oil will
be expressed by \ I gj = *216.

The results of this experiment also show that the rate of dif-
fusion is increased by an increase of temperature. Within cer-
tain limits, the diffusibility of different liquids seems to increase
proportionably with an increase of temperature.

The following experiment was made to determine the diffusi-
bility of different solutions of starch in water.

Experiment XI.

The first solution of starch contained \ per cent, of starch,
the second 1 per cent., and the third 2 per cent. ; that is, the
weights of starch dissolved in the same weights of water were as
the numbers in the geometrical progression \, 1, and 2. The
absorbent used was unsized paper of high absorbent power.

The results of the experiment gave the following formulas of
ascent of the different liquids : —

Formulae of ascent.
Distilled water . . . . T=MS2
Solution No. 1 . . . . T= 2 S2
Solution No. 2 .... T=56S2
Solution No. 3 . . . . T= 16 S2

Hence we find from equation (10), diffusibility of water being
unity,

Laws of Absorption of Liquids by Porous Substances. 507

Diffusibility sol. No. 1 =740= -74 x -6°.

„ „ No. 2 = *447 = *74x *6 very nearly.

„ „ No. 3 = -262 = -74 x -6s very nearly.

Here it will be seen that the numbers expressing the diffusi-
bility of the different solutions are very nearly in geometrical
progression.

Heuce we derive the following law : — If the per -cent age of
starch contained in three different solutions be expressed by an
ascending geometrical progression, the diffusibility of the solutions
will be expressed by a descending geometrical progression.

The results of the following experiment are confirmatory of
this law.

Experiment XII.

In this experiment the liquids used were six different solu-
tions of carbonate of potassa, containing respectively £, J, 1, 2, 4,
and 8 per cent, of the salt ; that is, the weights of salt dissolved
in equal parts of distilled water were as the numbers in the geo-
metrical progression J, -J, I, 2, 4, and 8. The absorbent used
was unsized paper.

The results of the experiment gave the following formulae of
ascent of the different liquids : —

Formulae of ascent.
Distilled water . . . . T=3'5S2
Solution No. 1 ... . T=3-25 S2
No. 2 . . . . T=3«75S2
No. 3 .... T= 4S2
No. 4 ... . T=4-33S2
No. 5 . . . . T= 5S2
No. 6 ... . T=5-33S2

Hence we find from equation (10), diffusibility of water being-
unity.

Diffusibility sol. No. 1 = 1-038
„ No. 2 =
„ No. 3 =

No. 4=
„ No. 5 =

„ No. 6 =

Hence it appears that the numbers expressing the diffusive-
ness of the different solutions are very nearly in geometrical
progression, thereby confirming the law enunciated in the fore-
going experiment.

The diffusibility of solution No. 1 is a little greater than that
of pure water. A slight addition of an alkaline salt to water
seems to increase its diffusiveness.

2L2

formula 1 -038 X -59^.

038

. . 1038

•978

. . -986

•935

. . -936

•898

. . -889

•838

. . -844

•810

. . -801

508 Mr. T. Tate's Experimental Researches on the

The following experiment was made to determine how far the
law of diffusion is affected by direct chemical action.

Experiment XIII.

The absorbent used in this "experiment was unsized paper
saturated with a solution of 8 per cent, of carbonate of potassa
and then carefully dried, so that the paper was uniformly impreg-
nated with the salt. The liquid was diluted sulphuric acid having
a specific gravity of 1013.

Ascent of liquid

Corresp. time

Value of T

in inches,

in minutes,

by formula

s.

T.

T=ll S2.

0

0

0

10

11

110

20

43

440

2-5

68

687

30

97

990

Hence it appears that the general formula, expressing the rate
of diffusion, holds true in cases where there is a known decided
chemical action. It would seem that the ascent of the liquid
through the pores of an absorbent is in most cases attended by
chemical action.

The diluted acid used in this experiment was found to have
the same diffusibility as distilled water, the formula of diffusion
being T = 3*5 S2 at mean temperature. The slow rate of diffu-
sion of the diluted sulphuric acid in this experiment is not a
little remarkable. In most cases direct chemical action tends to
accelerate the diffusion.

The following experiment was made to determine the amount
of heat evolved by the process of absorption.

Experiment XIV.

The bulb of a thermometer was infolded with dry unsized
paper, which extended about one inch below the bulb. The
extremity of the paper was brought in contact with water placed
in a small-mouthed bottle. The temperature of the water was
the same as that of the air, viz. 56°. As the liquid ascended
through the pores of the absorbent, the temperature, indicated
by the thermometer, gradually rose until it reached 61°, giving
a maximum rise of 5° due to the heat evolved by absorption.

The naked bulb of a thermometer was inserted in some dry
plasterof paris placed in an evaporating dish. A sufficient quantity
of water, having the same temperature as the air, viz 56°, was
then poured into the dish; after the higher portion of the
plaster of paris had become wet by absorption, the temperature,

Laws of Absorption of Liquids by Porous Substances. 509

indicated by the thermometer, rose to (360,5, giving a maximum
rise of 10o,5 due to the heat evolved by absorption.

This change of specific heat, which always takes place during
the process of absorption, is doubtless indicative of chemical
action.

It may be worthy of remark, that an absorbent may be used
again and again, with distilled water, without suffering any
change in its power of absorption.

The following experiments were made to determine a statical
measure of the force of absorption in different porous substances.

Experiment XV.

By means of the apparatus represented in the annexed dia-
gram, the effect of the force of absorption in elevating a column
of liquid may be strikingly ex-
hibited. ABCDa bent tube,
open at both extremities, having
the portion ABC considerably
wider than the other portion
CDK; the portion A B con-
tains mercury, and that of B C
water; FG a piece of dry
calico, having a narrow strip,
m n, proceeding from it, insert-
ed through the mercury in con-
tact with the water B C ; the
extremity K of the tube C D is
inserted in a vessel E, contain-
ing water. As the absorbent,
F G, draws the liquid from B C,
the water rises in the tube K C
in opposition to gravity. If the diameter of the tube C D be
T^ths of an inch, the water will have risen in the tube K C to
the height of about 9 inches in the course of six hours, the air
being in an average state of dryness ; and when the air is un-
usually warm and dry, to a much greater height in that time.
The effect is simply due to the force of absorption, there being
no endosmose connected with the phenomenon.

The following form of this apparatus enables us to measure the
force of absorption by the fall of a column of mercury.

L E D C a small bent tube proceeding from a wide tube or
cup L P, ground at the top, which is covered by a plate, P K,
of polished slate, having one or more small 'perforations, 0,
through it; FG an absorbent placed upon the plate. The
bent portion LEDC contains mercury, and the cup, L P, is
filled with water. As the liquid diffuses itself through the pores

rD

510 Prof. Maguus on the Conduction of Heat by Gases.

of the absorbent, the mercury
rises in the cup to supply the
place of the water thus absorb-
ed, and the column CD de-
scends. This goes on until the
force of absorption is balanced
by the downward pressure of
the mercury in the tube LE,
that is, by a column of mercury
measured by the descent of the
mercury in the tube C D. The
following results were obtained
by means of this apparatus : —

Unsized paper laid upon the plate caused the column of mer-
cury C D to descend 2'3 inches, which is equivalent to a column
of 31 inches of water.

Brick caused the column of mercury CD to descend 13
inches, which is equivalent to a column of 17 inches of water.

Plaster of parts, encased in a glass tube, caused the mercury to
descend 2*7 inches, which is equivalent to a column of 36 inches
of water. And so on to other absorbents.

Hastings, November 10, 1860.

[To be continued.]

LXVIII. On the Conduction of Heat by Gases. By G. Magnus*.

THE cooling of a body in vacuo depends simply on the ex-
change of heat by radiation between the cooling mass and
the encircling envelope. If the space contains gas, an ascending
current is formed, which accelerates the cooling, added to which
the property which the gas has of transmitting heat, or its
diathermancy, concurs in producing cooling, provided the gases
can conduct heat. Dulong and Petit, in enunciating their law
of the loss of heat, have neglected the last two actions, manifestly
because they are infinitely small compared with the influence of
the ascending currents. Since then it has been universally ad-
mitted that the differences in the cooling of different gases depend
on the different mobility of their particles. Cooling takes place
much more rapidly in hydrogen than in other gases. With the
same amount of heat this gas expands not more, but less than
atmospheric air ; the changes in density in the former gas are
less than in the latter. But it is the difference of specific gravity
which produces currents. If, therefore, different gases by contact
with a warmer body all become equally heated, the currents in

* Translated from the Bericht der Berliner Akademie, 1 860, p. 485.

Prof. Magnus on the Conduction of Heat by Gases. 511

those gases which have a greater coefficient of expansion must
be greater than in the rest ; for example, in carbonic acid more
than in hydrogen. As this is not the case, it must either be as-
sumed that the friction of the gaseous particles against each
other is so great that the influence of the greater expansion is
neutralized by it, which will with difficulty be admitted, or it
must be assumed that gases by contact with a hot body
become heated to a different extent. Such a difference in the
degree of heat would take place if the gases had different capa-
cities for heat ; but as the specific heats of hydrogen and atmo-
spheric air are the same, there remains no other explanation for
the more rapid cooling in hydrogen than that this gas can
transmit heat from particle to particle, in other words, can con-
duct it, and that it possesses this property in a higher degree
than other gases. Its low density appeared to be in disaccord-
ance with this idea, and it appeared necessary to decide by ex-
periments how far it is founded.

The impulse to these experiments was given by a repetition
of Mr. Grove's interesting observation, according to which a
platinum wire is less strongly heated when surrounded by
hydrogen than by atmospheric air, or another gas. In this
repetition it was found that hydrogen exerted its preventive
action even when a layer only 0*5 millirn. thick surrounded
the wire, and it was the same whether the tube containing it
was in a horizontal or vertical position. In such a narrow tube,
especially when it is horizontal, currents can scarcely occur;
and when there are none, there remains no other explanation
than that hydrogen conducts heat better than other bodies.

The simplest mode of ascertaining whether a gas conducts
heat, consists in warming it from above, and observing the
action on a thermometer placed within. It might be objected
to this method, that, even with heating from above, currents in
the gas might be formed, and that thereby the temperature in-
dicated by the thermometer in various gases might be different
without any difference in conductibility.

There is one method of testing this objection. For if, in fact,
a gas can conduct heat, the temperature assumed by a ther-
mometer in a space heated from above must be lower when the
conducting substance is wanting than when it is present ; that
is, it must be lower in vacuo than in a space filled with air.

In order to ascertain whether this was the case, a glass appa-
ratus was used, in which a thermometer, observable from with-
out, was firmly fixed. It could be filled with different gases,
and these could be variously dilated. The upper part of this
apparatus was maintained at the same temperature, namely that
of boiling water, and the temperature was observed which a

512 Mr. A. Cayley on a Relation between

thermometer introduced into the interior ultimately assumed.
Of course the experiments with this apparatus were not made
without numerous precautions ; it was more particularly neces-
sary that the whole apparatus should be always under the same
conditions, so as to give off the heat imparted to it always in the
same manner. For this it was necessary that the space sur-
rounding it should always be at the same temperature. In
these experiments the temperature of the surrounding space was
15 degrees.

In this way the following results were obtained : —

1. The temperature which a thermometer ultimately assumes
in a space heated from above, differs when this space is filled
with different gases.

2. In hydrogen the temperature is higher than in any other
gas.

3. In this gas the temperature is higher than in vacuo ; and
the denser the gas is, the higher is the temperature.

4. Hence hydrogen conducts heat like metals.

5. In all other gases the temperature is lower than in vacuo ;
and the denser they are, the lower is the temperature.

6. It cannot hence be concluded that gases do not conduct
heat, but only that they do this in so small a degree that the
action of conduction is cancelled by their diathermancy.

7. This remarkable property of hydrogen is evinced not only
when it moves freely, but also when it is contained between
eider down, or any loose substance which hinders its motion.

8. The great conductibility of this gas is a further confirma-
tion of its analogy with metals.

9. Hydrogen conducts not only heat, but also electricity,
better than other gases.

LXIX. On a Relation between two Ternary Cubic Forms,
By A. Cayley, Esq.*

THE cubic form
a^ + J^-f s3 + Qlxyz

is in general linearly transformable into the form

(X + Y + Z)3 + 27AXYZ.
In fact, writing

X=2fo-y-*,

Y = 2/y-<2r-o?,

Z = 2lz-sc— y,

* Communicated by the Author.

two Ternary Cubic Forms. 513

we have identically

(l-2/+4/2)(X + Y + Z)3-f24(/-l)3XYZ

and the value of k consequently is

l_ 8(/-l)3

9(l-2/+4/2)'

If, however, /=1 or /=— \, the transformation fails. In the
former case, viz. for /=1, the equations for the linear transforma-
tion become

X=2#— y—z,

Y=2y-z-x,

Z = 2z—x—y,

which give X + Y + Z = 0, so that X, Y, Z are no longer inde-
pendent ; and the formula of transformation becomes

(X + Y + Z)3=0.

It may be noticed that the invariant S of the form

x3 + y3 + z3 + 6lxyz

is S= — l+l4, so that 7=1 is one of the values which make S
vanish. And the above transformation is not applicable to the
cubic form x3 + y3 + z3 + 6xyz} which is a form for which S
..vanishes. The transformation, however, holds good for 1=0,
which is another value which makes S vanish ; or it does apply
to the form aP + y3-^^, for which S vanishes. The transforma-
tion, in fact, is

(X + Y + Z)3 + 24XYZ = -8(arJ+2,3 + 23),
with the linear equations

X=-y-z,
Y=-*-#,
Z = —x—y.
The above two forms for which S vanishes, viz.

#3 + y3 + z3 + 6xyz,
xS + yS + z3,

are, notwithstanding, equivalent to each other, as appears by the
identical equation

(x + y + z)3 + (x + coy + <w2*)3 + (x + ©2y + <oz)3
= 3(x3 + y3 + z3 + 6xyz),
where o> is an imaginary cube root or unity. In the latter of the

514 On a Relation between two Ternary Cubic Forms.

two cases of failure, viz. for 1= — £, the equations for the linear
transformations are

X = Y=Z=— x—y— z;

so that X, Y, Z are not only not independent, but they are con-
nected by two linear relations. And the formula of transforma-
tion becomes

(X + Y + Z)8-27XYZ=0,

which is, in fact, true in virtue of the equations X = Y = Z.
The two forms of equation,

x3-\-y8 + z3 + 6lxyz = 0f
(x+y + z)3 + 27kxyz=Q,

represent each of them equally well a curve of the third order
without a double point. In the first form the three real points
of inflexion are given by (# = 0, y-\-z = 0), (y = 0, z + x=0),
(2=0, x+yz=0) j or what is the same thing, the points in
question are the intersections of the lines x=0, y = 0, z = 0 with
the line x + y + z=0; or we have x+y+z=Q for the equation
of the line through the three points of inflexion. And the equa-
tions of the tangents at the points of inflexion are

2lx—y—z=0, 2ly—z—x=0, 2lz-x—y=0.

For the second form it is obvious that the points of inflexion are
the intersections of the lines x=0, y=0, z=0 with the line
x-t-y + z = 0; and, moreover, that the lines x = 0, y==0, z=0
are the tangents at the point of inflexion.

The first of the above-mentioned forms, however, cannot repre-
sent a curve with a double point. In fact the condition for its
doing so would be 1+8/^=0; but when this condition is
satisfied, the left-hand side breaks up into linear factors, and
the equation represents, not a proper curve of the third order,
but a system of three lines. The second form can represent a
curve having a double point ; viz. if k= — 1, the curve will have
a conjugate or isolated point at the point x^y=z. It is clear
a priori that (#=0, y = 0, z = 0 being real lines) neither of the
forms can represent a curve of the third order having a double
point with two real branches through it, since in this case the
curve has only one real point of inflexion.

I have elsewhere used the word " node " to denote a double
point, and I take the opportunity of suggesting the employment
of the words " crunode M (crus) and " acnode n (acus) to denote
respectively a double point with two real branches through it,
and a conjugate or isolated point.

2 Stone Buildings, W.C.,
October 19, 1860.

[ 515 j

LXX. Chemical Notices from Foreign Journals.
By E. Atkinson, Ph.D., F.C.S.

[Continued from p. 385.]

PROF. SCHROTTER has described* the occurrence of ozone
in a specimen of fluor-spar which is found at Wulsendorf.
It is a darkish-blue variety, and when scratched or rubbed in a
mortar, it emits a powerful odour closely resembling that of
bleaching powder. The phenomenon has long been known, and
has been ascribed to the presence of chlorous acid.

On rubbing the mineral in a mortar, Schrotter observed that
the odour emitted was exceedingly like that of ozone. When it
was triturated in a mortar with iodide of potassium solution, the
liquor became brown from the liberation of iodine, and when a
piece of ozone test-paper was held over the mortar it became di-
stinctly blue. This reaction might, however, have been produced
either by a chlorine compound or by ozone. But when tritu-
rated with water or with alkalies, although a powerful smell was
produced, no trace of a chlorine compound could be detected in
the liquid.

When the mineral was triturated with chloride of sodium,
chlorine was liberated, as was evident from the smell, and also
by the fact that the reaction for chlorine was obtained when a
plate moistened with nitrate of silver was held over the mixture.
This must have been due to ozone, which has the property of
expelling chlorine from its compounds ; it is inconceivable that
any oxygen compound of chlorine could have the property of
liberating chlorine under these circumstances. Besides, the
mineral, when triturated with pure wood-charcoal, emitted no
odour, while, as a control experiment showed, the reverse is the
case with hypochlorite of lime.

When the mineral was heated, a strong odour was perceived,
which afterwards disappeared. Heated more strongly it lost its
dark-blue colour, and appeared of a reddish-brown colour from
sesquioxide of iron.

The following experiment was conclusive as to the absence of
chlorine : — The anterior part of a piece of combustion tubing
was filled with pieces of the mineral, while the rest of the tube
contained pieces of porcelain. A potash apparatus containing
iodide of potassium and starch was fitted to the posterior part of
the tube. The part containing the mineral was gently warmed,
and the rest of the tube was heated to redness, while at the same
time purified air was passed through the tube. No liberation of
iodine was observed in the potash apparatus. Had any one of the
oxygen compounds of chlorine been present, in its passage over

* Sitz.-Ber. der Wiener Akademie, vol. xli.

516 M. Millon on Nitrification.

the porcelain it would have been decomposed into oxygen and
chlorine, which would have liberated some iodine, whereas ozone
would at that high temperature be converted into ordinary
oxygen, which would be without action on the iodide.

To determine the quantity of ozone, a given weight of the
mineral was triturated in a mortar with iodide of potassium, and
the liberated iodine estimated by means of hyposulphite of soda.
In this way its quantity was found to amount to 0*02 per cent.

The ozone doubtless exists ready formed in the mineral, as
the following experiment shows that fluor-spar can absorb ozone.
17 grms. of a specimen of fluor-spar, which by a preliminary ex-
periment was found to contain 0*00011 per cent, of ozone, was
exposed for six hours in a current of strongly ozonized air, and
at the expiration of that time was found to contain 0001 per
cent. Pieces of pumice exposed in a similar manner to ozonized
air were found to absorb ozone.

Millon has communicated the following observations on nitri-
fication*, which in another form have been already made by
Schdnbeint- Under the conditions of high temperature, nitre is
always produced with regularity, provided a humus product, an
ammoniacal salt, and a mixture of earthy carbonates are present.
The solid mass must further be constantly moistened and exposed
to the air.

The necessity of the presence of humus is not at once appa-
rent, and yet it gives a clue to the process. The alkaline humate
which is formed energetically absorbs oxygen, and this oxidation
is transferred to the ammonia. The part which humus plays is
evident from the fact that it may be replaced by other oxidizable
substances, such as phosphorus. When a stick of this substance
is placed in a large glass globe and half covered with ammoniacal
water, a slow combustion of the phosphorus soon commences and
incites that of the ammonia. After some time nitrate of am-
monia is found in the liquor. The ammonia in this experiment
may be replaced by carbonate of ammonia, but not by the hy-
drochlorate or the sulphate. It appears, therefore, that nitrifi-
cation takes places in the atmosphere between the emergent part
of the phosphorus, the water, the air, and the ammonia.

Millon also shows, as had already been done by TuttleJ, that
copper can be similarly used to effect nitrification.

Ammonia is not the only substance which can be thus oxidized.
When a stick of phosphorus is placed in a colourless solution of
a manganese salt, it speedily becomes of a beautiful violet tint.

* Comptes Rendus, October 8.

t Phil. Mag. vol. xiii. p. 440.

X Liebig's Annalen, voi. ci. p. 283.

Rose on the Heteromorphous Conditions of Carbonate of Lime. 517

G. Rose* has communicated the commencement of a series of
experiments on the circumstances under which the different forms
of carbonate of lime (calc-spar, Arragonite, and chalk) are formed.
When chloride of calcium was added to a fusing mixture of equi-
valents of carbonate of potash and carbonate of soda, it dissolved
without effervescence ; when a portion of the cooled mass was
placed in water it gradually dissolved, leaving a pulverulent
residue of carbonate of lime. Viewed under the microscope
shortly after treatment with water, it was found to consist of
small globules, which after twenty-four hours changed into well-
formed individual or aggregated rhombohedra.

When another piece was thrown into hot water and boiled, it
was seen to consist of microscopic prisms with occasional rhom-
bohedra. This residue, on standing, gradually changed into
aggregations of calc-spar.

The same results were obtained when calc-spar or oxalate of
lime were added to the fusing mixture, except that in the latter
case some carbonic oxide was given off.

As calc-spar had not been directly formed in these experiments,
Rose, with Siemen's assistance, repeated Sir James Hair's cele-
brated experiment, by which marble is said to be obtained when
chalk or compact limestone is heated in a closed vessel under
pressure. Fine chalk was pressed in a musket-barrel which was
hermetically sealed, and heated in a gas furnace, the temperature
of which could be raised so as to melt large masses of platinum.
During the experiment the barrel burst. On afterwards exami-
ning the contents, the chalk was agglomerated into a compact
light-bluish mass, full of cracks. The experiment was repeated
with small pieces of calc-spar, but the same result was obtained.
It appears thence that these substances are not changed into
distinctly crystallized calc-spar by being heated in a closed space.
Rose considers that Sir James Hall thought the compacted mass
to be crystalline marble.

When a solution of carbonate of lime in carbonic acid water
was allowed to stand, a crust and a sediment gradually formed.
The latter consisted of chalk, the former was found to be com-
posed of very perfect microscopic rhombohedra.

When the liquid was placed on a hot stove, a disengagement
of gas commenced, which lasted for six or eight hours. In this
case the crust which formed consisted chiefly of acicular crystals
of Arragonite, while the deposit was nothing but well-shaped
rhombohedra.

When the solution was evaporated, prisms of Arragonite and
rhombohedra, laminse and plates of calc-spar were obtained.

Hence by evaporating a solution of carbonate of lime in car-
* Ber. der Berl Akad. I860.

518 M. Carius on a New Method of Analysis.

bonic acid at ordinary or higher temperatures, all the three forms
are obtained — chalk, calc-spar, and Arragonite.

Calc-spar is formed under other circumstances. When a solu-
tion of bicarbonate of soda was precipitated with chloride of cal-
cium, and the milky liquid allowed to stand, rhombohedra with-
out Arragonite were obtained; but when chloride of calcium
was precipitated by neutral carbonate of soda, Arragonite only
was obtained. It appeared as if carbonate of lime only separated
as calc-spar when surrounded by an atmosphere of carbonic acid.

To determine the limits within which the two forms are pro-
duced, the fused mass was gradually added to water at different
temperatures. The result was, that between 100° and 90° Arra-
gonite was almost exclusively formed : below that point, princi-
pally prisms of Arragonite and rhombohedra of calc-spar; at
70° the rhombohedra predominated, and laminae of calc-spar
appeared, and at 30° the formation of Arragonite ceased. The
limit to its formation appeared to lie between 50° and 30°.

The author is still engaged with the subject.

Carius has described* a new method of elementary analysis,
by which sulphur, phosphorus, and chlorine in organic bodies
may be determined. It consists in heating the substance in
closed tubes with nitric acid.

The substance to be analysed is filled into small thin glass
bulbs which are sealed before the blowpipe. The bulb is then in-
troduced into a tube of about half an inch diameter sealed at one
end, and half-filled with nitric acid of sp. gr. 1*2. This tube is
then drawn out in the gas-flame, and, the nitric acid having been
raised to boiling, the tube is sealed. By careful management
the bulb is broken, and the tube then heated in a Bunsen's air-
bath. This consists of a rectangular sheet-iron or copper box,
about 14 inches long and 4 inches high ; in one end there are
two openings, which contain pieces of iron gas-pipe about an
inch wide and closed at one end. The tube to be heated is
placed in one of these pipes and loosely closed by a cork. The
bath is then heated by a Bunsen's burner, the temperature being
indicated by a thermometer. The advantage of this air-bath is,
that any possible explosion is quite harmless, provided the bath
be placed with the open end of the iron tube in the corner of a
room.

After the oxidation is complete, which occupies a few hours,
the finely drawn out end of the tube is softened in the blowpipe
flame; it bursts and gives exit to the gaseous products without
any loss of the liquid. The sulphur is present in the liquid con-

* Liebig's Annalen, October 1860.

M. Caron on Cementation, 519

tent3 of the tube as sulphuric acid, and is determined in the
usual way, with obvious analytical precautions.

The applicability of this method was shown by the analysis of
bisulphide of carbon, of sulphite of ethyle, and of many other
sulphur compounds, and gave very satisfactory results.

Some sulphur compounds by oxidation with nitric acid yield
the sulphur in the form of sulphurous acid. These are best de-
termined by fusion with nitrate of soda.

With chlorinated bodies, a part of the chlorine is usually found
in the free state among the gases, and a modification of the
method is necessary. This consists in opening the tube under a
solution of sulphite of soda, by which the chlorine is absorbed
and immediately converted into hydrochloric acid, which is de-
termined in the usual manner.

Bromine and iodine can also be estimated by this method,
which is further applicable to the case of metallic sulphides. The
analytical results were found in all cases to be very exact.

The following experiments were undertaken by Caron* to
ascertain the nature of the process of cementation.

An iron bar, completely surrounded by pieces of charcoal, was
packed in a porcelain tube which was placed in a reverberatory
furnace, and heated to redness, while pure hydrogen, carbonic
oxide, nitrogen, air, and carburetted hydrogen gases were passed
through the tube in successive operations, each lasting two hours.
In none of these cases was there any true cementation.

With ammonia it was different ; after two hours' heating, the
bar was immediately tempered and hammered, and again tem-
pered, and then exhibited a regular and beautiful cementation of
■£$ inch in depth. This was attributable to the action of am-
monia on carbon, forming at this temperature cyanide of ammo-
nium, which gives up carbon to the iron and forms steel. A
direct experiment was made, omitting the charcoal, and heating
an iron bar placed in a porcelain tube to redness in a current of
gaseous cyanide of ammonium. After two hours' heating, the
bar was treated as before, and was found quite cemented, espe-
cially at the end nearest the place at which the gas entered.

It seemed probable that this property of cementation was not
confined to cyanide of ammonium, but was shared by other alka-
line cyanides : the cementation by means of yellow prussiate of
potash is probably of this kind. To decide this point experi-
mentally, the bar was placed in the tube surrounded by charcoal
impregnated with carbonate of potass, and heated to redness in a
current of air. Under these circumstances, as is well known,
cyanide of potassium is formed. After two hours the bar was
* Comptes Rendus, October 8, 1860.

520 M. Carlet on the Formation ofRacemic Acid.

found cemented in a magnificent manner to a depth of -fo inch.
Soda, baryta, and strontia act in the same manner, but this is
not the case with lime. This doubtless arises from the fact
(which was proved by experiment) that it does not form cyanide
of calcium when heated to rednes3 in a current of cyanide of
ammonium.

The action of the various receipts for cementation may be ex-
plained by the formation of cyanides. It will be found that in
all cases they contain the elements of the formation of alkaline
cyanides.

The production of tartaric acid by the oxidation of milk-sugar,
which Liebig discovered, has been already noticed in this Journal*.
Carlet f has investigated the action of nitric acid on dulcine, a
saccharine substance resembling mannite, which is obtained from
Madagascar. He employed, with some modifications, Liebig's
process. The oxidation of dulcine had been previously studied
by Laurent and Jacquelain, who obtained mucic and oxalic acids.
Besides these, Carlet found about 1^ to 2 per cent, tartaric acid,
and a saccharine substance which appears to have the formula
C12 H12 O12; it differs from dulcine in not being coloured yellow
by potash, and in reducing oxide of bismuth, which dulcine does
not do.

In addition to these, Carlet ascertained the existence oiracemic
acid in quantities of about 1^ per cent, of the dulcine taken.
The crystals of this acid were found to be identical with those
prepared in other ways, both in form and in chemical properties.
A more striking proof was, that it was optically inactive, but
could be transformed into dextro-tartaric acid and lsevo-tar-
taric acid. This was effected under Pasteur's cooperation by
preparing racemate of cinchonidine and exposing it to crystalli-
zation. After some days laevo-tartrate crystallized out, and after-
wards dextro-tartrate, from which the respective acids were ob-
tained. The great interest of this lies in the fact that dulcine,
an optically inactive substance, gives rise to a substance which,
though also inactive, can be decomposed into two bodies which
are capable of deviating the plane of polarization in opposite
directions to an equal extent. In the case of Liebig' s experi-
ment, tartaric acid, which is a right-polarizing substance, is ob-
tained from milk-sugar, which is also right-polarizing. With
reference to dulcine, two hypotheses may be made — either that
an optically active substance can be obtained from an optically
inactive substance, or, which is more probable, that dulcine is
only apparently inactive, and is really composed of two substances,
one right-polarizing and the other left-polarizing, which just

* Phil. Mag. vol. xviii. p. 483. t Comptes Rendus, vol. li. p. 37.

M. Frohde on a new Aromatic Acid, 521

neutralize one another. This is probably the case with many
other substances : they are in the same condition as racemic aci(J,
which was supposed to be inactive, until Pasteur showed the
reverse.

Among the oxidation products of gelatine and albuminous
substances, Schlieper observed the presence of an oily body with
an odour like that of cinnamic aldehyde. It occurs along with
hydrocyanic acid, acetonitrile, propionitrile, valeronitrile, and
hydride of benzoyle. It was also found by Giickelberger among
the oxidation products of fibrine, albumen, and caseine. "Frohde
has investigated this body*, and has found it to be an aldehyde,
which by oxidation is converted into a new aromatic acid.

He obtained it in greatest quantity by the oxidation of gela-
tine by a mixture of sulphuric acid and bichromate of potass ;
the distillate from this action was neutralized with carbonate of
soda, and the liquid evaporated to dryness : the soda salts were
decomposed with sulphuric acid, and the liberated solid acids
freed from the accompanying volatile fatty acids by filtration
and by crystallization. The solid acids contained the new acid ;
it was separated from benzoic acid, which accompanies it, by
treatment with hot water, in which it is insoluble, while benzoic
acid readily dissolves. The quantity was found to be about
y1^ per cent, of the gelatine taken, that of benzoic acid being
■J. per cent.

The melting-point of the new acid is 97°, and it solidifies at
93 — 94°. It is readily soluble in ammonia and in ether. It
expels carbonic acid from carbonates ; ignited, it burns with a
smoky flame like benzoic acid. It has the formula C12 H* O4,
and the author names it collinic acid. Its neutral silver salt has
the formula C12 H3 AgO4; and there is a basic salt, C12 H3 AgO4,
AgO. The baryta salt has the formula C12 H3 BaO4 + HO. The
acid yields with iron a reddish-yellow precipitate.

The aldehyde of collinic acid is a viscous colourless liquid,

which by absorption of oxygen assumes a golden-yellow colour.

When digested with a strong solution of ammonia, it is con-

(C12 H3)3~l
verted into a crystalline body, which is apparently v J 3 f N2,

corresponding to hydrobenzamide.

Kolbe has given a preliminary notice f of some interesting re-
searches which have been made in his laboratory.

Vogt investigated the action of reducing agents on the body
(C12H6) (S204) CI, in the expectation of replacing chlorine by

* Journal fur Praktische Chemie, vol. lxxx. p. 34 1.
f Liebig's Annalen, September 1860.

Phil Mag, 8, 4. No. 136. Bwpph Vol. 20. 2 M

522 Vogt and Kalle on some new Organic Compounds.

C12H5"|

hydrogen, and so forming a body jj >-S204, which, on

Kolbe's view, would be an aldehyde derived from sulphuric acid.
He found that the chloride was in fact reduced, but that the re-
duction went further, and yielded a new body, C12 H6 S2. This is
a volatile stinking liquid, resembling mercaptan, and which, in
contact with oxide of mercury, forms a body, C12 H5 H&S2.

This body is, in fact, the mercaptan of an alcohol, C12 H6 O2,
which is the next lower homologue of the alcohol of benzoic acid,
C14H802. This latter body is usually called toluylic alcohol
by continental chemists, and the hitherto hypothetical alcohol,
C12H602, which is isomeric with phenylic alcohol, is called
benzylic alcohol.

By treating the new sulphur-alcohol with pentachloride of
phosphorus, Vogt obtained a chloride with an odour like chlo-
ride of toluyle, and which is probably chloride of benzyle,
Cl2H5Cl; from this he hopes to get the alcohol C12H602, and
the acid Cl2H404. This latter, it may be observed, would be
isomeric, and probably identical with Fronde* s new acid.

Kalle had investigated the action of chloride of benzoyle on
zinc-ethyle, and had obtained a body, C,8H10O2, which was a

C12H51

mixed acetone, /-14TT5 fC202. The publication of Freund's re-
searches caused a discontinuance of these experiments. He
tried the action of zinc-ethyle on the body (C12 H5) (S204) CI,
by which he hoped to obtain a body of the nature of an acetone,

C12HH
but containing sulphur, n4jr^ f S204. The two bodies, in

fact, readily mix and form a solid white mass, which appears to
be a compound of chloride of zinc and the new body. When
this mixture is dissolved in water and evaporated, a new substance
is obtained. This is not the above body: it has the formula
C12 H6 S2 O4, and Kolbe regards it as an aldehyde analogous to
hydride of benzoyle :

cl2^5|s2o4 cl2**5jc2o2

New Body. Benzoic aldehyde.

Its formation might be represented by supposing that the
acetone had first been formed, and that then this body had been
decomposed by the action of water. Thus :

^4H5Vs204 + 2IIO==C12jII5|s204 + C4H5OHO.

Pfaundler has examined the action of pentachloride of phos-
phorus on camphor*. When equivalents of these substances
* Liebig's Annalen, July I860.

Sensibility of the Human Ear for the Pitch of Musical Notes. 523

were mixed, the mass assumed a crumbly appearance : there
was no action in the cold ; but when heated to 60° a copious
disengagement of hydrochloric acid gas took place, and a yel-
lowish liquid was formed which commenced to boil at 83°.
When this liquid was treated with water, a white flaky substance
was deposited which crystallized from alcohol in beautiful feathery
interwoven crystals. These, on analysis, were found to have the
formula C20 H15C1, and their formation was obviously in accord-
ance with the equation

C20H1602 + PC15=P02C13 + HC1 + C20H15C1.

When two equivalents of pentachloride were used for one of
camphor, the reaction was found to be essentially the same, but
the mass required to be heated to 100°. On subsequent mix-
ture with water a viscous oil separated, which only became solid
after a few days. This mass, by suitable treatment, yielded the
body C20 H16' CI2 in crystals like the first. Placed over sulphuric
acid, it gave off hydrochloric acid, and produced the first com-
pound. It is probable that its formation proceeds in accordance
with the equation

C20H16O2 + PCl5=PO2Cl3 + C20H16Cl2,

and that, in consequence of the heat, a portion of the body
C20H16 CI2 is decomposed.

This latter chloride was treated with sodium-alcohol, acetate
of silver, and with ammonia, but the experiments did not give
definite results. The compound C20 H15 CI does not act on the
plane of polarization. The other produces a small right devia-
tion.

LXXI. On the Sensitiveness of the Human Ear to the Pitch of
Musical Notes. By F. Fessel*.

THE Conservatory of Music at Cologne has recently decided
on adopting, as a standard, the new Parisian tuning-fork ;
and the Concert Society here intend introducing the new pitch
at the next winter concert.

In consequence of my having expressed a wish to possess a
tuning-fork precisely similar to that belonging to the Conserva-
tory, the fork that had been procured from Paris was kindly
placed at my disposal.

In tuning forks I invariably pursue Scheibler's plan, which
has hitherto proved itself the only safe one. The fork to be
tuned, before having its vibrations compared with the seconds'
pendulum, is, as is well known, tuned as far as possible by ear.
My instrument and the seconds' pendulum happening on this

* Translated from Poggendorff's Annalen, No. 9, 1860, by F, Guthrie,

3M3

524 Sensibility of the Human Ear for the Pitch of Musical Notes.

occasion to be in different rooms for the sake of convenience, I
naturally endeavoured to finish tuning my fork by ear only. In
this, however, I found I could not succeed ; and having investi-
gated all the circumstances with the greatest care, I was led to
the following remarkable conclusion.

I observed that a fork which I had tuned by holding it to my
right ear while the standard was held to my left, when compared
with the fork used for the exact pitch, made one vibration too
many in the course of several seconds ; while a fork tuned by
being held to my left ear while the standard was held to my
right, vibrated less rapidly than the other. The fork in accurate
pitch gave the lower note. Consequently T hear all notes some-
what higher with my right ear than with my left.

I have since examined my musical friends, and I have not yet
found one, even among part-musicians, whose ears are precisely
alike in estimating the pitch of musical notes. By continued
practice I am able to distinguish, by a simple experiment, with
which ear anyone hears the highest*. In this experiment I have
never yet failed. The person under examination holds a care-
fully tuned fork in each hand, and having sounded them simul-
taneously, he brings them successively the one to the right, the
other to the left ear. I place my right ear at equal distances
from both of his, my left being turned away and covered lightly
with my hand.

In this position that ear of the person under examination
near which the fork is held which seems to me to have the high-
est pitch, hears all sounds higher than the other. If the tuning-
forks are exchanged, precisely the same phenomenon results
with respect both to the person under examination and to the
listener. As far as my present experience extends, most people
(here in Cologne) hear higher with the right ear than with the
left.

These experiments are so striking that no one has hitherto
attempted to dispute them. Indeed I had secured myself against
contradiction, by always requesting the gentlemen whose hearing
I tested to state their own opinions distinctly before I acquainted
them with my explanation of the phenomenon. This precau-
tion seemed to me to be necessary, since no one could blame a
musician for resisting the imputation that he heard differently
with different ears. In the end all were extremely astonished.
I pass over the various playful questions and remarks that have
been made to me — " Whether for the future, before begin-
ning a concert, the hearers are to be examined and a place
allotted to each according!)', where he may be able to hear with
satisfaction " — " Whether instrumentalists are to be separated
* Without their having told me anything on the subject.

Notes to the Meditation on Poncelet's Theorem. 525

into two divisions, one of which is to use the A right pitch, the
other the A left" &c. I content myself with simply asserting
the fact as I have found it.

The reason for this difference of hearing is probably that the
external passage of the ear is set in vibration, like a speaking-
trumpet, by the sounds that enter it, and that this vibration
modifies the pitch of the entering sound more or less according
to the form of the individual ear.

The supposition that the waves of sound, before impinging on
the tympanum, have to pass through a thin film which covers it,
is less probable, since such a film would of course be subject to
change from time to time, and thus the whole phenomenon
might be altered.

As may be supposed, I have not as yet been able to collect
any information on this subject.

If, in measuring the number of vibrations of musical notes,
the above circumstance has not been taken into account, some
modest doubt of the accuracy of the results may not be altogether
unreasonable.

Cologne, September 1860.

LXXII. Notes to the Meditation on Poncelet's Theorem, including
a Valuation of the two new Definite Integrals

*»£ log cos <£ rl log (l+V^— b2 (cos <f>)%)

By J. J. Sylvester, M.A.,F.R.S., Professor of Mathematics
in the Royal Military Academy, Woolwich*.

Note A.

THE method given in the October Number of the Magazine
for approximately representing a quadratic surd by a
rational fraction is equally applicable to a surd of any degree.
To fix the ideas, suppose we wish to approximate in this manner

to-v/ll

If we assume N as the first approximation, and make

i^p+v7!^ m=p+j0v/e; n=p+/92^/r;

where p3 = l, and write

Communicated by the Author.

526 Prof. Sylvester's Notes to the

FgrrL' + ^M' + ^N',

%±M*, %=%&, U8=J?B*,

r8 r3 xl

V — — JH* V— ^R* V„—^iP*

r3 rj *j

we may easily establish the following propositions, which indeed
are almost self-evident: —

(1) Each U and V is a rational fraction.

(2) When i= oo, eachU=Rs, each V=R*.

(3) For all finite values of i, R* is intermediate between the

least and greatest U, and R1* between the least and greatest V.

So in general if k is any prime number, we may form (&— 1)
cycles, each cycle containing k fractions possessing precisely

analogous properties as regards representing approximately and

i
limiting the successive powers of R*. By means of these for-
mulae [the theory of which might be extended to algebraic quan-
tities of every order (in Abel's sense of the word)], we obtain a
complete command over the integration of surd quantities in
general as they may appear in any physical problem, being
thereby enabled to represent the integrals, not merely arithmeti-
cally, but analytically (which is of much higher importance) by
logarithmic and circular functions to any degree of accuracy that
may be required, and with known assignable numerical limits of
error.

Note B.

This note relates to the concluding paragraph of the long

note at page 313 in the October Number of the Magazine.

2
I find that the ith inferior limit to F(c) — log j, when c differs

indefinitely little from unity given by the method therein ex-
plained, is

2*-l
. 2 2v*=i C°S 2k w /. 2*-l y

v1+(sm_-v

and that the superior limit is

Meditation on Poncelet's Theorem. 527

kir
cos — 7-
, 2 7T , 2v^=i r. » . / • ^Y

lo^ + ^+7^47A77'."l^v cos vnT;-

V1 + (smT)

When i=oo these limits of course come together, and the finite
sums resolve themselves into the definite integral

~ 1 ®t */i , / •==ri cos" J sin t) ,
7tJ0 Vl + (sinT)2 v ;'

of which, therefore, the value must be log 2. Hence, writing
(sin r)2=cos 20, we obtain

I

\ flsinfl log2 7r
\/cosT= V2 4'

iVote C/

It may be shown that any of the expressions for N* derived
from making « = oo in the general formulae given in Note A, are
in fact tantamount to its representation as a definite integral of
a very simple kind. I shall not go into the proof of this here ;
it may be sufficient to indicate that it depends upon the fact
that the equation of infinite degree ($#)*+ (^<r)i + (^)f4-&c,
may be resolved into sets of factors of a known form. In
the question before us, the function to be so resolved is the
denominator of any one of the quantities analogous to U or V
in Note A ; and cj)X, tyx, $x . . . become linear functions of x
with imaginary coefficients. Its resolution into factors is ren-
dered possible by the circumstance that only two of the quanti-
ties <£, ^r, d . . . can bear a finite ratio to each other for any given
value of x, and consequently all the roots of the equation

(<^)**+ (^xy+ [&*)'... =o*

are contained among the roots of the several binary equations

((f>x)i=(ylrx)if (cj)%y={$a;y, &c. :
which are the roots of any one of these equations (as ex, gr. of
the first) that belong to the given equation will be determined by
the condition that they must make the norms of all the other
functions {ex. gr. of §x) indefinitely small as compared with the
norms of those two which appear in it (ex.gr. <j>x, ifrx). In this
manner, if the total number of the functions is k, supposing

* My friend M. Jordan, of the Ecole des Mines (author of a remarkable
thesis on groups), has developed some interesting geometrical consequences
arising out of the study of this equation, which I hope he may be induced
to publish.

528 Prof. Sylvester's Notes to the

fayfrj & • • . to be all linear functions of x} each binomial equation

out of its entire stock of i roots will contribute — 5 — = roots

k—

available towards the solution of the given equation. Mr. Cayley
has remarked to me the analogy between this determination and
Newton's method of finding the form of the several parabolic
equations y — cx^ which represent the branches of a given alge-
braical curve at its origin. In the equation to the given curve
c#x is to be substituted for y ; the terms will then all become
powers of x (an infinitesimal) whose indices will be linear func-
tions of X ; every pair of them in turn is equated to zero, and of
all the values of \ thus obtained only those will be preserved
which cause the two equated linear functions of X belonging to
any given pair of terms to be less than all the others, and con-
sequently the terms themselves (whose indices the linear func-
tions are) infinitely greater than all the other terms.

Linear functions of a variable figure in both investigations,
viz. in Newton's as indices of the same infinitesimal quantity, in
mine as quantities whose infinite index is the same* ; but the
logic and mode of procedure (utterly unlike as are the questions
in their origin and subject matter) is the same in either case.

Note D.
The remark contained in the preceding note, as to the effect

of representing N * by an infinite rational fraction being iden-
tical with that of expressing it as a definite integral, combined
with a consideration of the cause of the success of the particular
method referred to in Note B, has led me to the investigation
following, of the value of the complete elliptic function of the
first species. As usual denoting it by F(c), we have

F(C)=r

Jo

\0-

^l-c^sinfl)2

-Sfl/df00 / cosfl

~?rJo Jo ^l-c2(sin0)* + (cos0)V

* In a word, Newton's equation is an exponential one made up of
nothings, mine an algebraical one made up of infinities.

Meditation on Poncelet's Theorem, 529

where

r_CT ja COS0

Jo (l + *2)-(c2+tf2)(sin0)2

= W+WW W1*** ^^)~^W}'

Let x — tan cj>, b = a/ 1 — c2;
then

F(c)-irvi-^cos^{i°g((scc^+^^^:^-ios&}

-|logi.F(4)4§R,

where

ir

J* Y l\/l-bHcos6)2J

f¥ log(l + \/l-62(cos</>)2)
1 #d> ^ — ^-.

Jo ' */l-Z>2(cos</>)2

It will presently appear that these two definite integrals are
equal to one another !

f°
Let V2r= 1 (cos cf>)2r log (cos </>).

Then we may easily establish the formula of reduction,
_2r-lv 1.3.5..(2r-3) tt

2r~ 2r V2r-2 2.4<6..(2r-2)2r2 j

7T

and since (as is well known) V0=— log 2, we have

V4=l5f(los3-r3-3Ti)'

„ 1.3.5 tt/. 1 1 1 \

Ve=2A6 2 (l0S 3-r2-0-0j'
&c. = &c.

530 Prof. Sylvester's Notes to the

Hence, by expanding the denominator in a series proceeding
according to powers of (cos <f>)2, it is readily seen that the first
integral becomes

To find the second integral, we must obtain the general term
in the expansion in a series of powers of / of— g' T— - '

(where t stands for b cos </>), i. e. of , -. J efr(j — -^ \

i say of ft(Q =^i-a^. Now

«-i-+

1 1 1.3 1.3.5

Hence, writing

. (l+y,l-<*) =iog 2+ K/+ . . .+ K2l_2f"-2+ K2jf» +&c,
5 v/l-i2

and equating the coefficients of t2i, we obtain

2i(2i-i) (K2j -k2(_2) + (2i- i)K2j_2= -1,|;f,g;(28~1),

_2»-llr 1.3.5...2J-3

"2i — iv? — *2t-2'

2i T2,~2 2.4.6...(i-2)2i

Meditation on Poncelet's Theorem, 531

Thus

K0=log2,

K4=l4(log2^r12""A)'

&c. = &c,
and consequently

f;»iog(i+vT-y(co»»)«

J„ ^ l-b"2 (cos <j>f

{log3+Q)2(log2-Il-3)^+(^)(loS2-iL_3-L)^+&e.}.

Thus, then, we obtain the following remarkable equalities :

(cos <p)

= log h(b) + 2 F^VWl-b*^*)*)

6 Jo v/l-62(coscf>)2

or

J

(C0S</>)'
log(l+\/l— 62(COS(^)2)

o ^l -a* (cos £)*

log COS (/>

2

7T

= |Fc+i-log4FJ.

When 6 is indefinitely small, it is obvious from either of these
equations that

F(e) = -|logS| + 21og2 = logj,

Legendre's well-known formula previously referred to.

The equality of the first two definite integrals in the sorites

532 Notes to the Meditation on Poncelct's Theorem,
above given, is, as we have seen, a consequence of the equality

log(i-fVi-g) m 2 c *d0pog cos e '' log cos Q (cos e^t2

vl — t2 'v*

2

+ log cos 6 (cos 0)4*2 + &c. } .

Hence we have

,0 log cos 6 - 21og(l+\/r=^r) *
!ff l-62(cos0 ^"tt ^rT6«

£

The extreme facility and brevity with which the method in the
text gives the value of P(c) fori indefinitely small is worthy of
notice, as in the usual text-books it is obtained by a very indirect
and circuitous process. We may obtain in like manner the value of

i

"d6

(l-<?sm<9) v/l_c2(sin<9)2

on the same supposition as to c, whether 1 — e vanishes with
(1 — c) or remains finite when c = l. On the latter supposition,
the definite integral in question has for its value

1,21, 2

i3ilo^+rz^iog(TT^.

When es=l, this becomes infinite j when e= —1, the second term
becomes 7 + 0 l°g%> ana ^e entire integral is - log^ + - ;

4
when e = 0, it is log j-. Subtracting the half of the latter integral

from the former, we shall obtain

1

£

'i tf(l-8in0)»_l
l0 ™ (cos0)3 "2'

which is easily verified.

By taking successively e=\/ — n, e=—\/—n, and adding
together the halves of the two integrals corresponding to these
suppositions, we obtain the ultimate value of the complete elliptic

* From this it will readily be seen that when n is any integer we may

obtain 1 * — log cos 0 , processes of differentiation in a form in-

J0 (I-*2 (cos Wff
volving only algebraical and logarithmic quantities, and so, from what pre-
cedes, when n is any half-integer, in terms of such quantities and of com-
plete elliptic functions.

Notices respecting New Booh. 533

integral of the third kind, viz.

d6 1

j;

l+»(sin0)« v/l-c2(sin6>)^

from the general formula above given, always of course subject
to the condition that c is supposed indefinitely near to 1*.
K, Woolwich Common,
November 1860.

LXXIIT. Notices respecting New Books.

An Elementary Treatise on the Dynamics of a System of Rigid Bodies.
With numerous Examples. By Edward John Routh, M.A.,
Fellow and Assistant Tutor of St. Peters College, Cambridge; Ex-
aminer in the University of London. Cambridge : Macmillan and
Co. 1860.

MR. ROUTH was Senior Wrangler in 1854, and is already
known as the joint author with Lord Brougham, of ' The
Analytical View of Newton's Principia.' His present work is in-
tended as a text-book for students at Cambridge, and will no doubt
take its place as such. We notice in it several of the more recent
methods of investigation, and such novelties, for instance, as the
reference of the motion to ' moving axes/ which have not hitherto
been incorporated into elementary books.

We should have been glad to have seen the analytical processes
applied to such questions as the motion of a locomotive, and other
practical problems, instead of the purely fictitious and useless cases
which seem to be the peculiar delight of Cambridge mathematicians ;
e.g., such as the following: — " A perfectly rough, circular, hori-
zontal board is capable of revolving freely round a vertical axis
through its centre. A man whose weight is equal to that of the
board walks on and round it at the edge : when he has completed
the circuit, what will be his position in space?" (P. 53.) We feel
tempted to parody this, and ask, " When the student has completed
his circuit round a hundred such questions as this, what will be his
position in science ?" We believe it is not long since the Board of
Mathematical Studies at Cambridge received some very strong hints
on this subject from one of the most distinguished men of science in
England, whose own mathematical attainments have always been
applied to objects of real use and practical importance, instead of
being frittered away in trifling ingenuity.

* It seems to be expected of every pilgrim up the slopes of the mathe-
matical Parnassus, that he will at some point or other of his journey sit
down and invent a definite integral or two towards the increase of the com-
mon stock. The author of these notes has been somewhat late in acquit-
ting himself of this debt of honour, but ventures to hope that the principal
results contained in the text above may be thought not unworthy of a
place in some future edition of that noble and sumptuous monument of
Dutch learning, industry, and fine taste, the invaluable collection of defi-
nite integrals by M, Bierens de Haan.

[ 534 ]
LXXIV. Proceedings of Learned Societies.

ROYAL SOCIETY.

[Continued from p. 483.]
March 15, 18G0. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.

THE following communications were read : —
"On the Light radiated by heated Bodies." By Balfour
Stewart, Esq., A.M.

In two papers read before the Royal Society of Edinburgh in the
years 1858 and 1859, and published in their Transactions, I have
described some experiments on radiant heat, which would seem to
involve an extension of Prevost's theory of radiation, known as the
theory of exchanges.

As the paper which I have now the honour to submit to this
Society will detail analogous experiments on radiant light, I may
be permitted briefly to refer to those points in my previous papers
which are thus intimately connected with the present subject.

In attempting to unfold the logical consequences of Prevost's
theory, certain properties of radiant heat present themselves to our
view, many of which are capable of experimental verification.

The following are some of these ; and, for convenience-sake, I
shall follow up the statement of each (before proceeding to the next)
with a description of the analogous property of Tadiant light, as in
this way the similarity which exists between heat and light will be
most readily perceived.

f In the first place, the heat radiated by a thin plate of any sub-
stance at a given temperature, is proportional to the absorptive
capacity of that substance for the heat of that temperature ; or, in
few words, its radiation is equal to its absorption.

Rock-salt, for instance, has a small absorptive capacity for heat of
212° F., and, in consequence, its radiation when heated to 21 2° F. is
comparatively small. In pqint of fact, a plate of this substance,
0*18 inch thick, only gives out 15 per cent, of the heat which
lamp-black radiates at the same temperature. Glass, on the other
hand, absorbing nearly all the heat of 212° F. which falls upon it,
has at this temperature a radiation comparatively great, and nearly
equal to that of lamp-black. A similar law holds with regard to
radiant light.

If a piece of perfectly transparent glass be heated in an ordinary
fire, removed to the dark, and there viewed, it will be found to emit
scarcely any light ; if the glass be slightly coloured, its radiation
will be more copious ; the amount of light given out, as far as I
have been able to make the comparison, invariably depending upon
the depth of colour or absorptive power of the glass for light, pro-
vided its colour stands heating. A good way of performing this
experiment is to heat a dark glass by the side of a colourless one, by
means of a chemical tongs, in some uniform field of heat. "When
viewed in the dark together, the contrast is very striking between
the bright light of the one and the bare visibility of the other.

Royal Society. 535

A stratum of heated gas may likewise be instanced as a substance
which neither absorbs nor emits light to a sensible extent ; and it has
similar properties with respect to heat.

Let us now proceed to another consequence of Prevost's theory.
It is well known, from Melloni's experiments, that thin plates of
various substances have the property of sifting the heat which falls
upon them ; they stop certain rays, and allow others to pass, — the
heat stopped being of one description, and the heat passed of
another. Now, it may be shown to flow from the theory of ex-
changes, that the heat radiated by a thin plate of any substance at a
given temperature is precisely that description of heat which the
plate absorbs when heat of that temperature is allowed to fall upon
it. The heat which it absorbs being that kind of heat which has
a difficulty in passing through it, if the heat which it radiates be of
this description also, it follows that the heat given out by a plate of
any substance will experience difficulty in passing through a screen
of the same substance. This we find to be the case : thus, a plate
of rock-salt 0*77 inch thick passes only 30 per cent, of the heat from
a thin plate of rock-salt heated to 212° F., whereas it will pass 75
per cent, of heat from lamp-black at that temperature. The same
thing holds with regard to glass. A thin plate of crown glass will
only pass half as much heat from heated crown glass as from heated
lamp-black. But this peculiar quality of the radiating plate is de-
stroyed if we coat the side of it furthest from the screen with lamp-
black ; it then behaves precisely as lamp-black alone would do. The
reason of this is that the rays of heat given out by the glass are the
equivalent of those which it absorbs from the lamp-black behind ;
so that both together give out the same heat in quantity and quality
as lamp-black would alone.

We have here also analogous properties of light. Let us take a
number of differently coloured glasses. With respect to the light of
an ordinary fire, these may be divided into two groups ; viz. those
which redden, and those which whiten the fire when we look through
them. The first group comprises red and orange glasses ; the second
group green and blue glasses.

Glasses of the former group absorb the whiter, glasses of the
latter group, the redder descriptions of light. We should therefore
expect red and orange glasses to give out, when heated, a peculiarly
white light, and green and blue glasses a peculiarly red light. A
number of red and orange glasses have been found which fulfil this
expectation. Among the reds, those coloured by gold, when re-
moved from the fire and held in the dark, give out a milky-white,
or even greenish light; and the orange glasses used by photo-
graphers do the same. Other glasses, of a dingy red tint, give out,
when heated, light slightly whiter than the ordinary light of their
temperature ; while there are others in which I have not, by this
somewhat rude method of experimenting, been able to detect a
sensible peculiarity of tint : yet this is not to be wondered at, if it
be remembered that the following is the method in which the ex-
periment is made. The glass under examination is held in a tongs,

536 Royal Society : —

along with another glass, opaque or nearly so, which gives out light
of the ordinary description. They are heated together in the same
field of heat, and then viewed in the dark as they cool. During
this process the tint of each changes, becoming somewhat redder
as the temperature falls. A difference in the temperature of the
two glasses might therefore cloak or even reverse the peculiar differ-
ence of tint which it is sought to establish, unless this is very
marked. This difficulty would be got over if we could by any means
compare glasses of different tints at precisely the same temperature
in the dark together ; but I have not yet succeeded in contriving an
apparatus for this purpose.

With respect to glasses that whiten the fire when used as screens,
these all, without exception, as far as I have tried, give out a red
description of light ; and this is peculiarly remarkable in some light-
green glasses.

The following circumstance renders some glasses unfit for experi-
ment. They absorb nearly all the red light of low temperature,
and it is only when the light rises to a white that a notable propor-
tion is allowed to pass. Now if the law be true that the radiation
is equal to the absorption, these glasses should, at a low red heat,
give out nearly the whole light belonging to their temperature, the
same as if they were opaque. It is only therefore when we raise
the temperature that we cau expect any result in the way of pecu-
liarity of tint ; for it is only then that the glasses, as screens, allow
a notable proportion of light to pass, and that of a peculiar cha-
racter ; but the glass has now assumed a pasty condition, which
renders it unfit to work with. Those glasses, therefore, are to be
preferred that allow a considerable proportion of all the kinds of
light to pass : for, just as in heat the radiation is most peculiar in
rock-salt, which absorbs but little heat ; so in light the best results
are obtained by glasses that absorb only a small proportion of the
light that falls upon them. As a proof of this, I may mention that
difference of tint is very noticeable in the process of spinning threads
of coloured glass. The heated red glass thread has, when being
spun, a pale green hue, while the green glass thread has, under the
same circumstances, a decidedly reddish appearance. These threads
do not absorb much light, but what they do absorb is of a peculiar
kind.

It has been mentioned that a screen of glass is peculiarly opaque
for heat from glass ; but if the side of the radiating plate furthest
from the screen be coated with lamp-black, its heat now passes
the glass screen as readily as ordinary heat of that temperature.
A similar fact is noticeable with regard to light. A red glass,
which, when heated and viewed in the dark, gives out a greenish
light, while in the fire scarcely appears to differ in tint from the
surrounding coals ; and the same fact holds for all coloured glasses.
Ultimately they all appear to lose their colour in the fire as they ap-
proach in temperature the coals around them. This may be ex-
{)lained thus : — the red glass, for instance, still gives out its greenish
ight ; but it passes red light from the coals behind it, in such a

Mr. B. Stewart on the Light radiated from Heated Bodies, 537

manner that the light which it radiates precisely makes up for that
which it absorbs ; so that we have virtually a coal radiation coming
partly from and partly through the glass.

Let us now consider Prevost's theory with regard to bodies of
indefinite thickness. One of its consequences was experimentally
discovered by Leslie ; viz. that metals which are good reflectors of
heat are very bad radiators. As a variety of this experiment, I have
endeavoured to show that a powdered diathermanous body wil
radiate less than powdered bodies which are opaque for heat. Thus,
if a plate of table-salt have one side blackened, the white side will
radiate only 83 per cent, of that which the blackened side radiates
at the temperature of 212° F. No such difference is observed in
sugar, which, though white for light, is black for heat of 212°.

We have here also similar facts with regard to light. If a pot of
red-hot lead or tin be carried to the dark, and the dross scummed
aside by means of a red-hot iron ladle, the liquid metal momentarily
disclosed will appear less luminous than the surrounding dross, — the
difference being more observable in the case of tin, which has a
higher reflecting power than lead. Also, if a piece of platinum,
partly polished and partly tarnished, be held above a flame in a dark
room, the tarnished portion will shine much more brilliantly than
the polished. Again, if we take a china cup with a white and black
pattern, and heat it to a white heat in the fire, while there we shall
not perceive much difference between the white and black of the
pattern ; but if we bring it into a dark room, we shall perceive the
black to shine much more brilliantly than the white. This reversal
of the pattern presents a very curious appearance.

Finally, it is a consequence of Prevost's theory and an experi-
mental fact, that opaque bodies, generally speaking, radiate the same
description of heat at the same temperature. In like manner, the
light which they radiate is of the same description at the same tem-
perature ; one body is not red while a second is yellow and a third
white, but they are all either red or yellow, or white together.

An analogy has thus been established between radiant heat and
light in certain of their properties. Now two opinions have been en-
tertained with regard to light : —

1st. Some have regarded it as differing from radiant heat only in
wave length.

2nd. Others have regarded the two as physically distinct, although
possessing many properties in common. It has even been thought
that some kinds of light have no heating effect on the bodies on
which they fall.

I cannot but think that the facts just stated countenance the
former opinion rather than the latter : for Prevost's theory consists
of the three following hypotheses : —

] st. That if an enclosure of any kind be kept at a uniform tem-
perature, any body placed within the enclosure, and surrounded by
it on all sides, will ultimately attain that temperature.

2nd. That all bodies are constantly giving out radiant heat, at a
rate depending upon their substance and temperature, but independent
of the substance or temperature of the bodies that surround them.

Phil Mag. S. 4. No. 136. SuppL Vol. 20. 2 N

538

Royal Society s —

3rd. And, consequently, that when a body is kept at a uniform
temperature, it receives back just as much heat as it gives out.

From these three assumptions may be deduced all the facts that
have been stated with regard to radiant heat ; but in the argument
it is essential that the rays under consideration shall have the pro-
perty of heating the bodies on which they fall, and by which they
are absorbed. If this be not granted, the argument fails. Now
radiant light, or those rays only that affect the retina, have been
found to possess properties analogous to those which radiant heat
thus possesses in virtue of its departure lowering the temperature of
the body which it leaves, and its absorption raising that of the body
on which it falls. If, therefore, we suppose all kinds of radiant
light to have the property of raising (however little) the temperature
of the body by which they are absorbed, the facts that have been
stated in this paper regarding light may be shown to be a natural
consequence of Prevost's theory of exchanges ; but if, on the other
hand, we do not admit that all the kinds of radiant light given out
by heated bodies possess this property, then in that case those facts
cannot be explained by Prevost's theory, but they will require a new
theory to account for them.

This circumstance induces me to think that all the descriptions of
light radiated by heated bodies have the power of heating, more or
less, those bodies by which they are absorbed. Viewing the matter
in this light, I have constructed the following Table, in which the
logical consequences of Prevost's theory are stated in the first
column, while opposite these in the second column are detailed the
different experiments which they serve to explain.
Table of the consequences of Prevosfs theory, and the facts which
they explain.
Consequences of Prevost's theory. Facts which these consequences explain.

r Rock-salt which absorbs little heat
of 212°, F., gives out little ; while glass,
which absorbs much, gives out much.

The heat radiated .by rock-salt has
great difficulty in passing through a
screen of rock-salt — the heat radiated
by glass in passing through a screen of
glass.

The radiation of a thin plate or par- Colourless glass, when heated, gives
tide is equal to its absorption, and that out little light, opaque glass a great deal,
for every description of heat— that is to.} Red giass> which absorbs the greenish
say, in quality as well as in quantity. rays> gjve8 out greenish rays ; while green

glass, which absorbs the red rays, gives
out red rays.

When a plate of glass is coated on its
further side with lamp-black, its heat is
the same as lamp-black heat.

All coloured glasses appear to lose
their colour in the fire.

Metals radiate little, both of heat and
Those opaque bodies which reflect *&*• ^abte-salt, which is white for
most, radiate least. Opaque bodies ge- I h«at.of H*! «£?te» ^ ***.*"&*'
nerally give out the same kind of rays
at the same temperature : these words
also express the known fact.

■4 which is black. When a black and white
china cup is heated in the fire and held
in the dark, the black of the pattern is
more luminous than the white.

Mr. B. Stewart on the Light radiated from Heated Bodies. 539

In conclusion, I may be permitted to remark regarding these laws
of light, that from their simple nature some of them may have been
observed before, but I think they are now for the first time con-
nected with a theory of radiation.

Supplement (added March 7, 1860). — Since writing the above,
the law which asserts that the absorption of a thin plate or particle
is proportional to its radiation for every description of light, has
received a very beautiful confirmation.

In the Philosophical Magazine for this month, pages 194-196,
Professor Stokes has noticed some very interesting experiments of
M. Foucault, and also of Professor Kirchhoff. M. Foucault finds as
the result of his experiments, " that the voltaic arc formed between
charcoal poles presents us with a medium which emits the ray D of
the solar spectrum on its own account, and which at the same time
absorbs it when it comes from another quarter." Professor Kirchhoff,
again, finds as the result of his experiments on the spectra of coloured
flames, " that coloured flames, in the spectra of which bright sharp
lines present themselves, so weaken rays of the colour of these lines
when such rays pass through the flames, that, in place of the bright
lines, dark ones appear as soon as there is brought behind the flame
a source of light of sufficient intensity, in the spectrum of which these
lines are otherwise wanting."

We thus see that the same media which in a heated state emit
rays of a certain refrangibility in great abundance, have also the
property of stopping these very rays when they fall upon them from
another quarter, or, in other words, their absorption of such rays is
proportional to their radiation of them.

Supplement (added March 8, 1860). — The following fact noticed
by Professor Kirchhoff is also in accordance with the theory brought
forward in this paper.

" The spectrum of the Drummond light," he remarks, " contains,
as a general rule, the two bright lines D, if the luminous spot of the
cylinder of lime has not long been exposed to the white heat ; if the
cylinder remains unmoved these lines become weaker, and finally vanish
altogether. If they have vanished, or only faintly appear, an alcohol
flame into which salt has been put, and which is placed between
the cylinder of lime and the slit, causes two dark lines of remarkable
sharpness and fineness to show themselves in their stead ; but the
Drummond light requires, in order that the lines D should come out
in it dark, a salt-flame of lower temperature. The flame of alcohol
containing water is fitted for this, but the flame of Bunsen's gas -lamp
is not. With the latter the smallest mixture of common salt, as
soon as it makes itself generally perceptible, causes the bright lines
of sodium to show themselves."

Now, when we heat a piece of ruby glass in the fire, we have an
analogous phenomenon. As long as the ruby glass is of a lower
temperature than the coals behind it, the light given out is of a red
description, because the ruby glass stops the green : the green here

2N2

540 Boyal Society : —

is precisely analogous therefore to the line D, which is stopped by an
alcohol flame into which salt has been put. Should, however, the
ruby glass be of a much higher temperature than the coals behind it,
the" greenish light which it radiates overpowers the red which it
transmits, so that the light which reaches the eye is green more than
red. This is precisely analogous to what is observed when a Bunsen's
gas-lamp with a little salt is placed before the Drummond light, when
the line D is no longer dark but bright.

In fact, the law, " the absorption of a particle is equal to its radia-
tion, and that for every kind of light," only applies to the case where
the temperature of the particle is equal to that of the source of the
light which passes through the particle. If the temperature of the
source of light be greater, one quality of light will predominate ; if,
on the other hand, the temperature of the particle be greater, another
quality of light will predominate.

" On the Luminous Discharge of Voltaic Batteries, when examined
in Carbonic Acid Vacua." By J. P. Gassiot, Esq., F.R.S.

On the 24th of May, 1859 (Proceedings, May 26, 1859), I com-
municated to the Royal Society a short notice of my having obtained
the stratified discharge from a voltaic battery of 3520 elements
charged with rain-water ; and also with one of 400 elements charged
with nitric and sulphuric acids, each cell of both batteries being
insulated. I stated also that with the latter (as I had previ-
ously shown with the former), spark discharges passed between two
terminal copper plates through the air, before the completion of the
circuit.

The well-known luminous arc in air, as usually obtained from
an extended series of the nitric-acid battery, was very brilliant, but
from the small size of the porous cells (3 inches long, \ inch broad)
containing the nitric acid, it was only tried by a momentary action.
With the water-battery I have never been able to obtain a continuous
discharge in air similar to the voltaic arc ; whether from points or
plates, the discharges from this battery are invariably in the form of
minute, clearly defined, and separated sparks.

Although the water-battery consisted of nearly nine times as many
metallic elements as the nitric-acid battery, it exhibited by the gold-
leaf electroscope very little increased signs of tension.

This is in accordance with the results obtained by me in 1 844, when
I showed that the tension of a single cell increased in force according
to the chemical energy of the exciting liquid. " In all the experi-
ments I made, the higher the chemical affinities of the elements used,
the greater was the development of evidence of tension" (Philosophical
Transactions, 1844, part 1. p. 52).

Recently, through the kind introduction of Professor Wheatstone,
I have had an opportunity of experimenting with 512 series of
Daniell's constant battery ; and my present object is to present to the
Royal Society a short account of the results I have obtained, and to
describe the appearance and character of the voltaic discharge of
these several batteries when taken in vacua.

On the Luminous Discharge of Voltaic Batteries. 541

The vacuum-tubes I used were prepared by means of carbonic acid
(Philosophical Transactions, 1859, part 1. p. 137). For the sake of
reference I will denote these by the original numbers which I am
accustomed to attach as the vacua are completed : — in the following
experiments these were 146, 187, 190, 196, 202, and 219.

No. 146 is 24 inches long and 18 inches in circumference, and has
a copper disc 4 inches diameter at one terminal and a brass wire at
the other : this vessel is figured in my last communication. No. 187
and 196 (see fig. 1) are each about 6 inches long and 1 inch
diameter, with gas-coke balls \ inch diameter, attached to the
hermetically sealed platinum wires, the wires being protected by glass
tubing as far as the balls, placed inside the tube 3 inches apart.

Fig. 1.

No. 190 has brass wires, and No. 202 silver wires -attached to the
platinum : both these tubes (fig. 2) are of the same dimensions as
No. 187 and 196. No. 219 is 4 inches long, has gas-coke balls of

Fig. 2.

t J

about |th of an inch in diameter, and 1 inch apart : the caustic
potash originally attached to this tube has been scaled off; the form
is shown in fig. 3.

Fig. 3.

>

With the inductive coil the discharge in 146 exhibits a large cloud-
like luminosity on the plate, which in these experiments was always
made the negative terminal. On the positive wire, minute luminous
spots were visible. At intervals, apparently by some sudden energetic
action, flashes of bright stratified light would dart through the
vacuum ; but by carefully adjusting the contact breaker, the discharge
could be made to pass, producing a white glow on the negative plate,
without to the eye affording any appearance of an intermittent
discharge.

In 187 and 196 the stratifications were narrow from the positive

1 1 1 Royal Society : —

terminal, the negative ball being surrounded with a narrow halo of
light similar to that in 6g. 1 A (p. 545), but smaller. In 190 there
was a red tinge on the cloud-like discharge near the positive terminal ;
on the approach of a magnet, two or three additional clouds were
brought out, the negative wire being covered with a luminous glow
extending to the sides of the tube parallel to the end of the negative
wire. 202 exhibited a remarkably well-defined cloud-like discharge,
the several clouds being clearly and distinctly separated. No. 219:
the appearance of the discharge in this tube was similar to that in

Fig. 3 A.

fig. 3 A, with a particularly brilliant glow around the negative ball, but
without any stratifications from the positive.

Having thus described the appearances of the induced discharge in
these tubes, I now proceed to the description of experiments made
in the same vacua, — 1st, with the water-battery of 3520 cells ; 2ndly,
with the 5 1 2 series of Daniell's constant battery ; and lastly, with 400
series of Grove's nitric-acid battery.

With the water-battery, as I have stated in my previous commu-
nication, the stratified discharge, similar in character to that of the
inductive coil, was obtained, not only in 146 and the other tubes,
but also through 146 and any one of the others at the same time.

From the risk of fracture, I have not ventured again to heat the
potash in 146, but I have invariably found that whenever the potash
in any of the other tubes was heated, the discharge from the water-
battery, instead of increasing in distinctness and brilliancy, entirely
ceased.

The discharge from the water-battery through each of the tubes
had the appearance of being continuous, and the needle of the
galvanometer, placed on the circuit, showed a steady deflection.
To test whether the discharge was continuous, I attached No. 219 to
my rotating apparatus (Philosophical Transactions, 1859, part 1.
p. 158); the discharges were then clearly separated, so that even
with this apparatus they were shown to be intermittent.

As the water in the battery, after a lapse of some weeks, had
partially evaporated, the action was so reduced that it would no longer
pass through any of the vacuum-tubes except 219, in which it
assumed the appearance in fig. 3 B. In this state it remained for
three orfour weeks; and whenever from change of temperature moisture
was deposited on the surface of the glass tubes, the luminous discharge
disappeared when the tubes were touched by the hand or by a wire,
reappearing as the hand or wire was withdrawn. A portion of the
discharge from this battery was evidently lost by insufficient insulation,
reduced by accumulated dust and moisture. I have not the requisite

On the Luminous Discharge of Voltaic Batteries, 543

facilities at command, but a thoroughly well-insulated battery of 3000
or 4000 series would produce effects well worthy of examination.

Fig. 3 B.

BanieWs Constant Battery.

On the 27th of December, 1859, by the introduction of Professor
Wheatstone, I had the opportunity of experimenting with the large
battery belonging to the Telegraph Company at its Factory, Camden
Town; Messrs. Wheatstone, Latimer Clarke, and Bartholomew were
present. My object was to ascertain whether a luminous discharge
could be obtained through the vacuum-tubes from the battery, which
consists of 512 series of Daniell's elements, zinc and copper. The
zinc plates are 2 by 3| inches, the copper 3| by 3| inches ; the cells
are insulated in series of 10 and 1 2, suspended on trays by gutta-percha
bands. I experimented with three of my vacuum-tubes, Nos. 187, 1 96,
and 219, with 187 and 196 ; no sign of any luminous discharge could
be observed ; the electroscopes (Peltier's and a gold-leaf), by the
tension, showed that the current did not pass.

With 219 the brilliant glow around the negative ball, as is shown
in the same tube by the induction coil, was visible with very trifling
luminosity on the positive. I have attempted to show this appearance
in fig. 3 A.

Various lengths, viz. 110 yards, 1, 2, 4, 8 and 16 miles of covered
copper wire, the 110 yards covered with india-rubber, and the other
lengths with gutta-percha, are kept immersed in a water-tank for the
purpose of experiments at the factory ; an opportunity was therefore
offered of testing the action of the battery on these wires by means
of vacuum-tubes. This immersed wire is designated the cable, acting
in this respect in a manner analogous to submarine wires.

The general results obtained, and repeatedly verified, may be
briefly stated as follows : — From the 110 yards to the greatest length
of 16 miles, it took from half to one and one quarter of a second for
the cable to receive as much of the charge of the whole battery as
could pass through the vacuum-tube 219, the time being denoted
by the appearance of the luminosity in the negative ball (see fig. 3 A).

With 110 yards the discharge of a charge previously given to the
cable was instantaneous ; it appeared to be nearly momentary with
one mile, and the time then progressively increased according to the
length of the cable previously charged, until with the 16 miles it
took one and a quarter to one and a half seconds before the luminous
glow on the ball in the vacuum-tube disappeared.

It was beautiful to see the regularity with which the glow appeared

544 Royal Society i —

and disappeared in these experiments, first at one terminal and then
at the other, according as the cable was charged or discharged.

After the cable had received the discharge to the greatest intensity
that could be obtained through the tube 219, the full charge of the
battery was then completed by cutting off the tube from the circuit
by means of a wire. On removing the wire, and substituting the
earth for the battery, a discharge took place ; but a residuary charge
was always found, which could not pass through the vacuum. If
this residuary was allowed to remain in the cable, and the battery
again substituted for the earth, no additional charge could be made
to pass from the battery through the vacuum-tube ; but so soon as
this residuary was discharged, the cable again became charged
through the tube as before*.

We were particularly fortunate with these experiments ; for on
Mr. Wheatstone testing the capability or power of the battery, he as-
certained that on taking from it only 32 cells, thus reducing the num-
ber to 480, the discharge could not pass through the vacuum-tube.

Grove's Nitric-Acid Battery,

Each set of elements in the battery were inserted in a glass ves-
sel with a stem 6 inches long ; the stems were carefully cleaned and
dried. These precautions, with the high chemical affinity of the
elements, raised the tension of each terminal, as denoted by gold-
leaf electroscopes, to nearly that of the larger series of the water-
battery. A succession of spark-discharges could be taken between
the copper discs of my micrometer-electrometer, one disc being
attached to the zinc, and the other to the platinum end of the
battery.

In the following experiments, the different vacuum-tubes were
introduced between one of the copper discs and the battery, as also
a galvanometer. By this arrangement the circuit could be gradually
completed without any risk of disarranging the apparatus, and the
spark discharged obtained before the copper discs of the micro-
meter-electrometer came into contact.

" In 146, on the completion of the current, the discharge of the
battery passed with a display of magnificent strata of most dazzling
brightness. On separating the discs by means of a micrometer
screw, the luminous discharges presented the same appearance as
when taken from an induction coil, but brighter. On the copper
plate in the vessel there was a white layer, and then a dark space
about one inch broad; then a bluish atmosphere, curved like the,

* If one of the wires of the vacuum-tube No. 219 is connected with the inner
coating of a Leyden jar, and the other with the prime conductor of an electrical
machine, when the machine is excited a luminous glow will be observed round
one of the balls, similar to that obtained during the charging of the cable by the
voltaic battery, and the jar will become gradually charged. On the excitation of
the electrical machine being stopped, if a pointed wire is presented to the prime
conductor, the jar will be gradually discharged, and the luminous glow appears
on the other ball of the vacuum-tube ; if several similar tubes are arranged in
series, and the jar is discharged through longer carbonic-acid vacua, the stria;
can be obtained in the latter.

On the Luminous Discharge of Voltaic Batteries, 545

plate, evidently three negative envelopes on a great scale. When
the plate was positive, the effect was comparatively feeble." The
preceding is an extract from notes made by the Rev. Dr. T. R. Ro-
binson, when he first witnessed the experiments in my laboratory,
on the 5th of August, 1859. With the same vacuum I have
always obtained similar results.

In 187 and 196 (fig, 1) with carbon-balls in the tubes, the discharge
of the nitric-acid battery elicits intense heat, and probably changes
the condition of the vacuum. On the 5th of August, 1859, "the
discharge in 187 presented a stream of light of intolerable brightness
[I again quote from Dr. Robinson's notes], in which, through the
plate of green glass, with which he observed the phenomena, strata
could be observed. This soon changed to a sphere of light on the
positive ball, which became red-hot, the negative being surrounded
by magnificent envelopes, whilst with the horseshoe magnet the
positive light was drawn out into strata. The needle of a galvano-
meter in circuit was violently deflected, and the polarity reversed,
settling at a deflection of 45°. On heating the potassa, the dis-
charge again bursts into a sun-like flame, subsequently subsiding
into three or four large strata, of a cloud-like shape, but intensely
bright."

On a subsequent occasion I found that the discharge did not pass
for about a minute after the circuit was completed, when a fine glow
appeared on the negative ball, fig. 1 A. Around the positive ball

Kg. 1 A.

there was a trifling glow, in a few seconds a momentary brilliant
flash, and the discharge ceased. The potash was then again heated ;
the large negative glow reappeared, followed almost instantly by a
remarkably brilliant stratified discharge, with intense chemical action
in the battery, denoted by the evolution of nitrous fumes ; at this
moment I separated the discs of the micrometer-electrometer, and thus
broke the circuit.

I now arranged the apparatus by attaching gold-leaf electroscopes
to both terminals, and introduced the galvanometer, so as to enable
me to examine more carefully the action that would take place when
the potassa was heated. On heating the potassa, the fine negative
glow (fig. 1 A) was again developed ; the leaves of the electroscope
did not close ; but as the negative glow increased, the needle of the
galvanometer was suddenly deflected, immediately (although the glow
continued) returning to zero ; as more heat was applied a small globe

546

Royal Society

of light appeared on the positive (fig. 1 B), and the needle gradu-
ally deflected 40° or 50°. On withdrawing the lamp, as the potash
cooled, the positive glow disappeared, the needle of the galvano-

Fig. 1 B.

meter receded, the glow on the negative remaining more or less bril-
liant,— this action and reaction alternating as the heat of the lamp
was applied or withdrawn from the potash.

When the heating of the potash was further increased, four or five
cloud-like and remarkably clear strata came out from the positive
(fig. 1 C) ; and these were quickly followed by a sudden discharge

Fig. 1 C.

+I

1-

am

of the most dazzling brightness, which remained for several seconds.
The stratifications, which were conical in shape, I have endeavoured,
although very faintly, to depict in fig. 1 D. The needle of the gal-

Fig. 1 D.

I-

^*>»

vanometerwas suddenly and violently deflected, striking with consider-
able force the two corks placed to protect it on the compass card.
At the instant this discharge took place, and not before, the leaves of
the electroscopes collapsed. This, with the intense chemical action ob-
servable in the battery, proved that the entire current was passing.

The preceding experiment was repeated with tube No. 196, with
nearly the same results, the needle first deflecting 40° and then 80°.
On further heating the tube, the same sudden intense stratified light
appeared, after which the discharge ceased.

On the Luminous Discharge of Voltaic Batteries. 547

No. 187 was then replaced in the circuit, and the same phenomena
as already described were obtained.

I now again avail myself of Dr. Robinson's notes of the experi-
ments made on the 5th of August. Tube 190 is of the same dimen-
sions as 187 and 196; but instead of the coke balls, it has brass
wires attached to the platinum. In this tube (190) the luminous
discharge did not appear until the caustic potassa was heated, when
most dazzling strata were observed. Dr. Robinson says, — " I had
to use a dark-green glass to examine the strata ; as I was observing,
the last stratum rolled leisurely away, like a globe of light, from the
others, to the negative glow, in which it appeared to dissolve. As
the potassa cooled, the strata shrunk up and dissolved at the positive
wire, as did the glow ; and when the dark negative reached the
point, all luminosity ceased."

On a subsequent occasion the first discharge in the tube (190)
exhibited a fine purple negative glow, with two tawny cloud-like stra-
tifications at the positive. This discharge exhibited the fluorescence
of the glass tube in a remarkable manner. The circuit was then
broken; on again completing it, I was somewhat surprised at
finding the luminous discharge was no longer perceptible. I then
slightly heated the tube with a spirit-lamp ; the stratified discharge
reappeared ; the needle of the galvanometer deflected about 65°,
but the leaves of the electroscopes were very slightly affected.
On separating the plates of the micrometer-electrometer, sparks
passed ; the stratifications in 1 90 became confused, intermingling with
each other, and no longer presenting that clearness of definition
which I have described.

With tube 202, which is of the same dimensions, with silver in
lieu of brass terminal wires, there was not any discharge from the
battery until the potash was heated. At first it presented a fine
white glow on the negative wire, then one of a tawny red colour on
the positive; and on heat being applied, stratifications, as in 190,
were observed.

The battery was then connected to the wires of tube 219, the same
with which the experiments with Daniell's battery were made. This
showed the luminous negative as in fig. 3 A, but more brilliant than
with the constant battery — producing bright scintillations at the
positive, as if particles of the carbon were fused and thrown off.

By the preceding experiments, I ascertained that a disruptive or
spark-discharge could be obtained in air from the nitric-acid, as well
as from the water-battery; and that when these discharges were
passed through the highly attenuated matter contained in carbonic
acid vacua, the same luminous and stratified appearance was pro-
duced as by an inductive coil, a proof that whatever may be the
cause of the phenomena, it could not arise from any peculiar action
of that apparatus.

With the ordinary arrangement of the voltaic battery, in which
the insulation of the cells is disregarded, the luminous discharge is
usually obtained by completing the circuit, and then separating the

548 Royal Society : —

terminal wires or the charcoal points, the length of the arc being in
relation to the number of the elements of the battery.

With the water-battery I have never been able to obtain the
slightest appearance of an arc-discharge ; for whether the terminals
of the battery were the plates of my micrometer-electrometer, me-
tallic wires, or charcoal, the result was the same ; viz. clearly sepa-
rated and distinct sparks, which continued until the water in the
cells had nearly evaporated. With four hundred (each cell being
insulated) of Grove's nitric-acid battery, similar spark-discharges were
obtained between the plates of my micrometer-electrometer, without
producing the voltaic arc, although by a momentary completion of
the circuit it was obtained with great brilliancy.

In carbonic-acid vacuum tubes, and particularly in those in which
carbon-balls were inserted, the disruptive, as well as the voltaic arc
discharge (under the conditions described), was obtained from the
nitric-acid battery ; and in both instances the stratified appearance
was observed, the difference being, that with the arc-discharge the
stratifications were far more vivid and brilliant, and the discharge
itself evidently more energetic. With the disruptive discharge, the
needle of the galvanometer was but slightly deflected, nor could any
apparent chemical action be observed in the battery ; but instantly
on the production of the arc-discharge, the needle of the galvano-
meter was strongly deflected, and in all the cells of the battery it
was evident that intense chemical action had been produced.

If carbon-balls are attached to the wires of a carbonic-acid vacuum
tube, the arc-discharge is obtained from a nitric-acid battery when-
ever the potash is heated. This process facilitates the discharge,
and assists the disintegration of the carbon particles ; and these in a
minute state of division are subsequently found attached to the sides
of the glass. It is these particles which produce the arc- discharge,
with its intense vivid light so suddenly observed, with far more bril-
liant effects than the usual stratified discharge. During its passage
the conducting power of the vacuum-tube is found to be greatly
enhanced, as shown by the galvanometer, the electroscope, and the
intense chemical action in the battery.

The same explanation that I ventured to offer in the Bakerian
Lecture for 1858, as to the cause of the stratified discharge arising
from the impulses of a force acting on highly attenuated but resist-
ing media, is also applicable to the discharge of the voltaic battery
in vacua ; while the fact of this discharge, even its full intensity
having been now ascertained to be also stratified, leads me to the
conclusion, that the ordinary discharge of the voltaic battery, under
every condition, is not continuous, but intermittent — that it consists
of a series of pulsations or vibrations of greater or lesser velocity,
according to the resistance in the chemical or metallic elements of
the battery, or the conducting media through which the discharge

On the Volumetric Relations of Ozone. 549

March 29, 1860. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.

The following communications were read : —

" On the Volumetric Relations of Ozone, and the Action of the
Electrical Discharge on Oxygen and other Gases." By Thomas
Andrews, M.D., F.R.S., and P. G. Tait, Esq., M.A.

This paper contains the full details of the authors' experiments
on the volumetric changes which occur in the formation of ozone.
From three distinct series of experiments, performed by different
methods, they show that when ozone is formed from pure oxygen by
the action of the electrical discharge, a condensation takes place, as
had already been announced in a former Note published in the
• Proceedings/ But the condensation is much greater than the earlier
experiments of the authors on the expansion by heat of electrolytic
ozone had indicated. It is, in fact, so great, that if the allotropic
view of the constitution of ozone be correct, the density of that body,
as compared with oxygen, would be represented by a number cor-
responding to the density of a solid or liquid rather than that of a
gaseous substance. This conclusion follows necessarily from the
authors' experiments, unless it be assumed that when ozone comes
into contact with such substances as iodine, or a solution of iodide of
potassium, one portion of it is changed back into common oxygen,
while the remainder enters into combination, and that these portions
are so related to one another, that the expansion due to the one is
exactly equal to the contraction arising from the other. For the
details of the experiments and of the methods of investigation em-
ployed, reference must be made to the original paper.

The second part of the communication is devoted to the action of
the silent discharge and of the electrical spark on other gases.
Hydrogen and nitrogen undergo no change of volume when exposed
to the action of either form of discharge. Cyanogen is readily de-
composed by the spark, but presents so great a resistance to the
passage of electricity, that the action of the silent discharge can
scarcely be observed. Protoxide of nitrogen is readily attacked by
both forms of discharge, with increase of volume and formation of
nitrogen and hyponitric acid. Deutoxide of nitrogen exhibits the
remarkable example of a gas which, under the action either of the
silent discharge or of the spark, undergoes, like oxygen, a diminu-
tion of volume. It also is resolved into nitrogen and hyponitric
acid. Carbonic oxide has given results of great interest; but the
nature of the reaction has been only partially investigated. The
silent discharge decomposes this gas with production of a substance
of a bronze colour on the positive wire. The spark acts differently,
destroying, as in the case of oxygen, the greater part of the con-
traction produced by the silent discharge. The authors are engaged
in the further prosecution of this inquiry.

" On the Equation of Differences for an Equation of any Order,
and in particular for the Equations of the Orders Two, Three, Four,
and Five." By Arthur Cayley, Esq., F.R.S.

550

Intelligence and Miscellaneous Articles.

" On the Theory of Elliptic Motion." By Arthur Cayley, Esq.,
F.R.S.

On the Application of Electrical Discharges from the Induction

Coil to the purposes of Illummation.'
F.R.S.

The subjoined figure represents a carbonic-
acid vacuum tube of about ^ of an inch inter-
nal diameter, wound in the form of a flattened
spiral. The wider ends of the tube, in which
the platinum wires are sealed, are 2 inches in
length and about ^ an inch in diameter, and
are shown by the dotted lines ; they are enclosed
in a wooden case (indicated by the surrounding
entire line), so as to permit only the spiral to be
exposed.

When the discharge from a Ruhmkorff's in-
duction apparatus is passed through the vacuum-
tube, the spiral becomes intensely luminous, ex-
hibiting a brilliant white light. Mr. Gassiot,
who exhibited the experiment at the meeting
of the Society, caused the discharge from the
induction coil to pass through two miles of cop-
per wire ; with the same coil excited so as to
give a spark through air of one inch in length,
he ascertained that the luminosity in the spiral
was not reduced when the discharge passed
through 14 miles of No. 32 copper wire.

By J. P. Gassiot, Esq.,

LXXV. Intelligence and Miscellaneous Articles.

ON THE ALLEGED PRACTICE OF ARSENIC-EATING IN STYRIA.
BY DR. H. E. ROSCOE.

Professor Roscoe being anxious to obtain further definite informa-
tion respecting the extraordinary statements of Von Tschudi, quoted
by Johnston in his ' Chemistry of Common Life,' that persons in
Styria are in the habit of regularly taking doses of arsenious acid,
varying in quantity from 2 to 5 grains daily, was supplied, through
the kindness of his friend Professor Pebal of Lemberg, with a series
of letters written by seventeen medical men of Styria to the govern-
ment medical inspector at Gratz, concerning the alleged practice.
After reviewing the opinions of Dr. Taylor, Mr. Kesteven, and Mr.
Heisch upon the subject, and having mentioned the results and
conclusions arrived at by those who had previously interested them-
selves with the subject, Mr. Roscoe stated that all the letters received
from the medical men in Styria agree in acknowledging the general
prevalence of a belief that certain persons are in the habit of conti-

Intelligence and Miscellaneous Articles. 551

nually taking arsenic in quantities usually supposed sufficient to
produce death. Many of the reporting medical men had no expe-
rience of the practice ; others describe certain cases of arsenic-eating
which have not come under their personal notice, but which they
have been told of by trustworthy people whose names are given ;
whilst others, again, report upon cases which they themselves have
observed. Professor Roscoe proceeded to bring forward, in the first
place, evidence bearing upon the question, "Is or is not arsenious
acid, or arsenic in any other form, well known to, and distributed
amongst the people of Styria ?" He said that he had received 6 grms.
of a white substance forwarded by Professor Gottlieb, of Gratz,
accompanied by a certificate from the district judge of Knittelfeld
in Styria, stating that this substance was brought to him by a
peasant woman, who told him that she had seen her farm-labourer
eating it, and that she gave it up to justice to put a stop to so evil
a practice. An accurate chemical analysis showed that the substance
was pure arsenious acid. Extracts from many of the reports of the
medical men were then read, all stating that arsenious acid, called
" Hidrach " by the Styrian peasants, is well known and widely dis-
tributed in that country. The second question to which Mr. Roscoe
sought to obtain an answer was, whether arsenic is or is not re-
gularly taken by persons in Styria in quantities usually supposed
to produce immediate death ? The most narrowly examined, and
therefore the most interesting, case of arsenic-eating is one recorded
by Dr. Schafer. In presence of Dr. Knappe, of Oberzehring, a man
thirty years of age and in robust health ate, on the 22nd of Febru-
ary, 1860, a piece of arsenious acid weighing A\ grains, and on
the 23rd another piece weighing 5| grains. His urine was carefully
examined, and shown to contain arsenic ; on the 24th he went away
in his usual health. He informed Dr. Knappe that he was in the
habit of taking the above quantities three or four times each week.
A number of other cases, witnessed by the medical men themselves,
of persons eating arsenic, were then detailed. Dr. Holler, of Hart-
berg, says that he and other persons, named in his report, guarantee
that they are together acquainted with forty persons who eat arsenic ;
and Dr. Forcher, of Gratz, gives a list of eleven people in his neigh-
bourhood who indulge in the practice. Professor Roscoe did not
think it necessary to translate the reports in extenso ; he gave extracts
containing the portions immediately bearing upon the two questions
at issue, and deposited authentic copies .of the original reports with
the Society for the purpose of reference. He concluded that deci-
sive evidence had, in his opinion, been brought forward, not only to
prove that arsenic is well known and widely distributed in Styria,
but that it is likewise regularly eaten, for what purpose he did not
at the moment investigate, in quantities usually considered sufficient
to produce immediate death. — From the Proceedings of the Manchester
Literary and Philosophical Society, October 30, 1860.

552

Intelligence and Miscellaneous Articles.

ON THE DENSITY OF MIXTURES OF ALCOHOL AND WATER.
BY M. VON BAUMHAUER.

The author has made a series of determinations of the density of
mixtures of alcohol and water. The alcohol was obtained from two
different sources, and was rectified first over dried carbonate of potash,
and then five times from burnt lime. Thus prepared, one of the
specimens had the specific gravity 0'7946 at 15° C., and the other
0*7947 at -the same temperature. This number agrees with that
found by Pouillet for absolute alcohol prepared by Fremy, and was
not changed by further rectification. The mixtures were made in
carefully graduated tubes at 15°, and the distilled water was freed
from air by continued boiling and cooling in vacuo. The alcohol
and the water were weighed as a control. The results were reduced
to water at its greatest density. They are collated with those ob-
tained by Pouillet, from which they are seen to differ materially.

Alcohol in
100 vols.

Pouillet.

Baumhauer.

First series.

Second series.

100

07940

0-7939

0-7940

95

8161

8119

8121

90

8339

8283

8283

85

8495

8438

8432

80

8638

8576

8572

75

8772

8708

8708

70

8899

8837

8838

65

9019

8959

8963

60

9133

9079

9081

55

9240

9193

9196

50

9340

9301

9302

45

9432

9394

9400

40

9515

9485

9491

35

9587

9567

9569

30

9648

9635

9636

25

9692

9696

20

9746

9747

15

9799

9800

10

9855

9855

5

9919

9918

0

9901

9991

9991

Comptes Rendus, vol. 1. p. 591

ON THE THERMAL EFFECTS OF FLUIDS IN MOTION.
BY DR. JOULE AND PROFESSOR W. THOMSON.

In our paper published in the Philosophical Transactions for 1854,
we explained the object of our experiments to ascertain the differ-

Intelligence and Miscellaneous Articles.

553

ence of temperature between the high- and low-pressure sides of a
porous plug through which elastic fluids were forced. Our experi-
ments were then limited to air and carbonic acid. With new appa-
ratus, obtained by an allotment from the Government grant, we have
been able to determine the thermal effect with various other elastic
fluids. The following is a brief summary of our principal results at
a low temperature (about 7° Cent.) .

Thermal effect

Elastic fluid.

per 100 lbs. pressure

on the square inch,

in degrees Centigrade.

Air.

1-6 Cold.

3-9 Air

+ 96*1 Hydrogen ....

0*116 Heat.

7*9 Air

+ 92*1 Nitrogen

1-772 Cold.

5-1 Air

+ 94-9 Oxvgen

1-936 Cold.

3-5 Air

+ 96*5 Carbonic acid ..

8-19 Cold.

58-3 Air

+ 41*7 Hydrogen ....

07 Cold.

62-5 Air

+ 3 7' 5 Carbonic acid . .

3-486 Cold.

54 "6 Nitrogen +45*4 Oxygen

1-696 Cold.

4'23 Air

f +46*47 Hydrogen . . "1
\ +49 '3 Carbonic acid J

2-848 Cold.

Further experiments are being made at high temperatures, which
show, in the gases in which a cooling effect is found, a decrease of
this effect, and an increase of the heating effect in hydrogen. The
results at present arrived at indicate invariably that a mixture of gases
gives a smaller cooling effect than that deduced from the average of

the effects of the pure gases. -
Society for June 14, 1860.

-From the Proceedings of the Royal

ON THE TEMPERATURE OP WATER IN THE SPHEROIDAL STATE.
BY C. MARIGNAC.

M. Boutigny's experiments have led to the conclusion that the
temperature of bodies in the spheroidal state is constant, and is
somewhat below the boiling-point of the body. That of water is
96°*5. Other experimenters, however, have not found so high a
temperature.

M. de Luca* considers that the direct determination of the tem-
perature of water in the spheroidal state, by means of a thermometer
immersed in the spheroid, is liable to serious errors. He has esti-
mated it by means of a coloured solution, which becomes decolorized
at a certain temperature. He used for this purpose iodized starch, the

* Comptes Rendus, July 23, 1860.
Phil Mag. S. 4. No. 136. Suppl. Vol. 20.

20

554 Intelligence and Miscellaneous Articles.

blue colour of which disappears at 80°, and the decolorization com-
mences even at 50°. When a portion of this liquid is made to pass
into the spheroidal state in a platinum crucible strongly heated, it
does not become decolorized, and the spheroid retains its colour to
the end. According to M. de Luca, this experiment proves that
the temperature of water in the spheroidal state does not exceed 80°,
and is even below 50°.

M. de Luca also states that a spheroid of albumen containing
twice its volume of water becomes opalescent on its surface only,
while the centre remains limpid and transparent, so that it can be
dissolved in water, coagulated by heat, and the albumen precipitated
by alcohol.

The author (says M. Marignac) would probably have obtained
more desisive results by placing in suspension in water substances
fusible at fixed temperatures. The reactions to which he appeals
do not take place at perfectly distinct points ; they are possible
within considerable ranges of the thermometric scale, but are acce-
lerated by a higher temperature. Those who have had occasion to
exhibit the decolorization of iodized starch, must have seen that the
temperature reaches boiling before the colour disappears, and it is
only decolorized even after some time, although, as M. de Luca
says, when exposed for some time to 80° it is also decolorized. The
direct measurement of the temperature of the spheroidal state is un-
doubtedly liable to error from the influence of the radiant heat of
the sides of the incandescent crucible. But this affects the stem,
and not the bulb of the thermometer, and is therefore inconsiderable.

The following simple experiment gives a method of determining
the real temperature of the spheroidal state, not in an absolutely exact
manner, but at any rate with a certain approximation, and with com-
plete security.

For this purpose as large a quantity of water as possible is brought
into the spheroidal state, and without removing the lamp, the cru-
cible is inclined so that the water falls into a small thin platinum
crucible placed at its side, and containing a small thermometer.
Another experiment is then made in the same manner, but simply
with boiling water.

The temperature of the crucible and the thermometer depend on
the mass of the water ; and as it would be difficult always to work
with the same quantity of water, a crucible should be taken small
enough to be completely filled with the water placed in it.

This experiment was repeated several times, and the results have
not varied much. With water in the spheroidal state, the thermo-
meter rose to 86° or 87°; with boiling water it was 90°. These
experiments seem to prove that the temperature of water in the
spheroidal state is higher than that attributed to it by M. de Luca ;
they confirm, however, the number admitted by Boutigny. — Biblio-
tfuque Universelle, September 20, I860.

555

INDEX to VOL. XX.

on the synthesis of,

Acetone,

201.'

Acetovalerianic acid, 42.
Acetylene, on the properties and com-
position of, 196.
Acids, bibasic, on the constitution of

the, 48.
Acroleine, investigation of, 200.
Acrylic acid, on the formation of, 381 .
Actinometer, on several forms of, 50,

406.
Alcohol and water, on the density of

mixtures of, 552.
Alcohols, poly e thy lenic, on new, 293.
Aldehyde, on a new isomer of, 199.
Alkaloids, on new, given off during

putrefaction, 387.
Alloys, on the electric conducting

power of, 63 ; on the expansion of,

230 ; of aluminum, on the, 377-
Alluard (M.) on the specific and latent

heat of naphthaline, 488.
Aluminum, on alloys of, 3/7.
Amidobenzoic acid, researches on,

380.
Ammonias, on the diatomic, 66.
Amyle, on the hydride of, 379.
Amylene, on the oxide of, 44.
Analysis, elementary, on a new method

of, 518.
Andrews (Prof.) on the volumetric
, relations of ozone, 549.
Anisic alcohol, on the constitution of,

294.
Antimony, on the presence of, in the

beds of streams and rivers, 304 ;

on the volumetric determination of,

342.
Arsenic, on the presence of, in the

beds of streams and rivers, 304 ;

on the occurrence of, in coal, 408 ;

on the alleged practice of eating,
550.

Atkinson's (Dr. E.) chemical notices,
41, 139, 196, 290, 374, 515.

August (F.) on a new species of stereo-
scopic phenomenon, 329.

Barium, on the spectrum reaction of,
104.

Barometer, on a new self-registering,
263.

Bauer (M.) on the oxide of amylene,
44 ; on a new isomer of aldehyde,
199 ; on the hydride of amyle, 379.

Baumhauer (M. von) on the density
of mixtures of alcohol and water,
552.

Beetz (Prof. W.) on the molecular
changes produced bv magnetiza-
tion, 458.

Benzylic alcohol, on a new homologue
of, 225.

Berthelot (M.) on acetylene, 196.

Blakiston (Capt.) on a remarkable ice
shower, 168.

Books, new : — Brook Smith's Arith-
metic in Theory and Practice, 61 ;
Lunn's Treatise on Motion, 62 ;
Boole's Calculus of Finite Differ-
ences, ib. ; Pratt's Treatise on
Attractions, ib. ; Routh's Dynamics
of a System of Rigid Bodies, 533.

Boracite, on the preparation of, 378.

Breithaupt (Prof.) on thirteen systems
of crystallization in the mineral
kingdom, 129.

Brewster (Sir D.) on the lines of the
solar spectrum, 385.
j Bun sen (Prof.) on chemical analysis
by spectrum-observations, 89.

Burnett (C. J.) on several forms of
actinometer, 50, 406.
202

556

INDE X.

Cahours (M.) on organo-metallic radi-
cals, 197.

Calcium, on the spectrum reaction of,
101 ; on the preparation of, 376.

Calvert (Dr. F. C.) on the expansion
of metals and alloys, 2.30 ; on new
volatile alkaloids given off during
putrefaction, 387.

Campbell (D.) on the presence of
arsenic and antimony in the beds
of streams and rivers, 304.

Camphor, on the action of pentachlo-
ride of phosphorus on, 522.

Cannizaro (M.) on the constitution of
anisic alcohol, 294.

Cappa (M.) on the mineral products
formed by sublimation in the erup-
tion of Vesuvius in 1858, 87.

Carius (M.) on a new method of ele-
mentary analysis, 518.

Carlet (M.) on the action of nitric
acid on dulcine, 520.

Carmichael (Rev. R.) on symmetrical
integration, 348.

Caron (M.) on the preparation of
calcium, 376* ; on the nature of the
process of cementation, 519.

Cayley (A.) on a problem of double
partitions, 337 ; on a system of
algebraic equations, 341 ; on the
cubic centre of a line with respect
to three lines and a line, 418; on
a relation between two ternary
cubic forms, 512.

Cementation, on the nature of the
process of, 519.

Cespitine, on the preparation and
constitution of, 111.

Challis (Prof.) on a theory of the
force of electricity, 280 ; on a theory
of galvanic force, 431.

Chemical notices, 41, 139, 196, 290,
374, 515.

Chromatic dispersion, on certain laws
of, 143, 253.

Church (A.) on the bases produced by
the destructive distillation of peat,
110.

Chydenius (M.) on the crystallization
of thoria, 378.

Cocaine, on the properties of, 141.

Cockle (J.) on a theory of transcen-
dental roots, 145, 369.

Collinic acid, on the production and
properties of, 521.

Cotannite, analysis of, 87.

T iv ! ullization, on several new systems

of, 129.
Cubic forms, on a relation between

two ternary, 512.
Cyanogen, on the formation of, 296.
Dahlander (G. R.) on new figures of
equilibrium for revolving fluids,
119; on a theorem relating to the
attraction of the ellipse, 125; on
the form assumed by a fluid shell
revolving within a hollow spheroid,
426.
Darwinite, on the new mineral, 423.
Dawson (Dr. J. W.) on a fossil fern
from the lower coal-measures of
Nova Scotia, 485.
De la Rue (Dr. W.) on the resin of

Ficus rubiginosa, 225.
Dessaignes (M.) on the conversion of

tartaric into succinic acid, 50.
Deville (C.) on the origin of granite,
175.
* Deville (H.Ste.-Claire) on the decom-
position of bodies by heat, 448.
Dichrooscope, description of the, 352.
Dove (Prof. H. W.) on difference in
size of medals of different metals
obtained by stamping and by cast-
ing in the same mould, 327; on
the dichrooscope, 352.
yDrion (M.) on the liquefaction of
r " gases, 202.
Dufour (L.) on the density of ice, %

248.
Dulcine, on the action of nitric acid

on, 520.
Dupre (A. and F.) on the spectrum -
analysis of the London waters, 373.
Ear, on the sensitiveness of the hu-
man, to the pitch of musical notes,
523.
Earnshaw (Rev. S.) on a new theore-
tical determination of the velocity
of sound, 37, 186.
Earth, on the thickness of the crust
of the, 194 ; on the pressure of, on \
revetment walls, 489.
Eisenlohr (F.) on the relation between
the direction of the vibration of light
and the plane of polarization, 486.
f Electric light of mercury, on the, 249.
Electrical phenomena accompanying

muscular contraction, on, 388.
Electricity, on a theory of the force
of, 280 ; on the law of propagation
of, in imperfect conductors, 401.

INDEX.

557

Electricity, atmospheric, researches
on, 327, 360.

Electrolysis, on the transmission of,
across glass, 126.

Electromotive force, on the measure-
ment of, 316.

Electrostatic force, on the measure-
ment of, 233.

Ellipse, on a theorem relating to the
attraction of the, 125.

Engelhardt (M.) on the formation of
ice at the bottom of water, 166.

Equations, algebraic, on a system of,
341.

Equilibrium, on new figures of, for
revolving fluids, 119.

Ethylene, on the oxide of, 290.

Eyes, on the focal power of, for hori-
zontal and vertical rays, 480.

Falconer (Dr.) on the ossiferous caves
of Gower, 241.

Ferns, fossil, observations on some,
485. >

Fessel (F.) on the sensitiveness of the
human ear to the pitch of musical
notes, 523.

Fisher (Rev. O.) on the denudation
of soft strata, 483.

Fittig (M.) on the preparation and
properties of pinakone, 201.

FitzRoy(Rear-Admiral)onthe storms t
of October and November 1859, 65.
* Flame, on the spectra of different
f kinds of, 169.

Fluid shell, on the form assumed by
a, revolving within a hollow sphe-
roid, 426.

Fluids, on new figures of equilibrium
for revolving, 119; in motion, on
the thermal effects of, 552.

Fluor-spar, on the occurrence of
ozone in, 515.

Fluozirconates, on the, 87.

Forbes (D.) on Darwinite, a new mi-
neral from Chile, 423.
/ Fremy (M.) on the colouring matter
of leaves, 142.

Freund (M.) on the synthesis of ace-
tone, 201.
Frohde (M.) on collinic acid, 521.
Fulminic acid, researches on, 295.

Functions, rational, on approximation

to the integrals of, 446.
Furfurol, researches on, 381.
Galvanic force, on a theory of, 431.
Gases, illustrations of the dynamical

theory of, 21 ; on the liquefaction
of, 202 ; on the conduction of heat
by, 510.
Gassiot (J. P.) on the voltaic discharge
in vacuo, 74 ; on vacua as indicated
by the mercurial siphon-gauge and ,
the electrical discharge, 223 ; on ,
the luminous discharge of voltaic |
batteries, 540 ; on the application 1 p *
of luminous discharges to the pur- ( (F*~
poses of illumination, 550.
Gaugain (M.) on the law of propaga-
tion of electricity in imperfect con-
ductors, 401.
Geological Society, proceedings of

the, 84, 164, 400, 483.
Geuther (M.) on acroleine, 200.
Gladstone (Dr. J.' H.) on the electric
light of mercury, 249 ; on the lines
of the solar spectrum, 385.
Glycol, on compounds of, 41.
Gore (G.) on the movements of liquid *■>
metals and electrolytes in the vol-
taic circuit, 149 ; on an apparatus
for generating hydrogen and other **"
gases, 405.
Granite, on the origin of, 175.
Greg (R. P.) on the periodicity of the
solar spots and induced meteorolo-
gical disturbances, 246, 271.
Griess (P.) on a new method of sub-
stitution, 226.
Grove (W. R.) on the transmission of

electrolysis across glass, 126.
Harley (Dr. G.) on the saccharine

function of the liver, 224.
Hauer (M. v.) on selenic acid and se-

leniates, 296.
Heat, on the relation between the ra-
diating and absorbing powers of
bodies for, 1 ; on the decomposition
of bodies by, 448 ; on the conduc-
tion of, by gases, 510.
Hofmann(I)r.) on the polyammonias,

66.
Hopkins (T.) on the forces that pro-
duce the great currents of the air
and of the ocean, 74.
Hiibner (M.) on acroleine, 200.
Ice, on the formation of, at the
bottom of water, 166 ; on a remark-
able shower of, 168 ; on the density
of, 248.
Inductive spark, on the, 441. — .■ i...—

Integration, symmetrical, illustrations
of, 348.

558

INDEX.

Iodobenzoic acid, on the formation
of, 226.

Isethionic acid, on some derivatives
of, 47.

Jervis (W. P.) on certain rocks of
miocene and eocene age in Tus-
cany, 240.

.1 ours (T. It.) on Foraminifera from the
upper triassic clays near Derby, 85.

Jones (T. W.) on the focal power of
eves for horizontal and vertical
rays, 480.

Joule (Dr.) on the thermal effects of
fluids in motion, 552.

Kalle (M.) on the action of chloride
of benzoyle on zincethyle, 522.

Kirchhoff (Prof. G.) on the relation
between the radiating and absorb-
ing powers of bodies for light and
heat, 1 ; on chemical analysis by
spectrum-observations, 89.

Kolbe (Prof.) on the constitution of
<< organic compounds, 45 ; on isethi-
onic acid, 47 ; on the constitution
of bibasic acids, 48 ; on the con-
— -stitution of salicylic acid, 382.

Kiindig (M.) on the action of chlo-
rine on valerianic aldehyde, 19.9.

Lartet (E.) on the coexistence of man
with certain extinct quadrupeds,
239.

Lautemann (M.) on salicylic acid and
its homologues, 382.

Leaves, on the colouring matter of,
142.

Le Roux (M.) on the phenomena of
heat which accompanies the vibra-
tory motion of bodies, 247.

Light, on the relation between the
radiating and absorbing powers of
bodies for, 1 ; on the analogy of
sound and, 190; on the relation
between the direction of the vibra-
tion of, and the plane of polariza-
tion, 486' ; radiated by heated bo-
dies, on the, 534.

Lime, on the heteromorphous condi-
tions of the carbonate of, 517-

Liquids, on the laws of absorption of,
by porous substances, 364, 500.

Lithium, on the spectrum reaction of,
96.

Liver, on the saccharine function of
the, 224.

Loir (M.) on the liquefaction of gases,
202.

Lourenco (M.) on compound itinis
of glycol, 41 ; on some new poly-
ethylenic alcohols, 293.

Lowe (G. C.) on the expansion of
metals and alloys, 230.

Magnetic declination at Pekin, on the
solar-diurnal variation of the, 4(J9.

force, on the interruption of the

voltaic discharge in vacuo by, 74.

phaenomenon, on a, 328.

Magnetization, on the molecular
changes produced by, 458.

Magnus (Prof.) on the conduction of
heat by gases, 510.

Man, on the coexistence of, with cer*
tain extinct quadrupeds, 239.

Margueritte (M.) on the formation
of cyanogen, 296.

Marignac (C.) on the fluozirconates
and on the formula of zirconia, 87 ;
on the temperature of water in the
spheroidal state, 553.

Matteucci (Prof. C.) on the electrical
phenomena which accompany mus-
cular contraction, 388.

Matthiessen (Dr. A.) on the electric
conducting power of alloys, 63. ^

Maxwell (Prof. J. C.) on the dynami-
cal theory of gases, 21.

Mercury, on the electric light of, 2-19.

Merrifield (C. \V.) on approximation
to the integrals of irrational func-
tions, 446.

Metal, on a new fusible, 403.

Metals, on the expansion of, 230.

Michel (M.) on alloys of aluminum,

377.

Millon (M.) on nitrification, 516.

Mineral products formed by sublima-
tion in the eruption of Vesuvius in
1858, analysis of, 87.

Mucic acid, on the products of fer-
mentation of, 380.

Miiller (Dr. H.) on the resin of Ficus
rubiginosa, 225.

Naphthaline, on the specific and
latent heat of, 488.

Nerve, on the action of a galvanic
current on, 390.

Nitrification, observations on, 516.

Nordenskiold (M.) on the crystalliza-
tion of thoria, 378.

Odling (Dr. W.) on acids and salts, 78.

Organic compounds, on the constitu-
tion of, 45.

Organo-metallic radicals, on the, 197.

INDEX.

559

Owen (E.) on thebasesproduced by the
destructive distillation of peat, 110.

Ozone, on the occurrence of, in fluor-
spar, 515; on the volumetric rela-
tions of, 549.

Parker (W. K.) on Foraminifera from
the Upper Triassic Clays near
Derby, 85.

Partitions, double, on a problem of,
337.

Peat, on the bases produced by the
destructive distillation of, 110.

Pfaundler (M.) on the action of penta-
chloride of phosphorus on camphor,
522.

Phosphate of lime, on the frequent
occurrence of, in human urine,
224.

Phylloxanthine, 143.

Pinakone, on the preparation and
properties of, 201.

Poncelet's (M.) approximate linear
valuation of surd forms, on, 203,
307, 525.

Ponton (M.) on the laws of chromatic
dispersion, 253.
s. Potassium, on the spectrum reaction
* of, 98.

Pratt (Archdeacon) on the thickness
of the crust of the earth, 194.

Prestwich (J.) on the presence of
London clay in Norfolk, 84.

Radcliffe (Dr. C. B.) on the muscular
movements resulting from the ac-
tion of a galvanic current upon
nerve, 390.

Racemic acid, on the formation of,
from dulcine, 520.

Regnault (M.) on the elastic force of
vapours, 275.

Richter (M.) on artificial boracite, 378.

Rijke (Dr. P. L.) on the inductive
spark, 441.

Roots, transcendental, note on, 369.

Roscoe (Dr.) on the alleged practice of
arsenic-eating in Styria, 550.

Rose (Prof. G.) on the heteromor-
phous conditions of the carbonate
of lime, 517.

Royal Institution, proceedings of the,
78.

Royal Society, proceedings of the, 63,
149, 223, 316, 385, 469, 534.

Ruhmkorff (M.) on a magnetic phe-
nomenon, 328.

Sabine (Major-General) on the solar-

diurnal variation of the magnetic
declination at Pekin, 469.

Salicylic acid, on the constitution of,
382.

Satellites, on the form of, revolving
at small distances from their pri-
maries, 409.

Scheibler (M.) On the tungstates, 374.

Schischkoff(M.)on fulminic acid, 295.

Schmidt (M.) on the action of redu-
cing agents on malic and succinic
acids, 49 ; on the action of nitrous
acid on sulphanilic acid, 139.

Schneider (R.) on the volumetric
determination of antimony, 342.

Schrotter (Prof.) on the occurrence of
ozone in fluor-spar, 515.

Schulz (M.) on furfuroi, 381.

Schwanert (M.) on furfuroi, 381.

Selenic acid, on a new method of pre-
paring, 296, 297.

Silicic acid, on the different conditions
of, 175.

Silver, on some new salts of the sub-
oxide of, 376.

Smith (Dr. R. A.) on arsenic in coal,
408.

Sodium, on the spectrum reaction of,
94, 174.

Solar eclipse of July 18, 1860, photo-
graphic observations of the, 192.

spots, on the periodicity of, 246,

271.

Sound, on a new theoretical deter-
mination of the velocity of, 37, 186.

Sourdeval (M.) on the formation of
cyanogen, 296.

Spectrum, on the radiative power of
bodies with regard to the dark rays
of the, 169 ; on the lines of the,
385.

Spectrum-observations, chemical ana-
lysis by, 89, 173.

Spiller ( J.), photographic observations
of the solar eclipse of July 18 by,
192.

Stereoscopic phenomenon, on a new
species of, 329.

Stewart (B.) on certain laws of chro-
matic dispersion, 143; on the ra-
diative powers of bodies with re-
gard to the dark or heat-producing
rays of the spectrum, 169 ; on a
minimum and maximum mercurial
thermometer, 228 ; on the light
radiated by heated bodies, 534.

560

INDEX.

Strontium, on the spectrum reaction
of, 99.

Succinic acid, on the conversion of,
into tartaric acid, 50.

Sumnoethylenic acid, 43.

Sulphanilic acid, on the action of ni-
trous acid on, 13.9.

Swan (Prof.) on chemical analysis by
spectrum-observations, 1/3.

Sycoceryle, on the acetate of, 225.

Sylvester (Prof. J. J.) on Poncelet's
approximate linear valuation of
surd forms, 203, 307, 525 ; on the
pressure of earth on revetment-
walls, 489.

Tait (P. G.) on the volumetric rela-
tions of ozone, 549.

Tartaric acid, on the transformation
of, into succinic acid, 50.

Tate (T.) on a new self-registering
mercury barometer, 263 ; on the
construction of a new air-thermo-
meter, 298 ; on the laws of absorp-
tion of liquids by porous sub-
stances, 364, 500.

Thermometer, on a new minimum
and maximum mercurial, 228 ; on
the construction of a new air-,
298.

Thomson (Prof. W.) on the measure-
ment of electrostatic force, 233 ; on
the measurement of electromotive
force, 316 ; on atmospheric electri-
city, 360; on the thermal effects
of fluids in motion, 552.

Thoria, on the crystallization of, 378.

Thunder, on the velocity of the sound
of, 37.

Transcendental roots, on a theory of,
145.

Tungstatcs, on the, 3/4.

Valerianic aldehyde, on the action of
chlorine upon, 199.

Vapours, on the elastic force of, 275.

Vaughan (D.) on the form of satel-
lites revolving at small distances
from their primaries, 409.

Vision, on the theory of binocular, 329.

Vogt (M.) on some new organic com-
pounds, 522.

Volpicelli (M.) on atmospheric elec-
tricity, 327.

Voltaic batteries, on the luminous
discharge of, 540.

circuit, on the movements of

liquid metals and electrolytes in
the, 149.

Wall (G. P.) on the geology of Vene-
zuela and Trinidad, 164.

Water, on the temperature of, in the
spheroidal state, 553.

Waters, spectrum-analysis of Lon-
don, 373.

Weber (M.) on some compounds of
selenium, 296.

Wbhler (Prof.) on the properties of
cocaine, 141 ; on some new salts of
the suboxide of silver, 376; on
alloys of aluminum, 377-

Wood's fusible metal, 403.

Wurz (M.) on the oxide of ethylene,
290 ; on the synthetical formation
of some new acids, 292. —•■

Zinc-ethyle, on the action of chloride
of benzoyle on, 522.

Zirconia, on the formula of, 8 .

END OF THE TWENTIETH VOLUME.

PRINTED BY TAYLOR AND FRANCIS,
RED LION COURT, FLEET STREET.

FLAMMAM.

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